Table onter
SOFTWARE TECHNOLOGY TRANSITION MODEL DYNAMICAL
SYSTEM MODEL
Michael S. Saboe
US Amy Next Gen Software Technology Area
Attn: Associate Director AMSTA_TR_R/265
Warren MI, 48397-5000
SaboeM@TACOM.Amy.mil
Abstract
This paper considers an information theoretic and dynamical systems technology transfer model. The
model enables decision-makers to “engineer” resource and risk programmatic issues. Analysis with the
model enables prediction and prescriptive action for a research or program manager. The model deals
with entropy as defined in information theory. The TechTx Basic Entropy model addresses macro level
trends of a technology at the community level. The dynamical systems TechTx Entropy Feedback model, is
based on non-linear control theory. The paper develops the state quantities to develop state functions for
analysis of an evolutionary technology process. This summary paper focuses on the elements required to
model the technology transfer process. Specifically, this paper develops the fundamentals for a rigorous
software technology transfer model as required by the TechTx Entropy Feedback model. The relationship
of entropy (Sq) as defined for information by Shannon, and the eigenvalue (A), the norm of a dynamical
system is explored. The Lyapunov number is a natural measure developed from the eigenvalue of a
dynamical system, e.g. related to entropy. The significance of the eigenvalue for a communications
software technology transfer model is discussed. The model shows that the TechTx Basic Entropy and
TechTx Entropy Feedback models converge at the same rate. Empirical data with tens of thousands of
data points provides a tight confidence interval and demonstrate that the messages conform to a Boltzmann
distribution. The paper describes a method to measure the temperature of an evolutionary information
theoretic process. This temperature is measured in degrees (°Saboe[]) based in information units. The
result is a rich set of analytical tools previously unavailable to be used for policy and programmatic issues
to reduce risk, increase efficiency and accelerate maturation of a desired technology.
Software Technology Transition Model
Dynamical System Model
Abstract.
1 Introduction.
2 Motivation
3. Technology Transition Models
Topical Threads of Research to Date...
Classic Diffusion Tech Tx Models (Rogers
1983, 1999).......
Software Technology Transition Framework,
Advocate/Receptor..... 12
4. Information Theory A pplied to Technology
Transition... 6
BwNNee
8
5. TechTx Feedback Entropy model.
6. Dynamical Systems Model...
7. A “Technology Transfer Engine’
8. Value and Usage.
References...
Appendix...
1 INTRODUCTION
This paper discusses the elements of a new
technology transfer model that can be represented
mathematically. This provides a method for analysis
for both predictive and prescriptive activities. All of
the existing work in software technology transfer is
lacking mathematical models. The models addressed
are 1) TechTx Basic Entropy, and 2) TechTx Entropy
Feedback. Each of these models represents a
macroscopic and a discrete representation of an
evolutionary communicating system. The
mathematical implications of the dynamical system
model are developed. Both models represent an
extension to the state-of-the-art for predicting the
arrival of technologies. The models are validated
with over 100,000 data points, collected in one
instance over 21 years.
The most significant contribution is the
development of a set of state equations, similar to
those used in statistical mechanics. A temperature is
defined for an evolutionary communications process.
Other intensive and extensive variables are defined. A
method is shown to determine a conserved quantity
(information terms in message), entropy, pressure, and
volume.
Finally, a method to represent an engine is
provided to show the application of the approach as an
engineering model.
The key underlying communication diffusion
research of Rogers (Rogers 1983, 1995) is pervasive in
Buxton 1991, Raghavan 1988, 1989, Fichman 1993,
1994, Jaakkola 1995, Fowler 1994, Pfleeger 1999, and
many more. The paper suggests preliminary analysis
of the basic elemental tools required for a software
technology transition cycle analysis approach. This
work is motivated (Section 2) by the need for an
acquirer, or research program manager, to assess risk
related to the maturity date of a technology. Data and
charts that summarize relevant aspects of this work are
presented. A sample data set for “software
engineering” is illustrated using current methods.
Section 3 addresses the implementation details
required to address a software technology model.
This paper presents a general set of state
variable for software technology transition. These
models provide a method to analyze and later
prescribe the size and probability of a technology
maturing at a given time. The elements of the
analytical model proposed promise to permit analysis
of various alternatives for policy and investment
trades. Tools that build on this analysis approach can
help identify leverage points and opportunities to
accelerate progress in a repeatable and rigorous
process enabling quantification of maturity at a given
date and confidence in a subject technologies stability.
2 MOTIVATION
At the International Conference on Software
Engineering 2000, the keynote speech (Shaw 2001)
illustrated the trends in maturation of software
technology. The model cited was one from 1985
(Redwine 1985). It seems apparent that a good model
for technology maturation and transition is lacking for
software engineering. There are no references in the
software technology transition literature that indicates
that this was a good model for analyzing, predicting
and prescribing exits. There is a clear need based on
the researcher's extensive personal experience (nearly
30 years at every level of industry and the Department
of Defense). Discussions with the software
technology transition program at the Software
Engineering Institute (SEI) consistently indicated that
there is a critical lack of and need for an analytical
model of the type proposed. The elements of an
analytical model proposed promise to permit analysis
of various altematives for policy and investment
trades. Tools that build on this analysis approach can
help identify leverage points and opportunities to
accelerate progress in a repeatable and rigorous
process.
With such tools, a decision-maker can
determine the confidence with which a technology or
group of technologies will stabilize and converge in a
given time frame. For example (see Figure 2-1), a
program might expect a portfolio of technologies to
arrive by year 06 with an 80% certainty, but the model
might show that in 06, there is only 60% certainty of
being available using the current trends. The desired
80% certainty would not be available until 08. If the
technology is not predicted to arrive as required, the
model will point to the areas for remedy with a
prescriptive solution to organize, train and equip an
organization in order to change the confidence of
arrival of the technology for the program's required
schedule.
Program Office Use for Risk
Assessment and Rx
Example:
Program Office Wants
80% by/06 with 80% certainty
Analysis indicates 08
What nodes / programmatics
‘need to be put into place to
shift curve to left?
From desired system curve
06 08 Algebraically Solve for node response curves(s)
Determine how many and parallel serial
Figure 2-1 Program Office Use of Objective Model
3 TECHNOLOGY TRANSITION MODELS
The research validation follows the strategy
shown in Figure 3-1. The proposed TechTx Basic
Entropy model “X” asks the question, “Can we do
better?” in assessing the maturity of a technology,
“Y”. Validation compares it to the existing methods.
The TechTx Entropy Learning Curve model, while not
discussed in this paper, builds off the TechTx Basic
Entropy model. In this model, the technology transfer
maturation process is characterized by learning curves.
The TechTx Entropy Feedback model is the most
difficult challenge and the subject of the paper for the
Systems Dynamical Society. Here the research is
asking, “Can it be done at all?” The TechTx Entropy
Feedback model was developed. The model is
exercised with data from the TechTx Basic Entropy
model. The validation is of the form, matching the
model’s stabilization equation form of the information
theoretic and the dynamical systems model. The data
is real world data, and the research suggests that the
models are representative of the behavior seen in the
real world for this class of processes.
Two OtherTechTx Entropy Learning Curve
TechiTx Entropy Feedback Models
Question — Result Validation
Figure 3-1 Validation Strategy (Source: After
Shaw 2001)
The proposed model was compared with the
traditional diffusion of innovations communication
model to predict trends and the maturation of a
technology. The traditional model is the baseline
model and uses the message-counting method. The
first proposed model is the TechTx Basic Entropy
model. This is the first improvement over the
traditional model and uses the content of the message,
measured in the information dimension of entropy.
Entropy is represented in information units - bits.
Section 4 includes a brief review of entropy in
information theory will be provided.
The dynamical systems model is the TechTx Entropy
Taped
Model in Tech Tx Literature Model Feature Information ontol
———
‘Shannon Envopy oF
Messages
Joint entropy
{formation in,
tnfoemation Out
Intemal and Extemal
Relationship
Structure Changes Model-
Goodness of
Technology Alone
causes Diffusion
Tdenties Minimum
riumber of nodes
(senders and
Technology Model
receptors)
‘extensions may
address vacuum and
External AATENCEE
affect the human
behavior to assimilate a
Technology
pressure
Taanifes Enttopy a5 2
factorthatcan
influence the
acceptance of 2
technalog
Tnstiuion Building Model
Equilbrium ve ConfictModel Equlibrums an
Instrument for Balance
Conflicts a Instrument
to apply Pressure
‘Convergence in
Enuopy yields balance
Large Differences in
Entropy yields
Pressure
Quantifes the
Information Being
A Technology is
Delivered to Adopters
Through a Channel, if ‘Acted on, and
Understood itis acted Quantfes notion of
upon, ‘Understood * in tems
of Entropy and
feaming ture
‘Communication Model
Problem solving Model Present Hypothesis
Test Hypothesis with
Data and Logic
Hypothesizes a
Mathematical Model
and Explains based on
Daa boats
Table 1 Technology Transfer Models, Features,
and Relation to Proposed Model
Feedback model. The feedback model is designed to
operate at the organizational node level. This model
can accommodate a producer-advocate creation of new
information. The information is provided in the form
of a work product as a “message” consisting of terms.
The model includes a feedback request transition anda
clarification transition of the messages. Learning is
factored into the amount of feedback requested and
permits tuning of the dynamical system model. The
characteristics of the TechTx Entropy Feedback model
are discussed. Introduction of the model lays the
groundwork for future research.
1. Context and Overview
Let's set a context. Induction! is a process of
inferring a general law or principle from the
observations of particular instances. This is inductive
inference. Inductive reasoning is a more general
concept than inductive inference. It is a process of
assigning a probability (or credibility) to a law or
proposition from observation of particular instances.
Inductive inference draws conclusions on rejecting or
accepting a proposition, possibly without total
justification. Inductive reasoning only changes the
degree of our belief in proposition. Deductive
reasoning of inference derives the absolute truth or
false hood of a proposition. This is a case of inductive
reasoning.
This approach to explaining things around us
dates back at least to Epicurus (342?-270?BC) (Li
1993, p. 274). Let’s consider theory formulation in
science as the process of obtaining a compact
description of past observations together with future
ones. Let us suggest that the: preliminary data of an
investigator, the hypothesis proposed, the
experimental design and setups, the trials performed,
the outcomes obtained, the new hypothesis
formulated, etc., can be encoded as an initial segment
of an infinite binary sequence. The investigator
obtains increasingly longer initial segments of an
infinite binary sequence by performing more and more
experiments. To describe the underlying regularity in
the sequence, the investigator tries to formulate a
theory that governs the sequence based on the outcome
of past experiments. Candidate theories or hypotheses
are identified from the sequences starting with the
observation of the initial segment.
There are many different possible infinite
sequences or histories on which the investigator can
embark. The phenomenon the investigator is trying to
understand or the strategy used can be stochastic. In
this type of view, a phenomenon can be identified with
a measure, i.e. probability distribution, on a
continuous sample space.
This research attempts to express the task of
learning a certain concept as in terms of sequences
over a basic alphabet. We express what we know as a
finite sequence over the alphabet. An experiment to
acquire more knowledge is encoded as a sequence
over the alphabet, the outcome is encoded over the
alphabet, and new experiments are encoded over the
alphabet, and so on. This way we can view a concept
as a probability distribution (measure) over a sample
space of all one way infinite binary sequences. Each
1 The Oxford Dictionary defines induction this way.
sequence corresponds to one never ending sequential
history of conjectures, refutations, and confirmations.
The distribution can be said to be the concept of
phenomenon involved. We can predict what is likely
to tum up next with an initial segment. Using
Bayesian analysis (Bayes 1763) to compute the
conditional probability, we can predict and extrapolate
future outcomes. This is the general thrust of this
research.
Let’s develop an analogy of the flow of
communication to a physical model to illustrate the
concept. When two people meet, they converse, and
consequently modify their thinking to some extent.
These modifications are brought to subsequent
meetings and modified further. The word for this is
dissemination or diffusion. There is a flow of
communication in society, just as there is a flow of
correlations in matter. Let's explore this idea of
correlations using the analogy of a physical system
and look at what happens in terms of distribution
functions.
Consider a glass of water’, We may
visualize the interactions as leading to collisions
between the molecules. We can describe the water
containing them in terms of a statistical ensemble.
The water is not aging if we were to consider the
individual molecules over geologic time3. Yet, there
is a natural time order in the system from a statistical
point of view. Aging is a property of populations, as
in the biological theory of evolution as developed by
Darwin. It is a statistical distribution that approaches
the equilibriumdistribution.
Consider a probability distribution p(x:, %)
dependent on the two variables x;, x. If x; and x» are
independent, we can factor p(x1, X2)= pi(xi) pr(X2).
The probability p(x1, %:) is the product of the two
probabilities. On the other hand, if p(xi, x.) cannot be
factored, x; and x) are correlated (Bayes 1763 p299).
Retum to the glass of water molecules. The collisions
between the molecules have two effects: they make the
velocity distribution more symmetrical, and they
2 his discussion follows from Prigogine 1997.
3 Newton scholium differentiates time this way. “Time,
space, place, and motion ... quantities are popularly conceived
solely with reference to the objects of sense perception... 1.
Absolute, true, mathematical time, in and of itself and of its own
nature, with out reference to anything extemal flows uniformly and
by another name it is called duration. Relative, apparent, and
common time is any sensible and extemal measure (precise or
imprecise) of duration by means of motion; such a measure - for
example, a month, a year - is commonly used instead of true time.”
(Newton 1726 p408)
produce correlations (see Figure 3-2). However, two
correlated particles will eventually collide with a third
one (see Figure 3-3). Binary correlations are then
transformed into tertiary ones, etc. Prigogine
illustrated this molecular model, and it has been
verified (Prigogine 1997 p79).
Collisions and Correlations
ie) ie) fo)
om
(2) O°
Before Collision "After Collision,
The collision of two particles creates a correlation between them
(represented by the wavy line)
Source: After Prigogine 1997
Nov 2001, n
Nsaboe
Ph. Defense 2001
Figure 3-2 Collisions and Correlations
(Source: After Prigogine 1997)
Flow of Correlations
° One
°
e
aeOee O—* 0
°
(e)
o.|o
°
Before Collision After Collision
Successive collisions lead to binary, tertiary, .. correlations
Source: After Prigogine 1997
Nov 2001 n
M Saboe
Ph. Defense 2002,
Figure 3-3 Flow of Correlations
We could conceive of inverse processes that
make the velocity distribution less symmetrical by
destroying correlations. Processes that invert the
velocity of particles for a physical world as in Figure
3-3 have been reproduced. However, this inverted
flow of correlations can only be achieved for a short
time, with limited numbers of particles. Then we
again have a directed flow of correlations involving an
ever-increasing number of particles leading the system
to equilibrium
We now have a flow of correlations that are
ordered in time just as there is a flow of
communication in society. There is a method to
describe this irreversibility. This statistical description
is dynamics of correlations leading to the equilibrium
solution.
In this research, we use messages instead of
particles. This turns out to be a conserved quantity
(conserved quantities shared between two systems
need not be restricted to energy’, or mass, or volume,
the conserved quantity could be a number of measures,
even money) (Y akavenko 2000) (Farmer 1999). We
are concerned with a deterministic dynamical system
as an especially simple type of dynamical system,
corresponding to dynamical system maps. Contrary to
what occurs in ordinary dynamics, time in maps acts
only at discrete intervals. Maps represent a simplified
form of dynamics that make it easy to compare the
individual level of descriptions (trajectories) with the
statistical description.
2. Communication, Continuity
Communication is a process in which
participants create and share information with one
another in order to reach a mutual understanding. This
definition implies that communication is a process of
convergence (or divergence) as two or more
individuals exchange information in order to move
toward each other (or apart) in the meanings they
ascribe to entities (objects, acts, events, etc) (Rogers
1983). Rogers and Kinkaid represent this
communication in the general case as a two-way
process of convergence rather than a one-way linear
act in which one individual seeks to transfer a message
to another. (Rogers Kinkaid 1981).
This simple concept of human (or machine)
communication seems to accurately describe certain
communication acts or events involved in technology
diffusion.
3. Diffusion
Diffusion is the process by which an
innovation is communicated through certain channels
over time among the members of a social system. It is
4 Energy is an interesting term. It is a primitive term. Itis a
mathematical abstraction that has no existence apart from its
functional relationship to variables or coordinates that do have a
physical interpretation and that can be measured (Abbott 1989 pl).
The 1* law of thermodynamics is merely a formal statement
asserting that energy is conserved. This represents a primitive
statement about a primitive concept. Moreover, both are linked.
The T* law depends on the concept of energy, and it is equally true
that energy is the essential thermodynamic function precisely
because it allows the formulation of the 1 law.
a special type of communication, in that the messages
are concerned with new ideas (Rogers 1983). For
example, when a change agent seeks to persuade a
client to adopt an innovation. Examining what occurs
in the time step prior to an event and after an event, it
is clear the event is only a part of a process of
exchange between individuals (or machines). Rogers
asserts that it is the newness of the message content of
the communication that gives diffusion a special
character. The newness implies that some degree of
uncertainty is involved.
4, Uncertainty and Confidence
Let's set the context. How do we make
choices in the face of uncertainty? We know that a
reasonable person having some historical experience
with a true coin A, would assign a degree of belief
(subjective probability) of about .5 probability for
heads. Based on the history with the coin, we would
be rather confident in that belief. Now imagine a coin
B, and we know absolutely nothing about this coin.
We don't know whether it has two heads or two tails or
if itis a fair coin. Yet, if we had to pick, we would be
compelled to assign a single .5 probability, since we
lack any information to indicate a greater or lesser
belief in heads vs. tails. But, our confidence in .5 for
coin B would surely be less.
On the one hand, it is not the psychological
sensation of confidence that we are interested in.
Rather, as an engineer or decision-maker, the
consequences of the decisions are the driving issue.
When we have the option of acquiring information
through an informational action, we are likely to
invest energy (money, effort) before making a decision
that results in a terminal action. We would be willing
to invest this additional effort in acquiring information
about coin B vs. A. So we see that one’s
informational actions, though not one’s terminal
actions, do depend on one’s confidence in beliefs.
This notion of confidence plays an important
role in this discourse's assessment of a software
technology.
5. Chance,
Mixing
Aggregation through
Today we tend to regard knowledge as a
process more than a state. This stems partly from the
epistemologies of the philosophies of science:
Coumot's probablism and his comparative studies of
various types of notions set the stage for such an
understanding. Critical reviews of historical works,
which reveal the oppositions among the various types
of scientific thought, clearly promote such a
development. Even after the victory of Newton,
physics believed for hundreds of years in the absolute
character of its principles. So, the arguments
developed in this research very much depend on the
state and maturity of the knowledge process for
software engineering.
Another probabilistic feature of software
technology transition is chance. Chance is a curious
notion which is defined by Cournot as an interference
of independent causal series and which generally can
be designated under the term "mixture". (Piaget 1977,
p. 19) This is an important concept to expose.
Mixture is irreversible and grows with an increasingly
weaker probability of return to the initial state’. This
starts to address the aggregation typical of
composition of terms and integrating domains and
technologies.
Topical Threads of Research to Date
The following sections review key efforts and
models that have been identified in the literature. This
review is meant to illustrate the state of the practice for
technology transfer models. Further, it helps establish
desirable aspects that should be addressed by a model.
Technology transfer (TechTx) or transition is referred
to as diffusion in the literature. This section reviews
the basics of technology transition through the current
state of software technology transfer as seen in the
literature through 2000. Various theories and
principles felt to be underlying human behavior and
learning are presented first. The technology transition
models basics identified in the literature are then
summarized. Seven models researched identify a facet
or feature of technology transfer. These models are
shown in Table 1. Table 1 shows the model, a key
feature of the model, and indication that the model
proposed in this research address that feature. Each of
these models in Table 1 are summarized in the next
few paragraphs.
Ts The Theory of Human Needs (Leagans 1979)
The theory of human needs (Leagans 1979, p.
15) has a number of components. These are as
follows: the facts, the perception of the facts, human
attitudes or value judgements about the facts, and
human actions related to the facts as they perceive
them. Leagans establishes a framework addressing the
complexity factors that affect behavior with respect to
technology transfer. The model elements suggested in
this paper had to be general enough to permit lower
level detailed elaboration that address these details.
This requirement for generality is driven by the need
to address refined implementation aspects of
technology transfer. The proposed model addresses
this through the mechanism of the learning curve.
2, Structure Changes - Internal and External
Relationship (Piaget)
While Piaget's work was not focused on technology
transfer, his work is fundamental to learning schemes
and an accommodation of these schemes to the
environmental situation (Piaget 1963, p. 103). He
develops the relationship between the genotype
(internal) and phenotype (external) information
influences. Yet, neither internal nor external factors
can individually explain human development of skills.
We can think of this leaning in terms of the
acquisition of technology. During human knowledge
and skill development, it seems to tend toward the
establishment of equilibrium of the internal and
external factors. (Piaget 1967, p. 113) The proposed
model explored in this paper addresses this in several
ways. First, the Shannon entropy approach, which
takes a vocabulary as input and a vocabulary as output,
and from the joint entropy (Bayesian) relationships,
yields a grammar. In the TechTx Entropy Feedback
models, the vocabulary-grammar relationship between
internal and external factors is incorporated using
Shannon’ s statistical approach to entropy. The TechTx
Entropy Feedback model adds mixing. It also
accommodates structural changes (more explicitly
addressing the external factor) due to feedback from
extemal nodes.
3, Technology Model
The technology model (Leagans 1979) deals
with potential. This model suggests that the
attractiveness of a new technology alone is sufficiently
strong to induce wide diffusion, acceptance and
adoption by users. It tends to assume that users would
use the new technology and attendant parts of the
technology successfully without the persuasions of an
organized education system. This model has proven
highly inadequate when trying to introduce technology
to large masses of users, rather than the elite self-
motivated few (Leagans 1979, p. 17). This
inadequacy is also consistent with the small
percentage of innovators and early adopters identified
by Rogers. (Rogers 1983 p. 247) However, it does
imply that a pressure or a vacuum may have some
influence. The model currently being explored seems
to be able to be extended to see the effects of a
vacuum, e.g. the growth of the internet creates a
requirement and hence a vacuum, and intelligent
agents move in to fill the void. This is analogous to
the saying, “necessity is the mother of invention.”
4, Institution-Building Model
The laws of maximum and minimum are
often referred to as the “limitation factors”. These
factors are used to explain the forces influencing
biological, e.g. plant growth. Briefly the laws say, “If
one of the participating nutritional constituents of the
soil or atmosphere are deficient, or wanting or lacking
in assimilability, either the plant does not grow or its
organs develop only imperfectly.” (AAAS 1972).
This has been applied to human behavior with the
following rationale (Leagans 1979, p. 13): human
behavior is the dependent variable. The assumption is
that man can influence the economic, biological, and
other forms of change to the extent that he controls the
forces (nutrients) that influence change and the status
quo. There is the implication here that there is a
vector of forces that can be added up. In this context,
Leagans argues that people see one or more inhibitors
(limiting factors) and one or more incentives to
innovation, simultaneously in any situation. These
variables contain and exert varying force on the
dependent variable - human behavior, and that when
the deficiencies (inhibitors) are weakened or removed,
the balance or equilibrium of opposing forces will be
altered. Changes in human behavior are expected to
be proportionate to the amount of cumulative
influence exerted by the change incentives present.
These changes are the net sum of the counteracting
influences or change inhibitors operating in the
situation.
The model in this paper uses information
theory to quantify the information entropy in terms of
mutual information, joint and conditional entropy and
to address the relationship of these forces. In the
model, the information previously published is
persistent and influences the output. The proposed
TechTx Entropy Feedback model builds on the
contribution of feedback. The feedback is seen as
proportional to the cumulative influence of the change
incentives (information) present. The feedback
control model used herein is non-linear. This
addresses the comment by Leagans (Leagans 1979, p.
14) that “the input-output function is not always
linear.” He states that the influencing factors vary by
situation. The result is probabilistic. This derives from
the fact of variation in the nature of each interaction.
For the research herein, we address this by means of
an ensemble of very probabilistic, primitive
communication interactions using both information
and control theory.
5. Equilibrium vs. Conflict Model
In the equilibrium vs. conflict model,
equilibrium is regarded as an instrument for achieving
balance, while conflict is an instrument for applying
pressure. Some combination of these divergent
approaches does in fact operate in most models as a
force for motivating people to adopt new patterns of
behavior. This is consistent with Piaget and the
tendency toward the establishment of an equilibrium
of these factors. In developing the mathematical
model of this study, it was interesting to discover that
the communication control model used can settle
down into equilibrium (oscillating), repellor or
attractor stable state. Oscillation is seen under some
conditions of the feedback model. When there is a
vacuum, or pressure is applied to a node, learning is
more rapid, up to a point. This can be seen in the
proposed model.
Prigogine (Prigogine 1980, 1984), who won
the Nobel Prize in 1977, says that living (read this as
evolving) systems are rarely static, and if they are,
they are likely to atrophy and die from stagnation.
Living organisms do not thrive in a state of balanced
equilibrium, but usually in fluctuating restlessness.
The data presented exhibits exactly the behavior
described by Prigogine. Consumers, organizations,
and the technology evolution system itself seem to act
as a living organism. The model developed herein
addresses these concerns.
6. Communication Model
The communication model is considered the
classical model for diffusion of technology. It is well
developed and documented by Rogers (Rogers 1983,
1995). This consists of making a new technology
discovery, delivering it to potential adopters through
various communication channels, and then being
understood and acted upon by the consumer. The
communications model is generally seen as a macro
model.
Almost every well-researched technology
transfer model addresses the communication model.
Leagans (Leagans 1979, p. 19) cites Rogers (Rogers
1975), who identified several shortcomings of the
model. These include the need to address greater
process orientation, greater attention to causality, and
recognition that the adoption requires a physical or
overt act. This paper addresses these shortcomings in
the formulation of the mathematical model in sections
4 and 5. The process aspect is in the message and
feedback loops in the control model. Causality and
overt act are built into the transforming function f(x:)
ina time step in Sections 4 and 5.
7. Problem Solving Model
This model presents a hypothesis of an
explanation of a troubled situation. It tests the
hypothesis with data and logic developed putting those
specific results into a model. The hypothesis for
solving the problem is formulated. Implementing
programs and evaluations to assess the consequences
tests the proposed solutions. This
evaluation/implementation includes the means and the
ends. Boehm and Basili (Boehm 1999, 2000)
essentially are espousing that the Department of
Defense institute a National effort with Centers for
Empirically Based Software Engineering (CeBase) to
address transition, using essentially this model.
The study develops a model at a macro, or
strategic, level to predict and plan the technology
portfolio of a National Technology Transition effort.
The current model efforts and elements are reflected in
the Department of Defense Software Engineering
Science and Technology Summit findings (Boehm
2001).
Classic Diffusion Tech Tx Models (Rogers 1983,
1995)
The Diffusion of Innovation (Rogers 1983,
1995) is one of the most valuable readings on
technology transition in general. The approaches of
virtually all aspects of technology diffusion are
covered. Rogers discusses a communication model
that depicts the classic business school "S" curve
(Rogers 1983, p. 47). This is a cumulative plot of
publications covering a given topic over time. Further,
he categorizes the four main elements of diffusion of
innovations as follows:
+ The Innovation
+ Communication Channels
° Time
+ A Social System
He lays out clear definitions that are
commonly accepted in the literature of technology
transition and diffusion. Rogers’ lexicon can also be
seen in the software engineering technology transfer
literature. (see Moore 1991, Redwine 1984, Fowler
1994, Fichman 1993, Zelkowitz 1995, and Pfleeger
1999).
Looking at Rogers’ work, you can see all of
the elements of a communication system. He
classifies and distributes the types of adopters (see
Figure 3-2) as Innovators, Early Adopters, Early
Majority, Late Majority, and Laggards. He stresses
the uncertainty-reduction aspect of technology. He, as
do many, use the terms “innovation” and “technology”
as synonyms.
i
Ly
Innovators <[
Early <<}
—
Laggards <=}
Figure 3-4. Distribution of Adopters.
(Source: Rogers 1983, p. 11).
Rogers identifies technology as a design for
actions that reduce the uncertainty in the cause and
effect relationship involved in achieving a desired
outcome. (Rogers 1983, p. 12). The technology
developed in the case of this study is itself the
technology transfer model. The proposed model in
this paper provides a method to analyze options for
instrumental actions in order to reduce uncertainty in
the arrival of a given set of software technologies.
1, The Innovation
In the literature, technology generally is seen
as having two components, hardware and software.
Rogers is speaking of hardware and software in the
most general sense, not limited to computers. 1)
hardware consists of the tool that embodies the
technology as material or physical objects. 2)
Software consists of the information base of the tool.
Technological innovation creates one type of
uncertainty in the minds of potential adopters (about
its expected consequences), as well as representing an
opportunity for reduced uncertainty in another sense
(that of the information base of the technology itself).
The latter is the potential uncertainty reduction
representing the possible efficacy of the innovation in
solving an adopter’ s need or perceived problem.
Once information-seeking activities have
reduced the uncertainty about the innovation's
consequences to a tolerable level, a decision to use
innovation will be made. The models in this paper
address the innovation-decision process, which is
essentially an information seeking, information
sending, and information processing process. While
this is not visible in the TechTx Basic Entropy model,
the effects of the learning curve are found in the
TechTx Entropy Learning model. The TechTx
Entropy Feedback model factors in the request for
clarification and feedback in order to reduce the
uncertainty about the advantages and disadvantages of
the innovation.
Innovation |
Probability of Use%
= === Innovation It
sees Innovation Ill
L Time (t)
Figure 3-5. Diffusion. (Source: Rogers 1983,
p. 11)
2. Communication
The primary model in Rogers 1983 is a
communication model. While Rogers lays out the
communication channel element as component critical
to diffusion, he performs and references an enormous
amount of empirical data without addressing the
model in terms of a communications system.
Applying communication and information theory
methods to this observation is indeed an area that
could benefit the study of software technology
transfer. The benefit of an information theory and
communication model approach has not been
addressed to date. The model developed in this paper
suggests a quantitative method to address the
communication model using Shannon’s entropy, the
bakers’ transformation (an entropy) of the control
model and learning curves.
3. Time
Time is an important element of the diffusion
process. Time does not exist independently of events.
It is an aspect of every activity. We think in terms of
astronomical time, or time differences similar to
asking a person on the street for the time and they look
at their watch. Rogers and all of the technology
transition literature address this type of time. This is
time as described in classical physics. We in western
scientific tradition take this for granted since the
writings of the philosopher Aristotle, in which time is
closely related to motion and therefore to space. This
is a classical interpretation of time in which the
present separates the past from the future.
In the basic work Process and Reality,
Whitehead emphasizes that the simple location in
space-time cannot be sufficient and that the
embedding of matter in stream of influence is essential
(Prigogine 1983). Whitehead emphasizes that no
entities, no states can be defined without activity. No
passive matter can lead to a creative universe.
It is only recently that time can be expressed
in a precise mathematical form. Since we are faced
with Planck’s Paradox, with the absence of a physical
reality, this study moves toward the mathematical
notion of time as taken with the use of the bakers’
transformation in time steps and presented by
Prigogine (Prigogine 1983).
The bakers’ transformation is essentially the
folding and stretching that results in mixing. To better
understand the function, let's examine two examples
normally given to describe the process. Imagine
Rome, when we observe the city, we see architecture
and buildings from many time periods. They are all
interspersed and mixed into the city. These areas and
remnants, which are interspersed, are the result of
mixing at a number of iterations. The other example,
and the one where the bakers’ transformation gets its
name, is folding and stretching of dough horizontally
and vertically. Take a piece of dough, and place a spot
of sauce on the dough. Fold the dough. Stretch the
dough to be the original area again. Then successively
repeat the iteration action. We can let X be the
function that represents the value corresponding to the
application of n bakers’ transformations.
Xns1 = F (Xn) (3.1)
The various functions X, are functions of
internal time. The intemal time is an operator like the
one used in quantum mechanics. The age of partition
X, is the number n of iterations i that are to be
performed to go from X, to X,. Whenever the internal
time exists, it is an operator, and not a number.
Further discussion can be found in Prigogine
(Prigogine 1983), Farmer, York Ott, (Farmer 1983),
McCauley, (McCauley 1993), and Baker (Baker
1990). This is the form of the finite difference
equations used in the models.
4, Social Structure
The social structure provides the network and
media to transmit the messages in the communication-
diffusion model. Rogers (Rogers 1983 p. 25) quoted
Katz, “It is unthinkable to study diffusion without
some knowledge of the social structure in which
potential adopters are located as it is to study blood
circulation without knowledge of the structure of the
veins and arteries.” The social system is a set of
interrelated units that are engaged in joint problem
solving to accomplish a common goal (Rogers 1983
10
p.24). In other words, the model is a kind of graph.
There is more to it than interrelated units
when establishing the network of individuals and
organizations. Hargadon (Hargadon 1997) provides
an interesting insight via an ethnography on these
network mechanisms, for technology brokering and
innovation in a development firm that produces one of
a kind products. He identifies the mixing mechanisms
and the feedback process, building on historical data
and experience. The experience is held in informal
networks and is communicated in terms that are
aggregations and abstractions of terms that were used
in prior internal efforts. Typical of the communication
were short hand descriptions that would sound like,
“We can build this with a X like a Y from the Z
project.” In this dialog, Y is an abstract chunk of a
previous project. Correlations are established in the
participant's mind's eye.
Allen (Allen 1977, 1983) emphasizes the
importance of the “messages” from outside
organizations. He indicated that as many as 80 percent
of the messages come from sources outside the
organization. This is interesting since the model
proposed will draw on external sources of information
providing “messages”.
There is a method to determine effective -
efficient network size and diversity, referred to as
optimizing structural holes of social capital (Burt
1992). Essentially social capital is found in
relationships - whom you know. It is managed, and it
aggregates from people to organizations and can be
orchestrated to build an effective social structure and
network. The model proposed in this paper addresses
the node linkages of authors and corporate sources by
using the joint entropy of Shannon. While the models
herein do not develop these details, the models have
been developed to accommodate a structural hole
analysis. The approach chosen enables later
refinements as detailed node relationships are
developed for lower level models, e.g. references cited
or actual studies of message traffic of a receiver node.
In competitiveness, or survival, social capital
is organized naturally around the human behavior and
the principle of least effort. In simple terms, this
principle of least effort says that a person solving the
immediate problems will be viewed against the
background of the person’s future problems, as
estimated by the person. Moreover, the person will
strive to solve the person’s problems in such a way as
to minimize the total work that must be expended in
solving both the person's immediate problems and the
person's future problems. That in tum means that the
person will strive to minimize the probable average
rate of his work-expenditure (over time). In addition,
in so doing he will be minimizing his effort (Zipf
1965, p. 1).
In the area of software engineering, Boehm
(Boehm 1989) developed a Theory W to help
individuals and organizations to negotiate win-win
conditions, given constraints and alternatives. Theory
W is a management theory and approach which says
that making winners of the key stakeholders is a
necessary and sufficient condition for an effort’s
success. (Boehm 1998) First-hand experience by the
Amy (Saboe 2001a) over the last 10 years with the
WinWin process model and tool, indicates that Theory
W does provide a method for a group of individuals
(and by extension this could be seen as representative
of organizations) to analyze and act over a larger
visible decision space when acquiring a software
engineering process technology. This does enable the
principle of least effort to be used in a group setting in
a quantitative fashion.
The current research addresses minimum
effort through the study of joint entropies in the
model. Minimizing the rate of change of entropy, i.e.
watching a technology mature, is something that can
be observed in the model. On the prescriptive side,
actions can be taken to get the technology to stabilize
quicker, by investing in refinements, redundancy of
the message set, propagation of the messages, and
analyzing the effect on the entropy, and hence the
principle of least effort.
With the foregoing, we are armed with the
basics that influence technology _ transfer.
“Software Engineering" Technology Diffusion
Measured by "Messages" Generated (Saboe 2000)
Stcted Do
ae ene Or a oe aT a
cur
5. Experiment 0
Everywhere”
“Count Every Message
The initial study, called experiment 0,
evaluated the technology “Software Engineering” to
determine if indeed there was a better way to get a
handle on maturation of technology. During this
experiment, the effort looked at all print messages
available. Software engineering “messages” were
counted starting in 1968. The leading indicator
messages appeared to be graduate programs that
performed research and published messages in the
form of Master's theses, and Ph.D. dissertations.
Searching Dissertation Abstracts, 628 of these
messages were found over a 30-year period. Messages
showed up on software engineering technology in the
form of books and technical proceedings. 5226 of
these book/technical proceeding messages were found
from a source going back 50 years. Messages in the
form of articles in abstracted journals had a yield of
3764 messages, over a 10-year period, from a journal
universe of 12,500 journal titles. Messages similar to
these were searched in another source, the Applied
Science and Engineering Abstracts. The result was
1677 messages over a 20-year period. This yielded the
data shown in Figure 3-6. The data for this chart is
found in the appendix. This is a typical message-
counting approach. Even when the data is not
cumulative, we can see that there are general trends.
We can make a few qualitative observations
from the message-count data for software engineering.
Looking at the messages published each year in
Figure 3-6, we get a sense of capacity. The research
messages from the research institutions seem to be one
of the limiting factors. Books and technical
proceedings top out as well, also giving an indication
of steady state capacity. Articles seem to be still
growing. Articles are shorter and therefore more of a
gloss than the high-end messages in the form of a
book or a technical report, thesis or dissertation. These
high-end messages are where one would expect the
] new ideas to come from. It is easy to see that the
Monterey Workshop 2001
Figure 3-6 “Software Engineering” Messages
Initial Data.
(Source: Saboe 2000, 2001)
The first experiment, which we refer to as
experiment 0, starts to quantify this for software
engineering, and is seen in Figure 3-6. Figure 3-6
illustrates the message-counting approach of Rogers
for the technology. We have the number of messages
published in a given year on the Y-axis, and time in
years on the X-axis.
capacity to produce this type of high-end messages has
stabilized. The academic research infrastructure is
only capable of producing on the order of 100 “new
idea” messages per year. Producers of books and
technical reports add another 300 messages per year at
capacity. While researchers producing high-end
messages containing new information are not the only
source of new information, we see they have a
capacity limit in the number of messages produced. In
order to build a nationally competitive infrastructure,
these are the types of leverage points to which
research managers and government policy makers
need to have access.
ane
While this is interesting, the message-
counting approach is limited in its analytical value. It
is a very labor-intensive effort with minimum
quantitative yield that would enable better-informed
decisions for proactive actions. The idea to find a
representative sample of messages for the technology
under examination pointed to professional societies.
While their databases would not cover every message,
they would yield a rich enough source to potentially
bear meaningful fruit.
6. Crossing the Chasm
ha)
03b
aah
Chasm and Fissures in
Technology Transition.
Figure 3-5.
(Source: After Moore 1991)
Moore (Moore 1991) identified a chasm
between the early adopters and early majority.
Fissures were identified between the other adopter
segments of the communiy. At least two factors
contribute. First, the communication channel between
the segments of the community may be non-existent or
spotty. Second, if the communicaiton channel existed
and was established, there is an impedence mismatch
between advocates and receptors in different
communitiy segments.
7. States of Software Technology
Redwine et. al. (Redwine 1984) studied 14
different cases in considerable detail. They identified
five major phases, and two sub phases, 4a and 4b, that
a technology passes through as it matures. Figure 3-7
shows the states. While the analysis is extremely good
for the cases studied, there is a bit of imprecision in
states 4a and 4b, e.g. popularization throughout 40%
and 70% of the community respectively. It is
extremely difficult to determine based on their
methods, or any other reasonable approach, how to
12
determine what the total community is.
During the validation of this research, data
has been gathered on five of the fourteen technologies
in addition to more current technologies. This data is
found in other research (Saboe 2002).
States of Software Technology Transition
(Redwine 1984)
tial Evidence of Value and Applicability
4 —eriarcenenang rapa neal
tau
Tahanconartandeopmaton enema
sable Capabities Come Avalale
Deveoprant and Benson
minal Paper of don System
Appearance of akey tea undetying the echnology
ora clear stculadon of he probien
°
States of Software Technology
Figure 3-7.
Transition. (Source: Saboe 2001, Redwine 1984)
Software Technology Transition Framework,
Advocate/Receptor
The Software Engineering Institute has been
the single most prolific source on the subject of
software engineering technology transfer. This is
readily understood since this Federally Funded
Research and Development Center was established
with a primary mission to establish transfer of
software engineering technology to the Department of
Defense. Fowler (Fowler 1994) developed a
framework for technology transfer identifying
advocates and receptors (change agents) mediating
between producers and consumers (see Figure 3-8).
In this work, three life cycles of technology transition
are presented: research and development, new product
development, and implementation. Emphasis on the
need for common terms between receptors, consumers,
and researchers is identified as an important aspect of
the SEI studies. This paper’s model accounts for this
finding. A clear signal, with minimum noise and need
for requests for feedback, between a sender and
receiver improves technology transfer.
Software Technology Transition Framework
Producer Consumer Model with Advocates and Receptors
(Fowler 1984)
Figure 3-8. Software Technology Transition
Framework.
(Source: Fowler 1991)
This paper does not address the lower level
implementation details of that framework; rather it
builds an analytical framework useful to determine
probability of success and quantity and redundancy of
messages that need to be sent as a clear signal.
Significant additional work (Forrester 2000,
Fowler 1992, Fowler 1992a, Fowler 1990) has been
developed at the SEI. This work primarily focuses on
the lower level implementation details of the
framework, e.g. methods on how to plan and
effectively communicate technology to an
organization.
Saboe (Saboe 2001) has mapped the
framework of Forrester into the phases and state
transition points of Redwine (See Figure 3-9).
States and Producer Consumer
Software Tech Tx Model (Saboe 2000)
Usable Capabilities Come Available
1 CearDetiniton ofa Solution Approach via a
‘Seminal Paper of a Demonstration System
Appearance of key Iden underiying te technology
of a clear articulation ofthe problem
oF Shia
Monterey Werkshop 20001
21 June 2002 8
Figure 3-9. Mapping of the SEI Transition
Framework and Redwine'’s Stages.
(Source: Saboe 2002)
1, Extension to Address Standardization Effects
(Fichman 1993)
Fichman and Kemerer (Fichman 1993)
focused on organizational and community-wide
13
technology adoption. They develop a two dimensional
framework based on theories relating to organization
and communities. They particularly bring the
economics of standardization to the literature for the
first time in the software engineering process
technology literature. This work points out the
economic factors affecting technology adoption.
These are summarized as follows:
Prior Technology Drag
A prior technology provides significant
benefits because there is a large and mature installed
base. The research model of this paper addresses
“pushback” by measures of the entropy. e.g. the terms
of the technology show up more and more in the
community lexicon. The more familiar, the less likely
the technology will be pushed back and the less
requests for clarification will be required. In the
TechTx Basic Entropy, the measure of entropy as input
gives synthetic metric for the technology drag.
Irreversibility of Investments
Adoption of the technology requires
irreversible investments in areas such as products,
training, and accumulated project experience. For
example, once the money is spent on a technology, it
is gone. It cannot be spent again. Another example is
closer to the thermodynamic aspect of irreversibility.
Once the community or a node in the community is
exposed to a technology, you can not unexpose them.
The future is influenced by that exposure to a product,
training and prior experience. This paper addresses
this resisting organizational force of prior experience,
training and exposure through the entropy aspect of
the model. In the control theory part of the model, the
requests for feedback become less if the input
messages represent well-understood messages by the
resources and assets in the node.
Sponsorship
Strong sponsorship seems be beneficial in
moving a technology to standardization when a single
entity (person, organization, consortium) exists to
define the technology, set standards, subsidize early
adopters, and otherwise promote adoption of the new
technology. This paper suggests that setting standards
reduces the noise in the producer-(advocate-receptor)-
consumer lexicon, thereby reducing the rate of change
of the entropy. In addition, large quantities with a
limited amount of new terms introduced published
each year, would reflect sponsorship. Even if there
were not a single entity with resources focused to
promote the technology the models would suggest that
the technology is approaching stability, and
converging. While the model does not address
resources explicitly, the result of concentrated, with
the same vocabulary, messages with new information
either reduces entropy, moving the vocabulary toward
stability, or retards the movement toward stability and
convergence. The change in entropy, as the result of
new messages in the result of effort, implies resource
consumption to produce the messages. The stability
and convergence (i.e. decrease in the rate of change of
entropy) suggest the lexicon is becoming standardized.
This may be defacto. The vocabulary, communication
network approach and the change agent (sender -
receiver) aspect of the model address this factor which
was seen as desirable and identified by Fichman and
Kemerer (Fichman 1993).
Expectations
Technology benefits from an extended period
of widespread expectations that it will be pervasively
adopted in the future. This paper sets up the ability to
further analyze the notion of expectations. However,
this is the topic for further research as identified in the
final sections. | Work addressing mathematical
concepts of momentum and potential can be developed
based on the elements of the initial model.
The work by Fichman and Kemerer also
identifies attributes of innovations. Although Rogers
addressed and identified five generic attributes of
innovations (1) relative advantage, (2) compatibility,
(3) complexity, (4) trialability, and (5) observability,
his work is based mostly on study of individuals. Van
de Ven (Van de Ven 1991) argues that these same
innovation attributes play an important role in
adoptions by organizations. The Rogers’ attributes
have been generally adopted by the community due to
the familiarity to the diffusion of innovations
community. Others (Moore 1987), (Kwon 1987) use
these as well. Alternate taxonomies show up in
Leonard— Barton (Leonard-Barton 1988), who
identify transferability, organizational complexity, and
divisibility; Pennings (Pennings 1987) identifies
concreteness, divisibility and cost; and Eveland and
Toratzky (Eveland 1990) identify trialability,
lumpiness, adaptability, degree of packaging, and the
“hardness” of the underlying science. Zelkowitz
(Zelkowitz 1998) relates different styles to Rogers’
attributes and characteristics of the adopter type. In
most cases, all of these can be mapped back to Rogers’
original attributes.
This research was constructed to address
Rogers’ compatibility, complexity, and trialability in
terms of the entropy metric. Relative advantage is
addressed only indirectly, but the mechanism is there
to compare two or more competing technology
entropy metric curves and to determine the rate of
change, crossover, and probability of arrival of a
technology’s maturity. Studies that spot Redwine’s
observable (first four) state transition points in data are
made for five of the fourteen technologies they
studied. It is premature to say that we can make any
predictions by spotting observable points alone.
However, future research could spot the observable
14
events and attempt to correlate probability of success
with the entropy metric. .
2. Diffusion/Infusion Issues (Zelkowitz 1995)
Zelkowitz (Zelkowitz 1995, 1998) has
extensive experience with infusing technology into
organizations. Infusing is differentiated from
diffusion as it relates to internal adoption by a
particular target organization, while diffusion
generally refers to movement of the technology to the
broader user community in a macro sense. His study
within NASA builds on the “experience factory” work
with NASA’s Software Engineering Lab and the
experimental approaches of Basili (Basili 1994,
1994a). He studies the differences in the industry-
wide phenomenon of a technology specifically
focusing on the infusion process which actually make
the changes in the current state of technology. This
paper addresses infusion process in f(x) and the
interactions as successfully retransmitted messages
from a change agent (receptor) to a consumer. The
fraction of messages that need clarification (B) address
the efficiency of the infusion process. If all of the
material is well understood into highly encrypted, and
without a lot of noise, the technology is passed
directly to the consumer. At the macro diffusion level,
looking at the entropy rate of change for the ensemble
of nodes, we see the associated clarification (B's)
which give us the average rate for the request for
feedback (lack of understanding) of a technology. This
in tum can be fed to infusion, where the technology
program manager and adopter organization can further
study the details of the infusion process. Individual B
values for an organization and a given technology can
be measured, if it is so desired.
3. Technology Transfer and the Learning Curve
(Nishiyama 2000), (Hanakawa 1998)
During infusion, there is evidence that the
learning curve is in play. The skill level and the
improvement in productivity due to the technology,
productivity loss during transfer, and the combined
effects, net gain (Nishiyama 2000). The leaming
curve impacts on assimilating a new technology into a
project were seen by the number of tasks performed
over a study of several projects (Hanakawa 1998).
This study in software development and others suggest
the learning curve of Newell and Rosenbloom (Newell
1981) for power law chunking is appropriate for the
various types of learning that need to be handled. This
paper refines the basic control model f(x) with the
power law learning curve chunking model equations.
While this is not important for the development of the
basic model in this research, it provides the linkage to
all manner of studies of organizational learning and
ultimately, the breakeven and return on investment
curves (Nishiyama 2000). This can be developed to
make resource decisions, both for the infrastructure
and fora specific research program or organization.
There is a broad base of literature on learning
curves. During the study for this research, a large
number of papers were reviewed. (Anderson 1981,
Guiliksen 1934, Knecht 1974, Langley 1981, Lewis
1981, Mazur 1978, Newell 1981, Nembhard 2000,
Miller 1956, Vigil 1994, Yelle 1979) and many more.
Several of these are discussed elsewhere (Saboe 2002)
in the learning curve section of that research.
These papers developed the basic
relationships from learning curves, through relevance
to software engineering. Anderson (Anderson 1981)
is from Carnegie Mellon University, and the book he
compiled under NSF and DARPA funding has a
strong bent to showing the relevance to software
development. (Langley 1981), (Lewis 1981), (Newell
1981). Linkage to distributions of terms and statistics
of language and Zipf’s law for the principle of least
effort, are connected through (Mandlebrot 1953),
(Simon 1955), (Snoddy 1926), and (Zipf 1949, 1965).
Mapping of Motives of Actors (Pfleeger 1999)
While the work by Pfleeger (Pfleeger 1999)
never explicitly defines technology transfer, it
provides the most comprehensive literature summary
of the essential software technology literature. While
not addressing all of the transfer field literature, or
even all of the software technology studied in this
area, the paper is an excellent review, a great overview
and starting point. There are several important
contributions beyond the survey of the field. She
describes the process and roles involved in order to
move technology in a transition from idea (technology
creation) to adoption (technology diffusion). The
generation of evidence, packaging, support and
attention to the audience are identified as essential
elements in the process of transfer. In this paper, these
characteristics are primarily addressed in the
clarification (f) in the control model. The clarification
(B) values are driven by the commonality of terms to
the audience measures in terms of the frequencies and
entropy metric.
Pflegger also maps the motivations of the
adopters to the category of adopter (innovators, early
adopters, etc. per Rogers 1983) (Table 1). Also
identified are the effects of rules imposed on an
organization, a standards committee or a customer.
These rules can encourage the success of a technology
(this push or pull) when other models fail. For
instance, she cites the effect of the Department of
Defense’s endorsements of products,
recommendations for process improvement, or
mandatory rules about tools as a positive influence to
15
encourage “laggards” to take risks and try new
technologies. The successful technology requires not
only a new idea, she claims, but also a receptive
audience with a particular adoption style. The various
models (people mover, communications, on the shelf,
vendor and rule as introduced by Pflegger) are mapped
to the level of risk the adopter community is willing to
take.
Adopter Level of | Adopter Model
Category Risk
Innovators Very High People-mover model
Early adopter High Communication
model
Early Majority Moderate On-the-shelf model
Late Majority Low Vendor model
Laggards Very Low Rule model
Table 1 Relationships among Adopters, Risk and
likely Transfer Model.
(Source: Pflegger 1999)
So to reduce the impedance mismatch
between researcher and the method of moving the
technology, “message” has to be matched with the
audience. While Pflegger cites Zelkowitz and other
studies that look at the actual implementation details
of the transfer process, it is useful to note the factors
that affect clarification requests @) in this research.
Another way to view the stream of messages is to
suggest all that does not move to the consumer is in
the feedback-entropy streams. Pflegger, Zelkowitz,
the SEI and others generally are looking at the
implementation details of technology transfer. All of
the research to date generally looks at technology
transfer from this perspective. This paper addresses a
macro process, useful to the research manager and
program managers, to assess the risk of the technology
maturing at a given time. Implementation in a specific
program of a technology should try to minimize the
clarification requests (B). This is done by insuring that
the mismatch is minimized, using messages that are
matched for the audience. The message is packaging
of the evidence . Pflegger (Pflegger 1999) and Schum
(Schum 1994) describe evidence.
Types of Evidence Characteristics
Tangible Objects
Documents
Images
Measurements
Charts
Relationships
Direct Observations
Second-hand
Opinion
Testimonial (unequivocal)
Testimonial (equivocal) Complete
equivocation
Probabilistic
argument
Missing tangibles or
testimony
Contradictory data
Partial data
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Census data
Table 2. Messages in Forms of Evidence.
(Source: After Schum 1994, Pflegger 1999)
Schum presents the categories of evidence
seen in Table 2. The specific observational sense,
objectivity and veracity of the message enable
decisions to adopt or not adopt. In terms of this paper,
if message is clear, unambiguous, and well
understood, the advocate can pass on the message to
the receptor with little to no requests for feedback.
Schum and Pfleeger argue for this packaging of the
message. This research supports those observations
with the Shannon entropy component where noise and
non-signal are minimized, e.g. the vocabulary
converges between advocate and receptor.
4. INFORMATION THEORY APPLIED TO
TECHNOLOGY TRANSITION
Informally, information measurement can be
understood as anything that increases the variance also
increases the information. Generally, variance is
usually stated in units of measure, e.g. meters, volts,
etc. The amount of information is a dimensionless
quantity. When we have a large variance, we are very
ignorant about what is going to happen. If we are very
ignorant, then when we make an observation, it gives
us a lot of information. On the other hand, if the
variance is small, we know in advance of our
observation how the result is likely to come out;
hence, we get little information from making the
observation.
1. Information, Uncertainty
Information is a difference in matter-energy
[change of status - i.e. state] that affects the
16
uncertainty in a situation where a choice exists among
a set of alternatives (Rogers Kincaid 1981).
"Information is something which reduces uncertainty.
Communication is exchange of information.” (Wiio
1980, p. 18) Information is the ability to choose
between alternatives reliably. Before you send me an
email, I cannot reliably, guess your message. After I
receive it, I can do so. I have gained information
(www.aip.org).
Uncertainty is the degree to which a number
of altematives, the multiplicity of options, are
perceived with respect to the occurrence of the event
and the relative probability of the outcomes.
Uncertainty implies a lack of predictability, of
structure and /or information. This multiplicity of
option states can be quantified in terms of entropy.
Entropy and uncertainty can be considered
synonymous (Jaynes 1957). Jaynes made the linkage
between statistical mechanics as we know it from
(Gibbs 1903), and entropy as we know it is
thermodynamics, by relating a common concept to
both - maximum entropy. Mathematically, maximum
entropy has the important property that no possibility
is ignored. It assigns positive weight to every possible
situation that is not absolutely excluded from the
information. It is the state where we can deal with
equilibrium properties. According to Jaynes, this is
quite similar to an ergodic property.
The macro equilibriumstate of a system (this
is what we see in classical thermodynamics), is the
macro equilibrium entropy, S. From Boltzmann, we
get
S =kP ({p,}) (4.1)
This is when the maximum value P of the
statistical entropy functional P ({p;}) through the
Boltzmann constant? k. Where P ({pi)= In Q is the
uncertainty. Where k for {nats, bits, bytes, orJoules/°
is 1138x107)
In2'1n256
respectively. We can convert the natural log, In, to
log easily.
Kelvin}
_Inx
1n2
log, x (4.2)
The probability distribution {p} is on the set
of available microstates Q={i} or multiplicity. The
functional S=kP ({pi}) needs to satisfy two general
properties. (i) P must be positive, taking the value
zero only in the case of absolute certainty (pj = 0 for
all states, except for a given state j for which p; = 1).
5 shannon (1948) quickly points out that k is just a convenient
constant to relate to our physical world.
(ii) P must increase monotonically with increasing
uncertainty. In addition, a third condition is required.
(iii) The P is additive for independent sources of
uncertainty (Bayes 1763), (Planes 2002). Because of
this, we have the property of extensibility. This means
if you add or subtract these quantities which contribute
to uncertainty, the system size - the extent -- changes.
Adding these quantities requires a product of the
probabilities.
We can compose a system like this, with a
system composed of two subsystems which are
independent, A and B, so that the set of microstates is
Qasg = QaxQg. Each microstate (i,j) can be specified
by fixing a state i€Q, of subsystem A and a state
jz of subsystem B. If a probability density,
Day =P; Pp, then P 4? =P A +P %. (Planes
2002), (Munster 1969).
> ({p.}) =“ plog,(p) 43)
1)
2. Extensive and intensive properties
Extensive properties in the physical world are
volume, mass, particles, energy, money, messages,
records, etc. Intensive properties (e.g. pressure and
temperature) on the other hand are independent of the
size of the system. A method to determine whether a
property is extensive or intensive is to divide the
system into two equal parts with a partition. Each part
will have the same value for the intensive properties,
but half for the extensive properties.
Extensive and Intensive
Properties
? hen
e P
P
Extensive changes with the extent or size of the system
Intensive properties are not affected by the system size
Examples:
Extensive:mass, volume, energy, money, messages
Intensive: temperature, pressure
Figure 4-1 Extensive and Intensive
properties
It would be valuable to identify analogous
extensive and intensive properties in the technology
transition model, or in or general terms.
Property Extensive Intensive Thermodynamics/ Tech Transfer/ Information/
Physical Communication System
Particle Mass x * N particles per + Unit of entities, e.g. Term per
mole some standard message length
Volume xX * L’ (length’) or * v*snodes consisting of
+ _ AL (Area * length) authors * state change
Energy xX + eV, Joules, BTU’s | * Some conserved property
+ Messages, information
Temperature xX * °K degreeskelvin | * Some measure of change is
cardinal related to two
variables ext and or int
Entropy xX * Sab + — Similarly defined for
+ S=kP ({pi}) information (Shannon 1948)
+ S=kinW * S=kP ({pi})
* Alwaysincreases | * S=-2pjilog2pi
+ Additive for + Maximum entropy -
Independent uniformly distributed
Identical probabilities, same as
Distributions thermodynamics
Pressure xX * Force perArea * Messages per node
Density x + Extensive property | * Messages per node (author)
pervolume
Table 4-1 Property Relationships
17
Particles are analogous to sets of terms in a message in
this model. A message is made up of sets of terms.
Counting all of the sets of terms is the same as
determining the number of entities, particles. Just like
in molecules, some entities have more weight than
others. If all null and single term sets have the same
weight, the analogy is a set of sets of terms e.g. {},
{A}, {B}, {C}, {AB}, {AC}, {BC}, {ABC}. {A} is
“lighter” than {AC} which is a composite of two if a
term is made up of {A}+{C}. There should be some
relationship between changing the status of a term and
analogous principles in the physical world. e. g.
Newton’s laws (see the next section).
Volume in the physical world, is in three
dimensions measured in some length units. We can
get a volume with units of 1° by measuring the volume.
Integration over small dl is used in continuous space.
For a discrete system, we count the points defined in
phase space. For the models, this volume is defined
in only two dimensions, nodes (a publisher) and state
points.
In a classical thermodynamics model, energy
is measured in Joules, or BTU. It is often convenient
to measure energy units in electron volts, which is the
kinetic energy of an electron that has been accelerated
through a voltage difference of one volt. This is
moving an electron from its status at point A to point
B. This is directly related to the conservation
principle, the 1* law of thermodynamics, and
Newton's 3° law. The first law of thermodynamics
says that energy is conserved and transformed.
Energy is a primitive and essential thermodynamic
function. It is a mathematical abstraction. (Abbott
1989, pl). Newton’s 2"? and 3° laws similarly
constructed using the principle of conservation.
Law 1 “Every body preserves in its state of
being at rest or moving uniformly straight forward
except insofar as it compelled to change its state by
forces impressed.”
Law 2 “A change in motion is proportional to
the motive force impressed and takes place along a
straight line in which a force is impressed.”
Law 3 “To any action [change of state] there
is always an opposite and equal reaction; in other
words, the actions of two bodies upon each other are
always equal and always opposite in direction”®,
(Newton 1726, p417).
Newton says in definition 3 of law 1,
“because of inertia of matter, it is only with difficulty
put out of its state either of resting or of moving.” In
6 This is the exact statement taken from Newton’s original
work, Modem texts have often changed the wording slightly on
each of his laws, but the original statements give us the closer intent
of the law to this
18
Newton's interleaved copy of edition 2, he adds the
following which was never printed: “I do not mean
Kepler's force of inertia, by which bodies are moved
toward rest, but a force of remaining in the same state
either of resting or moving.” (Newton 1726 p404).
Change of state, status, must overcome some inertia.
E.g. changing vo to v; meaning to change from an initial
state, say a velocity, to anew velocity. Even to change
one orientation of one atom, or one bit, such a change
of state, takes some force or stimulus. Something must
happen to change the state of information otherwise it
stays in its current state.
Below we show the relationship using a Venn
diagram, that shows the probability of two sets can
represent this conservation through correlations of
extensive properties at the intersection consisting of
mutual information. The left hand subsystem A is
composed of the sum of the uncorrelated part P_ (A|B),
plus the correlated part I(A;B) still equal to the total and
the P (A), where I(A;B) is the shared mutual
information. This is the equal and opposite amount
required by the 2" and 3” laws of Newton. Similarly,
the right hand subsystem B is composed of the sum of
the uncorrelated part P (BJA), plus the correlated part
1(A;B) which is still equal to the total and the P (B).
Looking at relation 4, I(A;B) =(B;A) and other relations
in Figure 4-3, we see how the conservation principle is
realized. The key is not conservation of energy in this
research, but rather the conservation of the correlated
components of extensive properties in two interacting
subsystems (Planes 2002). What one subset looses, the
other gains.
3. Entropy Review
Entropy, as a concept, can readily be seen as
logical entropy (think of it as a measure of uncertainty,
noise, non-signal, process inefficiencies, the percentage
of work resulting in defects and requiring rework, etc.)
and physical or thermodynamic entropy (i.e. mixed-up-
ed-ness, disorder, disorganization, etc), which is the
quantity of energy not available to do work. Logical
entropy is Shannon's entropy (S,,)as defined by
Shannon on his treatise on communication theory
(Shannon 1948). Shannon's theory says that the
entropy of an information source measures how well its
behavior (e.g. the next symbol in a sequence it
produced) can be predicted.
Mixing entropy can be represented by the
eigenvalue of a bakers’ transformation function. This
bakers’ transformation in state space represents
entropy in terms of folding, stretching, translation and
rotation (Speigel 1998 p292). This transformation is the
representation of a dissipative structure. These are
structures with an innate capacity to dissipate anything
that comes in to disturb the system. The term
“dissipate” is somewhat unfortunate, because what
really occurs is integration not dissipation (O’Murchu
1997 p.168). The entropy is the quantity of
information not available to help us work, yet is
valuable to understand if the objective is propagation
and diffusion. The relationships are developed below.
Recently a number of undergraduate texts are
illustrating entropy as the accessible state multiplicity
for quantities that must be conserved -- e.g. volume,
and particles. The notion of conservation of a quantity
is important to this research, as this could be
momentum or more importantly information. This is
understood from the —_ logical-mathematical
interpretation of the equations vs. physical
interpretations. It requires us to step back and look at
conserved quantities in the mathematical sense, then
map those to our problem. Further, entropy,
temperature or coldness (1/T) and heat capacity have
been developed on the basis of information units alone
(Fraundorf 2000).
The definition of information entropy here is
related to the definition of entropy in thermodynamics.
What follows is a basic review of entropy in
information theory after Shannon, Jaynes,
Kolmogorov, Uspenski, and others as found in Li, (Li
1993) and Cover (Cover 1991). This review section is
drawn from Cover (Cover 1991 p13).
Let X be a discrete random variable with
alphabet = and a_ probability mass function
p(x)=Pr{X=x}, x=. p(x) and p(y) refer to two
different random variables and are in fact two different
probability mass functions p,(x) and p(y).
The definition of information entropy is:
8, (X) =} pOdlog, pls) (4.4)
te
Sy is the entropy measured in bits, and the log
is base 2. For example, the entropy of a fair coin toss
is 1 bit. The convention of 0 log 0 =0 is used, which
comes from continuity since x lox x +0, as x 70.
The base of the log is two for the natural units as
developed by Shannon (Shannon 1948). The entropy
is a function of the distribution of X. It does not
depend on the actual values taken by the random
variable X, but only on the probabilities.
If X~p(x), then the expected value E of a
random variable g(X) is denoted
E,9(X) => g(x)p(9) (4.5)
The ‘entropy of X can be interpreted as the
where X is drawn
1
expected value of log
p(X)
according to the probability mass function p(x). Thus
19
S$, =E, los (4.6)
1 =H, 10g rx)
Certain properties must be satisfied. This is
done axiomatically or by answering some natural
questions such as “What is the average length of the
shortest description of the random variable?” Asa
result we find
s, 20
(4.7)
0 <p(x) <1 implies log(1/ p(x)) 20
Here is an example. Let
ith probabili
with probability p (48)
with probability 1—p
x f
then.
S, (X) =—plog p —(—p)log(1—p) =S, (p) (4.9)
We see that Sy = 1 bit when p=1/2. Figure
4-2 shows the basic properties of entropy. It is a
concave function of the distribution and equals 0 when
p=0 or 1. This makes sense because when p=0 or 1,
the variable is not random and there is no uncertainty.
The entropy is maximum when p=.5, which
corresponds to the maximum value of the entropy.
Entropy vs Probability
Engr Pattie
“8 Entropy Si
Su =- 2 p(x) loge p(x)
Si =-(p) log (20)! og (+
Figure 4-2 Entropy vs Probability
Here is another example. Let
with probability 1/2,
with probability 1/4,
with probability 1/8,
with probability 1/8.
The entropy of X is
(4.10)
[p
4
th
1 1 11 Td. 4 2
S, (X) =—log— — log — -—log — —log — =— bits
2 24 4 8 8 8 8 4
(4.11)
Suppose we wish to determine the value of X
with the minimum number of binary questions. An
efficient first question is “Is X=a?” This splits the
probability in half. If the answer to the question is no,
the second question can be, “Is X=b?” The third
question is “Is X=c?” The resulting expected number
of binary questions is 1.75. This turns out to be the
expected number of binary questions required to
determine the value of X. It can be shown that the
minimum number of binary questions required to
determine X lies between Sy(X) and Sy(X +1).
Let’s now introduce the definitions for joint
and conditional entropy and mutual information..
These are key facets of the technology transfer models
proposed.
Joint entropy Sy(X,Y) of a pair of discrete
random variables (X,Y) with a joint distribution (X,Y)
can be considered to be a single vector-valued random
variable. It is defined as
8,04Y) => px ylog p(x y) (412)
12a
which can also be expressed as
S, (X,Y) = log p(X, Y) (4.13)
The conditional entropy of a random variable given
another is defined as the expected value of the
entropies of the conditional distributions, averaged
over the conditioning random variable. If
(X,Y)~p(x,y), then the conditional entropy Sy (Y|X) is
8, @ |X) =} pos, & |X =x)
1€
(4.14)
=> way Pt y| log pl yl x) (4.15)
1
=> py wlogplyly (4.16)
=-£,,,,log pW |X) (4.17)
This is shown in the Venn diagram in Figure 4-3.
Mutual Information and Entropy
HOOD SOK ae i
HOY) Sl Q)
fae SaKY) GB)
ro)
(5)
OGY)
yx
1GY)
10) = ar
SulKY)
0K)
Figure 4-3 Mutual Information, Joint and Conditional
Entropy
20
Relative entropy or the Kullback Leibler
distance between two probability masses p(x) and q(x)
is defined as
D(pliq) p(x)log a (4.18)
E, lo PO) (4.19)
*FaX)
Similar to earlier developments, we use the
convention based on continuity of arguments that
dlog? =0 and plog =00, (Cover 1991, p18)
While it is not a true distance between
distributions, it is useful to think of relative entropy as a
“distance” between distributions. The mutual
information which was introduced before is the
measure of the amount of information that one random
variable contains about another random variable. It is
the reduction in the uncertainty of one random variable
due to the knowledge of the other. Assume we have
two random variables X, and Y with a joint probability
mass function p(x,y) and marginal probability mass
functions p(x) and p(y). The mutual information I(X;Y)
is the relative entropy between joint distribution and
the product distribution p(x)p(y
1(X;Y) Ee! weleg a 5° (4.20)
p(x, y)|| p(x) p(y) (4.21)
rai Y)
p(X) BY),
It is important to see that the mutual
information I(X;Y)=I(Y;X)
I(X;Y) =S, (X) -S, (X | Y) (4.23)
The mutual information I(X;Y) is the reduction
in uncertainty of X due to knowledge of Y. By
symmetry it follows that
1(¥;X) =1(X;Y) =S,(Y) -S, W |X ) 4.24)
That is X says as much aboutY as Y says about
X. Since Sy (X,Y) =S,(X) +S, W |X) we have
I(X;Y) $8, (X) +8, (Y) -S, (X,Y) (4.25)
In addition, we see that
1(X;X) =S,(X) S$, (X |X) =S,(X)
(4.26)
The mutual information of a random variable
with itself is the entropy of the random variable.
Mutual information and the symmetry we see
here is what will enable the conservation principle to be
met. As X correlates with Y it is realized in the same
~™ p(xy) (4.22)
amount of mutual information. This is easy, as we
saw in Figure 4-3.
To bridge the gap between communication
theory and capacity of human performance an analogy
is made between, a human accepting input and
generating output and a communication system. This
is seen as the overlap in a Venn diagram, where input
variance is represented by the circle to the left and the
output variance is the circle to the right, and at the
intersection is the amount of transmitted information.
Miller (Miller 1956) suggests that an individual is a
communication channel. He states for a human,
“when we increase the amount of input information,
the transmitted information will increase at first and
will eventually level off at some asymptotic level.”
He indicated that this is the channel capacity of the
observer, the human.
Now we have enough information theory to
understand the models. Consider the entropy as a
representation of the terms in a vocabulary, which are
available to the researchers in a time step. A
researcher reaches into the pool of messages, which
are constituted by terms. We can compute entropy
contribution of a term in a given time step by
computing p(x) for the term. Summing all of the terms
we have the entropy at time stepk.
The balance of the paper will discuss the
findings of the model. The details will follow. Here
is a brief, heuristic summary of the data using
illustrations.
Traditional Model - Message-Counting
Figure 4-4 Message Counting Linear Model
The message counting model seen in Figure
4-4 typically used provides a very good correlation
and is quite linear. Possibly an information theoretic
and dynamical systems model can be built that
enables richer analysis.
For an information - communication model
to work we need to determine the change in entropy
overatime step. In Figure 4-5, we see how entropy
and messages vary over time. Messages are a
21
conserved extensive quantity, and the information
entropy is related to the message terms.
Jan31 2002 sabe
Syren yams sucity
Figure 4-5 Entropy and messages over time
In Figure 4-5, we see that we would like an
illustration of the joint entropy related to technology at
a given time step. Further, we would like a method to
compare to different technologies, Figure 4-6. This is
done through the mechanism of relative entropy.
Figure 46 illustrates two technologies, we
now have a mechanism to determine how close these
technologies are in a crude sense. However, there are
other factors are work. For example, what is the mind
share, the volume of nodes operating on the messages?
y=6.6188%0"%
R?=0.9405
Figure 4-6 Entropy vs time
4. Interacting Subsystems
Let's imagine a super system (the
community’s world of knowledge) that consists of two
subsystems. These subsystems represent what is known
and what is unknown at a given time. The sum of the
two subsystem’s extensive variables, messages N, and
nodes V is constant. Here the conserved extensive
variable properties are N messages, and the sum of all
the nodes, v which is the volume. This will define a
control volume. Now we will take a virtual partition
and have it progress expanding subsystem A to the
right. As this partition passes over some nodes, effort is
made by the nodes and they “discover” a term. They
stimulate and change the internal configuration of the
system by converting an undiscovered term (a null)
into a communicated discovered term.
This can be seen in Figure 47. On the left
hand side we see “!!!s” representing terms that have
been discovered (answers), on the right hand side of
the partition we see “???s” representing terms that are
yet undiscovered (questions). The Venn diagrams
indicate the subsystems A and B, joint, conditional
entropies and mutual information, as illustrated earlier.
Now examine what this looks like with a sample
alphabet as in Figure 4-8. The nulls {} are terms that
have not yet been discovered at the frontier of the
research in time. In this simplified example, we are
assuming a fixed set of terms in the alphabet, and a
fixed number of nodes. This will permit the
development of the general relationships between
extensive and intensive variables in a state equation.
Later, once we have seen these relationships, we can
start with an initial condition representing the number
of terms and nodes, and add more vocabulary to the
system or more author nodes any way we wish. This
permits the design of a desired solution in the form of
an enaine.
Interacting Systems
$Y) Sy OGY) SOY)
s, m s, Swi Su
Toy 9 oon mn)
@ we a
» 9 ®
y¥ +
a Cae B_ ‘ire sepinceasen vm
Figure 4-7 Interacting Systems A and B
ca
if
tte
tot
1s 18
14 t
£1 H
ott 5
= af
£ £ £ d
ttt Hl
z a 1
3 To Tt 4
a_i tiers ‘l {
z tucheed progern 1g £ ii £ 1 i 2
138 5 fasttiewtsrosi ¢tete ts propre rete ests
Te 2 ferworcieeny tl¢te¢t i i Data ts I VT?
YM ww Wh? FE FP | PP | FE | a | |
Figure 4-8 Subset of an alphabet in two Interacting systems !!! and ???
Messages in Two Subsystems
ntarcting Systm A and 8 (Constant Messoes in Tot Systm AB)
Figure 4-9 Messages in two subsystems
22
In Figure 49, we see that as system A
expands, the number of terms discovered increases, at
the same rate that the number of terms undiscovered
decreases. This model satisfies our conservation
principle for extensive quantities.
Next, in Figure 4-10, we examine the entropy
relationship. The horizontal line at the top of the figure
is the joint entropy of the system. Since this is a closed
system, this is not changing, however, the internal
distribution will change. That entropy related to
subsystem A will increase, as there are more and more
choices to make in order to get complete information.
Subsystem B will decrease from a high entropy (all of
the unknown terms) to a lower entropy as there
becomes less and less left to be discovered. The lower
curve shows the mutual information. When the
distance between the center of the two probability
masses, or subsystems, decreases, there is a higher
correlation.
Entropy vs Messages
Two Subsystems
Son A = sos som + 4sm2
Siva =-oo0ene-oo02sk 74307
Pee P Ore Pee SPSESORS OPIS IEESEED
Figure 4-10 Entropy vs Messages Two interacting
Systems
Following reasoning similar to that used in
statistical, and condensed particle physics (Schroeder
2000) (Fraundorff 2000), we can find some useful
relationships. The slope of the curves of the two
subsystems give us some important information about
thermal equilibrium. Recall the from the canonical
ensemble discussion of free energy, that the
temperature T is the parameter controlling free energy,
or the conserved property. In this case of messages,
we can write
T MM
So the temperature is related to slope of the
change in entropy to change in messages curve. When
the curves in the figure cross over, the system is at an
equilibrium point. Let’s look at a general relationship
that shows the increase in one system is related to the
negative slope or, the decrease in the other.
(4.27)
(4.28)
The incremental change in Sq, divided by the
change in na messages, is equal to the change in
23
entropy, Ss, forsystem B again compared to the change
in the conserved quantity, in this case ny. Rewriting we
get
(4.29)
‘A A
The second term has a B in the numerator and
A in the denominator. An, is the same as -Ang, since
what we discover in messages is the same as what is
removed from the undiscovered system. We can
rewrite this for a system at equilibrium as
(4.30)
The thing that is the same for both systems
when they are at thermal equilibrium is the slope of the
entropy message graph. This slope must somehow be
related to the temperature of the system. The 2" law of
thermodynamics tells us that the conserved property
will tend to flow into the subsystem with the steeper
entropy vs. message graph, and out of the object with
the shallower entropy vs. message graph (Schroeder
2000 p87).
According to Schroeder, the former “wants to”
gain the free conserved property (messages) in order to
increase its entropy. If there is an imbalance between
the two subsystems, the latter doesn’t so much “mind”
losing a few messages (since the entropy will not
decrease much). A steep slope must correspond to a
low temperature, while a shallow slope corresponds to a
high temperature.
Now we can see in the lower curve of Figure
4-13, the relationship of the temperature (the right had
Y axis) of sub-system A as the partition moves over the
time steps. More activity increases the temperature.
The temperature is measured in degrees as we would in
a physical system; however, these degrees are
developed from information units. This is “the”
fundamental temperature unit developed from the
relationship of entropy, and the conserved quantity.
Note that there are temperature fluctuations.
This is consistent with Prigogine’s observation about
evolving systems. A dynamical system will help
explain these fluctuations.
Pressure (A) Messages per node
Pressure and Temperature
vs timestep
‘Temperature and Pressure vs Timestep
250 P(A)=0.0058k +1.1055 120000
——Messsages per Node (A) z= |
—+—Temp (A) from Polynomial R 0.9642 =
——= Linear (Temp (A) from Polynomial)
——— Linear (Messages per Node (A))
100000
80000
60000
40000
20000
0.00
eRe S88R33 8
k Timestep (months)
Figure 4-11 Pressure and Temperature °Saboe[] vs time - two interacting systems
24
‘Temperature (B) (Saboe Degrees)
Pressure is defined as the <messages> processed per
node, where the <messages> represent the average in
the time step per node. The pressure can also be seen
to increase as the temperature increases. While
messages are not physical molecules as in a
thermodynamic system, they seem to behave as a gas
might, as the temperature goes down the pressure
goes down.
Figure 4-13 shows the relationship directly between
pressure and temperature.
Typically, a state diagram viewed by engineers is a
temperature - entropy, orT-S, diagram. In the lower
curve of Figure 4-14, the T-S is illustrated. This is
the entropy of sub-system A with entropy (upper x
axis) and temperature (secondary y axis on the right).
The figure also shows entropy of subsystem A (left Y
axis) and messages n on the x axis. From this
information in a closed system we can see the trends
for a given technology over time. In a way we have
the ability to define the heat capacity” (say Cp, heat
capacity at constant pressure) in bits. This allows us
to move to an open system, like an engine and add
nodes, volume, and increase message flow. We can
then compute our effort required from a desired
“engine” to develop a technology.
AU =nC ,AT (4.31)
This also implies the equivalent of Camot’s
cycle, which can tell us the maximum efficiency we
can expect.
Another interesting point is that the set of
sets of terms, reduced to primitive message
combinations follows a Boltzmann distribution,
Figure 4-12. On the x axis, is the q-level,
representing the number of terms in set. The lower
curve on the y-axis is the frequency of sets. The
upper curve assigns a weight to each set. It is
interesting to note, as well, that these curves plotted
over the time steps examined (up to 21 years)
essentially remain stationary.
This permits conjecture in the deeper
meanings of the distribution of terms. Further, state
transitions moving from one q-level to another, must
somehow be affected by an impulsive stimuli of
some sort. That implies both the notion of kinetic
and potential “energy”. These topics are subject for
7 Heat capacity for sate equations are property relations and
as such are independent of the type of process. C, is the amount
of “stimuli” transferred to a system per unit “message” per unit
degree rise during a constant pressure process.
25
future research.
Figure 4-12 Boltzmann Distribution of Sets of
Terms (primitive messages)
Pressure Temperature
Pressure vs Temperature Saboe Degrees
Figure 4-13 Pressure vs Temperature °Saboe []
Temperature - Entropy (T-S)
Entopy 2 Interacting Systems 7.5 (A)
MM. Saboe 1725/02
Figure 4-14 Entropy -- Messages, and
Temperature - Entropy
5. Dynamical Systems Model
This is the information theoretic view. Now
we marry up a dynamical systems model with an
information theoretic model. When both stabilize in
arate represented by equations of the same form, we
have a match.
Figure 4-15 shows a map of the state space.
The legend shows The Java Entropy map marked
with a triangle (&) and a dashed line. The marker
represents data, the dashed line is an indicator of the
curve that the data would be fit to. Similarly the
circle (O) and dashed line legend for the A da points.
The state space map is shows that the data is
oscillating in the early stages. This shows that the
vocabulary and threads of research have not settled
down at first. Based on observation, see Figure
4-15, as the entropy increases, but at declining rate,
the data starts to approach the y=x line. The spacing
between each data point gets closer together. This
indicated that the data is moving toward a stabilizing
attractor basin. A method to quantify this
stabilization is discussed in the next sub-section.
nopy Discrete Tne Map
Figure 4-15 Java and Ada State Space Finite
Difference Map Entropy (Sis1, Si)
6. State Space Representation
Recall that the bakers’ transformation
example illustrates the mixing of a spot of sauce on
the piece dough, then folding and stretching of
dough. In technology maturation, a node is locally
taking in a chunk of dough, messages out of the pool
of messages persistent in history, and mixing them
along with new information, i.e. a new term, which
represents yet another spot on the dough. These
areas contain remnants from bakers’ transformations
of other nodes that performed the mixing and adding
function throughout time. A performing node may
perform a number of iterations. Other nodes also
perform the folding, stretching and mixing function
before and concurrent with the local node. The
nodes successively repeat the iteration action. We
26
can let X be the function that represents the value
corresponding to the application of n_ bakers’
transformations.
F (Xn) (4.32)
The various functions X, are functions of
internal time. The internal time is an operator like
the one used in quantum mechanics. The age of
partition X, is the number n of iterations i that are to
be performed to go from X, to Xy. The eigenvalue of
the characteristic equation has a relationship in
natural units to entropy. This relationship is through
the Lyapunov exponent, which gives the stretching
rate per iteration averaged over the trajectory.
Xnti =
So in Figure 4-15 we see a plot of a one-
dimensional map. Taking the derivative in this case
yields A The goodness of fit is determined through
the finite difference method known to determine
convergence and stability points in dimensions using
the Lyapunov number and the Lyapunov exponent A.
The Lyapunov numbers quantify the stability of an
orbit around an attractor. The Lyapunov numbers
are the absolute values of the eigenvalues of the
Jacobian matrix at a fixed point. The Lyaponuv
exponent is the logarithm of the Lyapunov numbers
(Farmer 1983).
qd
rN =lim= > lal £(x) | (4.33)
nen 4
These dimensions represent an entropy
measure for non-linear systems in stable or chaotic
regions.
We compute entropy two ways. One is
from data, which is acquired experimentally. The
other is from a model of the process of transferring
(transforming) information. The experimental
entropy data is related to the information we know
about a topic. We refer to this as Shannon’ s entropy
(Sq). The data Sq is gathered over time stepsk. We
perform regression on this data and have as a result a
function that is of the power law form e.g. y=bx",
where m is the slope and b is the intercept in log-log
linear form. We also have a model of a non -linear
dynamical system. The Lyaponuv exponent of a
map gives the sensitive dependence upon initial
conditions that is characteristic of chaotic behavior.
Further discussion can be found in Prigogine
(Prigogine 1983), Farmer, Y ork Ott, (Farmer 1983),
McCauley, (McCauley 1993), and Baker (Baker
1990). The following description follows the
development found in Farmer (Farmer 1983) and
Baker (Baker 1990).
The eigenvalue of the Jacobian® of the
finite difference equations representing the
dynamical system is also related to entropy. In fact,
the relationship is through the Lyaponuv number.
The Lyaponuv number and this relationship is
defined asJ, = [J (Xn) J (Xn1).. J(X:)] where J (x) is the
Jacobian matrix of the map] (x) = (@F/ax) with j,(n)=
jo(n)... 2jp(m) are the magnitudes of the eigenvalues
ofJ,. The Lyaponuv numbers are
A= lim. o[j(n)}”, i=1,2,...p . (4.34)
The Lyaponuv exponent is the smallest,
positive, real nth root taken. We follow Farmer's
assumption that almost every (Farmer’s emphasis)
initial condition in the basin of the attractor has the
same Lyapunov numbers. This followed from his
empirical evidence, and the data in this model does
not meet the exceptional conditions that he
identifies.
6. One Dimensional Finite Difference
Representation of Sy.
We determine the one-dimensional model
for computation of this entropy for the TechTx Basic
Entropy model in a form compatible with the two
dimensional micro level model. This is
Si. =£(8,,)
h=f'()
The macro entropy is partitioned and
allocated to the performer and affiliated organization
nodes. This enables computation of the system
entropy at the nodal level. This provides the method
of computing the Lyaponuv dimension from A to
(4.35)
(4.36)
measure the non-linear system entropy S,, cg at the
micro level or for simplicity of notation, Ss. Note
that this differs from the entropy Sy in Figure 46,
which is the information entropy, NOT the entropy
measure for the stability or chaos of the system.
The general form for the transformation is
Su, = £(Sy,). We have from our earlier TechTx
Basic Entropy discussion the macro entropy vs time.
While we recognize that we have to partition and
allocate the entropy to the performing nodes, we can
use the macro function for illustrative purposes here.
8 The Jacobian matrix is simply the derivative of a p-
dimensional map function F. We use the form Xu+1 = F(X),
where X is ap-dimensional vector
27
We develop the relationships using a power law
here. However, as experimentation progressed, it
became apparent for the technology we were
evaluating, the exponent was always almost 1. As
the power law may be the right fit for some
technologies, we develop this more general
relationship here. For the linear fit, the derivative
reduces simply to a constant - the slope m. At the
end of the day for the linear fit proved to be a very
good and simple relation that gave most satisfactory
results. Having fit the entropy over time, if we have
a power function, it is in the general form of
Sy, =bk"
To get to the general finite difference form,
we have
Sy =bk”
a
k Bu, [F (4.37)
oy
Sy,, =b(k 4)"
Recall the general form of the finite
difference transform is
Sinn =£(Sy,) (4.38)
To get to the derivative, we use (4.37)
eliminate k resulting in
i off
=b ra
O
aa (4.39)
To find A we get
i oft 4s
dS, Su, OS, OF
A= aay + z 4.40
se gy pee
Recall that A was required to compute the
Lyaponuv dimension from A to measure the non-
linear system entropy, Sg to quantify the stability of
the system.
7. Two Dimensional Finite Difference
Representation of Sy,
Similarly, we develop a two dimensional
model using the finite difference method. For n
dimensional maps there are n Lyapunov exponents
X, since stretching can occur for each axis.
‘A two dimensional model’ is used for the
computation of the Lyapunov dimension from A to
measure the non-linear system entropy S,.
=F(S,,,Nj,)
Aa Hy? dy
| (4.41)
* =6(S,,,N,)
Ik i
Functions F and G are defined as one-to-
one functions in R. We assume that the partial
derivatives exist. Now using A as defined in (4.41)
1
or (4.42) A =limf ji where jj are the
eigenvalues of A-jj[|=0 and A is the Jacobean of
transformation is defined as DT
IF
—OF,G) _(Spu
pT 35 Go
Hit
Here we are computing F and G to develop
the transfer function and to correlate these two
dimensions to determine Sg from A, the Lyapunov
exponent. The interesting feature of the bakers’
transformation is that it is a dissipative function in
state space if the sum of the exponents is negative.
The micro level and macro level
computations both should approach or diverge from
stability in the same manner, if the models are
correct. In this case Sy would yield a strong
correlation to Sg, In this model there is an
adjustable performance index parameter, to reflect
efficiency. Elsewhere this related to the leaming
curve. The performance index parameters are
adjusted to tune the micro model and to match the
Sg. Using the TechTx Learning Curve model (Saboe
2002), we are provided a method to identify the
performance bands and half-life of performance
improvement, for maturing of the technology.
5. TECHTX FEEDBACK ENTROPY MODEL
1. Communication and Control Model
9 The two-dimensional model for the bakers transformation
using both information and entropy is found in Saboe 2002. Only
the one dimensional model is developed in this paper.
28
Let's give an example of information being
exchanged at the micro level. Consider some
coupled nodes in a communication system. This
example is adapted from Brown (Brown 2000). This
system described will be represented in a dynamical
system model, which ends up being the bakers’
transformation.
We can develop and represent the system in
a model of information and the state as it flows from
the advocate and receptor as seen in Figure 5-1.
Model the following communication nodes, a sender
(S), a receiver (R), and a consumer (C). A simple
function with inputs as messages and outputs as
messages associated with each node carries the
dynamical information about each node.
Dynamical System of the advocate
receptor Tech Tx Interaction
Repeats
each time step
Sender now is
i the previous receiver S ~>R
State Diagram of
Information Flow in
Nodes of a Technology
Transfer Organization
Figure 5-1. Dynamical System Model of
Advocate-Receptor Interaction.
The sender is an advocate. This is a
researcher, or in the terms of Fowler (Fowler 1994)
an advocate and producer. The sender issues new
work products as messages. The receiver is a change
agent, or the receptor. The sender develops research,
advances and publishes a message as a work product,
thesis, article, technical report, demo, etc. The
message is observable, e.g. measurable and
countable. We can generally only measure output.
We can measure output in terms of messages and
terms from which the messages are made up. Except
for one type of input, it is usually difficult to
quantify, or measure all of the input.
The receiver receives the message. If the
message is understood completely, i.e. no need for
clarification, the receiver retransmits the processed
message and a local state transition occurs on the
node, as the receiver becomes a sender. The
consumer node becomes a receiver, and so on further
down the technology transition food chain. On the
other hand, if some percentage of the messages is not
understood, the receiver asks for clarification in
terms of feedback from the sender. The sender then
sends clarification in response for the request for
clarification.
Once the consumer understands the
message, the consumer can execute the work
products. Since a change agent becomes a sender,
and the consumer becomes a receptor, each is
capable of issuing requests for clarification and
providing clarification.
This elemental system (Figure 5-2a)
consists of a send unit and a receive unit. The
receiver unit is able to retransmit or execute an
action when there is little uncertainty in the terminal
action to be taken. At that point, the receiver
executes the action and becomes a send unit, since
someone else (another potential receive unit) can
witness the evidence of a signal. Let's assume for
the moment a clear, noiseless signal from the sender.
If the receive unit understands the encryption and
protocol of the sender, it is able instantaneously to
resend the message or to act. No effort is required to
handle the encryption and protocol.
If the message received is well understood,
the unit R (at time step t, ) can receive the messages
from unit S (sent at time step t,1), immediately and
resends or performs an action, observable as a
message, to another (or the same) receiver at a later
time step (t.:1). Figure 5-2a shows this basic state
transition model. Note, that there is also a term p'
representing message state transition arcs from
outside the local control volume. The message traffic
from the receiver R is a sum of the messages from
the earlier send unit and multiple streams persistent
in history that are available to the receive node and
selected (filtered) as input. The sum of the messages
is available to be processed by node R.
2. Entropy in the Communication Control Model
We can also have the case where there are
messages with entropy (noise, or unknown signal) as
input to R. This can be accommodated as seen in
Figure 5-2b. Now, we add the concept of a "think"
state transition. This is the case where the messages
received could not be effectively processed. Some
intemal processing is required. There is yet another
type of "think" state transition. This is represented
by feedback in order to clarify the entropy, noise or
non-signal received. Figure 5-3 illustrates the
elemental notion presented in Figure 5-2b and adds
two feedback loop state transition arcs pgand ps, For
initial model development and clarity, we assume
that the quantity of messages in the think loop pg are
equivalent to the number of messages sent back to
the send unit in p4, These are subsequently fed to a
receive unit as clarification at some later time step as
Ps. It is possible that the send unit has to use
multiple time steps and its own think loop. Further,
29
it is possible that the receive unit has to do more
intemal processing (and learning) which could store,
for more than one time step, a number of prior
messages awaiting action. We want to avoid or
minimize a design that has this characteristic. The
system would appear to have slow response to
transients, and the hysterisis effects resulting from
these time step delays can put the node and system in
an unstable mode of operation. While some of this
effect is able, the model should be able to
accommodate these aspects as well. These
refinements can be added later.
The nodes can be in two states, Xx, ye, The
state represented by variable y, is the quantity of
messages or tasks orders that have been executed by
an organizational unit, or node at time t, . The state
x, is the quantity of messages / task orders received
by the organization at time ty. x, consists of two
parts. One is the quantity of messages / task orders
that arrive from the outside the organizational node.
The second part is the set of internal messages / task
orders that must be processed/executed by the unit
due to the content of the messages / task orders
processed in the previous time step (feedback) ty.;
Software Technology Transition
Communications State Model
“Basic” and with “think state”
a) Basic state transition ~ interaction ~
well understood effort
o b) Basic Interaction with a ‘think state” ps
(Pr = Pi +P’ tecrsoloaes P3)
g
‘ee snd ne Hat (OF wal, ea
fuse signa from earlier ine stops
remade sate (afoul,
thin and eodack sates
Figure 5-2. Software Technology Transition
Basic and "Think" State.
(Source: Saboe 2001)
Software Technology Transition
Communications State Model
“Think” and feedback
or tne es hat be ead a,
ei
ayaa arable cei uode whch may be processed
Figure 5-3. Software Technology Transition
“think" and Feedback.
(Source: Saboe 2001)
On the other hand, let's assume that the
receiver has to process some internal messages in
order to unpack the message. Now there is a delay
before the message can be resent. Going a little
further, if the receiver received noise, an unclear
signal, or unknown signal it may have to request
clarification, delaying a time step or do some
additional correction processing. This uses up node
capacity. If the message is simple and concrete, or
agrees in abstraction (state level) or is at a higher
level meta-statement, the amount of processing and
effort that it takes to correct the poor signal is less
than one that is more complicated and more densely
packed. From this, we might say that abstraction is a
form of information hiding. Encapsulation of this
form provides leverage and can reduce the "entropy"
of the system.
6. DYNAMICAL SYSTEMS MODEL
Assume we have available a macro level
model of technology transfer to represent the
community level technology maturation. That macro
model can identify the stability and convergence of
an ensemble of nodes. The macro model can be
partitioned into a number of nodes (organizational
units and sub units that compose the organizational
units). The macro model is represented in terms of
entropy dimensions of natural measure (Farmer
1983) i.e. both the information entropy Sy and the
bakers’ transformation entropy Sg, representing the
transfer (transform) function. We now would like to
develop a model that represents the interaction
between nodes at the micro level. This model will
complete a linkage from macro to micro levels and
permit implementation models (infusion, learning,
etc) to bridge to the macro-micro infrastructure scale
models. This section will explore a feedback model
30
at the organizational node and sub-organizational
node level we incorporate control theory and use the
bakers’ transformation.
The model should incorporate a factor for
leamming, and address requests for clarification and
the ability to model the process load in requesting
clarification messages and receiving clarification
messages. This model will permit tuning an
organization to ensure efficient processing of
technology messages. We will develop a node
response curve and associated system response
curve. Determination of the bakers’ transformation
entropy from the Lyapunov number and exponent
will permit an assessment of the node performance
in terms of stability and confidence of convergence
to a steady stable state, or chaotic state.
1. Assumptions
Assume nodes made up of people and
machines that can do a task, such as publish a work
product as a message. A node is modeled in terms of
the messages it receives verses the messages it
processes. The work product (message) is the
representation of something that can be understood
by communicating in terms familiar to the sender
and receiver. Just as a map is not the road system
but symbols from a vocabulary of terms, which
represent a common understanding of the lay of the
land of a road system. The terms are measured in
information units - bits. As input, the processing
node receives work product. These represent
messages. Output from a node is also observed and
measured in messages. A technology generating or
processing node produces the output by acting on
input to reduce uncertainty in the cause and effect
relationship involved in achieving a desired result.
This is reasonable since this is what elements of a
node do. This is true for the activities of researchers,
producers in general as advocates, or receivers,
change-agent and consumer as receptors. This
assumption is also consistent with the observation by
Rogers (Rogers 1983). Within this context, we
examine the meaning of the concepts of stability,
equilibrium, attractors, chaos, eigenvalues, and
eigenvectors, and the relationship to technology
transition, system node dynamics. Convergence of
an organizational node on a fixed point depends on
the nature of the eigenvalues of the derivative of the
dynamical system at the fixed point. The direction
of convergence depends on the direction of the
eigenvectors. We discuss seven cases elsewhere
(Saboe 2002). A useful term that will frequently
arise in the following discussion is an orbit. The
orbit of a dynamical system is that sequence of
points in the state-space phase plane that corresponds
to successive time steps in the system.
2. Context
We assume that all of the nodes have
functions of equivalent form. Rather than model the
efficiency in a node, the efficiency is built into the
tuning parameter B. This performance index can be
attributed to nodes in a performance band (See
Saboe 2002 TechTx Learning Curve Model). The
nodes, in different performance bands, inherit the
performance parameters of their band. The node is
modeled in terms of the messages it receives versus
those it carries out or processes. The individual
nodes are assumed heterogeneous, varying in size
and composition, or a mix of people with varying
skills and tools to perform the function. For ease in
validation computations, we assume the
organizational nodes that have say a performance
index in the range of +/- 10 of the mean, all would
have the same efficiency (leaming curve function
parameters). Should we wish to calibrate an
individual node or all of the nodes in the band the
model will still be applicable. The capacity of a
node in the band can be calculated. The amount and
complexity of the message flow acted on, and
generated, applies pressure to an organizational
node. Demands on the organizational node as sender
or receiver components are among the pressures that
require modeling and analysis. But we do know this
intensive property from the macroscopic analysis.
Other pressures are internal to an organizational
node to ensure smooth functioning. These intemal
pressures come in the form of messages as well,
procedures, interfaces, meetings, collaborations and
other interactions that consume resources. These are
important facets to model since they provide
feedback pressures on the components. External
pressures are also among the features that determines
organizational node dynamics and should be
modeled.
All of the pressures mentioned so far can be
thought of as messages passing between
organizational nodes and between the organizational
nodes and the environment. This concept facilitates
modeling organizational node states that can be
organized as messages received by the component
and processed by a component. In this respect, the
organizational nodes are analogous to a
communications network. The analog is simple and
useful. There are however at least two important
differences. One is that an organization will adapt to
and absorb pressures that would cause a network to
breakdown. This is because the network is not
hardwired. It is also difficult to predict the
31
breakdown capacity in advance. We could address
ranges of capacity by banding the organization into
performance index bands. This does not however
mean that a node is at capacity. The potential for the
technology transfer system to breakdown is
important to model. A simple source of collapse is
when the demands on the system exceed its ability to
adapt and the node reaches a state of demoralization.
We have mechanisms to model this, however for
purposes of illustrating the model, are at or below
capacity. We can ignore for now this breakdown at
over capacity issue.
The model for organizational dynamics is
drawn from (Brown 2000). This model can be
represented in state space using messages (N). This
is closely related to the entropy as we saw earlier.
The state space is mapped onto the x-axis (input) and
y-axis (output) as follows: x, the inputN,, in
messages, and the output in y, N,. 4, Where k
represents the time step (the internal time as an
operator, and not a number). Where k represents
internal time iterations as discussed earlier. We
would not have synchronous discrete time steps in a
network that includes nodes comprised of
organizations and people.
Nya =£(N,) (6.1)
This function represents the bakers’
transformation. For the ensemble of nodes
performing the function N,,,, =f(N,), we have
the vector (capital F) representation N,,, =F (N,,)
We narrow our discussion from the
ensemble of nodes that can appear on the network or
disappear to a typical group of nodes, the sender,
receiver and consumer.
The model uses two state variables for the
system node representing the messages received and
messages processed. We shall apply the message
information in terms of the number of messages of
the incoming and processed messages. The
significance of the system of equations is that the
eigenfunction characteristic equation represents the
bakers’ transformation of folding, stretching and
rotating. The eigenvalue of this dissipative function
is also entropy and represents mixing. Elsewhere
(Saboe 2002), the potential significance of the values
of the eigenfunction are discussed.
Now we will develop the equations for this
model. The relationship between the state transition
diagram and a dynamical system is shown in Figure
6-1.
The sender publishes messages Ux (a
number of messages) at time step k. Input messages
at time step k to the receiver are indicated by X, (a
number of messages). The output messages from the
receiver is at time stepk is given by Y,. (a number of
messages) Some percentage of the messages output
from a prior time step yx, are indicated by B, a
rational number.
This process is repeated for the next time
step Xx+1 and yis1. The crossed circle immediately to
the left of the receiver node represents the collection
point where the different parts of the input message
stream is combined for the input message count x,.
In Figure 6-1, f{(x,) represents the function to
transform the input messages into output messages.
It takes a time step to complete the processing. A
way to view the nodes processing is that for a
message to move through a node, it takes a time step.
Relationship of State
Diagram to
Dynamical Systems
Model
Figure 6-1. Dynamical Systems Model.
The x; state variable consists of two parts. One part
of the state is the messages that come from outside
the receiver node uy. The second part of the state
variable is clarification of messages that was
requested from the previous time step y,1. Initially
we assume that the quantity of messages processed
(yx) is a function of x, This function has the
following simple properties:
(1) ifx, =0 theny,,; =0
and
(2) asx, © then yx, 0
Condition (1) is obvious - no input, then
no output. Condition (2) says that the system grinds
to a halt if the message demand is too great. We can
assume that as the number of messages received
becomes infinite, the messages processed have to
32
approach some limiting value, which is the capacity
of the system. The system can be represented by the
following equations. However, for the systems we
are seeing, we are not at capacity, and this condition
can be finessed out of the picture in low pressure,
low temperature situations. We can determine when
this happens by partitioning the macroscopic
community into smaller and smaller partitions. Then
we can observe the performance of nodes with a
technology and in the environment of the day.
Xa =BY.4 Hy
Vea =£(%)
f(x,) is called the node response curve. Elsewhere
(Saboe 2002) the important relations between the
node response curve and the system response curve
are developed. We need only concern ourselves, for
this exposition, on the node response curve and its
ultimate relationship to the macroscopic information
theoretic model.
(6.2)
The above is a second order system of finite
difference equations with the response curve
VY, =£(X,) represented by the following three-
dimensional dynamical system. Where x,
clarification from the prior time step, is substituted
fory,.1 and using the mapping (Kreyszig 1993 p419)
we get
Xi. q ae 2, Hy 4
Axil
Yeu =! Gx f(x, )
Gert k Vx
Let’s consider the time step k+1. The
periodic points determine the dynamics of the
system. In particular, the fixed points are of interest.
These are the equilibriumpoints. The coordinates of
the fixed points X, Y, Z are given by
xo Pt At
Hed x
The
x=u+Bf(x).
The derivative of the transformation T is
given by the Jacobian
(6.3)
(6.4)
fixed point condition becomes
_0(X,Y,Z)
J= ata y.z) (6.5)
eX aX aX f
ox OY aZ
thy oY av
= (6.6)
[ox oy 0zF
oZ OZ OZ
fx Oy Oz
o0 O BO
DT = f(x) 0 0 (6.7)
q 0 1 OF
Where DT is the Jacobean of
transformation T. Find the eigenvalues j, which are
the roots of the characteristic equation:
|A—jl| =0 (6.8)
Where A is the Jacobian of the DT transformation,
and | is the identity matrix. More specifically the
determinant
|DT —jI|
is the characteristic equation when set equal
to zero.
(6.9)
=}? +B £'(x) =0
There are three eigenvalues for the solutions
of the equation j°=B f(x). There are two
complex conjugate eigenvalues and one real
eigenvalue. The three eigenvalues may be
represented as
(6.10)
i jee") jer
where
j =(B £(x))""
is the real root of the equation. From the
model, we conclude that |i.| <B| f(x). The
(6.11)
system is stable when | j,| <1, in equilibrium when
the nom is |j,|=1, and unstable when |j,| >1
(Farmer 1983, Baker 1990, Brown 2000).
This gives some insight into the structural
stability aspect. The control theory element of the
33
current research model addresses mixing, and
structural changes due to feedback from external
nodes. The value of the norm (<1, =1, >1, real
imaginary, etc) of the eigenfunction characteristic
equation assimilation of reality based on experiences
from prior time steps.
From this, we see that for small enough B or
large enough up we can achieve stability. For the
technology transition system, we desire stability and
convergence. With a stable model at the
organizational level, we have organization nodes,
which are not thrashing or wasting effort. With
stable nodes, we can build a stable infrastructure
composed of those nodes. This will also yield
convergence of the technology.
The data that we can measure is the number
of messages published at some time k. We can also
measure output yi+2, k+1k kt, k2. The output message
data is simply the offset published by a time step e.g.
Utc). The difficulty we have is, that the macro data
cannot be
to empirically support f(x)
arrived at directly.
The derivative f(x) can be obtained
using parametric differentiation. Our system curve
from empirical data is the output y, which represents
u offset by an interval c from a prior time step.
Initially, for the data examined, this interval was one
year. In effect, this provides an immediate memory
for chunking of three registers because it take three
time steps to clear all of a message when there is a
request for clarification.
As this immediate memory, represented in
time steps is expanded, the error from the modeled to
predicted should start to diminish. Therefore:
Y =y, [Ue (6.12)
X =B f(x) +u, =Bu,-, Hi
(6.13)
Now deriving from (6.12) and (6.13) we get
yyy -<dY _dY /dt
10) ax “ax yat
The following result was obtained using
parametric differentiation of (6.14) and substituting
(6.12) and (6.13)
(6.14)
Wt.)
f(x) =
Buy. Wy
(6.15)
Wecan substitute f(x) into (6.11) which
defines the real eigenvalue:
uv 13
j= On ve) q (6.16)
“Hl Bue Bur Ay A
or explicitly to enable programming from the data
sets
13
O duy.) d
j =H8 dt (6.17)
The point where the graph intersects the
line y=x is the equilibrium point. The slope of
y=u+ Bf(x) at the fixed point is the real eigenvalue of
the matrix DT(Xo). By changing the parameter B we
change the shape of the graph and thus we change
the slope where the fixed point is found. Also by
changing uo, we change the location of the fixed
point along the horizontal axis and thus the
eigenvalue. By starting uo at 0, we first have a fixed
point whose real eigenvalue is positive and less than
1. This is ideal in that it indicates that the system
will converge to a point where it remains stable and
made sense as the review of the various
characteristics of the eigenvalue were developed.
See these graphs and the various interpretations of
their meaning in the appendix.
For the moment, let’s go back to the model
consisting of sender, receiver and consumer, Figure
5-2. Now let’s focus in on the receiver, look at the
inputs, and outputs of this node. It turns out that any
of these nodes looks like a receiver in the general
sense. The sender can also be picking up new
messages from others, in which case the sender acts
like a receiver. The sender can also be requesting
clarification and be receiving clarification in the
same manner as the receiver. Likewise the consumer
gets input and outputs. So our model can be seen in
Figure 6-2 to have all of the features but represented
only in a single node, the receiver. We also have a
useful sign convention. All of the inputs to the node
are positive and outputs are negative.
Software Technology Transition
General Node Inputs and Output
‘Bus. input a new pubsherin tis
rie step
‘pals the output, the publication in the time
step
‘sand py are memory in and out
‘pean p’ are request fr feedback out of
anid inta the node respectively
‘ps and, are responses to
clarfeation requests out of and into the
node respectively
‘he nfomats concen ina outot
the nade sneer) ==
BEEP PAtPS= DEB HS Hy
Figure 6-2. General Node Inputs and Outputs.
We are now in a position to think of an
ensemble of nodes. Essentially a distribution of
these nodes performing the bakers’ transformation.
Just like a physical system or communication
system, we now can speak of a macro stochastic
process in terms of entropy and information.
Let’s go to the basic equation (4.27). Recall
our conserved property is messages N - information
in our case. Using Shannon's entropy Sy and N for
the number of messages we get
1 _ 08,
(6.18)
T,, aN
From the section dealing with the
information theoretic aspects of Interacting
Subsystems, we saw how T varied with a time step.
Now we can observe the control model, Sg as a
function of the same time steps. We have the
opportunity to relate the two entropy measures, Sy
and Sz since they are related to the same information
system of messages N. We are dealing with the
same information flows, hence the same system, so
this seems reasonable. Recall S, is related to
Lyapunov’s exponent A which comes from the
eigenvalue j.
We found the relationship of messages
verse time step in Figure 45 was very satisfactorily
modeled as a linear equation for this technology set.
(It could be different for other technologies, this is
why we have dealt with the relationships in terms of
functions, eigenvalues and derivatives.) In this case,
the derivative of the linear model reduced to a
constant in equation (4.40).
Initially, to determine the form of the
functions, the average value B10% was used. This
was done by iterative guesses of a fixed B. This
approximation of & was used to satisfy the
macroscopic rate of change of entropy. The curves
can be seen in Figure 6-3. By observation, we see
both the entropy measures as a function of time step.
Sx,, the information theory entropy measure is on the
left y axis, and the Sg which comes from the
eigenvalue of the micro control model (hence in the
range of 0 to 1), is on the right hand y axis. Both
curves are of the same form. They follow the power
law, in this case, with a good R*. This suggests that
the model does approximate the observed conditions.
Entropy S,, and Dynamical System j
Entropy (SB) f0, B)
Figure 6-3 Macro Equilibrium Sy and
Eigenvalue A Stabilization
At this point we are considering the
“community” a large node. In the real world, the
community is partitioned into a volume of
performing nodes, and different performance rates.
Elsewhere (Saboe 2002) methods of relating these
partitions to learning curves are discussed. The
learning curve implies B varies with tasks performed,
and this in turn can be shown in terms of time steps.
We can also comment a bit further on the
relationship of the two entropies. In order to do this,
we have to develop Sx a bit more since it is based on
the real eigenvalue A.
t ={term]
2° ={msg}
Where 2"isa family of all the subsets of set
t often called the power set. Here is an example.
T{A, B, C, D} (6.20)
[]’
Lasc JAC} {D},
(6.19)
ar Fass ncrnone.enncn
Unsec },{A.B,D},{B,C,D},{A,C,D},
Hevco
| | | | |
(1.21)
Now when the number of elements in | =4,
we get atl =2! =16. Note also the distribution
of sets. This makes available the partition function
(the most useful formula in statistical mechanics.) A
number of useful relationships can be developed
from the set distributions.
Recall that S,; =—}” plog, p from (4.4)
Let’s define the operators in the
transformation of the control model.
B =4B,f (+),g(+)} (6.22)
where B, f(*)9,g(*)q definea
transformation Sg that works on B.
B ={(B, f)} which is a set of operator
combinations. Simplified we have
S, => i(B.f) (6.23)
Jo = real eigenvalue of
where
Jo =YB EF (6.25)
We sum the As over the number of send
units in the sample that publish.
We are now in the position to relate the two
entropies Sy and Sp. It also makes intuitive sense.
The idea that Kolmogorov had is there are objects
and there are descriptions (encodings) of objects, and
the complexity of an object is the minimal size of
this description. If we have one publisher, and the
publisher encodes a message, we can sum all of the
publishers and messages (a countable number) and
say some real things about the ensemble of messages
(objects) and publishers (elemental control model
nodes). This can be represented by a program (this
is a process) in a finite length for the nodes and
messages generated. That is there is a “decidable”
partial ordering defined on the set. The term
“decidable” means there is an algorithm for y’ and
y’’, whether y’ < y’’ ornot.
On an intuitive level, (per Uspensky) the
elements of a “space can be taken as informations,
and y' < y’’ means that the information y'’ is a
refinement of the information y’ (and hence y’’ is
closer to some limit value to which both y’ and y’’
serve as approximations.” This even sounds like
technology maturation.
Now let’s take these two entropy approaches
(plotted on the left hand y-axis and now coincident)
and determine B. B,as we recall represents the
amount of feedback required and is plotted on the
right hand y-axis. In Figure 6-4, we see that initially
the feedback required is very high, which then
bottoms out, and then increases. As shown in Figure
6-4, we are asking for the amount of feedback of the
system, this technology’s world, required for the
entire ensemble of publishers. If we adjust for the
number of authors and as shown in Figure 6-5, we
can see the effect of “mindshare”. In this figure, B
per author is the asymptotic curve plotted against the
primary y-axis. Publishers, i.e. nodes, which
represent the volume is the increasing curve plotted
against the secondary y-axis. We are now
representing the system on a per node basis. This is
the now in terms of messages and feedback per unit
volume (nodes) an extensive variable.
We have more authors absorbing a smaller and
smaller fraction of the information persistent in the
world. In other words, more information means
more decisions (the number of decisions are directly
related to entropy), and there is a limit to how many
decisions a node can make per unit time.
These two figures’ curves also seem to provide
some hint as to where innovators, and early majority
(the advancement phases of the technology) shift to
early and late majority (the diffusion phase of the
technology’s life).
Entropy (Lyapunov, (Beta))
Mar 20027 2 8S 6 7 a 8 we
Moe
Pometr2002
Figure 6-4 8, feedback required varies with time
36
Beta and ‘Mindshare”
Figure 6-5 8 adjusted for “mindshare”
7. A “TECHNOLOGY TRANSFER ENGINE”
Now that we have established the basic
relationships of the TechTx Entropy models, lets put
it in the framework of a system. We can put it all
together as an evolutionary, technology transfer
system that has probabilistic effects at the macro
level and deterministic, dynamical effects at the
microstate level. We have to the tools to analyze a
program and represent it as an engine. These
technology transition dynamics tools permit us to
engineer a solution to get maximum efficiency out of
our resources.
It is useful to define a control volume that is
typical of the system. In a traditional continuous
system in a physical world, a control volume
identifies boundaries of the system. In such a
continuous system, say an engine, a mass flows a
distance and contributes to the work performed. It is
not unusual to partition up a continuous control
volume into stages, e.g. a compressor, a combustor, a
diffuser. As the mass (in our case a message n)
flows from stage to stage we can consider its macro
state property transition at the system and locally of
the nodes (compressor, combustor, diffuser). There
are n messages flowing each one unique, but we can
characterize the state of an ensemble, so the system
and the nodes take on different state properties at
different stages of the process for the complete
elaboration of the message-node state combinations.
For now let’s look at all three stages in terms of the
technology transfer dynamics message model with
the message moving through the control volume.
This causes both local and system level state
transitions.
Control Volume
Continuous and Discrete Example
pod
on
a ie
‘Compressor Combustr Turtine
dist
‘Comprecsotombustor Turin A i
\CompressiCombuct Turbine
The nodes transition to a different state as the mass mis present.
This is the analog of a discrete state machine in a continuous system
Figure 7-1 Illustration of a Control Volume -- a
Continuous System or as a Discrete State Machine
Similarly, in this discrete state machine, we have
drawn the boundaries around the three subsystems.
Full elaboration of all of the messages (n) states
within the control volume would represent all the
possible states of the bounded system. With this we
can represent an individual interaction, an
organizational interaction or even a macro
technology transfer system such as the economy and
analyze and prescribe using cycle diagrams like
Figure 7-2. This type of diagram is familiar to most
engineers.
Let's examine some of the state diagrams
and system quantities in Figure 7-2.
State Space Diagram
Intensive Properties Temperature, Entropy
Figure 7-2 Cycle Diagram
One could image that the compressor,
which moves a technology from the null or ambient
state (with focused research as in academic and basic
research facilities.) This is the sate transition process
path from 1-2.
Here we have a process depicted in macro
state space that originates at point 1 with Tio,PioSio
which are the ambient temperature and pressure of
the surroundings, a reservoir. In the normal sense of
37
use, we see this as work, energy or heat. In
technology transfer dynamics, we can think of this as
effort, which is added to the system, yielding
“energetic” messages. We see an isentropic,
(constant entropy) compression as the system moves
along the path 12 to T2,PniSio. This says the
temperature is increasing because some effort is
being done to reduce the volume, or increase the
messages in the same volume of performing nodes in
which the interaction between entities occurs.
More occurrences of terms consistently
show up in messages. Terms are combined to get to
concepts that are more powerful. While there are
more messages for the same volume, i.e. nodes, the
message term content has higher density. In the
model proposed, there would be fewer nodes, but
doing very intense research, i.e. producing much
high quality messages. They closely interact and
publish messages generally within the confines of
the system.
During the progression form state point2 to
3, energy in the form of effort is added at a constant
pressure. Entropy, Si, increases to S,j. Think of this
as a demonstration. No new basic research is being
performed, the science is being scaled up and loaded
with a lot of energy that will make it attractive to
consumers. This occurs when the technology is
diffused from state 3 to 4. A high pressure,
concentrated set of messages escapes into a larger
volume to get a drop back to ambient. In order for
this to happen the message entities must some how
move to a bigger volume, must some how escape.
This is where work is taken out, as products are
delivered to a market (ambient). This is shown as a
constant entropy line, which a rapid drop from
ThiPni Shi, at state point 3, to state point 4, Ts,PioSni.
Work, in thermodynamic terms, is represented by
extensive property rate changes. For example,
W =n, (T; -T,) (74)
Where W is work yield, is the result of some
stimuli as we saw in (4.31),and Ni is the message
flow rate in terms of messages per time step. This is
a very ideal cycle description that would be a typical
start point to determine the minimum nodes (authors)
and messages to be managed to achieve a technology
transition objective. Recall, we are developing the
basis for an engineering model. Reality will demand
that we can’t achieve a constant entropy line from
P1-P2. It will likely follow a polytropic path.
Further, efficiencies of the components must be
addressed. Finally, we recognize that people, and
organizations are not machines. We would have to
calibrate and experiment with known components to
determine component (node) efficiency n, and
failure rates (burnout or collapse of morale from
over work.
8. VALUE AND USAGE
The research tied together fundamental
elements underlying technology __ transition.
Currently, systematic techniques for assessing macro
mechanisms for transferring software engineering
technologies has been thoroughly reviewed and
systematized. This paper developed the fundamental
elements of an industrial model of a software
technology transition engine. The mechanisms were
developed utilizing information theory,
communication theory, chaos control theory, and
learning curve principles. The combination of those
scientifically sound mechanisms provides a basis for
assessing, and / or prescribing a portfolio of
technologies and the implementing macro
infrastructure. A program manager armed with a
simple browser interface, augmented and driven by
these algorithms, should be able establish the
answers to questions similar to those posed in Figure
8-1. Linkages to lower level models and
implementation methods are provided. This research
provides the theoretical framework, and an entropy
based engineering model, for a practical method for
a program manager to establish a high capacity
transition channel, which accelerates technology
maturation and insertion.
This model can be used in a prescriptive
manner. From a large research investment portfolio
manager’s perspective, e.g. the Department of
Defense Science and Technology base, this enables
decisions to be made as to the number of nodes
(researchers) which should be funded. It also
provides a basis for policy development and
decisions using quantitative approaches in concert
with the current qualitative assessments.
The model was validated (Saboe 2002) on
data samples assess the following technologies:
software engineering, software technology transfer,
Ada, Java, abstract data types, rate monotonic
analysis, cost models, software work breakdown
structures. Also included in Saboe 2002 is an
extensive annotated bibliography on software
technology transfer and related references, and a
bibliography including related material from
philosophy, psychology, math, physics,
thermodynamics, management, economics, game
theory, technology transfer, software engineering,
and systems engineering. The appendix of this paper
illustrates a number of signatures of systems that
may be found in various technology’s studies.
A broad area of future research is now open
38
for examination. The application of the fundamental
tool set, and the definition of information
temperature, provides a robust capability to describe,
develop, or analyze a software technology transition
engine. Further, the model was developed to
accommodate any evolutionary process. One could
conceivably apply this to the software development
process. Finally, it seems within the realm of
imagination that software itself could be modeled
using the relationships presented herein.
Now, it is left to the community to
determine whether this is satisfactory to open the
discussion that supports the following logic:
* since we should be able to accept that a process
is just a program (Osterweil 1987) and
* software can represent the program, and
+ the engine is the representation of a process
that was based on axiomatic and logical
transfers from established science and
engineering (physics and thermodynamics)
+ The basic elements of the physics of software
have been developed.
Reprise -- Program Office Use for
Risk Assessment and Rx
Example:
Program Office Wants
80% by 06 with 80% certainty
Analysis indicates 08
60% +
Whatnodes / programmatics
need to be put into place to
shift curve to left?
Calculated system curve
‘Able to solve for node response curves(s)
Can lead to Rx as to
how many and parallel serial efforts required
Figure 8-1 Usage of the Model when implemented
ina tool
Michael S. Saboe is an Associate Director at the US
Amny Tank Automotive Research, Development and
Engineering Center in Warren, Michigan. He runs
the US Amy Next Generation Software Engineering
Technology Area where he has responsibility for the
US Army Main Battle Tank Software sustainment
activities. He has nearly 30 years of software
experience that began with real time software efforts
in 1973 on gas turbine engine control systems. He
was the chair of the DoD Joint Logistics
Commanders Computer Resource Management
group, and has been a DARPA PI since the 1980's.
Saboe received his Ph.D. in Software Engineering at
the Naval Postgraduate School in Monterey CA. He
is a professor at the Naval Postgraduate School as
well.
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APPENDIX
This appendix gives some insight into the control
theory element of the current research model when
maps exhibit eigenvalues in the following seven
cases. The value of the norm (<1, =1, >1, real
imaginary, etc) of the eigenfunction characteristic
equation assimilation of reality based on experiences
from prior time steps. A detail discussion can be
found in Saboe 2002.
The eigenvalue of the system is significant.
The eigenvalue represents an entropy metric, a
measure. A more robust representation of the bakers
transformation using a two dimensional model for
the bakers transformation is found in Saboe 2002.
This represents bakers transformation which consists
of both information and entropy as suggested in
equation (4.1)
Hic =F(Si,,Ni,)
=G(S,
Ta rk
(4.1)
This system represents the dynamical aspect
of folding and mixing, as well as the information
theoretic approach representative of the alphabet,
vocabulary and grammar of a technology.
Using straight forward methods from
control theory, we develop the characteristic
equation of the system and find the eigenvalue. The
figure below illustrates some representative
attractors. The space between the successive points
represents the distance between the successive states
of the system. Curvature and branches are also
features to be considered and explained.
k
Eigenvalues - Attractors
Space between the successive points represents the distance
between successive states of the system
Features to consider:
1) Space between conseCutive points
ene 2) Curvature of the orbit
3) Any Branches present
sabae 2»
Eigenvalues in these state space maps
represent attractors (sinks) and repellors (sources).
Eigenvalues near 1.0 are generally indicative of
smooth, orderly transitions between _ states.
Eigenvalues near zero may represent rapid
convergence to a single position or state. If the
nodes represent organizations rather than individual
publishers, the size of the organizational nodes
should be reflected in the size of the eigenvalues.
The following two figures illustrate actual
examples of observed instabilities and convergence
for the Ada programming language. This is
representative of map based on a theoretical case 5,
below, where the eigenvalue has a complex
conjugate with the real part less than one. It appears
that the system stabilizes and then
The empirical data for A da has a confidence
interval of +0.3% . This is developed from over 118,000
42
data points. Other data sets yield similar confidence
intervals.
World Entropy S,(X,Y), Sxa(X,¥)
a SORE Te te
World Entropy S\(X,¥), SsalX,¥)
Input, Output
at Te Ta W Sabot Tia
Piedad sexy, *
Seven cases that may be seen are illustrated
below. Each figure briefly describes a case that may
be observed in actual data.
Case 1
Eigenvalues: Real, Positive and <1
+ Suggests a
hb, Defense 2001
Case 2
Eigenvalues: one positive and gpgepeg
The system
rechnolog
separate braf
converges to
Depends on scale -- could be a
small node capable of extremes
Organization
oscilltes will
+ Messages processed greater than
received
~ Gould be Sxfained by node size
~ capability, atrton(retentoninsertion
~ new actors without orgaization/
technology experience 27
saboe
np. Detense 2001
Case 3
Eigenvalues: one positive and one negative -- but
size of Eigenvalues make a di
+ Froma dynamicd
cases 2and 319
tech transfer or diganizational
perspective introfc a
+ Messages processed exceed
messages received!
= Significant discovery opensiup @
botleneck
~ Creal massiathieved “phase change
Accautts 6 mem and could happen
ifmuliple time steps are required to
process or learn
Case 4
Eigenvalues: both negati
+ Similar toc
branches a
oscilating
+ neafonsti ge
mesgages received to
processed is changing with
each time step’
Top branch, messages
received increasing while
processed is decreasing
Bottom branch, opposite f tue
sabe
Case5
Eigenvalues: Complex conjugate
with the real part <1
St
f conve
lected in t
sin —¢
a + Eccentricity should make
sense
+ Could there be a real basis
7 for a softwareevolution
co: spiral model?!
Now 2001 WSaboe x0
pn. Detense 2001
43
Case 6
Eigenvalues: purely ima aii
a central b
. inpvey reasonable as
long as sensible
~ angular velocity
~ eccenticity
~ average diameter of orbit
(semi major and minor
axes of the ellipse)
ov 2002 satoe a
Php, Defense 2001
Case7
Eigenvalues: Complex Conjugate with negative
real part having absolute val
+ Similarto ¢
different as
previous stifes as it
converges retain
+ This must be explained in
terms of the nodes, modeled
hb, Defense 2001
Forcing Bifurcation
+ Fixed «0.3 increasing
‘amount of clarification required
inereases overhead
+ Arrow points to‘Stable librium to
which the rade converges
+ Branches expiained because
system is three dimensional and has
‘two complex conjugate eigenvalues
that are causing a delay rotation
+ Ashiftsfrom positive to
negative with increasing u
re pn betes 2001
Additional discussion on these cases and bifurcation
will be found in a paper to be published in October
2002, at the Monterrey 2002 workshop.
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