COGNITIVE%20MODELING%20AS%20A%20TOOL%20IN%20THE%20PROCESS%20OF%20KNOWLEDGE%20LARGE%20SYSTEMS

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COGNITIVE MODELING AS A TOOL IN THE PROCESS OF
KNOWLEDGE LARGE SYSTEMS
CML-2010, Dubrovnik

• Galina Gorelova

Cognitive Mechanisms for Decision Making
Cognitive Aspects of Information Technologies
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Technological Instituteat South Federal
University, Taganrog
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Contents
CML-2010, Dubrovnik

• 1.Introduction The problem of understanding the
  process of learning a Large-scale systems.
  Sustainable development Large-scale systems
• 2. Basic concepts associated with cognitive
  modeling
• 3. Formalizing the problem of the study of a
  larger system
• 4. Presentation of the main tasks, models and
  methods in cognitive modeling technology
• 5. The scheme of interrelated techniques of
  cognitive methodology
• 6.Examples of cognitive modeling

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Introduction. The problem of understanding the
process of learning a Large-scale systems.
Sustainable development Large-scale systems
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The purpose of the study of a Large-scale
systems? Can sustainable development of a
Large-scale systems?

• The problem of understanding the process of
  learning a Large-scale systems. Is it possible to
  "manage" this process?

The methodology of cognitive modeling is
developed as a product of synthesis and
utilization of systems theory and systems
analysis, operations research,, management
theory, decision theory, statistics, mathematical
programming, intelligent systems, etc.
How does the expert having the idea of applying
knowledge from one area to study specific complex
system? How, in what sequence and why this
knowledge is applied? How does it directs the
process of learning? What were the results may
lead the management of a complex system of
knowledge?
One theory, a method (or even a group of methods)
do not allow to consider all aspects of the
problems of a large system. Most consider only
the side effects, which directed the attention of
the researcher or determined by the social order
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Object of research Large-scale Systems
(socio-economic, environmental, social
engineering, etc.)
Subject of research The phenomena and processes
in Large-scale systems, models and methods for
the study of Large-scale systems
The main objectives Study and understanding of
the mechanism of phenomena in Large-scale
systems, prediction of their possible development
paths for the development of governance aimed at
sustainable development and the prevention
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Sustainable development

• Researching of the problem of sustainable
  development of complicated socio-economic,
  political and ecological systems in its complex
  comprehension as interdisciplinary problem and
  multi-aspect strategy has been determined among
  the main tasks in the international community in
  the mid-90s of the last century.
• A complex problem and possible approaches of its
  solution for Russia is presented in the
  encyclopedic monograph Koptyug et al.
• New paradigm jf Russia's development in the XXI
  century (Comprehensive analysis of the problems
  of sustainable development ideas and results)/
  Ed. V.A. Koptyug, V.M. Matrosov, V.K. Levashov.
  M. "Academia", 2000, 416 pp.
• The most close to the notion of sustainable
  development term in Russia understanding is the
  concept of noospheric development Vernadcky.

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The notion of Sustainable development
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• We assume the following New paradigm
• Sustainable development of a system is a complex
  dynamic feature of class manageability, combining
  the requirements
• 1) hit of development trajectory at a certain
  time in the target set of states
• 2) no trajectory spillover in the prospective
  time range of a certain number of "safe" states
• 3) almost monotone increasing of some indicators
  of development (for example, quality of life,
  etc.) at a certain time interval and then saving
  them in the specified range of admissible values
  
• 4) an asymptotic stability (stabilize ability) of
  program trajectory
• 5) harmonizing interests of sides.

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Global security - is "vital security interests of
the world's population (current and future
generations and nature (the Earth's biosphere))
from threats to their survival and sustainable
development (of global disasters), taking into
account the factors of the global economy"
The New Paradigm ..., c. 13
(1) L(t)gtL F(t)gtF J(t)gtJ S(t)gtS
B(t)gtB Z(t)gtZ R(t)gtR ? t?t0 t1,

• where L, F, J, S, B, Z, R - performance
  evaluation of global security for safety of world
  development in the model (1) L - life
  expectancy F - consumption per capita food (food
  per person) J - consumption of industrial goods
  per capita (industrial goods per person) S -
  average social spending per capita (services per
  person) B - biomass of terrestrial vegetation Z
  - the level of pollution R - remaining at the
  end of the XXI century natural resources (volume
  traditional, non-renewable, and non-traditional,
  reclaimed, natural resources). Maximum value of
  L, F, J, S, B, Z, R are selected on the basis of
  medical, sociological and environmental research
  in international projects or on the basis of
  estimates given in the decisions of international
  forums and organizations

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2. Basic concepts associated with cognitive
modeling
The content and program of research of complex
systems can be specified as a model of a
meta-system research
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3. Formalizing the problem of the study of a
larger system
The content and program of research of complex
systems can be specified as a model of a
meta-system research
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All of this is incorporated in a formal
meta-studies and decision-making. Original model
- the model proposed in the works Kulba V.V. (ISP
RAS)
?ognitive integration
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The main feature of our research - cognitive
integration in the system of both known and newly
developed methods and models
MO (Y, U, P) - identifies a model system i which
the vector Y - endogenous variables,
characterizing the phase state of the object, U -
vector of controlled variables, P - vector of
resources allocated ME (X) - a model of
the environment, X - exogenous variables MOE -
model of interaction between the object and the
environment MD (Q) - a model of system behavior,
Q - the perturbing effects MMO and MME - model
for measuring the state of the system and the
environment MU - model management systems (not
included in the meta, if only to solve the
problem the study site) M? - a model of expert
A - generally the choice processes of change of
the object
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Cognitive integration
Important! Addressing the challenges of
sustainable development of complex systems
requires an interdisciplinary approach!
In our studies, this campaign is implemented by
means of cognitive modeling, cognitive
integration of disparate knowledge in various
fields of knowledge.

• The main distinguishing feature of our research -
  cognitive integration in the system of both known
  and newly developed methods and models created in
  the process of cognition of the object entity.
• The ideal goal - creating a tool which implements
  a union and to help you develop and validate a
  strategy for sustainable development of
  Large-scale Systems

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Cognitive integration - a process that takes
place in the minds of the expert.
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• And - this is important!
• carried out by a continuous, iterative process of
  decision-making expert, supported by special
  tools. We are now on the way to develop the
  appropriate supporting mathematical and software
  tools for this. And try to understand and explain
  why and how such integration occurs. And how it
  can be practically used.
• Apparently, the latter is an area of contact
  research in the field of cognitive psychology,
  linguistics, neurophysiology, intelligent
  systems, artificial intelligence and so on.
  Thus, the process of cognition of the object
  entity and its results are included deliberately
  by us in the process of cognitive modeling
  Currently, under the cognitive modeling, we
  understand the interlinked problems of system

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• 4. Presentation of the main tasks, models and
  methods in cognitive modeling technology

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2. System tasks of cognitive analysis
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Traditional task of cognitive analysis
New task of cognitive analysis

• 1. Identification of the object
• 2. Analysis of the ways and cycles
• 3. Scenario analysis
• 4. Solve the inverse problem

5. Analysis of sustainability 6.
Observability 7. Controllability 8.
Connectedness, complexity 9. Optimization 10.
Adaptability 11. Self-organization 12.
Disasters 13. Sensitivity studies 14. Search for
solutions games 15. Decision-making
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Figure 1.
EXAMPLE
1. Identification of the object
3. Scenario analysis
Figures 2.
Scenario ?1 (q11) Scenario
?2 (q11, q3 - 1)
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3. Cognitive models
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The task 1. Identification of the object
3.1. Known cognitive models
(3)
Cognitive map
Parametric vector of function graph
(4)
where

• G is a cognitive map, and i1,2,n is a set of
  vertices (objects of the studied system, for
  example, production, population, resources,
  etc.) is a set of edges - relationship between
  objects in the system (positive, negative, zero
  in observing situation), g 1,2, ... k,
• F F (X, E) F (xi, xj, eij) is edge
  transformation functional that relates to each
  edge a sign, or a weight coefficient wij,  or a
  function F(xi , xj , eij) fij

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3.2. Hierarchical cognitive models
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IG ltGk, Gk1,Ek,gt, k 2,
where Gkltvi(k), ?ij(k) gt, where Gk -
is a cognitive map k-level, V(1) vi(1)
set of vertices of the lower level, V(k) vi(k)
the set of vertices k level,Relationship
between the vertices of one level- the arc
?ij(k), ?(k) ?ij(k) relations between
vertices of different level ? k,k1, Ek
?k,k1.
(5)
Figure 3.
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3.3. Simulation games on hierarchical cognitive
maps in the interaction of complex systems
Interaction systems
Model of multistep games
Figure 4.
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4.1.Impulsive modeling scenarios for the system
on cognitive models
The task 3. Scenario analysis
A model of a pulsed process mapping scenario
(5)

• where ?i(n) - the value of impulse at the vertex
  vi in the previous moment - cycle modeling (n),
  ?i(n1) - a researcher interested in the (n 1)
  moment fij impulse conversion function Pj(n)-
  the value momentum at the vertices vj, adjacent
  to the vertex vi Qi(n) - vector of disturbances
  and control actions made to the top of vi at the
  time n. A set of realizations of impulse
  processes is called "scenario" and points to the
  possible developments of situations. The
  situation is characterized by a pulse simulation
  set ?, Q in each step of modeling.

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The algorithm is based on a puls simulation
calculation formulas (6), obtained from the
expression (5)
(6)
where

• A - matrix of relations of the graph G
• I - identity matrix

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4.2. Stability analysis
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The task 5. Analysis of sustainability

• Sustainability (Known Theorems)
• (1) Vertex Vj is stable in value, if the sequence
  of values (x (t) t 0,1, ...) is bounded.
• Vertex Vj is resistant to disturbance, if the
  sequence of pulses is limited to
• (rj (t) t 0,1, ...).
• A weighted digraph is resistant to perturbation
  (value) if every vertex has this property.
• (2) Theorem on the stability of the perturbation.
  A weighted digraph G, the characteristic values
  are different, it is resistant to perturbation
  for the propagation of any disturbance if and
  only if every characteristic value of G modulo at
  most one.
• (3) Theorem on the stability of the initial
  value. A weighted digraph G is stable in the
  initial value for a simple process of propagation
  of the perturbation if and only if the digraph G
  is stable to perturbations, for a simple process
  of propagation of the perturbation and the unit
  is not a characteristic value of G.
• The system is called structurally stable if the
  topological nature of the trajectories of all
  systems close to it is the same as a standard.

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Structurally stable
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Odd loop (positive feedback) has a positive
product of signs of all of its constituent arcs,
odd (negative feedback) - negative
Odd cycle is the simplest model of structural
instability, as any change in the initial
parameter in any of its top leads to unbounded
growth module parameters vertices cycle
Figure 5.
Any change in the parameter of any vertex of odd
cycle only leads to the oscillation parameters of
peaks
Figure 6.
The vertex xi is absolutely stable for a given
pulse process, if the sequence of absolute values
of the parameters in the top ( xi (n) n
0,1 ...) is bounded
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Figure 7.
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Example
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The task 8. Connectedness, complexity
4.3. Topological analysis
Figure 8.
Figure 9.
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Figure 10.
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4.4.Model decision problems the problem of the
optimum value
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The task 15. Decision-making
(7)
X ? X??? Y ? Y???
where f (Mh, t) - function of the effectiveness
of the optimum value of the parameters Mh
distribution of random variables Y and time t f
(Y, Mh, t) - density of Y, C (Y) - useful areas S
values Y.
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5. The scheme of interrelated techniques of
cognitive methodology and Software system of
cognitive modeling
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Figure 11.
Scheme of cognitive modeling of socio-economic
system
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Figure 12. Software system of cognitive
modeling (?? ??)
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6. Examples of cognitive modeling
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Example ?1.
While identifying the object was originally
developed bigger cognitive map, the objects which
in the future if necessary, turned in the
individual cognitive maps. For example, in the
enlarged map of regional socio-economic mechanism
of object "industrial output" can be discovered
in the cognitive maps, and includes cognitive map
"Small Business
Figure 13.
Socio-economic mechanism at the regional level
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Pulse processes while bringing disturbance in
node V2 (manufacture growth), q21
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Figures 14.
q2 1
Charts are located in such a way that the
beginning of the pulse process for them was at
the same level (for ease of analysis of images)
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Pulse processes while bringing disturbance in
node q21, q71 (manufacture growth,
interregional and foreign exchange)  
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Figures 15.
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Figure 16. Pulse processes while bringing
disturbance in node q91 (Population growth)
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Modeling System Small business"
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Example ?2.

• Small business is one of the major reserves of
  dynamic economic development of regions of the
  Southern Federal District, as the prevailing
  economic structure and the redundancy of labor
  resources of individual regions objectively
  determine the possibility of development of this
  sector. Of particular importance to this segment
  of the economy has to meet the challenges of
  sustainable and sound development of the region,
  providing employment, crime prevention, solving
  local government in light of the Federal Law "On
  General Principles of Local Self-Government in
  the Russian Federation ? 131-FZ of 06.10.2003g

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Cognitive map "Small Business"
Figure 17.
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Analysis of simplicial complexes "Small Business"
The concepts of cognitive maps Small business
(MP)
V00 - Number of small enterprises V01 -
Investitsii MP V02 - Turnover MP V03 - Number
of employees at the MP V04 - Profit MP V05 -
Quality products, services, MP V06 - Innovations
V07 - Professional quality employees V08 -
Consumer demand V09 - Competition V10 -
Availability of credit V11 - Infrastructure
V12 - NGO programs support the development of
MP V13 - Imperfect tax system V14 - Corruption
V15 - Administrative barriers
Figure 18.
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Example ?3.
The cognitive maps "Regional socio-economic
system in terms of adaptation peoples of southern
Russia to the transformational change"
Figure 19.
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The concepts of cognitive maps "Regional
socio-economic system in terms of adaptation
peoples of southern Russia to the
transformational change"
V0 - sustainable development of the region, V1 -
successful adaptation of peoples, V2 - An
individual's ability to adapt, V3 - resources
adaptation capacity V4 - economic condition V5 -
social status V6 - globalization, V7 -
regionalization, V8 - geopolitical factors V10 -
a violation of cultural traditions and imposition
of new, V11 - demographics, V12 - national and
ethnic structure of population
V13 - ethnic hierarchy of the urban
population V14 - social organizations of
Southern Russia V15 - Islamic organizations V17
- Cossack society V18 - Diaspora V19 -
conflict-generating, V20 - class contradictions
V21 youth V22 - scientific and educational
complex south of Russia, V23 - authorities V24
- territorial features V25 - deviant
behavior, V26 - media V27 - clan, V28 migration
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Scheme of interaction models of computing
devices, tasks and expert
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Example ?4.
Figure 20.
?G? ltG?, X?, F?gt - a model of computing devices
in the form of a parametric functional ? -graph,
in which GB ltV?,E?gt - cognitive map, graph in
which vertices Ve (v?i) - the set of vertices
agents (individual computers), E? (e?ij) - the
set of arcs connecting the vertices (v?i, v?i
v?j), i, j 1,2, ... n? Arriving at the input
VU task - oriented acyclic functional ? -graph G?
ltV?, E?gt - a model problem where V? (v?i) -
the set of vertices (separate tasks or parts of
them), E? (e?ij) - the set of arcs connecting
the vertices (v?i, v?j), i, j 1,2, ... n? M??
(?G?, ?G?, E) - a model of interaction of the
?? graph and graph problems E (e?i?j) - the
set of arcs connecting the vertices of problems
with the vertices of a graph of computing
devices Q, X (xi), i 1,2 ,..., k - input
system (factors) Y (y1 ,..., yi ,..., ym) -
output of the system, the numerical
characteristics of the purposes of the study
("optimization", "optimization criteria,"
"objective function ...)
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References

• Koptyug, et al., 2000 New paradigm jf Russia's
  development in the XXI century (Comprehensive
  analysis of the problems of sustainable
  development ideas and results)/ Ed. V.A.
  Koptyug, V.M. Matrosov, V.K. Levashov. M.
  "Academia", 2000, 416 pp.
• Maksimov, 2001. V.I V.I. Maksimov Cognitive
  technology - from ignorance to understanding /
  Sat. Proceedings 1 st International Conference
  "Cognitive analysis and development management
  situations", (SASC'2001) - Moscow IPU RAN, 2001.
  - Vol.1, pp 4-18
• Abramova et al., 2006 The human factor in
  management. Ed. N.I. Abramova, KS Ginsberg, D.A.
  Novikov. - M. KomKniga, 2006.
• Roberts, 1978 Roberts F. Graph Theory and its
  Applications to Problems of Society, Society for
  Industrial and Applied Mathematics, Philadelphia,
  1978.
• Gorelova et al., 2002 Gorelova G.V., Dzarimov
  N.H., Acceptance of Decisions on the Cognitive
  Cards of Socially-Economic Systems// IEEE
  International Conference on Artificial
  Intelligence Systems (ICAIS 2002), Divnomorskoe,
  Russia. Computer city IEEE, 2002. ?
  7996-1733. ?p. 128-129.
• Gorelova et al., 2002,Gorelova, et al., 2006
  Gorelova G.V., Zaharova E.N., Radchenko C.A.
  Researches of semi-structured problems for
  social-economical systemsCognitive approach.
  Rostov RGY, 2006.
• Atkin, 1997 Atkin R. H. Combinatorial
  Connectivies in Social Systems. An Application
  of  Simplicial Complex Structures to the Study of
  Large Organisations, Interdisciplinary Systems
  Research, 1997.
• Barcelo, et al., 1998 Barcelo H., Kramer X.,
  Laubenbacher R., Weaver C. Foundations of
  Connectivity Theory for Simplicial Complexes,
  Department of Mathematical Sciense, New Mexico,
  1998
• Mnukhin, 1996 Mnukhin V. The Modular Homology
  of  Inclusion  Maps and Group Actions, J. of
  Combinatorial Theory, S. A 74, 1996, pp.285-300,
  Article NO. 0051
• John Casti,1979 John Casti Connectivity,
  Complexity, and Catastrophe in Large-scale
  Systems. /A Wiley Iinterscience Publication
  International Institute for Applied Systems
  Analysis. - Chichester- New York- Brisbane-
  Toronto John Wiley and Sons, 1979

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• The results of the various phases of studies
  consistently reported at conferences, published
  in journals and monographs.
• This report is a certain generalization of the
  results and reflections on the theme of
  "cognitive modeling of complex systems"

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CML-2010, Dubrovnik
Thank you for your attention!
Galina Gorelova Technological Institute at South
Federal University, Taganrog Nekrasovskiy 14,
347922, ??? 17-? Russia
g.v.gorelova_at_gmail.com
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