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On the Use of Network-Oriented Modeling: A Discussion

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This chapter is a discussion in which some of the main issues addressed in the book are briefly reviewed. In particular, Network-Oriented Modeling based on adaptive temporal-causal networks is discussed and how generic and applicable it is as a modeling approach and as a computational paradigm.
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Chapter 18
On the Use of Network-Oriented Modelling:
A Discussion
Jan Treur
Behavioural Informatics Group
Vrije Universiteit Amsterdam, The Netherlands
https://www.researchgate.net/profile/Jan_Treur
http://www.few.vu.nl/~treur
Abstract
This chapter is a discussion in which some of the main issues addressed in the book
are briefly reviewed. In particular, Network-Oriented Modelling based on adaptive
temporal-causal networks is discussed and how generic and applicable it is as a
modelling approach and as a computational paradigm.
18.1 Introduction
This book started in Chapter 1 by a review of traditionally used means to address the
complexity of individual and social human processes. These means often concern
assumptions on separation and isolation of parts of processes. Due to the shortcomings of
these assumptions, over time they have often led to strong debates. Many human processes
involve sub-processes running simultaneously in parallel, thereby intensely interacting in
cyclic manners. This offers an important challenge to be addressed, and it was recognized
that a modelling perspective is needed that addresses such intense cyclic interactions and
their dynamics. A Network-Oriented Modelling perspective was proposed here as an
alternative way to address complexity. Using this perspective, different elements of a
process can be distinguished, but it does not separate or isolate them. Instead it emphasizes
and explicitly models how they run and interact simultaneously. By incorporating a
temporal dimension, it is modelled how they can have intense and circular causal
interaction, and the timing of such processes can be modelled.
18.2 Network-Oriented Modelling
Although the notion of network itself and its use in different contexts can be traced back to
the years 1940 to 1960 (see Chapter 1, Section 1.4), the notion of Network-Oriented
Modelling as a modelling approach (also indicated by NOM) can be found only in more
recent literature, and only for specific domains. More specifically, this notion is used in
different forms in the context of modelling organisations and social systems (e.g., Elzas,
1985; Chung, Choi, and Kim, 2003; Naudé, Le Maitre, de Jong, Mans, and Hugo, 2008), of
modelling metabolic processes (e.g., Cottret and Jourdan, 2010), and of modelling
electromagnetic systems (e.g., Russer and Cangellaris, 2001; Felsen, Mongiardo, and
Russer, 2002; Felsen, Mongiardo, and Russer, 2009). The Network-Oriented Modelling
approaches put forward in this literature are specific for the domains addressed,
respectively social systems, metabolic processes and electromagnetic systems. An
interesting challenge is to achieve unification of such Network-Oriented Modelling
methods. The Network-Oriented Modelling approach described in this book was developed
with the domain of mental and social human processes in mind (but also with inspiration
from modelling metabolic processes within bacteria; e.g., Jonker, Snoep, Treur,
Westerhoff, and Wijngaards, 2002; 2008), thus unifying at least both individual human
processes and social processes, as has been illustrated by many example models in this
book. However, the scope of applicability is much wider, as discussed in some more detail
in Section 18.3.
The Network-Oriented Modelling approach presented in this book uses adaptive temporal-
causal networks as a vehicle. The temporal perspective allows to model the dynamics of the
interaction processes within networks and of networks well. A conceptual representation of
a model represents in a declarative manner states and connections between them. States
have (activation) levels that vary over time. The connections stand for (causal) impacts of
states on each other. Furthermore, the notion of weight of a connection is used to be able to
express differences in strengths of impact. Moreover, combination functions are used to
express how to aggregate multiple causal impacts on a state. Within adaptive networks also
these weights can vary over time. Finally, the notion of speed factor expresses the speed of
change of a state and is used to model timing of processes.
18.3 Genericity of a Network-Oriented Modelling Approach
In this section it is discussed how generic the presented Network-Oriented Modelling
approach is. More specifically, it is discussed how temporal-causal networks subsume
smooth continuous dynamical systems, discrete dynamical systems and computational
processes more in general.
Network-Oriented Modelling and Continuous Dynamical Systems
In Chapter 2, Section 2.9 it has been discussed that any smooth continuous dynamical
system (which by definition is a state-determined system) can be modelled as a temporal-
causal network model, by choosing suitable parameters such as connection weights, speed
factors and combination functions. In this sense this Network-Oriented Modelling approach
is as general as dynamic modelling approaches put forward, for example, in (Ashby, 1960;
Forrester, 1973, 1987; Thelen and Smith, 1994; Port and van Gelder, 1995; van Gelder and
Port, 1995; Beer, 1995; Kelso, 1995; van Gelder, 1998), and neural network approaches
such as described, for example in (Grossberg, 1969; Hopfield, 1982, 1984; Hirsch, 1989;
Funahashi and Nakamura, 1993). This indicates that using this Network-Oriented
Modelling approach does not limit the scope of the modelling.
Network-Oriented Modelling and Discrete Dynamical Systems
The numerical representations of temporal-causal network models can be used to model
continuous dynamical systems. But they can also be used to model discrete binary
processes based on values 0 or 1 for the states. To this end, set time step t = 1, speed
factor Y = 1 for all states Y, connection weight X,Y = 1 for all states X and Y with a
connection from X to Y, and assume that all combination functions cY(…) only generate
values 0 or 1, when applied to values 0 or 1. Then the difference equation for a state Y
becomes
Y(t+1) = Y(t) + [cY(X1(t), …, Xk(t)) – Y(t)]
which simply can be rewritten as:
Y(t+1) = cY(X1(t), …, Xk(t))
This takes the form of a general evolution or transition rule for a discrete dynamical system
of which the (overall) states are defined as vectors (X1(t), …, Xk(t)) with values 0 or 1, and
transitions of overall states are defined as
(X1(t+1), …, Xk(t+1)) = (cX1(X1(t), …, Xk(t)), …, cXk(X1(t), …, Xk(t)))
or in vector notation X with X(t) = (X1(t), …, Xk(t)):
X(t+1) = c(X(t))
where for V = (V1, …, Vk) it is defined c(V) = (cX1(V), …, cXk(V)).
This shows how the Network-Oriented Modelling approach based on temporal-causal
networks subsumes modelling by discrete dynamical systems. Note that the above approach
abstracts from the temporal aspect by setting t and all speed factors 1. However, also
timed variants of discrete dynamical systems can be covered.
Network-Oriented Modelling and Computational Processes
Any real implemented computational process in principle is a deterministic smooth
continuous process of a state-determined system in the physical world. Therefore it could
be claimed that the temporal-causal network modelling approach in theory covers all
computational processes. Within theoretical analyses often variants of transition systems or
finite state machines are used as universal ways to specify computational processes.
Conceptually such types of representations of (state) transitions can easily be related to
causal relations as considered in the temporal-causal network modelling approach. In more
detail, the format for discrete dynamical systems described above as a special case can be
used to model transition systems or finite state machines within the temporal-causal
network modelling approach: by defining c(X) = Y if and only if within a finite state
machine or transition system there is a transition from the overall state represented as X to
the overall state represented as Y. This also provides support for the theoretical claim that
computational processes can be covered by the temporal-causal network modelling
approach. However, to support such a general claim for any specific practical
computational paradigm could be a nontrivial challenge. For example, although perhaps
theoretically possible, to obtain a temporal-causal network representation for a
computational process described in some procedural (parallel) programming language, in
practice may require some effort. This may be similar to transformations of procedural
specifications into other types of declarative representations, for example, into (temporal)
logical or functional formats.
18.4 Applicability of Network-Oriented Modelling
The Network-Oriented Modelling approach has turned out useful in particular for
computational modelling in a multidisciplinary context. Moreover, network models as
obtained can form a solid basis to develop smart applications.
Applicability for Modelling in a Multidisciplinary Context
As discussed in Chapters 1 and 2 the temporal-causal network modelling approach used
here makes it easy to take into account theories and findings about dynamics of processes
from any scientific discipline, as commonly such processes are described in terms of causal
relations.
In particular, this applies to complex brain processes known from Cognitive, Affective and
Social Neuroscience, which, for example, often involve dynamics based on interrelating
cycles. Also recall the quotation of Phelps in Chapter 1, Section 1.2: ‘Adding the
complexity of emotion to the study of cognition can be daunting, but investigations of the
neural mechanisms underlying these behaviours can help clarify the structure and
mechanisms.’ (Phelps, 2006, pp. 46-47). A Network-Oriented Modelling approach enables
to address in an integrative manner complex cognitive, affective and social phenomena
such as dynamics by or of social interaction, the integration of emotions within cognitive
processes, internal simulation of external processes, mirroring of mental processes of
others, and Hebbian learning; e.g., (Hebb, 1949, Gerstner and Kistler, 2002; Keysers and
Perrett, 2004; Keysers and Gazzola, 2014). It also has been discussed in Chapter 1 how a
Network-Oriented Modelling approach relates to perspectives in Philosophy of Mind (e.g.,
Kim, 1996), in particular to (causal) networks of mental states. Furthermore, it has been
discussed in Chapter 1 how the approach relates to the philosophical perspective on
dynamics in the physical world that is indicated as the clockwork universe; e.g., (Descartes,
1634; Laplace, 1825). In an abstract sense this perspective relates to the notion of state-
determined system; e.g., (Ashby, 1960).
For processes in a social context, social phenomena such as shared understanding and
collective power show how bridges between individual persons are constructed. The
behaviour of each person is based on internal states such as goals, emotions and beliefs.
Therefore from a naïve viewpoint such sharedness and collectiveness would be considered
as very improbable. But specific mechanisms do their work in tuning the individual mental
processes to each other, mostly in an unconscious manner, and lead to the emergence of
shared mental states and collective behaviour. Knowledge about these mechanisms from
Social Neuroscience can be exploited to model corresponding computational mechanisms.
It has been discussed in Chapter 7 how from a neuroscientific perspective, mirror neurons
and internal simulation are core mechanisms for this.
From the applications to model complex phenomena by a Network-Oriented Modelling
approach, within the book models for the following complex phenomena in a
multidisciplinary context have been discussed:
Embodiment, as-if body loops, mindfulness (Chapter 3)
Imagination, visualisation and dreaming as internal simulation (Chapter 4)
Mirroring of other minds (Chapter 7)
Integration of affective and cognitive processes (Chapters 3, 6, 7, 10)
Fear extinction learning (Chapter 5)
Emotions as a basis for rationality (Chapter 6)
Empathic understanding (Chapters 7, 9)
Emergence of shared understanding and collective action (Chapter 7)
Group processes and crowd behavior (Chapter 7)
Prior and retrospective ownership of actions (Chapter 8)
Social contagion (Chapters 7, 11)
Social responsiveness (Chapter 9)
Joint decisions (Chapter 10)
Social network evolution (Chapter 11)
Applicability for the development of Smart Applications
The topics addressed have a number of possible applications. An example of such an
application is to analyse the spread of a healthy or unhealthy lifestyle in society. Another
example is to analyse crowd behaviour in emergency situations. A wider area of
application, as discussed in Chapter 16, addresses smart applications in the context of
Ambient Intelligence or socio-technical systems that consist of humans and devices, such
as smartphones, and use of social media. For such applications, in addition to analysis of
the relevant processes, also for the support side the design of these devices and media can
be an important aim. This may concern, for example, safe evacuation in an emergency
situation or strengthening development of a healthy lifestyle. Other application areas may
address, for example, support and mediation in collective decision making and avoiding or
resolving conflicts that may develop. The Network-Oriented Modelling approach as
presented makes modeling complex human and social processes more manageable, and
extends the range of what is possible. To facilitate applications, dedicated software is
available supporting the design of network models in a conceptual manner, automatically
transforming them into an executable format and performing simulation experiments.
18.5 Finally
Summarizing, the Network-Oriented Modelling approach based on temporal-causal
networks as described here, provides a complex systems modelling approach that enables a
modeller to design high level conceptual model representations in the form of cyclic graphs
(or connection matrices), which can be systematically transformed in an automated manner
into executable numerical representations that can be used to perform simulation
experiments. The modelling approach makes it easy to take into account on the one hand
theories and findings from any domain from, for example, biological, psychological,
neurological or social sciences, as such theories and findings are often formulated in terms
of causal relations. This applies, among others, to mental processes based on complex brain
networks, which, for example, often involve dynamics based on interrelating and adaptive
cycles, but equally well it applies to social networks and their adaptive dynamics. This
enables to address complex adaptive phenomena such as the integration of emotions within
all kinds of cognitive processes, of internal simulation and mirroring of mental processes of
others, and dynamic social interaction patterns. By using temporal-causal relations from
those domains as a main vehicle and structure for network models, the obtained network
models get a strong relation to the large body of empirically founded knowledge from the
Neurosciences and Social Sciences. This makes them scientifically justifiable to an extent
that is not attainable for black box models which lack such a relation.
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  • Jan 1989
  • NEURAL NETWORKS
The activation dynamics of nets are considered from a rigorous mathematical point of view. A net is identified with the dynamical system defined by a continuously differentiable vector field on the space of activation vectors, with fixed weights, biases, and inputs. Chaotic and oscillatory nets are briefly discussed, but the main goal is to find conditions guaranteeing that the trajectory of every (or almost every) initial activation state converges to an equilibrium. Several new results of this type are proved. These are illustrated with applications to additive nets. Cascades of nets are considered and a cascade decomposition theorem is proved. An extension of the Cohen-Grossberg convergence theorem is proved for certain nets with nonsymmetric weight matrices.
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Hebbian learning and predictive mirror neurons for actions, sensations and emotions
Article
Full-text available
Spike-timing-dependent plasticity is considered the neurophysiological basis of Hebbian learning and has been shown to be sensitive to both contingency and contiguity between pre- and postsynaptic activity. Here, we will examine how applying this Hebbian learning rule to a system of interconnected neurons in the presence of direct or indirect re-afference (e.g. seeing/hearing one's own actions) predicts the emergence of mirror neurons with predictive properties. In this framework, we analyse how mirror neurons become a dynamic system that performs active inferences about the actions of others and allows joint actions despite sensorimotor delays. We explore how this system performs a projection of the self onto others, with egocentric biases to contribute to mind-reading. Finally, we argue that Hebbian learning predicts mirror-like neurons for sensations and emotions and review evidence for the presence of such vicarious activations outside the motor system.
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A Dynamic Systems Approach to the Development of Cognition and Action
Book
  • Jul 1994
A Dynamic Systems Approach to the Development of Cognition and Action presents a comprehensive and detailed theory of early human development based on the principles of dynamic systems theory. Beginning with their own research in motor, perceptual, and cognitive development, Thelen and Smith raise fundamental questions about prevailing assumptions in the field. They propose a new theory of the development of cognition and action, unifying recent advances in dynamic systems theory with current research in neuroscience and neural development. In particular, they show how by processes of exploration and selection, multimodal experiences form the bases for self-organizing perception-action categories. Thelen and Smith offer a radical alternative to current cognitive theory, both in their emphasis on dynamic representation and in their focus on processes of change. Among the first attempt to apply complexity theory to psychology, they suggest reinterpretations of several classic issues in early cognitive development. The book is divided into three sections. The first discusses the nature of developmental processes in general terms, the second covers dynamic principles in process and mechanism, and the third looks at how a dynamic theory can be applied to enduring puzzles of development. Cognitive Psychology series Bradford Books imprint
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Neural networks and physical systems with emergent collective computational abilities
Article
  • Apr 1982
Computational properties of use to biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.
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Electromagnetic Field Computation by Network Methods
Chapter
  • Feb 2009
Many applications in science and technology rely increasingly on electromagnetic field computations in either man-made or natural complex structures [1]. Wireless communication systems, for example, pose challenging problems with respect to field propagation prediction, microwave hardware design, compatibility issues, biological hazards, etc. Because different problems have their own combination of geometrical features and scales, frequency ranges, dielectric inhomogeneities, etc., no single method is best suited for handling all possible cases; instead, a combination of methods (hybridization) is needed to attain the greatest flexibility and efficiency.
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Electromagnetic Field Computation by Network Methods
Book
  • Jan 2009
In this monograph, the authors propose a systematic and rigorous treatment of electromagnetic field representations in complex structures. The architecture suggested in this book accommodates use of different numerical methods as well as alternative Green's function representations in each of the subdomains resulting from a partitioning of the overall problem. The subdomains are regions of space where electromagnetic energy is stored and are described in terms of equivalent circuit representations based either on lumped element circuits or on transmission lines. Connection networks connect the subcircuits representing the subdomains. The connection networks are lossless, don't store energy and represent the overall problem topology. This is similar to what is done in circuit theory and permits a phrasing of the solution of EM field problems in complex structures by Network-oriented methods. © Springer-Verlag Berlin Heidelberg 2009. All rights are reserved.
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