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44
Rate distortion manifolds as model spaces for cognitive information
 In preparation
, 2007
"... The rate distortion manifold is considered as a carrier for elements of the theory of information proposed by C. E. Shannon combined with the semantic precepts of F. Dretske’s theory of communication. This type of information space was suggested by R. Wallace as a possible geometric–topological desc ..."
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Cited by 6 (3 self)
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The rate distortion manifold is considered as a carrier for elements of the theory of information proposed by C. E. Shannon combined with the semantic precepts of F. Dretske’s theory of communication. This type of information space was suggested by R. Wallace as a possible geometric–topological descriptive model for incorporating a dynamic information based treatment of the Global Workspace theory of B. Baars. We outline a more formal mathematical description for this class of information space and further clarify its structural content and overall interpretation within prospectively a broad range of cognitive situations that apply to individuals, human institutions, distributed cognition and massively parallel intelligent machine design. Povzetek: Predstavljena je formalna definicija prostora za opisovanje kognitivnih procesov. 1
Independence and Conditional Independence in Causal Systems
, 2008
"... We study the interrelations between (conditional) independence and causal relations in settable systems. We provide definitions in terms of functional dependence for direct, indirect, and total causality as well as for (indirect) causality via and exclusive of a set of variables. We then provide nec ..."
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Cited by 5 (2 self)
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We study the interrelations between (conditional) independence and causal relations in settable systems. We provide definitions in terms of functional dependence for direct, indirect, and total causality as well as for (indirect) causality via and exclusive of a set of variables. We then provide necessary and sufficient causal and stochastic conditions for (conditional) dependence among random vectors of interest in settable systems. Immediate corollaries ensure the validity of Reichenbach’s principle of common cause and its informative extension, the conditional Reichenbach principle of common cause. We relate our results to notions of dseparation and Dseparation in the artificial intelligence literature.
Running as fast as it can: How spiking dynamics form object groupings in the laminar circuits of visual cortex
 JOURNAL OF COMPUTATIONAL NEUROSCIENCE
, 2010
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Independence and Conditional Independence in Structural Systems
, 2008
"... We study the interrelations between (conditional) independence and causal relations in systems of structural equations. We provide definitions in terms of functional dependence for direct, indirect, and total causality as well as for (indirect) causality via and exclusive of a set of variables. We t ..."
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Cited by 2 (2 self)
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We study the interrelations between (conditional) independence and causal relations in systems of structural equations. We provide definitions in terms of functional dependence for direct, indirect, and total causality as well as for (indirect) causality via and exclusive of a set of variables. We then provide necessary and sufficient causal and stochastic conditions for (conditional) dependence among random vectors of interest in structural systems. Immediate corollaries ensure the validity of Reichenbach’s principle of common cause and its informative extension, the conditional Reichenbach principle of common cause. We relate our results to notions of d separation and D separation in the artificial intelligence literature.
Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation
, 2009
"... Abstract. We consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possi ..."
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Abstract. We consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possible dynamics. Focusing on transitive (strongly connected) networks that have only one type of cell (identical cell networks) we address three questions relating the network structure to dynamics. The first question is how the structure of the network may force the existence of invariant subspaces (synchrony subspaces). The second question is how these invariant subspaces can support robust heteroclinic attractors. Finally, we investigate how the dynamics of coupled cell networks with different structures and numbers of cells can be related; in particular we consider the sets of possible “inflations ” of a coupled cell network that are obtained by replacing one cell by many of the same type, in such a way that the original network dynamics is still present within a synchrony subspace. We illustrate the results with a number of examples of networks of up to six cells.
Heteroclinic Ratchets in a System of Four Coupled
 Oscillators’, J. Nonlinear Sci
"... We study an unusual but robust phenomenon that appears in an example system of four coupled phase oscillators. The coupling is preserved under only one symmetry, but there are a number of invariant subspaces and degenerate bifurcations forced by the coupling structure, and we investigate these. We s ..."
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We study an unusual but robust phenomenon that appears in an example system of four coupled phase oscillators. The coupling is preserved under only one symmetry, but there are a number of invariant subspaces and degenerate bifurcations forced by the coupling structure, and we investigate these. We show that the system can have a robust attractor that responds to a specific detuning ∆ between certain pairs of the oscillators by a breaking of phase locking for arbitrary ∆> 0 but not for ∆ ≤ 0. As the dynamical mechanism behind this is a particular type of heteroclinic network, we call this a ‘heteroclinic ratchet ’ because of its dynamical resemblance to a mechanical ratchet.
The Frozen Accident’ as an Evolutionary Adaptation: A Rate Distortion Theory Perspective on the Dynamics and Symmetries of Genetic Coding Mechanisms. Informatica 36:53–73
, 2012
"... We survey some interpretations and related issues concerning ‘the frozen accident ’ hypothesis proposed by Francis Crick and how it can be explained in terms of several natural mechanisms involving errorcorrection codes, spin glasses, symmetry breaking and the characteristic robustness of genetic ne ..."
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We survey some interpretations and related issues concerning ‘the frozen accident ’ hypothesis proposed by Francis Crick and how it can be explained in terms of several natural mechanisms involving errorcorrection codes, spin glasses, symmetry breaking and the characteristic robustness of genetic networks. The approach to most of these questions involves using elements of Shannon’s rate distortion theory incorporating a semantic system which is meaningful for the relevant alphabets and vocabulary implemented in transmission of the genetic code. We apply the fundamental homology between information source uncertainty with the free energy density of a thermodynamical system with respect to transcriptional regulators and the communication channels of sequence/structure in proteins. The collective outcome of these processes supports previous suggestions that ‘the frozen accident ’ may in fact have been a temporal evolutionary adaptation. Povzetek: Članek obravnava izvor genetskega kodiranja. 1
GENE EXPRESSION AND ITS DISCONTENTS  Developmental disorders as dysfunctions of epigenetic cognition
, 2009
"... Reductionist treatments of the epigenetic regulation of gene expression suffer the same mereological and sufficiency fallacies that haunt both contemporary systems biology and neural network models of high order cognition. Shifting perspective from the massively parallel space of gene matrix interac ..."
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Reductionist treatments of the epigenetic regulation of gene expression suffer the same mereological and sufficiency fallacies that haunt both contemporary systems biology and neural network models of high order cognition. Shifting perspective from the massively parallel space of gene matrix interactions to the grammar/syntax of the time series of developmentally expressed phenotypes using a cognitive paradigm permits import of techniques from statistical physics via the homology between information source uncertainty and free energy density. This produces a broad spectrum of ‘coevolutionary’ probability models of development and its pathologies in which epigenetic regulation and the effects of embedding environment are analogous to a tunable enzyme catalyst. A cognitive paradigm naturally incorporates memory, leading directly to models of epigenetic inheritance, as affected by environmental exposures, in the largest sense. Understanding gene expression, development, and their dysfunctions will require data analysis tools considerably more sophisticated than the present crop of simplistic models abducted from neural network studies or stochastic chemical reaction theory.