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Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review
, 2009
"... A novel Algebraic Topology approach to Supersymmetry (SUSY) and Symmetry Breaking in Quantum Field and Quantum Gravity theories is presented with a view to developing a wide range of physical applications. These include: controlled nuclear fusion and other nuclear reaction studies in quantum chromod ..."
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A novel Algebraic Topology approach to Supersymmetry (SUSY) and Symmetry Breaking in Quantum Field and Quantum Gravity theories is presented with a view to developing a wide range of physical applications. These include: controlled nuclear fusion and other nuclear reaction studies in quantum chromodynamics, nonlinear physics at high energy densities, dynamic JahnTeller effects, superfluidity, high temperature superconductors, multiple scattering by molecular systems, molecular or atomic paracrystal structures, nanomaterials, ferromagnetism in glassy materials, spin glasses, quantum phase transitions and supergravity. This approach requires a unified conceptual framework that utilizes extended symmetries and quantum groupoid, algebroid and functorial representations of non–Abelian higher dimensional structures pertinent to quantized spacetime topology and state space geometry of quantum operator algebras. Fourier transforms, generalized Fourier–Stieltjes transforms, and duality relations link, respectively, the quantum groups and quantum groupoids with their dual algebraic structures; quantum double constructions are also discussed in this context in relation to quasitriangular, quasiHopf algebras, bialgebroids, GrassmannHopf algebras and Higher Dimensional Algebra. On the one hand, this quantum
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
Version 6.3 Embodied cognition, embodied regulation, and the Data Rate Theorem
, 2014
"... The Data Rate Theorem carries deep implications for theories of embodied cognition, extensions providing a spectrum of necessary conditions dynamic statistical models useful in empirical studies. A large deviations argument, however, implies that the regulation and stabilization of such systems is ..."
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The Data Rate Theorem carries deep implications for theories of embodied cognition, extensions providing a spectrum of necessary conditions dynamic statistical models useful in empirical studies. A large deviations argument, however, implies that the regulation and stabilization of such systems is itself an interpenetrating phenomenon necessarily convoluted with embodied cognition. For humans, the central regulatory role of culture has long been known. Although a groundstate collapse analogous to generalized anxiety appears ubiquitous to such systems, lack of cultural modulation in realtime automatons or distributed cognition manmachine ‘cockpits ’ makes them subject to a pathology under which ‘all possible targets are enemies’. Key words: automaton; control; enaction; language; machine psychiatry; stabilization...[O]ur first move is simply to treat perceptionaction problems and language problems as the same kind of thing... Linguistic information is a task resource in exactly the same way as perceptual information... Our behavior emerges from a pool of potential task resources that include the body, the environment and... the brain.
A formal approach to the molecular fuzzy lockandkey
"... Abstract The fuzzy lockandkey (FLK) powers a vast array of sophisticated logic gates at interand intracellular levels. We invoke representations of groupoid tiling wreath products analogous to the study of nonrigid molecules or of related fuzzy symmetry extensions to build a Morse Function th ..."
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Abstract The fuzzy lockandkey (FLK) powers a vast array of sophisticated logic gates at interand intracellular levels. We invoke representations of groupoid tiling wreath products analogous to the study of nonrigid molecules or of related fuzzy symmetry extensions to build a Morse Function that can describe spontaneous symmetry breaking phase transitions driven by information catalysis. The Function can, however, also be used to construct an Onsagerlike stochastic dynamics, linked to the phase transition approach by the rich stability criteria associated with stochastic differential equations. The two methods provide complementary ways of looking at the FLK. A limit condition emerging from the stochastic dynamics gives insight into a cellular 'generalized inflammation' requiring progressively higher commitment of metabolic free energy for maintenance of basic FLK processes. These results suggest that more systematic study may illuminate pathologies associated with the failure of the FLK, a centrallyimportant but enigmatic biological process.
Version 6 Foundations of computational psychiatry: a mathematical treatment of embodied cognition and its disorders
"... Abstract The Data Rate Theorem that establishes a formal linkage between realtime linear control theory and information theory carries deep implications for the study of embodied cognition and its dysfunctions across human, machine, and composite manmachine cockpit entities. The stabilization of ..."
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Abstract The Data Rate Theorem that establishes a formal linkage between realtime linear control theory and information theory carries deep implications for the study of embodied cognition and its dysfunctions across human, machine, and composite manmachine cockpit entities. The stabilization of such cognition is a dynamic process deeply intertwined with it, constituting, in a sense, the riverbanks directing the flow of a stream of generalized consciousness. The fundamental role of culture in human life has long been understood. Here we argue that, not only is culture, in the words of the evolutionary anthropologist Robert Boyd, 'as much a part of human biology as the enamel on our teeth', but that it is an important part of the disorders of embodied cognition that different communities socially construct as mental illness. A shift in perspective on such illness is badly needed, from naive geneticism and a simplistic 'biomarker' focus to a broad cognitive theory that recognizes the central roles of culture, socioeconomic structure, their histories and their dynamics, in human development. Unfortunately, stabilizing analogs to cultural influence are unavailable to highorder realtime machine and cockpit systems that, increasingly, will be tasked with control of critical enterprises ranging from communication, power, and travel networks to nuclear and chemical reactors, organized deadly force, and so on.
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"... Previous theoretical work on consciousness and other punctuated global broadcasts associated with attention states has focused on the evolutionary exaptation of the inevitable signal crosstalk between related sets of unconscious cognitive modules (UCM). This has invoked a groupoid treatment of the ..."
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Previous theoretical work on consciousness and other punctuated global broadcasts associated with attention states has focused on the evolutionary exaptation of the inevitable signal crosstalk between related sets of unconscious cognitive modules (UCM). This has invoked a groupoid treatment of the equivalence class structure arising from information sources 'dual', in a formal sense, to the UCM, via a standard spontaneous symmetry breaking/lifting methodology abducted from statistical physics, and through an index theorem approach based on an Onsagerlike stochastic differential equations model. Surprisingly, similar arguments can be applied to the formally 'fuzzy' generalizations that are likely to better fit actual biological complexities.
Version 12 The cultural epigenetics of
, 2009
"... psychopathology: The missing heritability of complex diseases found? ..."
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.
Metabolism, . . .  Insights from a groupoid stereochemistry
, 2008
"... This work reconsiders recent ideas on the origin of biological homochirality, using a groupoid Morse Theory approach to stereochemistry. On Earth, limited metabolic free energy density may have served as a low temperatureanalog to ‘freeze’ the system in the lowest energy state, i.e., the set of sim ..."
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This work reconsiders recent ideas on the origin of biological homochirality, using a groupoid Morse Theory approach to stereochemistry. On Earth, limited metabolic free energy density may have served as a low temperatureanalog to ‘freeze’ the system in the lowest energy state, i.e., the set of simplest homochiral transitive groupoids representing reproductive chemistries. These engaged in Darwinian competition until a single configuration survived. Subsequent pathdependent evolutionary process lockedin this initial condition. Astrobiological outcomes, in the presence of higher initial metabolic free energy densities, could well be considerably richer, for example, of mixed chirality. One result would be a complicated distribution across a statistically large sample of extraterrestrial stereochemistry.