# James F. Glazebrook's research while affiliated with University of Illinois, Urbana-Champaign and other places

## Publications (94)

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Macromolecular protein complexes catalyze essential physiological processes that sustain life. Various interactions between protein subunits could increase the effective mass of certain peptide groups, thereby compartmentalizing protein $\alpha$-helices. Here, we study the differential effects of applied massive barriers upon the soliton-assisted e...
Preprint
We show how any system with morphological degrees of freedom and locally limited free energy will, under the constraints of the free energy principle, evolve toward a neuromorphic morphology that supports hierarchical computations in which each level of the hierarchy enacts a coarse-graining of its inputs, and dually a fine-graining of its outputs....
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Full-text available
Macromolecular protein complexes catalyze essential physiological processes that sustain life. Various interactions between protein subunits could increase the effective mass of certain peptide groups, thereby compartmentalizing protein α-helices. Here, we study the differential effects of applied massive barriers upon the soliton-assisted energy t...
Article
Conceptual and mathematical models of neurons have lagged behind empirical understanding for decades. Here we extend previous work in modeling biological systems with fully scale-independent quantum information-theoretic tools to develop a uniform, scalable representation of synapses, dendritic and axonal processes, neurons, and local networks of n...
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We introduce novel methods for implementing generic quantum information within a scale-free architecture. For a given observable system, we show how observational outcomes are taken to be finite bit strings induced by measurement operators derived from a holographic screen bounding the system. In this framework, measurements of identified systems w...
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The Free Energy Principle (FEP) states that under suitable conditions of weak coupling, random dynamical systems with sufficient degrees of freedom will behave so as to minimize an upper bound, formalized as a variational free energy, on surprisal (a.k.a., self-information). This upper bound can be read as a Bayesian prediction error. Equivalently,...
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Protein α-helices provide an ordered biological environment that is conducive to soliton-assisted energy transport. The nonlinear interaction between amide I excitons and phonon deformations induced in the hydrogen-bonded lattice of peptide groups leads to self-trapping of the amide I energy, thereby creating a localized quasiparticle (soliton) tha...
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Protein α-helices provide an ordered biological environment that is conducive to soliton-assisted energy transport. The nonlinear interaction between amide I excitons and phonon deformations induced in the hydrogen-bonded lattice of peptide groups leads to self-trapping of the amide I energy, thereby creating a localized quasiparticle (soliton) tha...
Preprint
Full-text available
Conceptual and mathematical models of neurons have lagged behind empirical understanding for decades. Here we extend previous work in modeling biological systems with fully scale-independent quantum information-theoretic tools to develop a uniform, scalable representation of synapses, dendritic and axonal processes, neurons, and local networks of n...
Preprint
Full-text available
The Free Energy Principle (FEP) states that under suitable conditions of weak coupling, random dynamical systems with sufficient degrees of freedom will behave so as to minimize an upper bound, formalized as a variational free energy, on surprisal (a.k.a., self-information). This upper bound can be read as a Bayesian prediction error. Equivalently,...
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Theories of consciousness and cognition that assume a neural substrate automatically regard phylogenetically basal, nonneural systems as nonconscious and noncognitive. Here, we advance a scale-free characterization of consciousness and cognition that regards basal systems, including synthetic constructs, as not only informative about the structure...
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Any interaction between finite quantum systems in a separable joint state can be viewed as encoding classical information on an induced holographic screen. Here we show that when such an interaction is represented as a measurement, the quantum reference frames (QRFs) deployed to identify systems and pick out their pointer states induce decoherence,...
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The essential biological processes that sustain life are catalyzed by protein nano-engines, which maintain living systems in far-from-equilibrium ordered states. To investigate energetic processes in proteins, we have analyzed the system of generalized Davydov equations that govern the quantum dynamics of multiple amide I exciton quanta propagating...
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Recent theories developing broad notions of context and its effects on inference are becoming increasingly important in fields as diverse as cognitive psychology, information science and quantum information theory and computing. Here we introduce a novel and general approach to the characterisation of contextuality using the techniques of Chu space...
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The electric activities of cortical pyramidal neurons are supported by structurally stable, morphologically complex axo-dendritic trees. Anatomical differences between axons and dendrites in regard to their length or caliber reflect the underlying functional specializations, for input or output of neural information, respectively. For a proper asse...
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The electric activities of cortical pyramidal neurons are supported by structurally stable, morphologically complex axo-dendritic trees. Anatomical differences between axons and dendrites in regard to their length or caliber reflect the underlying functional specializations, for input or output of neural information, respectively. For a proper asse...
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We apply previously developed Chu space and Channel Theory methods, focusing on the construction of Cone-Cocone Diagrams (CCCDs), to study the role of epistemic feelings, particularly feelings of confidence, in dual process models of problem solving. We specifically consider “Bayesian brain” models of probabilistic inference within a global neurona...
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Biological order provided by α-helical secondary protein structures is an important resource exploitable by living organisms for increasing the efficiency of energy transport. In particular, self-trapping of amide I energy quanta by the induced phonon deformation of the hydrogen-bonded lattice of peptide groups is capable of generating either pinne...
Preprint
Full-text available
Biological order provided by $\alpha$-helical secondary protein structures is an important resource exploitable by living organisms for increasing the efficiency of energy transport. In particular, self-trapping of amide I energy quanta by the induced phonon deformation of the hydrogen-bonded lattice of peptide groups is capable of generating eithe...
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Gilead et al. propose an ontology of abstract representations based on folk-psychological conceptions of cognitive architecture. There is, however, no evidence that the experience of cognition reveals the architecture of cognition. Scale-free architectural models propose that cognition has the same computational architecture from sub-cellular to wh...
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Descriptions of measurement typically neglect the observations required to identify the apparatus employed to either prepare or register the final state of the “system of interest.” Here, we employ category-theoretic methods, particularly the theory of classifiers, to characterize the full interaction between observer and world in terms of informat...
Preprint
Full-text available
The essential biological processes that sustain life are catalyzed by protein nano-engines, which maintain living systems in far-from-equilibrium ordered states. To investigate energetic processes in proteins, we have analyzed the system of generalized Davydov equations that govern the quantum dynamics of multiple amide I exciton quanta propagating...
Article
Full-text available
Protein clamps provide the cell with effective mechanisms for sensing of environmental changes and triggering adaptations that maintain homeostasis. The general physical mechanism behind protein clamping action, however, is poorly understood. Here, we explore the Davydov model for quantum transport of amide I energy, which is self-trapped in solito...
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The transport of energy inside protein α-helices is studied by deriving a system of quantum equations of motion from the Davydov Hamiltonian with the use of the Schrödinger equation and the generalized Ehrenfest theorem. Numerically solving the system of quantum equations of motion for different initial distributions of the amide I energy over the...
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Chu Spaces and Channel Theory are well-established areas of investigation in the general context of category theory when applied to semantically-based information flow. In this Part I of a two-part work, we review a range of related concepts and examples showing how these methods can be applied to logic and computer science, including Formal Concep...
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Twenty five years ago, Sir John Carew Eccles together with Friedrich Beck proposed a quantum mechanical model of neurotransmitter release at synapses in the human cerebral cortex. The model endorsed causal influence of human consciousness upon the functioning of synapses in the brain through quantum tunneling of unidentified quasiparticles that tri...
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Chu Spaces and Channel Theory are well established areas of investigation in the general context of category theory. We review a range of examples and applications of these methods in logic and computer science, including Formal Concept Analysis, distributed systems and ontology development. We then employ these methods to describe human object per...
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In the context of orientable circuits and subcomplexes of these as representing certain singular spaces, we consider characteristic class formulas generalizing those classical results as seen for the Riemann-Hurwitz formula for regulating the topology of branched covering maps and that for monoidal transformations which include the standard blowing...
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Autism spectrum disorder (ASD) is increasingly being conceptualized as a spectrum disorder of connectome development. We review evidence suggesting that ASD is characterized by a positive feedback loop that amplifies small functional variations in early-developing sensory-processing pathways into structural and functional imbalances in the global n...
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We consider a generalized Riemann-Hurwitz formula as it may be applied to rational maps between projective varieties having an indeterminacy set and fold-like singularities. The case of a holomorphic branched covering map is recalled. Then we see how the formula can be applied to iterated maps having branch-like singularities, degree lowering curve...
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Lax pairs featuring in the theory of integrable systems are known to be constructed from a commutative algebra of formal pseudodifferential operators known as the Burchnall- Chaundy algebra. Such pairs induce the well known KP flows on a restricted infinite-dimensional Grassmannian. The latter can be exhibited as a Banach homogeneous space construc...
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We consider a generalized Riemann-Hurwitz formula as it may be applied to rational maps between projective varieties having an indeterminacy set and fold-like singularities. The case of a holomorphic branched covering map is recalled. Then we see how the formula can be applied to iterated maps having branch-like singularities. Separately, we consid...
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We commence this review by outlining the challenges faced by physical theories of consciousness and briefly describe the two main approaches based on classical or quantum mechanics. Next, we provide a detailed exposition of the motivation, the theoretical construction and experimental falsification of the celebrated model due to Beck and Eccles con...
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We study the background to problems of functional connectivity in autism spectrum disorders within the neurocognitive framework of the global workspace model. This we proceed to do by observing network irregularities detracting from that of a well-formed small world network architecture. This is discussed in terms of pathologies in functional conne...
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We recall some results on generalized determinants which support a theory of operator τ -functions in the context of their predeterminants which are operators valued in a Banach–Lie group that are derived from the transition maps of certain Banach bundles. Related to this study is a class of Banach–Lie algebras known as L *-algebras from which seve...
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We were deeply saddened to learn of the sudden death of our colleague, friend, and member of the Editorial Board of Quanta, Professor Ion C. Baianu, who unexpectedly passed away in Urbana, Illinois, USA, on February 10, 2013. Ion left behind his wife, Kimiko, his son, Stephen, and daughters, Antonia and Christina. He also left behind the achievemen...
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The Burchnall–Chaundy algebra is a commutative algebra of formal pseudodifferential operators that is instrumental for constructing Lax pairs. It has been shown that via an operator-theory modification of the Sato correspondence, there is an associated C*-algebra: the Burchnall–Chaundy C*-algebra. Commencing with the relationship between a Baxter L...
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A CATEGORY THEORY AND HIGHER DIMENSIONAL ALGEBRA APPROACH TO COMPLEX SYSTEMS BIOLOGY, META-SYSTEMS AND ONTOLOGICAL THEORY OF LEVELS: EMERGENCE OF LIFE, SOCIETY, HUMAN CONSCIOUSNESS AND ARTIFICIAL INTELLIGENCE I. C. Baianu, Ronald Brown and James F. Glazebrook Journal: Acta Universitatis Apulensis, Alba Iulia: Conf. Proceedings: Understanding Intell...
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In this monograph we present a novel approach to the problems raised by higher complexity in both nature and the human society, by considering the most complex levels of objective existence as ontological meta-levels, such as those present in the creative human minds and civilized, modern societies. Thus, a theory' about theories is called a meta...
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We describe a neurobiological framework for membrane fusion and exocytosis within the SNARE (SNARE is an acronym for soluble NSF attachment protein receptor, where NSF abbreviates N-ethylmaleimide–sensitive fusion protein) complex using vibrationally assisted tunneling and a quantum Davydov soliton mechanism. The main feature concerns how the resul...
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We introduce the twisted coupled vortex equations defined over a closed Kähler manifold X. There is an associated notion of stability for certain triples of holomorphic data on X. We establish a Hitchin–Kobayashi correspondence which relates the existence of solutions to these equations and the stability of a corresponding triple.
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Baianu, I.C., Glazebrook, J.F. and Brown, R. 2011."A category theory and higher dimensional algebra approach to complex systems biology, meta-systems and ontological theory of levels: Emergence of Life, Society, Human Consciousness and Artificial Intelligence". Acta Universitatis Apulensis, Alba Iulia. 52:11--144.
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We survey some interpretations and related issues concerning the frozen hypothesis due to F. Crick and how it can be explained in terms of several natural mechanisms involving error correction codes, spin glasses, symmetry breaking and the characteristic robustness of genetic networks. The approach to most of these questions involves using elements...
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A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item...
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We present an operator-coefficient version of Sato's infinite-dimensional Grassmann manifold, and tau-function. In this context, the Burchnall-Chaundy ring of commuting differential operators becomes a C*-algebra, to which we apply the Brown-Douglas-Fillmore theory, and topological invariants of the spectral ring become readily available. We constr...
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Several features of an analytic (infinite-dimensional) Grassmannian of (commensurable) subspaces of a Hilbert space were developed in the context of integrable PDEs (KP hierarchy). We extended some of those features when polarized separable Hilbert spaces are generalized to a class of polarized Hilbert modules, in particular the Baker and tau-funct...
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Given a Banach algebra we construct a principal bundle with connection over the similarity class of projections in the algebra and compute the curvature of the connection. The associated vector bundle and the connection are a universal bundle with attendant connection. When the algebra is the linear operators over a Hilbert module, we establish an...
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We outline a model for a cognitive epigenetic system based on elements of the Shannon theory of information and the statistical physics of the generalized Onsager relations. Particular attention is paid to the concept of the rate distortion function and from another direction as motivated by the thermodynamics of computing, the fundamental homology...
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116. Baianu, I.C., Glazebrook, J. F. and Brown, R. 2011. "Quantum Symmetries, Operator Algebra and Quantum Groupoid Representations: Paracrystalline Systems and Global Symmetry Breaking". Intl. J. Rev. Res. Appl. Sci. (IJRRAS),9(2): 163-206.
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113. Baianu, I.C., Brown, R, and Glazebrook, J.F. 2011. A Quantum Algebraic Topology Framework for Multiscale Quantum Computations. Intl. Journal Maths and Computational Methods Sci. and Technol.,Vol. 1, No.6: 62-93.
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In the beginning of the 20th century the groundbreaking work of Ramon y Cajal firmly established the neuron doctrine, according to which neurons are the basic structural and functional units of the nervous system. Von Weldeyer coined the term “neuron” in 1891, but the huge leap forward in neuroscience was due to Cajal’s meticulous microscopic obser...
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Relational structures of organisms and the human mind are naturally represented in terms of novel variable topology concepts, non-Abelian categories and Higher Dimensional Algebra{ relatively new concepts that would be defined in this tutorial paper. A unifying theme of local-to-global approaches to organismic development, evolution and human consc...
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111. Baianu, I. C., Georgescu, G., Glazebrook, J.F.., and Brown, R. 2010. Łukasiewicz-Moisil, Many--Valued Logic Algebras of Highly-Complex Systems. BRAIN-- Broad Research in Artificial Intelligence and Neuroscience, 1: 1-- 12.
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110. Baianu, I.C. and Glazebrook, J.F.. 2010. Complex Systems Biology: A novel categorical and ontology framework. Journal of Information Technology Research (JTIR), 2: 41-60
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Networks of small worlds and Red Queen dynamic structures as analytic-descriptive methods are ubiquitous in expanding areas of research in the cognitive neurosciences, sociopsychological systems and parallel machine cognition. In the setting of the Baars Global Workspace theory, we apply a semantically oriented information-theoretic mechanism, maki...
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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 densitie...
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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 informat...
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A novel Algebraic Topology approach to Supersymmetry (SUSY) and Symme-try Breaking in Quantum Field and Quantum Gravity theories is presented with a view to developing a wide range of physical applications, such as: nuclear fusion and other nuclear reactions in quantum chromodynamics, nonlinear physics at high energy densities, dynamic Jahn-Teller...
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A non-Abelian, Universal SpaceTime Ontology is introduced in terms of Categories, Functors, Natural Transformations, Higher Dimensional Algebra and the Theory of Levels. A Paradigm shift towards Non-Commutative Spacetime structures with remarkable asymmetries or broken symmetries, such as the CPT-symmetry violation, is proposed. This has the potent...
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Current wisdom in classical neuroscience suggests that the only direct action of the electric field in neurons is upon voltage-gated ion channels which open and close their gates during the passage of ions. The intraneuronal biochemical activities are thought to be modulated indirectly either by entering into the cytoplasm ions that act as second m...
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We discuss a framework for subneuronal processing of information in terms of certain biophysical principles subject to the dynamics of solitary waves and stochastic processes. A particular focus concerns the propagation of electromagnetic solitons within neurons resulting from the interaction between the cytosolic water electric dipole field and th...
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In this paper we present a model for estimation of the C-terminal tubulin tail (CTT) dynamics in cytoskeletal microtubules of nerve cells. We show that the screened Coulomb interaction between a target CTT and the negatively charged microtubule surface as well as its immediate CTT neighbours results in confinement of the CTT motion within a restric...
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We show that commutative rings of formal pseudodifferential operators can be conjugated as subrings in noncommutative Banach algebras of operators in the presence of certain eigenfunctions. Techniques involve those of the Sato Grassmannian as used in the study of the KP hierarchy as well as the geometry of an infinite dimensional Stiefel bundle wit...
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We describe a biophysical framework for subneuronal processing of information via certain quantum mechanical processes and solitonic interactions as applicable to neuronal microtubules. In particular, we describe how certain energase actions and vibrationally assisted tunneling may influence the conformational dynamics of the neuronal cytoskeletal...
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A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz– Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formula...
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INTRODUCTION TO FOLIATIONS AND LIE GROUPOIDS (Cambridge Studies in Advanced Mathematics 91) By I. MOERDIJK and J. MRČUN: 173 pp., £30.00 (US\$50.00), ISBN 0-521-83197-0 (Cambridge University Press, 2003) - - Volume 37 Issue 2 - James F. Glazebrook
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Neurons are highly specialized cells that input, process, store and output information. Interneuronal communication is achieved in four basic ways: (i) Ca2+ evoked exocytosis with chemical neurotransmission, (ii) gap junction electrotonic coupling, (iii) secretion of neurosteroids, nitric oxide and derivatives of the arachidonic acid acting in para...
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Commencing from a monoidal semigroup A, we consider the geometry of the space W(A) of pseudoregular elements. When A is a Banachable algebra we show that there exist certain subspaces of W(A) that can be realized as submanifolds of A. The space W(A) contains certain subspaces constituting the Stiefel manifolds of framings for A. We establish severa...
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Given a Kaehlerian holomorphic fiber bundle whose fiber is a compact homogeneous Kaehler manifold, we describe the perturbed Hermitian-Einstein equations relative to certain holomorphic vector bundles. With respect to special metrics on the holomorphic bundles, there is a dimensional reduction procedure which reduces these equations to a system of...
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We construct a Fourier–Mukai transform for smooth complex vector bundles E over a torus bundle π:M→B, the vector bundles being endowed with various structures of increasing complexity. At a minimum, we consider vector bundles E with a flat partial unitary connection, that is families or deformations of flat vector bundles (or unitary local systems)...
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Commencing from a monoidal semigroup A, we consider the geometry of the space W (A) of pseudoregular elements. When A is a Ba-nachable algebra we show that there exist certain subspaces of W (A) that can be realized as submanifolds of A. The space W (A) contains certain sub-spaces constituting the Stiefel manifolds of framings for A . We establish...
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Our main aim is to associate a holonomy Lie groupoid to the connective structure of an abelian gerbe. The construction has analogies with a procedure for the holonomy Lie groupoid of a foliation, in using a locally Lie groupoid and a globalisation procedure. We show that path connections and 2-holonomy on line bundles may be formulated using the no...
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Given a complex Banach algebra, we consider the Stiefel bun- dle relative to the similarity class of a fixed projection. In the holomorphic category the Stiefel bundle is a holomorphic locally trivial principal bundle over a certain Grassmann manifold. Our main application concerns the holo- morphic parametrization of framings for projections. In t...
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We introduce the Stiefel bundle associated to a given Banachable algebra and study the properties of this analytic principal fiber bundle over the Grassmannian of equivalence classes of idempotents in the algebra. Our main application concerns the bounded linear operators of a Banach space. In particular, the problem of smooth parametrization of su...
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We introduce the twisted coupled vortex equations defined over a closed Kähler manifold X. There is an associated notion of stability for certain triples of holomorphic data on X. We establish a Hitchin-Kobayashi correspondence which relates the existence of solutions to these equations and the stability of a corresponding triple.
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Infinite dimensional fiber spaces arise naturally in the theory of representations of C*-algebras. Often there are cases where one has to deal with more general notions of dierentiability. In order to create a unified framework, we introduce the notion of a D -space and a D -group action within a given category D. Then we present a self-contained a...
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. The technique of dimensional reduction of an integrable system usually requires symmetry arising from a group action. In this paper we study a situation in which a dimensional reduction can be achieved despite the absence of any such global symmetry. We consider certain holomorphic vector bundles over a Kahler manifold which is itself the total s...
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Studying smooth families of certain subspaces of a Banach space X entails a construction of a Grassmann manifold defined over the similarity class of a projection in a Banach space. Standard principles of fiber bundle theory can be adapted to describe these families in terms of smooth maps from a possibly infinite-dimensional paracompact manifold t...
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In order to use the technique of dimensional reduction, it is usually necessary for there to be a symmetry coming from a group action. In this paper we consider a situation in which there is no such symmetry, but in which a type of dimensional reduction is nevertheless possible. We obtain a relation between the Coupled Vortex equations on a closed...
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With regards to certain Riemannian foliations we consider Kasparov pairings of leafwise and transverse Dirac operators. Relative to a pairing with a transversal class we commence by establishing an index formula for foliations with leaves of nonpositive sectional curvature. The underlying ideas are then developed in a more general setting leading t...
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The theory of characteristic classes of foliated bundles is applied to the study of a class of geometric Dirac operators. For a foliation of even codimension with minimally immersed leaves on the base, the nature of chiral anomalies is examined in view of the cohomology,of the truncated Weil algebra. A foliated Wess-Zumino term is deflned and for c...
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We describe a family of differential operators parametrized by the transversal vector potentials of a Riemannian foliation relative to the Clifford algebra of the foliation. This family is non-elliptic but in certain ways behaves like a standard Dirac family in the absolute case as a result of its elliptic-like regularity properties. The analytic a...