362 research outputs found
Categorical Ontology of Complex Systems, Meta-Systems and Theory of Levels: The Emergence of Life, Human Consciousness and Society
Single cell interactomics in simpler organisms, as well as somatic cell interactomics in multicellular organisms, involve biomolecular interactions in complex signalling pathways that were recently represented in modular terms by quantum automata with ‘reversible behavior’ representing normal cell cycling and division. Other implications of such quantum automata, modular modeling of signaling pathways and cell differentiation during development are in the fields of neural plasticity and brain development leading to quantum-weave dynamic patterns and specific molecular processes underlying extensive memory, learning, anticipation mechanisms and the emergence of human consciousness during the early brain development in children. Cell interactomics is here represented for the first time as a mixture of ‘classical’ states that determine molecular dynamics subject to Boltzmann statistics and ‘steady-state’, metabolic (multi-stable) manifolds, together with ‘configuration’ spaces of metastable quantum states emerging from complex quantum dynamics of interacting networks of biomolecules, such as proteins and nucleic acids that are now collectively defined as quantum interactomics. On the other hand, the time dependent evolution over several generations of cancer cells --that are generally known to undergo frequent and extensive genetic mutations and, indeed, suffer genomic transformations at the chromosome level (such as extensive chromosomal aberrations found in many colon cancers)-- cannot be correctly represented in the ‘standard’ terms of quantum automaton modules, as the normal somatic cells can. This significant difference at the cancer cell genomic level is therefore reflected in major changes in cancer cell interactomics often from one cancer cell ‘cycle’ to the next, and thus it requires substantial changes in the modeling strategies, mathematical tools and experimental designs aimed at understanding cancer mechanisms. Novel solutions to this important problem in carcinogenesis are proposed and experimental validation procedures are suggested. From a medical research and clinical standpoint, this approach has important consequences for addressing and preventing the development of cancer resistance to medical therapy in ongoing clinical trials involving stage III cancer patients, as well as improving the designs of future clinical trials for cancer treatments.\ud
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KEYWORDS: Emergence of Life and Human Consciousness;\ud
Proteomics; Artificial Intelligence; Complex Systems Dynamics; Quantum Automata models and Quantum Interactomics; quantum-weave dynamic patterns underlying human consciousness; specific molecular processes underlying extensive memory, learning, anticipation mechanisms and human consciousness; emergence of human consciousness during the early brain development in children; Cancer cell ‘cycling’; interacting networks of proteins and nucleic acids; genetic mutations and chromosomal aberrations in cancers, such as colon cancer; development of cancer resistance to therapy; ongoing clinical trials involving stage III cancer patients’ possible improvements of the designs for future clinical trials and cancer treatments. \ud
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From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics
Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation
From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics
Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation
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Topological dualities in the Ising model
We relate two classical dualities in low-dimensional quantum field theory:
Kramers-Wannier duality of the Ising and related lattice models in
dimensions, with electromagnetic duality for finite gauge theories in
dimensions. The relation is mediated by the notion of boundary field theory:
Ising models are boundary theories for pure gauge theory in one dimension
higher. Thus the Ising order/disorder operators are endpoints of Wilson/'t
Hooft defects of gauge theory. Symmetry breaking on low-energy states reflects
the multiplicity of topological boundary states. In the process we describe
lattice theories as (extended) topological field theories with boundaries and
domain walls. This allows us to generalize the duality to non-abelian groups;
finite, semi-simple Hopf algebras; and, in a different direction, to finite
homotopy theories in arbitrary dimension
Hilbert schemes and -ification of Khovanov-Rozansky homology
We define a deformation of the triply graded Khovanov-Rozansky homology of a
link depending on a choice of parameters for each component of ,
which satisfies link-splitting properties similar to the Batson-Seed invariant.
Keeping the as formal variables yields a link homology valued in triply
graded modules over . We conjecture that
this invariant restores the missing symmetry of the
triply graded Khovanov-Rozansky homology, and in addition satisfies a number of
predictions coming from a conjectural connection with Hilbert schemes of points
in the plane. We compute this invariant for all positive powers of the full
twist and match it to the family of ideals appearing in Haiman's description of
the isospectral Hilbert scheme
Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review
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 Jahn-Teller 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 quasi-triangular, quasi-Hopf algebras,
bialgebroids, Grassmann-Hopf algebras and higher dimensional algebra. On the
one hand, this quantum algebraic approach is known to provide solutions to the
quantum Yang-Baxter equation. On the other hand, our novel approach to extended
quantum symmetries and their associated representations is shown to be relevant
to locally covariant general relativity theories that are consistent with
either nonlocal quantum field theories or local bosonic (spin) models with the
extended quantum symmetry of entangled, 'string-net condensed' (ground) states
Equivariant Iterated Loop Space Theory and Permutative \u3cem\u3eG\u3c/em\u3e–Categories
We set up operadic foundations for equivariant iterated loop space theory. We start by building up from a discussion of the approximation theorem and recognition principle for V–fold loop G–spaces to several avatars of a recognition principle for infinite loop G–spaces. We then explain what genuine permutative G–categories are and, more generally, what E∞–G–categories are, giving examples showing how they arise. As an application, we prove the equivariant Barratt–Priddy–Quillen theorem as a statement about genuine G–spectra and use it to give a new, categorical proof of the tom Dieck splitting theorem for suspension G–spectra. Other examples are geared towards equivariant algebraic K–theory
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