323 research outputs found
A classical groupoid model for quantum networks
We give a mathematical analysis of a new type of classical computer network
architecture, intended as a model of a new technology that has recently been
proposed in industry. Our approach is based on groubits, generalizations of
classical bits based on groupoids. This network architecture allows the direct
execution of a number of protocols that are usually associated with quantum
networks, including teleportation, dense coding and secure key distribution
A Classical Groupoid Model for Quantum Networks
We give a mathematical analysis of a new type of classical computer network architecture, intended as a model of a new technology that has recently been proposed in industry. Our approach is based on groubits, generalizations of classical bits based on groupoids. This network architecture allows the direct execution of a number of protocols that are usually associated with quantum networks, including teleportation, dense coding and secure key distribution
Ćukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems
A novel approach to self-organizing, highly-complex systems (HCS), such as living organisms and artificial intelligent systems (AIs), is presented which is relevant to Cognition, Medical Bioinformatics and Computational Neuroscience. Quantum Automata (QAs) were defined in our previous work as generalized, probabilistic automata with quantum state spaces (Baianu, 1971). Their next-state functions operate through transitions between quantum states defined by the quantum equations of motion in the Schroedinger representation, with both initial and boundary conditions in space-time. Such quantum automata operate with a quantum logic, or Q-logic, significantly different from either Boolean or Ćukasiewicz many-valued logic. A new theorem is proposed which states that the category of quantum automata and automata--homomorphisms has both limits and colimits. Therefore, both categories of quantum automata and classical automata (sequential machines) are bicomplete. A second new theorem establishes that the standard automata category is a subcategory of the quantum automata category. The quantum automata category has a faithful representation in the category of Generalized (M,R)--Systems which are open, dynamic biosystem networks with defined biological relations that represent physiological functions of primordial organisms, single cells and higher organisms
Non-commutative fermion mass matrix and gravity
The first part is an introductory description of a small cross-section of the
literature on algebraic methods in non-perturbative quantum gravity with a
specific focus on viewing algebra as a laboratory in which to deepen
understanding of the nature of geometry. This helps to set the context for the
second part, in which we describe a new algebraic characterisation of the Dirac
operator in non-commutative geometry and then use it in a calculation on the
form of the fermion mass matrix. Assimilating and building on the various ideas
described in the first part, the final part consists of an outline of a
speculative perspective on (non-commutative) quantum spectral gravity. This is
the second of a pair of papers so far on this project.Comment: To appear in Int. J. Mod. Phys. A Previous title: An outlook on
quantum gravity from an algebraic perspective. 39 pages, 1 xy-pic figure,
LaTex Reasons for new version: added references, change of title and some
comments more up-to-dat
Renormalization of Discrete Models without Background
Conventional renormalization methods in statistical physics and lattice
quantum field theory assume a flat metric background. We outline here a
generalization of such methods to models on discretized spaces without metric
background. Cellular decompositions play the role of discretizations. The group
of scale transformations is replaced by the groupoid of changes of cellular
decompositions. We introduce cellular moves which generate this groupoid and
allow to define a renormalization groupoid flow.
We proceed to test our approach on several models. Quantum BF theory is the
simplest example as it is almost topological and the renormalization almost
trivial. More interesting is generalized lattice gauge theory for which a
qualitative picture of the renormalization groupoid flow can be given. This is
confirmed by the exact renormalization in dimension two.
A main motivation for our approach are discrete models of quantum gravity. We
investigate both the Reisenberger and the Barrett-Crane spin foam model in view
of their amenability to a renormalization treatment. In the second case a lack
of tunable local parameters prompts us to introduce a new model. For the
Reisenberger and the new model we discuss qualitative aspects of the
renormalization groupoid flow. In both cases quantum BF theory is the UV fixed
point.Comment: 40 pages, 17 figures, LaTeX + AMS + XY-pic + eps; added subsection
4.3 on relation to spin network diagrams, reference added, minor adjustment
Quantum lattice gauge fields and groupoid C*-algebras
We present an operator-algebraic approach to the quantization and reduction
of lattice field theories. Our approach uses groupoid C*-algebras to describe
the observables and exploits Rieffel induction to implement the quantum gauge
symmetries. We introduce direct systems of Hilbert spaces and direct systems of
(observable) C*-algebras, and, dually, corresponding inverse systems of
configuration spaces and (pair) groupoids. The continuum and thermodynamic
limit of the theory can then be described by taking the corresponding limits,
thereby keeping the duality between the Hilbert space and observable C*-algebra
on the one hand, and the configuration space and the pair groupoid on the
other. Since all constructions are equivariant with respect to the gauge group,
the reduction procedure applies in the limit as well.Comment: 23 pages, 6 figure
Spin Foams and Noncommutative Geometry
We extend the formalism of embedded spin networks and spin foams to include
topological data that encode the underlying three-manifold or four-manifold as
a branched cover. These data are expressed as monodromies, in a way similar to
the encoding of the gravitational field via holonomies. We then describe
convolution algebras of spin networks and spin foams, based on the different
ways in which the same topology can be realized as a branched covering via
covering moves, and on possible composition operations on spin foams. We
illustrate the case of the groupoid algebra of the equivalence relation
determined by covering moves and a 2-semigroupoid algebra arising from a
2-category of spin foams with composition operations corresponding to a fibered
product of the branched coverings and the gluing of cobordisms. The spin foam
amplitudes then give rise to dynamical flows on these algebras, and the
existence of low temperature equilibrium states of Gibbs form is related to
questions on the existence of topological invariants of embedded graphs and
embedded two-complexes with given properties. We end by sketching a possible
approach to combining the spin network and spin foam formalism with matter
within the framework of spectral triples in noncommutative geometry.Comment: 48 pages LaTeX, 30 PDF figure
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 âreversible behaviorâ 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 âclassicalâ states that determine molecular dynamics subject to Boltzmann statistics and âsteady-stateâ, metabolic (multi-stable) manifolds, together with âconfigurationâ 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 âstandardâ 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 âcycleâ 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 âcyclingâ; 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 patientsâ possible improvements of the designs for future clinical trials and cancer treatments. \ud
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