296 results match your criteria Algebras And Representation Theory[Journal]


Algebraic Study of diatomic Molecules: homonuclear molecules H and N.

Sci Rep 2020 May 6;10(1):7663. Epub 2020 May 6.

Department of Theoretical Physics and Astrophysics, University of Tabriz, Tabriz, 51664, Iran.

It is the aim of this study to discuss for two-body systems like homonuclear molecules in which eigenvalues and eigenfunctions are obtained by exact solutions of the solvable models based on SU(1, 1) Lie algebras. Exact solutions of the solvable Hamiltonian regarding the relative motion in a two-body system on Lie algebras were obtained. The U(1) ↔ O(2), U(3) ↔ O(4) and U(3) ↔ O(4) transitional Hamiltonians are employed to described for H and N molecules. Read More

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http://dx.doi.org/10.1038/s41598-020-64266-zDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7203175PMC

Classification of Rota-Baxter operators on semigroup algebras of order two and three.

Commun Algebra 2019 4;47(8):3094-3116. Epub 2019 Mar 4.

Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria.

In this paper, we determine all the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra. We determine the matrices for these Rota-Baxter operators by directly solving the defining equations of the operators. We also produce a Mathematica procedure to predict and verify these solutions. Read More

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http://dx.doi.org/10.1080/00927872.2018.1552278DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7083595PMC

Pseudo-loop conditions.

Bull Lond Math Soc 2019 Oct 12;51(5):917-936. Epub 2019 Sep 12.

Institut für Diskrete Mathematik und Geometrie Technische Universität Wien Wiedner Hauptstrasse 8-10/104 1040 Wien Austria.

About a decade ago, it was realised that the satisfaction of a given (or ) of the form in an algebra is equivalent to the algebra forcing a loop into any graph on which it acts and which contains a certain finite subgraph associated with the identity. Such identities have since also been called , and this characterisation has produced spectacular results in universal algebra, such as the satisfaction of a in any arbitrary non-trivial finite idempotent algebra. We initiate, from this viewpoint, the systematic study of sets of identities of the form , which we call . Read More

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http://dx.doi.org/10.1112/blms.12286DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6999673PMC
October 2019

A broad class of discrete-time hypercomplex-valued Hopfield neural networks.

Neural Netw 2020 Feb 18;122:54-67. Epub 2019 Oct 18.

Department of Applied Mathematics, University of Campinas, Rua Sérgio Buarque de Holanda, 651, Campinas-SP, CEP 13083-859, Brazil. Electronic address:

In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel hypercomplex number systems referred to as real-part associative hypercomplex number systems. Real-part associative hypercomplex number systems generalize the well-known Cayley-Dickson algebras and real Clifford algebras and include the systems of real numbers, complex numbers, dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as particular instances. Read More

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http://dx.doi.org/10.1016/j.neunet.2019.09.040DOI Listing
February 2020
4 Reads

Non-locality, contextuality and valuation algebras: a general theory of disagreement.

Philos Trans A Math Phys Eng Sci 2019 Nov 16;377(2157):20190036. Epub 2019 Sep 16.

Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK.

We establish a strong link between two apparently unrelated topics: the study of conflicting information in the formal framework of valuation algebras, and the phenomena of non-locality and contextuality. In particular, we show that these peculiar features of quantum theory are mathematically equivalent to a general notion of between information sources. This result vastly generalizes previously observed connections between contextuality, relat- ional databases, constraint satisfaction problems and logical paradoxes, and gives further proof that contextual behaviour is not a phenomenon limited to quantum physics, but pervades various domains of mathematics and computer science. Read More

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http://dx.doi.org/10.1098/rsta.2019.0036DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6754714PMC
November 2019

Rota-Baxter operators and post-Lie algebra structures on semisimple Lie algebras.

Commun Algebra 2019 11;47(5):2280-2296. Epub 2019 Jan 11.

Fakultät für Mathematik, Universität Wien, Wien, Austria.

Rota-Baxter operators of weight 1 on are in bijective correspondence to post-Lie algebra structures on pairs , where is complete. We use such Rota-Baxter operators to study the existence and classification of post-Lie algebra structures on pairs of Lie algebras , where is semisimple. We show that for semisimple and , with or simple, the existence of a post-Lie algebra structure on such a pair implies that and are isomorphic, and hence both simple. Read More

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http://dx.doi.org/10.1080/00927872.2018.1536206DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6636903PMC
January 2019

Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms.

J Chem Phys 2019 Jul;151(1):014107

William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA.

In this paper, we discuss the extension of the recently introduced subsystem embedding subalgebra coupled cluster (SES-CC) formalism to unitary CC formalisms. In analogy to the standard single-reference SES-CC formalism, its unitary CC extension allows one to include the dynamical (outside the active space) correlation effects in an SES induced complete active space (CAS) effective Hamiltonian. In contrast to the standard single-reference SES-CC theory, the unitary CC approach results in a Hermitian form of the effective Hamiltonian. Read More

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http://dx.doi.org/10.1063/1.5094643DOI Listing
July 2019
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Ideals and their complements in commutative semirings.

Soft comput 2019 31;23(14):5385-5392. Epub 2018 Aug 31.

1Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic.

We study conditions under which the lattice of ideals of a given a commutative semiring is complemented. At first we check when the annihilator of a given ideal of is a complement of . Further, we study complements of annihilator ideals. Read More

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http://dx.doi.org/10.1007/s00500-018-3493-2DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6559127PMC
August 2018
1 Read

Operations and structures derived from non-associative MV-algebras.

Soft comput 2019 15;23(12):3935-3944. Epub 2018 Jun 15.

1Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic.

The so-called non-associative MV-algebras were introduced recently by the first author and J. Kühr in order to have an appropriate tool for certain logics used in expert systems where associativity of the binary operation is excluded, see, e.g. Read More

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http://dx.doi.org/10.1007/s00500-018-3309-4DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6500511PMC
June 2018
2 Reads

On Construction of Projection Operators.

Authors:
Artur F Izmaylov

J Phys Chem A 2019 Apr 8;123(15):3429-3433. Epub 2019 Apr 8.

Department of Physical and Environmental Sciences , University of Toronto Scarborough , Toronto , Ontario M1C 1A4 , Canada.

The problem of construction of projection operators on eigensubspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution ensures proper physical symmetries in development of approximate methods. The projector form is sought as a function of symmetry operators and their eigenvalues characterizing the eigensubspace of interest. Read More

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http://dx.doi.org/10.1021/acs.jpca.9b01103DOI Listing
April 2019
3 Reads

Clifford Algebras Meet Tree Decompositions.

Algorithmica 2019 30;81(2):497-518. Epub 2018 Jul 30.

Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Warsaw, Poland.

We introduce the non-commutative subset convolution-a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of quaternions used mainly in the quantum field theory. We apply this tool to speed up algorithms counting subgraphs parameterized by the treewidth of a graph. Read More

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http://dx.doi.org/10.1007/s00453-018-0489-3DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6386049PMC
July 2018
2 Reads

Orthogonal Stochastic Duality Functions from Lie Algebra Representations.

J Stat Phys 2019 19;174(1):97-119. Epub 2018 Oct 19.

Technische Universiteit Delft, DIAM, PO Box 5031, 2600 GA Delft, The Netherlands.

We obtain stochastic duality functions for specific Markov processes using representation theory of Lie algebras. The duality functions come from the kernel of a unitary intertwiner between -representations, which provides (generalized) orthogonality relations for the duality functions. In particular, we consider representations of the Heisenberg algebra and . Read More

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http://dx.doi.org/10.1007/s10955-018-2178-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6383627PMC
October 2018
4 Reads

Colombeau algebras without asymptotics.

Authors:
Eduard A Nigsch

J Pseudodiffer Oper Appl 2019 23;10(1):133-154. Epub 2017 Nov 23.

Wolfgang Pauli Institute, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

We present a construction of algebras of generalized functions of Colombeau-type which, instead of asymptotic estimates with respect to a regularization parameter, employs only topological estimates on certain spaces of kernels for its definition. Read More

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http://dx.doi.org/10.1007/s11868-017-0230-zDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6373394PMC
November 2017
11 Reads

Quantum Groups as Hidden Symmetries of Quantum Impurities.

Phys Rev Lett 2018 Dec;121(25):255302

IST Austria (Institute of Science and Technology Austria), Am Campus 1, 3400 Klosterneuburg, Austria.

We present an approach to interacting quantum many-body systems based on the notion of quantum groups, also known as q-deformed Lie algebras. In particular, we show that, if the symmetry of a free quantum particle corresponds to a Lie group G, in the presence of a many-body environment this particle can be described by a deformed group, G_{q}. Crucially, the single deformation parameter, q, contains all the information about the many-particle interactions in the system. Read More

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http://dx.doi.org/10.1103/PhysRevLett.121.255302DOI Listing
December 2018
4 Reads

Developing a new approach for (biological) optimal control problems: Application to optimization of laccase production with a comparison between response surface methodology and novel geometric procedure.

Math Biosci 2019 03 19;309:23-33. Epub 2018 Dec 19.

Fouman Faculty of Engineering, College of Engineering, University of Tehran, P. O. Box 43581-39115, Guilan, Iran. Electronic address:

Laccase production by indigenous fungus, Phanerochaete chrysosporium, requires solving optimal problems to determine the maximum production of the enzyme within a definite time period and conditions specified in the solid-state fermentation process. For this purpose, parallel to response surface methodology, an analytical approach has been proposed based on the advanced concepts of Poisson geometry and Lie groups, which lead to a system of the Hamiltonian equations. Despite the dating of the Hamiltonian approach to solving biological problems, the novelty of this paper is based on the expression of a Hamiltonian system in notions of Poisson geometry, Lie algebras and symmetry groups and first integrals. Read More

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https://linkinghub.elsevier.com/retrieve/pii/S00255564183060
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http://dx.doi.org/10.1016/j.mbs.2018.12.013DOI Listing
March 2019
5 Reads

Reduction of quantum systems and the local Gauss law.

Lett Math Phys 2018 3;108(11):2515-2522. Epub 2018 May 3.

Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.

We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796-1808, 2002; J Math Phys 46:032303, 2004). Read More

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http://dx.doi.org/10.1007/s11005-018-1092-xDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182777PMC
May 2018
2 Reads

A new generalization of -algebras.

Heliyon 2018 Oct 17;4(10):e00863. Epub 2018 Oct 17.

Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand.

In this paper we introduce the notion of -algebras as a generalization of -algebras, we investigate its elementary properties. The aim of this paper is to investigate the concept of filters, left ideals (right ideal, ideal) and fuzzy filters in -algebras. Moreover, we investigate relationships between left ideals and filters in -algebras. Read More

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http://dx.doi.org/10.1016/j.heliyon.2018.e00863DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6197410PMC
October 2018
2 Reads

Graph-algebras-Faithful representations and mediating objects in mathematics.

Authors:
Jessica Carter

Endeavour 2018 Jun - Sep;42(2-3):180-188. Epub 2018 Aug 31.

Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark. Electronic address:

I consider the role of diagrams in contemporary mathematics. More specifically the role of certain diagrams-so-called directed graphs-will be investigated. I propose that these graphs act as mediating objects. Read More

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http://dx.doi.org/10.1016/j.endeavour.2018.07.006DOI Listing
December 2018
2 Reads

Efficient and Robust Direct Image Registration Based on Joint Geometric and Photometric Lie Algebra.

IEEE Trans Image Process 2018 Dec 10;27(12):6010-6024. Epub 2018 Aug 10.

This paper considers the joint geometric and photometric image registration problem. The inverse compositional (IC) algorithm and the efficient second-order minimization (ESM) algorithm are two typical efficient methods applied to the geometric registration problem. Their efficiency stems from the utilization of the group structure of geometric transformations. Read More

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http://dx.doi.org/10.1109/TIP.2018.2864895DOI Listing
December 2018
2 Reads

Lie-Markov Models Derived from Finite Semigroups.

Bull Math Biol 2019 02 2;81(2):361-383. Epub 2018 Aug 2.

School of Physical Sciences, University of Tasmania, Hobart, Australia.

We present and explore a general method for deriving a Lie-Markov model from a finite semigroup. If the degree of the semigroup is k, the resulting model is a continuous-time Markov chain on k-states and, as a consequence of the product rule in the semigroup, satisfies the property of multiplicative closure. This means that the product of any two probability substitution matrices taken from the model produces another substitution matrix also in the model. Read More

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http://dx.doi.org/10.1007/s11538-018-0455-xDOI Listing
February 2019
2 Reads

Quantum heat engines: Limit cycles and exceptional points.

Phys Rev E 2018 Jun;97(6-1):062153

Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel.

We show that the inability of a quantum Otto cycle to reach a limit cycle is connected with the propagator of the cycle being noncompact. For a working fluid consisting of quantum harmonic oscillators, the transition point in parameter space where this instability occurs is associated with a non-Hermitian degeneracy (exceptional point) of the eigenvalues of the propagator. In particular, a third-order exceptional point is observed at the transition from the region where the eigenvalues are complex numbers to the region where all the eigenvalues are real. Read More

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http://dx.doi.org/10.1103/PhysRevE.97.062153DOI Listing
June 2018
3 Reads

Global exponential stability of octonion-valued neural networks with leakage delay and mixed delays.

Neural Netw 2018 Sep 14;105:277-293. Epub 2018 Jun 14.

Department of Computer and Software Engineering, Polytechnic University Timişoara, Blvd. V. Pârvan, No. 2, 300223 Timişoara, Romania. Electronic address:

This paper discusses octonion-valued neural networks (OVNNs) with leakage delay, time-varying delays, and distributed delays, for which the states, weights, and activation functions belong to the normed division algebra of octonions. The octonion algebra is a nonassociative and noncommutative generalization of the complex and quaternion algebras, but does not belong to the category of Clifford algebras, which are associative. In order to avoid the nonassociativity of the octonion algebra and also the noncommutativity of the quaternion algebra, the Cayley-Dickson construction is used to decompose the OVNNs into 4 complex-valued systems. Read More

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http://dx.doi.org/10.1016/j.neunet.2018.05.006DOI Listing
September 2018
3 Reads

Cluster Adjacency Properties of Scattering Amplitudes in N=4 Supersymmetric Yang-Mills Theory.

Phys Rev Lett 2018 Apr;120(16):161601

School of Physics & Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.

We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalize the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the symbol, they dictate which letters can appear consecutively. Read More

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http://dx.doi.org/10.1103/PhysRevLett.120.161601DOI Listing
April 2018
3 Reads

Toward a Definition of Complexity for Quantum Field Theory States.

Phys Rev Lett 2018 Mar;120(12):121602

Max Planck Institute for Gravitational Physics, Potsdam-Golm D-14476, Germany.

We investigate notions of complexity of states in continuous many-body quantum systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of the multiscale entanglement renormalization ansatz. Our proposal for quantifying state complexity is based on the Fubini-Study metric. Read More

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http://dx.doi.org/10.1103/PhysRevLett.120.121602DOI Listing
March 2018
5 Reads

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.

Phys Rev Lett 2018 Feb;120(8):081601

CRST and School of Physics and Astronomy Queen Mary University of London, London E1 4NS, United Kingdom.

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. Read More

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http://dx.doi.org/10.1103/PhysRevLett.120.081601DOI Listing
February 2018
3 Reads

Normal forms for Poisson maps and symplectic groupoids around Poisson transversals.

Lett Math Phys 2018 4;108(3):711-735. Epub 2017 Oct 4.

2IMAPP, Radboud University Nijmegen, 6500 GL Nijmegen, The Netherlands.

Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals. Read More

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http://dx.doi.org/10.1007/s11005-017-1007-2DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5818580PMC
October 2017
2 Reads

Filtrations on Springer fiber cohomology and Kostka polynomials.

Lett Math Phys 2018 26;108(3):679-698. Epub 2017 Sep 26.

2Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ UK.

We prove a conjecture which expresses the bigraded Poisson-de Rham homology of the nilpotent cone of a semisimple Lie algebra in terms of the generalized (one-variable) Kostka polynomials, via a formula suggested by Lusztig. This allows us to construct a canonical family of filtrations on the flag variety cohomology, and hence on irreducible representations of the Weyl group, whose Hilbert series are given by the generalized Kostka polynomials. We deduce consequences for the cohomology of all Springer fibers. Read More

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http://dx.doi.org/10.1007/s11005-017-1002-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5818583PMC
September 2017
3 Reads

Poisson traces, D-modules, and symplectic resolutions.

Lett Math Phys 2018 5;108(3):633-678. Epub 2017 Dec 5.

2Imperial College London, London, UK.

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. Read More

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http://dx.doi.org/10.1007/s11005-017-1024-1DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5818674PMC
December 2017
2 Reads

Perfect -Colored Matchings and -Gonal Tilings.

Graphs Comb 2018 10;34(6):1333-1346. Epub 2018 Nov 10.

1Institute of Software Technology, Graz University of Technology, Graz, Austria.

We derive a simple bijection between geometric plane perfect matchings on 2 points in convex position and triangulations on points in convex position. We then extend this bijection to monochromatic plane perfect matchings on periodically -colored vertices and -gonal tilings of convex point sets. These structures are related to a generalization of Temperley-Lieb algebras and our bijections provide explicit one-to-one relations between matchings and tilings. Read More

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http://dx.doi.org/10.1007/s00373-018-1967-8DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6936358PMC
November 2018

Amenability of coarse spaces and -algebras.

Bull Math Sci 2018 9;8(2):257-306. Epub 2017 Nov 9.

5Department of Mathematics, Penn State University, 109 McAllister Building, University Park, PA 16802 USA.

In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally finite extended metric spaces and for general algebras over fields. In the context of algebras we also study the relation of amenability with proper infiniteness. Read More

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http://link.springer.com/10.1007/s13373-017-0109-6
Publisher Site
http://dx.doi.org/10.1007/s13373-017-0109-6DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6434994PMC
November 2017
18 Reads

as a symmetry of division algebraic ladder operators.

Authors:
C Furey

Eur Phys J C Part Fields 2018 12;78(5):375. Epub 2018 May 12.

1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA UK.

We demonstrate a model which captures certain attractive features of (5) theory, while providing a possible escape from proton decay. In this paper we show how ladder operators arise from the division algebras , , , and . From the () symmetry of these ladder operators, we then demonstrate a model which has much structural similarity to Georgi and Glashow's (5) grand unified theory. Read More

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http://link.springer.com/10.1140/epjc/s10052-018-5844-7
Publisher Site
http://dx.doi.org/10.1140/epjc/s10052-018-5844-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6435233PMC
May 2018
20 Reads

Approximation of the generalized Cauchy-Jensen functional equation in -algebras.

J Inequal Appl 2018 12;2018(1):236. Epub 2018 Sep 12.

1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand.

In this paper, we prove Hyers-Ulam-Rassias stability of -algebra homomorphisms for the following generalized Cauchy-Jensen equation: for all and for any fixed positive integer , which was introduced by Gao et al. [ 3:63-77, 2009], on -algebras by using fixed poind alternative theorem. Moreover, we introduce and investigate Hyers-Ulam-Rassias stability of generalized -derivation for such functional equations on -algebras by the same method. Read More

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http://dx.doi.org/10.1186/s13660-018-1824-6DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6154084PMC
September 2018
2 Reads

What Chern-Simons theory assigns to a point.

Proc Natl Acad Sci U S A 2017 12 5;114(51):13418-13423. Epub 2017 Dec 5.

Mathematical Institute, Oxford University, Oxford OX2 6GG, United Kingdom

We answer the questions, "What does Chern-Simons theory assign to a point?" and "What kind of mathematical object does Chern-Simons theory assign to a point?" Our answer to the first question is representations of the based loop group. More precisely, we identify a certain class of projective unitary representations of the based loop group [Formula: see text] We define the fusion product of such representations, and we prove that, modulo certain conjectures, the Drinfel'd center of that representation category of [Formula: see text] is equivalent to the category of positive energy representations of the free loop group [Formula: see text] The abovementioned conjectures are known to hold when the gauge group is abelian or of type [Formula: see text] Our answer to the second question is bicommutant categories. The latter are higher categorical analogs of von Neumann algebras: They are tensor categories that are equivalent to their bicommutant inside [Formula: see text], the category of bimodules over a hyperfinite [Formula: see text] factor. Read More

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http://dx.doi.org/10.1073/pnas.1711591114DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5754777PMC
December 2017
3 Reads

Convex congruences.

Soft comput 2017 9;21(19):5641-5645. Epub 2016 Aug 9.

Faculty of Mathematics and Geoinformation, Institute of Discrete Mathematics and Geometry, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria.

For an algebra [Formula: see text] belonging to a quasivariety [Formula: see text], the quotient [Formula: see text] need not belong to [Formula: see text] for every [Formula: see text]. The natural question arises for which [Formula: see text]. We consider algebras [Formula: see text] of type (2, 0) where a partial order relation is determined by the operations [Formula: see text] and 1. Read More

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http://dx.doi.org/10.1007/s00500-016-2306-8DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5613104PMC
August 2016
2 Reads

Knowledge-driven computational modeling in Alzheimer's disease research: Current state and future trends.

Alzheimers Dement 2017 Nov 14;13(11):1292-1302. Epub 2017 Sep 14.

Department of Molecular and Integrative Physiology, and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, USA.

Neurodegenerative diseases such as Alzheimer's disease (AD) follow a slowly progressing dysfunctional trajectory, with a large presymptomatic component and many comorbidities. Using preclinical models and large-scale omics studies ranging from genetics to imaging, a large number of processes that might be involved in AD pathology at different stages and levels have been identified. The sheer number of putative hypotheses makes it almost impossible to estimate their contribution to the clinical outcome and to develop a comprehensive view on the pathological processes driving the clinical phenotype. Read More

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http://dx.doi.org/10.1016/j.jalz.2017.08.011DOI Listing
November 2017
25 Reads

Parametric model measurement: reframing traditional measurement ideas in neuropsychological practice and research.

Clin Neuropsychol 2017 Aug - Oct;31(6-7):1047-1072. Epub 2017 Jun 15.

c San Diego State University/University of California San Diego Joint Doctoral Program in Clinical Psychology , San Diego , CA , USA.

Objective: Neuropsychology is an applied measurement field with its psychometric work primarily built upon classical test theory (CTT). We describe a series of psychometric models to supplement the use of CTT in neuropsychological research and test development.

Method: We introduce increasingly complex psychometric models as measurement algebras, which include model parameters that represent abilities and item properties. Read More

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http://dx.doi.org/10.1080/13854046.2017.1334829DOI Listing
February 2018
10 Reads

Simple nuclear *-algebras not isomorphic to their opposites.

Proc Natl Acad Sci U S A 2017 06 30;114(24):6244-6249. Epub 2017 May 30.

Department of Mathematics, Ben-Gurion University of the Negev, Be'er Sheva 84105, Israel.

We show that it is consistent with Zermelo-Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable [Formula: see text]-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra [Formula: see text] or of the canonical anticommutation relations (CAR) algebra. Read More

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http://dx.doi.org/10.1073/pnas.1619936114DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5474777PMC
June 2017
2 Reads

Modeling electron fractionalization with unconventional Fock spaces.

Authors:
Emilio Cobanera

J Phys Condens Matter 2017 Aug 8;29(30):305602. Epub 2017 May 8.

Present address: Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, NH 03755, United States of America.

It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. Read More

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http://dx.doi.org/10.1088/1361-648X/aa718fDOI Listing
August 2017
3 Reads

Quantum field theory and coalgebraic logic in theoretical computer science.

Prog Biophys Mol Biol 2017 11 4;130(Pt A):39-52. Epub 2017 May 4.

Dipartimento di Fisica "E.R.Caianiello", Università di Salerno, INFN Gruppo collegato di Salerno, Fisciano (SA) 84084, Italy. Electronic address:

We suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical dual equivalence between the category of the q-deformed Hopf Coalgebras and the category of the q-deformed Hopf Algebras in quantum field theory (QFT), interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems in far-from-equilibrium conditions, with an evident significance also for biological sciences. Our study is in fact inspired by applications to neuroscience where the brain memory capacity, for instance, has been modeled by using the QFT unitarily inequivalent representations. Read More

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http://dx.doi.org/10.1016/j.pbiomolbio.2017.04.006DOI Listing
November 2017
9 Reads

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras.

Proc Math Phys Eng Sci 2017 Jan;473(2197):20160461

Laboratory 'Group analysis of mathematical models in natural and engineering sciences' , Ufa State Aviation Technical University , 450 008 Ufa, Russia.

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures. Read More

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http://dx.doi.org/10.1098/rspa.2016.0461DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5312120PMC
January 2017
2 Reads

Asymptotic aspect of derivations in Banach algebras.

J Inequal Appl 2017 6;2017(1):36. Epub 2017 Feb 6.

Department of Mathematics, Chungnam National University, 99 Daehangno, Yuseong-gu, Daejeon, 34134 Korea.

We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. Read More

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http://dx.doi.org/10.1186/s13660-017-1308-0DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5306381PMC
February 2017
4 Reads

Higher-Dimensional Automorphic Lie Algebras.

Found Comut Math 2017 11;17(4):987-1035. Epub 2016 Apr 11.

1Department of Mathematics, Faculty of Sciences, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands.

The paper presents the complete classification of Automorphic Lie Algebras based on , where the symmetry group is finite and acts on by inner automorphisms, has no trivial summands, and where the poles are in any of the exceptional -orbits in . A key feature of the classification is the study of the algebras in the context of . This provides on the one hand a powerful tool from the computational point of view; on the other, it opens new questions from an algebraic perspective (e. Read More

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http://dx.doi.org/10.1007/s10208-016-9312-1DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6979533PMC

Global symmetries and SUSY.

Lett Math Phys 2017 13;107(8):1545-1556. Epub 2017 Mar 13.

3Centre for Research in String Theory, Queen Mary University of London, London, E1 4NS UK.

We prove that theories that arise by taking free hypermultiplets and gauging a subgroup of , the non-R global symmetry of the free theory, have a remaining global symmetry, which is a direct sum of unitary, symplectic, and special orthogonal factors. This implies that theories that have but not global symmetries, such as Gaiotto's theories, are not likely to arise as IR fixed points of RG flows from weakly coupled gauge theories. Read More

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http://dx.doi.org/10.1007/s11005-017-0952-0DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6961485PMC

Infinite order decompositions of C*-algebras.

Springerplus 2016 21;5(1):1827. Epub 2016 Oct 21.

Faculty of Mathematics, Andizhan State University, Andizhan, Uzbekistan.

The present paper is devoted to infinite order decompositions of C*-algebras. It is proved that an infinite order decomposition (IOD) of a C*-algebra forms the complexification of an order unit space, and, if the C*-algebra is monotone complete (not necessarily weakly closed) then its IOD is also monotone complete ordered vector space. Also it is established that an IOD of a C*-algebra is a C*-algebra if and only if this C*-algebra is a von Neumann algebra. Read More

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http://dx.doi.org/10.1186/s40064-016-3468-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5074999PMC
October 2016
6 Reads

Analytic real algebras.

Springerplus 2016 29;5(1):1684. Epub 2016 Sep 29.

Department of Mathematics, Chungbuk National University, Cheongju, 28644 Korea.

In this paper we construct some real algebras by using elementary functions, and discuss some relations between several axioms and its related conditions for such functions. We obtain some conditions for real-valued functions to be a (edge) -algebra. Read More

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http://dx.doi.org/10.1186/s40064-016-3334-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5042926PMC
September 2016
9 Reads

On discrete evolutionary dynamics driven by quadratic interactions.

Theory Biosci 2016 Dec 21;135(4):187-200. Epub 2016 Jul 21.

Laboratoire de Physique Théorique et Modélisation, CNRS-UMR 8089 et Université de Cergy-Pontoise, 2 Avenue Adolphe Chauvin, 95302, Cergy-Pontoise, France.

After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or train) algebras. In this setup, any quadratic offspring interaction can produce any type of offspring and after the use of specific changes of basis, we study the evolution and possible stability of some examples. We also consider some examples that cannot be treated using the framework of genetic algebras. Read More

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http://dx.doi.org/10.1007/s12064-016-0232-zDOI Listing
December 2016
2 Reads

Ideals and primitive elements of some relatively free Lie algebras.

Springerplus 2016 22;5(1):833. Epub 2016 Jun 22.

Department of Mathematics, Çukurova University, 01330 Adana, Turkey.

Let F be a free Lie algebra of finite rank over a field K. We prove that if an ideal [Formula: see text] of the algebra [Formula: see text] contains a primitive element [Formula: see text] then the element [Formula: see text] is primitive. We also show that, in the Lie algebra [Formula: see text] there exists an element [Formula: see text] such that the ideal [Formula: see text] contains a primitive element [Formula: see text] but, [Formula: see text] and [Formula: see text] are not conjugate by means of an inner automorphism. Read More

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http://dx.doi.org/10.1186/s40064-016-2545-2DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4917519PMC
July 2016
3 Reads

Neurons the decision makers, Part I: The firing function of a single neuron.

Authors:
Thomas Saaty

Neural Netw 2017 Feb 6;86:102-114. Epub 2016 May 6.

University of Pittsburgh, United States. Electronic address:

This paper is concerned with understanding synthesis of electric signals in the neural system based on making pairwise comparisons. Fundamentally, every person and every animal are born with the talent to compare stimuli from things that share properties in space or over time. Comparisons always need experience to distinguish among things. Read More

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http://dx.doi.org/10.1016/j.neunet.2016.04.003DOI Listing
February 2017
2 Reads

Quantum walks, deformed relativity and Hopf algebra symmetries.

Philos Trans A Math Phys Eng Sci 2016 May;374(2068)

QUIT group, Dipartimento di Fisica, Università degli Studi di Pavia, and INFN, Gruppo IV, via Bassi 6, 27100 Pavia, Italy.

We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. Read More

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http://dx.doi.org/10.1098/rsta.2015.0232DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4843635PMC
May 2016
4 Reads

The birth of out of the spinors of the icosahedron.

Proc Math Phys Eng Sci 2016 Jan;472(2185):20150504

Departments of Mathematics and Biology , York Centre for Complex Systems Analysis, University of York , Heslington, York YO10 5GG, UK.

is prominent in mathematics and theoretical physics, and is generally viewed as an exceptional symmetry in an eight-dimensional (8D) space very different from the space we inhabit; for instance, the Lie group features heavily in 10D superstring theory. Contrary to that point of view, here we show that the root system can in fact be constructed from the icosahedron alone and can thus be viewed purely in terms of 3D geometry. The 240 roots of arise in the 8D Clifford algebra of 3D space as a double cover of the 120 elements of the icosahedral group, generated by the root system . Read More

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http://dx.doi.org/10.1098/rspa.2015.0504DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4786034PMC
January 2016
5 Reads