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Journal articles on the topic 'Higher Dimensional Algebra of Networks'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Baianu, I. C., R. Brown, G. Georgescu, and J. F. Glazebrook. "Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks." Axiomathes 16, no. 1-2 (2006): 65–122. http://dx.doi.org/10.1007/s10516-005-3973-8.

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2

Duleba, I. "Impact of control representations on efficiency of local nonholonomic motion planning." Bulletin of the Polish Academy of Sciences: Technical Sciences 59, no. 2 (2011): 213–18. http://dx.doi.org/10.2478/v10175-011-0026-x.

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Impact of control representations on efficiency of local nonholonomic motion planning In this paper various control representations selected from a family of harmonic controls were examined for the task of locally optimal motion planning of nonholonomic systems. To avoid dependence of results either on a particular system or a current point in a state space, considerations were carried out in a sub-space of a formal Lie algebra associated with a family of controlled systems. Analytical and simulation results are presented for two inputs and three dimensional state space and some hints for high

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3

C., Baianu, and F. Glazebrook J. "BRAIN Journal - Categorial Ontology of Complex Systems, Meta-Systems and Levels: The Emergence of Life, Human Consciousness and Society." BRAIN. Broad Research in Artificial Intelligence and Neuroscience 1, SPECIAL ISSUE ON COMPLEXITY IN SCIENCES AND ARTIFICIAL INTELLIGENCE (2010): 119–207. https://doi.org/10.5281/zenodo.1036710.

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ABSTRACT 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 consciousness leads to novel patterns of relations that emerge in super- and ultra- complex systems in terms of compositions of local procedures [1]. The claim is defended in this paper that human consciousness is unique and should be viewed as a

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4

Zhang, Xiaoyu, Yichao Wang, Xiting Peng, and Chaofeng Zhang. "An Efficient Method for Solving Two-Dimensional Partial Differential Equations with the Deep Operator Network." Axioms 12, no. 12 (2023): 1095. http://dx.doi.org/10.3390/axioms12121095.

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Partial differential equations (PDEs) usually apply for modeling complex physical phenomena in the real world, and the corresponding solution is the key to interpreting these problems. Generally, traditional solving methods suffer from inefficiency and time consumption. At the same time, the current rise in machine learning algorithms, represented by the Deep Operator Network (DeepONet), could compensate for these shortcomings and effectively predict the solutions of PDEs by learning the operators from the data. The current deep learning-based methods focus on solving one-dimensional PDEs, but

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5

Chen, Tinggui, Xiaohua Yin, Jianjun Yang, Guodong Cong, and Guoping Li. "Modeling Multi-Dimensional Public Opinion Process Based on Complex Network Dynamics Model in the Context of Derived Topics." Axioms 10, no. 4 (2021): 270. http://dx.doi.org/10.3390/axioms10040270.

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With the rapid development of the Internet, the speed with which information can be updated and propagated has accelerated, resulting in wide variations in public opinion. Usually, after the occurrence of some newsworthy event, discussion topics are generated in networks that influence the formation of initial public opinion. After a period of propagation, some of these topics are further derived into new subtopics, which intertwine with the initial public opinion to form a multidimensional public opinion. This paper is concerned with the formation process of multi-dimensional public opinion i

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6

Baez, John C., and Martin Neuchl. "Higher Dimensional Algebra." Advances in Mathematics 121, no. 2 (1996): 196–244. http://dx.doi.org/10.1006/aima.1996.0052.

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7

Bose, Bella, Arash Shamaei, and Mary Flahive. "Higher Dimensional Gaussian Networks." IEEE Transactions on Parallel and Distributed Systems 27, no. 9 (2016): 2628–38. http://dx.doi.org/10.1109/tpds.2015.2504936.

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8

Garcı́a, Fabián, Julio Solano, Ivan Stojmenovic, and Milos Stojmenovic. "Higher dimensional hexagonal networks." Journal of Parallel and Distributed Computing 63, no. 11 (2003): 1164–72. http://dx.doi.org/10.1016/j.jpdc.2003.07.001.

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9

CARLE, JEAN, JEAN-FRÉDŔIC MYOUPO, and IVAN STOJMENOVIC. "HIGHER DIMENSIONAL HONEYCOMB NETWORKS." Journal of Interconnection Networks 02, no. 04 (2001): 391–420. http://dx.doi.org/10.1142/s0219265901000464.

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We define the higher dimensional honeycomb graphs as a generalization of hexagonal plane tessellation, and consider it as a multiprocessor interconnection network. A 3-D honeycomb mesh network with n nodes has degree 4 and diameter approximately 3.63n. The network cost, defined as the product of degree and diameter, is about 20 percents better for the 3-D honeycomb than for the 3-D mesh. We describe the addressing scheme, the routing and broadcasting algorithms for three-dimensional and higher dimensional honeycombs. Furthermore, a formula for the diameter of a higher dimensional honeycomb net

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10

Baez, John C., and Laurel Langford. "Higher-dimensional algebra IV: 2-tangles." Advances in Mathematics 180, no. 2 (2003): 705–64. http://dx.doi.org/10.1016/s0001-8708(03)00018-5.

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11

Baez, John C., and James Dolan. "Higher-Dimensional Algebra III.n-Categories and the Algebra of Opetopes." Advances in Mathematics 135, no. 2 (1998): 145–206. http://dx.doi.org/10.1006/aima.1997.1695.

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12

Hussain, Zaid, and Arash Shamaei. "Higher dimensional Eisenstein–Jacobi networks." Journal of Parallel and Distributed Computing 102 (April 2017): 91–102. http://dx.doi.org/10.1016/j.jpdc.2016.11.006.

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13

Baez, John C. "Higher-Dimensional Algebra II. 2-Hilbert Spaces." Advances in Mathematics 127, no. 2 (1997): 125–89. http://dx.doi.org/10.1006/aima.1997.1617.

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14

Das, A., S. Okubo, and S. A. Pernice. "Higher-Dimensional SUSY Quantum Mechanics." Modern Physics Letters A 12, no. 08 (1997): 581–88. http://dx.doi.org/10.1142/s0217732397000601.

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Higher-dimensional supersymmetric quantum mechanics is studied. General properties of the two-dimensional case are presented. For three spatial dimensions or higher, a spin structure is shown to arise naturally from the nonrelativistic supersymmetry algebra.

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15

Baez, John C., and James Dolan. "Higher‐dimensional algebra and topological quantum field theory." Journal of Mathematical Physics 36, no. 11 (1995): 6073–105. http://dx.doi.org/10.1063/1.531236.

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16

Gurevich, D. I., and P. A. Saponov. "Higher-Dimensional Representations of the Reflection Equation Algebra." Theoretical and Mathematical Physics 139, no. 1 (2004): 486–99. http://dx.doi.org/10.1023/b:tamp.0000022741.80096.b3.

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17

Valenzuela, Mauricio. "Higher Spin Symmetries of the Free Schrödinger Equation." Advances in Mathematical Physics 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/5739410.

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It is shown that the Schrödinger symmetry algebra of a free particle indspatial dimensions can be embedded into a representation of the higher spin algebra. The latter spans an infinite dimensional algebra of higher-order symmetry generators of the free Schrödinger equation. An explicit representation of the maximal finite dimensional subalgebra of the higher spin algebra is given in terms of nonrelativistic generators. We show also how to convert Vasiliev’s equations into an explicit nonrelativistic covariant form, such that they might apply to nonrelativistic systems. Our procedure reveals t

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18

Chung, Won Sang. "Generalized higher-order Snyder model." Modern Physics Letters A 32, no. 19 (2017): 1750098. http://dx.doi.org/10.1142/s0217732317500985.

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In this paper we consider the higher-order generalization of the Snyder algebra. We find the modified inner product for this algebra. We also discuss the one-dimensional hydrogen atom eigenvalue problem. We find the invariant phase space volume for the generalized Snyder algebra. Finally we use the density of states in three dimension to discuss the Maxwellian distribution and cosmological constant.

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19

FRADKIN, E. S., and V. YA. LINETSKY. "INFINITE-DIMENSIONAL GENERALIZATIONS OF SIMPLE LIE ALGEBRAS." Modern Physics Letters A 05, no. 24 (1990): 1967–77. http://dx.doi.org/10.1142/s0217732390002249.

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Infinite-dimensional algebras associated with simple finite-dimensional Lie algebra g are considered. Higher-spin generalizations of sl(2) are studied in detail. Those of the Virasoro algebra are viewed as their "analytic continuations". Applications in higher-spin theory and in conformal QFT are discussed.

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20

XU, XIULI, XINBO GONG, YUFENG ZHANG, and MING SONG. "A NEW HIGHER-DIMENSIONAL LOOP ALGEBRA AND ITS APPLICATION." Modern Physics Letters B 22, no. 18 (2008): 1757–65. http://dx.doi.org/10.1142/s0217984908016455.

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With the help of the cycled numbers, a higher-dimensional loop algebra is constructed, whose dimension is 4(s+1). For computing convenience, we only take s = 1 as an example. By employing loop algebra [Formula: see text], a generalized Toda hierarchy is obtained with possessing two-Hamiltonian structure, which is also reduced to the well-known Toda hierarchy.

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21

Mahfonz, Amr M., Hany N. Zaky, Ahmed S. Ismail, and Eiman T. Abou El Dahab. "Mathematical Model for Omnidirectional Sensor Network Using Clifford Algebra." Journal of Physics: Conference Series 2304, no. 1 (2022): 012001. http://dx.doi.org/10.1088/1742-6596/2304/1/012001.

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Abstract Wireless Sensor Networks are now very important and more usable in industrial, agricultural, commercial and military applications. Studies on wireless sensor networks have several aspects such as location, deployment, tracking. The most critical parameter of studying wireless sensor networks is sensor nodes deployment to obtain optimum coverage for the network used to minimize energy and cost. The goal of this work is to introduce a new coverage proposal to calculate the required number of sensors for a wireless sensor network in order to achieve optimum coverage for a particular task

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22

Farhi, Nadir. "A Min-Plus Algebra System Theory for Traffic Networks." Mathematics 11, no. 19 (2023): 4028. http://dx.doi.org/10.3390/math11194028.

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In this article, we introduce a comprehensive system theory based on the min-plus algebra of 2×2 matrices of functions. This novel approach enables the algebraic construction of traffic networks and the analytical derivation of performance bounds for such networks. We use the term “traffic networks” or “congestion networks” to refer to networks where high densities of transported particles lead to flow drops, as commonly observed in road networks. Initially, we present a model for a segment or section of a link within the network and demonstrate that the dynamics can be expressed linearly with

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23

Ritter, Patricia, and Christian Sämann. "L∞-algebra models and higher Chern–Simons theories." Reviews in Mathematical Physics 28, no. 09 (2016): 1650021. http://dx.doi.org/10.1142/s0129055x16500215.

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We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the first part, we review in detail how higher Chern–Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of [Formula: see text]-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In the second part, we demonstrate that Nambu–Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct o

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24

Bokhari, Ashfaque H., and A. H. Kara. "Gauge symmetries and isometries in higher dimensions." Modern Physics Letters A 35, no. 37 (2020): 2050310. http://dx.doi.org/10.1142/s0217732320503101.

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We study the invariance properties of five-dimensional metrics and their corresponding geodesic equations of motion. In this context a number of five-dimensional models of the Einstein–Gauss–Bonnet (EGB) theory leading to black holes, wormholes and spacetime horns arising in a variety of situations are discussed in the context of variational symmetries of which each vector field, via Noether’s theorem (NT), provides a nontrivial conservation law. In particular, it is shown that algebraic structure of isometries and the variational conservation laws of the five-dimensional Einstein–Bonnet metri

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25

Rieffel, Marc A. "Projective Modules over Higher-Dimensional Non-Commutative Tori." Canadian Journal of Mathematics 40, no. 2 (1988): 257–338. http://dx.doi.org/10.4153/cjm-1988-012-9.

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The non-commutative tori provide probably the most accessible interesting examples of non-commutative differentiable manifolds. We can identify an ordinary n-torus Tn with its algebra, C(Tn), of continuous complex-valued functions under pointwise multiplication. But C(Tn) is the universal C*-algebra generated by n commuting unitary operators. By definition, [15, 16, 50], a non-commutative n-torus is the universal C*-algebra generated by n unitary operators which, while they need not commute, have as multiplicative commutators various fixed scalar multiples of the identity operator. As Connes h

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26

Spicer, Calum. "Higher-dimensional foliated Mori theory." Compositio Mathematica 156, no. 1 (2019): 1–38. http://dx.doi.org/10.1112/s0010437x19007681.

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We develop some foundational results in a higher-dimensional foliated Mori theory, and show how these results can be used to prove a structure theorem for the Kleiman–Mori cone of curves in terms of the numerical properties of $K_{{\mathcal{F}}}$ for rank 2 foliations on threefolds. We also make progress toward realizing a minimal model program (MMP) for rank 2 foliations on threefolds.

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27

Falda, Marco. "Spatial Reasoning with Integrated Qualitative-Metric Fuzzy Constraint Networks." JUCS - Journal of Universal Computer Science 16, no. (11) (2010): 1390–409. https://doi.org/10.3217/jucs-016-11-1390.

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Qualitative Spatial Reasoning can be greatly improved if metric information can be represented and reasoning can be performed on it; moreover, modelling vagueness and uncertainty in both qualitative and metric relations allows reasoning in a more flexible way about data coming from real world. In this paper Rectangle Algebra is integrated with a bi-dimensional Point Algebra by defining a set of 25 Point-Region relations, in this way a Spatial Qualitative Algebra (SQA) among point and regions is obtained. Besides, SQA is extended to deal with uncertain data by means of the Fuzzy Sets Theory. Fu

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28

MARTÍNEZ-MORÁS, FERNANDO, JAVIER MAS, and EDUARDO RAMOS. "DIFFEOMORPHISMS FROM HIGHER-DIMENSIONAL W-ALGEBRAS." Modern Physics Letters A 08, no. 23 (1993): 2189–97. http://dx.doi.org/10.1142/s0217732393001914.

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Classical W-algebras in higher dimensions have recently been constructed. In this letter we show that there is a finitely generated subalgebra which is isomorphic to the algebra of local diffeomorphisms in D dimensions. Moreover, there is a tower of infinitely many fields transforming under this subalgebra as symmetric tensorial one-densities. We also unravel a structure isomorphic to the Schouten symmetric bracket, providing a natural generalization of w∞ in higher dimensions.

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29

Zhang, Yufeng, and Wang Yan. "A higher-dimensional Lie algebra and its decomposed subalgebras." Physics Letters A 360, no. 1 (2006): 92–98. http://dx.doi.org/10.1016/j.physleta.2006.07.066.

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30

Basener, Richard F. "Higher Dimensional Spaces of Functions on the Spectrum of a Uniform Algebra." Canadian Mathematical Bulletin 50, no. 1 (2007): 3–10. http://dx.doi.org/10.4153/cmb-2007-001-4.

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AbstractIn this paper we introduce a nested family of spaces of continuous functions defined on the spectrum of a uniform algebra. The smallest space in the family is the uniform algebra itself. In the “finite dimensional” case, from some point on the spaces will be the space of all continuous complex-valued functions on the spectrum. These spaces are defined in terms of solutions to the nonlinear Cauchy–Riemann equations as introduced by the author in 1976, so they are not generally linear spaces of functions. However, these spaces do shed light on the higher dimensional properties of a unifo

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31

Inami, Takeo, Tatsuya Ueno, and Hiroaki Kanno. "Higher-Dimensional WZW Model on Kähler Manifold and Toroidal Lie Algebra." Modern Physics Letters A 12, no. 36 (1997): 2757–64. http://dx.doi.org/10.1142/s0217732397002909.

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We construct a generalization of the two-dimensional Wess–Zumino–Witten model on a 2n-dimensional Kähler manifold as a group-valued nonlinear sigma model with an anomaly term containing the Kähler form. The model is shown to have an infinite-dimensional symmetry which generates an n-toroidal Lie algebra. The classical equation of motion turns out to be the Donaldson–Uhlenbeck–Yau equation, which is a 2n-dimensional generalization of the self-dual Yang–Mills equation.

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32

Pourabbas, A. "Higher Dimensional Cohomology of Weighted Sequence Algebras." Journal of the Australian Mathematical Society 75, no. 1 (2003): 57–68. http://dx.doi.org/10.1017/s1446788700003475.

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AbstractIt is well known that c0(Z) is amenable and so its global dimension is zero. In this paper we will investigate the cyclic and Hochschild cohomology of Banach algebra c0 (Z, ω-1) and its unitisation with coefficients in its dual space, where ω is a weight on Z which satisfies inf {ω(i)} = 0.Moreover we show that the weak homological bi-dimension of c0 (Z, ω-1) is infinity.

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33

Kruckman, Alex, and Aristotelis Panagiotopoulos. "Higher-dimensional obstructions for star reductions." Fundamenta Mathematicae 255, no. 2 (2021): 209–30. http://dx.doi.org/10.4064/fm35-2-2021.

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34

Roseman, Dennis. "Elementary moves for higher dimensional knots." Fundamenta Mathematicae 184 (2004): 291–310. http://dx.doi.org/10.4064/fm184-0-16.

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35

Bienvenu, Pierre-Yves. "A higher-dimensional Siegel–Walfisz theorem." Acta Arithmetica 179, no. 1 (2017): 79–100. http://dx.doi.org/10.4064/aa8600-10-2016.

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36

Cegarra, A. M., and M. Bullejos. "Cohomology and higher dimensional Baer invariants." Journal of Algebra 132, no. 2 (1990): 321–39. http://dx.doi.org/10.1016/0021-8693(90)90133-9.

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37

Carls, Robert, David Kohel, and David Lubicz. "Higher-dimensional 3-adic CM construction." Journal of Algebra 319, no. 3 (2008): 971–1006. http://dx.doi.org/10.1016/j.jalgebra.2007.11.016.

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38

Abdulabbas Hassoon, Kawthar, and Hassan Rashed Yassein. "A new multi-dimensional public key cryptosystem via KAH-Octo algebra." Journal of Discrete Mathematical Sciences and Cryptography 28, no. 2 (2025): 349–54. https://doi.org/10.47974/jdmsc-2018.

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The security of information must be maintained is necessary to be maintained because different data is distributed via networks that raises the possibility of data loss. In this paper, is concerned with establishing a new public key cryptosystem called KAOTR using KAHOcto algebra, which consists of two public keys and four private keys by submitting a high speed and acceptable security.

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39

Ivanov, A. O., I. V. Ptitsyna, and A. A. Tuzhilin. "CLASSIFICATION OF CLOSED MINIMAL NETWORKS ON FLAT TWO-DIMENSIONAL TORI." Russian Academy of Sciences. Sbornik Mathematics 77, no. 2 (1994): 391–425. http://dx.doi.org/10.1070/sm1994v077n02abeh003448.

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40

Wang, Haiying, Jack Murdoch Moore, Michael Small, Jun Wang, Huijie Yang, and Changgui Gu. "Epidemic dynamics on higher-dimensional small world networks." Applied Mathematics and Computation 421 (May 2022): 126911. http://dx.doi.org/10.1016/j.amc.2021.126911.

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41

Khan, Usman A., Soummya Kar, and José M. F. Moura. "Higher Dimensional Consensus: Learning in Large-Scale Networks." IEEE Transactions on Signal Processing 58, no. 5 (2010): 2836–49. http://dx.doi.org/10.1109/tsp.2010.2042482.

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42

Li, Haisheng. "A higher-dimensional generalization of the notion of vertex algebra." Journal of Algebra 262, no. 1 (2003): 1–41. http://dx.doi.org/10.1016/s0021-8693(03)00018-8.

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43

Lekili, Yankı, and Alexander Polishchuk. "Homological mirror symmetry for higher-dimensional pairs of pants." Compositio Mathematica 156, no. 7 (2020): 1310–47. http://dx.doi.org/10.1112/s0010437x20007150.

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Using Auroux’s description of Fukaya categories of symmetric products of punctured surfaces, we compute the partially wrapped Fukaya category of the complement of $k+1$ generic hyperplanes in $\mathbb{CP}^{n}$, for $k\geqslant n$, with respect to certain stops in terms of the endomorphism algebra of a generating set of objects. The stops are chosen so that the resulting algebra is formal. In the case of the complement of $n+2$ generic hyperplanes in $\mathbb{C}P^{n}$ ($n$-dimensional pair of pants), we show that our partial wrapped Fukaya category is equivalent to a certain categorical resolut

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44

POLYAKOV, DIMITRI. "NEW DISCRETE STATES IN TWO-DIMENSIONAL SUPERGRAVITY." International Journal of Modern Physics A 22, no. 07 (2007): 1375–94. http://dx.doi.org/10.1142/s0217751x07035148.

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Two-dimensional string theory is known to contain the set of discrete states that are the SU (2) multiplets generated by the lowering operator of the SU (2) current algebra. Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. In this paper we show that the interaction of d = 2 superstrings with the superconformal β - γ ghosts enlarges the actual algebra of the dimension 1 currents and hence the new ghost-dependent discrete states appear. Generally, these states are the SU (N) multiplets if the algebra includes the currents of ghost numbers n : -N ≤ n

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45

The, Nguyen Van, and Le Anh Vinh. "Expanding phenomena over higher dimensional matrix rings." Journal of Number Theory 216 (November 2020): 174–91. http://dx.doi.org/10.1016/j.jnt.2020.02.011.

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46

Cegarra, A. M., M. Bullejos, and A. R. Garzón. "Higher dimensional obstruction theory in algebraic categories." Journal of Pure and Applied Algebra 49, no. 1-2 (1987): 43–102. http://dx.doi.org/10.1016/0022-4049(87)90123-x.

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47

BORISOV, DENNIS. "WHAT IS THE HIGHER-DIMENSIONAL INFINITESIMAL GROUPOID OF A MANIFOLD?" Journal of the Australian Mathematical Society 90, no. 2 (2011): 155–70. http://dx.doi.org/10.1017/s1446788711001248.

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AbstractThe construction (by Kapranov) of the space of infinitesimal paths on a manifold is extended to include higher-dimensional infinitesimal objects, encoding contractions of infinitesimal loops. This full infinitesimal groupoid is shown to have the algebra of polyvector fields as its nonlinear cohomology.

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48

FRADKIN, E. S., and V. YA. LINETSKY. "A NEW CLASS OF INFINITE-DIMENSIONAL LIE ALGEBRAS: AN ANALYTICAL CONTINUATION OF THE ARBITRARY FINITE-DIMENSIONAL SEMISIMPLE LIE ALGEBRA." Modern Physics Letters A 05, no. 15 (1990): 1167–74. http://dx.doi.org/10.1142/s021773239000130x.

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With any semisimple Lie algebra g we can associate an infinite-dimensional Lie algebra AC (g) which is an analytic continuation of g from its root system to its root lattice. The manifest expressions for the structure constants of analytic continuations of the symplectic Lie algebras sp 2n are obtained by the Poisson-bracket realizations method and AC (g) for g = sl n and so n are discussed. The representations, central extension, supersymmetric and higher spin generalizations are considered. The Virasoro theory is a particular case where g = sp 2.

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49

Shang, Yilun. "Lie algebraic discussion for affinity based information diffusion in social networks." Open Physics 15, no. 1 (2017): 705–11. http://dx.doi.org/10.1515/phys-2017-0083.

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AbstractIn this paper we develop a dynamical information diffusion model which features the affinity of people with information disseminated in social networks. Four types of agents,i.e., susceptible, informed, known, and refractory ones, are involved in the system, and the affinity mechanism composing of an affinity threshold which represents the fitness of information to be propagated is incorporated. The model can be generally described by a time-inhomogeneous Markov chain, which is governed by its master (Kolmogorov) equation. Based on the Wei-Norman method, we derive analytical solutions

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50

Chapman, Robin. "Reciprocity laws for generalized higher dimensional Dedekind sums." Acta Arithmetica 93, no. 2 (2000): 189–99. http://dx.doi.org/10.4064/aa-93-2-189-199.

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