Relevant bibliographies by topics / Higher Dimensional Algebra of Networks

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Higher Dimensional Algebra of Networks'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Higher Dimensional Algebra of Networks"

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Yoon, Seok Ho. "Explicit class field theory : one dimensional and higher dimensional." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/50367/.

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This thesis investigates class field theory for one dimensional fields and higher dimensional fields. For one dimensional fields we cover the cases of local fields and global fields of positive characteristic. For higher dimensional fields we study the case of higher local fields of positive characteristic. The main content of the thesis is divided into two parts. The first part solves several problems directly related to Neukirch's axiomatic class field theory method. We first prove the famous Hilbert 90 Theorem in the case of tamely ramified extensions of local fields in an explicit way. Thi
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Oliver, Thomas David. "Higher dimensional adeles, mean-periodicity and zeta functions of arithmetic surfaces." Thesis, University of Nottingham, 2014. http://eprints.nottingham.ac.uk/14518/.

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This thesis is concerned with the analytic properties of arithmetic zeta functions, which remain largely conjectural at the time of writing. We will focus primarily on the most basic amongst them - meromorphic continuation and functional equation. Our weapon of choice is the so-called “mean-periodicity correspondence”, which provides a passage between nicely behaved arithmetic schemes and mean-periodic functions in certain functional spaces. In what follows, there are two major themes. 1. The comparison of the mean-periodicity properties of zeta functions with the much better known, but noneth
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CHESSA, Stefano. "Quantum Information Capacities for Networks and Higher Dimensional Channels." Doctoral thesis, Scuola Normale Superiore, 2022. https://hdl.handle.net/11384/125264.

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Griffiths, Rhiannon Cerys. "Slices of Globular Operads for Higher Categories." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1623155240596704.

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Books on the topic "Higher Dimensional Algebra of Networks"

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Makkai, Mihály. Models, logics, and higher-dimensional categories: A tribute to the work of Mihaly Makkai. American Mathematical Society, 2011.

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editor, Donagi Ron, Douglas, Michael (Michael R.), editor, Kamenova Ljudmila 1978 editor, and Roček M. (Martin) editor, eds. String-Math 2013: Conference, June 17-21, 2013, Simons Center for Geometry and Physics, Stony Brook, NY. American Mathematical Society, 2014.

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Fonseca, Carlos M. da. A panorama of mathematics: Pure and applied : Conference on Mathematics and Its Applications, November 14-17, 2014, Kuwait University, Safat, Kuwait. American Mathematical Society, 2016.

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Peternell, Thomas, and Joichi Miyaoka. Geometry of Higher Dimensional Algebraic Varieties. Birkhauser Verlag, 2012.

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Peternell, Thomas, and Joichi Miyaoka. Geometry of Higher Dimensional Algebraic Varieties (Oberwolfach Seminars). Birkhäuser Basel, 2004.

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(Editor), Marco Andreatta, and Thomas Peternell (Editor), eds. Higher Dimensional Complex Varieties: Proceedings of the International Conference Held in Trento, Italy, June 15-24, 1994. Walter de Gruyter, 1996.

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Invitation to Nonlinear Algebra. American Mathematical Society, 2021.

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Surveys on Recent Developments in Algebraic Geometry. American Mathematical Society, 2017.

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Algebraic Groups: Structure and Actions. American Mathematical Society, 2017.

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Noncommutative geometry and global analysis: Conference in honor of Henri Moscovici, June 29-July 4, 2009, Bonn, Germany. American Mathematical Society, 2011.

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Book chapters on the topic "Higher Dimensional Algebra of Networks"

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Cubarsi, Rafael. "Higher-dimensional chords." In Chord Transformations in Higher-Dimensional Networks. Chapman and Hall/CRC, 2025. https://doi.org/10.1201/9781003597964-5.

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Brînzănescu, Vasile. "Hodge Invariants of Higher-Dimensional Analogues of Kodaira Surfaces." In Bridging Algebra, Geometry, and Topology. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09186-0_6.

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Takayama, Yukihide. "Extraction of concurrent processes from higher dimensional automata." In Trees in Algebra and Programming — CAAP '96. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61064-2_30.

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Cubarsi, Rafael. "Modes and chords." In Chord Transformations in Higher-Dimensional Networks. Chapman and Hall/CRC, 2025. https://doi.org/10.1201/9781003597964-2.

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Cubarsi, Rafael. "Introduction." In Chord Transformations in Higher-Dimensional Networks. Chapman and Hall/CRC, 2025. https://doi.org/10.1201/9781003597964-1.

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Cubarsi, Rafael. "Operations on the mode." In Chord Transformations in Higher-Dimensional Networks. Chapman and Hall/CRC, 2025. https://doi.org/10.1201/9781003597964-7.

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Cubarsi, Rafael. "Operations on the root." In Chord Transformations in Higher-Dimensional Networks. Chapman and Hall/CRC, 2025. https://doi.org/10.1201/9781003597964-6.

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Cubarsi, Rafael. "Subchords." In Chord Transformations in Higher-Dimensional Networks. Chapman and Hall/CRC, 2025. https://doi.org/10.1201/9781003597964-3.

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Cubarsi, Rafael. "Trichords." In Chord Transformations in Higher-Dimensional Networks. Chapman and Hall/CRC, 2025. https://doi.org/10.1201/9781003597964-4.

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Cubarsi, Rafael. "Chord transformations." In Chord Transformations in Higher-Dimensional Networks. Chapman and Hall/CRC, 2025. https://doi.org/10.1201/9781003597964-8.

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Conference papers on the topic "Higher Dimensional Algebra of Networks"

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Sergienko, Alexander V., David S. Simon, Anthony Manni, Christopher Schwarze, and Abdoulaye Ndao. "Higher-dimensional HOM effect with directionally unbiased linear-optical multiports enable entangled state routing in quantum networks." In Quantum Communications and Quantum Imaging XXII, edited by Keith S. Deacon and Ronald E. Meyers. SPIE, 2024. http://dx.doi.org/10.1117/12.3027277.

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Schwarze, Christopher, David S. Simon, Anthony Manni, Abdoulaye Ndao, and Alexander V. Sergienko. "Higher-dimensional HOM effect with directionally unbiased linear-optical multiports enables entangled state routing in quantum networks." In Quantum 2.0. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/quantum.2024.qth3a.23.

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A four-port beamsplitter only maps between two input and output modes. We introduce a more general four-port scatterer that supports a broader class of state transformations, enabling a higher-dimensional HOM effect and entangled state routing.
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Verma, Gajanand, William Heath, and Constantinos Theodoropoulos. "Efficient approximation of the Koopman operator for large-scale nonlinear systems." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.169758.

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Implementing Model Predictive Control (MPC) for large-scale nonlinear systems is often computationally challenging due to the intensive online optimization required. To address this, various reduced-order linearization techniques have been developed. The Koopman operator linearizes a nonlinear system by mapping it into an infinite-dimensional space of observables, enabling the application of linear control strategies. While Artificial Neural Networks (ANNs) can approximate the Koopman operator in a data-driven manner, training these networks becomes computationally intensive for high-dimension
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Vlasov, Alexander Y. "Algebra of quantum computations with higher dimensional systems." In SPIE Proceedings, edited by Yuri I. Ozhigov. SPIE, 2003. http://dx.doi.org/10.1117/12.517863.

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Assefa, Dawit, Harry Keller, and David A. Jaffray. "Multi-Parametric MR Image Processing using Higher Dimensional Vector Algebra." In Imaging and Signal Processing in Healthcare and Technology. ACTAPRESS, 2011. http://dx.doi.org/10.2316/p.2011.737-023.

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Shamaei, Arash, Bella Bose, and Mary Flahive. "Higher Dimensional Gaussian Networks." In 2014 IEEE International Parallel & Distributed Processing Symposium Workshops (IPDPSW). IEEE, 2014. http://dx.doi.org/10.1109/ipdpsw.2014.161.

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Griffin, R. D., and J. N. Lee. "Hardware and Software System Design for Hybrid Optical-Electronic Signal Processing." In Optical Computing. Optica Publishing Group, 1991. http://dx.doi.org/10.1364/optcomp.1991.me31.

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Many workers have demonstrated the potential of optical techniques to process high bandwidth data at very high computation rates.1,2 Optical processors have been proposed for such diverse applications as pattern recognition, neural networks, switching, digital computing, filtering, transformations, and matrix algebra. Since most of these methods implement specialized processors, they must be integrated into presently available digital electronic systems to obtain the necessary degree of control and flexibility for practical applications. Few systems exist today that realize the potential of th
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Khan, Usman A., Soummya Kar, and Jose M. F. Moura. "Higher dimensional consensus algorithms in sensor networks." In ICASSP 2009 - 2009 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2009. http://dx.doi.org/10.1109/icassp.2009.4960219.

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Chen Xiaoqiang, Wang Qiao, and Wu Lenan. "Singularity analysis of higher dimensional signals." In Proceedings of 2003 International Conference on Neural Networks and Signal Processing. IEEE, 2003. http://dx.doi.org/10.1109/icnnsp.2003.1279375.

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van der Schaft, A. J., and B. M. Maschke. "Conservation laws and open systems on higher-dimensional networks." In 2008 47th IEEE Conference on Decision and Control. IEEE, 2008. http://dx.doi.org/10.1109/cdc.2008.4738952.

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Reports on the topic "Higher Dimensional Algebra of Networks"

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Semerikov, Serhiy, Illia Teplytskyi, Yuliia Yechkalo, Oksana Markova, Vladimir Soloviev, and Arnold Kiv. Computer Simulation of Neural Networks Using Spreadsheets: Dr. Anderson, Welcome Back. [б. в.], 2019. http://dx.doi.org/10.31812/123456789/3178.

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The authors of the given article continue the series presented by the 2018 paper “Computer Simulation of Neural Networks Using Spreadsheets: The Dawn of the Age of Camelot”. This time, they consider mathematical informatics as the basis of higher engineering education fundamentalization. Mathematical informatics deals with smart simulation, information security, long-term data storage and big data management, artificial intelligence systems, etc. The authors suggest studying basic principles of mathematical informatics by applying cloud-oriented means of various levels including those traditio
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Meni, Mackenzie, Ryan White, Michael Mayo, and Kevin Pilkiewicz. Entropy-based guidance of deep neural networks for accelerated convergence and improved performance. Engineer Research and Development Center (U.S.), 2025. https://doi.org/10.21079/11681/49805.

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Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building and training them are not straightforward processes. To add structure to these efforts, we derive new mathematical results to efficiently measure the changes in entropy as fully-connected and convolutional neural networks process data. By measuring the change in entropy as networks process data effectively, patterns critical to a well-performing network can
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