M. Kobayashi et al., Hyperbolic-Valued Hopfield Neural Networks in Hybrid Mode


Kobayashi, Masaki et al., Hyperbolic-Valued Hopfield Neural Networks in Hybrid Mode, Neurocomputing. 2021, Available online 23 February 2021, In Press, Journal Pre-proof, DOI: https://doi.org/10.1016/j.neucom.2021.01.121 .
 
Abstract: A complex-valued Hopfield neural network (CHNN) has been applied as a multistate neural associative memory. Continue reading

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New book by Ichino+Prasanna: Periods of Quaternionic Shimura Varieties. I.


Periods of Quaternionic Shimura Varieties. I.Contemporary Mathematics, Volume: 762; 2021; 214 pp;  Softcover MSC: Primary 11; Print ISBN: 978-1-4704-4894-3, Product Code: CONM/762, List Price: $122.00

Authors: Atsushi Ichino: Kyoto University, Kyoto, Japan, Kartik Prasanna: University of Michigan, Ann Arbor, MI

This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimura’s algebraicity conjectures on these periods. Continue reading

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New book: L.A.B. San Martin: Lie Groups


Note: Communicated by Nek Valous, National Center for Tumor Diseases (NCT), Heidelberg.

Title: Lie Groups
Author: Luiz Antonio Barrera San Martin
About:
This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles.
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P.R. Girard et al: Dual Hyperquaternion Poincaré Groups


Girard, P.R., Clarysse, P., Pujol, R., Goutte, R., Delachartre, P.: Dual Hyperquaternion Poincaré Groups. Adv. Appl. Clifford Algebras 31, 15 (2021). https://doi.org/10.1007/s00006-021-01120-z

Abstract. A new representation of the Poincaré groups in n dimensions via dual hyperquaternions is developed, hyperquaternions being defined as a tensor product of quaternion algebras (or a subalgebra thereof). Continue reading

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CfP: Empowering Novel Geometric Algebra for Graphics & Engineering Workshop @ CGI 2021 – 6th Sep. 2021


Empowering Novel Geometric Algebra for Graphics & Engineering Workshop @ CGI 2021 – 6th Sep. 2021

1st Call for Papers

URL: http://www.cgs-network.org/cgi21/?page_id=1817

The ACM Siggraph 2001 and 2003 saw Geometric Algebra (GA) featured in the form of a Keynote and a Course. Since then the Continue reading

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AACA Vol. 31, Issue 1 – ToC Alert


In this issue
 
 
Open Access
 
 
 

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C. Castro: Octonionic Strings, Branes and Three Fermion Generations


Carlos Castro, Octonionic Strings, Branes and Three Fermion Generations, 17 pages, 2021, Preprint: https://vixra.org/abs/2101.0060 (PDF).

Abstract: Actions for strings and $p$-branes moving in octonionic-spacetime backgrounds and endowed with octonionic-valued metrics are constructed. Continue reading

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P. Lian: Hausdorff‐Young inequalities and multiplier theorems for quaternionic operator‐valued Fourier transforms


Pan Lian, Hausdorff‐Young inequalities and multiplier theorems for quaternionic operator‐valued Fourier transforms, Math Meth Appl Sci. 2021; pp. 1– 11. DOI: https://doi.org/10.1002/mma.7211

Abstract: Due to the non‐commutativity of quaternions, there are three kinds of quaternionic Banach spaces, i.e. the right sided, the left sided, and the two sided ones. Continue reading

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Valle & Lobo: Hypercomplex-valued recurrent correlation neural networks


Marcos Eduardo Valle and Rodolfo Anibal Lobo, Hypercomplex-valued recurrent correlation neural networks, Neurocomputing, Volume 432, 7 April 2021, Pages 111-123, DOI: https://doi.org/10.1016/j.neucom.2020.12.034

Abstract: Recurrent correlation neural networks (RCNNs), introduced by Chiueh and Goodman as an improved version of the bipolar correlation-based Hopfield neural network, Continue reading

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De Martino, Diki: On the quaternionic short-time Fourier and Segal-Bargmann transforms


Antonino De Martino, Kamal Diki, On the quaternionic short-time Fourier and Segal-Bargmann transforms, preprint: https://arxiv.org/abs/2009.00073, 23 pages.

Abstract: In this paper, we study a special one dimensional quaternion short-time Fourier transform (QSTFT). Continue reading

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