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For a twisted partial action \Theta of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A X_\Theta G is proved to be associative. Given a G-graded k-algebra B =…

Rings and Algebras · Mathematics 2010-03-16 M. Dokuchaev , R. Exel , J. J. Simon

In Knowledge Management, variations in information expressions have proven a real challenge. In particular, classical semantic relations (e.g. synonymy) do not connect words with different parts-of-speech. The method proposed tries to…

Information Retrieval · Computer Science 2010-10-28 Bernard Jacquemin

This work presents a recursive construction for simple $t$-designs using resolutions of the ingredient designs. The result extends a construction of $t$-designs in our recent paper [39]. Essentially, the method in [39] describes the blocks…

Combinatorics · Mathematics 2016-12-07 Tran van Trung

This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…

Logic in Computer Science · Computer Science 2018-08-21 Anton Salikhmetov

We propose an operationally-based deductive proof method for program equivalence. It is based on encoding the language semantics as logically constrained term rewriting systems (LCTRSs) and the two programs as terms. The main feature of our…

Logic in Computer Science · Computer Science 2020-01-28 Ştefan Ciobâcă , Dorel Lucanu , Andrei Sebastian Buruiană

I present a bijection on integer partitions that leads to recursive expressions, closed formulae and generating functions for the cardinality of certain sets of partitions of a positive integer $n$. The bijection leads also to a product on…

Combinatorics · Mathematics 2009-06-17 Alain Goupil

We introduce the key concepts of duality mappings and metric extensor. The fundamental identities involving the duality mappings are presented, and we disclose the logical equivalence between the so-called metric tensor and the metric…

Mathematical Physics · Physics 2012-09-19 Antonio Manuel Moya

In recent years, bundle recommendation systems have gained significant attention in both academia and industry due to their ability to enhance user experience and increase sales by recommending a set of items as a bundle rather than…

Information Retrieval · Computer Science 2026-02-27 Meng Sun , Lin Li , Ming Li , Xiaohui Tao , Dong Zhang , Qing Xie , Peipei Wang , Jimmy Xiangji Huang

Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…

Numerical Analysis · Mathematics 2024-10-01 Katherine Keegan , Elizabeth Newman

Recurrence properties of systems and associated sets of integers that suffice for recurrence are classical objects in topological dynamics. We describe relations between recurrence in different sorts of systems, study ways to formulate…

Dynamical Systems · Mathematics 2014-08-13 Bernard Host , Bryna Kra , Alejandro Maass

We study the existence of the product of two weighted modulation spaces. For this purpose we discuss two different strategies. The more simple one allows transparent proofs in various situations. However, our second method allows a closer…

Functional Analysis · Mathematics 2016-02-02 Maximilian Reich , Winfried Sickel

Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…

Logic in Computer Science · Computer Science 2011-01-31 Luís Pinto , Tarmo Uustalu

If Com is the reduced commutative operad, the category of Com-algebras in spectra is the category of nounital commutative ring spectra. The theme of this survey is that many important constructions on Com-algebras are given by taking the…

Algebraic Topology · Mathematics 2024-10-08 Nicholas J. Kuhn

In this contribution we explore choice revision, a sort of belief change in which the new information is represented by a set of sentences and the agent could accept some of the sentences while rejecting the others. We propose a generalized…

Logic in Computer Science · Computer Science 2018-05-04 Li Zhang

We define a bar construction endofunctor on the category of commutative augmented monoids $A$ of a symmetric monoidal category $\mathcal{V}$ endowed with a left adjoint monoidal functor $F:s\mathbf{Set}\to \mathcal{V}$. To do this, we need…

Algebraic Topology · Mathematics 2017-09-21 Bruno Stonek

Replication of experimental results has been a challenge faced by many scientific disciplines, including the field of machine learning. Recent work on the theory of machine learning has formalized replicability as the demand that an…

Machine Learning · Computer Science 2026-04-15 Eric Eaton , Marcel Hussing , Michael Kearns , Aaron Roth , Sikata Bela Sengupta , Jessica Sorrell

Finite Euler product is known to be one of the classical zeta functions in number theory. In [1], [2] and [3], we have introduced some multivariable zeta functions and studied their definable probability distributions on R^d. They include…

Probability · Mathematics 2012-04-19 Takahiro Aoyama , Takashi Nakamura

We introduce a new type of multiple zeta functions, which we call bilateral zeta functions, analogous to the Barnes zeta functions. The bilateral zeta function is a periodic function and shares certain basic properties of Barnes zeta…

Classical Analysis and ODEs · Mathematics 2013-04-02 Genki Shibukawa

Natural language processing has greatly benefited from the introduction of the attention mechanism. However, standard attention models are of limited interpretability for tasks that involve a series of inference steps. We describe an…

Computation and Language · Computer Science 2018-09-03 Martin Tutek , Jan Šnajder

Randomized iterative algorithms, such as the randomized Kaczmarz method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights…