Search results for " Algebra"
showing 10 items of 2082 documents
Accelerometry - Simple, but challenging
2017
Smoktunowicz, Agata; Vishne, Uzi An affine prime non-semiprimitive monomial algebra with quadratic growth, Adv. in Appl. Math. 37 (2006), no. 4, 511-…
2007
The authors give a simple construction of a prime monomial algebra on two generators over an arbitrary field which has quadratic growth and is neither semiprimitive nor PI. This answers a question raised in [J. P. Bell, J. Algebra 263 (2003), no. 1, 159--175; MR1974084 (2004d:16042)]
Non-commutative Ring Learning with Errors from Cyclic Algebras
2022
AbstractThe Learning with Errors (LWE) problem is the fundamental backbone of modern lattice-based cryptography, allowing one to establish cryptography on the hardness of well-studied computational problems. However, schemes based on LWE are often impractical, so Ring LWE was introduced as a form of ‘structured’ LWE, trading off a hard to quantify loss of security for an increase in efficiency by working over a well-chosen ring. Another popular variant, Module LWE, generalizes this exchange by implementing a module structure over a ring. In this work, we introduce a novel variant of LWE over cyclic algebras (CLWE) to replicate the addition of the ring structure taking LWE to Ring LWE by add…
On the tensor degree of finite groups
2013
We study the number of elements $x$ and $y$ of a finite group $G$ such that $x \otimes y= 1_{_{G \otimes G}}$ in the nonabelian tensor square $G \otimes G$ of $G$. This number, divided by $|G|^2$, is called the tensor degree of $G$ and has connection with the exterior degree, introduced few years ago in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343]. The analysis of upper and lower bounds of the tensor degree allows us to find interesting structural restrictions for the whole group.
Análisis e interpretación de los términos literales por parte de los alumnos de la Educación Secundaria
2017
El objetivo de este estudio es describir y analizar las interpretaciones de los términos literales algebraicos que realiza una muestra de 27 alumnos y alumnas entre 15 y 16 años de un instituto de la ciudad de Valencia. Se les administró un test basado en investigaciones del Dr. Küchemann entre finales de los años 70 y principios de los años 80. Se realizó un análisis detallado de las dificultades y errores que presentaron así como de alguno de los ítems que se utilizaron para identificar dichas interpretaciones. Posteriormente se entrevistó de modo individual a 2 alumnos para conocer la justificación de sus respuestas. La mayor parte de los alumnos mostraron dificultades en la interpretaci…
A classification of $\protect \mathbb{R}$-Fuchsian subgroups of Picard modular groups
2018
Simulating Secularities: Challenges and Opportunities in the Computational Science of (Non)Religion
2021
This article provides scholars of nonreligion and secularism with an introduction to some of the major opportunities and challenges associated with the growing application of computational methods to the phenomena they study. It also illustrates these opportunities and challenges by describing several overlapping research projects and some of the models of (non)religion they have produced. Finally, the article addresses some of the significant philosophical issues surrounding the use of computer modeling and simulation, focusing on the ethical and epistemological concerns that these tools often raise. I invite scholars of nonreligion to consider adding these techniques to their methodologic…
Algebraic models of the real affine plane
2017
We introduce a new invariant, the real (logarithmic)-Kodaira dimension, that allows to distinguish smooth real algebraic surfaces up to birational diffeomorphism. As an application, we construct infinite families of smooth rational real algebraic surfaces with trivial homology groups, whose real loci are diffeomorphic to $\mathbb{R}^2$, but which are pairwise not birationally diffeomorphic. There are thus infinitely many non-trivial models of the real affine plane, contrary to the compact case.
Convergence Analysis of Distributed Set-Valued Information Systems
2016
This paper focuses on the convergence of information in distributed systems of agents communicating over a network. The information on which the convergence is sought is not rep- resented by real numbers, as often in the literature, rather by sets. The dynamics of the evolution of information across the net- work is accordingly described by set-valued iterative maps. While the study of convergence of set-valued iterative maps is highly complex in general, this paper focuses on Boolean maps, which are comprised of arbitrary combinations of unions, intersections, and complements of sets. For these important class of systems, we provide tools to study both global and local convergence. A distr…
Feature extraction from remote sensing data using Kernel Orthonormalized PLS
2007
This paper presents the study of a sparse kernel-based method for non-linear feature extraction in the context of remote sensing classification and regression problems. The so-called kernel orthonormalized PLS algorithm with reduced complexity (rKOPLS) has two core parts: (i) a kernel version of OPLS (called KOPLS), and (ii) a sparse (reduced) approximation for large scale data sets, which ultimately leads to rKOPLS. The method demonstrates good capabilities in terms of expressive power of the extracted features and scalability.