检索结果-内蒙古大学图书馆

number of arithmetic progressions in dense random subsets of DOUBLE-STRUCK CAPITAL Z/nDOUBLE-STRUCK CAPITAL Z

学校读者我要写书评

暂无评论

ISRAEL JOURNAL OF MATHEMATICS 2021年第2期244卷 589-620页

作者： Berkowitz, Ross Sah, Ashwin Sawhney, Mehtaab Yale Univ Dept Math New Haven CT 06520 USA MIT Dept Math Cambridge MA 02139 USA

We examine the behavior of the number of k-term arithmetic progressions in a random subset of DOUBLE-STRUCK CAPITAL Z/nDOUBLE-STRUCK CAPITAL Z. We prove that if a set is chosen by including each element of DOUBLE-STRUCK CAPITAL Z/nDOUBLE-STRUCK CAPITAL Z independently with constant probability p, then the resulting distribution of k-term arithmetic progressions in that set, while obeying a central limit theorem, does not obey a local central limit theorem. The methods involve decomposing the random variable into homogeneous degree d polynomials with respect to the Walsh/Fourier basis. Proving a suitable multivariate central limit theorem for each component of the expansion gives the desired result.

关键词： Mathematics general algebra Group theory and Generalizations Analysis applications of Mathematics Theoretical Mathematical and Computational Physics

A Survey on Time Series Data Classification: Blockchain Technologies and Security Concerns 28th

学校读者我要写书评

暂无评论

A Survey on Time Series Data Classification: Blockchain Tech...

28th International Conference on Knowledge Based and Intelligent information and Engineering Systems, KES 2024

作者： Alsayyad, Ahmed Faris Abid Ali, Alaa Abid Muslam Mabrouk, Mohamed Al-Shammari, Ahmed Zrigui, Mounir Research Laboratory in Algebra Numbers Theory and Intelligent Systems RLANTIS University of Monastir Monastir Tunisia Department of Computer Science College of Computer Science and Information Technology University of Al-Qadisiyah Al Diwaniyah58002 Iraq Al-Qadisiyah University Al-Qadisiyah Iraq Military Academy Fondok Jedid Tunisia

The difficulties about user security and privacy have appeared as significant concerns in recent years. The number of cyber-attacks grows at a concerning velocity, hence rendering internet users susceptible to malicious activities perpetrated by hackers. Data mining approaches are employed to extract accurate results from massive and complex databases. Furthermore, the utilization of Blockchain (BC) approaches is increasingly popular in current Internet of Things (IoT) applications as an opportunity to address issues related to privacy and security. Lots of studies have been performed on algorithms for data mining and techniques concerning blockchain. Time series data is a commonly used form of data. Time Series Classification (TSC) refers to the creation of predictive models that generate a target variable or label based on linear or sequential data inputs across a considerable duration. The possible results may be presented in either ordinal or numerical form. Even so, previous studies have shown major limitations when it comes to handling privacy and security issues that can't be applicable in dynamic instances, as well as the substantial computational cost necessary. Moreover, correctly determining the amount of sensitive parameters required to complete the classification process remains a challenge. We have put forth a comprehensive survey on the classification of blockchain data. In the first phase of our study, we conducted an analysis and categorization of both conventional data classification approaches and contemporary time series data classification techniques. We further discussed limitations and strengths of existing techniques. Finally, we highlight future research problems and directions. © 2024 The Authors.

关键词： Differential privacy

Rewriting theory for the life sciences: A unifying theory of CTMC semantics

学校读者我要写书评

暂无评论

THEORETICAL computer SCIENCE 2021年 884卷 68-115页

作者： Behr, Nicolas Krivine, Jean Andersen, Jakob L. Merkle, Daniel Univ Paris Inst Rech Informat Fondamentale CNRS UMR 8243 8 Pl Aurelie Nemours F-75205 Paris 13 France Univ Southern Denmark Dept Math & Comp Sci Campusvej 55 DK-5230 Odense M Denmark

The KAPPA biochemistry and the MOD organic chemistry frameworks are amongst the most intensely developed applications of rewriting-based methods in the life sciences to date. A typical feature of these types of rewriting theories is the necessity to implement certain structural constraints on the objects to be rewritten (a protein is empirically found to have a certain signature of sites, a carbon atom can form at most four bonds, ...). In this paper, we contribute a number of original developments that permit to implement a universal theory of continuous-time Markov chains (CTMCs) for stochastic rewriting systems. Our core mathematical concepts are a novel rule algebra construction for the relevant setting of rewriting rules with conditions, both in Double- and in Sesqui-Pushout semantics, augmented by a suitable stochastic mechanics formalism extension that permits to derive dynamical evolution equations for pattern-counting statistics. A second main contribution of our paper is a novel framework of restricted rewriting theories, which comprises a rule-algebra calculus under the restriction to so-called constraint-preserving completions of application conditions (for rules considered to act only upon objects of the underlying category satisfying a globally fixed set of structural constraints). This novel framework in turn renders a faithful encoding of bio- and organo-chemical rewriting in the sense of KAPPA and MOD possible, which allows us to derive a rewriting-based formulation of reaction systems including a full-fledged CTMC semantics as instances of our universal CTMC framework. While offering an interesting new perspective and conceptual simplification of this semantics in the setting of KAPPA, both the formal encoding and the CTMC semantics of organo-chemical reaction systems as motivated by the MOD framework are the first such results of their kind. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Double-pushout rewriting Sesqui-pushout rewriting Rule algebra theory Stochastic mechanics Biochemistry Organic chemistry Algorithmic cheminformatics

学校读者我要写书评

暂无评论

LSU Factorization

LSU Factorization

International Conference on Computational Science and Computational Intelligence (CSCI)

作者： Gennadi Malaschonok Faculty of Computer Science National University of Kyiv-Mohyla Academy Kyiv Ukraine

ISBN: (数字)9798350361513

ISBN: (纸本)9798350372304

The matrix LU factorization algorithm is a funda-mental algorithm in linear algebra. We propose a generalization of the LU and LEU algorithms to accommodate the case of a commutative domain and its field of quotients. This algorithm decomposes any matrix A into a product of three matrices A=LSU, where each element of the triangular matrices L and U is a minor of matrix A. The number of non-zero elements in matrix S is equal to rank(A), and each of them is the inverse of the product of a specific pair of matrix A minors. The algorithm's complexity is equivalent to that of matrix multiplication.

关键词： Accuracy Scientific computing Linear algebra polynomials Complexity theory Sparse matrices Matrix decomposition

UNIVERSAL CONSTRUCTIONS FOR POISSON algebraS. applications

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Agore, A.L. Militaru, G. Vrije Universiteit Brussel Pleinlaan 2 BrusselsB-1050 Belgium Max Planck Institut für Mathematik Vivatsgasse 7 Bonn53111 Germany Simion Stoilow Institute of Mathematics Romanian Academy P.O. Box 1-764 Bucharest014700 Romania Faculty of Mathematics and Computer Science University of Bucharest Str. Academiei 14 Bucharest 1RO-010014 Romania

We introduce the universal algebra of two Poisson algebras P and Q as a commutative algebra A := P(P, Q) satisfying a certain universal property. The universal algebra is shown to exist for any finite dimensional Poisson algebra P and several of its applications are highlighted. For any Poisson P-module U, we construct a functor U⨷-: AM→ QPMfrom the category of A-modules to the category of Poisson Q-modules which has a left adjoint whenever U is finite dimensional. Similarly, if V is an A-module, then there exists another functor -⨷V : PPM→ QPMconnecting the categories of Poisson representations of P and Q and the latter functor also admits a left adjoint if V is finite dimensional. If P is n-dimensional, then P(P) := P(P, P) is the initial object in the category of all commutative bialgebras coacting on P. As an algebra, P(P) can be deescribed as the quotient of the polynomial algebra k[Xij | i, j = 1, , n] through an ideal generated by 2n3 non-homogeneous polynomials of degree ≤ 2. Two applications are provided. The first one describes the automorphisms group AutPoiss(P) as the group of all invertible group-like elements of the finite dual P(P)o. Secondly, we show that for an abelian group G, all G-gradings on P can be explicitly described and classified in terms of the universal coacting bialgebra P(P). Copyright © 2023, The Authors. All rights reserved.

关键词： Group theory

Logarithmic uncertainty principle for Clifford-wavelet transform

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Arfaoui, Sabrine Banouh, Hicham Mabrouk, Anouar Ben Laboratory of Algebra Number Theory and Nonlinear Analysis LR18ES15 Department of Mathematics Faculty of Sciences University of Monastir Monastir5019 Tunisia Higher Institute of Computer Science El-Kef University of Jendouba Saleh Ayech - Kef 7100 5 Street of Tunisia Departement of Mathematics Faculty of Sciences and Applied Sciences University of Akli Mohand Oulhadj of Bouira Bouira10000 Algeria Higher Institute of Applied Mathematics and Computer Science University of Kairaouan Street of Assad Ibn Alfourat Kairouan3100 Tunisia Laboratory of Algebra Number Theory and Nonlinear Analysis LR18ES15 Department of Mathematics Faculty of Sciences Monastir5019 Tunisia Department of Mathematics Faculty of Sciences University of Tabuk King Faisal Rd Tabuk47512 Saudi Arabia

The uncertainty principle constitutes one of the famous physical concepts which continues to attract researchers from different related fields since its discovery due to its utility in many applications. Among the classical (Fourier-based) forms, modified variants such as wavelet-based and logarithmic versions have been investigated by researchers. In the present work we are concerned with the development of a new logarithmic uncertainty principle combining both wavelets and logarithmic variants in the Clifford wavelet transform *** Codes 30G35, 42C40, 42B10, 15A66 © 2024, CC0.

关键词： Wavelet transforms

Certifying Rings of Integers in number Fields

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Baanen, Anne Villarello, Alain Chavarri Dahmen, Sander R. Vrije Universiteit Amsterdam Amsterdam Netherlands Lean FRO United States

number fields and their rings of integers, which generalize the rational numbers and the integers, are foundational objects in number theory. There are several computer algebra systems and databases concerned with the computational aspects of these. In particular, computing the ring of integers of a given number field is one of the main tasks of computational algebraic number theory. In this paper, we describe a formalization in Lean 4 for certifying such computations. In order to accomplish this, we developed several data types amenable to computation. Moreover, many other underlying mathematical concepts and results had to be formalized, most of which are also of independent interest. These include resultants and discriminants, as well as methods for proving irreducibility of univariate polynomials over finite fields and over the rational numbers. To illustrate the feasibility of our strategy, we formally verified entries from the number fields section of the L-functions and modular forms database (LMFDB). These concern, for several number fields, the explicitly given integral basis of the ring of integers and the discriminant. To accomplish this, we wrote SageMath code that computes the corresponding certificates and outputs a Lean proof of the statement to be *** Codes 68V20, 11Y40, 11R09, 11R04, 11R29 © 2024, CC BY-NC-SA.

关键词： number theory

Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Magron, Victor Koprowski, Przemyslaw Vaccon, Tristan CNRS LAAS Institut de Mathématiques de Toulouse Toulouse France University of Silesia in Katowice Institute of Mathematics Katowice Poland Université de Limoges CNRS XLIM UMR Limoges7252 France

Pourchet proved in 1971 that every nonnegative univariate polynomial with rational coefficients is a sum of five or fewer squares. Nonetheless, there are no known algorithms for constructing such a decomposition. The sole purpose of the present paper is to present a set of algorithms that decompose a given nonnegative polynomial into a sum of six (five under some unproven conjecture or when allowing weights) squares of polynomials. Moreover, we prove that the binary complexity can be expressed polynomially in terms of classical operations of computer algebra and algorithmic number theory. Copyright © 2023, The Authors. All rights reserved.

关键词： polynomials

Review of Recent Systems for Detecting and Diagnosing Pronunciation Errors 6

学校读者我要写书评

暂无评论

Review of Recent Systems for Detecting and Diagnosing Pronun...

6th IEEE International Conference on Advanced Systems and Emergent Technologies, IC_ASET 2023

作者： Dabbabi, Karim Mars, Abdelkarim Research Unite of Analysis and Processing of Electrical and Energetic Systems Faculty of Sciences of Tunis Tunis Tunisia Research Laboratory in Algebra Number Theory and Intelligent Systems Faculty of Sciences of Monastir Monastir Tunisia

ISBN: (纸本)9798350321029

Nowadays, computer Aided Language Learning (CALL) frameworks have attracted a lot of attention because of their capability, adaptability, and flexibility in improving people's language skills. The field of Mispronunciation Detection and Diagnosis (MDD) is considered one of the applications of these frameworks and has recently benefited from the rapid innovation spawned in deep learning models and different acoustic, phonetic, and linguistic features. The various manner of combinations of different features and deep learning architectures for different MDD systems require huge amount of annotated textual data to be pretrained and hence achieved good performances. However, providing a large amount of annotated textual data for pre-training is a tedious and time-consuming operation. For this, a pre-trained acoustic model from unannotated data can be a good alternative. In this article, we present different MDD systems categorized according to the pre-training mode: pre-trained approaches without annotated text data and pre-trained approaches with annotated text data. Experimental results, advantages, disadvantages and additional improvements for each method explored for each category are presented and discussed. © 2023 IEEE.

关键词： Linguistics