Relevant bibliographies by topics / Algebra expressions

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

Academic literature on the topic 'Algebra expressions'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Algebra expressions"

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Paredaens, Jan, and Dirk Van Gucht. "Converting nested algebra expressions into flat algebra expressions." ACM Transactions on Database Systems 17, no. 1 (1992): 65–93. http://dx.doi.org/10.1145/128765.128768.

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Yang, Bo. "A Proof Method for Correctness of Database Query Program." Advanced Materials Research 121-122 (June 2010): 464–69. http://dx.doi.org/10.4028/www.scientific.net/amr.121-122.464.

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It is necessary that formal proof for correctness of relational algebra expressions. It can effectively improve the reliability of database query program. The aim of the present study is to present a proof method for correctness of relational algebra expressions. The basic idea about this proof method is explained as follows. Based on the semantics of relational algebra operators, according to the characteristic of relational algebra expressions, we can formally derivate the semantic of an algebra relational expression. And then we can compare this semantic with the specification. If they are equal logically, the relational algebra expression is correct, otherwise, the relational algebra expression is wrong. This article explains the mean and necessity of proving the correctness of relational algebra expressions. Some rules of formal deduction are presented. Based on it, we present a proof method for correctness of relational algebra expressions. Next, a application is given to illustrate this proof method. At last, conclusions and discussions about this proof method are given. As far as we known, there is no other work which is about proof method for the correctness of a relational algebra expression to the database query specification based on the given semantics.
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Lukichev, Maxim, Boris Novikov, and Pankaj Mehra. "An XML-algebra for efficient set-at-a-time execution." Computer Science and Information Systems 9, no. 1 (2012): 63–80. http://dx.doi.org/10.2298/csis100804037l.

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The importance of XML query optimization is growing due to the rising number of XML-intensive data mining tasks. Earlier work on algebras for XML query focused mostly on rule-based optimization and used node-at-a-time execution model. Heavy query workloads in modern applications require cost-based optimization which is naturally supported by the set-at-a-time execution model. This paper introduces an algebra with only set-at-a-time operations, and discusses expression reduction methods and lazy evaluation techniques based on the algebra. Our experiments demonstrate that, for queries with complex conditional and quantified expressions, the proposed algebra results in plans with much better performance than those produced by the state-of-the-art algebras. For relatively simple queries, the proposed methods are expected to yield plans with comparable performance.
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Goldman, Ronald N. "Illicit expressions in vector algebra." ACM Transactions on Graphics 4, no. 3 (1985): 223–43. http://dx.doi.org/10.1145/282957.282969.

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CÁRDENAS, V., S. LEPE, and J. SAAVEDRA. "CURRENT ALGEBRA IN THE PATH INTEGRAL FRAMEWORK." Modern Physics Letters A 13, no. 27 (1998): 2193–98. http://dx.doi.org/10.1142/s0217732398002333.

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In this letter we describe an approach to the current algebra based on the path integral formalism. We use this method for Abelian and non-Abelian quantum field theories in (1+1) and (2+1) dimensions and the correct expressions are obtained. Our results show the independence of the regularization of the current algebras.
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BARBARIN, F., E. RAGOUCY, and P. SORBA. "NONPOLYNOMIAL REALIZATIONS OF ${\mathcal W}$ ALGEBRAS." International Journal of Modern Physics A 11, no. 16 (1996): 2835–70. http://dx.doi.org/10.1142/s0217751x96001383.

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Relaxing first-class constraint conditions in the usual Drinfeld—Sokolov Hamiltonian reduction leads, after symmetry fixing, to realizations of [Formula: see text] algebras expressed in terms of all the J current components. General results are given for [Formula: see text] a nonexceptional simple (finite and affine) algebra. Such calculations directly provide the commutant, in the (closure of) [Formula: see text] enveloping algebra, of the nilpotent subalgebra [Formula: see text], where the subscript refers to the chosen gradation in [Formula: see text]. In the affine case, explicit expressions are presented for the Virasoro, [Formula: see text], and Bershadsky algebras at the quantum level.
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Korniłowicz, Artur, Ievgen Ivanov, and Mykola Nikitchenko. "Kleene Algebra of Partial Predicates." Formalized Mathematics 26, no. 1 (2018): 11–20. http://dx.doi.org/10.2478/forma-2018-0002.

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Summary We show that the set of all partial predicates over a set D together with the disjunction, conjunction, and negation operations, defined in accordance with the truth tables of S.C. Kleene’s strong logic of indeterminacy [17], forms a Kleene algebra. A Kleene algebra is a De Morgan algebra [3] (also called quasi-Boolean algebra) which satisfies the condition x ∧¬:x ⩽ y ∨¬ :y (sometimes called the normality axiom). We use the formalization of De Morgan algebras from [8]. The term “Kleene algebra” was introduced by A. Monteiro and D. Brignole in [3]. A similar notion of a “normal i-lattice” had been previously studied by J.A. Kalman [16]. More details about the origin of this notion and its relation to other notions can be found in [24, 4, 1, 2]. It should be noted that there is a different widely known class of algebras, also called Kleene algebras [22, 6], which generalize the algebra of regular expressions, however, the term “Kleene algebra” used in this paper does not refer to them. Algebras of partial predicates naturally arise in computability theory in the study on partial recursive predicates. They were studied in connection with non-classical logics [17, 5, 18, 32, 29, 30]. A partial predicate also corresponds to the notion of a partial set [26] on a given domain, which represents a (partial) property which for any given element of this domain may hold, not hold, or neither hold nor not hold. The field of all partial sets on a given domain is an algebra with generalized operations of union, intersection, complement, and three constants (0, 1, n which is the fixed point of complement) which can be generalized to an equational class of algebras called DMF-algebras (De Morgan algebras with a single fixed point of involution) [25]. In [27] partial sets and DMF-algebras were considered as a basis for unification of set-theoretic and linguistic approaches to probability. Partial predicates over classes of mathematical models of data were used for formalizing semantics of computer programs in the composition-nominative approach to program formalization [31, 28, 33, 15], for formalizing extensions of the Floyd-Hoare logic [7, 9] which allow reasoning about properties of programs in the case of partial pre- and postconditions [23, 20, 19, 21], for formalizing dynamical models with partial behaviors in the context of the mathematical systems theory [11, 13, 14, 12, 10].
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Fritzsche, Stephan. "Symbolic Evaluation of Expressions from Racah’s Algebra." Symmetry 13, no. 9 (2021): 1558. http://dx.doi.org/10.3390/sym13091558.

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Based on the rotational symmetry of isolated quantum systems, Racah’s algebra plays a significant role in nuclear, atomic and molecular physics, and at several places elsewhere. For N-particle (quantum) systems, for example, this algebra helps carry out the integration over the angular coordinates analytically and, thus, to reduce them to systems with only N (radial) coordinates. However, the use of Racah’s algebra quickly leads to complex expressions, which are written in terms of generalized Clebsch–Gordan coefficients, Wigner n-j symbols, (tensor) spherical harmonics and/or rotation matrices. While the evaluation of these expressions is straightforward in principle, it often becomes laborious and prone to making errors in practice. We here expand Jac, the Jena Atomic Calculator, to facilitate the sum-rule evaluation of typical expressions from Racah’s algebra. A set of new and revised functions supports the simplification and subsequent use of such expressions in daily research work or as part of lengthy derivations. A few examples below show the recoupling of angular momenta and demonstrate how Jac can be readily applied to find compact expressions for further numerical studies. The present extension makes Jac a more flexible and powerful toolbox in order to deal with atomic and quantum many-particle systems.
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Mickelsson, Jouko. "3D Current Algebra and Twisted K Theory." Reviews in Mathematical Physics 30, no. 07 (2018): 1840011. http://dx.doi.org/10.1142/s0129055x18400111.

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Equivariant twisted K theory classes on compact Lie groups [Formula: see text] can be realized as families of Fredholm operators acting in a tensor product of a fermionic Fock space and a representation space of a central extension of the loop algebra [Formula: see text] using a supersymmetric Wess–Zumino–Witten model. The aim of the present paper is to extend the construction to higher loop algebras using an abelian extension of a 3D current algebra. We have only partial success: Instead of true Fredholm operators we have formal algebraic expressions in terms of the generators of the current algebra and an infinite dimensional Clifford algebra. These give rise to sesquilinear forms in a Hilbert bundle which transform in the expected way with respect to 3D gauge transformations but do not define true Hilbert space operators.
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Grigoryan, T. A. "SOME RESULTS ON REGULAR EXPRESSIONS FOR MULTITAPE FINITE AUTOMATA." Proceedings of the YSU A: Physical and Mathematical Sciences 53, no. 2 (249) (2019): 82–90. http://dx.doi.org/10.46991/pysu:a/2019.53.2.082.

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We consider sets of word tuples accepted by multitape finite automata. We use the known notation for regular expressions that describes languages accepted by one-tape automata. Nevertheless, the interpretation of the "concatenation" operation is different in this case. The algebra of events for multitape finite automata is defined in the same way as for one-tape automata. It is shown that the introduced algebra is a Kleene algebra. It is also, shown that some known results for the algebra of events accepted by one-tape finite automata are valid in this case too.
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Dissertations / Theses on the topic "Algebra expressions"

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Jansen, Anthony Robert 1973. "Encoding and parsing of algebraic expressions by experienced users of mathematics." Monash University, School of Computer Science and Software Engineering, 2002. http://arrow.monash.edu.au/hdl/1959.1/8059.

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Mouilleron, Christophe. "Efficient computation with structured matrices and arithmetic expressions." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00688388.

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Designing efficient code in practice for a given computation is a hard task. In this thesis, we tackle this issue in two different situations. The first part of the thesis introduces some algorithmic improvements in structured linear algebra. We first show how to extend an algorithm by Cardinal for inverting Cauchy-like matrices to the other common structures. This approach, which mainly relies on products of the type "structured matrix × matrix", leads to a theoretical speed-up of a factor up to 7 that we also observe in practice. Then, we extend some works on Toeplitz-like matrices and prove that, for any of the common structures, the product of an n×n structured matrix of displacement rank α by an n×α matrix can be computed in Õ(α^(ω-1)n). This leads to direct inversion algorithms in Õ(α^(ω-1)n) , that do not rely on a reduction to the Toeplitz-like case. The second part of the thesis deals with the implementation of arithmetic expressions. This topic raises several issues like finding the minimum number of operations, and maximizing the speed or the accuracy when using some finite-precision arithmetic. Making use of the inductive nature of arithmetic expressions enables the design of algorithms that help to answer such questions. We thus present a set of algorithms for generating evaluation schemes, counting them, and optimizing them according to one or several criteria. These algorithms are part of a library that we have developed and used, among other things, in order to decrease the running time of a code generator for a mathematical library, and to study optimality issues about the evaluation of a small degree polynomial with scalar coefficients at a matrix point.
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Brunet, Paul. "Algebras of Relations : from algorithms to formal proofs." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSE1198/document.

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Les algèbres de relations apparaissent naturellement dans de nombreux cadres, en informatique comme en mathématiques. Elles constituent en particulier un formalisme tout à fait adapté à la sémantique des programmes impératifs. Les algèbres de Kleene constituent un point de départ : ces algèbres jouissent de résultats de décidabilités très satisfaisants, et admettent une axiomatisation complète. L'objectif de cette thèse a été d'étendre les résultats connus sur les algèbres de Kleene à des extensions de celles-ci.Nous nous sommes tout d'abord intéressés à une extension connue : les algèbres de Kleene avec converse. La décidabilité de ces algèbres était déjà connue, mais l'algorithme prouvant ce résultat était trop compliqué pour être utilisé en pratique. Nous avons donné un algorithme plus simple, plus efficace, et dont la correction est plus facile à établir. Ceci nous a permis de placer ce problème dans la classe de complexité PSpace-complete.Nous avons ensuite étudié les allégories de Kleene. Sur cette extension, peu de résultats étaient connus. En suivant des résultats sur des algèbres proches, nous avons établi l'équivalence du problème d'égalité dans les allégories de Kleene à l'égalité de certains ensembles de graphes. Nous avons ensuite développé un modèle d'automate original (les automates de Petri), basé sur les réseaux de Petri, et avons établi l'équivalence de notre problème original avec le problème de comparaison de ces automates. Nous avons enfin développé un algorithme pour effectuer cette comparaison dans le cadre restreint des treillis de Kleene sans identité. Cet algorithme utilise un espace exponentiel. Néanmoins, nous avons pu établir que la comparaison d'automates de Petri dans ce cas est ExpSpace-complète. Enfin, nous nous sommes intéressés aux algèbres de Kleene Nominales. Nous avons réalisé que les descriptions existantes de ces algèbres n'étaient pas adaptées à la sémantique relationnelle des programmes. Nous les avons donc modifiées pour nos besoins, et ce faisant avons trouvé diverses variations naturelles de ce modèle. Nous avons donc étudié en détails et en Coq les ponts que l'on peut établir entre ces variantes, et entre le modèle “classique” et notre nouvelle version<br>Algebras of relations appear naturally in many contexts, in computer science as well as in mathematics. They constitute a framework well suited to the semantics of imperative programs. Kleene algebra are a starting point: these algebras enjoy very strong decidability properties, and a complete axiomatisation. The goal of this thesis was to export known results from Kleene algebra to some of its extensions. We first considered a known extension: Kleene algebras with converse. Decidability of these algebras was already known, but the algorithm witnessing this result was too complicated to be practical. We proposed a simpler algorithm, more efficient, and whose correctness is easier to establish. It allowed us to prove that this problem lies in the complexity class PSpace-complete.Then we studied Kleene allegories. Few results were known about this extension. Following results about closely related algebras, we established the equivalence between equality in Kleene allegories and equality of certain sets of graphs. We then developed an original automaton model (so-called Petri automata), based on Petri nets. We proved the equivalence between the original problem and comparing these automata. In the restricted setting of identity-free Kleene lattices, we also provided an algorithm performing this comparison. This algorithm uses exponential space. However, we proved that the problem of comparing Petri automata lies in the class ExpSpace-complete.Finally, we studied Nominal Kleene algebras. We realised that existing descriptions of these algebra were not suited to relational semantics of programming languages. We thus modified them accordingly, and doing so uncovered several natural variations of this model. We then studied formally the bridges one could build between these variations, and between the existing model and our new version of it. This study was conducted using the proof assistant Coq
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Prokopová, Dagmar. "Vizualizace výrazů procesní algebry pi-kalkul." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2017. http://www.nusl.cz/ntk/nusl-363857.

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This work deals with the problem of visual representation of Pi-calculus expressions. The theoretical part of this paper discusses general principles of process algebras as well as specific properties of individual models, with a focus on Pi-calculus. Also included is the comparison of several text and graphical representations of expressions. The main part of the thesis deals with the design and implementation of an application for converting text representation of expressions into graphical representation. In addition to the text and graphical representation, an internal tree representation designed to work with expressions within the application is also proposed. The thesis also describes algorithms for finding feasible reductions, performing reductions and expression simplification that operate with the proposed tree representation.
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Oikawa, Márcio Katsumi. "Geração de expressões algébricas para processos de negócio usando reduções de digrafos série-paralelo." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/45/45134/tde-27102008-100359/.

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Modelagem e controle de execução são duas abordagens do gerenciamento de processos de negócio que, embora complementares, têm se desenvolvido independentemente. Por um lado, a modelagem é normalmente conduzida por especialistas de negócio e explora aspectos semânticos do processo. Por outro lado, o controle de execução estuda mecanismos consistentes e eficientes de implementação. Este trabalho apresenta um método algorítmico que relaciona modelagem e controle de execução, por meio da geração de expressões algébricas a partir de digrafos acíclicos. Por hipótese, assumimos que modelos de processos de negócio são formados por estruturas baseadas em grafos, e mecanismos de controle de execução são baseados na interpretação de expressões de álgebra de processos. Para a geração de expressões algébricas, esta tese apresenta as propriedades topológicas de digrafos série-paralelo e define um sistema de transformação baseado em redução de digrafos. Além disso, um algoritmo de identificação de digrafos série-paralelo e geração de expressões algébricas é apresentado. O texto também discute o tratamento de digrafos que não são série-paralelo e apresenta, para alguns desses casos, soluções baseadas em mudanças topológicas. Finalmente, o algoritmo é ilustrado com o estudo de caso de uma aplicação real.<br>Modeling and execution control are complementary approaches of business process management that have been developed independently. On one hand, modeling is usually performed by business specialists and explores semantical aspects of the business process. On other hand, execution control studies consistent and efficient mechanisms for implementation. This work presents an algorithmic method which joins modeling and execution control through algebraic expression generation from acyclic digraphs. By hypothesis, we assume that business process models are defined by graph structures, and execution control mechanisms are based on interpretation of process algebra expressions. For algebraic expression generation, this thesis presents the topological properties of series-parallel digraphs and defines a transformation system based on digraph reduction. Therefore, we present an algorithm for identification of series-parallel digraphs and generation of algebraic expressions. This work also discusses the treatment of non-series-parallel digraphs and presents solutions based on topological changing for some cases. Finally, the algorithm is illustrated with a case study based on a real system.
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Gupta, Davender Nath. "Expressing imaging algorithms using a C++ based image algebra programming environment /." Online version of thesis, 1990. http://hdl.handle.net/1850/11370.

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Sangiorgi, Davide. "Expressing mobility in process algebras : first-order and higher-order paradigms." Thesis, University of Edinburgh, 1993. http://hdl.handle.net/1842/6569.

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We study mobile systems, i.e. systems with a dynamically changing communication topology, from a process algebras point of view. Mobility can be introduced in process algebras by allowing names or terms to be transmitted. We distinguish these two approaches as first-order and higher-order. The major target of the thesis is the comparison between them. The prototypical calculus in the first-order paradigm is the π-calculus. By generalising its sort discipline we derive an w-order extension called Higher-Order π-calculus (HOπ). We show that such an extension does not add expressiveness to the π-calculus: Higher-order processes can be faithfully compiled down to first-order, and respecting the behavioural equivalence we adopted in the calculi. Such an equivalence is based on the notion of bisimulation, a fundamental concept of process algebras. Unfortunately, the standard definition of bisimulation is unsatisfactory in a higher-order calculus because it is over-discriminating. To overcome the problem, we propose barbed bisimulation. Its advantage is that it can be defined uniformly in different calculi because it only requires that the calculus possesses an interaction or reduction relation. As a test for barbed bisimulation, we show that in CCS and π-calculus, it allows us to recover the familiar bisimulation-based equivalences. We also give simpler characterisations of the equivalences utilised in HOπ. For this we exploit a special kind of agents called triggers, with which it is possible to reason fairly efficiently in a higher-order calculus notwithstanding the complexity of its transitions. Finally, we use the compilation from HOπ to π-calculus to investigate Milner's
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Aleem, Hosam Abdel. "An algebraic approach to modelling the regulation of gene expression." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/an-algebraic-approach-to-modelling-the-regulation-of-gene-expression(d5d400b5-690e-4f32-9fd6-c80e4db455f3).html.

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Biotechnology is witnessing a remarkable growth evident both in the types of new products and in the innovative new processes developed. More efficient process design, optimisation and troubleshooting can be achieved through a better understanding of the underlying biological processes inside the cell; a key one of which is the regulation of gene expression. For engineers such understanding is attained through mathematical modelling, and the most commonly used models of gene expression regulation are those based on differential equations, as they give quantitative results. However, those results are undermined by several difficulties including the large number of parameters some of which, such as kinetic constants, are difficult to determine. This prompted the development of qualitative models, most notably Boolean models, based on the assumption that biological variables are binary in nature, e.g. a gene can be on or off and a chemical species present or absent. There are situations however, where different actions take place in the cell at different threshold values of the biological variables, and hence the binary assumption no longer holds.The purpose of this study was to develop a method for modelling gene regulatory functions where the variables can be thought of as taking more than two discrete values. A method was developed, where, with the appropriate assumptions the biological variables can be regarded as elements of an algebraic structure known as a finite field, in which case the regulatory function can be considered as a function on such a field.The formulation was adopted from electronic engineering, and leads to a polynomial known as the Reed-Muller expansion of the discrete function.The model was first developed for the more familiar binary case. It was given three different algebraic interpretations each enabling the study of a different biological problem, albeit related to gene regulation. The first interpretation is as a function on a Boolean algebra, but using the Exclusive OR (XOR) operation instead of the OR operation. The discriminating superiority of the XOR allows a more efficient determination of the gene regulatory function from the data, a problem known as reverse engineering.The second interpretation is as a polynomial on a finite field, where analogy with the Taylor series expansion of a real valued function allowed the coefficients of the expansion to be thought of as conveying sensitivity information. Furthermore a method was devised to detect mutation in the cell by regarding the problem as detecting a fault in a digital circuit.The third interpretation is as a transform on a discrete function space, which was demonstrated to be useful in synthetic biology design. The method was then extended to the multiple-valued case and demonstrated with modelling the gene regulation of a well known example system, the bacteriophage lambda.
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Kernert, David. "Density-Aware Linear Algebra in a Column-Oriented In-Memory Database System." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-210043.

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Linear algebra operations appear in nearly every application in advanced analytics, machine learning, and of various science domains. Until today, many data analysts and scientists tend to use statistics software packages or hand-crafted solutions for their analysis. In the era of data deluge, however, the external statistics packages and custom analysis programs that often run on single-workstations are incapable to keep up with the vast increase in data volume and size. In particular, there is an increasing demand of scientists for large scale data manipulation, orchestration, and advanced data management capabilities. These are among the key features of a mature relational database management system (DBMS). With the rise of main memory database systems, it now has become feasible to also consider applications that built up on linear algebra. This thesis presents a deep integration of linear algebra functionality into an in-memory column-oriented database system. In particular, this work shows that it has become feasible to execute linear algebra queries on large data sets directly in a DBMS-integrated engine (LAPEG), without the need of transferring data and being restricted by hard disc latencies. From various application examples that are cited in this work, we deduce a number of requirements that are relevant for a database system that includes linear algebra functionality. Beside the deep integration of matrices and numerical algorithms, these include optimization of expressions, transparent matrix handling, scalability and data-parallelism, and data manipulation capabilities. These requirements are addressed by our linear algebra engine. In particular, the core contributions of this thesis are: firstly, we show that the columnar storage layer of an in-memory DBMS yields an easy adoption of efficient sparse matrix data types and algorithms. Furthermore, we show that the execution of linear algebra expressions significantly benefits from different techniques that are inspired from database technology. In a novel way, we implemented several of these optimization strategies in LAPEG’s optimizer (SpMachO), which uses an advanced density estimation method (SpProdest) to predict the matrix density of intermediate results. Moreover, we present an adaptive matrix data type AT Matrix to obviate the need of scientists for selecting appropriate matrix representations. The tiled substructure of AT Matrix is exploited by our matrix multiplication to saturate the different sockets of a multicore main-memory platform, reaching up to a speed-up of 6x compared to alternative approaches. Finally, a major part of this thesis is devoted to the topic of data manipulation; where we propose a matrix manipulation API and present different mutable matrix types to enable fast insertions and deletes. We finally conclude that our linear algebra engine is well-suited to process dynamic, large matrix workloads in an optimized way. In particular, the DBMS-integrated LAPEG is filling the linear algebra gap, and makes columnar in-memory DBMS attractive as efficient, scalable ad-hoc analysis platform for scientists.
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Scott, J., I. Reiten, O. Iyama, and A. B. Buan. "Cluster structures for 2-Calabi-Yau categories and unipotent groups." Cambridge University Press, 2009. http://hdl.handle.net/2237/14400.

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Books on the topic "Algebra expressions"

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Where germs lurk: Writing, simplifying, and evaluating expressions. Teacher Created Materials, 2012.

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Mary, Stroh, and Sopris West, eds. Transitional mathematics: Student workbook : understanding algebraic expressions. Sopris West, 2005.

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Büchi, J. Richard. Finite automata, their algebras and grammars: Towards a theory of formal expressions. Edited by Siefkes Dirk. Springer-Verlag, 1989.

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Foerster, Paul A. Algebra I: Expressions, Equations, and Applications. 3rd ed. Pearson Prentice Hall, 1994.

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Foerster, Paul A. Algebra 1: Expressions, Equations, and Applications. Scott Foresman & Co, 1999.

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Algebra 1 (Expressions, Equasions, and Applications). Addison-Wesley, 1990.

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PUBLISHER, PRENTICE HALL. OnRamp to Algebra: Expressions, Equations, and Exponents. Pearson School, 2012.

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Murray, Hughes, Peter; Souviney, Randall Britt. Algebra Makes Sense Book 1 (Teacher Guide) Equations and Algebraic Expressions. Dale Seymour Publications, 2002.

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Radical Expressions (Lifepac Math Grade 9-Algebra 1). Alpha Omega Publications (AZ), 2001.

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U. of Utrecht) National Science Foundation (U. of Wisc. Britannica Mathematics in Context: Expressions and Formulas (Algebra). Holt, Rinehart and Winston, 2006.

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Book chapters on the topic "Algebra expressions"

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Gelfand, Israel M., and Alexander Shen. "Rational expressions." In Algebra. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0335-3_33.

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Breach, Mark. "Algebra — factors of expressions." In Fundamental Maths. Macmillan Education UK, 2011. http://dx.doi.org/10.1007/978-0-230-36624-4_12.

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Gillis, Joris J. M., and Jan Van den Bussche. "Induction of Relational Algebra Expressions." In Inductive Logic Programming. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13840-9_4.

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Kozen, Dexter C. "Kleene Algebra and Regular Expressions." In Automata and Computability. Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1844-9_10.

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López, César Pérez. "Algebraic Expressions, Polynomials, Equations and Systems." In MATLAB Linear Algebra. Apress, 2014. http://dx.doi.org/10.1007/978-1-4842-0322-4_4.

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Brenner, Richard L. "Simplifying Large Algebraic Expressions by Computer." In Applications of Computer Algebra. Springer US, 1985. http://dx.doi.org/10.1007/978-1-4684-6888-5_17.

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Andreescu, Titu. "Polynomial Expressions of Linear Transformations and Matrices." In Essential Linear Algebra with Applications. Springer New York, 2014. http://dx.doi.org/10.1007/978-0-8176-4636-3_8.

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López, César Pérez. "Algebraic Expressions and Operations: Factoring Algebraic Fractions." In MATLAB Symbolic Algebra and Calculus Tools. Apress, 2014. http://dx.doi.org/10.1007/978-1-4842-0343-9_2.

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Fabregat-Traver, Diego, and Paolo Bientinesi. "Knowledge-Based Automatic Generation of Partitioned Matrix Expressions." In Computer Algebra in Scientific Computing. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23568-9_12.

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Jacobs, Bart. "A Bialgebraic Review of Deterministic Automata, Regular Expressions and Languages." In Algebra, Meaning, and Computation. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11780274_20.

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Conference papers on the topic "Algebra expressions"

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Lima Gandra, Ana Paula, Ana Paula Aires, and Paula Catarino. "ALGEBRA TITLES IN BASIC EDUCATION: AN EXAMPLE WITH ALGEBRAIC EXPRESSIONS." In International Conference on Education and New Learning Technologies. IATED, 2017. http://dx.doi.org/10.21125/edulearn.2017.1439.

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Hou, Wen-Chi, Gultekin Ozsoyoglu, and Baldeo K. Taneja. "Statistical estimators for relational algebra expressions." In the seventh ACM SIGACT-SIGMOD-SIGART symposium. ACM Press, 1988. http://dx.doi.org/10.1145/308386.308455.

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van den Boom, Ton J. J., and Bart De Schutter. "Analytic expressions in stochastic max-plus-linear algebra." In 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, 2014. http://dx.doi.org/10.1109/cdc.2014.7039629.

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Shan, Ming-Chien, and Marie-Anne Neimat. "Optimization of relational algebra expressions containing recursion operators." In the 19th annual conference. ACM Press, 1991. http://dx.doi.org/10.1145/327164.327292.

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Omori, Hideki, Yoshiaki Maeda, Naoya Miyazaki, and Akira Yoshioka. "Expressions of algebra elements and transcendental noncommutative calculus." In Proceedings of the International Sendai-Beijing Joint Workshop. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812779649_0001.

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Mohamed, Maher G. "Acceleration Analysis of Platform-Type Manipulators." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/mech-1013.

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Abstract The screw algebra is used to efficiently derive expressions in compact form for both the angular accelerations of the moving links and the linear accelerations of points on the links of platform-type manipulators. The analysis employs the property that the acceleration state of the manipulator platform can be determined by considering the acceleration states of the links of only one — any one — of the manipulator legs. The obtained expressions provide an ease in symbolic and algebraic manipulation. The analysis is then extended to specify the acceleration center point of ithe nstantaneous motion of the manipulator platform. The acceleration center point is then used in expressing the distribution of the acceleration field of the platform instant motion which is important in manipulator synthesis. The special case of planar manipulators is studied and simpler expressions are derived. Numerical examples are presented for the analysis of a 3-DOF planar platform-type and of a 6-DOF spatial “Stewart Platform” manipulators to illustrate the analysis procedure.
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Shiakolas, Panos S., David C. Wilhite, and Sara E. McCaslin. "Comparison of Computer Algebra Systems for Closed Form Stiffness Matrix Generation." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-88263.

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Computer algebra systems (CAS) have been advantageously employed to generate closed form expressions for finite elements. The advantages relate to the time improvements or savings realized by employing closed form generated expressions as compared to numerical integration. However as the element order increases, the size of the closed form generated expressions become unmanageable causing the source code files to possibly become unusable due to their size. One approach to reducing the size of the source files is to take advantage of the utilities found in CAS to identify common expressions or sub-expressions. In this manuscript we present on-going research by comparing two widely used CAS, Mathematica and Maple, as they relate to identifying common expressions in low order tetrahedral finite element stiffness matrices generated in symbolic form, associated time savings and possible issues. The results indicate that the use of CAS could be advantageously employed to identify common subexpressions through pattern matching to further reduce the size of the generated source files and realize time improvements during execution of the source codes. In addition, the developed procedures could be easily applied to higher order elements with much larger number of entries of closed form expressions where even more savings could be realized.
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Argent-Katwala, Ashok, Jeremy T. Bradley, and Nicholas J. Dingle. "Expressing performance requirements using regular expressions to specify stochastic probes over process algebra models." In the fourth international workshop. ACM Press, 2004. http://dx.doi.org/10.1145/974044.974051.

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Fisun, Mykola, Hlib Horban, and Kandyba Ihor. "Processing of Relational Algebra Expressions by the Shunting Yard Algorithm." In 2019 IEEE 14th International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT). IEEE, 2019. http://dx.doi.org/10.1109/stc-csit.2019.8929740.

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Paredaens, Jan, and Dirk Van Gucht. "Possibilities and limitations of using flat operators in nested algebra expressions." In the seventh ACM SIGACT-SIGMOD-SIGART symposium. ACM Press, 1988. http://dx.doi.org/10.1145/308386.308402.

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