1,390 research outputs found
Parallel and distributed Gr\"obner bases computation in JAS
This paper considers parallel Gr\"obner bases algorithms on distributed
memory parallel computers with multi-core compute nodes. We summarize three
different Gr\"obner bases implementations: shared memory parallel, pure
distributed memory parallel and distributed memory combined with shared memory
parallelism. The last algorithm, called distributed hybrid, uses only one
control communication channel between the master node and the worker nodes and
keeps polynomials in shared memory on a node. The polynomials are transported
asynchronous to the control-flow of the algorithm in a separate distributed
data structure. The implementation is generic and works for all implemented
(exact) fields. We present new performance measurements and discuss the
performance of the algorithms.Comment: 14 pages, 8 tables, 13 figure
Cross domain recommender systems using matrix and tensor factorization
Today, the amount and importance of available data on the internet are growing exponentially. These digital data has become a primary source of information and the people’s life bonded to them tightly. The data comes in diverse shapes and from various resources and users utilize them in almost all their personal or social activities. However, selecting a desirable option from the huge list of available options can be really frustrating and time-consuming. Recommender systems aim to ease this process by finding the proper items which are more likely to be interested by users. Undoubtedly, there is not even one social media or online service which can continue its’ work properly without using recommender systems. On the other hand, almost all available recommendation techniques suffer from some common issues: the data sparsity, the cold-start, and the new-user problems.
This thesis tackles the mentioned problems using different methods. While, most of the recommender methods rely on using single domain information, in this thesis, the main focus is on using multi-domain information to create cross-domain recommender systems. A cross-domain recommender system is not only able to handle the cold-start and new-user situations much better, but it also helps to incorporate different features exposed in diverse domains together and capture a better understanding of the users’ preferences which means producing more accurate recommendations.
In this thesis, a pre-clustering stage is proposed to reduce the data sparsity as well. Various cross-domain knowledge-based recommender systems are suggested to recommend items in two popular social media, the Twitter and LinkedIn, by using different information available in both domains. The state of art techniques in this field, namely matrix factorization and tensor decomposition, are implemented to develop cross-domain recommender systems. The presented recommender systems based on the coupled nonnegative matrix factorization and PARAFAC-style tensor decomposition are evaluated using real-world datasets and it is shown that they superior to the baseline matrix factorization collaborative filtering. In addition, network analysis is performed on the extracted data from Twitter and LinkedIn
A Symbolic Transformation Language and its Application to a Multiscale Method
The context of this work is the design of a software, called MEMSALab,
dedicated to the automatic derivation of multiscale models of arrays of micro-
and nanosystems. In this domain a model is a partial differential equation.
Multiscale methods approximate it by another partial differential equation
which can be numerically simulated in a reasonable time. The challenge consists
in taking into account a wide range of geometries combining thin and periodic
structures with the possibility of multiple nested scales.
In this paper we present a transformation language that will make the
development of MEMSALab more feasible. It is proposed as a Maple package for
rule-based programming, rewriting strategies and their combination with
standard Maple code. We illustrate the practical interest of this language by
using it to encode two examples of multiscale derivations, namely the two-scale
limit of the derivative operator and the two-scale model of the stationary heat
equation.Comment: 36 page
Formal Foundations for Information-Preserving Model Synchronization Processes Based on Triple Graph Grammars
Zwischen verschiedenen Artefakten, die Informationen teilen, wieder Konsistenz herzustellen, nachdem eines von ihnen geändert wurde, ist ein wichtiges Problem, das in verschiedenen Bereichen der Informatik auftaucht. Mit dieser Dissertation legen wir eine Lösung für das grundlegende Modellsynchronisationsproblem vor. Bei diesem Problem ist ein Paar solcher Artefakte (Modelle) gegeben, von denen eines geändert wurde; Aufgabe ist die Wiederherstellung der Konsistenz. Tripelgraphgrammatiken (TGGs) sind ein etablierter und geeigneter Formalismus, um dieses und verwandte Probleme anzugehen. Da sie auf der algebraischen Theorie der Graphtransformation und dem (Double-)Pushout Zugang zu Ersetzungssystemen basieren, sind sie besonders geeignet, um Lösungen zu entwickeln, deren Eigenschaften formal bewiesen werden können. Doch obwohl TGG-basierte Ansätze etabliert sind, leiden viele von ihnen unter dem Problem des Informationsverlustes. Wenn ein Modell geändert wurde, können während eines Synchronisationsprozesses Informationen verloren gehen, die nur im zweiten Modell vorliegen. Das liegt daran, dass solche Synchronisationsprozesse darauf zurückfallen Konsistenz dadurch wiederherzustellen, dass sie das geänderte Modell (bzw. große Teile von ihm) neu übersetzen. Wir schlagen einen TGG-basierten Ansatz vor, der fortgeschrittene Features von TGGs unterstützt (Attribute und negative Constraints), durchgängig formalisiert ist, implementiert und inkrementell in dem Sinne ist, dass er den Informationsverlust im Vergleich mit vorherigen Ansätzen drastisch reduziert. Bisher gibt es keinen TGG-basierten Ansatz mit vergleichbaren Eigenschaften.
Zentraler Beitrag dieser Dissertation ist es, diesen Ansatz formal auszuarbeiten und seine wesentlichen Eigenschaften, nämlich Korrektheit, Vollständigkeit und Termination, zu beweisen. Die entscheidende neue Idee unseres Ansatzes ist es, Reparaturregeln anzuwenden. Dies sind spezielle Regeln, die es erlauben, Änderungen an einem Modell direkt zu propagieren anstatt auf Neuübersetzung zurückzugreifen. Um diese Reparaturregeln erstellen und anwenden zu können, entwickeln wir grundlegende Beiträge zur Theorie der algebraischen Graphtransformation. Zunächst entwickeln wir eine neue Art der sequentiellen Komposition von Regeln. Im Gegensatz zur gewöhnlichen Komposition, die zu Regeln führt, die Elemente löschen und dann wieder neu erzeugen, können wir Regeln herleiten, die solche Elemente stattdessen bewahren. Technisch gesehen findet der Synchronisationsprozess, den wir entwickeln, außerdem in der Kategorie der partiellen Tripelgraphen statt und nicht in der der normalen Tripelgraphen. Daher müssen wir sicherstellen, dass die für Double-Pushout-Ersetzungssysteme ausgearbeitete Theorie immer noch gültig ist. Dazu entwickeln wir eine (kategorientheoretische) Konstruktion neuer Kategorien aus gegebenen und zeigen, dass (i) diese Konstruktion die Axiome erhält, die nötig sind, um die Theorie für Double-Pushout-Ersetzungssysteme zu entwickeln, und (ii) partielle Tripelgraphen als eine solche Kategorie konstruiert werden können. Zusammen ermöglichen diese beiden grundsätzlichen Beiträge es uns, unsere Lösung für das grundlegende Modellsynchronisationsproblem vollständig formal auszuarbeiten und ihre zentralen Eigenschaften zu beweisen.Restoring consistency between different information-sharing artifacts after one of them has been changed is an important problem that arises in several areas of computer science. In this thesis, we provide a solution to the basic model synchronization problem. There, a pair of such artifacts (models), one of which has been changed, is given and consistency shall be restored. Triple graph grammars (TGGs) are an established and suitable formalism to address this and related problems. Being based on the algebraic theory of graph transformation and (double-)pushout rewriting, they are especially suited to develop solutions whose properties can be formally proven. Despite being established, many TGG-based solutions do not satisfactorily deal with the problem of information loss. When one model is changed, in the process of restoring consistency such solutions may lose information that is only present in the second model because the synchronization process resorts to restoring consistency by re-translating (large parts of) the updated model. We introduce a TGG-based approach that supports advanced features of TGGs (attributes and negative constraints), is comprehensively formalized, implemented, and is incremental in the sense that it drastically reduces the amount of information loss compared to former approaches. Up to now, a TGG-based approach with these characteristics is not available.
The central contribution of this thesis is to formally develop that approach and to prove its essential properties, namely correctness, completeness, and termination. The crucial new idea in our approach is the use of repair rules, which are special rules that allow one to directly propagate changes from one model to the other instead of resorting to re-translation. To be able to construct and apply these repair rules, we contribute more fundamentally to the theory of algebraic graph transformation. First, we develop a new kind of sequential rule composition. Whereas the conventional composition of rules leads to rules that delete and re-create elements, we can compute rules that preserve such elements instead. Furthermore, technically the setting in which the synchronization process we develop takes place is the category of partial triple graphs and not the one of ordinary triple graphs. Hence, we have to ensure that the elaborate theory of double-pushout rewriting still applies. Therefore, we develop a (category-theoretic) construction of new categories from given ones and show that (i) this construction preserves the axioms that are necessary to develop the theory of double-pushout rewriting and (ii) partial triple graphs can be constructed as such a category. Together, those two more fundamental contributions enable us to develop our solution to the basic model synchronization problem in a fully formal manner and to prove its central properties
Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 B.C.--2017) and another new proof
In this article, we provide a comprehensive historical survey of 183
different proofs of famous Euclid's theorem on the infinitude of prime numbers.
The author is trying to collect almost all the known proofs on infinitude of
primes, including some proofs that can be easily obtained as consequences of
some known problems or divisibility properties. Furthermore, here are listed
numerous elementary proofs of the infinitude of primes in different arithmetic
progressions.
All the references concerning the proofs of Euclid's theorem that use similar
methods and ideas are exposed subsequently. Namely, presented proofs are
divided into 8 subsections of Section 2 in dependence of the methods that are
used in them. {\bf Related new 14 proofs (2012-2017) are given in the last
subsection of Section 2.} In the next section, we survey mainly elementary
proofs of the infinitude of primes in different arithmetic progressions.
Presented proofs are special cases of Dirichlet's theorem. In Section 4, we
give a new simple "Euclidean's proof" of the infinitude of primes.Comment: 70 pages. In this extended third version of the article, 14 new
proofs of the infnitude of primes are added (2012-2017
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