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Author : Воронка Зірка,Романовська Юлія,Рудник Тетяна
Publisher : Geneza
Page : 134 pages
File Size : 55,5 Mb
Release : 1994-01-01
Category : Foreign Language Study
ISBN : 9785770764147
Навчально-методичний комплекс "Let's Start! - 2" розрахований на дітей, що вивчають англійську мову другий рік.
Author : Bentert, Matthias
Publisher : Universitätsverlag der TU Berlin
Page : 218 pages
File Size : 50,8 Mb
Release : 2021-11-18
Category : Computers
ISBN : 9783798332096
In dieser Arbeit entwickeln wir schnellere exakte Algorithmen (schneller bezüglich der Worst-Case-Laufzeit) für Spezialfälle von Graphproblemen. Diese Algorithmen beruhen größtenteils auf dynamischem Programmieren und auf 2-SAT-Programmierung. Dynamisches Programmieren beschreibt den Vorgang, ein Problem rekursiv in Unterprobleme zu zerteilen, sodass diese Unterprobleme gemeinsame Unterunterprobleme haben. Wenn diese Unterprobleme optimal gelöst wurden, dann kombiniert das dynamische Programm diese Lösungen zu einer optimalen Lösung des Ursprungsproblems. 2-SAT-Programmierung bezeichnet den Prozess, ein Problem durch eine Menge von 2-SAT-Formeln (aussagenlogische Formeln in konjunktiver Normalform, wobei jede Klausel aus maximal zwei Literalen besteht) auszudrücken. Dabei müssen erfüllende Wahrheitswertbelegungen für eine Teilmenge der 2-SAT-Formeln zu einer Lösung des Ursprungsproblems korrespondieren. Wenn eine 2-SAT-Formel erfüllbar ist, dann kann eine erfüllende Wahrheitswertbelegung in Linearzeit in der Länge der Formel berechnet werden. Wenn entsprechende 2-SAT-Formeln also in polynomieller Zeit in der Eingabegröße des Ursprungsproblems erstellt werden können, dann kann das Ursprungsproblem in polynomieller Zeit gelöst werden. Im folgenden beschreiben wir die Hauptresultate der Arbeit. Bei dem Diameter-Problem wird die größte Distanz zwischen zwei beliebigen Knoten in einem gegebenen ungerichteten Graphen gesucht. Das Ergebnis (der Durchmesser des Eingabegraphen) gehört zu den wichtigsten Parametern der Graphanalyse. In dieser Arbeit erzielen wir sowohl positive als auch negative Ergebnisse für Diameter. Wir konzentrieren uns dabei auf parametrisierte Algorithmen für Parameterkombinationen, die in vielen praktischen Anwendungen klein sind, und auf Parameter, die eine Distanz zur Trivialität messen. Bei dem Problem Length-Bounded Cut geht es darum, ob es eine Kantenmenge begrenzter Größe in einem Eingabegraphen gibt, sodass das Entfernen dieser Kanten die Distanz zwischen zwei gegebenen Knoten auf ein gegebenes Minimum erhöht. Wir bestätigen in dieser Arbeit eine Vermutung aus der wissenschaftlichen Literatur, dass Length-Bounded Cut in polynomieller Zeit in der Eingabegröße auf Einheitsintervallgraphen (Intervallgraphen, in denen jedes Intervall die gleiche Länge hat) gelöst werden kann. Der Algorithmus basiert auf dynamischem Programmieren. k-Disjoint Shortest Paths beschreibt das Problem, knotendisjunkte Pfade zwischen k gegebenen Knotenpaaren zu suchen, sodass jeder der k Pfade ein kürzester Pfad zwischen den jeweiligen Endknoten ist. Wir beschreiben ein dynamisches Programm mit einer Laufzeit n^O((k+1)!) für dieses Problem, wobei n die Anzahl der Knoten im Eingabegraphen ist. Dies zeigt, dass k-Disjoint Shortest Paths in polynomieller Zeit für jedes konstante k gelöst werden kann, was für über 20 Jahre ein ungelöstes Problem der algorithmischen Graphentheorie war. Das Problem Tree Containment fragt, ob ein gegebener phylogenetischer Baum T in einem gegebenen phylogenetischen Netzwerk N enthalten ist. Ein phylogenetisches Netzwerk (bzw. ein phylogenetischer Baum) ist ein gerichteter azyklischer Graph (bzw. ein gerichteter Baum) mit genau einer Quelle, in dem jeder Knoten höchstens eine ausgehende oder höchstens eine eingehende Kante hat und jedes Blatt eine Beschriftung trägt. Das Problem stammt aus der Bioinformatik aus dem Bereich der Suche nach dem Baums des Lebens (der Geschichte der Artenbildung). Wir führen eine neue Variante des Problems ein, die wir Soft Tree Containment nennen und die bestimmte Unsicherheitsfaktoren berücksichtigt. Wir zeigen mit Hilfe von 2-SAT-Programmierung, dass Soft Tree Containment in polynomieller Zeit gelöst werden kann, wenn N ein phylogenetischer Baum ist, in dem jeweils maximal zwei Blätter die gleiche Beschriftung tragen. Wir ergänzen dieses Ergebnis mit dem Beweis, dass Soft Tree Containment NP-schwer ist, selbst wenn N auf phylogenetische Bäume beschränkt ist, in denen jeweils maximal drei Blätter die gleiche Beschriftung tragen. Abschließend betrachten wir das Problem Reachable Object. Hierbei wird nach einer Sequenz von rationalen Tauschoperationen zwischen Agentinnen gesucht, sodass eine bestimmte Agentin ein bestimmtes Objekt erhält. Eine Tauschoperation ist rational, wenn beide an dem Tausch beteiligten Agentinnen ihr neues Objekt gegenüber dem jeweiligen alten Objekt bevorzugen. Reachable Object ist eine Verallgemeinerung des bekannten und viel untersuchten Problems Housing Market. Hierbei sind die Agentinnen in einem Graphen angeordnet und nur benachbarte Agentinnen können Objekte miteinander tauschen. Wir zeigen, dass Reachable Object NP-schwer ist, selbst wenn jede Agentin maximal drei Objekte gegenüber ihrem Startobjekt bevorzugt und dass Reachable Object polynomzeitlösbar ist, wenn jede Agentin maximal zwei Objekte gegenüber ihrem Startobjekt bevorzugt. Wir geben außerdem einen Polynomzeitalgorithmus für den Spezialfall an, in dem der Graph der Agentinnen ein Kreis ist. Dieser Polynomzeitalgorithmus basiert auf 2-SAT-Programmierung. This thesis presents faster (in terms of worst-case running times) exact algorithms for special cases of graph problems through dynamic programming and 2-SAT programming. Dynamic programming describes the procedure of breaking down a problem recursively into overlapping subproblems, that is, subproblems with common subsubproblems. Given optimal solutions to these subproblems, the dynamic program then combines them into an optimal solution for the original problem. 2-SAT programming refers to the procedure of reducing a problem to a set of 2-SAT formulas, that is, boolean formulas in conjunctive normal form in which each clause contains at most two literals. Computing whether such a formula is satisfiable (and computing a satisfying truth assignment, if one exists) takes linear time in the formula length. Hence, when satisfying truth assignments to some 2-SAT formulas correspond to a solution of the original problem and all formulas can be computed efficiently, that is, in polynomial time in the input size of the original problem, then the original problem can be solved in polynomial time. We next describe our main results. Diameter asks for the maximal distance between any two vertices in a given undirected graph. It is arguably among the most fundamental graph parameters. We provide both positive and negative parameterized results for distance-from-triviality-type parameters and parameter combinations that were observed to be small in real-world applications. In Length-Bounded Cut, we search for a bounded-size set of edges that intersects all paths between two given vertices of at most some given length. We confirm a conjecture from the literature by providing a polynomial-time algorithm for proper interval graphs which is based on dynamic programming. k-Disjoint Shortest Paths is the problem of finding (vertex-)disjoint paths between given vertex terminals such that each of these paths is a shortest path between the respective terminals. Its complexity for constant k > 2 has been an open problem for over 20 years. Using dynamic programming, we show that k-Disjoint Shortest Paths can be solved in polynomial time for each constant k. The problem Tree Containment asks whether a phylogenetic tree T is contained in a phylogenetic network N. A phylogenetic network (or tree) is a leaf-labeled single-source directed acyclic graph (or tree) in which each vertex has in-degree at most one or out-degree at most one. The problem stems from computational biology in the context of the tree of life (the history of speciation). We introduce a particular variant that resembles certain types of uncertainty in the input. We show that if each leaf label occurs at most twice in a phylogenetic tree N, then the problem can be solved in polynomial time and if labels can occur up to three times, then the problem becomes NP-hard. Lastly, Reachable Object is the problem of deciding whether there is a sequence of rational trades of objects among agents such that a given agent can obtain a certain object. A rational trade is a swap of objects between two agents where both agents profit from the swap, that is, they receive objects they prefer over the objects they trade away. This problem can be seen as a natural generalization of the well-known and well-studied Housing Market problem where the agents are arranged in a graph and only neighboring agents can trade objects. We prove a dichotomy result that states that the problem is polynomial-time solvable if each agent prefers at most two objects over its initially held object and it is NP-hard if each agent prefers at most three objects over its initially held object. We also provide a polynomial-time 2-SAT program for the case where the graph of agents is a cycle.
Author : Stefano Leonardi
Publisher : Springer Science & Business Media
Page : 654 pages
File Size : 49,6 Mb
Release : 2009-12-07
Category : Computers
ISBN : 9783642108402
This volume contains the papers presented at WINE 2009:the 5th International Workshop on Internet and Network Economics held December 14–18, 2009, in Rome,attheDepartmentofComputerandSystemSciences,SapienzaUniversity of Rome. Over the past decade there has been growing interaction between researchers in theoretical computer science, networking and security, economics, mathem- ics, sociology, and management sciences devoted to the analysis of problems arising in the Internet and the worldwide web. The Workshop on Internet and Network Economics (WINE) is an interdisciplinary forum for the exchange of ideas and results arising in these varied ?elds. There were 142 submissions to the workshop including regular and short - pers.Allsubmissionswererigorouslypeer reviewedandevaluatedonthebasisof the quality of their contribution, originality,soundness, and signi?cance. Almost all submissions were reviewed by at least three Program Committee members. The committee decided to accept 34 regular papers and 29 short papers. The Best Student Paper award sponsored by Google Inc. was given to Saeed Alaei and AzarakhshMalekianfor the paper “An Analysisof Troubled Assets Reverse Auction.” The program also included three invited talks by S. Muthukrishnan (Google Inc.and RutgersUniversity),H. PeytonYoung (OxfordandJohns Hopkins U- versity)andEvaTardos(CornellUnversity).Threetutorialswerealsoo?eredon the days before the workshop, from Andrei Broder (Yahoo! Research) on C- putational Advertising, Nikhil Devanur and Kamal Jain (Microsoft Research) on Computational Issues in Market Equilibria, and Tim Roughgarden(Stanford University) on Bayesian and Worst-Case Revenue Maximization.
Author : Michael A. Bekos,Markus Chimani
Publisher : Springer Nature
Page : 368 pages
File Size : 49,9 Mb
Release : 2024-01-11
Category : Computers
ISBN : 9783031492723
This two-volume set LNCS 14465-14466 constitutes the proceedings of the 31st International Symposium on Graph Drawing and Network Visualization, GD 2023, held in Isola delle Femmine, Palermo, Italy, in September 2023. The 31 full papers, 7 short papers, presented together with 2 invited talks, and one contest report, were thoroughly reviewed and selected from the 100 submissions. The abstracts of 11 posters presented at the conference can be found in the back matter of the volume. The contributions were organized in topical sections as follows: beyond planarity; crossing numbers; linear layouts; geometric aspects; visualization challenges; graph representations; graph decompositions; topological aspects; parameterized complexity for drawings; planar graphs; frameworks; algorithmics.
Author : Christophe Breuil,Vytautas Paskunas
Publisher : American Mathematical Soc.
Page : 127 pages
File Size : 47,9 Mb
Release : 2012-02-22
Category : Mathematics
ISBN : 9780821852279
The authors construct new families of smooth admissible $\overline{\mathbb{F}}_p$-representations of $\mathrm{GL}_2(F)$, where $F$ is a finite extension of $\mathbb{Q}_p$. When $F$ is unramified, these representations have the $\mathrm{GL}_2({\mathcal O}_F)$-socle predicted by the recent generalizations of Serre's modularity conjecture. The authors' motivation is a hypothetical mod $p$ Langlands correspondence.
Author : George Nemhauser,Daniel Bienstock
Publisher : Springer
Page : 448 pages
File Size : 41,9 Mb
Release : 2004-07-27
Category : Mathematics
ISBN : 9783540259602
This volume contains the papers accepted for publication at IPCO X, the Tenth International Conference on Integer Programming and Combinatorial Optimization, held in New York City, New York, USA, June 7-11, 2004. The IPCO series of conferences presents recent results in theory, computation and applications of integer programming and combinatorial optimization. These conferences are sponsored by the Mathematical Programming Society, and are held in those years in which no International Symposium on Mathematical Programming takes place. IPCO VIII was held in Utrecht (The Netherlands) and IPCO IX was held in Cambridge (USA). A total of 109 abstracts, mostly of very high quality, were submitted. The Program Committee accepted 32, in order to meet the goal of having three days of talks with no parallel sessions. Thus, many excellent abstracts could not be accepted. The papers in this volume have not been refereed. It is expected that revised versions of the accepted papers will be submitted to standard scientific journals for publication. The Program Committee thanks all authors of submitted manuscripts for their support of IPCO. March 2004 George Nemhauser Daniel Bienstock Organization IPCO X was hosted by the Computational Optimization Research Center (CORC), Columbia University.
Author : Hans Ringström
Publisher : OUP Oxford
Page : 733 pages
File Size : 42,5 Mb
Release : 2013-05-23
Category : Science
ISBN : 9780199680290
A general introduction to the initial value problem for Einstein's equations coupled to collisionless matter. The book contains a proof of future stability of models of the universe consistent with the current observational data and a discussion of the restrictions on the possible shapes of the universe imposed by observations.
Author : Stefaan Caenepeel
Publisher : CRC Press
Page : 280 pages
File Size : 47,5 Mb
Release : 2020-08-26
Category : Mathematics
ISBN : 9781000103786
This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredients in the theory of Azumaya algebras: separability and Galois extensions of commutative rings, crossed products and Galois cohomology, Picard groups, and the Brauer group.
Author : Gregory F. Lawler
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 44,7 Mb
Release : 2012-11-06
Category : Mathematics
ISBN : 9781461459729
A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable. One of the most useful concepts for this purpose is that of the random walk which has applications in many areas, particularly in statistical physics and statistical chemistry. Originally published in 1991, Intersections of Random Walks focuses on and explores a number of problems dealing primarily with the nonintersection of random walks and the self-avoiding walk. Many of these problems arise in studying statistical physics and other critical phenomena. Topics include: discrete harmonic measure, including an introduction to diffusion limited aggregation (DLA); the probability that independent random walks do not intersect; and properties of walks without self-intersections. The present softcover reprint includes corrections and addenda from the 1996 printing, and makes this classic monograph available to a wider audience. With a self-contained introduction to the properties of simple random walks, and an emphasis on rigorous results, the book will be useful to researchers in probability and statistical physics and to graduate students interested in basic properties of random walks.
Author : I.A. Faradzev,A.A. Ivanov,M. Klin,A.J. Woldar
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 49,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401719728
X Köchendorffer, L.A. Kalu:lnin and their students in the 50s and 60s. Nowadays the most deeply developed is the theory of binary invariant relations and their combinatorial approximations. These combinatorial approximations arose repeatedly during this century under various names (Hecke algebras, centralizer rings, association schemes, coherent configurations, cellular rings, etc.-see the first paper of the collection for details) andin various branches of mathematics, both pure and applied. One of these approximations, the theory of cellular rings (cellular algebras), was developed at the end of the 60s by B. Yu. Weisfeiler and A.A. Leman in the course of the first serious attempt to study the complexity of the graph isomorphism problem, one of the central problems in the modern theory of combinatorial algorithms. At roughly the same time G.M. Adelson-Velskir, V.L. Arlazarov, I.A. Faradtev and their colleagues had developed a rather efficient tool for the constructive enumeration of combinatorial objects based on the branch and bound method. By means of this tool a number of "sports-like" results were obtained. Some of these results are still unsurpassed.
Author : Kumiyo Nakakoji,Yohei Murakami,Eric McCready
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 50,6 Mb
Release : 2010-08-11
Category : Computers
ISBN : 9783642148873
This book constitutes the refereed proceedings of 4 workshops held at the JSAI International Symposia on Artificial Intelligence 2010, in Tokyo, Japan, in November 2009. The 24 revised full papers presented were carefully reviewed and selected from 61 submissions. The papers are organized in the workshop sections Logic and Engineering of Natural Language Semantics (LENLS), Juris-Informatics (JURISIN), Knowledge Collaboration in Software Development (KCSD), and Learning with Logics and Logics for Learning (LLLL).
Author : Séverine Fiedler - Le Touzé
Publisher : CRC Press
Page : 238 pages
File Size : 41,9 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9780429838248
Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP2. Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as, can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book’s second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally, the third section contains plentiful applications and results around Hilbert’s sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology, algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert’s sixteenth problem About the Author: Séverine Fiedler-le Touzé has published several papers on this topic and has been invited to present at many conferences. She holds a Ph.D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley, California.
Author : Jean-Marc Adamo
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461300854
Recent advances in data collection, storage technologies, and computing power have made it possible for companies, government agencies and scientific laboratories to keep and manipulate vast amounts of data relating to their activities. This state-of-the-art monograph discusses essential algorithms for sophisticated data mining methods used with large-scale databases, focusing on two key topics: association rules and sequential pattern discovery. This will be an essential book for practitioners and professionals in computer science and computer engineering.
Author : Valentin E. Brimkov,Reneta P. Barneva
Publisher : Springer
Page : 357 pages
File Size : 55,5 Mb
Release : 2017-05-15
Category : Computers
ISBN : 9783319591087
This book constitutes the proceedings of the 18th International Workshop on Combinatorial Image Analysis, IWCIA 2017, held in Plovdiv, Bulgaria, in June 2017. The 27 revised full papers presented were carefully reviewed and selected from 47 submissions. The workshop is organized in topical sections of theoretical foundations and theory of applications, namely: discrete geometry and topology; tilings and patterns; grammars, models and other technical tools for image analysis; image segmentation, classification; reconstruction; compression; texture analysis; bioimaging.
Author : G. De Giacomo,A. Catala,B. Dilkina
Publisher : IOS Press
Page : 3122 pages
File Size : 44,5 Mb
Release : 2020-09-11
Category : Computers
ISBN : 9781643681016
This book presents the proceedings of the 24th European Conference on Artificial Intelligence (ECAI 2020), held in Santiago de Compostela, Spain, from 29 August to 8 September 2020. The conference was postponed from June, and much of it conducted online due to the COVID-19 restrictions. The conference is one of the principal occasions for researchers and practitioners of AI to meet and discuss the latest trends and challenges in all fields of AI and to demonstrate innovative applications and uses of advanced AI technology. The book also includes the proceedings of the 10th Conference on Prestigious Applications of Artificial Intelligence (PAIS 2020) held at the same time. A record number of more than 1,700 submissions was received for ECAI 2020, of which 1,443 were reviewed. Of these, 361 full-papers and 36 highlight papers were accepted (an acceptance rate of 25% for full-papers and 45% for highlight papers). The book is divided into three sections: ECAI full papers; ECAI highlight papers; and PAIS papers. The topics of these papers cover all aspects of AI, including Agent-based and Multi-agent Systems; Computational Intelligence; Constraints and Satisfiability; Games and Virtual Environments; Heuristic Search; Human Aspects in AI; Information Retrieval and Filtering; Knowledge Representation and Reasoning; Machine Learning; Multidisciplinary Topics and Applications; Natural Language Processing; Planning and Scheduling; Robotics; Safe, Explainable, and Trustworthy AI; Semantic Technologies; Uncertainty in AI; and Vision. The book will be of interest to all those whose work involves the use of AI technology.
