### Book

## Graph Structures for Knowledge Representation and Reasoning Third International Workshop, GKR 2013, Beijing, China, August 3, 2013. Revised Selected Papers Editors: Madalina Croitoru, Sebastian Rudolph, Stefan Woltran, Christophe Gonzales. Springer International Publishing. 2014.

Graph Structures for Knowledge Representation and Reasoning 2014. Workshop on IJCAI-2014.

We develop a graph representation and learning technique for parse structures for paragraphs of text. We introduce Parse Thicket (PT) as a set of syntactic parse trees augmented by a number of arcs for inter-sentence word-word relations such as co-reference and taxonomic relations. These arcs are also derived from other sources, including Speech Act and Rhetoric Structure theories. We provide a detailed illustration of how PTs are built from parse trees and generalized as phrases by computing maximal common subgraphs. The proposed approach is subject to evaluation in the product search and recommendation domain, where search queries include multiple sentences. We draw the comparison for search relevance improvement by pair-wise sentence generalization, phrase-level generalization, and generalizations of PTs as graphs.

This paper describes our approach to document search based on the ontological resources and graph models. The approach is applicable in local networks and local computers. It can be useful for ontology engineering specialists or search specialists.

*The article describes the original software tools for an experimental estimation of computational complexity of software solutions for problems on graph models of systems. The classes of the solved problems and the tools for analysis of results are listed. The method based on selection of graph models by their structural complexity is introduced.*

One of the key advances in genome assembly that has led to a significant improvement in contig lengths has been improved algorithms for utilization of paired reads (mate-pairs). While in most assemblers, mate-pair information is used in a post-processing step, the recently proposed Paired de Bruijn Graph (PDBG) approach incorporates the mate-pair information directly in the assembly graph structure. However, the PDBG approach faces difficulties when the variation in the insert sizes is high. To address this problem, we first transform mate-pairs into edge-pair histograms that allow one to better estimate the distance between edges in the assembly graph that represent regions linked by multiple mate-pairs. Further, we combine the ideas of mate-pair transformation and PDBGs to construct new data structures for genome assembly: pathsets and pathset graphs.

Process models and graphs are commonly used for modeling and visualization of processes. They may represent sets of objects or events linked with each other in some way. Wide use of models in such languages engenders necessity of tools for creating and editing them. This paper describes the model editor which allows for dealing with classical graphs, Petri nets, finite-state machines and their systems. Additionally, the tool has a list of features like simulation of Petri nets, import and export of models in different storage formats. Carassius is a modular tool which can be extended with, for example, new formalisms. In the paper one can find a detailed description of a couple of layout algorithms that can be used for visualizing Petri nets and graphs. Carassius might be useful for educational and research purposes because of its simplicity, range of features and variety of supported notations.

The book contains the necessary information from the algorithm theory, graph theory, combinatorics. It is considered partially recursive functions, Turing machines, some versions of the algorithms (associative calculus, the system of substitutions, grammars, Post's productions, Marcov's normal algorithms, operator algorithms). The main types of graphs are described (multigraphs, pseudographs, Eulerian graphs, Hamiltonian graphs, trees, bipartite graphs, matchings, Petri nets, planar graphs, transport nets). Some algorithms often used in practice on graphs are given. It is considered classical combinatorial configurations and their generating functions, recurrent sequences. It is put in a basis of the book long-term experience of teaching by authors the discipline «Discrete mathematics» at the business informatics faculty, at the computer science faculty* *of National Research University Higher School of Economics, and at the automatics and computer technique faculty of National research university Moscow power engineering institute. The book is intended for the students of a bachelor degree, trained at the computer science faculties in the directions 09.03.01 Informatics and computational technique, 09.03.02 Informational systems and technologies, 09.03.03 Applied informatics, 09.03.04 Software Engineering, and also for IT experts and developers of software products.

In this paper we present some preliminary results for text corpus visualization by means of so-called reference graphs. The nodes of this graph stand for key words or phrases extracted from the texts and the edges represent the reference relation. The node A refers to the node B if the corresponding key word / phrase B is more likely to co-occur with key word / phrase A than to occur on its own. Since reference graphs are directed graphs, we are able to use graphtheoretic algorithms for further analysis of the text corpus. The visualization technique is tested on our own Web-based corpus of Russian-language newspapers.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.