### Book

## New trends in Stochastic Modeling and Data Analysis

This is the first book devoted to the 3rd Stochastic Modeling Techniques and Data Analysis (SMTDA) International Conference held in Lisbon, Portugal, June 11-14, 2014. Revised and expanded forms of papers from the conference presentations are included. SMTDA main objective is to publish papers, both theoretical or practical, presenting new results having potential for solving real-life problems. Another important objective is to present new methods for solving these problems by analyzing the relevant data. Also, the use of recent advances in different fields is promoted such as for example, new optimization and statistical methods, data warehouse, data mining and knowledge systems, computing-aided decision supports and neural computing. The first Chapter includes papers on Asymptotic Analysis of Stochastic Systems with Complex Structure, whereas contributions on Markov and semi-Markov models are included in the second Chapter. Papers on Clustering and Partitioning for particular cases are included in the third Chapter, and papers on Survival Analysis and Branching Processes are presented in the fourth Chapter. Papers on Stochastics methods and techniques are presented in the fifth Chapter along with Data Analysis papers included in the sixth Chapter. Chapter seven includes papers on Demography and Related Applications, whereas Stochastic Processes, Copulas and Actuarial Applications are analyzed in Chapter eight. Many thanks to the authors for their contribution and our sincere thanks to the referees to their hard work and dedication in providing an improved book form. We acknowledge the valuable support of the SMTDA committees and the secretariat. We are happy for editing another book of the SMTDA series.

This book constitutes the refereed proceedings of the 10th International Conference on Formal Concept Analysis, ICFCA 2012, held in Leuven, Belgium in May 2012. The 20 revised full papers presented together with 6 invited talks were carefully reviewed and selected from 68 submissions. The topics covered in this volume range from recent advances in machine learning and data mining; mining terrorist networks and revealing criminals; concept-based process mining; to scalability issues in FCA and rough sets.

In this paper we propose the software system CORDIET-Helthcare which we are currently developing in collaboration with the Katholieke Universiteit Leuven, Moscow Higher School of Economics and the GZA-hospital group located in Antwerp. The main aim of this system is to offer healthcare management staff a user-friendly and powerful data analysis environment. Using state of the art techniques from computer science and mathematics we show how CORDIET-Helthcare can be used to gain insight in existing care processes and reveal actionable knowledge which can be used to improve the current way of working.

This book constitutes the second part of the refereed proceedings of the 10th International Conference on Formal Concept Analysis, ICFCA 2012, held in Leuven, Belgium in May 2012. The topics covered in this volume range from recent advances in machine learning and data mining; mining terrorist networks and revealing criminals; concept-based process mining; to scalability issues in FCA and rough sets.

This is a textbook in data analysis. Its contents are heavily influenced by the idea that data analysis should help in enhancing and augmenting knowledge of the domain as represented by the concepts and statements of relation between them. According to this view, two main pathways for data analysis are summarization, for developing and augmenting concepts, and correlation, for enhancing and establishing relations. Visualization, in this context, is a way of presenting results in a cognitively comfortable way. The term *summarization* is understood quite broadly here to embrace not only simple summaries like totals and means, but also more complex summaries such as the principal components of a set of features or cluster structures in a set of entities.

The material presented in this perspective makes a unique mix of subjects from the fields of statistical data analysis, data mining, and computational intelligence, which follow different systems of presentation.

We describe FCART software system, a universal integrated environment for knowledge and data engineers with a set of research tools based on Formal Concept Analysis. The system is intended for knowledge discovery from big dynamic data collections, including text collections. FCART allows the user to load structured and unstructured data (texts and various metainformation) from heterogeneous data sources, build data snapshots, compose queries, generate and visualize concept lattices, clusters, attribute dependencies, and other useful analytical artifacts. Full preprocessing scenario is considered.

Formal Concept Analysis Research Toolbox (FCART) is an integrated environment for knowledge and data engineers with a set of research tools based on Formal Concept Analysis. FCART allows a user to load structured and unstructured data (including texts with various metadata) from heterogeneous data sources into local data storage, compose scaling queries for data snapshots, and then research classical and some innovative FCA artifacts in analytic sessions.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.