### Working paper

## Loop groups, Clusters, Dimers and Integrable systems

Intellectual capital is very heterogeneous so it’s usual practice to divide it into some groups of more similar and homogeneous intellectual assets. It’s widespread to distinguish human capital (knowledge, skills of employees etc.), structural capital (business‐processes, innovations, corporate culture etc.) and relational capital (brand, reputation, relationships with customers etc.). The literature supports the significance of intellectual capital influence on company’s value creation. Researchers find a strong dependence of corporate performance on intellectual assets in different countries and economy branches. But their findings about a character of intellectual capital transformation in corporate value are ambiguous. Importance of human, structural and relational capital and interrelationships between them vary highly across papers. It may be explained by high firm specificity of corporate value creation. It doesn’t mean impossibility of intercompany research but requires a comparability of analyzed firms. Empirical researches on the theme of intellectual capital are often limited to particular country and industry. This restriction makes investigated companies more comparable. But we suppose there is a lot of other significant aspects of firm specificity that may impact on transformation of intellectual assets into corporate value such as firm size, amount of intangible assets, total firm efficiency etc. These variables are sometimes considered as additional factors of corporate value. But we suppose these criteria may define the model of corporate value creation in principle. This study is targeted to reveal some main types of companies and investigate a specificity of corporate value creation model for each of them. We expect to discover significant differences in models mostly related to importance and significance of particular intellectual assets. This paper is empirical and quantitative. Our sample embraces about 200 large public European industrial companies from 7 countries (Denmark, Germany, Great Britain, Finland, Netherlands, Portugal and Spain) for 2005‐2009 years. The database includes: 1. Information from financial statement. The source is Amadeus database (Bureau Van Dijk). 2. A set of nonfinancial proxy indicators (quantitative and qualitative) displaying a state of human, structural and relational capital. This data has been collected from open Internet sources such as companies’ sites. Methodology of the research combines statistic methods (cluster analysis and factor analysis) and econometrics (regression analysis). Clustering distinguishes some main types of companies. Factor analysis constructs integral indices for human, structural and relational capital on the base of initial proxy set. Regression is an instrument of modeling the corporate value creation. We found significant differences between models of corporate value creation. Human, structural and relational capitals differently transform into firm value in each type of companies. Our findings have some practical implications. For example prioritizing investments in intellectual assets should take into account a firm’s specificity more deeply. This study comprises research findings from the ‘Intellectual Capital Evaluation” Project carried out within The Higher School of Economics’ 2011 Academic Fund Program.

Recently, a three-stage version of K-Means has been introduced, at which not only clusters and their centers, but also feature weights are adjusted to minimize the summary p-th power of the Minkowski p-distance between entities and centroids of their clusters. The value of the Minkowski exponent p appears to be instrumental in the ability of the method to recover clusters hidden in data. This paper advances into the problem of finding the best p for a Minkowski metric-based version of K-Means, in each of the following two settings: semi-supervised and unsupervised. This paper presents experimental evidence that solutions found with the proposed approaches are sufficiently close to the optimum.

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.

This is a lecture note based on the series of lectures on the dispersionless integrable hierarchies delivered by the authore in June, 2013, at the Rikkyo University, Tokyo, Japan. The contents are survey on dispersionless integrable hierarchies, including introduction to integrable systems in general, and on their connections with complex analysis.

The author researches the issues of usage of economical and statistical indices of functioning of special economical zones. The combination of economical approach with technocratic favors the creation of complex method of assessment of usefulness and efficiency of innovations, their screening, distribution of limited resources and also presupposes formation of wide applied aspect.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

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.

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.