### Working paper

## KEY BORROWERS DETECTED BY THE INTENSITIES OF THEIR SHORT-RANGE INTERACTIONS

The language RCC8RCC8is a widely-studied formalism for describing topological arrangements of spatial regions. The variables of this language range over the collection of non-empty, regular closed sets of *n *-dimensional Euclidean space, here denoted RC+(Rn)RC+(Rn), and its non-logical primitives allow us to specify how the interiors, exteriors and boundaries of these sets intersect. The key question is the *satisfiability problem *: given a finite set of atomic RCC8RCC8-constraints in *m* variables, determine whether there exists an *m *-tuple of elements of RC+(Rn)RC+(Rn)satisfying them. These problems are known to coincide for all n≥1n≥1, so that RCC8RCC8-satisfiability is independent of dimension. This common satisfiability problem is NLogSpace-complete. Unfortunately, RCC8RCC8lacks the means to say that a spatial region comprises a ‘single piece’, and the present article investigates what happens when this facility is added. We consider two extensions of RCC8RCC8: RCC8cRCC8c, in which we can state that a region is *connected *, and RCC8c∘RCC8c∘, in which we can instead state that a region has a *connected interior*. The satisfiability problems for both these languages are easily seen to depend on the dimension *n *, for n≤3n≤3. Furthermore, in the case of RCC8c∘RCC8c∘, we show that there exist finite sets of constraints that are satisfiable over RC+(R2)RC+(R2), but only by ‘wild’ regions having no possible physical meaning. This prompts us to consider interpretations over the more restrictive domain of non-empty, regular closed, *polyhedral * sets, RCP+(Rn)RCP+(Rn). We show that (a) the satisfiability problems for RCC8cRCC8c(equivalently, RCC8c∘RCC8c∘) over RC+(R)RC+(R)and RCP+(R)RCP+(R)are distinct and both NP-complete; (b) the satisfiability problems for RCC8cRCC8cover RC+(R2)RC+(R2)and RCP+(R2)RCP+(R2)are identical and NP-complete; (c) the satisfiability problems for RCC8c∘RCC8c∘over RC+(R2)RC+(R2)and RCP+(R2)RCP+(R2)are distinct, and the latter is NP-complete. Decidability of the satisfiability problem for RCC8c∘RCC8c∘over RC+(R2)RC+(R2)is open. For n≥3n≥3, RCC8cRCC8cand RCC8c∘RCC8c∘are not interestingly different from RCC8RCC8. We finish by answering the following question: given that a set of RCC8cRCC8c- or RCC8c∘RCC8c∘-constraints is satisfiable over RC+(Rn)RC+(Rn)or RCP+(Rn)RCP+(Rn), how complex is the simplest satisfying assignment? In particular, we exhibit, for both languages, a sequence of constraints ΦnΦn, satisfiable over RCP+(R2)RCP+(R2), such that the size of ΦnΦngrows polynomially in *n *, while the smallest configuration of polygons satisfying ΦnΦn cuts the plane into a number of pieces that grows exponentially. We further show that, over RC+(R2)RC+(R2), RCC8cRCC8c again requires exponentially large satisfying diagrams, while RCC8c∘RCC8c∘ can force regions in satisfying configurations to have infinitely many components.

This paper demonstrates that most existing voting schemes represent or can be rewritten as weighted games. However, axiomatics for power indices defined on simple games are not directly applied to weighted games, since related operations become ill-posed. The author shows that the majority of axiomatics can be adapted to weighted games. Finally, a series of examples are provided.

Commonly in network analysis a graph (network) is represented by its adjacency matrix, and the latter may have an enormous order. We show that in many situations (generalizing the case of regular graph) a much smaller matrix (referred as type adjacency matrix) may be used instead. We introduce concepts of the types of nodes and of the type adjacency matrix, study properties of the latter and demonstrate some of its applications in social and economic network analysis. In particular, we consider centrality measures in undirected networks and dynamic patterns in a development model based on the structure of optimal paths in directed weighted networks.

Monograph by S. Khasyanova «Upgrading Banking Regulation and Supervision in Russia in the line with International Standards» is devoted to the study of the development of banking regulation and supervision in Russia on the basis of international principles and standards. The process of implementation of international principles and standards of banking regulation in the Russian Federation and the following consequences are analyzed in the context of financial stability. Particular attention is paid to macroeconomic regulation and development of prudential regulations and requirements for banks, taking into account banking sector peculiarities. The regulation of systemic risk, identification of systemically important banks and applied to them a particular regulatory regime were investigated. The Deposit Insurance System and its role in enhancing the stability of banks as well as its directions of improvement are also considered in the study. The book is intended for professionals in the field of finance and banking, teachers and students of universities’ economic and financial departments.

We study game equilibria in a network, in each node of which an economy is described by a two-period model of endogenous growth with production and knowledge externalities. Each node obtains an externality produced by the sum of knowledge in neighbour nodes. Uniqueness of the inner equilibrium is proved. Ways of behaviour of agent (passive, active, or hyperactive) in dependence on received externalities are studied. Classification of networks based on a notion of type of node is provided. It is shown that the inner equilibrium depends not on the network’s size or topology but on its structure in terms of the types of nodes, and in networks with similar types structure agents in nodes of the same type behave similarly. Changes of the equilibrium under changes in the network structure are studied, as well as network formation, in particular, connection of network components, and appearance of new links.

We offer a general approach to describing power indices that account for preferences as suggested by F. Aleskerov. We construct two axiomatizations of these indices. Our construction generalizes the Laruelle-Valenciano axioms for Banzhaf (Penrose) and Shapley-Shubik indices. We obtain new sets of axioms for these indices, in particular, sets without the anonymity axiom.

At calculation of the power indices, both well-known (Banzhaf, Shapley-Shubik and others and new (depending on the agent preferences) indices, one generally has to enumerate almost all coalitions, that is, the subsets of the set of players, which makes calculations impossible if the number of players exceeds fifty. Yet, if all players have an integer number of votes, there are players with the same number of votes, many coalitions have equal total number of votes or the sum of votes of all players is small, then the algorithms based on calculations using the generating functions become efficient. But these algorithms works only for classical power indices and some particular types of the power indices based on agents’ preferences. In this paper we consider an important specific case when all players have the same number of votes. For classical power indices in this case all players have the same power. However, it is not the case for the indices which allow preferences of agents. We introduce effective algorithms for calculation of the latter indices for most types of these indices.

The paper examines the structure, governance, and balance sheets of state-controlled banks in Russia, which accounted for over 55 percent of the total assets in the country's banking system in early 2012. The author offers a credible estimate of the size of the country's state banking sector by including banks that are indirectly owned by public organizations. Contrary to some predictions based on the theoretical literature on economic transition, he explains the relatively high profitability and efficiency of Russian state-controlled banks by pointing to their competitive position in such functions as acquisition and disposal of assets on behalf of the government. Also suggested in the paper is a different way of looking at market concentration in Russia (by consolidating the market shares of core state-controlled banks), which produces a picture of a more concentrated market than officially reported. Lastly, one of the author's interesting conclusions is that China provides a better benchmark than the formerly centrally planned economies of Central and Eastern Europe by which to assess the viability of state ownership of banks in Russia and to evaluate the country's banking sector.

The paper examines the principles for the supervision of financial conglomerates proposed by BCBS in the consultative document published in December 2011. Moreover, the article proposes a number of suggestions worked out by the authors within the HSE research team.