Publications

All countries have responded with a wide range of measures to stop the propagation of coronavirus. We apply best tube Interval Data Envelopment Analysis, which allows to evaluate efficiency of quarantine measures using imprecise data. Using the Oxford COVID-19 Government Response Tracker’s (OxCGRT) data and proposed method, we construct timeseries of efficiency assessment of government responses to COVID-19. In addition, we separate all examined countries into several groups with similar patterns of quarantine measures efficiency.

Two aggregated regularized systems of equations for a multicomponent homogeneous gas mixture are considered. An entropy balance equation with a non-negative entropy production is derived for them in the presence of diffusion fluxes. The existence, uniqueness and $L^2$-dissipativity of weak solutions to an initial-boundary value problem for the systems linearized on a constant solution are established. The Petrovskii parabolicity and the local in time classical unique solvability of the Cauchy problem are also proved for the aggregated systems themselves.

There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them (Goranko in Filter and ultrafilter extensions of structures: universal-algebraic aspects, preprint, 2007) comes from modal logic and universal algebra, and in fact goes back to Jónsson and Tarski (Am J Math 73(4):891–939, 1951; 74(1):127–162, 1952). Another one (Saveliev in Lect Notes Comput Sci 6521:162–177, 2011; Saveliev in: Friedman, Koerwien, Müller (eds) The infinity project proceeding, Barcelona, 2012) comes from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups (Hindman and Strauss in Algebra in the Stone–Čech Compactification, W. de Gruyter, Berlin, 2012) as its main precursor. By a classical fact of general topology, the space of ultrafilters over a discrete space is its largest compactification. The main result of Saveliev (Lect Notes Comput Sci 6521:162–177, 2011; in: Friedman, Koerwien, Müller (eds) The infinity project proceeding, Barcelona, 2012), which confirms a canonicity of this extension, generalizes this fact to discrete spaces endowed with an arbitrary first-order structure. An analogous result for the former type of ultrafilter extensions was obtained in Saveliev (in On two types of ultrafilter extensions of binary relations. arXiv:2001.02456). Results of such kind are referred to as extension theorems. After a brief introduction, we offer a uniform approach to both types of extensions based on the idea to extend the extension procedure itself. We propose a generalization of the standard concept of first-order interpretations in which functional and relational symbols are interpreted rather by ultrafilters over sets of functions and relations than by functions and relations themselves, and define ultrafilter models with an appropriate semantics for them. We provide two specific operations which turn ultrafilter models into ordinary models, establish necessary and sufficient conditions under which the latter are the two canonical ultrafilter extensions of some ordinary models, and obtain a topological characterization of ultrafilter models. We generalize a restricted version of the extension theorem to ultrafilter models. To formulate the full version, we propose a wider concept of ultrafilter models with their semantics based on limits of ultrafilters, and show that the former concept can be identified, in a certain way, with a particular case of the latter; moreover, the new concept absorbs the ordinary concept of models. We provide two more specific operations which turn ultrafilter models in the narrow sense into ones in the wide sense, and establish necessary and sufficient conditions under which ultrafilter models in the wide sense are the images of ones in the narrow sense under these operations, and also are two canonical ultrafilter extensions of some ordinary models. Finally, we establish three full versions of the extension theorem for ultrafilter models in the wide sense. The results of the first three sections of this paper were partially announced in Poliakov and Saveliev (in: Kennedy, de Queiroz (eds) On two concepts of ultrafilter extensions of first-order models and their generalizations, Springer, Berlin, 2017).

 Controllability problems for some models of plates and beams with integral memory are  considered. The vibrational equation of the plate contains an Abelian kernel in the integral term, and  the vibrational equation of the beam contains a continuous kernel consisting of a finite sum of  decreasing exponential functions. It is proved that by controlling the whole domain, the first system  cannot be driven to a state of rest, and for the second system, controllability to rest is possible.

We propose an algorithm for linearizing systems of partial differential equations at constant solutions. The algorithm is based on an isomorphism constructed between the ring of linearized functions and the ring of special matrices, which makes it possible to simplify calculations in the process of linearization. The algorithm is illustrated by applying it to the quasigasdynamic system.

We present a new formulation of the hyperbolic singular value decomposition (HSVD) for an arbitrary complex (or real) matrix without hyperexchange matrices and redundant invariant parameters. In our formulation, we use only the concept of pseudo-unitary (or pseudo-orthogonal) matrices. We show that computing the HSVD in the general case is reduced to calculation of eigenvalues, eigenvectors, and generalized eigenvectors of some auxiliary matrices. The new formulation is more natural and useful for some applications. It naturally includes the ordinary singular value decomposition.

Over the last number of years there has been a growing interest in the analysis of complex networks which describe a wide range of real-world systems in nature and society. Identification of the central elements in such networks is one of the key research areas. Solutions to this problem are important for making strategic decisions and studying the behavior of dynamic processes, e.g. epidemic spread. The importance of nodes has been studied using various centrality measures. Generally, it should be considered that most real systems are not homogeneous: nodes may have individual attributes and influence each other in groups while connections between nodes may describe different types of relations. Thus, critical nodes detection is not a straightforward process.

New Centrality Measures in Networks presents a class of new centrality measures which take into account individual attributes of nodes, the possibility of group influence and long-range interactions and discusses all their new features. The book provides a wide range of applications of network analysis in several fields – financial networks, international migration, global trade, global food network, arms transfers, networks of terrorist groups, and networks of international journals in economics. Real-world studies of networks indicate that the proposed centrality measures can identify important nodes in different applications. Starting from the basic ideas, the development of the indices and their advantages compared to existing centrality measures are presented.

Features:

Built around real-world case studies in a variety of different areas (finance, migration, trade, etc.) Suitable for students and professional researchers with an interest in complex network analysis Paired with a software package for readers who wish to apply the proposed models of centrality (in Python) available at https://github.com/SergSHV/slric

We consider an initial-boundary value problem for the $n$-dimensional wave equation with the variable sound speed, $n\geq 1$. We construct three-level implicit in time compact in space (three-point in each space direction) 4th order finite-difference schemes on the uniform rectangular meshes including their one-parameter (for $n=2$) and three-parameter (for $n=3$) families. They are closely connected to some methods and schemes constructed recently by several authors. In a unified manner, we prove the conditional stability of schemes in the strong and weak energy norms together with the 4th order error estimate under natural conditions on the time step. We also give an example of extending a compact scheme for non-uniform in space and time rectangular meshes. We suggest simple effective iterative methods based on FFT to implement the schemes whose convergence rate, under the stability condition, is fast and independent on both the meshes and variable sound speed. A new effective initial guess to start iterations is given too. We also present promising results of numerical experiments.

Two operads are said to belong to the same Wilf class if they have the same generating series. We discuss possible Wilf classifications of non-symmetric operads with monomial relations. As a corollary, this would give the same classification for the operads with a finite Groebner basis.

Generally, there is no algorithm to decide whether two finitely presented operads belong to the same Wilf class. Still, we show that if an operad has a finite Groebner basis, then the monomial basis of the operad forms an unambiguous context-free language. Moreover, we discuss the deterministic grammar which defines the language. The generating series of the operad can be obtained as a result of an algorithmic elimination of variables from the algebraic system of equations defined by the Chomsky-Schützenberger enumeration theorem. We then focus on the case of binary operads with a single relation. The approach is based on the results by Rowland on pattern avoidance in binary trees. We improve and refine Rowland's calculations and empirically confirm his conjecture. Here we use both the algebraic elimination and the direct calculation of formal power series from algebraic systems of equations. Finally, we discuss the connection of Wilf classes with algorithms for the calculation of the Quillen homology of operads.

Usually, DEA methods are used for the assessment of a region’s disaster vulnerability. However, most of these methods work with precise values of all the characteristics of the regions. At the same time, in real life, quite often most of the data consists of expert estimates or approximate values. In this regard, we propose to use modified DEA methods, which will take into account inaccuracy of the data. We apply these methods to the evaluation of wildfire preventive measures in the Russian Federation regions.

We study difference schemes associated with a simplified linearized multidimensional hyperbolic quasi-gasdynamic system of differential equations. It is shown that an explicit two-level vector difference scheme with flux relaxation for a second-order hyperbolic equation with variable coefficients that is a perturbation of the transport equation with a parameter multiplying the highest derivatives can be reduced to an explicit three-level difference scheme. In the case of constant coefficients, the spectral condition for the time-uniform stability of this explicit three-level difference scheme is analyzed, and both sufficient and necessary conditions for this condition to hold are derived, in particular, in the form of Courant type conditions on the ratio of temporal and spatial steps.

The Sylvester equation and its particular case, the Lyapunov equation, are widely used in image processing, control theory, stability analysis, signal processing, model reduction, and many more. We present basis-free solution to the Sylvester equation in Clifford (geometric) algebra of arbitrary dimension. The basis-free solutions involve only the operations of Clifford (geometric) product, summation, and the operations of conjugation. To obtain the results, we use the concepts ofcharacteristic polynomial, determinant, adjugate, and inverse in Clifford algebras. For the first time, we give alternative formulas for the basis-free solution to the Sylvester equation in the case n = 4, the proofs for the case n = 5 and the case of arbitrary dimension n. The results can be used in symbolic computation.

In this paper, we solve the problem of computing the inverse in Clifford algebras of arbitrary dimension. We present basis-free formulas of different types (explicit and recursive) for the determinant, other characteristic polynomial coefficients, adjugate, and inverse in real Clifford algebras (or geometric algebras) over vector spaces of arbitrary dimension $n$. The formulas involve only the operations of multiplication, summation, and operations of conjugation without explicit use of matrix representation. We use methods of Clifford algebras (including the method of quaternion typification proposed by the author in previous papers and the method of operations of conjugation of special type presented in this paper) and generalizations of numerical methods of matrix theory (the Faddeev-LeVerrier algorithm based on the Cayley-Hamilton theorem; the method of calculating the characteristic polynomial coefficients using Bell polynomials) to the case of Clifford algebras in this paper. We present the construction of operations of conjugation of special type and study relations between these operations and the projection operations onto fixed subspaces of Clifford algebras. We use this construction in the analytical proof of formulas for the determinant, other characteristic polynomial coefficients, adjugate, and inverse in Clifford algebras. The basis-free formulas for the inverse give us basis-free solutions to linear algebraic equations, which are widely used in computer science, image and signal processing, physics, engineering, control theory, etc. The results of this paper can be used in symbolic computation.

The problem of the exact bounded control of oscillations of the two-dimensional membrane is considered. Control force is applied to the boundary of the membrane, which is located in a domain on a plane. The goal of the control is to drive the system to rest in a finite time.

Essays by and in Honor of William Gehrlein and Dominique Lepelley

Presents recent research on the analysis of voting rules using the probability approach

This book includes up-to-date contributions in the broadly defined area of probabilistic analysis of voting rules and decision mechanisms. Featuring papers from all fields of social choice and game theory, it presents probability arguments to allow readers to gain a better understanding of the properties of decision rules and of the functioning of modern democracies. In particular, it focuses on the legacy of William Gehrlein and Dominique Lepelley, two prominent scholars who have made important contributions to this field over the last fifty years. It covers a range of topics, including (but not limited to) computational and technical aspects of probability approaches, evaluation of the likelihood of voting paradoxes, power indices, empirical evaluations of voting rules, models of voters’ behavior, and strategic voting. The book gathers articles written in honor of Gehrlein and Lepelley along with original works written by the two scholars themselves.

This work is devoted to the methodology for identifying structurally close objects of the type “country_year” based on a system of indicators characterizing the state capacity 1996–2015. A comparison of clustering methods (including hierarchical clustering) with methods of analyzing patterns based on a pairwise comparison of indicators, ordinal-fixed and ordinal-invariant pattern clustering, is proposed. The possibility of sharing the methods of clustering and pattern analysis to obtain interpretable results from the point of view of political science is demonstrated. Groups of countries with similar development paths by reference years on the basis of a dynamic analysis of patterns are identified. The dynamic change in state capacity (from the point of view of the selected indicator system) of 166 countries of the world is determined.

About some climatic change in Russia.

In this note, we present basis-free definitions of subspaces of fixed grades of real Clifford algebras of arbitrary dimension. We do not use fixed basis of Clifford algebra and use only the properties of commutators and anticommutators.

We study necessary conditions for stability of a Numerov-type compact higher-order finite-diffe\-rence scheme for the 1D homogeneous wave equation in the case of non-uniform spatial meshes. We first show that the uniform in time stability cannot be valid in any spatial norm provided that the complex eigenvalues appear in the associated mesh eigenvalue problem. Moreover, we prove that then the solution norm grows exponentially in time making the scheme strongly non-dissipative and therefore impractical. Numerical results confirm this conclusion. In addition, for some sequences of refining spatial meshes, an excessively strong condition between steps in time and space is necessary (even for the non-uniform in time stability) which is familiar for explicit schemes in the parabolic case.

In this paper, homological methods together with the theory of formal languages of theoretical computer science are proved to be effective tools to determine the growth and the Hilbert series of an associative algebra. Namely, we construct a class of finitely presented associative algebras related to a family of context-free languages. This allows us to connect the Hilbert series of these algebras with the generating functions of such languages. In particular, we obtain a class of finitely presented graded algebras with non-rational algebraic Hilbert series.

We construct a new spatial finite-difference discretization for a regularized 3D Navier-Stokes-Cahn-Hilliard system of equations. The system {can be attributed to phase field type models} and describes flows of a viscous compressible isothermal two-component two-phase fluid with surface effects; the potential body force is also taken into account. In the discretization, the main sought functions are defined on one and the same mesh, and an original approximation of the solid wall boundary conditions (homogene\-ous with the discretization of equations) is suggested. The discretization has an important property of the total energy dissipativity allowing one to eliminate completely the so-called spurious currents. The discrete total mass and component mass conservation laws hold as well, and the discretization is also well-balanced for the equilibrium solutions. To ensure that the concentration $C$ remains within a physical\-ly meaningful interval $(0,1)$, the non-convex part of the Helmholtz free energy is taken in a special logarithmic form (the Flory-Huggins potential). The speed of sound can depend on $C$ that leads to different equilibrium mass densities of the ``pure'' phases. The results of numerical 3D simulations are also presented including those with a gravitational-type force. The positive role of the relaxation parameter is discussed too.

We introduce a new core selection to minimum cost spanning tree problems satisfying continuity, population and cost monotonicity, solidarity, and ranking. We prove that it Lorenz dominates every other allocation in the irreducible core of the problem, including the celebrated folk solution unless they yield the same outcome. Therefore, among the solutions satisfying solidarity, our solution generates the most egalitarian outcome for each problem.

In this paper, we consider inner automorphisms that leave invariant fixed subspaces of real and complex Clifford algebras — subspaces of fixed grades and subspaces determined by the reversion and the grade involution. We present groups of elements that define such inner automorphisms and study their properties. Some of these Lie groups can be interpreted as generalizations of Clifford, Lipschitz, and spin groups. We study the corresponding Lie algebras. Some of the results can be reformulated for the case of more general algebras — graded central simple algebras or graded central simple algebras with involution.

The indicators of regional sports development in the Russian Federation are analyzed to find regions with a similar sports development strategy (according to the chosen methodology and measures of closeness) and to identify dynamic groups in a four-year period. Some clustering and pattern analysis methods are described, and their use in the study is validated. The results obtained by classical clustering and ordinal-invariant pattern clustering methods are compared. The main state programs in the field of sports in the Russian Federation are highlighted and analyzed. The key aspects and problems of the state regulation of sports activities in the Russian Federation are indicated. Some ways for improving the existing regulatory and legal acts based on the dynamic analysis of regional patterns are proposed.

We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) for the $n$-dimensional non-homogeneous wave equation, $n\geq 1$. Their construction is accomplished by both the classical Numerov approach and alternative technique based on averaging of the equation, together with further necessary improvements of the arising scheme for $n\geq 2$. The alternative technique is applicable to other types of PDEs including parabolic and time-dependent Schr\"{o}dinger ones. The schemes are implicit and three-point in each spatial direction and time and include a scheme with a splitting operator for $n\geq 2$. For $n=1$ and the mesh on characteristics, the 4th order scheme becomes explicit and close to an exact four-point scheme. We present a conditional stability theorem covering the cases of stability in strong and weak energy norms with respect to both initial functions and free term in the equation. Its corollary ensures the 4th order error bound in the case of smooth solutions to the IBVP. The main schemes are generalized for non-uniform rectangular meshes. We also give results of numerical experiments showing the sensitive dependence of the error orders in three norms on the weak smoothness order of the initial functions and free term and essential advantages over the 2nd approximation order schemes in the non-smooth case as well.

We consider the fair division of a set of indivisible goods where each agent can receive more than one good, and monetary transfers are allowed. We show that if there are at least three goods to allocate, no efficient solution is population monotonic (PM) on the superadditive Cartesian product preference domain, and the Shapley solution is not PM even on the submodular domain. Moreover, the incompatibility between efficiency and PM prevails in the case of at least four goods on the subadditive Cartesian product domain. We also show that in case there are only two goods to allocate, the Shapley solution and the constrained egalitarian solution are PM on the subadditive preference domain but not on the full preference domain. For the two-good case, we provide a new tool (the hybrid solutions) to construct efficient solutions that are PM on the entire monotone preference domain. The hybrid Shapley solution and the hybrid constrained egalitarian solution are two important examples of such solutions.

We deal with 2D and 3D barotropic gas dynamics system of equations with two viscous regularizations: so-called quasi-gas dynamics (QGD) and quasi-hydrodynamics (QHD) ones. The system is linearized on a constant solution with any velocity, and an explicit two-level in time and symmetric three-point in each spatial direction finite-difference scheme on the uniform rectangular mesh is considered for the linearized system. We study L^2-dissipativity of solutions to the Cauchy problem for this scheme by the spectral method and present a criterion in the form of a matrix inequality containing symbols of symmetric matrices of convective and regularizing terms. Analyzing these inequality and matrices, we also derive explicit sufficient conditions and necessary conditions in the Courant-type form which are rather close to each other. For the QHD regularization, such conditions are derived for the first time in 2D and 3D cases, whereas, for the QGD regularization, they improve those that have recently been obtained. Explicit formulas for a scheme parameter that guarantee taking the maximal time step are given for these conditions. An important moment is a new choice of an ``average'' spatial mesh step ensuring the independence of the conditions from the ratios of the spatial mesh steps and, for the QGD regularization, from the Mach number as well.

Regional authorities consider the expediency of developing a new cargo transportation hub in the region in which it would provide transshipment services. It is considered that each transportation operator working in the region will use these services only if they are competitive with the currently existing ones. This competitiveness for a particular cargo means that the total transportation tariff for moving this cargo does not exceed (substantially or in principle) the (minimal) currently existing one as a result of including a transshipment via the hub in the transportation scheme for the cargo. A verifiable sufficient condition for the transshipment service competitiveness is proposed. Its verification consists of establishing the solvability of a system of linear inequalities being part of the system of constraints in the problem of finding optimal competitive transshipment tariffs for a set of cargoes expected to be moved via the hub. The latter problem is formulated as a quadratic programming one.