# Publications

In this paper we describe a methodology that allows researchers to measure empirically, in the form of well-defined indicators, the extent to which economic analysis and evidence is been applied in the enforcement of competition law, using data collected from the decisions of competition authorities. By mapping the value of these indicators to different legal standards, our methodology also allows one to identify the legal standards adopted in the assessment of different conducts that were investigated by the authorities. The policy implications of empirical work in this area are potentially very important, since the extent to which economic analysis is applied in the assessment of anti-competitive conduct by competition authorities may well influence the quality of this assessment (i.e. the quality of enforcing competition law, measured by the extent to which decision-errors and deterrence effects are minimised). Empirical analysis using the indicators can be used to undertake comparative analysis in different countries, to examine the extent to which authorities favour specific legal standards in the assessment of specific conducts and the way in which the judicial review process treats decisions depending on the legal standard used.

The universal mechanism of modulation instability (MI) has been discovered first for the Nonlinear Schr¨odinger equation (NLS) and is well studied in the frame of the higher order NLS equations. Recent studies demonstrated by pure existence theorems that also the higher order Korteweg-de Vries (KdV) equations might possess the MI. In this Letter we present explicit form of the conditions for the MI to appear in the KdV-family of equations of the general form ut + sup ux + uxxx =0 where s = ±1 with p > 0 being an arbitrary integer.

Realism- and geopolitics-inspired rhetoric was common currency in Russian foreign policy discourse throughout the 1990s. This led some commentators to adopt realism and geopolitics - realism’s more nationalist and strategic counterpart - as conceptual lenses for understanding Russian foreign policy. As a result, Russian foreign policy of the 2010s is still considered predominantly geopolitics-driven despite the fact that geopolitical vocabulary has virtually disappeared from foreign policy discourse while a desire to carve out spheres of influence have been officially pronounced utterly anachronistic and inappropriate, a “thing of the past”. Thus, a more nuanced interpretation views the rise of geopolitics in Russian post-Soviet foreign policy discourse as an attempt to tap into the symbolic and rhetorical power of geopolitics in order to reduce ontological insecurity brought about by the end of the Cold War. The chapter, therefore, advances a theoretical claim about the relevance of the constructivist and poststructuralist literature and very limited relevance of realism for understanding the twists and turns of Russian post-Soviet foreign policy. Methodologically, the chapter argues that an exploration of state identity rooted in the ontological security argument will benefit from employing discourse analysis. Empirically, the present study provides substantiation of the theoretical claim that the concept of hegemony captures well the historical trajectory of Russia’s relations with its ‘significant other’- Europe/the EU/the West – and provides important insights into the sources of Russia’s ontological insecurity in the 21st century.

A mathematically correct description is presented on the interrelations between the dynamics of divergence free vector fields on an oriented 3-dimensional manifold M and the dynamics of Hamiltonian systems. It is shown that for a given divergence free vector field Xwith a global cross-section there exist some 4-dimensional symplectic manifold M̃⊃M and a smooth Hamilton function H:M̃→R such that for some c∈R one gets M={H=c}and the Hamiltonian vector field XH restricted on this level coincides with X. For divergence free vector fields with singular points such an extension is impossible but the existence of local cross-section allows one to reduce the dynamics to the study of symplectic diffeomorphisms in some sub-domains of M. We also consider the case of a divergence free vector field X with a smooth integral having only finite number of critical levels. It is shown that such a noncritical level is always a 2-torus and restriction of X on it possesses a smooth invariant 2-form. The linearization of the flow on such a torus (i.e. the reduction to the constant vector field) is not always possible in contrast to the case of an integrable Hamiltonian system but in the analytic case (M and X are real analytic), due to the Kolmogorov theorem, such a linearization is possible for tori with Diophantine rotation numbers.

In this paper we find all possible periodic data for orientation preserving gradient-like diffeomorphisms of orientable surfaces with one saddle orbit. We also construct a system of this class for every admissible collection of periodic data.

In this paper, we consider the class of quasiconvex functions and its proper subclass of conic functions. The integer minimization problem of these functions is considered, assuming that the optimized function is defined by the comparison oracle. We will show that there is no a polynomial algorithm on log R to optimize quasiconvex functions in the ball of radius R using only the comparison oracle. On the other hand, if the optimized function is conic, then we show that there is a polynomial on log R algorithm (the dimension is fixed). We also present an exponential on the dimension lower bound for the oracle complexity of the conic function integer optimization problem. Additionally, we give examples of known problems that can be polynomially reduced to the minimization problem of functions in our classes.

Gaussian graphical model selection is a statistical problem

that identifies the Gaussian graphical model from observations. Existing

Gaussian graphical model selection methods focus on the error rate

for incorrect edge inclusion. However, when comparing statistical procedures,

it is also important to take into account the error rate for

incorrect edge exclusion. To handle this issue we consider the graphical

model selection problem in the framework of multiple decision theory.We

show that the statistical procedure based on simultaneous inference with

UMPU individual tests is optimal in the class of unbiased procedures.

Topological classification of even the simplest Morse-Smale diffeomorphisms on 3-manifolds does not fit into the concept of singling out a skeleton consisting of stable and unstable manifolds of periodic orbits. The reason for this lies primarily in the possible ``wild'' behaviour of separatrices of saddle points. Another difference between Morse-Smale diffeomorphisms in dimension 3 from their surface analogues lies in the variety of heteroclinic intersections: a connected component of such an intersection may be not only a point as in the two-dimensional case, but also a curve, compact or non-compact. The problem of a topological classification of Morse-Smale cascades on 3-manifolds either without heteroclinic points (gradient-like cascades) or without heteroclinic curves was solved in a series of papers from 2000 to 2006 by Ch. Bonatti, V. Grines, F. Laudenbach, V. Medvedev, E. Pecou, O. Pochinka. The present paper is devoted to a complete topological classification of the set $MS(M^3)$ of orientation preserving Morse-Smale diffeomorphisms $f$ given on smooth closed orientable 3-manifolds $M^3$. A complete topological invariant for a diffeomorphism $f\in MS(M^3)$ is an equivalent class of its scheme $S_f$, which contains an information on a periodic date and a topology of embedding of two-dimensional invariant manifolds of the saddle periodic points of $f$ into the ambient manifold.

We show that, up to topological conjugation,} the equivalence class of a Morse-Smale diffeomorphism without heteroclinic curves on a $3$-manifold is completely defined by an embedding of two-dimensional stable and unstable heteroclinic laminations to a characteristic space.

We present an analytical description of the class of unsteady vortex surface waves generated by non- uniformly distributed, time-harmonic pressure. The fluid motion is described by an exact solution of the equations of hydrodynamics generalizing the Gerstner solution. The trajectories of the fluid particles are circumferences. The particles on a free surface rotate around circumferences of the same radii, with the centers of the circumferences lying on different horizons. A family of waves has been found in which a variable pressure acts on a limited section of the free surface. The law of external pressure distribution includes an arbitrary function. An example of the evolution of a non-uniform wave packet is considered. The wave and pressure profiles, as well as vorticity distribution are studied. It is shown that, in the case of a uniform traveling wave of external pressure, the Gerstner solution is valid but with a different form of the dispersion relation. A possibility of observing the studied waves in laboratory and in the real ocean is discussed.

We investigate totally geodesic foliations (M, F) of arbitrary codimemsion q on n-dimensional pseudo-Riemannian manifolds for which the induced metrics on leaves don't degenerate. We assume that the q-dimensional orthogonal distribution D to (M, F) is an Ehresmann connection for this foliation. Since the usual graph G(F) is not Hausdorff manifold in general, we investigate the graph G(F, D) of the foliation with an Ehresmann connection D introduced early by the author. This graph is always Hausdorff manifold. We prove that on the graph G(F, D) a pseudo-Riemannian metric is defined, with respect to which the induced foliation and the simple foliations formed by the fibers of the canonical projections are totally geodesic. It is proved that the leaves of the induced foliation on the graph are nondegenerately reducible pseudo-Riemannian manifolds and their structure is described. The application to parallel foliations on nondegenerately reducible pseudo-Riemannian manifolds is considered. It is shown that every foliation defined by the suspension of a homomorphism of the fundamental group of a pseudo-Riemannian manifold belongs to the investigated class of foliations.

In the present paper axiom $A$ diffeomorphisms of closed 2-manifolds of genus $p \geq 2$ whose nonwandering set contains perfect spaciously situated one-dimensional attractor are considered. It is shown that such diffeomorphisms are topologically semiconjugate to pseudo-Anosov homeomorphism with the same induced automorphism of fundamental group. The main result of the paper is the following. Two diffeomorphisms from the given class are topologically conjugate on attractors if and only if corresponding pseudo-Anosov homeomorphisms are topologically conjugate by means of homeomorphism that maps a certain subset of one pseudo-Anosov map onto the certain subset of the other pseudo-Anosov map.

The review is devoted to the presentation of results, including recently obtained by the authors, on the topological classification of Morse-Smale systems and the topology of ambient manifolds.

We provide a definition of a two-colored graph of a Morse-Smale diffeomorphism without heteroclinical intersection defined on the sphere $S^n$, $n\geq 4$ and prove that this graph is the complete topological invariant for such diffeomorphisms.

The article is devoted to the identification of key factors that influence the educational activity of working citizens and the establishment of the role of adults educational programs and vocational education and trainings (AE&VET) in the macroeconomic development of regions and territories. Based on the analysis of the statistical data there was established a correlation between the supplementary education attainment rate and the volume of **fixed capital investment **per capita in the regions of the Russian Federation, which indicates the leading role of regional investors in the education and training of personnel. In the regions, where the volume of investments is growing, the coverage of the population with the continuous education is also increasing, aiming at the implementation of new technologies at the enterprises being built, which, in its turn, boosts the investment appeal of the territory. The authors formulated and confirmed the hypothesis that due to the launch of the educational programs via investments the labor productivity increases, which, in turn, together with the high correlation coefficients, has a positive impact on the growth rates of wages and gross regional product as a whole. Thus, it was concluded that the differentiation of subjects of the Russian Federation on socio-economic indicators is directly related to the general indicators of the regional AE&VET systems. It was noted that for the effective development of AE&VET at the current stage in Russia, it is necessary to incentive an active participation of all the stakeholders: the worker himself, the employers, the investors, the regional authorities and the government. Considering the lack of the employers’ willingness to finance the workers’ education and training, the authors justify the need to introduce state programs stimulating additional education, including budget certificates. The main provisions and conclusions of the article can be used for the development of the regional AE&VET-systems in the interests of ensuring the economic growth as well as the investment appeal of the territory.