Competing ideologies of Russia's civil society

Many analysts and public opinion makers in the West conflate the notions of Russia’s non-systemic liberal opposition and the country’s civil society. Indeed, despite garnering the support of a minority of Russia’s population, non-systemic liberal opposition represents a well-organized civic group with a clearly articulated agenda and the ability to take action. Yet, does Russia’s civil society end there? A closer look at the country’s politics shows that Russia has a substantial conservative-traditionalist faction that has also developed agenda for action and formulated opinions. This group is anti-liberal rather than illiberal ideologically and pro-strong state/pro a geopolitically independent Russia rather than pro-Kremlin politically. The interaction between liberal and conservative civic groups represents the battle of meanings, ideas, and ethics, and ultimately determines the future trajectory of Russia’s evolution. Thus, the analysis of Russia’s civil society must represent a rather more nuanced picture than a mere study of the liberal non-systemic opposition. This article will examine the complexity of Russia’s civil society scene with reference to the interplay between the liberal opposition and conservative majority factions. The paper will argue that such complexity stems from ideological value pluralism that falls far beyond the boundaries of the liberal consensus, often skewing our understanding of political practice in Russia

Numerical solution of Dirichlet problems for nonlinear parabolic equations by probability approach

A number of new layer methods solving Dirichlet problems for semilinear parabolic equations is constructed by using probabilistic representations of their solutions. The methods exploit the ideas of weak sense numerical integration of stochastic differential equations in bounded domain. In spite of the probabilistic nature these methods are nevertheless deterministic. Some convergence theorems are proved. Numerical tests are presented

Probabilistic methods for the incompressible navier-stokes equations with space periodic conditions

We propose and study a number of layer methods for Navier-Stokes equations (NSEs) with spatial periodic boundary conditions. The methods are constructed using probabilistic representations of solutions to NSEs and exploiting ideas of the weak sense numerical integration of stochastic differential equations. Despite their probabilistic nature, the layer methods are nevertheless deterministic. © ?Applied Probability Trust 2013

Unidirectional transport in stochastic ratchets

Constructive conditions for existence of the unidirectional transport are given for systems with state-dependent noise and for forced thermal ratchets. Using them, domains of parameters corresponding to the unidirectional transport are indicated. Some results of numerical experiments are presented

Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation

We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals resulting in a linear stochastic parabolic equation for vorticity. At each time step, the velocity is expressed via vorticity using a formula corresponding to the Biot-Savart-type law. We prove the first mean-square convergence order of the vorticity approximation

Regular oscillations in systems with stochastic resonance

Constructive sufficient conditions for regular oscillations in systems with stochastic resonance are given. For bistable systems, they rely on the fact that the probability of transition of a point from one well to the other with subsequent stay there during the half-period of the periodic forcing is close to 1. Using these conditions, domains of parameters corresponding to the regular oscillations are indicated. The regular oscillations are considered in bistable and monostable systems with additive and multiplicative noise. Special attention is paid to numerical methods. Algorithms based on numerical integration of stochastic differential equations turn out to be most natural both for simulation of sample trajectories and for solution of related boundary value problems of parabolic type. Results of numerical experiments are presented

Numerical analysis of Monte Carlo finite difference evaluation of Greeks

An error analysis of approximation of derivatives of the solution to the Cauchy problem for parabolic equations by finite differences is given taking into account that the solution itself is evaluated using weak-sense numerical integration of the corresponding system of stochastic differential equations together with the Monte Carlo technique. It is shown that finite differences are effective when the method of dependent realizations is exploited in the Monte Carlo simulations. This technique is applicable to evaluation of Greeks. In particular, it turns out that it is possible to evaluate both the option price and deltas by a single simulation run that reduces the computational costs. Results of some numerical experiments are presented

Numerical methods for nonlinear parabolic equations with small parameter based on probability approach

The probabilistic approach is used for constructing special layer methods to solve the Cauchy problem for semilinear parabolic equations with small parameter. In spite of the probabilistic nature these methods are nevertheless deterministic. The algorithms are tested by simulating the Burgers equation with small viscosity and the generalized KPP-equation with a small parameter