Solution of the Forward Problem in Magnetic-Field Tomography (MFT) Based on Magnetoencephalography (MEG)

This paper presents the methodology and some of the results of accurate solution of the forward problem in magnetic-field tomography based on magnetoencephalography for brain imaging. The solution is based on modeling and computation of magnetic-field distribution in and around the head produced by distributed 2-D cortical and 3-D volume lead current sources. The 3-D finite-element model of the brain incorporates realistic geometry based on accurate magnetic resonance imaging data and inhomogeneous conductivity properties. The model allows arbitrary placement of line, surface, and volume current sources. This gives flexibility in the source current approximation in terms of size, orientation, placement, and spatial distribution

Martin boundary of a reflected random walk on a half-space

The complete representation of the Martin compactification for reflected random walks on a half-space $\Z^d\times\N$ is obtained. It is shown that the full Martin compactification is in general not homeomorphic to the ``radial'' compactification obtained by Ney and Spitzer for the homogeneous random walks in $\Z^d$ : convergence of a sequence of points $z_n\in\Z^{d-1}\times\N$ to a point of on the Martin boundary does not imply convergence of the sequence $z_n/|z_n|$ on the unit sphere $S^d$. Our approach relies on the large deviation properties of the scaled processes and uses Pascal's method combined with the ratio limit theorem. The existence of non-radial limits is related to non-linear optimal large deviation trajectories.Comment: 42 pages, preprint, CNRS UMR 808

The Concept of the FSES HE of the Fourth Generation for Engineering Education in the Context of Implementing the Assignments of the President of Russia

Within the framework of the activities of the Coordinating Council of the Ministry of Science and Higher Education of the Russian Federation in the field of education “Engineering, Technology and Technical Sciences”, proposals have been developed for the implementation of a set of tasks for the development of higher education set by the President of Russia. The necessity of implementing different methodological and normative approaches to different areas of higher education is argued. The authors substantiate the concept of the fourth generation Federal State Educational Standard for the engineering field of education. A new approach to the organization of admission to universities is proposed, which allows students to choose the direction of training after completing the second year of study. An innovative structure of lists of specialties and areas of preparation of higher education is presented, which provides the possibility of implementing the concept of the fourth generation Federal State Educational Standard, as well as greater flexibility and enlargement of the lists

Is the Transfer of Russian Engineering Education to the American Liberal Arts System Relevant?

In his Address to the Federal Assembly on January 15, 2020, the President of Russia set the task “to enable students after their second year to choose a new direction or program of study, including related professions”. Solving this problem requires transformation of the higher education system in Russia. Discussion has arisen in the educational community about the ways of this transformation. One of the possible options was the transfer of Russian education to the American Liberal Arts system. In order to verify the feasibility of using the Liberal Arts system for the training of engineers, a comparative study was carried out. As a result, it was concluded that proposals to replace the Russian system of higher education with the American Liberal Arts system for engineering education are not relevant, because the main basic goals and principles of building these systems coincide and the existing differences are due to the specifics of engineering activities

Scientific and Professional Degrees in Russia: Developing Traditions into the Future

When studying the history of Russian education, one becomes convinced of the validity of the dialectical principles of spiral development. The period of cyclicality in the history of attestation of scientific personnel is approximately equal to a century. In the first quarter of every century, starting from the time of the tsar Peter the Great, events took place that brought the system to a fundamentally new level. But at the same time, the fundamental foundations laid by the tsar Peter the Great and Lomonosov remain constant. Analyzing the attestation system development spiral, we find ways to solve urgent problems, and the foremost among them is ensuring Russia’s technological sovereignty. A similar problem stood a century ago. It was fully resolved in the USSR, but the foundations for its solution were laid in 1917 in the decree issued by the Russian Provisional Government: “On granting the Petrograd Polytechnic Institute the right to award academic degrees”. In the socioeconomic conditions of the modern Russia, we need new solutions. In this article we offer the

The Hitting Times with Taboo for a Random Walk on an Integer Lattice

For a symmetric, homogeneous and irreducible random walk on d-dimensional integer lattice Z^d, having zero mean and a finite variance of jumps, we study the passage times (with possible infinite values) determined by the starting point x, the hitting state y and the taboo state z. We find the probability that these passages times are finite and analyze the tails of their cumulative distribution functions. In particular, it turns out that for the random walk on Z^d, except for a simple (nearest neighbor) random walk on Z, the order of the tail decrease is specified by dimension d only. In contrast, for a simple random walk on Z, the asymptotic properties of hitting times with taboo essentially depend on the mutual location of the points x, y and z. These problems originated in our recent study of branching random walk on Z^d with a single source of branching