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Saint Petersburg, Russia

Oparin V.,St Petersburg Academic University
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2016

The usual DPLL algorithm uses splittings (branchings) on single Boolean variables. We consider an extension to allow splitting on linear combinations mod 2, which yields a search tree called a linear splitting tree. We prove that the pigeonhole principle has linear splitting trees of size 2O(n). This is near-optimal since Itsykson and Sokolov [1] proved a 2Ω(n) lower bound. It improves on the size 2Θ(n log n) for splitting on single variables; thus the pigeonhole principle has a gap between linear splitting and the usual splitting on single variables. This is of particular interest since the pigeonhole principle is not based on linear constraints. We further prove that the perfect matching principle has splitting trees of size 2O(n). © Springer International Publishing Switzerland 2016. Source


Laussy F.P.,University of Southampton | Kavokin A.V.,University of Southampton | Kavokin A.V.,University of Rome Tor Vergata | Shelykh I.A.,University of Iceland | Shelykh I.A.,St Petersburg Academic University
Physical Review Letters | Year: 2010

We revisit the exciton mechanism of superconductivity in the framework of microcavity physics, replacing virtual excitons as a binding agent of Cooper pairs by excitations of an exciton-polariton Bose-Einstein condensate. We consider a model microcavity where a quantum well with a two-dimensional electron gas is sandwiched between two undoped quantum wells, where a polariton condensate is formed. We show that the critical temperature for superconductivity dramatically increases with the condensate population, opening a new route towards high-temperature superconductivity. © 2010 The American Physical Society. Source


Zhang X.,Beijing University of Posts and Telecommunications | Dubrovskii V.G.,RAS Ioffe Physical - Technical Institute | Sibirev N.V.,St Petersburg Academic University | Ren X.,Beijing University of Posts and Telecommunications
Crystal Growth and Design | Year: 2011

In view of a continuously growing interest in monolithic integration of dissimilar semiconductor materials in a nanostructure form, we present an analytical study of elastic strain energy in nanostructures of different isotropic geometries grown on lattice mismatched substrates. An analytical solution for the elastic stress field is derived, which is not restricted by the small aspect ratio or particular geometry. It is shown that, at a large enough aspect ratio, the relaxation of displacement fields with the vertical coordinate is exponential. This allows us to find an analytical expression for the strain energy density. The cases of rigid and elastic substrates are considered simultaneously. By minimizing the total energy, we obtain the elastic energy density as a function of aspect ratio for given nanostructure geometry. Our data indicate that the elastic energy is highly dependent on the island shape, with the relaxation becoming faster as the contact angle increases. We also present a simple expression for the elastic relaxation where the fitting coefficient depends on the geometry. A dislocation model is then considered to analyze the competition between the elastic and dislocation energies. We calculate the critical radius below which the plastic deformation is energetically suppressed. Our results demonstrate a good quantitative correlation with the available experimental data on III-V semiconductor nanowires grown on silicon substrates. © 2011 American Chemical Society. Source


Aganezov Jr. S.,St Petersburg Academic University
BMC bioinformatics | Year: 2012

In comparative genomics, the rearrangement distance between two genomes (equal the minimal number of genome rearrangements required to transform them into a single genome) is often used for measuring their evolutionary remoteness. Generalization of this measure to three genomes is known as the median score (while a resulting genome is called median genome). In contrast to the rearrangement distance between two genomes which can be computed in linear time, computing the median score for three genomes is NP-hard. This inspires a quest for simpler and faster approximations for the median score, the most natural of which appears to be the halved sum of pairwise distances which in fact represents a lower bound for the median score.In this work, we study relationship and interplay of pairwise distances between three genomes and their median score under the model of Double-Cut-and-Join (DCJ) rearrangements. Most remarkably we show that while a rearrangement may change the sum of pairwise distances by at most 2 (and thus change the lower bound by at most 1), even the most "powerful" rearrangements in this respect that increase the lower bound by 1 (by moving one genome farther away from each of the other two genomes), which we call strong, do not necessarily affect the median score. This observation implies that the two measures are not as well-correlated as one's intuition may suggest.We further prove that the median score attains the lower bound exactly on the triples of genomes that can be obtained from a single genome with strong rearrangements. While the sum of pairwise distances with the factor 2/3 represents an upper bound for the median score, its tightness remains unclear. Nonetheless, we show that the difference of the median score and its lower bound is not bounded by a constant. Source


Dubrovskii V.G.,RAS Ioffe Physical - Technical Institute | Nazarenko M.V.,St Petersburg Academic University
Journal of Chemical Physics | Year: 2010

This work addresses theory of nucleation and condensation based on the continuous Fokker-Plank type kinetic equation for the distribution of supercritical embryos over sizes beyond the deterministic limit, i.e., keeping the second derivative with respect to size. The first part of the work treats the nucleation stage. It is shown that the size spectrum should be generally obtained by the convolution of the initial distribution with the Gaussian-like Green function with spreading dispersion. It is then demonstrated that the fluctuation-induced effects can be safely neglected at the nucleation stage, where the spectrum broadening due to the nonlinear boundary condition is much larger than the fluctuational one. The crossover between the known triangular and double exponential distributions under different conditions of material influx into the system is demonstrated. Some examples of size distributions at the nucleation stage in different regimes of material influx are also presented. © 2010 American Institute of Physics. Source

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