TernausNetV2: Fully Convolutional Network for Instance Segmentation

The most common approaches to instance segmentation are complex and use two-stage networks with object proposals, conditional random-fields, template matching or recurrent neural networks. In this work we present TernausNetV2 - a simple fully convolutional network that allows extracting objects from a high-resolution satellite imagery on an instance level. The network has popular encoder-decoder type of architecture with skip connections but has a few essential modifications that allows using for semantic as well as for instance segmentation tasks. This approach is universal and allows to extend any network that has been successfully applied for semantic segmentation to perform instance segmentation task. In addition, we generalize network encoder that was pre-trained for RGB images to use additional input channels. It makes possible to use transfer learning from visual to a wider spectral range. For DeepGlobe-CVPR 2018 building detection sub-challenge, based on public leaderboard score, our approach shows superior performance in comparison to other methods. The source code corresponding pre-trained weights are publicly available at https://github.com/ternaus/TernausNetV

Existence of the Stark-Wannier quantum resonances

In this paper we prove the existence of the Stark-Wannier quantum resonances for one-dimensional Schrodinger operators with smooth periodic potential and small external homogeneous electric field. Such a result extends the existence result previously obtained in the case of periodic potentials with a finite number of open gaps.Comment: 30 pages, 1 figur

The spectral shift function and Levinson's theorem for quantum star graphs

We consider the Schr\"odinger operator on a star shaped graph with $n$ edges joined at a single vertex. We derive an expression for the trace of the difference of the perturbed and unperturbed resolvent in terms of a Wronskian. This leads to representations for the perturbation determinant and the spectral shift function, and to an analog of Levinson's formula

Feature Pyramid Network for Multi-Class Land Segmentation

Semantic segmentation is in-demand in satellite imagery processing. Because of the complex environment, automatic categorization and segmentation of land cover is a challenging problem. Solving it can help to overcome many obstacles in urban planning, environmental engineering or natural landscape monitoring. In this paper, we propose an approach for automatic multi-class land segmentation based on a fully convolutional neural network of feature pyramid network (FPN) family. This network is consisted of pre-trained on ImageNet Resnet50 encoder and neatly developed decoder. Based on validation results, leaderboard score and our own experience this network shows reliable results for the DEEPGLOBE - CVPR 2018 land cover classification sub-challenge. Moreover, this network moderately uses memory that allows using GTX 1080 or 1080 TI video cards to perform whole training and makes pretty fast predictions

Deeply subwavelength electromagnetic Tamm states in graphene metamaterials

We study localized modes at a surface of a multilayer structure made of graphene layers separated by dielectric layers. We demonstrate the existence of deeply subwavelength surface modes that can be associated with the electromagnetic Tamm states, with the frequencies in the THz frequency range the negative group velocities. We suggest that the dispersion properties of these Tamm surface modes can be tuned by varying the thickness of a dielectric cap layer

Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves

We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficient KdV-type equations can be rescaled into this equation. We study the long time behaviour of solutions with initial conditions close to a stable, B=0 solitary wave. We prove that for long time intervals, such solutions have the form of the solitary wave, whose centre and scale evolve according to a certain dynamical law involving the function B(t,x), plus an H^1-small fluctuation.Comment: 19 page

Orbital and asymptotic stability for standing waves of a NLS equation with concentrated nonlinearity in dimension three

We begin to study in this paper orbital and asymptotic stability of standing waves for a model of Schr\"odinger equation with concentrated nonlinearity in dimension three. The nonlinearity is obtained considering a {point} (or contact) interaction with strength $\alpha$, which consists of a singular perturbation of the laplacian described by a selfadjoint operator $H_{\alpha}$, where the strength $\alpha$ depends on the wavefunction: $i\dot u= H_\alpha u$, $\alpha=\alpha(u)$. If $q$ is the so-called charge of the domain element $u$, i.e. the coefficient of its singular part, we let the strength $\alpha$ depend on $u$ according to the law $\alpha=-\nu|q|^\sigma$, with $\nu > 0$. This characterizes the model as a focusing NLS with concentrated nonlinearity of power type. For such a model we prove the existence of standing waves of the form $u (t)=e^{i\omega t}\Phi_{\omega}$, which are orbitally stable in the range $\sigma \in (0,1)$, and orbitally unstable for $\sigma \geq 1.$ Moreover, we show that for $\sigma \in (0,\frac{1}{\sqrt 2})$ every standing wave is asymptotically stable in the following sense. Choosing initial data close to the stationary state in the energy norm, and belonging to a natural weighted $L^p$ space which allows dispersive estimates, the following resolution holds: $u(t) = e^{i\omega_{\infty} t} \Phi_{\omega_{\infty}} +U_t*\psi_{\infty} +r_{\infty}, \quad \textrm{as} \;\; t \rightarrow +\infty$, where $U$ is the free Schr\"odinger propagator, $\omega_{\infty} > 0$ and $\psi_{\infty}$, $r_{\infty} \in L^2(\R^3)$ with $\| r_{\infty} \|_{L^2} = O(t^{-5/4}) \quad \textrm{as} \;\; t \rightarrow +\infty$. Notice that in the present model the admitted nonlinearity for which asymptotic stability of solitons is proved is subcritical.Comment: Comments and clarifications added; several misprints correcte

Оценка коррупционных рисков в деятельности хозяйствующего субъекта

Purpose: of this work is to assess the possible corruption risks of economic entities of the Russian Federation. In order to achieve this goal, the following main problems were posed and solved in the work presented: the problematic of the appearance of corruption risks of an economic entity is disclosed; the concepts of modern assessment of corruption risks of economic entities of the Russian Federation are studied; an assessment of the current state of possible corruption risks in business entities and the possibilities for their further minimization are explored. Methods: the methodological basis of this article is the economic and statistical methods of analysis, regulatory documents in the field of assessment of the corruption risks of economic entities of the Russian Federation. Results: the results of the work were the development of the proposals for the solution of the problems of effective risk assessment and minimization of corruption risks. It has been established that the ability of a national socio-economic and political system of a society to ensure the integrated security of the life of modern society requires the coordination of a joint effort of state, social and economic structures and should be of systemic nature. Conclusions and Relevance: it is necessary to develop a qualitatively new program for development of a system of assessment and minimization of the corruption risks of economic entities in the Russian Federation, taking into account their following modernization and transition to a resource-innovative model of functioning. Conclusions are made about the specifics of modern approaches to the formation of an effective system of minimization of the corruption risks of economic entities of the Russian Federation. Practical implementation of these findings will make it possible to raise the activity of economic entities of the Russian Federation to a qualitatively new level, and the results of the article can be used for development of practical programs for ensuring the security of the national socio-economic and political system of society. Цель: Целью данной работы является проведение оценки возможных коррупционных рисков хозяйствующих субъектов РФ. Для достижения указанной цели исследования в представленной работе были поставлены и решены следующие основные задачи: раскрыта проблематика возникновения коррупционных рисков хозяйствующего субъекта; изучены понятия современной оценки коррупционных рисков хозяйствующих субъектов РФ; дана оценка современного состояния возможных коррупционных рисков в хозяйствующих субъектах и изучены возможности для дальнейшей их минимизации. Методология проведения работы: Методической основой данной статьи являются экономико-статистические методы анализа, нормативно-правовые документы в области оценки коррупционных рисков хозяйствующих субъектов РФ. Результаты работы: Разработка предложений по решению задач эффективной оценки и минимизации коррупционных рисков. Установлено, что способность национальной социально-экономической и политической системы общества к обеспечению комплексной безопасности жизнедеятельности современного общества требует согласований совместных усилий государственных, общественных и экономических структур и должно носить системный характер. Выводы: Необходима разработка качественно новой программы развития системы оценки и минимизации коррупционных рисков хозяйствующих субъектов РФ с учетом их последовательной модернизации и переходом на ресурсно-инновационную модель функционирования. Сделаны выводы о специфике современных подходов формирования эффективной системы минимизации коррупционных рисков хозяйствующих субъектов РФ. Практическая реализация выводов позволит поднять деятельность хозяйствующих субъектов РФ на качественно новый уровень, а также результаты статьи могут быть использованы для практической разработки программ обеспечения безопасности национальной социально-экономической и политической системы общества.

Theory of Nonlinear Dispersive Waves and Selection of the Ground State

A theory of time dependent nonlinear dispersive equations of the Schroedinger / Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear Master equations (NLME), governing the evolution of the mode powers, and by a novel multi-time scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include BEC large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, ``selection of the ground state'', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et. al. in nonlinear optical waveguides