Lower order terms in Szego type limit theorems on Zoll manifolds

This is a detailed version of the paper math.FA/0212273. The main motivation for this work was to find an explicit formula for a "Szego-regularized" determinant of a zeroth order pseudodifferential operator (PsDO) on a Zoll manifold. The idea of the Szego-regularization was suggested by V. Guillemin and K. Okikiolu. They have computed the second term in a Szego type expansion on a Zoll manifold of an arbitrary dimension. In the present work we compute the third asymptotic term in any dimension. In the case of dimension 2, our formula gives the above mentioned expression for the Szego-redularized determinant of a zeroth order PsDO. The proof uses a new combinatorial identity, which generalizes a formula due to G.A.Hunt and F.J.Dyson. This identity is related to the distribution of the maximum of a random walk with i.i.d. steps on the real line. The proof of this combinatorial identity together with historical remarks and a discussion of probabilistic and algebraic connections has been published separately.Comment: 39 pages, full version, submitte

Lieb-Thirring inequalities for geometrically induced bound states

We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page

Time evolution of the scattering data for a fourth-order linear differential operator

The time evolution of the scattering and spectral data is obtained for the differential operator $\displaystyle\frac{d^4}{dx^4} +\displaystyle\frac{d}{dx} u(x,t)\displaystyle\frac{d}{dx}+v(x,t),$ where $u(x,t)$ and $v(x,t)$ are real-valued potentials decaying exponentially as $x\to\pm\infty$ at each fixed $t.$ The result is relevant in a crucial step of the inverse scattering transform method that is used in solving the initial-value problem for a pair of coupled nonlinear partial differential equations satisfied by $u(x,t)$ and $v(x,t).$Comment: 19 page

The Scientific Advisory board resolution: Implementation of intermittently scanned Continuous Glucose monitoring in clinical practice to improve glycemic control

The Scientific Advisory Board chaired by Academician of the Russian Academy of Sciences, Peterkova V.A. was held 26 of November in Moscow to discuss the possibilities of continuous glucose monitoring technology (CGM) implementation into routine clinical practice in Russia in order to improve glycemic control in patients with diabetes mellitus (DM).The main aims for Advisory board were to determine the most significant indicators and parameters for CGM to be implemented in practice from a practical point of view of LMWH, necessary for implementation in clinical practice, for different patients groups with diabetes.The following questions and topics were raised within the discussion: the importance of additional indicators beyond glycated hemoglobin (HbA1c) for glycemic control assessment in diabetes patients, CGM positioning in International and Russian clinical guidelines, the accuracy of CGM devises and approaches to its assessment, the role of education programs for diabetic patients, including trainings in correct use and data interpretation and analysis of CGM data obtained, clinical evidence analysis for CGM in randomized trials and real world evidence

Feature fusion based deep spatiotemporal model for violence detection in videos

© Springer Nature Switzerland AG 2019. It is essential for public monitoring and security to detect violent behavior in surveillance videos. However, it requires constant human observation and attention, which is a challenging task. Autonomous detection of violent activities is essential for continuous, uninterrupted video surveillance systems. This paper proposed a novel method to detect violent activities in videos, using fused spatial feature maps, based on Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) units. The spatial features are extracted through CNN, and multi-level spatial features fusion method is used to combine the spatial features maps from two equally spaced sequential input video frames to incorporate motion characteristics. The additional residual layer blocks are used to further learn these fused spatial features to increase the classification accuracy of the network. The combined spatial features of input frames are then fed to LSTM units to learn the global temporal information. The output of this network classifies the violent or non-violent category present in the input video frame. Experimental results on three different standard benchmark datasets: Hockey Fight, Crowd Violence and BEHAVE show that the proposed algorithm provides better ability to recognize violent actions in different scenarios and results in improved performance compared to the state-of-the-art methods

Complex zeros of real ergodic eigenfunctions

We determine the limit distribution (as $\lambda \to \infty$) of complex zeros for holomorphic continuations \phi_{\lambda}^{\C} to Grauert tubes of real eigenfunctions of the Laplacian on a real analytic compact Riemannian manifold $(M, g)$ with ergodic geodesic flow. If $\{\phi_{j_k} \}$ is an ergodic sequence of eigenfunctions, we prove the weak limit formula \frac{1}{\lambda_j} [Z_{\phi_{j_k}^{\C}}] \to \frac{i}{\pi} \bar{\partial} {\partial} |\xi|_g, where [Z_{\phi_{j_k}^{\C}}] is the current of integration over the complex zeros and where $\bar{\partial}$ is with respect to the adapted complex structure of Lempert-Sz\"oke and Guillemin-Stenzel.Comment: Added some examples and references. Also added a new Corollary, and corrected some typo

Evaluating Multimedia Features and Fusion for Example-Based Event Detection

Multimedia event detection (MED) is a challenging problem because of the heterogeneous content and variable quality found in large collections of Internet videos. To study the value of multimedia features and fusion for representing and learning events from a set of example video clips, we created SESAME, a system for video SEarch with Speed and Accuracy for Multimedia Events. SESAME includes multiple bag-of-words event classifiers based on single data types: low-level visual, motion, and audio features; high-level semantic visual concepts; and automatic speech recognition. Event detection performance was evaluated for each event classifier. The performance of low-level visual and motion features was improved by the use of difference coding. The accuracy of the visual concepts was nearly as strong as that of the low-level visual features. Experiments with a number of fusion methods for combining the event detection scores from these classifiers revealed that simple fusion methods, such as arithmetic mean, perform as well as or better than other, more complex fusion methods. SESAME’s performance in the 2012 TRECVID MED evaluation was one of the best reported

Experimental study of direct photon emission in K- --> pi- pi0 gamma decay using ISTRA+ detector

The branching ratio in the charged-pion kinetic energy region of 55 to 90 MeV for the direct photon emission in the K- --> pi- pi0 gamma decay has been measured using in-flight decays detected with the ISTRA+ setup operating in the 25 GeV/c negative secondary beam of the U-70 PS. The value Br(DE)=[0.37+-0.39(stat)+-0.10(syst)]*10^(-5) obtained from the analysis of 930 completely reconstructed events is consistent with the average value of two stopped-kaon experiments, but it differs by 2.5 standard deviations from the average value of three in-flight-kaon experiments. The result is also compared with recent theoretical predictions.Comment: 13 pages, 8 figure