On the equivalence of modes of convergence for log-concave measures

An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note, we explore the extent to which different notions of distance between probability measures are comparable for log-concave distributions. Our results imply that weak convergence of isotropic log-concave distributions is equivalent to convergence in total variation, and is further equivalent to convergence in relative entropy when the limit measure is Gaussian.Comment: v3: Minor tweak in exposition. To appear in GAFA seminar note

Topologically decoherence-protected qubits with trapped ions

We show that trapped ions can be used to simulate a highly symmetrical Hamiltonian with eingenstates naturally protected against local sources of decoherence. This Hamiltonian involves long range coupling between particles and provides a more efficient protection than nearest neighbor models discussed in previous works. Our results open the perspective of experimentally realizing in controlled atomic systems, complex entangled states with decoherence times up to nine orders of magnitude longer than isolated quantum systems.Comment: 4 page

Rate of parity violation from measure concentration

We present a geometric argument determining the kinematic (phase-space) factor contributing to the relative rate at which degrees of freedom of one chirality come to dominate over degrees of freedom of opposite chirality, in models with parity violation. We rely on the measure concentration of a subset of a Euclidean cube which is controlled by an isoperimetric inequality. We provide an interpretation of this result in terms of ideas of Statistical Mechanics.Comment: 10 pages, no figure

Remarks on the Central Limit Theorem for Non-Convex Bodies

In this note, we study possible extensions of the Central Limit Theorem for non-convex bodies. First, we prove a Berry-Esseen type theorem for a certain class of unconditional bodies that are not necessarily convex. Then, we consider a widely-known class of non-convex bodies, the so-called p-convex bodies, and construct a counter-example for this class

Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture

ОБОБЩЕННЫЕ КРИТЕРИИ ИДЕНТИФИКАЦИИ ХИМИЧЕСКИХ СОЕДИНЕНИЙ МЕТОДАМИ ХРОМАТОГРАФИИ – МАСС-СПЕКТРОМЕТРИИ

Criteria of chemical identification used in target and non-target analysis during chromatography-mass spectrometry are reviewed. In both cases, the final criteria are comparable and have a close similarity of both chromatographic retention values (times or relative times) and mass spectra (individual ion masses, their relative peak intensities) of identified analytes and analytical standards. Similarity, usually, means maximum permissible deviations of those values from the corresponding standard values assigned to the known compounds. Identification criteria used are contained in the general guides on the chemical analysis issued by the international or national regulatory organizations. In the case of non-target identification, the analytes and the corresponding standards are unknown before the analysis. In the first stages of this kind of analysis, the candidate compounds are selected for the identification and then the candidate features are compared to those of the standard compounds with the use of the criteria suggested for the target analysis. During the selection of the candidates, one uses high resolution chromatography – tandem mass spectrometry, advanced computer methods of data processing and prediction, and performs searches in chemical data bases, collections of retention indices, and mass spectral libraries. The use of these techniques and workflows can be considered as a reliable condition of the candidates’ selection for the identification. The progress in non-target analysis depends on technique innovations in mass spectrometry, first, by improving the accuracy and reproducibility of ion masses. The development of computer technologies is no less important, which should ensure the emergence of more complete libraries of mass spectra and more accurate methods for predicting the mass spectrometric and chromatographic data.Keywords: chemical identification, mass spectrometry, chromatography, computers, quantitative criteria of identification DOI: http://dx.doi.org/10.15826/analitika.2020.24.3.003B.L.Milman1, I.K. Zhurkovich2 1 Institute of Experimental Medicine, ul. Akad. Pavlova 12, Saint Petersburg 197376, Russian Federation2 Institute of Toxicology, ul. Bekhtereva 1, Saint Petersburg 192019, Russian FederationПредставлен обзор критериев химической идентификации, применяемых в рамках целевого и нецелевого анализа методами хроматографии – масс-спектрометрии. Окончательные критерии в обоих случаях сопоставимы и предполагают близкое сходство характеристик хроматографического удерживания (времена или относительные времена) и масс-спектров (массы отдельных ионов, относительные интенсивности их пиков) идентифицируемых аналитов и аналитических стандартов. Сходство, как правило, означает максимально допустимые отклонения значений указанных величин, установленных для аналитов, от соответствующих справочных значений, приписанных известным соединениям. Используемые критерии идентификации включены в общие руководства по химическому анализу, подготовленные международными или национальными регулирующими организациями. В случае нецелевой идентификации аналиты и соответствующие стандарты неизвестны заранее. На первых этапах решения задач этого вида необходимо отобрать соединения − кандидаты на идентификацию, затем сравнить характеристики аналитов и  соответствующих аналитических стандартов, используя  критерии идентификации, аналогичные тем, которые сформулированы для целевого анализа. Для поиска кандидатов используют хроматографию и тандемную масс-спектрометрию высокого разрешения, продвинутые методы компьютерной обработки и предсказания данных, поиски в химических базах данных, сводках индексов удерживания и масс-спектральных библиотеках. Применение этих методов и процедур – условие надежности поиска кандидатов на идентификацию. Прогресс в области нецелевого анализа зависит от усовершенствования масс-спектрометрической техники, в первую очередь за счет повышения точности и воспроизводимости определения масс ионов. Не меньшее значение имеет развитие компьютерных технологий (информатики), что должно обеспечить появление более полных библиотек масс-спектров и более точных методов предсказания масс-спектрометрических и хроматографических данных.  Ключевые слова: химическая идентификация, масс-спектрометрия, хроматография, компьютеры, количественные критерии идентификацииDOI: http://dx.doi.org/10.15826/analitika.2020.24.3.00

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1

Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems

We obtain new principles for transferring log-Sobolev and Spectral-Gap inequalities from a source metric-measure space to a target one, when the curvature of the target space is bounded from below. As our main application, we obtain explicit estimates for the log-Sobolev and Spectral-Gap constants of various conservative spin system models, consisting of non-interacting and weakly-interacting particles, constrained to conserve the mean-spin. When the self-interaction is a perturbation of a strongly convex potential, this partially recovers and partially extends previous results of Caputo, Chafa\"{\i}, Grunewald, Landim, Lu, Menz, Otto, Panizo, Villani, Westdickenberg and Yau. When the self-interaction is only assumed to be (non-strongly) convex, as in the case of the two-sided exponential measure, we obtain sharp estimates on the system's spectral-gap as a function of the mean-spin, independently of the size of the system.Comment: 57 page

Microwave radiometric observations near 19.35, 92 and 183 GHz of precipitation in tropical storm Cora

Observations of rain cells in the remains of a decaying tropical storm were made by Airborne Microwave Radiometers at 19.35,92 and three frequencies near 183 GHz. Extremely low brightness temperatures, as low as 140 K were noted in the 92 and 183 GHz observations. These can be accounted for by the ice often associated with raindrop formation. Further, 183 GHz observations can be interpreted in terms of the height of the ice. The brightness temperatures observed suggest the presence of precipitation sized ice as high as 9 km or more