An explicit solution for a multimarginal mass transportation problem

We construct an explicit solution for the multimarginal transportation problem on the unit cube $[0,1]^3$ with the cost function $xyz$ and one-dimensional uniform projections. We show that the primal problem is concentrated on a set with non-constant local dimension and admits many solutions, whereas the solution to the corresponding dual problem is unique (up to addition of constants).Comment: 31 pages, 4 figures. The paper was completely rewritten. Heuristic considerations to find a solution of the primal problem added. Algorithm to find the primal problem solution numerically added (arbitrary marginals). The construction was generalized for a C(ln x + ln y + ln z), C is convex. Measure on the triangle was found with the support singular with respect to the Lebesgue measur

Avoidability of formulas with two variables

In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ of variables if there is no factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a non-erasing morphism. A pattern $p$ is said to be $k$-avoidable if there exists an infinite word over a $k$-letter alphabet that avoids $p$. We consider the patterns such that at most two variables appear at least twice, or equivalently, the formulas with at most two variables. For each such formula, we determine whether it is $2$-avoidable, and if it is $2$-avoidable, we determine whether it is avoided by exponentially many binary words

Выполнение индивидуальных заданий по полупроводниковой электронике при помощи образовательных сайтов сети Интернет

The report examines the author’s experience on the use of educational Internet sites by students in order to solve problems in the courses of semiconductor materials science and solid-state electronics. The pros and cons of the used websites are discussed, and the difficulties of the students work in an English-speaking environment are noted.В докладе анализируется опыт автора обучения студентов с использованием образовательных сайтов Интернета при решении задач по курсам полупроводникового материаловедения и твердотельной электроники. Рассматриваются достоинства и недостатки применяемых сайтов, отмечаются сложности работы студентов в англоязычной среде

Sorting with Teams

We fully solve a sorting problem with heterogeneous firms and multiple heterogeneous workers whose skills are imperfect substitutes. We show that optimal sorting, which we call mixed and countermonotonic, is comprised of two regions. In the first region, mediocre firms sort with mediocre workers and coworkers such that the output losses are equal across all these teams (mixing). In the second region, a high skill worker sorts with low skill coworkers and a high productivity firm (countermonotonicity). We characterize the equilibrium wages and firm values. Quantitatively, our model can generate the dispersion of earnings within and across US firms

Probation Institution in Russia

The author deals with the problems of taking under control the persons after a release from custody and rendering them help in social adaptation

SliceMatch: Geometry-guided Aggregation for Cross-View Pose Estimation

This work addresses cross-view camera pose estimation, i.e., determining the 3-Degrees-of-Freedom camera pose of a given ground-level image w.r.t. an aerial image of the local area. We propose SliceMatch, which consists of ground and aerial feature extractors, feature aggregators, and a pose predictor. The feature extractors extract dense features from the ground and aerial images. Given a set of candidate camera poses, the feature aggregators construct a single ground descriptor and a set of pose-dependent aerial descriptors. Notably, our novel aerial feature aggregator has a cross-view attention module for ground-view guided aerial feature selection and utilizes the geometric projection of the ground camera's viewing frustum on the aerial image to pool features. The efficient construction of aerial descriptors is achieved using precomputed masks. SliceMatch is trained using contrastive learning and pose estimation is formulated as a similarity comparison between the ground descriptor and the aerial descriptors. Compared to the state-of-the-art, SliceMatch achieves a 19% lower median localization error on the VIGOR benchmark using the same VGG16 backbone at 150 frames per second, and a 50% lower error when using a ResNet50 backbone

Single-shot carrier-envelope-phase measurement in ambient air

The ability to measure and control the carrier envelope phase (CEP) of few-cycle laser pulses is of paramount importance for both frequency metrology and attosecond science. Here, we present a phase meter relying on the CEP-dependent photocurrents induced by circularly polarized few-cycle pulses focused between electrodes in ambient air. The new device facilitates compact single-shot, CEP measurements under ambient conditions and promises CEP tagging at repetition rates orders of magnitude higher than most conventional CEP detection schemes as well as straightforward implementation at longer wavelengths