Efficient Numerical Methods to Solve Sparse Linear Equations with Application to PageRank

In this paper, we propose three methods to solve the PageRank problem for the transition matrices with both row and column sparsity. Our methods reduce the PageRank problem to the convex optimization problem over the simplex. The first algorithm is based on the gradient descent in L1 norm instead of the Euclidean one. The second algorithm extends the Frank-Wolfe to support sparse gradient updates. The third algorithm stands for the mirror descent algorithm with a randomized projection. We proof converges rates for these methods for sparse problems as well as numerical experiments support their effectiveness.Comment: 26 page

Моделирование влияния внешних воздействий на процесс автоматизированной посадки БпЛА-квадрокоптера на подвижную платформу с использованием технического зрения

This article describes a series of experiments in the Gazebo simulation environment aimed at studying the influence of external weather conditions on the automatic landing of an unmanned aerial vehicle (UAV) on a moving platform using computer vision and a previously developed control system based on PID and polynomial controllers. As part of the research, methods for modeling external weather conditions were developed and landing tests were carried out simulating weather conditions such as wind, light, fog and precipitation, including their combinations. In all experiments, successful landing on the platform was achieved; during the experiments, landing time and its accuracy were measured. The graphical and statistical analysis of the obtained results revealed the influence of illumination, precipitation and wind on the UAV landing time, and the introduction of wind into the simulation under any other external conditions led to the most significant increase in landing time. At the same time, the study failed to identify a systemic negative influence of external conditions on landing accuracy. The results obtained provide valuable information for further improvement of autonomous automatic landing systems for UAVs without the use of satellite navigation systems.В данной статье проводится описание серии экспериментов в симуляционной среде Gazebo, направленных на исследование влияния внешних погодных условий на автоматическую посадку беспилотного летательного аппарата (БпЛА) на движущуюся платформу с использованием компьютерного зрения и разработанной ранее системы управления, основанной на ПИД и полиномиальных регуляторах. В рамках исследования разработаны методы моделирования внешних погодных условий, и проведены тесты посадки с имитацией таких погодных условий, как ветер, освещенность, туман и осадки, включая их комбинации. Во всех экспериментах была достигнута успешная посадка на платформу, в ходе экспериментов измерялось время посадки и ее точность. Проведенный графический и статистический анализ полученных результатов выявил влияние освещенности, осадков и ветра на время посадки БпЛА, а введение ветра в симуляцию при любых других внешних условиях привело к наиболее значительному увеличению времени посадки. При этом в ходе исследования не удалось выявить системного негативного влияния внешних условий на точность посадки. Полученные результаты представляют ценную информацию для дальнейшего совершенствования систем автономной автоматической посадки БпЛА без использования спутниковых систем навигации

Improving Comprehension: Intelligent Tutoring System Explaining the Domain Rules When Students Break Them

Intelligent tutoring systems have become increasingly common in assisting students but are often aimed at isolated subject-domain tasks without creating a scaffolding system from lower- to higher-level cognitive skills, with low-level skills often neglected. We designed and developed an intelligent tutoring system, CompPrehension, which aims to improve the comprehension level of Bloom’s taxonomy. The system features plug-in-based architecture, easily adding new subject domains and learning strategies. It uses formal models and software reasoners to solve the problems and judge the answers, and generates explanatory feedback about the broken domain rules and follow-up questions to stimulate the students’ thinking. We developed two subject domain models: an Expressions domain for teaching the expression order of evaluation, and a Control Flow Statements domain for code-tracing tasks. The chief novelty of our research is that the developed models are capable of automatic problem classification, determining the knowledge required to solve them and so the pedagogical conditions to use the problem without human participation. More than 100 undergraduate first-year Computer Science students took part in evaluating the system. The results in both subject domains show medium but statistically significant learning gains after using the system for a few days; students with worse previous knowledge gained more. In the Control Flow Statements domain, the number of completed questions correlates positively with the post-test grades and learning gains. The students’ survey showed a slightly positive perception of the system