Strategy for Locating People to Reduce the Transmission of COVID-19 Using Different Interference Measures

COVID-19 is generally transmitted from person to person through small droplets of saliva emitted when talking, sneezing, coughing, or breathing. For this reason, social distancing and ventilation have been widely emphasized to control the pandemic. The spread of the virus has brought with it many challenges in locating people under distance constraints. The effects of wakes between turbines have been studied extensively in the literature on wind energy, and there are well-established interference models. Does this apply to the propagation functions of the virus? In this work, a parallel relationship between the two problems is proposed. A mixed-integer linear programming (MIP) model and a mixed-integer quadratic programming model (MIQP) are formulated to locate people to avoid the spread of COVID-19. Both models were constructed according to the distance constraints proposed by the World Health Organization and the interference functions representing the effects of wake between turbines. Extensive computational tests show that people should not be less than two meters apart, in agreement with the adapted Wells–Riley model, which indicates that 1.6 to 3.0 m (5.2 to 9.8 ft) is the safe social distance when considering the aerosol transmission of large droplets exhaled when speaking, while the distance can be up to 8.2 m (26 ft) if all the droplets in a calm air environment are taken into account.

Finite-time and spectral-finite methods of optimal filtering of discrete signals

На основе содержания теоремы ортогонального проецирования излагаются методы оптимальных, линейных рекуррентных оценок, в общем случае, не марковских, сигналов, на фоне произвольных помех. Предлагаемые алгоритмы оптимальной обработки дискретных сигналов являются альтернативными методу фильтрации Калмана, не отличающимися заметно от них по точности обработки и являющимися более универсальными и простыми при их реализации. Универсальность исследуемых методов определяется применимостью их к широкому классу моделей сигналов, не требующих марковского свойства оцениваемого сигнала и изменения структуры алгоритма оценки в зависимости от моделей помех измерения в виде случайного коррелированного процесса или белого шума. Более простые структуры алгоритмов рассматриваемых методов по отношению к фильтрации Калмана объясняются отсутствием необходимости представления модели в пространстве состояний и требования решать нелинейное уравнение Риккати для реализации алгоритма. Спектрально-финитный алгоритм оптимальной оценки сигнала осуществляет сжатие информации в спектральном аспекте на основе использования метода нахождения собственных чисел и векторов и позволяет осуществить понижение размерности векторов результатов измерений вплоть до скалярных величин без заметной потери точности оценки. В качестве исходной информации необходимо знание корреляционной функции и математического ожидания оцениваемого дискретного сигнала и дисперсии и математического ожидания дискретной помехи. Based on the content of the orthogonal projection theorem, methods of optimal, linear recurrent estimates of, in general, non-Markov signals, against the background of arbitrary interference, are presented. The proposed algorithms for optimal processing of discrete signals are alternative to the Kalman filtering method, which do not differ significantly from them in terms of processing accuracy and are more universal and simple to implement. The universality of the studied methods is determined by their applicability to a wide class of signal models that do not require the Markov property of the estimated signal and changes in the structure of the estimation algorithm depending on the measurement interference models in the form of a random correlated process or white noise. The simpler structures of the algorithms of the methods under consideration in relation to Kalman filtering are explained by the absence of the need to represent the model in the state space and the requirement to solve the nonlinear Riccati equation for the implementation of the algorithm.

Solution of the Interference Models Identification Problem

An approach to constructing the static characteristics of a system from experimental data is considered. It is noted that in many cases the problem is solved by applying the "black box" concept, according to which the data of an experiment containing the values of the measured input and output quantities are used. In practice, the input and output variables in the experiment are determined with certain errors. It is shown that in solving the problem within the framework of the conventional approach, the availability of various sources and generating factors of interference models is often ignored, which leads to a significant distortion of error estimates and to formation of an inadequate conversion characteristic. In view of this circumstance, the types and sources of errors appearing in constructing the static characteristic are determined, and the models of noises emerging during measurements under real field conditions and during a calibration experiment are studied, and it is shown that they have fundamentally different effects on the measurement result.

Grid cells encode local head direction

Grid and head direction codes represent cognitive spaces for navigation and memory. Pure grid cells generate grid codes that have been assumed to be independent of head direction, whereas conjunctive cells generate grid representations that are tuned to a single head direction. Here, we demonstrate that pure grid cells also encode head direction, but through distinct mechanisms. We show that individual firing fields of pure grid cells are tuned to multiple head directions, with the preferred sets of directions differing between fields. This local directionality is not predicted by previous continuous attractor or oscillatory interference models of grid firing but is accounted for by models in which pure grid cells integrate inputs from co-aligned conjunctive cells with firing rates that differ between their fields. Local directional signals from grid cells may contribute to downstream computations by decorrelating different points of view from the same location.

On some sufficient conditions for distributed QoS support in wireless networks

Given a wireless network where some pairs of communication links interfere with each other, we study sufficient conditions for determining whether a given set of minimum bandwidth Quality of Service (QoS) requirements can be satisfied. We are especially interested in distributed implementations which have low communication overhead and low processing complexity. Row constraints are known to be sufficient, and we introduce the notion of the induced star number of a graph and show that this quantity determines the performance of this condition. We further investigate this problem for some special classes of networks and interference models such as unit disk networks and primary interference constraints. We determine the exact worst-case performance of some distributed algorithms for admission control and thereby show that they can be arbitrarily far away from optimal; we then show that these algorithms are within a bounded factor away from optimal for some well known classes of networks and interference models.