We develop a prototypical stochastic model for a local search around a given home. The stochastic dynamic model is motivated by experimental findings of the motion of a fruit fly around a given spot of food but will generally describe the local search behavior. The local search consists of a sequence of two epochs. In the first the searcher explores new space around the home, whereas it returns to the home during the second epoch. In the proposed two-dimensional model both tasks are described by the same stochastic dynamics. The searcher moves with constant speed and its angular dynamics is driven by a symmetric α-stable noise source. The latter stands for the uncertainty to decide the new direction of motion. The main ingredient of the model is the nonlinear interaction dynamics of the searcher with its home. In order to determine the new heading direction, the searcher has to know the actual angles of its position to the home and of the heading vector. A bound state to the home is realized by a permanent switch of a repulsive and attractive forcing of the heading direction from the position direction corresponding to search and return epochs. Our investigation elucidates the analytic tractability of the deterministic and stochastic dynamics. Noise transforms the conservative deterministic dynamics into a dissipative one of the moments. The noise enables a faster finding of a target distinct from the home with optimal intensity. This optimal situation is related to the noise-dependent relaxation time. It is uniquely defined for all α and distinguishes between the stochastic dynamics before and after its value. For times large compared to this, we derive the corresponding Smoluchowski equation and find diffusive spreading of the searcher in the space. We report on the qualitative agreement with the experimentally observed spatial distribution, noisy oscillatory return times, and spatial autocorrelation function of the fruit fly. However, as a result of its simplicity, the model aims to reproduce the local search behavior of other units during their exploration of surrounding space and their quasiperiodic return to a home.
1 arXiv:1807.11261v1 [cond-mat.stat-mech] 30 Jul 2018We extend a recently introduced prototypical stochastic model describing uniformly the search and return of objects looking for new food sources around a given home.The model describes the kinematic motion of the object with constant speed in two dimensions. The angular dynamics is driven by noise and describes a "pursuit" and "escape" behavior of the heading and the position vectors. Pursuit behavior ensures the return to the home and the escaping between the two vectors realizes exploration of space in the vicinity of the given home. Noise is originated by environmental influences and during decision making of the object. We take symmetric α-stable noise since such noise is observed in experiments. We now investigate for the simplest possible case, the consequences of limited knowledge of the position angle of the home. We find that both noise type and noise strength can significantly increase the probability of returning to the home. First, we review shortly main findings of the model presented in the former manuscript. These are the stationary distance distribution of the noise driven conservative dynamics and the observation of an optimal noise for finding new food sources. Afterwards, we generalize the model by adding a constant shift γ within the interaction rule between the two vectors. The latter might be created by a permanent uncertainty of the correct home position. Non vanishing shifts transform the kinematics of the searcher to a dissipative dynamics. For the latter we discuss the novel deterministic properties and calculate the stationary spatial distribution around the home.
We present a robustness analysis of an inter-cities mobility complex network, motivated by the challenge of the COVID-19 pandemic and the seek for proper containment strategies. Brazilian data from 2016 are used to build a network with more than five thousand cities (nodes) and twenty-seven states with the edges representing the weekly flow of people between cities via terrestrial transports. Nodes are systematically isolated (removed from the network) either at random (failures) or guided by specific strategies (targeted attacks), and the impacts are assessed with three metrics: the number of components, the size of the giant component, and the total remaining flow of people. We propose strategies to identify which regions should be isolated first and their impact on people mobility. The results are compared with the so-called reactive strategy, which consists of isolating regions ordered by the date the first case of COVID-19 appeared. We assume that the nodes’ failures abstract individual municipal and state initiatives that are independent and possess a certain level of unpredictability. Differently, the targeted attacks are related to centralized strategies led by the federal government in agreement with municipalities and states. Removing a node means completely restricting the mobility of people between the referred city/state and the rest of the network. Results reveal that random failures do not cause a high impact on mobility restraint, but the coordinated isolation of specific cities with targeted attacks is crucial to detach entire network areas and thus prevent spreading. Moreover, the targeted attacks perform better than the reactive strategy for the three analyzed robustness metrics.
Abstract:Shadows exist in almost all aerial and outdoor images, and they can be useful for estimating Sun position estimation or measuring object size. On the other hand, they represent a problem in processes such as object detection/recognition, image matching, etc., because they may be confused with dark objects and change the image radiometric properties. We address this problem on aerial and outdoor color images in this work. We use a filter to find low intensities as a first step. For outdoor color images, we analyze spectrum ratio properties to refine the detection, and the results are assessed with a dataset containing ground truth. For the aerial case we validate the detections depending of the hue component of pixels. This stage takes into account that, in deep shadows, most pixels have blue or violet wavelengths because of an atmospheric scattering effect.Keywords: Shadow Detection; Aerial Images; Terrestrial Images. Resumo:Sombras estão presentes na maior parte das imagens aéreas e terrestres, e elas podem ser úteis para estimação da posição do Sol, ou para medir os tamanhos de objetos. Por outro lado, elas representam um problema em processamentos tais como detecção/reconhecimento de objetos, correspondência entre imagens, etc., pois podem ser confundidas com objetos escuros e mudar as propriedades radiométricas da imagem. Neste trabalho esse problema foi tratado em imagens aéreas e terrestres. Utilizou-se um filtro para encontrar áreas com baixas intensidades. Para as imagens terrestres, foram analisadas propriedades da razão do espectro das imagens para refinar a detecção, e os resultados foram avaliados por meio de um conjunto de dados contendo a verdade de campo. Para o caso aéreo as detecções são validadas dependendo da componente da matiz dos pixels. Esse estágio leva em consideração que em sombras profundas a maior parte dos pixels possuem comprimentos de onda na região do azul e violeta por conta de um efeito de espalhamento atmosférico.
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