查看更多>>摘要：Let HSh be the set of hexagonal systems with h hexagons and let n(i)(H ) denote the number of internal vertices of H is an element of & nbsp;HSh. It is well known that for every H is an element of & nbsp;HSh:0 <=& nbsp;n(i)(H) <=& nbsp;2 h + 1 - inverted right perpendicular root 2 h - 3inverted left & nbsp;perpendicular.The hexagonal systems which attain the lower bound of (1) are called catacondensed hexagonal systems, a class which has been extensively studied. On the other extreme we have the hexagonal systems which attain the upper bound of (1), which in contrast to the catacondensed hexagonal systems, we call anacondensed hexagonal systems, and denote them by A(h). We shall see in this paper that the number of anacondensed hexagonal systems in HSh have a super-polynomial growth for infinite values of h : for any t > 0 , there exist h large enough such that there are more than h(t) anacondensed hexagonal systems in HSh. Consequently, A(h)& nbsp;is a large class in HSh.One useful parameter associated to a hexagonal system is the so-called number of bay regions of H is an element of HSh, denoted by b(H). We will show how to construct anacondensed hexagonal systems with a given number of bay regions. Moreover, among all hexagonal systems in A(h), we find those which have extremal value of number of bay regions. This result has strong implications in the study of the extremal values of vertex-degree-based topological indices (molecular descriptors) over A(h).(c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We introduce a model to study the impact of catastrophes on evolutionary paths. If we do not allow catastrophes the number of changes in the maximum fitness of a population grows logarithmically with respect to time. Allowing catastrophes (no matter how rare) yields a drastically different behavior. When catastrophes are possible the number of changes in the maximum fitness of the population grows linearly with time. Moreover, the evolutionary paths are a lot less predictable when catastrophes are possible. Our results can be seen as supporting the hypothesis that catastrophes speed up evolution by disrupting dominant species and creating space for new species to emerge and evolve.(c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids the Gibbs phenomenon when we approximate a discontinuous function. In this work, we present a generalization to this method giving explicit expressions for all the weights for any order of the algorithm. It has a similar behavior to weighted essentially non oscillatory (WENO) technique but the design of the weights in this case is more simple. Also, we propose a new way to construct them obtaining the maximum order near the discontinuities. Some experiments are performed to demonstrate our results and to compare them with standard methods.(c) 2021 The Authors. Published by Elsevier Inc.This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
查看更多>>摘要：This paper investigates the reliable event-based dissipative filter design problem for net-worked system with quantization and sensor fault. The attention is focused on propos -ing an effective filtering design method for ensuring the resulting filtering error system is asymptotically stable and guarantees dissipativity performance. Firstly, the dissipativity performance analysis criterion is given to check whether the asymptotic stability and the dissipativity performance are satisfied. Then, based on this, the design method for dissipa-tive filter is established in terms of the classical linear matrix inequality technique. Finally, two practical examples are used to illustrate the effectiveness and feasibility of the devel-oped algorithm.(c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Partial differential equations have recently been established as a viable framework for image processing, particularly for image binarization. One drawback of this framework is the requirement for manual parameter tuning. In this work we propose a novel development wherein the spatio-temporal dynamics of the thresholding parameter are governed by an additional partial differential equation which is engineered to exhibit desirable traits. While the model can still be tuned manually to achieve optimal results, we show experimentally that the present framework is near optimal for the default choice of parameter, tau. This novel system enforces a smooth evolution of the threshold map while still offering locally adaptive thresholding properties, a requirement for non-uniformly illuminated images. The proposed model is applied to images through a rudimentary finite difference based numerical method due to the parallelizability and provable stability of the method. The proposed work offers an unsupervised binarization scheme and is bench-marked against state-of-the-art methods in the field. (C) 2021 Elsevier Inc. All rights reserved.
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