The development of artificial intelligence(AI) and the mining of biomedical data complement each other. From the direct use of computer vision results to analyze medical images for disease screening, to now integratin...
The development of artificial intelligence(AI) and the mining of biomedical data complement each other. From the direct use of computer vision results to analyze medical images for disease screening, to now integrating biological knowledge into models and even accelerating the development of new AI based on biological discoveries, the boundaries of both are constantly expanding, and their connections are becoming closer.
The computation of the radiative transfer equation is expensive mainly due to two stiff terms:the transport term and the collision *** stiffness in the former comes from the fact that particles(such as photons)travel ...
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The computation of the radiative transfer equation is expensive mainly due to two stiff terms:the transport term and the collision *** stiffness in the former comes from the fact that particles(such as photons)travel at the speed of light,while that in the latter is due to the strong scattering in the optically thick *** study the fully implicit scheme for this equation to account for the *** main challenge in the implicit treatment is the coupling between the spacial and angular coordinates that requires the large size of the to-be-inverted matrix,which is also ill-conditioned and not necessarily *** main idea is to utilize the spectral structure of the ill-conditioned matrix to construct a pre-conditioner,which,along with an exquisite split of the spatial and angular dependence,significantly improve the condition number and allows a matrix-free *** also design a fast solver to compute this pre-conditioner explicitly in *** method is shown to be efficient in both diffusive and free streaming limit,and the computational cost is comparable to the state-of-the-art *** examples including anisotropic scattering and two-dimensional problems are provided to validate the effectiveness of our method.
The microstructure of a material intimately affects the performance of a device made from this material. The microstructure, in turn, is affected by the processing pathway used to fabricate the device. This forms the ...
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The microstructure of a material intimately affects the performance of a device made from this material. The microstructure, in turn, is affected by the processing pathway used to fabricate the device. This forms the process–structure–property triangle that is central to material science. There has been increasing interest to comprehensively understand and subsequently exploit process–structure–property (PSP) relationships to design processing pathways that result in tailored microstructures exhibiting optimal properties. However, unraveling process–structure–property relationships usually requires systematic and tedious combinatorial search of process and system variables to identify the microstructures that are produced. This is further complicated by the necessity to interrogate the properties of the huge set of corresponding microstructures. Motivated by this challenge, we focus on developing a generic methodology to establish and explore PSP pathways. We leverage recent advances in high performance computing (HPC) and high throughput computing (HTC) with the premise that a domain expert should be able to focus on domain specific PSP problems while the highly specialized HPC/HTC knowledge needed to approach such problems should be hidden from the domain expert. Our hypothesis is that PSP exploration can be naturally formulated in terms of a standard paradigm in cloud computing, namely the MapReduce programming model. We show how reformulating PSP exploration into a MapReduce workflow enables us to take advantage of advances in cloud computing while requiring minimal specialized knowledge of HPC. We illustrate this generic approach by exploring PSP relationships relevant to organic photovoltaics. We focus on identifying microstructural traits that correlate with specific properties of the photovoltaic process: exciton generation, exciton dissociation and charge generation. We integrate a graph-based microstructure characterization tool, and a microstructure-aware
Dimension reduction techniques for dynamical systems on networks are considered to promote our understanding of the original high-dimensional dynamics. One strategy of dimension reduction is to derive a low-dimensiona...
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Dimension reduction techniques for dynamical systems on networks are considered to promote our understanding of the original high-dimensional dynamics. One strategy of dimension reduction is to derive a low-dimensional dynamical system whose behavior approximates the observables of the original dynamical system that are weighted linear summations of the state variables at the different nodes. Recently proposed methods use the leading eigenvector of the adjacency matrix of the network as the mixture weights to obtain such observables. In the present study, we explore performances of this type of one-dimensional reductions of dynamical systems on networks when we use non-leading eigenvectors of the adjacency matrix as the mixture weights. Our theory predicts that non-leading eigenvectors can be more efficient than the leading eigenvector and enables us to select the eigenvector minimizing the error. We numerically verify that the optimal non-leading eigenvector outperforms the leading eigenvector for some dynamical systems and networks. We also argue that, despite our theory, it is practically better to use the leading eigenvector as the mixture weights to avoid misplacing the bifurcation point too distantly and to be resistant against dynamical noise.
Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao et al. [Nature (London) 530, 307 ...
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Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao et al. [Nature (London) 530, 307 (2016)] proposed a theoretical framework to reduce dynamical systems on networks, which are high dimensional in general, to one-dimensional dynamical systems. The accuracy of this one-dimensional reduction relies on three approximations in addition to the assumption that the network has a negligible degree correlation. In the present study, we analyze the accuracy of the one-dimensional reduction assuming networks without degree correlation. We do so mainly through examining the validity of the individual assumptions underlying the method. Across five dynamical system models, we find that the accuracy of the one-dimensional reduction hinges on the spread of the equilibrium value of the state variable across the nodes in most cases. Specifically, the one-dimensional reduction tends to be accurate when the dispersion of the node's state is small. We also find that the correlation between the node's state and the node's degree, which is common for various dynamical systems on networks, is unrelated to the accuracy of the one-dimensional reduction.
Interevent times in temporal contact data from humans and animals typically obey heavy-tailed distributions, and this property impacts contagion and other dynamical processes on networks. We theoretically show that di...
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In social networks, interaction patterns typically change over time. We study opinion dynamics on tie-decay networks in which tie strength increases instantaneously when there is an interaction and decays exponentiall...
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In social networks, interaction patterns typically change over time. We study opinion dynamics on tie-decay networks in which tie strength increases instantaneously when there is an interaction and decays exponentially between interactions. Specifically, we formulate continuous-time Laplacian dynamics and a discrete-time DeGroot model of opinion dynamics on these tie-decay networks, and we carry out numerical computations for the continuous-time Laplacian dynamics. We examine the speed of convergence by studying the spectral gaps of combinatorial Laplacian matrices of tie-decay networks. First, we compare the spectral gaps of the Laplacian matrices of tie-decay networks that we construct from empirical data with the spectral gaps for corresponding randomized and aggregate networks. We find that the spectral gaps for the empirical networks tend to be smaller than those for the randomized and aggregate networks. Second, we study the spectral gap as a function of the tie-decay rate and time. Intuitively, we expect small tie-decay rates to lead to fast convergence because the influence of each interaction between two nodes lasts longer for smaller decay rates. Moreover, as time progresses and more interactions occur, we expect eventual convergence. However, we demonstrate that the spectral gap need not decrease monotonically with respect to the decay rate or increase monotonically with respect to time. Our results highlight the importance of the interplay between the times that edges strengthen and decay in temporal networks.
Interevent times in temporal contact data from humans and animals typically obey heavy-tailed distributions, which impacts contagion and other dynamical processes on networks. We theoretically show that distributions ...
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Interevent times in temporal contact data from humans and animals typically obey heavy-tailed distributions, which impacts contagion and other dynamical processes on networks. We theoretically show that distributions of interevent times heavier-tailed than exponential distributions are a consequence of the most basic metapopulation model used in epidemiology and ecology, in which individuals move from one patch to another according to the simple random walk. Our results hold true irrespective of the network structure and also for more realistic mobility rules such as high-order random walks and the recurrent mobility patterns used for modeling human dynamics.
Successfully anticipating sudden major changes in complex systems is a practical concern. Such complex systems often form a heterogeneous network, which may show multistage transitions in which some nodes experience a...
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Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze ...
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