查看更多>>摘要：The clearance of tuberculosis infection shows an elimination of infectious Mycobacterium tuberculosis (Mtb) pathogens and infected macrophage cells. The evidence shows the existence of individuals, who are still tested negative in tuberculin skin test after living with people with active tuberculosis for up to six months. Since the Mtb pathogen is spread from person to person through airborne particles, we build a continuous-time Markov chain (CTMC) model to describe the initial infection with small amount of inhaled bacteria. The CTMC model successfully simulates sample paths presenting disease clearance. We apply the theory of multitype branching processes to analytically approximate the probability of disease clearance. We also estimate the disease clearance time, which is as less than a month for R-0 is an element of [1, 1.5]. Our results demonstrate that the host immune factors affect both the probability and the time of the disease clearance. These relationships are linked by the basic reproduction number R-0. Our findings provide new mechanisms for disease prevention and therapy developments. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：An emerging datacenter network (DCN) with high scalability called HSDC is a server-centric DCN that can help cloud computing in supporting many inherent cloud services. For example, a server-centric DCN can initiate routing for data transmission. This paper investigates the construction of independent spanning trees (ISTs for short), a set of the rooted spanning trees associated with the disjoint-path property, in HSDC. Regarding multiple spanning trees as routing protocol, ISTs have applications in data transmission, e.g., fault-tolerant broadcasting and secure message distribution. We first establish the vertex-symmetry of HSDC. Then, by the structure that n-dimensional HSDC is a compound graph of an n-dimensional hypercube Q(n) and n-clique K-n, we amend the algorithm constructing ISTs for Q(n) to obtain the algorithm required by HSDC. Unlike most algorithms of recursively constructing tree structures, our algorithm can find every node's parent in each spanning tree directly via an easy computation relied upon only the node address and tree index. Consequently, we can implement the algorithm for constructing n ISTs in O(nN) time, where N = n2(n) is the number of vertices of n-dimensional HSDC; or parallelize the algorithm in O(n) time using Nprocessors. Remarkably, the diameter of the constructed ISTs is about twice the diameter of Q(n). (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The source localization problem has been studied by many researchers and applied to a wide range of areas including Global Positioning System (GPS) localization. Although there have been studies examining closed form solutions for cases with not so large noise, only the existence of local solution in L-2 minimization settings is known. In this paper, L-1 minimization with three measurements is studied, and nonuniqueness examples for the minimization are provided. Futher, the uniqueness of the solution in certain conditions is stated and proven. The proof is based on the analysis for the extreme points of the objective function. The singular points are the three source points and the three measurement circles. The critical points are the Fermat point and some points located inside of one measurement circle and outside two other circles. The numbers of the latter critical points are infinite for the equilateral measurement triangle and one for nonequilateral measurement triangle. The analysis for these critical points is also provided. Finally, a few numerical implementations are provided to clarify the uniqueness and nonuniqueness of the problem. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：A meshfree approach, the radial basis reproducing kernel particle method (RRKPM), is proposed in this study, which is based on the radial basis functions (RBFs) and the reproducing kernel particle method (RKPM). The presented approach eliminates the negative effects of different kernel functions on numerical accuracy, which has the advantages of greater accuracy and convergence. Furthermore, the presented approach is adopted to solve the elastoplastic problem of functionally graded materials (FGMs). Using Galerkin weak form of elastoplastic problem, the meshfree RRKPM for elastoplastic problem of FGMs is established, and the penalty method is employed to impose the essential boundary conditions, then the corresponding formulas are obtained. The effects of the scaling factor, loading steps, number of nodes and node distributions on computational results of numerical accuracy are discussed in detail, and the influences of different functional gradient indexes on displacements are studied. To validate the applicability and reliability of the presented meshfree RRKPM, several elastoplastic examples of FGMs are performed and compared to the RKPM and the finite element method (FEM) solutions. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：A maximal geodesic in a graph is a geodesic (alias shortest path) which is not a subpath of a longer geodesic. The geodesic-transversal problem in a graph G is introduced as the task to find a smallest set Sof vertices of G such that each maximal geodesic has at least one vertex in S. The minimum cardinality of such a set is the geodesic-transversal number gt(G) of G. It is proved that gt (G) = 1 if and only if G is a subdivided star and that the geodesic-transversal problem is NP-complete. Fast algorithms to determine the geodesic-transversal number of trees and of spread cactus graphs are designed, respectively. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper contributes to the computational study of the Maximum-Weight Bounded-Degree Rooted Tree Problem. Based on previous work, two types of formulations are introduced for the problem, along with some newly discovered constraints that can enhance the formulations. The separation problem for each family of constraints are studied in terms of their complexity and associated algorithms. We then compare the performance of four branch-and-cut frameworks in extensive computational simulations, especially the performance difference between original models and enhanced models with newly discovered constraints. Results show that the enhanced models have a significantly better performance than the original ones. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：A well-posed time weak form for linear structural dynamics is used to construct a Galerkin time quadrature element formulation. Radau quadrature rule and the generalized differential quadrature analog are used to turn the well-posed weak form into a set of linear equations. The stability and accuracy properties of the formulation are discussed. Numerical examples are given to show the high computational efficiency of the well-posed weak form time quadrature element formulation, as compared with a time finite element solution based on the same weak form using third-order Hermite interpolations. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Dobrynin and Sharafdini [Appl Math Comput 371 (2020) 124949] defined a stepwise transmission irregular (STI) graph as a graph in which transmissions of any two adjacent vertices differ by one. They posed two conjectures in their study of STI graphs. Here we resolve one of them and provide further computational support for the other one. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Two-grid fully discrete finite element approximations of the solution for a nonlinear hyperbolic integro-differential equation are considered and analyzed in this paper. The H-1-norm error estimate is derived, which shows that the optimal convergence order can be obtained when the coarse-grid of size Hand the fine-grid of size h satisfy h = O(H-2). Besides reducing the storage and saving a large amount of time, two-grid methods also keep the accuracy of convergence in calculations. Numerical examples are given to support our theoretical results and demonstrate the efficiency of the methods. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, a composite resilient anti-disturbance H-infinity control scheme is presented for the turbofan linear switched systems with uncertainties and external disturbances via the disturbance observer-based control (DOBC) approach. Since the single-point linearization model cannot be used to accurately describe the engine characteristics of the whole envelope, the multi-model switching method is adopted to preferably describe the working characteristics of the turbofan. A hybrid switching scheme based on state-dependent switching and minimum dwell time constraint is developed to ensure the stability of closed-loop systems and satisfy the dwell-time requirement of turbofan systems. Then, a robust resilient controller is built by combining the DOBC approach and resilient control technique. Based on the multiple Lyapunov functions method, some easy-to-test results are given to guarantee that the closed-loop switched systems are asymptotically stable with H-infinity property. Finally, the effectiveness of the proposed method is verified through some simulations and comparisons. (C) 2021 Elsevier Inc. All rights reserved.
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