查看更多>>摘要：Recent studies on network spreading dynamics often adopt pairwise interaction to describe the simple spreading process while using higher-order interaction to describe the collective behavior of the dynamical system on the network. However, the interaction between competing pathogens usually includes both pairwise and high-order interactions. Due to dynamic correlation, it is hard to solve the theory by considering two modes of interaction. Here, we propose a theoretical analysis framework based on Microscopic Markov Chain Approach (MMCA) to solve simplicial competing spreading involving pairwise and high-order interactions. Because of the competitive mechanism in the framework, a susceptible node can only be infected by one pathogen, and contagion can spread simultaneously through pairwise interactions (1-simplices) and higher-order interactions, i.e., 2simplices. The theory and simulation agree in good accuracy on real networks and artificial networks, which reveals the validity of the theoretical analysis and indicates that the initial density of the two pathogens and the infection rate of 1-simplices act together on the process of pathogen transmission. The effect of 1-simplices and 2-simplices infection rates of two pathogens are also included in the discussion. When the average degree of the network is fixed, in the case of a larger average number of 1-simplices incidents on a node, infection rates of pathogen A is greater than infection rates of pathogen B may result in final infection density of pathogen A greater than the final infection density of pathogen B. We discuss the influences of 1-simplices average degree and 2-simplices average degree on the final infection range. We find that with the increase of 1-simplices average degree, the pathogen may undergo a transition from outbreak to death while increasing the 2-simplices average degree is more conducive to spreading. Finally, in the study of two different seed selection strategies, we find that selecting the nodes with the highest degree as seeds can promote pathogen spreading more than randomly selecting seeds. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Given graphs G and H, the Turan number ex(G, H) of Hin G is the maximum number of edges in a subgraph of G that contains no H. Chen et al. determined ex(K-e1,(e2), kK(2)) for all 1 <= k = e(1) <= 2. De Silva et al. determined ex(Ke(,1)..,e(,k)Ke(r)) for all r >= 2 and 1 <= k = <= e(1) = center dot center dot center dot = e(r). Moreover, De Silva et al. proposed an interesting generalization of ex(Ke(,1)..,e(,k)Ke(r)): Determine ex(Ke(,1)..,e(,k)Ke(r)) for l = r. In this paper, we give a proof of ex(Ke(,1)..,e(,k)Ke(r)) = (k - 1) Sigma(l)(i=2)ei for all l = 2 and 1 = k = >= 1 = center dot center dot center dot = lambda. We also determine the Turan numbers ex (Ke(,1)..,e(,k)Ke(r)) for all k = 1 and e(4) = e(3) = e(2) = e(1) = 4(k - 1), which gives a positive solution to a problem due to De Silva et al. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper mainly studies an adaptive finite-time control problem for a kind of uncertain strict feedback systems with unknown control gains. First, the original strict-feedback system is transformed into a pure-feedback system. And then, we propose a modified adaptive finite-time design idea on the basis of the property of pre-assigned finite-time function (PFTF) and Nussbaum gain. The designed controller can make sure that all states converge to an arbitrarily region in finite-time and signals in the closed-loop system are finite-time bounded. Moreover, the presented controller is smooth and the settling time does not rely on the initial values and design parameters. Finally, the simulation study is made to illustrate the innovativeness for the proposed scheme. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We present here a regress-later based Monte Carlo approach that uses neural networks for pricing multi-asset discretely-monitored contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for interpretability of the model, a feature that is often desirable in the financial context. Specifically, the interpretation leads us to demonstrate that any discretely monitored contingent claim -possibly high-dimensional and path-dependent- under Markovian and no-arbitrage assumptions, can be semi-statically hedged using a portfolio of short maturity options. We also show, for Bermudan style derivatives, how the method can be used to obtain an upper and lower bound to the true price, where the lower bound is obtained by following a sub-optimal policy, while the upper bound is found by exploiting the dual formulation. Unlike other duality based upper bounds where one typically has to resort to nested simulation for constructing super-martingales, the martingales in the current approach come at no extra cost, without the need for any sub-simulations. We demonstrate through numerical examples the simplicity and efficiency of the method for both pricing and semi-static hedging of path-dependent options. (C) 2021 Elsevier Inc. All rights reserved.
Lachowicz, MiroslawLeszczynski, HenrykTopolski, Krzysztof A.
16页
查看更多>>摘要：In the present paper we study Euler-type approximations along characteristics for a class of kinetic equations that describe swarm formations in the case when the interactions rate is variable. The proposed numerical schemes preserve essential properties of the kinetic equations and in particular preserve the probabilistic measure and are able to approximate the solution almost to the appearance of blow-ups. The blow-ups are referred here to the self-organization swarm behavior. Moreover we define a class of exact solutions traveling wave-type equilibrium solutions that we called TWES. (C) 2021 The Authors. Published by Elsevier Inc.
查看更多>>摘要：The study of the conduction of fluids in magnetic fields has attracted a lot of interest in recent years. In this paper, we use new truly meshless methods for numerical solving of the unsteady 2D coupled magneto-hydrodynamic (MHD) equations with uniform and scattered distributions of nodes on regular and polar domains. These methods are implemented based on a generalization of the moving least squares approximation (GMLS) method and local weak forms of MHD equations. By observing the numerical results obtained from these methods and comparing them with others, one can find the efficiency, accuracy, and speed of these methods. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, the existence of the solution of a class of nonlinear stochastic functional integral equations is investigated. Such that the concept of measures of noncompactness, and Petryshyn's fixed point theorem in Banach space has been used. In addition to proving the theorems of the existence of the solution, by solving some examples, it is shown that the method is efficient. We also give an example that satisfies the conditions of our main theorem, while the conditions described in some other papers do not. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Punishing those who refuse to participate in common efforts is a known and intensively studied way to maintain cooperation among self-interested agents. But this act is costly, hence punishers who are generally also engaged in the original joint venture, become vulnerable, which jeopardizes the effectiveness of this incentive. As an alternative, we may hire special players, whose only duty is to watch the population and punish defectors. Such a policelike or mercenary punishment can be maintained by a tax-based fund. If this tax is negligible, a cyclic dominance may emerge among different strategies. When this tax is relevant then this solution disappears. In the latter case, the fine level becomes a significant factor that determines whether punisher players coexist with cooperators or alternatively with defectors. The maximal average outcome can be reached at an intermediate cost value of punishment. Our observations highlight that we should take special care when such kind of punishment and accompanying tax are introduced to reach a collective goal. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Considering the powerful ability of artificial neural network on data fitting, we have combined it with Wiener process in reliability estimation, while the previously published artificial neural network supported Wiener process based reliability estimation method only can utilize degradation testing data under normal use stress. However, the accelerated degradation tests and accelerated life tests are always performed to shorten the testing time. Hence, based on a general log-linear form acceleration model, we develop the artificial neural network supported Wiener process model into an accelerated testing model to utilize the accelerated testing data and improve the reliability estimating accuracy. Furthermore, the corresponding model training and parameter inferencing approaches are also constructed to apply the proposed model in reliability estimation. A simulation experiment and a case study on stress relaxation dataset are performed to verify the effectiveness of the proposed method. It is concluded that, the proposed method shows superiorities on population evaluation and individual predictions comparing the other methods, considering the accuracies of degradation modeling, life and reliability estimations. As a result, it is more suitable and practical than the previously published approaches. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper we consider one-dimensional Schrodinger operators S(q)u(x) = -(-d(2)/dx(2) + q(r) (x) + q(s) (x)) u(x), x is an element of R, where q(r) is an element of L-infinity (R) is a regular potential with compact support, and q(s) is an element of D' (R) is a singular potential q(s) (x) = Sigma(N)(j=1)(alpha(j)delta(x - x(j)) + beta(j)delta'(x - x(j))), alpha(j), beta(j) is an element of C that involves a finite number of point interactions. The eigenenergies associated to the bound states and the complex energies associated to the resonance states of operator S-q are given by the zeros of certain characteristic functions eta(+/-) that share the same structure up to an algebraic sign. The functions eta(+/-) are obtained explicitly in the form of power series of the spectral parameter, and the computation of the coefficients of the series is given by a recursive integration procedure. The results here presented are general enough to consider arbitrary regular potentials q(r) is an element of L-infinity (R) with compact support, even complexvalued, and point interactions with complex strengths alpha(j), beta(j) (j = 1,..., N). Moreover, our approach leads to an efficient numerical treatment of both the bound and resonance states. (C) 2021 Elsevier Inc. All rights reserved.
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Elsevier