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关键词： Matrix-free operator evaluation   discontinuous Galerkin methods   high-dimensional   high-order   Vlasov-Poisson equation   MPI-3.0 shared memory  

摘要： This work presents the efficient, matrix-free finite-element library hyper deal for solving partial differential equations in two up to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional finite-element library deal. II to create complex low-dimensional meshes and to operate on them individually. These meshes are combined via a tensor product on the fly, and the library provides new special-purpose highly optimized matrix-free functions exploiting domain decomposition as well as shared memory via MPI-3.0 features. Both node-level performance analyses and strong/weak-scaling studies on up to 147,456 CPU cores confirm the efficiency of the implementation. Results obtained with the library hyper . deal are reported for high-dimensional advection problems and for the solution of the Vlasov-Poisson equation in up to six-dimensional phase space.

关键词： Forward-backward-stochastic-differential-equations (FBSDE)   Leader-follower game   Major-minor (MM) game   Mean-field game (MFG)   Open-loop (OL) strategy   Stackelberg-Nash-Cournot (SNC) approximate equilibrium  

摘要： In this paper, we study a controlled linear-quadratic-Gaussian large population system combining three types of interactive agents mixed, which are respectively,major leader,minor leaders, andminor followers. In reality, they may represent three typical types of participants involved in market price formation: major supplier, minor suppliers and minor producers. The Stackelberg-Nash-Cournot (SNC) approximate equilibrium is derived from the combination of a major-minor mean-field game (MFG) and a leader-follower Stackelberg game. Although all agents are offorwardstates in that onlyinitialconditions are specified in their dynamics, our SNC analysis provides an MFG framework that is naturally in aforward-backwardstate in that bothinitialandterminalconditions are specified. This result differs from those reported in the literature on standard MFG frameworks, mainly as a result of the adoption of a Stackelberg structure. Through variational analysis, the consistency condition system can be represented by some fully-coupled forward-backward-stochastic-differential-equations with a high-dimensional block structure in an open-loop case. To sufficiently address the related solvability, we also derive the feedback form of the SNC approximate. equilibrium strategy via some coupled Riccati equations. Our study includes various mean-field game models as its special cases.

关键词： Testing   Libraries   Fuzzing   Tensors   Training   Task analysis   Computer bugs   Deep learning operators   deep learning libraries   defect detection   differential testing   fuzzing  

摘要： Deep learning (DL) libraries reduce the barriers to the DL model construction. In DL libraries, various building blocks are DL operators with different functionality, responsible for processing high-dimensional tensors during training and inference. Thus, the quality of operators could directly impact the quality of models. However, existing DL testing techniques mainly focus on robustness testing of trained neural network models and cannot locate DL operators' defects. The insufficient test input and undetermined test output in operator testing have become challenging for DL library developers. In this article, we propose an approach, namely Duo, which combines fuzzing techniques and differential testing techniques to generate input and evaluate corresponding output. It implements mutation-based fuzzing to produce tensor inputs by employing nine mutation operators derived from genetic algorithms and differential testing to evaluate outputs' correctness from multiple operator instances. Duo is implemented in a tool and used to evaluate seven operators from TensorFlow, PyTorch, MNN, and MXNet in an experiment. The result shows that Duo can expose defects of DL operators and realize multidimension evaluation for DL operators from different DL libraries.

关键词： virus   nucleic acid sensor   blood-testis barrier   testosterone   TNF-alpha  

摘要： The human testis can be infected by a large number of RNA and DNA viruses. While various RNA virus infections may induce orchitis and impair testicular functions, DNA virus infection rarely affects the testis. Mechanisms underlying the differential effects of RNA and DNA viral infections on the testis remain unclear. In the current study, we therefore examined the effects of viral RNA and DNA sensor signaling pathways on mouse Sertoli cells (SC) and Leydig cells (LC).The local injection of viral RNA analogue polyinosinic-polycytidylic acid [poly(I:C)] into the testis markedly disrupted spermatogenesis, whereas the injection of the herpes simplex virus (HSV) DNA analogue HSV60 did not affect spermatogenesis. Poly(I:C) dramatically induced the expression of the proinflammatory cytokines tumor necrosis factor alpha (TNF-alpha) and interleukin 6 in SC and LC through Toll-like receptor 3 and interferon beta promoter stimulator 1 signaling pathways, impairing the integrity of the blood-testis barrier and testosterone synthesis. Poly(I:C)-induced TNF-alpha production thus plays a critical role in the impairment of cell functions. In contrast, HSV60 predominantly induced the expression of type 1 interferons and antiviral proteins via the DNA sensor signaling pathway, which did not affect testicular cell functions. Accordingly, the Zika virus induced high levels of TNF-alpha, in SC and LC and impaired their respective cellular functions, whereas Herpes simplex virus type 2 principally induced antiviral responses and did not impair such functions. These results provide insights into the mechanisms by which RNA viral infections impair testicular functions.

关键词： algebra of DIQM   differential-integral quadrature method (DIQM)   exponential convergence   integration matrix   nonlinear Volterra integro-differential equations  

摘要： In this work, we introduce an integration matrix operator that is fully consistent with the differentiation matrix operator defined by the differential quadrature method (DQM). Using these operators, a generic differential-integral quadrature method "DIQM" is proposed to directly discretize an integro-differential equation as a system of algebraic equations. To extend the applicability of the proposed DIQM to solve nonlinear and/or variable coefficients integro-differential equation, some matrix manipulations are introduced. A stability analysis for Volterra integro-partial-differential equations is presented and the exponential convergence of the proposed method is examined. Various types of integro-differential equations are solved including ordinary/partial, linear/nonlinear, Volterra parabolic/hyperbolic integro-differential equations with different boundary and initial conditions. Numerical results demonstrate the exponential convergence and the applicability of DIQM.

关键词： Bilinear evolution models   Nash equilibria   Nash bargaining problem   Optimal control theory   Quantum evolution models   Lotka–Volterra models   Newton methods  

摘要： This paper is devoted to a theoretical and numerical investigation of Nash equilibria and Nash bargaining problems governed by bilinear (input-affine) differential models. These systems with a bilinear state-control structure arise in many applications in, e.g., biology, economics, physics, where competition between different species, agents, and forces needs to be modelled. For this purpose, the concept of Nash equilibria (NE) appears appropriate, and the building blocks of the resulting differential Nash games are different control functions associated with different players that pursue different non-cooperative objectives. In this framework, existence of Nash equilibria is proved and computed with a semi-smooth Newton scheme combined with a relaxation method. Further, a related Nash bargaining (NB) problem is discussed. This aims at determining an improvement of all players’ objectives with respect to the Nash equilibria. Results of numerical experiments successfully demonstrate the effectiveness of the proposed NE and NB computational framework.

关键词： Global attractor   Parabolic variational inequalities   Measure of noncompactness   Fixed point theory   Free boundary problem  

摘要： In this work, we consider an evolution model formulated by a parabolic differential inclusion and a parabolic variational inequality. We prove the solvability of our problem and show that the solution set generates a m-semiflow. In addition, the existence of a global attractor for the m-semiflow is proved by using the technique of measure of noncompactness. An example is given to illustrate our theoretical results for an evolution system arising from a Stefan problem.

关键词： Uncertain differential game   Cooperative behavior   Payoff distribution procedure   Subgame consistency condition   Resource extraction  

摘要： Uncertain differential game models conflicts and interests among players in the context of an uncertain dynamic system. However, cooperative behavior in uncertain differential game is an unexplored terrain. This paper proposes a spectrum of a cooperative uncertain differential game with transferrable payoffs. First, group rationality is achieved by maximizing the coalitional payoff through an uncertain optimal control method. Second, the concept of imputation is introduced as a solution, and a stability condition called subgame consistency condition for an imputation is proposed as well. Furthermore, the derivation of payoff distribution procedure for subgame consistent imputation is discussed. In addition, two optimal principles, i.e., Nash bargaining solution and Shapley value, are extended to this kind of model and are proved to be subgame consistent imputations, and their payoff distribution procedures are derived analytically. Finally, a two-person resource extraction game is studied for illustrating purpose.

关键词： muscarinic receptors   gastric cancer   pancreatic cancer   colorectal cancer   acetylcholine  

摘要： Cancers arising from gastrointestinal epithelial cells are common, aggressive, and difficult to treat. Progress in this area resulted from recognizing that the biological behavior of these cancers is highly dependent on bioactive molecules released by neurocrine, paracrine, and autocrine mechanisms within the tumor microenvironment. For many decades after its discovery as a neurotransmitter, acetylcholine was thought to be synthesized and released uniquely from neurons and considered the sole physiological ligand for muscarinic receptor subtypes, which were believed to have similar or redundant actions. In the intervening years, we learned this former dogma is not tenable. (1) Acetylcholine is not produced and released only by neurons. The cellular machinery required to synthesize and release acetylcholine is present in immune, cancer, and other cells, as well as in lower organisms (e.g., bacteria) that inhabit the gut. (2) Acetylcholine is not the sole physiological activator of muscarinic receptors. For example, selected bile acids can modulate muscarinic receptor function. (3) Muscarinic receptor subtypes anticipated to have overlapping functions based on similar G protein coupling and downstream signaling may have unexpectedly diverse actions. Here, we review the relevant research findings supporting these conclusions and discuss how the complexity of muscarinic receptor biology impacts health and disease, focusing on their role in the initiation and progression of gastric, pancreatic, and colon cancers.

关键词： Delays   Asymptotic stability   Time-varying systems   Delay systems   Numerical stability   Intellectual property   Trajectory   Delay-independent stability   positive systems   time-delay systems  

摘要： This article introduces novel results on linear coupled differential-difference systems with multiple time-varying delays. First, necessary and sufficient conditions for the positivity and delay-independent asymptotic stability of such systems are introduced. Then, exploiting the internally positive representation technique, we show how such stability results can be systematically exported to non-positive systems of the same class, yielding novel explicit sufficient conditions for their delay-independent stability. As a consequence, novel stability results on neutral-type systems, differential systems, and continuous-time difference systems with multiple delays are also obtained.