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In the first part of this two-paper series, a new Fragile Points Method (FPM), in both primal and mixed formulations, is presented for analyzing flexoelectric effects in 2D dielectric materials. In the present paper, a number of numerical results are provided as validations, including linear and quadratic patch tests, flexoelectric effects in continuous domains, and analyses of stationary cracks in dielectric materials. A discussion of the influence of the electroelastic stress is also given, showing that Maxwell stress could be significant and thus the full flexoelectric theory is recommended to be employed for nano-scale structures. The present primal as well as mixed FPMs also show their suitability and effectiveness in simulating crack initiation and propagation with flexoelectric effect. Flexoelectricity, coupled with piezoelectric effect, can help, hinder, or deflect the crack propagation paths and should not be neglected in nano-scale crack analysis. In FPM, no remeshing or trial function enhancement are required in modeling crack propagation. A new Bonding-Energy-Rate(BER)-based crack criterion as well as classic stress-based criterion are used for crack development simulations. Other complex problems such as dynamic crack developments, fracture, fragmentation and 3D flexoelectric analyses will be given in our future studies.

Flexoelectricity refers to a phenomenon which involves a coupling of the mechanical strain gradient and electric polarization. In this study, a meshless Fragile Points Method (FPM), is presented for analyzing flexoelectric effects in dielectric solids. Local, simple, polynomial and discontinuous trial and test functions are generated with the help of a local meshless Differential Quadrature approximation of derivatives. Both primal and mixed FPM are developed, based on two alternate flexoelectric theories, with or without the electric gradient effect and Maxwell stress. In the present primal as well as mixed FPM, only the displacements and electric potential are retained as explicit unknown variables at each internal Fragile Point in the final algebraic equations. Thus the number of unknowns in the final system of algebraic equations is kept to be absolutely minimal. An algorithm for simulating crack initiation and propagation using the present FPM is presented, with classic stress-based criterion as well as a Bonding-Energy-Rate(BER)-based criterion for crack development. The present primal and mixed FPM approaches represent clear advantages as compared to the current methods for computational flexoelectric analyses, using primal as well as mixed Finite Element Methods, Element Free Galerkin (EFG) Methods, Meshless Local Petrov Galerkin (MLPG) Methods, and Isogeometric Analysis (IGA) Methods, because of the following new features: they are simpler Galerkin meshless methods using polynomial trial and test functions; minimal DoFs per Point make it very user-friendly; arbitrary polygonal subdomains make it flexible for modeling complex geometries; the numerical integration of the primal as well as mixed FPM weak forms is trivially simple; and FPM can be easily employed in crack development simulations without remeshing or trial function enhancement.

We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to approximate the Nash policy during the Q-function updates. We prove that under certain conditions, by updating the regularized Q-function, the algorithm converges to a Nash equilibrium. We also demonstrate the proposed algorithm's ability to transfer previous training experiences, enabling the agents to adapt quickly to new environments. We provide a dynamic hyper-parameter scheduling scheme to further expedite convergence. Empirical results applied to a number of stochastic games verify that the proposed algorithm converges to the Nash equilibrium, while exhibiting a major speed-up over existing algorithms., Comment: Accepted at IJCAI-21

Network pruning can reduce the high computation cost of deep neural network (DNN) models. However, to maintain their accuracies, sparse models often carry randomly-distributed weights, leading to irregular computations. Consequently, sparse models cannot achieve meaningful speedup on commodity hardware (e.g., GPU) built for dense matrix computations. As such, prior works usually modify or design completely new sparsity-optimized architectures for exploiting sparsity. We propose an algorithm-software co-designed pruning method that achieves latency speedups on existing dense architectures. Our work builds upon the insight that the matrix multiplication generally breaks the large matrix into multiple smaller tiles for parallel execution. We propose a tiling-friendly "tile-wise" sparsity pattern, which maintains a regular pattern at the tile level for efficient execution but allows for irregular, arbitrary pruning at the global scale to maintain the high accuracy. We implement and evaluate the sparsity pattern on GPU tensor core, achieving a 1.95x speedup over the dense model., Comment: 12pages, ACM/IEEE Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC20)

A meshless Fragile Points Method (FPM) is presented for analyzing 2D flexoelectric problems. Local, simple, polynomial and discontinuous trial and test functions are generated with the help of a local meshless differential quadrature approximation of the first three derivatives. Interior Penalty Numerical Fluxes are employed to ensure the consistency of the method. Based on a Galerkin weak-form formulation, the present FPM leads to symmetric and sparse matrices, and avoids the difficulties of numerical integration in the previous meshfree methods. Numerical examples including isotropic and anisotropic materials with flexoelectric and piezoelectric effects are provided as validations. The present method is much simpler than the Finite Element Method, or the Element-Free Galerkin (EFG) and Meshless Local Petrov-Galerkin (MLPG) methods, and the numerical integration of the weak form is trivially simple.

We present a framework that incorporates the idea of bounded rationality into dynamic stochastic pursuit-evasion games. The solution of a stochastic game is characterized, in general, by its (Nash) equilibria in feedback form. However, computing these Nash equilibrium strategies may require extensive computational resources. In this paper, the agents are modeled as bounded rational entities having limited computational resources. We illustrate the framework by applying it to a pursuit-evasion game between two vehicles in a stochastic wind field, where both the pursuer and the evader are bounded rational. We show how such a game may be analyzed by properly casting it as an iterative sequence of finite-state Markov Decision Processes (MDPs). Leveraging tools and algorithms from cognitive hierarchy theory ("level-$k$ thinking") we compute the solution of the ensuing discrete game, while taking into consideration the rationality level of each agent. We also present an online algorithm for each agent to infer its opponent rationality level., Comment: 16 pages, 5 figures, submitted to Journal of Guidance, Control, and Dynamics

A new and effective computational approach is presented for analyzing transient heat conduction problems. The approach consists of a meshless Fragile Points Method (FPM) being utilized for spatial discretization, and a Local Variational Iteration (LVI) scheme for time discretization. Anisotropy and nonhomogeneity do not give rise to any difficulties in the present implementation. The meshless FPM is based on a Galerkin weak-form formulation and thus leads to symmetric matrices. Local, very simple, polynomial and discontinuous trial and test functions are employed. In the meshless FPM, Interior Penalty Numerical Fluxes are introduced to ensure the consistency of the method. The LVIM in the time domain is generated as a combination of the Variational Iteration Method (VIM) applied over a large time interval and numerical algorithms. A set of collocation nodes are employed in each finitely large time interval. The FPM + LVIM approach is capable of solving transient heat transfer problems in complex geometries with mixed boundary conditions, including pre-existing cracks. Numerical examples are presented in 2D and 3D domains. Both functionally graded materials and composite materials are considered. It is shown that, with suitable computational parameters, the FPM + LVIM approach is not only accurate, but also efficient, and has reliable stability under relatively large time intervals. The present methodology represents a considerable improvement to the current state of science in computational transient heat conduction in anisotropic nonhomogeneous media.

In a Shared Mobility on Demand Service (SMoDS), dynamic pricing plays an important role in the form of an incentive for the decision of the empowered passenger on the ride offer. Strategies for determining the dynamic tariff should be suitably designed so that the incurred demand and supply are balanced and therefore economic efficiency is achieved. In this manuscript, we formulate a discrete time Markov Decision Process (MDP) to determine the probability desired by the SMoDS platform corresponding to the acceptance rate of each empowered passenger at each state of the system. We use Estimated Waiting Time (EWT) as the metric for the balance between demand and supply, with the goal that EWT be regulated around a target value. We then develop a Dynamic Programming (DP) algorithm to derive the optimal policy of the MDP that regulates EWT around the target value. Computational experiments are conducted that demonstrate the regulation of EWT is effective, through various scenarios. The overall demonstration is carried out offline. The MDP formulation together with the DP algorithm can be utilized to an online determination of the dynamic tariff by integrating with our earlier works on Cumulative Prospect Theory based passenger behavioral modeling and the AltMin dynamic routing algorithm, and form the subject of future works., Comment: 17 pages, 6 figures, and has been accepted for publication at the 23rd IEEE International Conference on Intelligent Transportation Systems, 2020

Large geometry (e.g., orientation) variances are the key challenges in the scene text detection. In this work, we first conduct experiments to investigate the capacity of networks for learning geometry variances on detecting scene texts, and find that networks can handle only limited text geometry variances. Then, we put forward a novel Geometry Normalization Module (GNM) with multiple branches, each of which is composed of one Scale Normalization Unit and one Orientation Normalization Unit, to normalize each text instance to one desired canonical geometry range through at least one branch. The GNM is general and readily plugged into existing convolutional neural network based text detectors to construct end-to-end Geometry Normalization Networks (GNNets). Moreover, we propose a geometry-aware training scheme to effectively train the GNNets by sampling and augmenting text instances from a uniform geometry variance distribution. Finally, experiments on popular benchmarks of ICDAR 2015 and ICDAR 2017 MLT validate that our method outperforms all the state-of-the-art approaches remarkably by obtaining one-forward test F-scores of 88.52 and 74.54 respectively., Comment: ICCV 2019

We prove several structural properties of Steiner triple systems (STS) of order 3w+3 that include one or more transversal subdesigns TD(3,w). Using an exhaustive search, we find that there are 2004720 isomorphism classes of STS(21) including a subdesign TD(3,6), or, equivalently, a 6-by-6 latin square.

Cumulative Prospect Theory (CPT) is a modeling tool widely used in behavioral economics and cognitive psychology that captures subjective decision making of individuals under risk or uncertainty. In this paper, we propose a dynamic pricing strategy for Shared Mobility on Demand Services (SMoDSs) using a passenger behavioral model based on CPT. This dynamic pricing strategy together with dynamic routing via a constrained optimization algorithm that we have developed earlier, provide a complete solution customized for SMoDS of multi-passenger transportation. The basic principles of CPT and the derivation of the passenger behavioral model in the SMoDS context are described in detail. The implications of CPT on dynamic pricing of the SMoDS are delineated using computational experiments involving passenger preferences. These implications include interpretation of the classic fourfold pattern of risk attitudes, strong risk aversion over mixed prospects, and behavioral preferences of self reference. Overall, it is argued that the use of the CPT framework corresponds to a crucial building block in designing socio-technical systems by allowing quantification of subjective decision making under risk or uncertainty that is perceived to be otherwise qualitative., Comment: 17 pages, 6 figures, and has been accepted for publication at the 58th Annual Conference on Decision and Control, 2019

Travel time in urban centers is a significant contributor to the quality of living of its citizens. Mobility on Demand (MoD) services such as Uber and Lyft have revolutionized the transportation infrastructure, enabling new solutions for passengers. Shared MoD services have shown that a continuum of solutions can be provided between the traditional private transport for an individual and the public mass transit based transport, by making use of the underlying cyber-physical substrate that provides advanced, distributed, and networked computational and communicational support. In this paper, we propose a novel shared mobility service using a dynamic framework. This framework generates a dynamic route for multi-passenger transport, optimized to reduce time costs for both the shuttle and the passengers and is designed using a new concept of a space window. This concept introduces a degree of freedom that helps reduce the cost of the system involved in designing the optimal route. A specific algorithm based on the Alternating Minimization approach is proposed. Its analytical properties are characterized. Detailed computational experiments are carried out to demonstrate the advantages of the proposed approach and are shown to result in an order of magnitude improvement in the computational efficiency with minimal optimality gap when compared to a standard Mixed Integer Quadratically Constrained Programming based algorithm., Comment: 27 pages, 7 figures, has been accepted by ACM Transactions on Cyber-Physical Systems (TCPS), Special Issue on Transportation Cyber-Physical Systems