5,555 research outputs found

    Graduate Catalog of Studies, 2023-2024

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    UMSL Bulletin 2023-2024

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    The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp

    Graduate Catalog of Studies, 2023-2024

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    UMSL Bulletin 2022-2023

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    The 2022-2023 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1087/thumbnail.jp

    A Quasi-Newton Subspace Trust Region Algorithm for Least-square Problems in Min-max Optimization

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    The first-order optimality conditions of convexly constrained nonconvex-nonconcave min-max optimization problems formulate variational inequality problems, which are equivalent to a system of nonsmooth equations. In this paper, we propose a quasi-Newton subspace trust region (QNSTR) algorithm for the least-square problem defined by the smoothing approximation of the nonsmooth equation. Based on the structure of the least-square problem, we use an adaptive quasi-Newton formula to approximate the Hessian matrix and solve a low-dimensional strongly convex quadratic program with ellipse constraints in a subspace at each step of QNSTR algorithm. According to the structure of the adaptive quasi-Newton formula and the subspace technique, the strongly convex quadratic program at each step can be solved efficiently. We prove the global convergence of QNSTR algorithm to an ϵ\epsilon-first-order stationary point of the min-max optimization problem. Moreover, we present numerical results of QNSTR algorithm with different subspaces for the mixed generative adversarial networks in eye image segmentation using real data to show the efficiency and effectiveness of QNSTR algorithm for solving large scale min-max optimization problems

    Effects of municipal smoke-free ordinances on secondhand smoke exposure in the Republic of Korea

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    ObjectiveTo reduce premature deaths due to secondhand smoke (SHS) exposure among non-smokers, the Republic of Korea (ROK) adopted changes to the National Health Promotion Act, which allowed local governments to enact municipal ordinances to strengthen their authority to designate smoke-free areas and levy penalty fines. In this study, we examined national trends in SHS exposure after the introduction of these municipal ordinances at the city level in 2010.MethodsWe used interrupted time series analysis to assess whether the trends of SHS exposure in the workplace and at home, and the primary cigarette smoking rate changed following the policy adjustment in the national legislation in ROK. Population-standardized data for selected variables were retrieved from a nationally representative survey dataset and used to study the policy action’s effectiveness.ResultsFollowing the change in the legislation, SHS exposure in the workplace reversed course from an increasing (18% per year) trend prior to the introduction of these smoke-free ordinances to a decreasing (−10% per year) trend after adoption and enforcement of these laws (β2 = 0.18, p-value = 0.07; β3 = −0.10, p-value = 0.02). SHS exposure at home (β2 = 0.10, p-value = 0.09; β3 = −0.03, p-value = 0.14) and the primary cigarette smoking rate (β2 = 0.03, p-value = 0.10; β3 = 0.008, p-value = 0.15) showed no significant changes in the sampled period. Although analyses stratified by sex showed that the allowance of municipal ordinances resulted in reduced SHS exposure in the workplace for both males and females, they did not affect the primary cigarette smoking rate as much, especially among females.ConclusionStrengthening the role of local governments by giving them the authority to enact and enforce penalties on SHS exposure violation helped ROK to reduce SHS exposure in the workplace. However, smoking behaviors and related activities seemed to shift to less restrictive areas such as on the streets and in apartment hallways, negating some of the effects due to these ordinances. Future studies should investigate how smoke-free policies beyond public places can further reduce the SHS exposure in ROK

    Implicit Loss of Surjectivity and Facial Reduction: Theory and Applications

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    Facial reduction, pioneered by Borwein and Wolkowicz, is a preprocessing method that is commonly used to obtain strict feasibility in the reformulated, reduced constraint system. The importance of strict feasibility is often addressed in the context of the convergence results for interior point methods. Beyond the theoretical properties that the facial reduction conveys, we show that facial reduction, not only limited to interior point methods, leads to strong numerical performances in different classes of algorithms. In this thesis we study various consequences and the broad applicability of facial reduction. The thesis is organized in two parts. In the first part, we show the instabilities accompanied by the absence of strict feasibility through the lens of facially reduced systems. In particular, we exploit the implicit redundancies, revealed by each nontrivial facial reduction step, resulting in the implicit loss of surjectivity. This leads to the two-step facial reduction and two novel related notions of singularity. For the area of semidefinite programming, we use these singularities to strengthen a known bound on the solution rank, the Barvinok-Pataki bound. For the area of linear programming, we reveal degeneracies caused by the implicit redundancies. Furthermore, we propose a preprocessing tool that uses the simplex method. In the second part of this thesis, we continue with the semidefinite programs that do not have strictly feasible points. We focus on the doubly-nonnegative relaxation of the binary quadratic program and a semidefinite program with a nonlinear objective function. We closely work with two classes of algorithms, the splitting method and the Gauss-Newton interior point method. We elaborate on the advantages in building models from facial reduction. Moreover, we develop algorithms for real-world problems including the quadratic assignment problem, the protein side-chain positioning problem, and the key rate computation for quantum key distribution. Facial reduction continues to play an important role for providing robust reformulated models in both the theoretical and the practical aspects, resulting in successful numerical performances

    Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems

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    We consider a general class of nonsmooth optimal control problems with partial differential equation (PDE) constraints, which are very challenging due to its nonsmooth objective functionals and the resulting high-dimensional and ill-conditioned systems after discretization. We focus on the application of a primal-dual method, with which different types of variables can be treated individually and thus its main computation at each iteration only requires solving two PDEs. Our target is to accelerate the primal-dual method with either larger step sizes or operator learning techniques. For the accelerated primal-dual method with larger step sizes, its convergence can be still proved rigorously while it numerically accelerates the original primal-dual method in a simple and universal way. For the operator learning acceleration, we construct deep neural network surrogate models for the involved PDEs. Once a neural operator is learned, solving a PDE requires only a forward pass of the neural network, and the computational cost is thus substantially reduced. The accelerated primal-dual method with operator learning is mesh-free, numerically efficient, and scalable to different types of PDEs. The acceleration effectiveness of these two techniques is promisingly validated by some preliminary numerical results

    Mathematical Problems in Rock Mechanics and Rock Engineering

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    With increasing requirements for energy, resources and space, rock engineering projects are being constructed more often and are operated in large-scale environments with complex geology. Meanwhile, rock failures and rock instabilities occur more frequently, and severely threaten the safety and stability of rock engineering projects. It is well-recognized that rock has multi-scale structures and involves multi-scale fracture processes. Meanwhile, rocks are commonly subjected simultaneously to complex static stress and strong dynamic disturbance, providing a hotbed for the occurrence of rock failures. In addition, there are many multi-physics coupling processes in a rock mass. It is still difficult to understand these rock mechanics and characterize rock behavior during complex stress conditions, multi-physics processes, and multi-scale changes. Therefore, our understanding of rock mechanics and the prevention and control of failure and instability in rock engineering needs to be furthered. The primary aim of this Special Issue “Mathematical Problems in Rock Mechanics and Rock Engineering” is to bring together original research discussing innovative efforts regarding in situ observations, laboratory experiments and theoretical, numerical, and big-data-based methods to overcome the mathematical problems related to rock mechanics and rock engineering. It includes 12 manuscripts that illustrate the valuable efforts for addressing mathematical problems in rock mechanics and rock engineering
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