18 research outputs found

    Sparse Bilinear Logistic Regression

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    In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces, style/content factorization, and parallel factor analysis. The underlying optimization problem is bi-convex; we study its solution and develop an efficient algorithm based on block coordinate descent. We provide a theoretical guarantee for global convergence and estimate the asymptotical convergence rate using the Kurdyka-{\L}ojasiewicz inequality. A range of experiments with simulated and real data demonstrate that sparse bilinear logistic regression outperforms current techniques in several important applications.Comment: 27 pages, 5 figure

    Nonlinear differential systems of the third and fourth order

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    On the approximation of the Dirichlet to Neumann map for high contrast two phase composites

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    Many problems in the natural world have high contrast properties, like transport in composites, fluid in porous media and so on. These problems have huge numerical difficulties because of the singularities of their solutions. It may be really expensive to solve these problems directly by traditional numerical methods. It is necessary and important to understand these problems more in mathematical aspect first, and then using the mathematical results to simplify the original problems or develop more efficient numerical methods. In this thesis we are going to approximate the Dirichlet to Neumann map for the high contrast two phase composites. The mathematical formulation of our problem is to approximate the energy for an elliptic equation with arbitrary boundary conditions. The boundary conditions may have highly oscillations, which makes our problems very interesting and difficult. We developed a method to divide the domain into two different subdomains, one is close to and the other one is far from the boundary, and we can approximate the energy in these two subdomains separately. In the subdomain far from the boundary, the energy is not influenced that much by the boundary conditions. Methods for approximation of the energy in this subdomain are studied before. In the subdomain near the boundary, the energy depends on the boundary conditions a lot. We used a new method to approximate the energy there such that it works for any kind of boundary conditions. By this way, we can have the approximation for the total energy of high contrast problems with any boundary conditions. In other words, we can have a matrix up to any dimension to approximate the continuous Dirichlet to Neumann map of the high contrast composites. Then we will use this matrix as a preconditioner in domain decomposition methods, such that our numerical methods are very efficient to solve the problems in high contrast composites

    Mathematical control theory and Finance

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    Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to find solutions to ”real life” problems, as is the case in robotics, control of industrial processes or finance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the financial analyst to possess a high level of mathematical skills. Conversely, the complex challenges posed by the problems and models relevant to finance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical finance. Up to now, other branches of control theory have found comparatively less application in financial problems. To some extent, deterministic and stochastic control theories developed as different branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these fields has intensified. Some concepts from stochastic calculus (e.g., rough paths) have drawn the attention of the deterministic control theory community. Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic control. We strongly believe in the possibility of a fruitful collaboration between specialists of deterministic and stochastic control theory and specialists in finance, both from academic and business backgrounds. It is this kind of collaboration that the organizers of the Workshop on Mathematical Control Theory and Finance wished to foster. This volume collects a set of original papers based on plenary lectures and selected contributed talks presented at the Workshop. They cover a wide range of current research topics on the mathematics of control systems and applications to finance. They should appeal to all those who are interested in research at the junction of these three important fields as well as those who seek special topics within this scope.info:eu-repo/semantics/publishedVersio

    Change-point detection, segmentation, and related topics

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    Recent contributions to change-point detection, segmentation and inference for non-regular models are presented. Various problems are considered including the multiple change-point estimation with adaptive penalty for time series with different dependency structures, estimation of the singularity point in cusp-type models, inference for thresholded autoregressive models, and cross-segmentation of matrices

    On Stationary Schrödinger-Poisson Equations

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    We regard the Schrödinger-Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three-dimensional domain and establish the method of steepest descent. The electrostatic potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrödinger operator, the Fermi level and the quantum mechanical electron density operator for square integrable electrostatic potentials. On bounded sets of potentials the Fermi level is continuous and boundeq, and the electron density operator is monotone and Lipschitz continuous. - As a tool we develop a Riesz-Dunford functional calculus for semibounded self-adjoint operators using paths of integration which enclose a real half axis

    Modelling and Inverse Problems of Control for Distributed Parameter Systems; Proceedings of IFIP(W.G. 7.2)-IIASA Conference, July 24-28, 1989

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    The techniques of solving inverse problems that arise in the estimation and control of distributed parameter systems in the face of uncertainty as well as the applications of these to mathematical modelling for problems of applied system analysis (environmental issues, technological processes, biomathematical models, mathematical economy and other fields) are among the major topics of research at the Dynamic Systems Project of the Systems and Decision Sciences (SDS) Program at IIASA. In July 1989 the SDS Program was a coorganizer of a regular IFIP (WG 7.2) conference on Modelling and Inverse Problems of Control for Distributed Parameter Systems that was held at IIASA, and was attended by a number of prominent theorists and practitioners. One of the main purpose of this meeting was to review recent developments and perspectives in this field. The proceedings are presented in this volume

    Analysis and Computation of Equilibria and Regions of Stability, With Applications in Chemistry, Climatology, Ecology, Economics

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    This record has been put together in a limited time for prompt distribution. It is not a proceedings volume. Rather it is a collection of all memoranda, diagrams, and literature references that were circulated before the workshop, used to support presentations during the workshop, or written down to preserve some ideas and some outcomes of computations that arose from the workshop. The only organizing principle is the temporal sequence in which the materials were presented or prepared
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