23 research outputs found

    Inverse eigenvalue problems of tridiagonal symmetric matrices and tridiagonal bisymmetric matrices

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    AbstractThe problem of generating a matrix A with specified eigenpairs, where A is a tridiagonal symmetric matrix, is presented. A general expression of such a matrix is provided, and the set of such matrices is denoted by SE. Moreover, the corresponding least-squares problem under spectral constraint is considered when the set SE is empty, and the corresponding solution set is denoted by SL. The best approximation problem associated with SE(SL) is discussed, that is: to find the nearest matrix AÌ‚ in SE(SL) to a given matrix. The existence and uniqueness of the best approximation are proved and the expression of this nearest matrix is provided. At the same time, we also discuss similar problems when A is a tridiagonal bisymmetric matrix

    Author index for volumes 101–200

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    Mathematical models of branching actin networks: Results and methods.

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    Branching actin networks are made up of polymerous actin filaments and play a principle role in cell motility and other cellular processes. Inside the lamellipoidum, the thin extension at the leading edge of a motile cell, there is a dense actin network composed of branched filaments. That network organizes into regular patterns near the membrane and serves as an engine moving the membrane forward. There are good models explaining how an individual actin filament is able to generate force against a load, but it is not well understood how filament networks collectively generate force. Multiple patterns have been observed in the force-velocity relationships of actin networks. The first part of this dissertation uses a agent-based stochastic to attempt to explain those patterns. We find that the rate of filament turnover can determine the nature of the force-velocity relationship. Electron micrographs of actin networks have shown surprisingly regular patterns in the angle of filaments to the membrane. Several continuum models have been proposed to explain this regularity. In the second part of this work, those models are mathematically studied. It has been hypothesized, with numerical evidence, that the equations select for some small number of optimal orientation patterns. The results in chapter 3 imply that both orientation models uniquely select for an optimal orientation pattern. Also, a fitness function for each orientation pattern is derived. A number of properties of actin filaments have been studied by using atomistic models of actin monomers and filaments. In order to calculate statistical properties of these models, the conformational space needs to be effectively sampled. Current computing capabilities are unable to do so directly, so some form of enhanced sampling algorithm is needed. However, there is no standard way to compare existing methods nor test new methods. The last part of this dissertation proposes a model that would allow for standardized testing of a large class of enhanced sampling methods

    International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

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    The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

    Automated Reasoning

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    This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

    A Review of Computational Stochastic Elastoplasticity

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    Heterogeneous materials at the micro-structural level are usually subjected to several uncertainties. These materials behave according to an elastoplastic model, but with uncertain parameters. The present review discusses recent developments in numerical approaches to these kinds of uncertainties, which are modelled as random elds like Young's modulus, yield stress etc. To give full description of random phenomena of elastoplastic materials one needs adequate mathematical framework. The probability theory and theory of random elds fully cover that need. Therefore, they are together with the theory of stochastic nite element approach a subject of this review. The whole group of di erent numerical stochastic methods for the elastoplastic problem has roots in the classical theory of these materials. Therefore, we give here the classical formulation of plasticity in very concise form as well as some of often used methods for solving this kind of problems. The main issues of stochastic elastoplasticity as well as stochastic problems in general are stochastic partial di erential equations. In order to solve them we must discretise them. Methods of solving and discretisation are called stochastic methods. These methods like Monte Carlo, Perturbation method, Neumann series method, stochastic Galerkin method as well as some other very known methods are reviewed and discussed here
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