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51st Israel Annual Conference on Aerospace Sciences 2011

作者： Sigalov, Daniel Oshman, Yaakov Technion - Israel Institute of Technology Haifa 32000 Israel Interdepartmental Program for Applied Mathematics Israel Department of Aerospace Engineering Israel

ISBN: (纸本)9781617824012

We revisit the problem of tracking the state of a hybrid system capable of performing a bounded number of mode switches. In a previous paper we have addressed a version of the problem where we have assumed the existence of a deterministic, known hard bound on the number of mode transitions. In addition, it was assumed that the system can possess only two modes, e.g., the maneuvering and non-maneuvering regimes of a tracked target. In the present paper we relax both assumptions: we assume a soft, stochastic bound on the number of mode transitions, and altogether remove the restriction on the number of modes of the system (thus, e.g., the target can have multiple different maneuvering modes, in addition to the non-maneuvering one). While admitting an unlimited number of mode transitions, the soft bound renders that number finite with probability 1. In addition, similarly to the case where the number of transition was deterministically hard-bounded, the existence of the bound renders the mode switching mechanism non-Markov. Thus, the two formulations address similar, though not identical, problems, that cannot be solved by direct application of algorithms devised for hybrid systems having Markov mode switching mechanisms. The novel solution approach adopted herein is based on transforming the non-Markovian mode switching mechanism to an equivalent Markovian one, at the price of augmenting the mode definition, and increasing the dimension of the state space involved. A standard interacting multiple model (IMM) filter is then applied to the transformed (Markovian) problem in a straightforward manner. The performance of the new method is demonstrated via a simulation study comprising three examples, in which the new method is compared with 1) the filter for hard-bounded mode transitions, and 2) a standard IMM filter directly applied to the original problem. The study shows that even when working outside its operating envelope (e.g., when the number of mode switches is har

关键词： Hybrid systems

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Extension of the Greenspan model to asymmetric tumour growth

Extension of the Greenspan model to asymmetric tumour growth

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10th IEEE International Workshop on Biomedical engineering, BioEng 2011

作者： Dassios, George Kariotou, Fotini Division of Applied Mathematics Department of Chemical Engineering University of Patras 26504 Patras Greece Hellenic Open University 26222 Patras Greece

ISBN: (纸本)9781457705526

The Greenspan model is one of the most well defined mathematical approaches to the problem of tumour growth. It is built on principles of Fluid Mechanics and it has been applied to the growth of a spherical tumour. The present report attempts a generalization of the Greenspan model to the evolution of a tumour that has different growth characteristics in different spacial directions. Evidently, this behavior refers to the ellipsoidal geometry which models the anisotropic structure of the Euclidean space. It is of interest to realize that the ellipsoidal model of growth needs some non-trivial physical and mathematical adaptations of the corresponding spherical model, in order to end up with a reasonable and solvable algorithm that describes the evolution of the different tumour phases. © 2011 IEEE.

关键词： Tumors

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Estimated Radiation Dose Reduction Using Non-Linear Diffusion Method in Computed Radiography *

Estimated Radiation Dose Reduction Using Non-Linear Diffusio...

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Annual International Conference of the IEEE engineering in Medicine and Biology Society

作者： Ma. Guadalupe Sánchez Belén Juste Vicente Vidal Gumersindo Verdú Patricia Mayo Francisco Rodenas with the Departament Computing ITCG Cd. Guzmán Jal. Mexico with the Department of Informatics Systems and Computing Universitat Politècnica de València Valencia Spain with the Department of Chemical and Nuclear Engineering Universitat Politècnica de València Valencia Spain with the TITANIA Technology Services Grupo Dominguis Valencia Spain with the Departament of Applied Mathematics Universitat Politècnica de València Valencia Spain

ISBN: (纸本)9781424441198

In this paper we use a non-linear diffusion method to filter the inherent noise in a Computed Radiography (CR) for reducing the dose absorbed by the patients especially children in pediatric applications, related with the exposure mAs. The method is implemented in order to create a lower CR dose based on the selection of lower X-ray exposure and with a reduction of the noise using a non-linear diffusion method. The impact of several milliAmpere-seconds (mAs) setting on image quality has been studied using the RANDO phantom. The obtained results show good agreements between the filtered images and real images in terms of noise variance measurements. The new CR images allow medical researchers to analyze how a low dose affects the patient diagnosis.

关键词： Estimated Radiation Reduction

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Manifold learning techniques and model reduction for dissipative dynamics

Manifold learning techniques and model reduction for dissipa...

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Computing and Systems Technology Division - Core programming Topic at the 2011 AIChE Annual Meeting

作者： Sonday, Benjamin Rajendran, Karthikeyan Gear, William Singer, Amit Kevrekidis, Ioannis G. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Chemical and Biological Engineering Princeton University PrincetonNJ United States Mathematics and PACM Princeton University PrincetonNJ United States

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Sequential Lateral Solidification of Ultra-Thin a-Si Films

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MRS Online Proceedings Library 2011年第1期621卷 991-996页

作者： Hans S. Cho Dongbyum Kim Alexander B. Limanov Mark A. Crowder James S. Im Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics School of Engineering and Applied Science Columbia University New York USA

This paper demonstrates that Sequential Lateral Solidification (SLS) of Si can be carried out on films as thin as–and potentially much thinner than–250 Å. When compared to thicker Si films, however, the SLS-processed ultra-thin films contain more twins, and successful processing requires irradiation within a narrower laser energy density range and a smaller per-pulse translation distance. The physical interpretation of these findings is formulated by analyzing the details of the microstructures observed in single-pulse-irradiation-induced Controlled Super-Lateral Growth (C-SLG) experiments. SEM and TEM analyses reveal complicated microstructural details that we interpret as originating from breakdown of epitaxial growth during lateral solidification, an effect that is detrimental to the SLS process. Based on considerations of far-from- equilibrium solidification behavior of Si, it is argued that undercooling of the solidification interface below a threshold value at which solidification no longer proceeds epitaxially–arising from reduction in interfacial recalescence during lateral solidification of ultra-thin Si films, relative to that of thicker films–is responsible for the breakdown. Based on this model, we discuss how external parameters may be adjusted so as to permit optimal crystallization of ultra-thin Si films using SLS.

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Linear Optimal State Estimation in Systems with Independent Mode Transitions

Linear Optimal State Estimation in Systems with Independent ...

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IEEE Conference on Decision and Control

作者： Daniel Sigalov Tomer Michaeli Yaakov Oshman Interdepartmental Program for Applied Mathematics Department of Electrical Engineering Department of Aerospace Engineering

ISBN: (纸本)9781612848006

A generalized state space representation of a dynamical system with random modes is presented. The dynamics equation includes the effect of the state's linear minimum mean squared error (LMMSE) optimal estimate, representing the behavior of a closed loop control system featuring a state estimator. The measurement equation is allowed to depend on past LMMSE estimate of the state, which can be used to represent the fact that measurements are obtained from a validation window centered at the predicted measurement position and not from the entire surveillance region. The matrices comprising the system's mode constitute an independent stochastic process. It is shown that the proposed formulation generalizes several important problems considered in the past, and allows a unified modeling of new ones. The LMMSE optimal filter is derived for the considered general problem and is shown to reduce, in some special cases, to some well known classical algorithms. The new concept, as well as the derived algorithm, are demonstrated for the problem of target tracking in clutter, and are shown to attain performance that is competitive to that of several popular nonlinear methods.

关键词： State estimation State-space Representation Closed loop control systems Target tracking clutter Mean square error DYNAMICAL SYSTEMS random fashion UNIFIED MODEL

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Efficient tracking for hybrid systems with a bounded number of mode switches

Efficient tracking for hybrid systems with a bounded number ...

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50th Israel Annual Conference on Aerospace Sciences 2010

作者： Sigalov, Daniel Oshman, Yaakov Interdepartmental Program for Applied Mathematics Technion - Israel Institute of Technology Haifa 32000 Israel Department of Aerospace Engineering Technion - Israel Institute of Technology Haifa 32000 Israel

ISBN: (纸本)9781617380839

We consider the problem of tracking the state of a hybrid system capable of performing a bounded number of mode switches. The system is assumed to either follow a nominal model standing for, e.g., the non-maneuvering motion regime of a target, or the fault-free operation mode of a sensor, or obey an anomalous model representing, e.g., the abrupt evasive maneuvers of a target or the faulty operation of a sensor. The optimal tracking algorithm requires the implementation of a polynomially growing number of primitive Kalman filters. On the other hand, the system's switching dynamics is not Markov because of the a priori limited number of model switches, thus ruling out the use of popular estimation schemes such as the IMM and GPB algorithms. We derive an efficient estimation scheme that uses a number of primitive Kalman filters that is linear in the number of possible maneuvers. The scheme resembles the IMM algorithm in that it uses interaction between some of the primitive filters before every estimation cycle, thus reducing the number of such filters. The algorithm is fully derived, tested in simulation, and shown to outperform the state-of-the-art IMM filter in a typical example.

关键词： Kalman filters

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Linear optimal estimation problems in systems with actuator faults

Linear optimal estimation problems in systems with actuator ...

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作者： Sigalov, Daniel Oshman, Yaakov Technion - Israel Institute of Technology Program for Applied Mathematics Haifa 32000 Israel Technion - Israel Institute of Technology Department of Aerospace Engineering Haifa 32000 Israel

ISBN: (纸本)9781457702679

We consider estimating the state of a dynamic system subject to actuator faults. The discretely-valued fault mechanism renders the system hybrid, and results in anomalous changes in the dynamics equation that may be interpreted as random accelerations. Two closely related problem formulations are considered. In the first formulation multiple models are used to describe the system's behavior: one model stands for the nominal, fault-free actuator condition, all other models correspond to various actuator fault conditions, and the system can freely assume any model at any time. In the second formulation the abnormal mode is described by a single dynamical model, and the system can switch between the nominal and anomalous conditions a bounded number of times, with the bound assumed known. In both formulations, the minimum mean squared error (MMSE) optimal state estimator requires a polynomially growing number of primitive Kalman filters, and is, thus, computationally infeasible. We derive sequential, linear MMSE-optimal state estimation algorithms for both problem formulations. Depending only on the first two moments of the random quantities of the problem, linear optimal filters are robust with respect to the actual driving noise distributions, in the sense that they achieve the smallest worst-case estimation error of all other (nonlinear) filters. Although derived assuming seemingly different problem formulations, both filters share essentially the same structure, thus exposing a certain duality between the underlying problems. The performance of both estimators is demonstrated in a simulation study, where they are compared to the interacting multiple model filter. © 2011 IEEE.

关键词： Hybrid systems

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Tracking maneuvering targets with a soft bound on the number of maneuvers

Tracking maneuvering targets with a soft bound on the number...

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ISBN: (纸本)9781457702679

We revisit the problem of tracking the state of a hybrid system capable of performing a bounded number of mode switches. In a previous paper we have addressed a version of the problem where we have assumed the existence of a deterministic, known hard bound on the number of mode transitions. In addition, it was assumed that the system can possess only two modes, e.g., the maneuvering and non-maneuvering regimes of a tracked target. In the present paper we relax both assumptions: we assume a soft, stochastic bound on the number of mode transitions, and altogether remove the restriction on the number of modes of the system (thus, e.g., the target can have multiple different maneuvering modes, in addition to the non-maneuvering one). Similarly to the case where the number of transition was deterministically hard-bounded, the existence of the bound renders the mode switching mechanism non-Markov. Thus, the two formulations address similar, though not identical, problems, that cannot be solved by direct application of standard algorithms for hybrid systems. The novel solution approach is based on transforming the non-Markovian mode switching mechanism to an equivalent Markovian one, at the price of augmenting the mode definition. A standard interacting multiple model (IMM) filter is then applied to the transformed problem in a straightforward manner. The performance of the new method is demonstrated via a simulation study comprising three examples, in which the new method is compared with 1) the filter for hard-bounded mode transitions, and 2) a standard IMM filter directly applied to the original problem. The study shows that even when working outside its operating envelope, the new filter closely approximates the best filter for the scenario. © 2011 IEEE.

关键词： Hybrid systems

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Coarse graining the dynamics of heterogeneous oscillators in networks with spectral gaps

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Physical Review E 2011年第3期84卷 036708-036708页

作者： Karthikeyan Rajendran Ioannis G. Kevrekidis Department of Chemical and Biological Engineering Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

We present a computer-assisted approach to coarse graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph Laplacian suggests that the graph dynamics may quickly become low dimensional. Our first choice of coarse variables consists of the components of the oscillator states—their (complex) phase angles—along the leading eigenvectors of this Laplacian. We then use the equation-free framework, circumventing the derivation of explicit coarse-grained equations, to perform computational tasks such as coarse projective integration, coarse fixed-point, and coarse limit-cycle computations. In a second step, we explore an approach to incorporating oscillator heterogeneity in the coarse-graining process. The approach is based on the observation of fast-developing correlations between oscillator state and oscillator intrinsic properties and establishes a connection with tools developed in the context of uncertainty quantification.

关键词： GRAINING COMPUTER-aided design LAPLACIAN operator EIGENVECTORS HARMONIC oscillators

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