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Novel numerical inversions of two circular-arc radon transforms in Compton scattering tomography

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 2012年第6期20卷 809-839页

作者： Rigaud, Gael Nguyen, Mai K. Louis, Alfred K. ETIS ENSEA Univ Cergy Pontoise CNRS F-95000 Cergy Pontoise France Univ Saarland Fachbereich Math D-66041 Saarbrucken Germany

Compton scattering tomography (CST) is an alternative imaging process which reconstructs, in a two-dimensional slice, the electron density of an object by collecting radiation emitted from an external source and scattered throughout this object. The collected data at specific scattering energies appears essentially as the integral of the electron density on definite families of arcs of circles. Reconstruction of the unknown electron density is achieved by the inversion of the corresponding circular-arcs Radon transforms (CART). We review two existing CST modalities, their corresponding CART and establish their numerical inversion algorithms in the formalism of the so-called circular harmonic decomposition (CHD) for a function. The quality of the reconstructed images is illustrated by numerical simulations on test phantoms. Comparison with standard tomography performances demonstrates the efficiency and interest of this inversion method via CHD in imaging science such as biomedical imaging and non-destructive industrial testing.

关键词： compton scattering tomography inverse problems numerical algorithm biomedical imaging non-destructive testing

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numerical algorithmS FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH 1-D BROWNIAN MOTION: CONVERGENCE AND SIMULATIONS

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ESAIM-MATHEMATICAL MODELLING AND numerical ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 2011年第2期45卷 335-360页

作者： Peng, Shige Xu, Mingyu Shandong Univ Sch Math & Syst Sci Jinan 250100 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Key Lab Random Complex Struct & Data Sci Beijing Peoples R China Fudan Univ Sch Math Sci Dept Financial Math & Control Sci Shanghai 200433 Peoples R China

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.

关键词： Backward stochastic differential equations reflected stochastic differential equations with one barrier numerical algorithm numerical simulation

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A numerical solution to nonlinear second order three-point boundary value problems in the reproducing kernel space

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APPLIED MATHEMATICS AND COMPUTATION 2012年第14期218卷 7362-7368页

作者： Lin, Yingzhen Niu, Jing Cui, Minggen Harbin Inst Technol Dept Math Weihai 264209 Shandong Peoples R China Harbin Normal Univ Sch Math & Sci Harbin 150025 Heilongjiang Peoples R China

In this paper, a new numerical algorithm is provided to solve nonlinear three-point boundary value problems in a very favorable reproducing kernel space which satisfies all boundary conditions. Its reproducing kernel function is discussed in detail. We also prove that the approximate solution and its first and second order derivatives all converge uniformly. The numerical experiments show that the algorithm is quite accurate and efficient for solving nonlinear second order three-point boundary value problems. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Nonlinear problems Three-point boundary value conditions numerical algorithm Reproducing kernel function

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numerical reconstruction of one-photon mixed states by means of the degree of linear polarisation

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JOURNAL OF MODERN OPTICS 2012年第19期59卷 1700-1704页

作者： Michalik, Lukasz Domanski, Andrzej W. Warsaw Univ Technol Fac Phys PL-00662 Warsaw Poland

In this paper the authors present the idea for reconstructing one-photon states. Reconstructing a quantum state means measuring the probability distribution P that allows one to write the density operator for the analysed state. The most commonly known approach for the quantum reconstruction is the quantum tomography. Our alternative method assumes that the analysed field is coupled with the reference field which is described by the parameters settled during a measurement. In the proposed gedankenexperiment the degree of linear polarisation (DOLP) of this combined beam is measured using a rotating linear polariser. We state that it is possible to obtain the P-function by changing the parameters of reference beams and by preparing the series of DOLP measurements. This series of data leads to the system of equations. The values of the P-function at chosen points are the unknowns of this system. This article focuses on the numerical algorithm for solving these equations.

关键词： photons degree of linear polarisation quantum state reconstruction numerical algorithm

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SIMULTANEOUS POLYNOMIAL APPROXIMATION AND TOTAL VARIATION DENOISING

SIMULTANEOUS POLYNOMIAL APPROXIMATION AND TOTAL VARIATION DE...

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Ivan W. Selesnick Polytechnic Institute of New York University Brooklyn NY 11201 USA

ISBN: (纸本)9781479903573

This paper addresses the problem of smoothing data with additive step discontinuities. The problem formulation is based on least square polynomial approximation and total variation denoising. In earlier work, an ADMM algorithm was proposed to minimize a suitably defined sparsity-promoting cost function. In this paper, an algorithm is derived using the majorization-minimization optimization procedure. The new algorithm converges faster and, unlike the ADMM algorithm, has no parameters that need to be set. The proposed algorithm is formulated so as to utilize fast solvers for banded systems for high computational efficiency. This paper also gives optimality conditions so that the optimality of a result produced by the numerical algorithm can be readily validated.

关键词： ADMM optimality of a result produced numerical algorithm Polynomial optimality approximation Problem Formulation Concurrency algorithms Cost functions Polynomial approximation

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Reaction Control System using Hybrid Micro-Thrusters for Guided Sounding Rocket

Reaction Control System using Hybrid Micro-Thrusters for Gui...

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International Conference on Recent Advances in Space Technologies

作者： Teodor Viorel Chelaru Adrian Chelaru University POLITEHNICA of Bucharest - Research Center for Aeronautics and Space Ghe. Polizu 1 Bucharest Romania INCAS -National Institute for Aerospace Research "Elie Carafoli" B-dul Iuliu Maniu 220 061126 Bucharest Romania

ISBN: (纸本)9781467363952

The paper intend to develop a calculus model for an innovative Reaction Control System (RCS) using hybrid rocket engine technology. Our RCS uses several hybrid micro-thrusters with their thrust modulated by a separate control system. For RCS, each of the thrusters will be able to burn a few minutes and its thrust will be modulated within certain limits by controlling the oxidizer flow. In order to reduce size and weight of the RCS we will use a single oxidizer tank which will have as output a flow distributor. The basic idea is not to stop any of the engines during system's operation but to minimize their thrust reducing the oxidizer flow. This approach is avoiding the inconvenience of repeated stopping and starting of the engine, which can create reliability problems to the entire RCS. By creating thrust imbalance between various hybrid micro thrusters, one can create torques with which the attitude or the trajectory of the vehicle can be adjusted. In terms of calculation model developed, it starts from our theoretical and experimental studies, which aimed to build a computational model for hybrid rocket engine highlighting the scalability, stability and its controllability. These studies were presented in RAST 2011 and are based on our own experiments performed in Electromecanica Ploiesti. Based on this concept we achieve a calculation of the performances of the RCS and an evaluation in their size. Conclusions and any discussion will be focused on technological possibilities for achieving the system and possible areas of application for the RCS.

关键词： hybrid rocket engine nozzle orbital/suborbital vehicle numerical algorithm computation model combustion

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A novel numerical algorithm based on self-tuning controller to support TCP flows

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MATHEMATICS AND COMPUTERS IN SIMULATION 2008年第4期79卷 1178-1188页

作者： Xiong, N. Yang, L. T. Yang, Y. Defago, X. He, Y. Japan Adv Inst Sci & Technol Sch Informat Sci Nomi Ishikawa 9231211 Japan Wuhan Univ State Key Lab Software Engn Wuhan Peoples R China St Francis Xavier Univ Dept Comp Sci Antigonish NS B2G 1C0 Canada

Active queue management (AQM) is an effective method used in Internet routers for congestion control, and to achieve a trade off between link utilization and delay. The de facto standard, the random early detection (RED) AQM scheme, and most of its variants use average queue length as a congestion indicator to trigger packet dropping. This paper proposes a novel numerical algorithm based on self-tuning control circuit, called loss ratio and rate control RED (LRC-RED), to regulate the queue length with small variation and to achieve high utilization with small packet loss. This scheme is based on random early detection (RED) of the loss ratio and the total send rate control, and measures the latest packet loss ratio, then uses the latest packet loss ratio and the total input rate as complements to queue length in order to dynamically adjust packet drop probability. Furthermore, we also give a theoretical analysis of system stability and develop a simple, scalable and systematic guideline for the selection of feedback gains for the dynamic TCP/RED system to stabilize the queue length at a desirable level. Extensive simulations have been conducted with ns - 2. The simulation results have demonstrated that the proposed LRC-RED algorithm outperforms the loss ratio-based RED (LRED) [C. Wang, B. Li, Y.T. Hou, K. Sohraby, Y. Lin, LRED: a robust active queue management scheme based on packet loss ratio. in: Proceedings of IEEE INFOCOM 2004, IEEE, 2004] algorithm in terms of stability, fast response time and robustness. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Active queue management numerical algorithm Random early detection (RED) Congestion control TCP

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About the algebraic solutions of smallest enclosing cylinders problems

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APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2012年第3-4期23卷 151-164页

作者： Petitjean, Michel Univ Paris 07 INSERM MTi UMR S 973 F-75205 Paris 13 France

Given n points in Euclidean space E (d) , we propose an algebraic algorithm to compute the best fitting (d-1)-cylinder. This algorithm computes the unknown direction of the axis of the cylinder. The location of the axis and the radius of the cylinder are deduced analytically from this direction. Special attention is paid to the case d = 3 when n = 4 and n = 5. For the former, the minimal radius enclosing cylinder is computed algebrically from constrained minimization of a quartic form of the unknown direction of the axis. For the latter, an analytical condition of existence of the circumscribed cylinder is given, and the algorithm reduces to find the zeroes of an one unknown polynomial of degree at most 6. In both cases, the other parameters of the cylinder are deduced analytically. The minimal radius enclosing cylinder is computed analytically for the regular tetrahedron and for a trigonal bipyramids family with a symmetry axis of order 3.

关键词： Best fitting cylinder Smallest enclosing cylinder Minimal cylinder Circumscribed cylinder through five points numerical algorithm

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Multi-cell Optimal Downlink Beamforming algorithm with Per-base Station Power Constraints

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WIRELESS PERSONAL COMMUNICATIONS 2012年第4期62卷 893-906页

作者： Huang, Fan Wang, Yafeng Geng, Jian Yang, Dacheng Beijing Univ Posts & Telecommun Wireless Theories & Technol Lab WT&T Beijing 100088 Peoples R China Beijing Univ Posts & Telecommun Sch Informat & Telecommun Beijing 100088 Peoples R China Beijing Univ Posts & Telecommun Qualcomm Joint Res Ctr Beijing 100088 Peoples R China

We consider a problem of optimizing multi-cell downlink throughput in multiple-input single-output (MISO) beamforming with single user per sub-channel in the wireless communication system. Previous work based on the generalization of uplink-downlink duality has already reformulated the maximum achievable downlink throughput into dual uplink throughput maximization problem. Since the dual uplink problem is nonconvex, it is difficult to find its optimal solution. The main contribution of this paper is a novel practical algorithm based on heuristic to find the solution of beamforer design satisfying the necessary optimality conditions of the dual uplink problem. Meanwhile the converged beamforming vectors can in turn improve the system sum rate significantly. As the dual problem is a mixed optimization, we also provide algorithms for its two sub-optimal problems. Simulation results validate the convergence and the efficiency of proposed algorithms.

关键词： Multi-cell Downlink beamforming Throughput maximization Power constraint numerical algorithm

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Modeling of the World Ocean circulation with the four-dimensional assimilation of temperature and salinity fields

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IZVESTIYA ATMOSPHERIC AND OCEANIC PHYSICS 2012年第1期48卷 15-29页

作者： Marchuk, G. I. Zalesny, V. B. Russian Acad Sci Inst Numer Math Moscow 119333 Russia

The problem of modeling the World Ocean circulation with the four-dimensional assimilation of temperature and salinity fields is considered. A mathematical model of the ocean general circulation and a numerical algorithm for its solution are formulated. The model equations are written in a sigma coordinate system on the sphere with the North Pole shifted to the point of the continent (60A degrees E, 60.5A degrees N). The model has a flexible numerical structure and consists of two parts: the forward prognostic model and its adjoint analog. The numerical algorithm for solving the forward and adjoint problems is based on the method of multicomponent splitting. This method includes splitting with respect to physical processes and geometric coordinates. Three series of numerical experiments are performed: (1) a test solution to the problem of the four-dimensional variational assimilation, (2) modeling of the World Ocean circulation with the variational assimilation of climatic temperature and salinity fields, and (3) modeling of the World Ocean circulation with the variational assimilation of climatic temperature and salinity fields and the data of Argo buoys. The results of calculations demonstrate the expediency of using the model of World Ocean circulation with the procedure of assimilating observational data for a description of the general structure of thermohaline fields.

关键词： mathematical modeling the World Ocean numerical algorithm variational assimilation observational data

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