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Computational insights into tumor invasion dynamics: A finite element approach

MATHEMATICS AND COMPUTERS IN SIMULATION 2025年 229卷 814-829页

作者： Irum, Saba Almakayeel, Naif Deebani, Wejdan Lahore Univ Management Sci Syed Baber Ali Sch Sci & Engn Dept Elect Engn Lahore Pakistan King Khalid Univ Coll Engn Dept Ind Engn Abha 61421 Saudi Arabia King Abdulaziz Univ Coll Sci & Arts Dept Math Rabigh Saudi Arabia

The finite element scheme is proposed and analyzed for the solution of an acid-mediated tumor invasion model. The reaction-diffusion equation shows the evolution in the tumor cell density, H + ions concentration, and healthy tissue density over time. The coupled non-linear partial differential equations are discretized in time with the implicit Euler method and in space with standard Galerkin finite element. To solve the non-linear and coupled terms of the system a fixed point iteration scheme is presented. Moreover, a mass-lumped scheme is adopted to reduce the computation cost. The cut-off method is used to compute the bounded solutions of the PDEs. Finally, The effects of proliferation rate and healthy tissue degradation rate are investigated.

关键词： Tumor invasion Finite element Acid mediated model Spatial-temporal discretization fixed point algorithm Mathematical modeling of tumor

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Efficient primal-dual fixed point algorithms with dynamic stepsize for composite convex optimization problems

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MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING 2019年第3期30卷 1531-1544页

作者： Wen, Meng Tang, Yuchao Cui, Angang Peng, Jigen Xian Polytech Univ Sch Sci Xian 710048 Shaanxi Peoples R China Guangzhou Univ Sch Math & Informat Sci Guangzhou 510006 Guangdong Peoples R China NanChang Univ Dept Math Nanchang 330031 Jiangxi Peoples R China Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China

In this paper, we propose a new primal-dual fixed point algorithm with dynamic stepsize (PDFP2ODSn) for solving convex minimization problems involving the sum of a smooth function with Lipschitzian gradient and the composition of a nonsmooth convex function with a continuous linear operator. Based on modified Mann iteration and the firmly nonexpansive properties of the proximity operator, we achieve the convergence of the proposed algorithm. Moreover, we give the connection of the proposed algorithm with other existing PDFP2O (Chen et al. in Inverse Probl 29:025011-025033, 2013). Finally, we illustrate the efficiency of PDFP2ODSn through some numerical examples on the CT image reconstruction problem. Numerical results show that our iterative algorithm (PDFP2ODS) performs better than the original one (PDFP2O).

关键词： fixed point algorithm Convex separable minimization Proximity operator Dynamic stepsize

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regularization methods and fixed point algorithms for affine rank minimization problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2017年第3期67卷 543-569页

作者： Peng, Dingtao Xiu, Naihua Yu, Jian Guizhou Univ Sch Math & Stat Guiyang 550025 Guizhou Peoples R China Beijing Jiaotong Univ Sch Sci Beijing 100044 Peoples R China

The affine rank minimization problem is to minimize the rank of a matrix under linear constraints. It has many applications in various areas such as statistics, control, system identification and machine learning. Unlike the literatures which use the nuclear norm or the general Schatten quasi-norm to approximate the rank of a matrix, in this paper we use the Schatten 1 / 2 quasi-norm approximation which is a better approximation than the nuclear norm but leads to a nonconvex, nonsmooth and non-Lipschitz optimization problem. It is important that we give a global necessary optimality condition for the regularization problem by virtue of the special objective function. This is very different from the local optimality conditions usually used for the general regularization problems. Explicitly, the global necessary optimality condition for the regularization problem is a fixed point inclusion associated with the singular value half thresholding operator. Naturally, we propose a fixed point iterative scheme for the problem. We also provide the convergence analysis of this iteration. By discussing the location and setting of the optimal regularization parameter as well as using an approximate singular value decomposition procedure, we get a very efficient algorithm, half norm fixed point algorithm with an approximate SVD (HFPA algorithm), for the regularization problem. Numerical experiments on randomly generated and real matrix completion problems are presented to demonstrate the effectiveness of the proposed algorithm.

关键词： Affine rank minimization problem Matrix completion problem S-1/2 Regularization problem fixed point algorithm Singular value half thresholding operator

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Modified State Estimation with fixed point Update Based on Maximum Correntropy Criterion

Modified State Estimation with Fixed Point Update Based on M...

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IEEE International Conference on Industrial Technology (IEEE ICIT)

作者： Maki, Hayato Katsura, Seiichiro Keio Univ Kohoku Ku 3-14-1 Hiyoshi Yokohama Kanagawa Japan

ISBN: (纸本)9781538663769

It is well known that Kalman Filter is good for a state estimation on a linear system. The criterion is a square error function, which is efficient and sufficient for most systems. However, the square error evaluation function is often not sufficient in the systems under non-Gaussian noise. In recent years, an entropy has been attracting attention as an evaluation function changing to the square error criterion. Beginning with entropy of Shannon, its characteristics are related to higher-order statistics. When the entropy is set as criterion, all moments or all even moments of the state estimation error can be constrained. These characteristics have been utilized for learning system, adaptive filtering, and neuro-control. In this research, we focus on a correntropy, which has expanded Renyi 's entropy more generally, and the correntropy is utilized in order to estimate states of systems. This method uses multi-step ahead predictions, and aims to better state estimation. The method of multi-step ahead predictions is effective for the case that the system has not only statistic process noise but also other disturbances. Previous methods using the correntropy as a criterion are introduced here, and compared with modified method through experimental data.

关键词： State Estimation Correntropy Optimization fixed point algorithm

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Performance analysis of radix-2/3/5 decompositions in fixed point DIT FFT algorithms 10

Performance analysis of radix-2/3/5 decompositions in fixed ...

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10th International Conference on Computer Communication and Informatics (ICCCI)

作者： Jyotsna, Y. Nithiyameenatchi, N. Konguvel, E. Kannan, M. Anna Univ Dept Elect Engn MIT Campus Chennai Tamil Nadu India Sri Shakthi Inst Engn & Technol Dept Elect & Commun Engn Coimbatore Tamil Nadu India

ISBN: (数字)9781728145143

ISBN: (纸本)9781728145136

In this article, we focus on the extensively utilized algorithm for Fast Fourier Transform (FFT) radix-2 DecimationInTime (DIT). It proposes a variable-length FFT processor that can be reconfigured. The processor designed for different FFT / IFFT stages can perform 8, 16 and 32 point FFT / IFFT with different word length scaling modes. Furthermore, in many applications, the processor is suitable for various FFT / IFFT length requirements. Single-path delay feedback (SDF) pipeline architecture is incorporated in order to achieve higher throughput. Cadence NC Launch, RTL Compiler, Simvision Simulator and Altera DE2 FPGA EP2C35F672C6 board are used to test the design in TSMC 45 nm technology. We often worked with 2/3/5 radices and thus make a clear comparison between different radices and the efficiency associated with each of them. This work achieves better specifications for area use and delay. Meanwhile, the occupied resources are approximately same. Moreover, the performance of different FFT length is analyzed.

关键词： Single Delay Feedback (SDF) Radix 2/3/5 fixed point algorithm Fast Fourier Transform (FFT) Decimation In Time (DIT) Long Term Evolution(LTE)

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A variable dimension algorithm with the Dantzig-Wolfe decomposition for structured stationary point problems

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ZOR Zeitschrift für Operations Research Methods and Models of Operations Research 1992年第1期36卷 23-53页

作者： Dai, Y. Sekitani, K. Yamamoto, Y. Institute of Socio-Economic Planning University of Tsukuba Ibaraki 305 Japan

Given a set Ω of Rn and a function f from Ω into Rn we consider a problem of finding a point x* in Ω such that (x-x*)tf(x*){succeeds or equal to}0 holds for every point x in Ω. This problem is called the stationar... 详细信息

Given a set Ω of Rⁿ and a function f from Ω into Rⁿ we consider a problem of finding a point x^* in Ω such that (x-x^*)^tf(x^*){succeeds or equal to}0 holds for every point x in Ω. This problem is called the stationary point problem and the point x^* is called a stationary point. We present a variable dimension algorithm for solving the stationary point problem with an affine function f on a polytope Ω defined by constraints of linear equations and inequalities. We propose a system of equations whose solution set contains a piecewise linear path connecting a trivial starting point in Ω with a stationary point. The path can be followed by solving a series of linear programs which inherit the structure of constraints of Ω. The linear programs are solved efficiently with the Dantzig-Wolfe decomposition method by exploiting fully the structure. © 1992 Physica-Verlag.

关键词： bi-matrix game fixed point algorithm path-following portfolio selection stationary point traffic assignment variational inequality

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Pole structure assignment via non-regular static state feedback

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AUTOMATICA 1999年第9期35卷 1549-1555页

作者： Loiseau, JJ Zagalak, P Kucera, V Ecole Cent Nantes UMR 6597 CNRS Inst Rech Cybernet Nantes F-44321 Nantes 03 France Acad Sci Czech Republ Inst Informat Theory & Automat CR-18208 Prague Czech Republic Czech Tech Univ Fac Elect Engn Trnka Lab Automat Control Prague 12135 Czech Republic

The limits of the static state feedback u = Fx + Gv, with G not necessarily nonsingular, in altering the transmission pole structure of the linear system (x) over dot = Ax f Bu are studied. A necessary and sufficient condition for a list of polynomials to be the denominator polynomials of the Smith-McMillan form of the closed-loop transfer matrix (sl - A - BF)(-1)BG is established. The condition involves the calculation of the infimal set of the controllability indices that the system can attain through feedback while satisfying the Rosenbrock inequalities. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： linear systems static state feedback transmission poles controllability indices lattice of integer partitions fixed point algorithm

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A finite element approximation for the steady solution of a second-grade fluid model

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1999年第1-2期111卷 281-295页

作者： Sequeira, A Baía, M Univ Tecn Lisboa Dept Matemat Inst Super Tecn P-1049001 Lisbon Portugal Univ Tecn Lisboa Ctr Matemat Aplicada Inst Super Tecn P-1049001 Lisbon Portugal

The aim of this work is to present a finite element method for the approximation of the steady solution of an incompressible second-grade fluid model in two dimensions. The equations for second-grade fluids form a system of nonlinear partial differential equations of mixed elliptic-hyperbolic type (in the steady state). Using a fixed-point argument, associated with the decomposition of the system into a transport equation and a Stokes system, existence and uniqueness of the approximate solution are proved and error estimates are obtained. This technique allows the construction of a decoupled fixed-point algorithm converging to the discrete solution of the original problem. (C) 1999 Published by Elsevier Science B.V. All rights reserved.

关键词： second-grade fluid transport equation Stokes system FEM approximation fixed point algorithm

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New iterative algorithm for algebraic Riccati equation related to H_∞ control problem of singularly perturbed systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2001年第10期46卷 1659-1666页

作者： Mukaidani, H Xu, H Mizukami, K Hiroshima City Univ Fac Informat Sci Hiroshima Japan Univ Tsukuba Grad Sch Business Sci Tokyo Japan Hiroshima Kokusai Gakuin Univ Fac Engn Hiroshima Japan

In this note, we present the solution to the algebraic Riccati equation (ARE) with indefinite sign quadratic term related to the H-infinity control problem for singularly perturbed system by means of a Kleinman's type algorithm. The resulting algorithm is very efficient from the numerical point of view because the ARE is solvable even if the quadratic term has an indefinite sign. Moreover, the resulting iterative algorithm is quadratically convergent. We also present a new algorithm for solving the generalized algebraic Lyapunov equation (GALE) on the basis of the fixed point algorithm.

关键词： fixed point algorithm H-infinity control Kleinman algorithm singularly perturbed systems

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A Method of Independent Component Analysis Based on Radial Basis Function Networks Using Noise Estimation

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ELECTRONICS AND COMMUNICATIONS IN JAPAN 2008年第3期91卷 45-52页

作者： Zhang, Nuo Lu, Jianming Yahagi, Takashi Chiba Univ Chiba Japan

This paper proposes a robust independent component analysis (ICA) approach for noise reduction. Noise reduction is a difficult problem in ICA. model. In general signal processing applications, there is more than one interference signal which may have unknown characteristics. In these situations, traditional linear ICA may lead to poor results. Hence, noise reduction is preferred to be performed with nonlinear adaptive filtering. In this paper, a radial basis function network (RBFN) is employed to transform the observed signals into output space in a nonlinear manner. The weights of RBFN are updated by utilizing a modified fixed-point algorithm. The proposed method has not only the capacity of recovering the mixed signals, but also reducing noise with unknown characteristics from observed signals. The simulation results and analysis show that the proposed algorithm is suitable for practical unsupervised noise reduction problem. (C) 2008 Wiley Periodicals, Inc. Electron Comm Jpn, 91(3): 45-52, 2008;Published online in Wiley InterScience (***). DOI 10.1002/ecj.10073

关键词： independent component analysis (ICA) fixed point algorithm noise radial basis function network (RBFN)

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