This paper introduces a new type of fuzzy inference systems, denoted as dynamic evolving neural-fuzzy inference system (DENFIS), for adaptive online and offline learning, and their application for dynamic time series prediction. DENFIS evolve through incremental, hybrid (supervised/unsupervised), learning, and accommodate new input data, including new features, new classes, etc., through local element tuning. New fuzzy rules are created and updated during the operation of the system. At each time moment, the output of DENFIS is calculated through a fuzzy inference system based on m-most activated fuzzy rules which are dynamically chosen from a fuzzy rule set. Two approaches are proposed: (1) dynamic creation of a first-order Takagi-Sugeno-type fuzzy rule set for a DENFIS online model; and (2) creation of a first-order Takagi-Sugeno-type fuzzy rule set, or an expanded high-order one, for a DENFIS offline model. A set of fuzzy rules can be inserted into DENFIS before or during its learning process. Fuzzy rules can also be extracted during or after the learning process. An evolving clustering method (ECM), which is employed in both online and offline DENFIS models, is also introduced. It is demonstrated that DENFIS can effectively learn complex temporal sequences in an adaptive way and outperform some well-known, existing models.

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DENFIS: dynamic evolving neural-fuzzy inference system and its application for time-series prediction

Here we address the problem of parameter estimation (inverse problem) of nonlinear dynamic biochemical pathways. This problem is stated as a nonlinear programming (NLP) problem subject to nonlinear differential-algebraic constraints. These problems are known to be frequently ill-conditioned and multimodal. Thus, traditional (gradient-based) local optimization methods fail to arrive at satisfactory solutions. To surmount this limitation, the use of several state-of-the-art deterministic and stochastic global optimization methods is explored. A case study considering the estimation of 36 parameters of a nonlinear biochemical dynamic model is taken as a benchmark. Only a certain type of stochastic algorithm, evolution strategies (ES), is able to solve this problem successfully. Although these stochastic methods cannot guarantee global optimality with certainty, their robustness, plus the fact that in inverse problems they have a known lower bound for the cost function, make them the best available candidates.

/pdf/parameter-estimation-in-biochemical-pathways-a-comparison-of-2a8v24rhva.pdf

Parameter Estimation in Biochemical Pathways: A Comparison of Global Optimization Methods

I start by providing an updated summary of the penalized pixel-fitting (pPXF) method, which is used to extract the stellar and gas kinematics, as well as the stellar population of galaxies, via full spectrum fitting. I then focus on the problem of extracting the kinematic when the velocity dispersion $\sigma$ is smaller than the velocity sampling $\Delta V$, which is generally, by design, close to the instrumental dispersion $\sigma_{\rm inst}$. The standard approach consists of convolving templates with a discretized kernel, while fitting for its parameters. This is obviously very inaccurate when $\sigma<\Delta V/2$, due to undersampling. Oversampling can prevent this, but it has drawbacks. Here I present a more accurate and efficient alternative. It avoids the evaluation of the under-sampled kernel, and instead directly computes its well-sampled analytic Fourier transform, for use with the convolution theorem. A simple analytic transform exists when the kernel is described by the popular Gauss-Hermite parametrization (which includes the Gaussian as special case) for the line-of-sight velocity distribution. I describe how this idea was implemented in a significant upgrade to the publicly available pPXF software. The key advantage of the new approach is that it provides accurate velocities regardless of $\sigma$. This is important e.g. for spectroscopic surveys targeting galaxies with $\sigma\ll\sigma_{\rm inst}$, for galaxy redshift determinations, or for measuring line-of-sight velocities of individual stars. The proposed method could also be used to fix Gaussian convolution algorithms used in today's popular software packages.

Improving the full spectrum fitting method: accurate convolution with Gauss-Hermite functions

In this paper, we combine a new approach for linear time delay systems based on a descriptor representation with a recent result on bounding of cross products of vectors. A delay-dependent criterion for determining the stability of systems with time-varying delays is obtained. This criterion is used to derive an efficient stabilizing state-feedback design method for systems with parameter uncertainty, of either the polytopic or the norm-bounded types.

/pdf/an-improved-stabilization-method-for-linear-time-delay-4dp4tdg8bn.pdf

An improved stabilization method for linear time-delay systems

The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from The MathWorks, Inc. (a) for units of the Department of Defense: RESTRICTED RIGHTS LEGEND: Use, duplication, or disclosure by the Government is subject to restrictions as set forth in subparagraph (c)(1)(ii) of the Rights in Technical Data and Computer Software Clause at DFARS 252.227-7013. (b) for any other unit or agency: NOTICE-Notwithstanding any other lease or license agreement that may pertain to, or accompany the delivery of, the computer software and accompanying documentation, the rights of the Government regarding its use, reproduction and disclosure are as set forth in Clause 52.227-19(c)(2) of the FAR. Other product or brand names are trademarks or registered trademarks of their respective holders.

/pdf/optimization-toolbox-user-s-guide-b2064iob0t.pdf

Optimization Toolbox User's Guide

A subspace adaptation of the Coleman--Li trust region and interior method is proposed for solving large-scale bound-constrained minimization problems. This method can be implemented with either sparse Cholesky factorization or conjugate gradient computation. Under reasonable conditions the convergence properties of this subspace trust region method are as strong as those of its full-space version.
Computational performance on various large test problems is reported; advantages of our approach are demonstrated. Our experience indicates that our proposed method represents an efficient way to solve large bound-constrained minimization problems.

/pdf/a-subspace-interior-and-conjugate-gradient-method-for-large-2j15q9iyoa.pdf

Mary Ann Branch

Papers

Optimization Toolbox User's Guide

A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems

Optimization toolbox : for use with MATLAB