Direct iterative tuning via spectral analysis

A variety of Bayesian methods have recently been introduced for finding sparse representations from overcomplete dictionaries of candidate features. These methods often capitalize on latent structure inherent in sparse distributions to perform standard MAP estimation, variational Bayes, approximation using convex duality, or evidence maximization. Despite their reliance on sparsity-inducing priors however, these approaches may or may not actually lead to sparse representations in practice, and so it is a challenging task to determine which algorithm and sparse prior is appropriate. Rather than justifying prior selections and modelling assumptions based on the credibility of the full Bayesian model as is commonly done, this paper bases evaluations on the actual cost functions that emerge from each method. Two minimal conditions are postulated that ideally any sparse learning objective should satisfy. Out of all possible cost functions that can be obtained from the methods described above using (virtually) any sparse prior, a unique function is derived that satisfies these conditions. Both sparse Bayesian learning (SBL) and basis pursuit (BP) are special cases. Later, all methods are shown to be performing MAP estimation using potentially non-factorable implicit priors, which suggests new sparse learning cost functions.

This paper proposed a new global optimization approach for electric machine design problems. Its algorithm uses the error function between the actual cost function at a given computational step, and its limit value which is lower than the desired global minimum. The error function provides a good indication of how far or close the cost function is approaching its limit solution. This method may be considered to be self adaptive in a sense that the higher the error is, the higher the step size of the variables will be. This feature will help the function to escape local solutions and tend to reach the targeted solution. The proposed approach has been tested on various typical multimodal functions and particularly, applied to induction motor design optimization problems. The algorithm of this method is very simple and easy to implement but yet powerful and effective as highlighted in the test results.

The design space exploration (DSE) subsystem of a design automation tool is responsible for early identification of interesting zones of the design space. Evaluation of the exploration strategy used in a tool is extremely difficult because there is not enough information about either the design space or the actual cost function. This paper describes a software environment for quantitative evaluation of isolated exploration algorithms based on a completely simulated framework. A simple model of the design space allows easy representation of interesting properties of exploration algorithms.

In the cost-table approach to logic design, a function is realized as a combination of functions from a table. The objective of the synthesis is to find the least-cost realization, where realization cost is the sum of the costs of the functions used plus the cost of combining them. The costs of cost-table functions are defined by a cost function which represents chip area, speed, power dissipation, or a combination of these factors. It is shown that there is an arbitrarily large set S of cost functions which yield the same cost-table. This implies, for example, that every minimal realization of any function over a cost function in S is independent of the actual cost function used. With any cost function, if the cost of combining functions from a cost-table F is sufficiently large, the realizations behave as if the cost function belonged to S. That is, any minimal realization of a function f, using cost-table F, is one of the minimal realizations of f using F and a cost function in S. The interpretation of these results is that there are not as many distinct cost-tables as originally thought.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Autoregressive and cepstral analyses of motor unit action potentials

Measurements of electromagnetic interference in time-domain allow to reduce the scan time by several orders of magnitude, in comparison to automated scans performed by the tuned selective voltmeters, which are known as EMI receivers. Spectrum analyzer are used for frequency selective measurements of signals. Such analyzers can perform fast sweeps or scans over large bands. A drawback of spectrum analyzers is the long sweep time, when a high frequency resolution is required. In this paper an overview of methods and systems is shown which perform the measurement in time-domain and use the short-time fast Fourier transform for the calculation of the spectrum rather than a sequential measurement. Baseband systems allow to speed up scans by several orders of magnitude. Systems with a broadband downconversion and a broadband analog-to-digital converter system allow to extend the frequency range beyond the Nyquist frequency of todays available ADCs. Powerful Short-time fast Fourier transform processors allow to process several frequencies at the same time. A gapless processing allows to analyze unstationary signals as well as small narrowband signals.

In primary visual cortex (V1) of rats, orientation selective neurons do not show topographic organization on a larger scale (Ohki et al., 2005), in contrast to the columnar organization of orientation selective cells in V1 of cat and monkey. Accordingly, while orientation tuning in mass signals like the local field potential (LFP) has been described in recordings from cat V1, it can be assumed to be weak or absent in rodent V1. However, in monkey motor cortex, which also shows no clear columnar organization, information about the direction of the monkey’s hand movement could be extracted from LFP power spectra with high predictive power (Rickert et al., 2005). To reveal in how far global network tuning properties could be extracted from mass signals of primary sensory areas which do not show clear topographic organization, we performed in vivo multi-electrode recordings in V1 of anesthetized rats while presenting visual stimuli with clear direction information (moving edges and gratings). Spectral analysis of LFP signals from multiple channels was performed using adaptive multivariate auto-regression (AMVAR; Ding et al., 2000) after removing the first two statistical moments (mean and standard deviation across trials) from the signal. This method allows high spectral estimation accuracy with high temporal resolution superior to other methods of time-dependent spectral analysis like multi-tapering (Nalatore & Rangarajan, 2009). Direction tuning was assessed using circular statistical measures. For moving edges, significant directional tuning in the LFP power spectrum can be found during the onset transient up to 500 ms after stimulus onset. Tuning strength was not distributed evenly across the whole observed spectrum (<200 Hz), however, but limited to mainly two distinct frequency bands centered around ~30 Hz and ~70 Hz. Preliminary analysis of moving grating stimuli did not reveal significant tuning either in the onset transient or the steady state during stimulus presentation. These results suggest that, even in the absence of coarse scale organization of cortical networks with respect to tuning properties, information about the stimulus properties can be inferred with appropriate methods.

Introduction to the mathematical theory of control processes, Vol. I - Linear equations and quadratic criteria

Success/failure of adaptive control algorithms – especially those designed using the Linear Quadratic Gaussian criterion – depends on the quality of the process data used for model identification. One of the most harmful types of process data corruptions are outliers, i.e. ‘wrong data’ lying far away from the range of real data. The presence of outliers in the data negatively affects an estimation of the dynamics of the system. This effect is magnified when the outliers are grouped into blocks. In this paper, we propose an algorithm for outlier detection and removal. It is based on modelling the corrupted data by a two-component probabilistic mixture. The first component of the mixture models uncorrupted process data, while the second models outliers. When the outlier component is detected to be active, a prediction from the uncorrupted data component is computed and used as a reconstruction of the observed data. The resulting reconstruction filter is compared to standard methods on simulated and real data. The filter exhibits excellent properties, especially in the case of blocks of outliers.

The paper introduces the concept of mean square detectability and relates this to the recently introduced concept of mean square observability. It is shown that under appropriate mean square detectability and stabilizability conditions the infinite-horizon optimal control problem for the general case of linear discrete time systems and quadratic criteria, both with stochastic parameters which are statistically independent of time, has a unique solution when the control system is mean square stable. A simple necessary and sufficient condition, explicit in the system matrices, is given to determine if a system is mean square detectable. This condition also holds for deterministic systems to be detectable in the usual sense. The mean square detectability property coincides with the usual one if the parameters are deterministic.

This paper is an assessment of the current state of controllability and observability theories for linear partial differential equations, summarizing existing results and indicating open problems in the area. The emphasis is placed on hyperbolic and parabolic systems. Related subjects such as spectral determination, control of nonlinear equations, linear quadratic cost criteria and time optimal control are also discussed.

The objective of this paper is to integrate optimum control theory and input-output analysis in a model designed to provide elements toward policies of sectoral unemployment minimization. In the paper, the deterministic version of the optimum control problem with linear dynamic equation and quadratic performance criterion is briefly presented. In the model, the objective function contains an index that is regarded as representing the unemployment due to underutilization of sectoral capacity, which is minimized. The state variables are the sectoral gaps between actual output and potential (full-capacity) output; the control variables are the variations in the sectoral final demands accomplished by the government. In the empirical simulations, data from the Brazilian input-output table, built by IBGE, are used. The results show that the service and the civil construction sectors are the most responsive to policies intended to minimize sectoral unemployment, due to its wage coefficients and backward linkages, respectively. Other good reasons to stimulate those sectors are the acceptable degree of government intervention and the small consumption of imported inputs, which characterize them. Government intervention is then recommended to be concentrated on those two sectors.

Objectives: The study reviews the iterative solvers for solving Helmholtz equation. It also surveys the preconditioners for Krylov subspace methods for discrete Helmholtz equation. Numerical experiments based conclusions are drawn, after a thorough comparison of various preconditioners. Methods/Statistical Analysis: Five point finite difference scheme for two-dimensional Helmholtz equation is employed to obtain discrete analogue of Helmholtz equation. Krylov subspace method for is considered for iterations. Matrix based preconditioner ILU with variety of fill-in and operator based preconditioner complex shifted Laplace preconditioner (CSLP) are tested. Different shifts are proposed and experimented in CSLP. Optimization of shifts is recommended on basis of results. Spectral analysis is performed to validate results. Findings: For small wave number problem, ILU type preconditioned performs better and is fairly comparable with CSLP. However, increasing wave number makes unaffordable in terms of computational cost. The pure imaginary shift (0,1) and complex shift (1, / 4 π ) costsless time and number of iterations compared to other choices of shift. These choices are recommended when preconditioner is inverted directly. Approximate inversion may affect iterations, but will save solve time for large problems. Extensive spectral analysis, validating results, highlights this work. Application/Improvements: Dependency upon wave number is decreased with this recommended choice of shifts in CSLP. The number of iterations increases at very low rate when wave number is increased at rate of 2. Keywords: Helmholtz Equation, Iterative Methods, Krylov Subspace Methods, Preconditioners, Spectral Analysis

In this work, we propose a nonlinear dynamic inverse solution to the diffusion problem based on Krylov Subspace Methods with spatiotemporal constraints. The proposed approach is applied by considering, as a forward problem, a 1D diffusion problem with a nonlinear diffusion model. The dynamic inverse problem solution is obtained by considering a cost function with spatiotemporal constraints, where the Krylov subspace method named the Generalized Minimal Residual method is applied by considering a linearized diffusion model and spatiotemporal constraints. In addition, a Jacobian-based preconditioner is used to improve the convergence of the inverse solution. The proposed approach is evaluated under noise conditions by considering the reconstruction error and the relative residual error. It can be seen that the performance of the proposed approach is better when used with the preconditioner for the nonlinear diffusion model under noise conditions in comparison with the system without the preconditioner.

A few months before the foreseen SMOS launch date (first half of 2009), the interests of the scientists working on the Ocean Salinity Level 2 definition are mainly focused on improving the accuracy of the retrieval algorithm. The algorithm used is based on an iterative procedure in which a "cost function", that relates models, measurements, and auxiliary data, is minimized. For this reason most of the efforts are currently centered in the analysis and the optimization of the cost function. Within this frame, the study proposed represents a contribution to assess one of the pending issues in the definition of the cost function: The optimal weight to give to the MIRAS measurements. To do this a set of simulations have been run using: - The Océan PArallélisé (OPA) Model [1] as source of geophysical parameters; - The SMOS End-to-end Performance Simulator (SEPS) [2] as source of synthetic SMOS-like brightness temperatures imagery; - SMOS-Level2 Processor Simulator (SMOS-L2PS) [3] to perform the retrieval. Results are presented and discussed.