A Nondeterministic Minimization Algorithm

The problem of minimizing a multivariate function is recurrent in many disciplines as Physics, Mathematics, Engeneering and, of course, Computer Science. In this paper we describe a simple nondeterministic algorithm which is based on the idea of adaptive noise, and that proved to be particularly effective in the minimization of a class of multivariate, continuous valued, smooth functions, associated with some recent extension of regularization theory by Poggio and Girosi (1990). Results obtained by using this method and a more traditional gradient descent technique are also compared.

Empirical minimization

We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp. The method of proof we use is based on Talagrand’s concentration inequality for empirical processes.

Minimization of Reactive Probabilistic Automata

The problem of finite automata minimization is important for software and hardware designing. Different types of automata are used for modeling systems or machines with finite number of states. The limitation of number of states gives savings in resources and time. In this article we show specific type of probabilistic automata: the reactive probabilistic finite automata with accepting states (in brief the reactive probabilistic automata), and definitions of languages accepted by it. We present definition of bisimulation relation for automata's states and define relation of indistinguishableness of automata states, on base of which we could effectuate automata minimization. Next we present detailed algorithm reactive probabilistic automata’s minimization with determination of its complexity and analyse example solved with help of this algorithm.

Coding speech signals at very low rates (below 1 kb/s) with high intelligibility

This thesis presents an original approach to parametric speech coding at rates below 1 kbitsjsec, primarily for speech storage applications. Essential processes considered in this research encompass efficient characterization of evolutionary configuration of vocal tract to follow phonemic features with high fidelity, representation of speech excitation using minimal parameters with minor degradation in naturalness of synthesized speech, and finally, quantization of resulting parameters at the nominated rates. For encoding speech spectral features, a new method relying on Temporal Decomposition (TD) is developed which efficiently compresses spectral information through interpolation between most steady points over time trajectories of spectral parameters using a new basis function. The compression ratio provided by the method is independent of the updating rate of the feature vectors, hence allows high resolution in tracking significant temporal variations of speech formants with no effect on the spectral data rate. Accordingly, regardless of the quantization technique employed, the method yields a high compression ratio without sacrificing speech intelligibility. Several new techniques for improving performance of the interpolation of spectral parameters through phonetically-based analysis are proposed and implemented in this research, comprising event approximated TD, near-optimal shaping event approximating functions, efficient speech parametrization for TD on the basis of an extensive investigation originally reported in this thesis, and a hierarchical error minimization algorithm for decomposition of feature parameters which significantly reduces the complexity of the interpolation process. Speech excitation in this work is characterized based on a novel Multi-Band Excitation paradigm which accurately determines the harmonic structure in the LPC (linear predictive coding) residual spectra, within individual bands, using the concept 11 of Instantaneous Frequency (IF) estimation in frequency domain. The model yields aneffective two-band approximation to excitation and computes pitch and voicing with high accuracy as well. New methods for interpolative coding of pitch and gain contours are also developed in this thesis. For pitch, relying on the correlation between phonetic evolution and pitch variations during voiced speech segments, TD is employed to interpolate the pitch contour between critical points introduced by event centroids. This compresses pitch contour in the ratio of about 1/10 with negligible error. To approximate gain contour, a set of uniformly-distributed Gaussian event-like functions is used which reduces the amount of gain information to about 1/6 with acceptable accuracy. The thesis also addresses a new quantization method applied to spectral features on the basis of statistical properties and spectral sensitivity of spectral parameters extracted from TD-based analysis. The experimental results show that good quality speech, comparable to that of conventional coders at rates over 2 kbits/sec, can be achieved at rates 650-990 bits/sec.

A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary. Peter L. Bartlett, Alexander Rakhlin

On the optimality of sample-based estimates of the expectation of the empirical minimizer

We study sample-based estimates of the expectation of the function produced by the empirical minimization algorithm. We investigate the extent to which one can estimate the rate of convergence of the empirical minimizer in a data dependent manner. We establish three main results. First, we provide an algorithm that upper bounds the expectation of the empirical minimizer in a completely data-dependent manner. This bound is based on a structural result due to Bartlett and Mendelson, which relates expectations to sample averages. Second, we show that these structural upper bounds can be loose, compared to previous bounds. In particular, we demonstrate a class for which the expectation of the empirical minimizer decreases as O(1/n) for sample size n, although the upper bound based on structural properties is Ω(1). Third, we show that this looseness of the bound is inevitable: we present an example that shows that a sharp bound cannot be universally recovered from empirical data.

Identification of fluorescent beads using a coded aperture snapshot spectral imager.

We apply a coded aperture snapshot spectral imager (CASSI) to fluorescence microscopy. CASSI records a two-dimensional (2D) spectrally filtered projection of a three-dimensional (3D) spectral data cube. We minimize a convex quadratic function with total variation (TV) constraints for data cube estimation from the 2D snapshot. We adapt the TV minimization algorithm for direct fluorescent bead identification from CASSI measurements by combining a priori knowledge of the spectra associated with each bead type. Our proposed method creates a 2D bead identity image. Simulated fluorescence CASSI measurements are used to evaluate the behavior of the algorithm. We also record real CASSI measurements of a ten bead type fluorescence scene and create a 2D bead identity map. A baseline image from filtered-array imaging system verifies CASSI's 2D bead identity map.

Compressed sensing in digital tomosynthesis reconstruction

In this work we study a model for the breast image reconstruction in Digital Tomosynthesis, that is a non-invasive and non-destructive method for the three-dimensional visualization of the inner structures of an object, in which the data acquisition includes measuring a limited number of low-dose two-dimensional projections of an object by moving a detector and an X-ray tube around the object within a limited angular range. The problem of reconstructing 3D images from the projections provided in the Digital Tomosynthesis is an ill-posed inverse problem, that leads to a minimization problem with an object function that contains a data fitting term and a regularization term. The contribution of this thesis is to use the techniques of the compressed sensing, in particular replacing the standard least squares problem of data fitting with the problem of minimizing the 1-norm of the residuals, and using as regularization term the Total Variation (TV). We tested two different algorithms: a new alternating minimization algorithm (ADM), and a version of the more standard scaled projected gradient algorithm (SGP) that involves the 1-norm. We perform some experiments and analyse the performance of the two methods comparing relative errors, iterations number, times and the qualities of the reconstructed images. In conclusion we noticed that the use of the 1-norm and the Total Variation are valid tools in the formulation of the minimization problem for the image reconstruction resulting from Digital Tomosynthesis and the new algorithm ADM has reached a relative error comparable to a version of the classic algorithm SGP and proved best in speed and in the early appearance of the structures representing the masses.

Spectrally tunable light source based on light-emitting diodes for custom lighting solutions

This study describes a novel spectral LED-based tunable light source used for customized lighting solutions, especially for the reconstruction of CIE (Commission Internationale de l’Éclairage) standard illuminants. The light source comprises 31 spectral bands ranging from 400 to 700 nm, an integrating cube and a control board with a 16-bit resolution. A minimization algorithm to calculate the weighting values for each channel was applied to reproduce illuminants with precision. The differences in spectral fitting and colorimetric parameters showed that the reconstructed spectra were comparable to the standard, especially for the D65, D50, A and E illuminants. Accurate results were also obtained for illuminants with narrow peaks such as fluorescents (F2 and F11) and a high-pressure sodium lamp (HP1). In conclusion, the developed spectral LED-based light source and the minimization algorithm are able to reproduce any CIE standard illuminants with a high spectral and colorimetric accuracy able to advance available custom lighting systems useful in the industry and other fields such as museum lighting.

Estimation of concentration-dependent diffusion coefficient in drying process from the space-averaged concentration versus time with experimental data

The estimation of a concentration-dependent diffusion coefficient in a drying process is known as an inverse coefficient problem. The solution is sought wherein the space-average concentration is known as function of time (mass loss monitoring). The problem is stated as the minimization of a functional and gradient-based algorithms are used to solve it. Many numerical and experimental examples that demonstrate the effectiveness of the proposed approach are presented. Thin slab drying was carried out in an isothermal drying chamber built in our laboratory. The diffusion coefficients of fructose obtained with the present method are compared with existing literature results.

Desenvolvimento da célula base de microestruturas periódicas de compósitos sob otimização topológica

This thesis develops a new technique for composite microstructures projects by the Topology Optimization process, in order to maximize rigidity, making use of Deformation Energy Method and using a refining scheme h-adaptative to obtain a better defining the topological contours of the microstructure. This is done by distributing materials optimally in a region of pre-established project named as Cell Base. In this paper, the Finite Element Method is used to describe the field and for government equation solution. The mesh is refined iteratively refining so that the Finite Element Mesh is made on all the elements which represent solid materials, and all empty elements containing at least one node in a solid material region. The Finite Element Method chosen for the model is the linear triangular three nodes. As for the resolution of the nonlinear programming problem with constraints we were used Augmented Lagrangian method, and a minimization algorithm based on the direction of the Quasi-Newton type and Armijo-Wolfe conditions assisting in the lowering process. The Cell Base that represents the composite is found from the equivalence between a fictional material and a preescribe material, distributed optimally in the project area. The use of the strain energy method is justified for providing a lower computational cost due to a simpler formulation than traditional homogenization method. The results are presented prescription with change, in displacement with change, in volume restriction and from various initial values of relative densities.

Distribution feeder reconfiguration for loss minimization based on modified honey bee mating optimization algorithm

This paper presents an efficient algorithm for multi-objective distribution feeder reconfiguration based on Modified Honey Bee Mating Optimization (MHBMO) approach. The main objective of the Distribution feeder reconfiguration (DFR) is to minimize the real power loss, deviation of the nodes’ voltage. Because of the fact that the objectives are different and no commensurable, it is difficult to solve the problem by conventional approaches that may optimize a single objective. So the metahuristic algorithm has been applied to this problem. This paper describes the full algorithm to Objective functions paid, The results of simulations on a 32 bus distribution system is given and shown high accuracy and optimize the proposed algorithm in power loss minimization.

An algorithm for the minimization of two-level multiple-output networks.

Vita.

CVaR minimization by the SRA algorithm

Using the risk measure CV aR in �nancial analysis has become more and more popular recently. In this paper we apply CV aR for portfolio optimization. The problem is formulated as a two-stage stochastic programming model, and the SRA algorithm, a recently developed heuristic algorithm, is applied for minimizing CV aR.