Network Synthesis

Contains research objectives and reports on three research objectives

Dynamic quantum clustering: a method for visual exploration of structures in data

A given set of data-points in some feature space may be associated with a Schrodinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schrodinger equation. Moreover, we approximate this Hamiltonian formalism by a truncated calculation within a set of Gaussian wave functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition or feature filtering.Comment: 15 pages, 9 figure

Identification of network modules by optimization of ratio association

We introduce a novel method for identifying the modular structures of a network based on the maximization of an objective function: the ratio association. This cost function arises when the communities detection problem is described in the probabilistic autoencoder frame. An analogy with kernel k-means methods allows to develop an efficient optimization algorithm, based on the deterministic annealing scheme. The performance of the proposed method is shown on a real data set and on simulated networks

Brownian motion in a non-homogeneous force field and photonic force microscope

The Photonic Force Microscope (PFM) is an opto-mechanical technique based on an optical trap that can be assumed to probe forces in microscopic systems. This technique has been used to measure forces in the range of pico- and femto-Newton, assessing the mechanical properties of biomolecules as well as of other microscopic systems. For a correct use of the PFM, the force field to measure has to be invariable (homogeneous) on the scale of the Brownian motion of the trapped probe. This condition implicates that the force field must be conservative, excluding the possibility of a rotational component. However, there are cases where these assumptions are not fulfilled Here, we show how to improve the PFM technique in order to be able to deal with these cases. We introduce the theory of this enhanced PFM and we propose a concrete analysis workflow to reconstruct the force field from the experimental time-series of the probe position. Furthermore, we experimentally verify some particularly important cases, namely the case of a conservative or rotational force-field

Research and applications: Artificial intelligence

The program is reported for developing techniques in artificial intelligence and their application to the control of mobile automatons for carrying out tasks autonomously. Visual scene analysis, short-term problem solving, and long-term problem solving are discussed along with the PDP-15 simulator, LISP-FORTRAN-MACRO interface, resolution strategies, and cost effectiveness

Fractal Descriptors in the Fourier Domain Applied to Color Texture Analysis

The present work proposes the development of a novel method to provide descriptors for colored texture images. The method consists in two steps. In the first, we apply a linear transform in the color space of the image aiming at highlighting spatial structuring relations among the color of pixels. In a second moment, we apply a multiscale approach to the calculus of fractal dimension based on Fourier transform. From this multiscale operation, we extract the descriptors used to discriminate the texture represented in digital images. The accuracy of the method is verified in the classification of two color texture datasets, by comparing the performance of the proposed technique to other classical and state-of-the-art methods for color texture analysis. The results showed an advantage of almost 3% of the proposed technique over the second best approach.Comment: Chaos, Volume 21, Issue 4, 201

Network Synthesis

Contains research objectives and reports on three research projects

Phase transitions in optimal unsupervised learning

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P = alpha N points that are uniformly distributed in all the directions but one on the N-dimensional sphere. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two gaussians of variable separation and width. The typical optimal performance is measured through the overlap Ropt=B.J* where J* is the optimal guess of the symmetry breaking direction. Within this general scenario, the learning curves Ropt(alpha) may present first order transitions if the clusters are narrow enough. Close to these transitions, high performance states can be obtained through the minimization of the corresponding optimal potential, although these solutions are metastable, and therefore not learnable, within the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper contains one new section, Bayesian versus optimal solutions, where we explain in detail the results supporting our claim that bayesian learning may not be optimal. Figures 4 of the first submission was difficult to understand. We replaced it by two new figures (Figs. 4 and 5 in this new version) containing more detail

Microstructure identification via detrended fluctuation analysis of ultrasound signals

We describe an algorithm for simulating ultrasound propagation in random one-dimensional media, mimicking different microstructures by choosing physical properties such as domain sizes and mass densities from probability distributions. By combining a detrended fluctuation analysis (DFA) of the simulated ultrasound signals with tools from the pattern-recognition literature, we build a Gaussian classifier which is able to associate each ultrasound signal with its corresponding microstructure with a very high success rate. Furthermore, we also show that DFA data can be used to train a multilayer perceptron which estimates numerical values of physical properties associated with distinct microstructures.Comment: Submitted to Phys. Rev.