Differential resultants of super essential systems of linear OD-polynomials

The sparse differential resultant dres(P) of an overdetermined system P of generic nonhomogeneous ordinary differential polynomials, was formally defined recently by Li, Gao and Yuan (2011). In this note, a differential resultant formula dfres(P) is defined and proved to be nonzero for linear "super essential" systems. In the linear case, dres(P) is proved to be equal, up to a nonzero constant, to dfres(P*) for the supper essential subsystem P* of P.

On the Absence of Carrier Drift in Two-Terminal Devices and the Origin of Their Lowest Resistance per Carrier RK= h/q^2

After a criticism on today’s model for electrical noise in resistors, we pass to use a Quantum-compliant model based on the discreteness of electrical charge in a complex Admittance. From this new model we show that carrier drift viewed as charged particle motion in response to an electric field is unlike to occur in bulk regions of Solid-State devices where carriers react as dipoles against this field. The absence of the shot noise that charges drifting in resistors should produce and the evolution of the Phase Noise with the active power existing in the resonators of L-C oscillators, are two effects added in proof for this conduction model without carrier drift where the resistance of any two-terminal device becomes discrete and has a minimum value per carrier that is the Quantum resistance RK/(2pi)

Learning Bayesian networks from data by the incremental compilation of new network polynomials

Probabilistic graphical models are a huge research field in artificial intelligence nowadays. The scope of this work is the study of directed graphical models for the representation of discrete distributions. Two of the main research topics related to this area focus on performing inference over graphical models and on learning graphical models from data. Traditionally, the inference process and the learning process have been treated separately, but given that the learned models structure marks the inference complexity, this kind of strategies will sometimes produce very inefficient models. With the purpose of learning thinner models, in this master thesis we propose a new model for the representation of network polynomials, which we call polynomial trees. Polynomial trees are a complementary representation for Bayesian networks that allows an efficient evaluation of the inference complexity and provides a framework for exact inference. We also propose a set of methods for the incremental compilation of polynomial trees and an algorithm for learning polynomial trees from data using a greedy score+search method that includes the inference complexity as a penalization in the scoring function.

Conditional density approximations with mixtures of polynomials

Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities is found. We illustrate and study the methods using data sampled from known parametric distributions, and we demonstrate their applicability by learning models based on real neuroscience data. Finally, we compare the performance of the proposed methods with an approach for learning mixtures of truncated basis functions (MoTBFs). The empirical results show that the proposed methods generally yield models that are comparable to or significantly better than those found using the MoTBF-based method.

Orthogonal MCMC algorithms

Monte Carlo (MC) methods are widely used in signal processing, machine learning and stochastic optimization. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce a novel parallel interacting MCMC scheme, where the parallel chains share information using another MCMC technique working on the entire population of current states. These parallel ?vertical? chains are led by random-walk proposals, whereas the ?horizontal? MCMC uses a independent proposal, which can be easily adapted by making use of all the generated samples. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error, as well as robustness w.r.t. to initial values and parameter choice.

Experimento de propagación en banda Q con Alphasat: Técnicas para la compensación del desapuntamiento

El grupo de investigación GTIC-Radiocomunicaciones de la Universidad Politécnica de Madrid (UPM) participa en uno de los experimentos de propagación de APEX (Alphasat Propagation Experiment), denominado Alphasat propagation experiment by measuring the copolar level of the Q-Band beacon at 39.4 GHz. El experimento comenzó en abril de 2014, midiendo la señal de 39,4 GHz. Durante los primeros meses hasta septiembre de 2014, se hicieron medidas con apuntamiento fijo. El satélite no es geoestacionario sino que tiene una cierta inclinación, por lo que su posición aparente no es fija, describiendo una pequeña elipse en el cielo. Como consecuencia de esto se produce una variación sistemática en el nivel de la señal recibida que hay que eliminar. El presente Trabajo fin de Grado recoge técnicas útiles para llevar a cabo la compensación del desapuntamiento producido por el apuntamiento fijo configurado en el receptor diseñado por el grupo de investigación GTIC-Radiocomunicaciones de la UPM. El conjunto de datos utilizado, ha sido preprocesado con anterioridad llevándose a cabo un proceso de marcado y sincronización de los datos obtenidos a través de la baliza a 39,4 GHz enviada desde el Alphasat. A lo largo del documento se interpretarán y compararán los resultados obtenidos mediante gráficas elaboradas tras la aplicación de las técnicas que se describen en el desarrollo del mismo.

Bivariate Krawtchouk polynomials: Inversion and connection problems with the NAVIMA algorithm

In this paper we present a recurrent procedure to solve an inversion problem for monic bivariate Krawtchouk polynomials written in vector column form, giving its solution explicitly. As a by-product, a general connection problem between two vector column of monic bivariate Krawtchouk families is also explicitly solved. Moreover, in the non monic case and also for Krawtchouk families, several expansion formulas are given, but for polynomials written in scalar form.