Interpretación geométrica de redes neuronales recurrentes discretas mediante grafos completos

El objetivo del presente trabajo de investigación es explorar nuevas técnicas de implementación, basadas en grafos, para las Redes de Neuronas, con el fin de simplificar y optimizar las arquitecturas y la complejidad computacional de las mismas. Hemos centrado nuestra atención en una clase de Red de Neuronas: las Redes de Neuronas Recursivas (RNR), también conocidas como redes de Hopfield. El problema de obtener la matriz sináptica asociada con una RNR imponiendo un determinado número de vectores como puntos fijos, no está en absoluto resuelto, el número de vectores prototipo que pueden ser almacenados en la red, cuando se utiliza la ley de Hebb, es bastante limitado, la red se satura rápidamente cuando se pretende almacenar nuevos prototipos. La ley de Hebb necesita, por tanto, ser revisada. Algunas aproximaciones dirigidas a solventar dicho problema, han sido ya desarrolladas. Nosotros hemos desarrollado una nueva aproximación en la forma de implementar una RNR en orden a solucionar estos problemas. La matriz sináptica es obtenida mediante la superposición de las componentes de los vectores prototipo, sobre los vértices de un Grafo, lo cual puede ser también interpretado como una coloración de dicho grafo. Cuando el periodo de entrenamiento se termina, la matriz de adyacencia del Grafo Resultante o matriz de pesos, presenta ciertas propiedades por las cuales dichas matrices serán llamadas tetraédricas. La energía asociada a cualquier estado de la red es representado por un punto (a,b) de R2. Cada uno de los puntos de energía asociados a estados que disten lo mismo del vector cero está localizado sobre la misma línea de energía de R2. El espacio de vectores de estado puede, por tanto, clasificarse en n clases correspondientes a cada una de las n diferentes distancias que puede tener cualquier vector al vector cero. La matriz (n x n) de pesos puede reducirse a un n-vector; de esta forma, tanto el tiempo de computación como el espacio de memoria requerido par almacenar los pesos, son simplificados y optimizados. En la etapa de recuperación, es introducido un vector de parámetros R2, éste es utilizado para controlar la capacidad de la red: probaremos que lo mayor es la componente a¡, lo menor es el número de puntos fijos pertenecientes a la línea de energía R¡. Una vez que la capacidad de la red ha sido controlada mediante este parámetro, introducimos otro parámetro, definido como la desviación del vector de pesos relativos, este parámetro sirve para disminuir ostensiblemente el número de parásitos. A lo largo de todo el trabajo, hemos ido desarrollando un ejemplo, el cual nos ha servido para ir corroborando los resultados teóricos, los algoritmos están escritos en un pseudocódigo, aunque a su vez han sido implamentados utilizando el paquete Mathematica 2.2., mostrándolos en un volumen suplementario al texto.---ABSTRACT---The aim of the present research is intended to explore new specifícation techniques of Neural Networks based on Graphs to be used in the optimization and simplification of Network Architectures and Computational Complexhy. We have focused our attention in a, well known, class of Neural Networks: the Recursive Neural Networks, also known as Hopfield's Neural Networks. The general problem of constructing the synaptic matrix associated with a Recursive Neural Network imposing some vectors as fixed points is fer for completery solved, the number of prototype vectors (learning patterns) which can be stored by Hebb's law is rather limited and the memory will thus quickly reach saturation if new prototypes are continuously acquired in the course of time. Hebb's law needs thus to be revised in order to allow new prototypes to be stored at the expense of the older ones. Some approaches related with this problem has been developed. We have developed a new approach of implementing a Recursive Neural Network in order to sob/e these kind of problems, the synaptic matrix is obtained superposing the components of the prototype vectors over the vértices of a Graph which may be interpreted as a coloring of the Graph. When training is finished the adjacency matrix of the Resulting Graph or matrix of weights presents certain properties for which it may be called a tetrahedral matrix The energy associated to any possible state of the net is represented as a point (a,b) in R2. Every one of the energy points associated with state-vectors having the same Hamming distance to the zero vector are located over the same energy Une in R2. The state-vector space may be then classified in n classes according to the n different possible distances firom any of the state-vectors to the zero vector The (n x n) matrix of weights may also be reduced to a n-vector of weights, in this way the computational time and the memory space required for obtaining the weights is optimized and simplified. In the recall stage, a parameter vectora is introduced, this parameter is used for controlling the capacity of the net: it may be proved that the bigger is the r, component of J, the lower is the number of fixed points located in the r¡ energy line. Once the capacity of the net has been controlled by the ex parameter, we introduced other parameter, obtained as the relative weight vector deviation parameter, in order to reduce the number of spurious states. All along the present text, we have also developed an example, which serves as a prove for the theoretical results, the algorithms are shown in a pseudocode language in the text, these algorithm so as the graphics have been developed also using the Mathematica 2.2. mathematical package which are shown in a supplementary volume of the text.

In utero exposure to cigarette chemicals induces sex-specific disruption of one-carbon metabolism and DNA methylation in the human fetal liver

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Acknowledgements: We thank Ms Margaret Fraser, Ms Samantha Flannigan, and Dr Wing Yee Kwong for their expert assistance. The staff at Grampian NHS Pregnancy Counselling Service were essential for collecting fetuses. We thank Professor Geoffrey Hammond and Dr Marc Simard, University of British Colombia for helpful comments on the manuscript. Supported by grants as follows: Scottish Senior Clinical Fellowship (AJD); Chief Scientist Office (Scottish Executive, CZG/1/109 to PAF, & CZG/4/742 (PAF & PJOS); NHS Grampian Endowments 08/02 (PAF, SB & PJOS); the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no 212885 (PAF & SMR); the Medical Research Council grants MR/L010011/1 (PAF & PJOS) and MR/K018310/1 (AJD). None of the funding bodies played any role in the design, collection, analysis, and interpretation of data, in the writing of the manuscript, nor in the decision to submit the manuscript for publication

Validez de constructo de tres escalas de satisfacción del paciente mediante la estrategia de matrices multirrasgo-multimétodo

Se emplea el diseño de las matrices multirrasgo-multimétodo (MTMM) en la evaluación de la satisfacción del paciente. La muestra, extraída al azar simple, fue de 254 pacientes ingresados en tres hospitales del Servei Valencià de Salut de la provincia de Alicante, mayores de 16 años, conscientes y orientados. Los instrumentos de medida fueron tres escalas de satisfacción, dos de carácter general y una específica con los cuidados de enfermería, todas autoinformes. Los rasgos evaluados fueron varias dimensiones de satisfacción, y los métodos tres tipos de formulación de items y escalas de respuesta. Se ha empleado el análisis factorial confirmatorio, siguiéndose la estrategia de constrastar varios modelos alternativos (Widaman, 1985; Marsh, 1989). Los resulta dos indican que: la varianza de método es elevada, superior a la de rasgos; existe validez convergente; los rasgos están altamente correlacionados, pero hay evidencia de validez discriminante; dos métodos están altamente correlacionados; y no se ha podido estimar el modelo general de matrices MTMM.

An optimized pseudorandom generator using packed matrices

Most cryptographic services and information security protocols require a dependable source of random data; pseudorandom generators are convenient and efficient for this application working as one of the basic foundation blocks on which to build the required security infrastructure. We propose a modification of a previously published matricial pseudorandom generator that significantly improves performance and security by using word packed matrices and modifying key scheduling and bit extraction schemes. The resulting generator is then successfully compared to world class standards.

Análisis de las relaciones morfología-propiedades en nanocompuestos basados en matrices de copolímeros de bloque

El objetivo principal de la presente investigación ha sido desarrollar una nueva clase de materiales nanocompuestos orgánicos-inorgánicos basados en la capacidad de los copolímeros de bloque de auto-organizarse promoviendo la dispersión de nanopartículas, así como relacionar las diferentes morfologías obtenidas con las propiedades finales de los nanocompuestos. Para generar la nanoestructuración de estos nanocompuestos basados en copolímeros de bloque, como el poli(estireno-b-isopreno-b-estireno) (SIS) y el poli(estireno-b-butadieno-b-estireno) (SBS) en nanopartículas de plata, se han utilizado los conceptos de compatibilización y confinamiento. Es decir, las nanopartículas inorgánicas se confinaron en una sola fase del copolímero de bloque mediante tratamientos superficiales y su funcionalización física. En particular, se utilizaron surfactantes (el cloruro de tetrametilamonio, TMAC, y el dodecanotiol, DT) para favorecer la interacción entre las nanopartículas inorgánicas y la matriz polimérica. Teniendo en cuenta los cálculos teóricos de los parámetros de solubilidad obtenidos mediante la teoría de Hoftizer-Van Krevelen, y la electronegatividad propia de los diferentes elementos, los dos surfactantes elegidos tienen una muy buena compatibilidad con el bloque de estireno favoreciendo la localización de las nanopartículas de plata en este bloque.

Majorana Zero Modes in Graphene

A clear demonstration of topological superconductivity (TS) and Majorana zero modes remains one of the major pending goals in the field of topological materials. One common strategy to generate TS is through the coupling of an s-wave superconductor to a helical half-metallic system. Numerous proposals for the latter have been put forward in the literature, most of them based on semiconductors or topological insulators with strong spin-orbit coupling. Here, we demonstrate an alternative approach for the creation of TS in graphene-superconductor junctions without the need for spin-orbit coupling. Our prediction stems from the helicity of graphene’s zero-Landau-level edge states in the presence of interactions and from the possibility, experimentally demonstrated, of tuning their magnetic properties with in-plane magnetic fields. We show how canted antiferromagnetic ordering in the graphene bulk close to neutrality induces TS along the junction and gives rise to isolated, topologically protected Majorana bound states at either end. We also discuss possible strategies to detect their presence in graphene Josephson junctions through Fraunhofer pattern anomalies and Andreev spectroscopy. The latter, in particular, exhibits strong unambiguous signatures of the presence of the Majorana states in the form of universal zero-bias anomalies. Remarkable progress has recently been reported in the fabrication of the proposed type of junctions, which offers a promising outlook for Majorana physics in graphene systems.

Zero-non-zero patterned vector error correction modeling for I(2) cointegrated time series with applications in testing PPP and stock market relationships

Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero entries in all their coefficient matrices. However, applications of VECM models to financial market data have revealed that zero entries are often a necessary part of efficient modelling. In such cases, the use of full-order VECM models may lead to incorrect inferences. Specifically, if indirect causality or Granger non-causality exists among the variables, the use of over-parameterised full-order VECM models may weaken the power of statistical inference. In this paper, it is argued that the zero–non-zero (ZNZ) patterned VECM is a more straightforward and effective means of testing for both indirect causality and Granger non-causality. For a ZNZ patterned VECM framework for time series of integrated order two, we provide a new algorithm to select cointegrating and loading vectors that can contain zero entries. Two case studies are used to demonstrate the usefulness of the algorithm in tests of purchasing power parity and a three-variable system involving the stock market.

A study of the effects of postcure treatments on polyester-melamine coating matrices

The effect of postcure high energy (gamma), ultraviolet (UV) and thermal treatment on the properties of polyester-melamine clearcoats of a range of compositions has been investigated. Two initial cure conditions were used, of which one was '' optimally '' cured and the other undercured. It was found that postcure treatments, particularly gamma and UV, led to coatings of similar mechanical and thermal properties irrespective of initial cure, although the change in properties on postcure treatment was greater for the under-cured samples. The results were interpreted in terms of the effect of the treatments on the structure of the crosslinked matrices. The study suggests the possibility of the development of a dual-cure process for polyester-melamines, whereby cure optimization and property improvement can be achieved. This could also be used to '' correct '' for small variations in thermal cure levels brought about by adventitious online fluctuations in cure oven conditions.

Evaluating zero error noise thresholds by replica method for Gallager code ensembles

The replica method, developed in statistical physics, is employed in conjunction with Gallager's methodology to accurately evaluate zero error noise thresholds for Gallager code ensembles. Our approach generally provides more optimistic evaluations than those reported in the information theory literature for sparse matrices; the difference vanishes as the parity check matrix becomes dense.

A Characterization of Varieties of Associative Algebras of Exponent two

∗The first author was partially supported by MURST of Italy; the second author was par- tially supported by RFFI grant 99-01-00233.

Fermat's Equation in Matrices

The Fermat equation is solved in integral two by two matrices of determinant one as well as in finite order integral three by three matrices.

Differential Balanced Trees and (0,1) Matrices

* The research was supported by INTAS 00-397 and 00-626 Projects.

An inconsistency control system based on incomplete pairwise comparison matrices

Incomplete pairwise comparison matrix was introduced by Harker in 1987 for the case in which the decision maker does not fill in the whole matrix completely due to, e.g., time limitations. However, incomplete matrices occur in a natural way even if the decision maker provides a completely filled in matrix in the end. In each step of the total n(n–1)/2, an incomplete pairwise comparison is given, except for the last one where the matrix turns into complete. Recent results on incomplete matrices make it possible to estimate inconsistency indices CR and CM by the computation of tight lower bounds in each step of the filling in process. Additional information on ordinal inconsistency is also provided. Results can be applied in any decision support system based on pairwise comparison matrices. The decision maker gets an immediate feedback in case of mistypes, possibly causing a high level of inconsistency.

Solving the Least Squares Method problem in the AHP for 3 X 3 and 4 X 4 matrices

The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM) are of the possible tools for computing the priorities of the alternatives. A method for generating all the solutions of the LSM problem for 3 × 3 and 4 × 4 matrices is discussed in the paper. Our algorithms are based on the theory of resultants.

On Saaty's and Koczkodaj's inconsistencies of pairwise comparison matrices

The aim of the paper is to obtain some theoretical and numerical properties of Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices (PRM). In the case of 3 × 3 PRM, a differentiable one-to-one correspondence is given between Saaty’s inconsistency ratio and Koczkodaj’s inconsistency index based on the elements of PRM. In order to make a comparison of Saaty’s and Koczkodaj’s inconsistencies for 4 × 4 pairwise comparison matrices, the average value of the maximal eigenvalues of randomly generated n × n PRM is formulated, the elements aij (i < j) of which were randomly chosen from the ratio scale ... ... with equal probability 1/(2M − 1) and a ji is defined as 1/a ij . By statistical analysis, the empirical distributions of the maximal eigenvalues of the PRM depending on the dimension number are obtained. As the dimension number increases, the shape of distributions gets similar to that of the normal ones. Finally, the inconsistency of asymmetry is dealt with, showing a different type of inconsistency.