A Simple Approach to the Global Regime of Gaussian Ensembles of Random Matrices

We present simple proofs of several basic facts of the global regime (the existence and the form of the non-random limiting Normalized Counting Measure of eigenvalues, and the central limit theorem for the trace of the resolvent) for ensembles of random matrices, whose probability law involves the Gaussian distribution. The main difference with previous proofs is the systematic use of the Poincare - Nash inequality, allowing us to obtain the O(n - 2) bounds for the variance of the normalized trace of the resolvent that are valid up to the real axis in the spectral parameter.Наведено прості доведення низки основних фактів стосовно глобального режиму (існування та вигляд невипадкової граничної нормалізованої рахуючої міри для власних значень, центральна гранична теорема для сліду резольвенти) для ансамблів випадкових матриць, до ймовірнісного закону яких входить гауссів розподіл. Головна відмінність від попередніх доведень полягає у систематичному використанні нерівності Пуанкаре - Неша, що дозволило отримати оцінки порядку O(n - 2) для дисперсії нормалізованого сліду резольвенти, які справджуються до дійсної осі відносно спектрального параметра

Modelos de procesamiento de la información en el cerebro aplicados a Sistemas Conexionistas: Redes NeuroGliales Artificiales y Deep Learning

Programa Oficial de Doutoramento en Tecnoloxías da Información e as Comunicacións. 5032V01[Resumen] En el campo de la Inteligencia Artificial, los sistemas conexionistas se han inspirado en las neuronas ya que, según la visión clásica de la Neurociencia, eran las únicas células con capacidad para procesar la información. Descubrimientos recientes de Neurociencia han demostrado que las células gliales tienen un papel clave en el procesamiento de la información en el cerebro. Basándose en estos descubrimientos se han desarrollado las Redes NeuroGliales Artificiales (RNGA) que cuentan con dos tipos de elementos de procesado, neuronas y astrocitos. En esta tesis se ha continuado con esta línea de investigación multidisciplinar que combina la Neurociencia y la Inteligencia Artificial. Para ello, se ha desarrollado un nuevo comportamiento de los astrocitos que actúan sobre la salida de las neuronas en las RNGA. Se ha realizado una comparación con las Redes de Neuronas Artificiales (RNA) en cinco problemas de clasificación y se ha demostrado que el nuevo comportamiento de los astrocitos mejora de manera significativa los resultados. Tras demostrar la capacidad de los astrocitos para procesar la información, en esta tesis se ha desarrollado además una nueva metodología que permite por primera vez la creación de redes Deep Learning conteniendo miles de neuronas y astrocitos, denominadas Deep Neuron-Astrocyte Networks (DANAN). Tras probarlas en un problema de regresión, las DANAN obtienen mejores resultados que las RNA. Esto permitirá evaluar comportamientos más complejos de los astrocitos en las redes de Deep Learning, pudiendo incluso crearse redes de astrocitos en un futuro próximo.[Resumo] No campo da Intelixencia Artificial, os sistemas conexionistas inspiráronse nas neuronas xa que, segundo a visión clásica da Neuronciencia, eran as únicas células con capacidade para procesar a información. Descubrimentos recentes de Neurociencia demostraron que as células gliais teñen un papel crave no procesamento da información no cerebro. Baseándose nestes descubrimentos desenvolvéronse as Redes NeuroGliales Artificiais (RNGA) que contan con dous tipos de elementos de procesado, neuronas e astrocitos. Nesta tese continuouse con esta liña de investigación multidisciplinar que combina a Neurociencia e a Intelixencia Artificial. Para iso, desenvolveuse un novo comportamento dos astrocitos que actúan sobre a saída das neuronas nas RNGA. Realizouse unha comparación coas Redes de Neuronas Artificiais (RNA) en cinco problemas de clasificación e demostrouse que o novo comportamento dos astrocitos mellora de xeito significativo os resultados. Tras demostrar a capacidade dos astrocitos para procesar a información, nesta tese desenvolveuse ademais unha nova metodoloxía que permite por primeira vez a creación de redes Deep Learning contendo miles de neuronas e astrocitos, denominadas Deep Neuron-Astrocyte Networks (DANAN). Tras probalas nun problema de regresión, as DANAN obteñen mellores resultados cas RNA. Isto permitirá avaliar comportamentos máis complexos dos astrocitos nas redes de Deep Learning, podendo ata crearse redes de astrocitos nun futuro próximo.[Abstract] In the field of Artificial Intelligence, connectionist systems have been inspired by neurons and, according to the classical view of neuroscience, they were the only cells capable of processing information. The latest advances in Neuroscience have shown that glial cells have a key role in the processing of information in the brain. Based on these discoveries, Artificial NeuroGlial Networks (RNGA) have been developed, which have two types of processing elements, neurons and astrocytes. In this thesis, this line of multidisciplinary research that combines Neuroscience and Artificial Intelligence has been continued. For this goal, a new behavior of the astrocytes that act on the output of the neurons in the RNGA has been developed. A comparison has been made with the Artificial Neuron Networks (ANN) in five classification problems and it has been demonstrated that the new behavior of the astrocytes significantly improves the results. After prove the capacity of astrocytes for information processing, in this thesis has been developed a new methodology that allows for the first time the creation of Deep Learning networks containing thousands of neurons and astrocytes, called Deep Neuron-Astrocyte Networks (DANAN). After testing them in a regression problem, the DANAN obtain better results than ANN. This allows testing more complexes astrocyte behaviors in Deep Learning networks, and even creates astrocyte networks in the near future

Spherical Model in a Random Field

We investigate the properties of the Gibbs states and thermodynamic observables of the spherical model in a random field. We show that on the low-temperature critical line the magnetization of the model is not a self-averaging observable, but it self-averages conditionally. We also show that an arbitrarily weak homogeneous boundary field dominates over fluctuations of the random field once the model transits into a ferromagnetic phase. As a result, a homogeneous boundary field restores the conventional self-averaging of thermodynamic observables, like the magnetization and the susceptibility. We also investigate the effective field created at the sites of the lattice by the random field, and show that at the critical temperature of the spherical model the effective field undergoes a transition into a phase with long-range correlations $\sim r^{4-d}$.Comment: 29 page

Parallel computing for brain simulation

[Abstract] Background: The human brain is the most complex system in the known universe, it is therefore one of the greatest mysteries. It provides human beings with extraordinary abilities. However, until now it has not been understood yet how and why most of these abilities are produced. Aims: For decades, researchers have been trying to make computers reproduce these abilities, focusing on both understanding the nervous system and, on processing data in a more efficient way than before. Their aim is to make computers process information similarly to the brain. Important technological developments and vast multidisciplinary projects have allowed creating the first simulation with a number of neurons similar to that of a human brain. Conclusion: This paper presents an up-to-date review about the main research projects that are trying to simulate and/or emulate the human brain. They employ different types of computational models using parallel computing: digital models, analog models and hybrid models. This review includes the current applications of these works, as well as future trends. It is focused on various works that look for advanced progress in Neuroscience and still others which seek new discoveries in Computer Science (neuromorphic hardware, machine learning techniques). Their most outstanding characteristics are summarized and the latest advances and future plans are presented. In addition, this review points out the importance of considering not only neurons: Computational models of the brain should also include glial cells, given the proven importance of astrocytes in information processing.Galicia. Consellería de Cultura, Educación e Ordenación Universitaria; GRC2014/049Galicia. Consellería de Cultura, Educación e Ordenación Universitaria; R2014/039Instituto de Salud Carlos III; PI13/0028

Deep Artificial Neural Networks and Neuromorphic Chips for Big Data Analysis: Pharmaceutical and Bioinformatics Applications

[Abstract] Over the past decade, Deep Artificial Neural Networks (DNNs) have become the state-of-the-art algorithms in Machine Learning (ML), speech recognition, computer vision, natural language processing and many other tasks. This was made possible by the advancement in Big Data, Deep Learning (DL) and drastically increased chip processing abilities, especially general-purpose graphical processing units (GPGPUs). All this has created a growing interest in making the most of the potential offered by DNNs in almost every field. An overview of the main architectures of DNNs, and their usefulness in Pharmacology and Bioinformatics are presented in this work. The featured applications are: drug design, virtual screening (VS), Quantitative Structure–Activity Relationship (QSAR) research, protein structure prediction and genomics (and other omics) data mining. The future need of neuromorphic hardware for DNNs is also discussed, and the two most advanced chips are reviewed: IBM TrueNorth and SpiNNaker. In addition, this review points out the importance of considering not only neurons, as DNNs and neuromorphic chips should also include glial cells, given the proven importance of astrocytes, a type of glial cell which contributes to information processing in the brain. The Deep Artificial Neuron–Astrocyte Networks (DANAN) could overcome the difficulties in architecture design, learning process and scalability of the current ML methods.Galicia. Consellería de Cultura, Educación e Ordenación Universitaria; GRC2014/049Galicia. Consellería de Cultura, Educación e Ordenación Universitaria; R2014/039Instituto de Salud Carlos III; PI13/0028

An Extended Variational Principle for the SK Spin-Glass Model

The recent proof by F. Guerra that the Parisi ansatz provides a lower bound on the free energy of the SK spin-glass model could have been taken as offering some support to the validity of the purported solution. In this work we present a broader variational principle, in which the lower bound, as well as the actual value, are obtained through an optimization procedure for which ultrametic/hierarchal structures form only a subset of the variational class. The validity of Parisi's ansatz for the SK model is still in question. The new variational principle may be of help in critical review of the issue.Comment: 4 pages, Revtex

Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements

The random banded matrices (RBM) whose diagonal elements fluctuate much stronger than the off-diagonal ones were introduced recently by Shepelyansky as a convenient model for coherent propagation of two interacting particles in a random potential. We treat the problem analytically by using the mapping onto the same supersymmetric nonlinear $\sigma-$model that appeared earlier in consideration of the standard RBM ensemble, but with renormalized parameters. A Lorentzian form of the local density of states and a two-scale spatial structure of the eigenfunctions revealed recently by Jacquod and Shepelyansky are confirmed by direct calculation of the distribution of eigenfunction components.Comment: 7 pages,RevTex, no figures Submitted to Phys.Rev.

Smooth analysis of the condition number and the least singular value

Let \a be a complex random variable with mean zero and bounded variance. Let $N_{n}$ be the random matrix of size $n$ whose entries are iid copies of \a and $M$ be a fixed matrix of the same size. The goal of this paper is to give a general estimate for the condition number and least singular value of the matrix $M + N_{n}$, generalizing an earlier result of Spielman and Teng for the case when \a is gaussian. Our investigation reveals an interesting fact that the "core" matrix $M$ does play a role on tail bounds for the least singular value of $M+N_{n}$. This does not occur in Spielman-Teng studies when \a is gaussian. Consequently, our general estimate involves the norm $\|M\|$. In the special case when $\|M\|$ is relatively small, this estimate is nearly optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde

General machine learning model, review, and experimental-theoretic study of magnolol activity in enterotoxigenic induced oxidative stress

[Abstract] This study evaluated the antioxidative effects of magnolol based on the mouse model induced by Enterotoxigenic Escherichia coli (E. coli, ETEC). All experimental mice were equally treated with ETEC suspensions (3.45×109 CFU/ml) after oral administration of magnolol for 7 days at the dose of 0, 100, 300 and 500 mg/kg Body Weight (BW), respectively. The oxidative metabolites and antioxidases for each sample (organism of mouse) were determined: Malondialdehyde (MDA), Nitric Oxide (NO), Glutathione (GSH), Myeloperoxidase (MPO), Catalase (CAT), Superoxide Dismutase (SOD), and Glutathione Peroxidase (GPx). In addition, we also determined the corresponding mRNA expressions of CAT, SOD and GPx as well as the Total Antioxidant Capacity (T-AOC). The experiment was completed with a theoretical study that predicts a series of 79 ChEMBL activities of magnolol with 47 proteins in 18 organisms using a Quantitative Structure- Activity Relationship (QSAR) classifier based on the Moving Averages (MAs) of Rcpi descriptors in three types of experimental conditions (biological activity with specific units, protein target and organisms). Six Machine Learning methods from Weka software were tested and the best QSAR classification model was provided by Random Forest with True Positive Rate (TPR) of 0.701 and Area under Receiver Operating Characteristic (AUROC) of 0.790 (test subset, 10-fold crossvalidation). The model is predicting if the new ChEMBL activities are greater or lower than the average values for the magnolol targets in different organisms.National Natural Science Foundation of China; 30972166Hunan Provincial Education Department; 08A031Hunan Provincial Innovation Foundation for Postgraduate; CX2011B304Hunan Provincial Innovation Foundation for Postgraduate; CX2014B300Xunta de Galicia; R2014/039Xunta de Galicia; GRC2014/049Ministerio de Economía y Competitividad; UNLC08-1E-002Ministerio de Economía y Competitividad; UNLC13-13-350

Level-Spacing Distributions and the Bessel Kernel

The level spacing distributions which arise when one rescales the Laguerre or Jacobi ensembles of hermitian matrices is studied. These distributions are expressible in terms of a Fredholm determinant of an integral operator whose kernel is expressible in terms of Bessel functions of order $\alpha$. We derive a system of partial differential equations associated with the logarithmic derivative of this Fredholm determinant when the underlying domain is a union of intervals. In the case of a single interval this Fredholm determinant is a Painleve tau function.Comment: 18 pages, resubmitted to make postscript compatible, no changes to manuscript conten