Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Wavelet estimation in diffusions with periodicity

Wir betrachten einen zeitlich inhomogenen Diffusionsprozess, der durch eine stochastische Differentialgleichung gegeben wird, deren Driftterm ein deterministisches T-periodisches Signal beinhaltet, dessen Periodizität bekannt ist. Dieses Signal sei in einem Besovraum enthalten. Wir schätzen es mit Hilfe eines nichtparametrischen Waveletschätzers. Unser Schätzer ist von einem Wavelet-Dichteschätzer mit Thresholding inspiriert, der 1996 in einem klassischen iid-Modell von Donoho, Johnstone, Kerkyacharian und Picard konstruiert wurde. Unter gewissen Ergodizitätsvoraussetzungen an den Prozess können wir nichtparametrische Konvergenzraten angegeben, die bis auf einen logarithmischen Term den Raten im klassischen iid-Fall entsprechen. Diese Raten werden mit Hilfe von Orakel-Ungleichungen gezeigt, die auf Ergebnissen über Markovketten in diskreter Zeit von Clémencon, 2001, beruhen. Außerdem betrachten wir einen technisch einfacheren Spezialfall und zeigen einige Computersimulationen dieses Schätzers.

Evolutionary forces shaping genomic islands of population differentiation in humans

Background Levels of differentiation among populations depend both on demographic and selective factors: genetic drift and local adaptation increase population differentiation, which is eroded by gene flow and balancing selection. We describe here the genomic distribution and the properties of genomic regions with unusually high and low levels of population differentiation in humans to assess the influence of selective and neutral processes on human genetic structure. Methods Individual SNPs of the Human Genome Diversity Panel (HGDP) showing significantly high or low levels of population differentiation were detected under a hierarchical-island model (HIM). A Hidden Markov Model allowed us to detect genomic regions or islands of high or low population differentiation. Results Under the HIM, only 1.5% of all SNPs are significant at the 1% level, but their genomic spatial distribution is significantly non-random. We find evidence that local adaptation shaped high-differentiation islands, as they are enriched for non-synonymous SNPs and overlap with previously identified candidate regions for positive selection. Moreover there is a negative relationship between the size of islands and recombination rate, which is stronger for islands overlapping with genes. Gene ontology analysis supports the role of diet as a major selective pressure in those highly differentiated islands. Low-differentiation islands are also enriched for non-synonymous SNPs, and contain an overly high proportion of genes belonging to the 'Oncogenesis' biological process. Conclusions Even though selection seems to be acting in shaping islands of high population differentiation, neutral demographic processes might have promoted the appearance of some genomic islands since i) as much as 20% of islands are in non-genic regions ii) these non-genic islands are on average two times shorter than genic islands, suggesting a more rapid erosion by recombination, and iii) most loci are strongly differentiated between Africans and non-Africans, a result consistent with known human demographic history.

Offline grammar-based recognition of handwritten sentences

This paper proposes a sequential coupling of a Hidden Markov Model (HMM) recognizer for offline handwritten English sentences with a probabilistic bottom-up chart parser using Stochastic Context-Free Grammars (SCFG) extracted from a text corpus. Based on extensive experiments, we conclude that syntax analysis helps to improve recognition rates significantly.

A Pseudolikelihood Approach for Simultaneous Analysis of Array Comparative Genomic Hybridizations (aCGH)

DNA sequence copy number has been shown to be associated with cancer development and progression. Array-based Comparative Genomic Hybridization (aCGH) is a recent development that seeks to identify the copy number ratio at large numbers of markers across the genome. Due to experimental and biological variations across chromosomes and across hybridizations, current methods are limited to analyses of single chromosomes. We propose a more powerful approach that borrows strength across chromosomes and across hybridizations. We assume a Gaussian mixture model, with a hidden Markov dependence structure, and with random effects to allow for intertumoral variation, as well as intratumoral clonal variation. For ease of computation, we base estimation on a pseudolikelihood function. The method produces quantitative assessments of the likelihood of genetic alterations at each clone, along with a graphical display for simple visual interpretation. We assess the characteristics of the method through simulation studies and through analysis of a brain tumor aCGH data set. We show that the pseudolikelihood approach is superior to existing methods both in detecting small regions of copy number alteration and in accurately classifying regions of change when intratumoral clonal variation is present.

EVALUATING INFRASTRUCTURE PERFORMANCE TO ASSIST FACILITY MANAGEMENT TOWARD SUSTAINABLE SYSTEMS

Civil infrastructure provides essential services for the development of both society and economy. It is very important to manage systems efficiently to ensure sound performance. However, there are challenges in information extraction from available data, which also necessitates the establishment of methodologies and frameworks to assist stakeholders in the decision making process. This research proposes methodologies to evaluate systems performance by maximizing the use of available information, in an effort to build and maintain sustainable systems. Under the guidance of problem formulation from a holistic view proposed by Mukherjee and Muga, this research specifically investigates problem solving methods that measure and analyze metrics to support decision making. Failures are inevitable in system management. A methodology is developed to describe arrival pattern of failures in order to assist engineers in failure rescues and budget prioritization especially when funding is limited. It reveals that blockage arrivals are not totally random. Smaller meaningful subsets show good random behavior. Additional overtime failure rate is analyzed by applying existing reliability models and non-parametric approaches. A scheme is further proposed to depict rates over the lifetime of a given facility system. Further analysis of sub-data sets is also performed with the discussion of context reduction. Infrastructure condition is another important indicator of systems performance. The challenges in predicting facility condition are the transition probability estimates and model sensitivity analysis. Methods are proposed to estimate transition probabilities by investigating long term behavior of the model and the relationship between transition rates and probabilities. To integrate heterogeneities, model sensitivity is performed for the application of non-homogeneous Markov chains model. Scenarios are investigated by assuming transition probabilities follow a Weibull regressed function and fall within an interval estimate. For each scenario, multiple cases are simulated using a Monte Carlo simulation. Results show that variations on the outputs are sensitive to the probability regression. While for the interval estimate, outputs have similar variations to the inputs. Life cycle cost analysis and life cycle assessment of a sewer system are performed comparing three different pipe types, which are reinforced concrete pipe (RCP) and non-reinforced concrete pipe (NRCP), and vitrified clay pipe (VCP). Life cycle cost analysis is performed for material extraction, construction and rehabilitation phases. In the rehabilitation phase, Markov chains model is applied in the support of rehabilitation strategy. In the life cycle assessment, the Economic Input-Output Life Cycle Assessment (EIO-LCA) tools are used in estimating environmental emissions for all three phases. Emissions are then compared quantitatively among alternatives to support decision making.

Improved cerebellar tissue classification on magnetic resonance images of brain.

PURPOSE: To develop and implement a method for improved cerebellar tissue classification on the MRI of brain by automatically isolating the cerebellum prior to segmentation. MATERIALS AND METHODS: Dual fast spin echo (FSE) and fluid attenuation inversion recovery (FLAIR) images were acquired on 18 normal volunteers on a 3 T Philips scanner. The cerebellum was isolated from the rest of the brain using a symmetric inverse consistent nonlinear registration of individual brain with the parcellated template. The cerebellum was then separated by masking the anatomical image with individual FLAIR images. Tissues in both the cerebellum and rest of the brain were separately classified using hidden Markov random field (HMRF), a parametric method, and then combined to obtain tissue classification of the whole brain. The proposed method for tissue classification on real MR brain images was evaluated subjectively by two experts. The segmentation results on Brainweb images with varying noise and intensity nonuniformity levels were quantitatively compared with the ground truth by computing the Dice similarity indices. RESULTS: The proposed method significantly improved the cerebellar tissue classification on all normal volunteers included in this study without compromising the classification in remaining part of the brain. The average similarity indices for gray matter (GM) and white matter (WM) in the cerebellum are 89.81 (+/-2.34) and 93.04 (+/-2.41), demonstrating excellent performance of the proposed methodology. CONCLUSION: The proposed method significantly improved tissue classification in the cerebellum. The GM was overestimated when segmentation was performed on the whole brain as a single object.

Evaluating statistical methods used to estimate the number of postsynaptic receptors.

Calcium levels in spines play a significant role in determining the sign and magnitude of synaptic plasticity. The magnitude of calcium influx into spines is highly dependent on influx through N-methyl D-aspartate (NMDA) receptors, and therefore depends on the number of postsynaptic NMDA receptors in each spine. We have calculated previously how the number of postsynaptic NMDA receptors determines the mean and variance of calcium transients in the postsynaptic density, and how this alters the shape of plasticity curves. However, the number of postsynaptic NMDA receptors in the postsynaptic density is not well known. Anatomical methods for estimating the number of NMDA receptors produce estimates that are very different than those produced by physiological techniques. The physiological techniques are based on the statistics of synaptic transmission and it is difficult to experimentally estimate their precision. In this paper we use stochastic simulations in order to test the validity of a physiological estimation technique based on failure analysis. We find that the method is likely to underestimate the number of postsynaptic NMDA receptors, explain the source of the error, and re-derive a more precise estimation technique. We also show that the original failure analysis as well as our improved formulas are not robust to small estimation errors in key parameters.

Genome profiling of sterol synthesis shows convergent evolution in parasites and guides chemotherapeutic attack

Sterols are an essential class of lipids in eukaryotes, where they serve as structural components of membranes and play important roles as signaling molecules. Sterols are also of high pharmacological significance: cholesterol-lowering drugs are blockbusters in human health, and inhibitors of ergosterol biosynthesis are widely used as antifungals. Inhibitors of ergosterol synthesis are also being developed for Chagas's disease, caused by Trypanosoma cruzi. Here we develop an in silico pipeline to globally evaluate sterol metabolism and perform comparative genomics. We generate a library of hidden Markov model-based profiles for 42 sterol biosynthetic enzymes, which allows expressing the genomic makeup of a given species as a numerical vector. Hierarchical clustering of these vectors functionally groups eukaryote proteomes and reveals convergent evolution, in particular metabolic reduction in obligate endoparasites. We experimentally explore sterol metabolism by testing a set of sterol biosynthesis inhibitors against trypanosomatids, Plasmodium falciparum, Giardia, and mammalian cells, and by quantifying the expression levels of sterol biosynthetic genes during the different life stages of T. cruzi and Trypanosoma brucei. The phenotypic data correlate with genomic makeup for simvastatin, which showed activity against trypanosomatids. Other findings, such as the activity of terbinafine against Giardia, are not in agreement with the genotypic profile.

Genomics of Rapid Incipient Speciation in Sympatric Threespine Stickleback

Ecological speciation is the process by which reproductively isolated populations emerge as a consequence of divergent natural or ecologically-mediated sexual selection. Most genomic studies of ecological speciation have investigated allopatric populations, making it difficult to infer reproductive isolation. The few studies on sympatric ecotypes have focused on advanced stages of the speciation process after thousands of generations of divergence. As a consequence, we still do not know what genomic signatures of the early onset of ecological speciation look like. Here, we examined genomic differentiation among migratory lake and resident stream ecotypes of threespine stickleback reproducing in sympatry in one stream, and in parapatry in another stream. Importantly, these ecotypes started diverging less than 150 years ago. We obtained 34,756 SNPs with restriction-site associated DNA sequencing and identified genomic islands of differentiation using a Hidden Markov Model approach. Consistent with incipient ecological speciation, we found significant genomic differentiation between ecotypes both in sympatry and parapatry. Of 19 islands of differentiation resisting gene flow in sympatry, all were also differentiated in parapatry and were thus likely driven by divergent selection among habitats. These islands clustered in quantitative trait loci controlling divergent traits among the ecotypes, many of them concentrated in one region with low to intermediate recombination. Our findings suggest that adaptive genomic differentiation at many genetic loci can arise and persist in sympatry at the very early stage of ecotype divergence, and that the genomic architecture of adaptation may facilitate this.

Genome-wide algorithm for detecting CNV associations with diseases

SNP genotyping arrays have been developed to characterize single-nucleotide polymorphisms (SNPs) and DNA copy number variations (CNVs). The quality of the inferences about copy number can be affected by many factors including batch effects, DNA sample preparation, signal processing, and analytical approach. Nonparametric and model-based statistical algorithms have been developed to detect CNVs from SNP genotyping data. However, these algorithms lack specificity to detect small CNVs due to the high false positive rate when calling CNVs based on the intensity values. Association tests based on detected CNVs therefore lack power even if the CNVs affecting disease risk are common. In this research, by combining an existing Hidden Markov Model (HMM) and the logistic regression model, a new genome-wide logistic regression algorithm was developed to detect CNV associations with diseases. We showed that the new algorithm is more sensitive and can be more powerful in detecting CNV associations with diseases than an existing popular algorithm, especially when the CNV association signal is weak and a limited number of SNPs are located in the CNV.^

Técnicas de análisis, caracterización y detección de señales de voz en entornos acústicos adversos

Este trabajo de Tesis ha abordado el objetivo de dar robustez y mejorar la Detección de Actividad de Voz en entornos acústicos adversos con el fin de favorecer el comportamiento de muchas aplicaciones vocales, por ejemplo aplicaciones de telefonía basadas en reconocimiento automático de voz, aplicaciones en sistemas de transcripción automática, aplicaciones en sistemas multicanal, etc. En especial, aunque se han tenido en cuenta todos los tipos de ruido, se muestra especial interés en el estudio de las voces de fondo, principal fuente de error de la mayoría de los Detectores de Actividad en la actualidad. Las tareas llevadas a cabo poseen como punto de partida un Detector de Actividad basado en Modelos Ocultos de Markov, cuyo vector de características contiene dos componentes: la energía normalizada y la variación de la energía. Las aportaciones fundamentales de esta Tesis son las siguientes: 1) ampliación del vector de características de partida dotándole así de información espectral, 2) ajuste de los Modelos Ocultos de Markov al entorno y estudio de diferentes topologías y, finalmente, 3) estudio e inclusión de nuevas características, distintas de las del punto 1, para filtrar los pulsos de pronunciaciones que proceden de las voces de fondo. Los resultados de detección, teniendo en cuenta los tres puntos anteriores, muestran con creces los avances realizados y son significativamente mejores que los resultados obtenidos, bajo las mismas condiciones, con otros detectores de actividad de referencia. This work has been focused on improving the robustness at Voice Activity Detection in adverse acoustic environments in order to enhance the behavior of many vocal applications, for example telephony applications based on automatic speech recognition, automatic transcription applications, multichannel systems applications, and so on. In particular, though all types of noise have taken into account, this research has special interest in the study of pronunciations coming from far-field speakers, the main error source of most activity detectors today. The tasks carried out have, as starting point, a Hidden Markov Models Voice Activity Detector which a feature vector containing two components: normalized energy and delta energy. The key points of this Thesis are the following: 1) feature vector extension providing spectral information, 2) Hidden Markov Models adjustment to environment and study of different Hidden Markov Model topologies and, finally, 3) study and inclusion of new features, different from point 1, to reject the pronunciations coming from far-field speakers. Detection results, taking into account the above three points, show the advantages of using this method and are significantly better than the results obtained under the same conditions by other well-known voice activity detectors.

LiDAR simulation in modelled orchards to optimise the use of terretrial laser scanners and derived vegetative measures

Light detection and ranging (LiDAR) technology is beginning to have an impact on agriculture. Canopy volume and/or fruit tree leaf area can be estimated using terrestrial laser sensors based on this technology. However, the use of these devices may have different options depending on the resolution and scanning mode. As a consequence, data accuracy and LiDAR derived parameters are affected by sensor configuration, and may vary according to vegetative characteristics of tree crops. Given this scenario, users and suppliers of these devices need to know how to use the sensor in each case. This paper presents a computer program to determine the best configuration, allowing simulation and evaluation of different LiDAR configurations in various tree structures (or training systems). The ultimate goal is to optimise the use of laser scanners in field operations. The software presented generates a virtual orchard, and then allows the scanning simulation with a laser sensor. Trees are created using a hidden Markov tree (HMT) model. Varying the foliar structure of the orchard the LiDAR simulation was applied to twenty different artificially created orchards with or without leaves from two positions (lateral and zenith). To validate the laser sensor configuration, leaf surface of simulated trees was compared with the parameters obtained by LiDAR measurements: the impacted leaf area, the impacted total area (leaves and wood), and th impacted area in the three outer layers of leaves.

HF spectrum activity prediction model based on HMM for cognitive radio applications

Although most of the research on Cognitive Radio is focused on communication bands above the HF upper limit (30 MHz), Cognitive Radio principles can also be applied to HF communications to make use of the extremely scarce spectrum more efficiently. In this work we consider legacy users as primary users since these users transmit without resorting to any smart procedure, and our stations using the HFDVL (HF Data+Voice Link) architecture as secondary users. Our goal is to enhance an efficient use of the HF band by detecting the presence of uncoordinated primary users and avoiding collisions with them while transmitting in different HF channels using our broad-band HF transceiver. A model of the primary user activity dynamics in the HF band is developed in this work to make short-term predictions of the sojourn time of a primary user in the band and avoid collisions. It is based on Hidden Markov Models (HMM) which are a powerful tool for modelling stochastic random processes and are trained with real measurements of the 14 MHz band. By using the proposed HMM based model, the prediction model achieves an average 10.3% prediction error rate with one minute-long channel knowledge but it can be reduced when this knowledge is extended: with the previous 8 min knowledge, an average 5.8% prediction error rate is achieved. These results suggest that the resulting activity model for the HF band could actually be used to predict primary users activity and included in a future HF cognitive radio based station.

Efficiency improvement of HF communications using cognitive radio principles

Cognitive Radio principles can be applied to HF communications to make a more efficient use of the extremely scarce spectrum. In this contribution we focus on analyzing the usage of the available channels done by the legacy users, which are regarded as primary users since they are allowed to transmit without resorting any smart procedure, and consider the possibilities for our stations -over the HFDVL (HF Data+Voice Link) architecture- to participate as secondary users. Our goal is to enhance an efficient use of the HF band by detecting the presence of uncoordinated primary users and avoiding collisions with them while transmitting in different HF channels using our broad-band HF transceiver. A model of the primary user activity dynamics in the HF band is developed in this work. It is based on Hidden Markov Models (HMM) which are a powerful tool for modelling stochastic random processes, and is trained with real measurements from the 14 MHz band.