A graph-theoretical approach in brain functional networks. Possible implications in EEG studies

Abstract Background Recently, it was realized that the functional connectivity networks estimated from actual brain-imaging technologies (MEG, fMRI and EEG) can be analyzed by means of the graph theory, that is a mathematical representation of a network, which is essentially reduced to nodes and connections between them. Methods We used high-resolution EEG technology to enhance the poor spatial information of the EEG activity on the scalp and it gives a measure of the electrical activity on the cortical surface. Afterwards, we used the Directed Transfer Function (DTF) that is a multivariate spectral measure for the estimation of the directional influences between any given pair of channels in a multivariate dataset. Finally, a graph theoretical approach was used to model the brain networks as graphs. These methods were used to analyze the structure of cortical connectivity during the attempt to move a paralyzed limb in a group (N=5) of spinal cord injured patients and during the movement execution in a group (N=5) of healthy subjects. Results Analysis performed on the cortical networks estimated from the group of normal and SCI patients revealed that both groups present few nodes with a high out-degree value (i.e. outgoing links). This property is valid in the networks estimated for all the frequency bands investigated. In particular, cingulate motor areas (CMAs) ROIs act as ‘‘hubs’’ for the outflow of information in both groups, SCI and healthy. Results also suggest that spinal cord injuries affect the functional architecture of the cortical network sub-serving the volition of motor acts mainly in its local feature property. In particular, a higher local efficiency El can be observed in the SCI patients for three frequency bands, theta (3-6 Hz), alpha (7-12 Hz) and beta (13-29 Hz). By taking into account all the possible pathways between different ROI couples, we were able to separate clearly the network properties of the SCI group from the CTRL group. In particular, we report a sort of compensatory mechanism in the SCI patients for the Theta (3-6 Hz) frequency band, indicating a higher level of “activation” Ω within the cortical network during the motor task. The activation index is directly related to diffusion, a type of dynamics that underlies several biological systems including possible spreading of neuronal activation across several cortical regions. Conclusions The present study aims at demonstrating the possible applications of graph theoretical approaches in the analyses of brain functional connectivity from EEG signals. In particular, the methodological aspects of the i) cortical activity from scalp EEG signals, ii) functional connectivity estimations iii) graph theoretical indexes are emphasized in the present paper to show their impact in a real application.

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.

On the renormalization flow representation of field theory and some applications

In this thesis we discuss a representation of quantum mechanics and quantum and statistical field theory based on a functional renormalization flow equation for the one-particle-irreducible average effective action, and we employ it to get information on some specific systems.

Statistical mechanics of polymer models: rigorous results and applications

Monomer-dimer models are amongst the models in statistical mechanics which found application in many areas of science, ranging from biology to social sciences. This model describes a many-body system in which monoatomic and diatomic particles subject to hard-core interactions get deposited on a graph. In our work we provide an extension of this model to higher-order particles. The aim of our work is threefold: first we study the thermodynamic properties of the newly introduced model. We solve analytically some regular cases and find that, differently from the original, our extension admits phase transitions. Then we tackle the inverse problem, both from an analytical and numerical perspective. Finally we propose an application to aggregation phenomena in virtual messaging services.

A graph theoretic approach to testing associations between disparate sources of functional genomic data

The last few years have seen the advent of high-throughput technologies to analyze various properties of the transcriptome and proteome of several organisms. The congruency of these different data sources, or lack thereof, can shed light on the mechanisms that govern cellular function. A central challenge for bioinformatics research is to develop a unified framework for combining the multiple sources of functional genomics information and testing associations between them, thus obtaining a robust and integrated view of the underlying biology. We present a graph theoretic approach to test the significance of the association between multiple disparate sources of functional genomics data by proposing two statistical tests, namely edge permutation and node label permutation tests. We demonstrate the use of the proposed tests by finding significant association between a Gene Ontology-derived "predictome" and data obtained from mRNA expression and phenotypic experiments for Saccharomyces cerevisiae. Moreover, we employ the graph theoretic framework to recast a surprising discrepancy presented in Giaever et al. (2002) between gene expression and knockout phenotype, using expression data from a different set of experiments.

Fixed block configuration GDDs with block size 6 and (3, r)-regular graphs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Most of the definitions used in the thesis will be defined, and we provide a basic survey of topics in graph theory and design theory pertinent to the topics studied in this thesis. In Chapter 2, we are concerned with the study of fixed block configuration group divisible designs, GDD(n; m; k; λ1; λ2). We study those GDDs in which each block has configuration (s; t), that is, GDDs in which each block has exactly s points from one of the two groups and t points from the other. Chapter 2 begins with an overview of previous results and constructions for small group size and block sizes 3, 4 and 5. Chapter 2 is largely devoted to presenting constructions and results about GDDs with two groups and block size 6. We show the necessary conditions are sufficient for the existence of GDD(n, 2, 6; λ1, λ2) with fixed block configuration (3; 3). For configuration (1; 5), we give minimal or nearminimal index constructions for all group sizes n ≥ 5 except n = 10, 15, 160, or 190. For configuration (2, 4), we provide constructions for several families ofGDD(n, 2, 6; λ1, λ2)s. Chapter 3 addresses characterizing (3, r)-regular graphs. We begin with providing previous results on the well studied class of (2, r)-regular graphs and some results on the structure of large (t; r)-regular graphs. In Chapter 3, we completely characterize all (3, 1)-regular and (3, 2)-regular graphs, as well has sharpen existing bounds on the order of large (3, r)- regular graphs of a certain form for r ≥ 3. Finally, the appendix gives computational data resulting from Sage and C programs used to generate (3, 3)-regular graphs on less than 10 vertices.

Edge coloring BIBDS and constructing MOELRs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Some historical uses and background are touched upon as well. The majority of the definitions are contained within this chapter as well. In Chapter 2 we consider the question whether one can decompose λ copies of monochromatic Kv into copies of Kk such that each copy of the Kk contains at most one edge from each Kv. This is called a proper edge coloring (Hurd, Sarvate, [29]). The majority of the content in this section is a wide variety of examples to explain the constructions used in Chapters 3 and 4. In Chapters 3 and 4 we investigate how to properly color BIBD(v, k, λ) for k = 4, and 5. Not only will there be direct constructions of relatively small BIBDs, we also prove some generalized constructions used within. In Chapter 5 we talk about an alternate solution to Chapters 3 and 4. A purely graph theoretical solution using matchings, augmenting paths, and theorems about the edgechromatic number is used to develop a theorem that than covers all possible cases. We also discuss how this method performed compared to the methods in Chapters 3 and 4. In Chapter 6, we switch topics to Latin rectangles that have the same number of symbols and an equivalent sized matrix to Latin squares. Suppose ab = n2. We define an equitable Latin rectangle as an a × b matrix on a set of n symbols where each symbol appears either [b/n] or [b/n] times in each row of the matrix and either [a/n] or [a/n] times in each column of the matrix. Two equitable Latin rectangles are orthogonal in the usual way. Denote a set of ka × b mutually orthogonal equitable Latin rectangles as a k–MOELR(a, b; n). We show that there exists a k–MOELR(a, b; n) for all a, b, n where k is at least 3 with some exceptions.

The Theory of Alloy Deposition and The Effect of a Rotating Cathode Upon Such Deposition, with Special Attention to the Possibility of Depositing Sterling Silver

In the past few years a great deal of atten­tion has been given to the electrodeposition of alloys. For the main part, this investigation has been of scien­tific interest only; but in a few instances, such work has attained commercial importance.

What is the Relation between Human Practical Action and an Accompanying Discourse? Discussing the Status of Practical Theory

The article discusses the function of an accompanying discourse in relation to the genesis of human practical action. On the one side, theory cannot be taken as the ground for practical action; practical action is not a realisation of intentions. On the other hand, human practical action is accompanied by series of explanations, justifications, declarations of intent, pre‑ and post-rationalisations, motivations etc. These accompanying discourses seem in one way or the other to be necessary for the actual realisation of human practical action. Following Pierre Bourdieu, it is suggested that an accompanying discourse cannot in a meaningful manner be separated from the human practical action, that practical theory should be regarded not as theory but as part of practice, and that practical theory first of all provides a common language for talking about practice and hence for reproducing a fundamentally arbitrary idea of the genesis of human practical action. Parallels are drawn to the education/formal training of semi-professionals.

Importance of vegetation, topography and flow paths for water transit times of base flow in alpine headwater catchments

The mean transit time (MTT) of water in a catchment gives information about storage, flow paths, sources of water and thus also about retention and release of solutes in a catchment. To our knowledge there are only a few catchment studies on the influence of vegetation cover changes on base flow MTTs. The main changes in vegetation cover in the Swiss Alps are massive shrub encroachment and forest expansion into formerly open habitats. Four small and relatively steep headwater catchments in the Swiss Alps (Ursern Valley) were investigated to relate different vegetation cover to water transit times. Time series of water stable isotopes were used to calculate MTTs. The high temporal variation of the stable isotope signals in precipitation was strongly dampened in stream base flow samples. MTTs of the four catchments were 70 to 102 weeks. The strong dampening of the stable isotope input signal as well as stream water geochemistry points to deeper flow paths and mixing of waters of different ages at the catchments' outlets. MTTs were neither related to topographic indices nor vegetation cover. The major part of the quickly infiltrating precipitation likely percolates through fractured and partially karstified deeper rock zones, which increases the control of bedrock flow paths on MTT. Snow accumulation and the timing of its melt play an important role for stable isotope dynamics during spring and early summer. We conclude that, in mountainous headwater catchments with relatively shallow soil layers, the hydrogeological and geochemical patterns (i.e. geochemistry, porosity and hydraulic conductivity of rocks) and snow dynamics influence storage, mixing and release of water in a stronger way than vegetation cover or topography do.

Gender Stereotypes and Gendered Vocational Aspirations among Secondary School Students

Research Topic/Aim: Horizontal gender inequalities appear to be rather stable, with girls more often choosing ‘female' service professions, and boys choosing career paths related to science, technology, engineering or mathematics, since measures to bring more women into typical ‘male' jobs and more men into typical ‘female' jobs did not turn out to be sustainable. This paper focuses on gender stereotypes, namely non-egalitarian patriarchal gender-role orientations and gender associations of the school subjects German and mathematics. Dealing with and abolishing such gender stereotypes may be key strategy to reach sustainability regarding more equal vocational choices. Thus, gender stereotypes will be theorised and empirically analysed as a major predictor of gender-typical vocational perspectives considering interest in these school subjects as a mediating factor. Furthermore, we focus on structural patriarchy as a root of gender-role orientations, and teacher gender regarding its impact on gendered images of subjects. Theoretical and methodology framework: Our analyses of gender segregation in vocational aspirations and vocational choice center on Gottfredson's (2002; Gottfredson and Becker, 1981) Theory of Circumscription, Compromise and Self-Creation. One of the main assumptions of this theory is that people associate jobs with particular sexes and those jobs that do not fit particular gender roles are not considered. Empirical analyses are based on survey data of eighth-graders in the Swiss canton of Bern (N = 672). Structural Equation Models (SEM) for male and female students are estimated. Conclusions/Findings: Results reveal different patterns for boys and girls; for boys, gender-typical (male) vocational perspective could be explained via gender role orientations, interest in mathematics and gender associations of the school subjects, for girls, the factors under consideration could be empirically linked to ‘atypical vocational perspective'. Relevance to Nordic educational research: The study focuses on gender relations in society and how they are reproduced. Gender segregation in vocational choice and at the labour market is a universal issue - affecting both egalitarian and non-egalitarian gender regimes in similar ways. Although in general Northern countries appear to be more equal regarding gender inequality, gender segregation is rather persistent (Jarman, Blackburn and Brooks, 2012) and therefore remains a relevant topic.

Assessing the function of the fronto-parietal attention network: Insights from resting-state fMRI and the attentional network test

In the recent past, various intrinsic connectivity networks (ICN) have been identified in the resting brain. It has been hypothesized that the fronto-parietal ICN is involved in attentional processes. Evidence for this claim stems from task-related activation studies that show a joint activation of the implicated brain regions during tasks that require sustained attention. In this study, we used functional magnetic resonance imaging (fMRI) to demonstrate that functional connectivity within the fronto-parietal network at rest directly relates to attention. We applied graph theory to functional connectivity data from multiple regions of interest and tested for associations with behavioral measures of attention as provided by the attentional network test (ANT), which we acquired in a separate session outside the MRI environment. We found robust statistical associations with centrality measures of global and local connectivity of nodes within the network with the alerting and executive control subfunctions of attention. The results provide further evidence for the functional significance of ICN and the hypothesized role of the fronto-parietal attention network. Hum Brain Mapp , 2013. © 2013 Wiley Periodicals, Inc.

Forest connectivity restoration through reforestation: an integrated methodology for prioritizing agricultural lands and selecting reforestation species

Forest connectivity restoration is a major goal in natural resource planning. Given the high amount of abandoned cultivated lands, setting efficient methods for the reforestation of agricultural lands offers a good opportunity to face this issue. However, reforestations must be carefully planned, which poses two main challenges. In first place, to determine those agricultural lands that, once reforested, would meet more effectively the planning goals. As a further step, in order to grant the success of the activity, it is fairly advisable to select those tree species that are more adapted to each particular environment. Here we intend to give response to both requirements by proposing a sequential and integrated methodology that has been implemented in two Spanish forest districts, which are formed by several landscape types that were previously defined and characterized. Using the software Conefor Sensinode, a powerful tool for quantifying habitat availability that is based on graph theory concepts, we determined the landscapes where forest planning should have connectivity as a major concern and, afterwards, we detected the agricultural patches that would contribute most to enhance connectivity if they were reforested. The subsequent reforestation species assessment was performed within these priority patches. Using penalized logistic regressions we fitted ecological niche models for the Spanish native tree species. The models were trained with species distribution data from the Spanish Forest Map and used climatic and lithological variables as predictors. Model predictions were used to build ordered lists of suitable species for each priority patch. The lists include dominant and non dominant tree species and allow adding biodiversity goals to the reforestation planning. The result of this combined methodology is a map of agricultural patches that would contribute most to uphold forest connectivity if they were reforested and a list of suitable tree species for each patch ordered by occurrence probability. Therefore the proposed methodology may be useful for suitable and efficient forest planning and landscape designing.

Game Theory Models for Multi-Robot Patrolling of Infraestructures

Abstract This work is focused on the problem of performing multi‐robot patrolling for infrastructure security applications in order to protect a known environment at critical facilities. Thus, given a set of robots and a set of points of interest, the patrolling task consists of constantly visiting these points at irregular time intervals for security purposes. Current existing solutions for these types of applications are predictable and inflexible. Moreover, most of the previous centralized and deterministic solutions and only few efforts have been made to integrate dynamic methods. Therefore, the development of new dynamic and decentralized collaborative approaches in order to solve the aforementioned problem by implementing learning models from Game Theory. The model selected in this work that includes belief‐based and reinforcement models as special cases is called Experience‐Weighted Attraction. The problem has been defined using concepts of Graph Theory to represent the environment in order to work with such Game Theory techniques. Finally, the proposed methods have been evaluated experimentally by using a patrolling simulator. The results obtained have been compared with previous available