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.

Speech Graphs Provide a Quantitative Measure of Thought Disorder in Psychosis

Background: Psychosis has various causes, including mania and schizophrenia. Since the differential diagnosis of psychosis is exclusively based on subjective assessments of oral interviews with patients, an objective quantification of the speech disturbances that characterize mania and schizophrenia is in order. In principle, such quantification could be achieved by the analysis of speech graphs. A graph represents a network with nodes connected by edges; in speech graphs, nodes correspond to words and edges correspond to semantic and grammatical relationships. Methodology/Principal Findings: To quantify speech differences related to psychosis, interviews with schizophrenics, manics and normal subjects were recorded and represented as graphs. Manics scored significantly higher than schizophrenics in ten graph measures. Psychopathological symptoms such as logorrhea, poor speech, and flight of thoughts were grasped by the analysis even when verbosity differences were discounted. Binary classifiers based on speech graph measures sorted schizophrenics from manics with up to 93.8% of sensitivity and 93.7% of specificity. In contrast, sorting based on the scores of two standard psychiatric scales (BPRS and PANSS) reached only 62.5% of sensitivity and specificity. Conclusions/Significance: The results demonstrate that alterations of the thought process manifested in the speech of psychotic patients can be objectively measured using graph-theoretical tools, developed to capture specific features of the normal and dysfunctional flow of thought, such as divergence and recurrence. The quantitative analysis of speech graphs is not redundant with standard psychometric scales but rather complementary, as it yields a very accurate sorting of schizophrenics and manics. Overall, the results point to automated psychiatric diagnosis based not on what is said, but on how it is said.

Theoretical models for the antitrypanosomal activity of thiosemicarbazone derivatives

Thiosemicarbazones are cruzain inhibitors which have been identified as potential antitrypanosomal agents. In this work, several molecular properties were calculated at the density functional theory (DFT)/B3LYP/6-311G* level for a set of 44 thiosemicarbazones. Unsupervised and supervised pattern recognition techniques (hierarchical cluster analysis, principal component analysis, kth-nearest neighbors, and soft independent modeling by class analogy) were used to obtain structureactivity relationship models, which are able to classify unknown compounds according to their activities. The chemometric analyses performed here revealed that 12 descriptors can be considered responsible for the discrimination between high and low activity compounds. Classification models were validated with an external test set, showing that predictive classifications were achieved with the selected variable set. The results obtained here are in good agreement with previous findings from the literature, suggesting that our models can be useful on further investigations on the molecular determinants for the antichagasic activity. (C) 2012 Wiley Periodicals, Inc.

Fuzzy Connectedness Image Segmentation in Graph Cut Formulation: A Linear-Time Algorithm and a Comparative Analysis

A deep theoretical analysis of the graph cut image segmentation framework presented in this paper simultaneously translates into important contributions in several directions. The most important practical contribution of this work is a full theoretical description, and implementation, of a novel powerful segmentation algorithm, GC(max). The output of GC(max) coincides with a version of a segmentation algorithm known as Iterative Relative Fuzzy Connectedness, IRFC. However, GC(max) is considerably faster than the classic IRFC algorithm, which we prove theoretically and show experimentally. Specifically, we prove that, in the worst case scenario, the GC(max) algorithm runs in linear time with respect to the variable M=|C|+|Z|, where |C| is the image scene size and |Z| is the size of the allowable range, Z, of the associated weight/affinity function. For most implementations, Z is identical to the set of allowable image intensity values, and its size can be treated as small with respect to |C|, meaning that O(M)=O(|C|). In such a situation, GC(max) runs in linear time with respect to the image size |C|. We show that the output of GC(max) constitutes a solution of a graph cut energy minimization problem, in which the energy is defined as the a"" (a) norm ayenF (P) ayen(a) of the map F (P) that associates, with every element e from the boundary of an object P, its weight w(e). This formulation brings IRFC algorithms to the realm of the graph cut energy minimizers, with energy functions ayenF (P) ayen (q) for qa[1,a]. Of these, the best known minimization problem is for the energy ayenF (P) ayen(1), which is solved by the classic min-cut/max-flow algorithm, referred to often as the Graph Cut algorithm. We notice that a minimization problem for ayenF (P) ayen (q) , qa[1,a), is identical to that for ayenF (P) ayen(1), when the original weight function w is replaced by w (q) . Thus, any algorithm GC(sum) solving the ayenF (P) ayen(1) minimization problem, solves also one for ayenF (P) ayen (q) with qa[1,a), so just two algorithms, GC(sum) and GC(max), are enough to solve all ayenF (P) ayen (q) -minimization problems. We also show that, for any fixed weight assignment, the solutions of the ayenF (P) ayen (q) -minimization problems converge to a solution of the ayenF (P) ayen(a)-minimization problem (ayenF (P) ayen(a)=lim (q -> a)ayenF (P) ayen (q) is not enough to deduce that). An experimental comparison of the performance of GC(max) and GC(sum) algorithms is included. This concentrates on comparing the actual (as opposed to provable worst scenario) algorithms' running time, as well as the influence of the choice of the seeds on the output.

Integrated biomarker responses as environmental status descriptors of a coastal zone (Sao Paulo, Brazil)

Sao Paulo state (Brazil) has one of the most overpopulated coastal zones in South America, where previous studies have already detected sediment and water contamination. However, biological-based monitoring considering signals of xenobiotic exposure and effects are scarce. The present study employed a battery of biomarkers under field conditions to assess the environmental quality of this coastal zone. For this purpose, the activity of CYP 450, antioxidant enzymes, DNA damage, lipid peroxidation and lysosomal membrane were analysed in caged mussels and integrated using Factorial Analysis. A representation of estimated factor scores was performed in order to confirm the factor descriptions characterizing the studied areas. Biomarker responses indicated signals of mussels` impaired health during the monitoring, which pointed to the impact of different sources of contaminants in the water quality and identified critical areas. This integrated approach produced a rapid, sensitive and cost-effective assessment, which could be incorporated as a descriptor of environmental status in future coastal zones biomonitoring. (C) 2011 Elsevier Inc. All rights reserved.

Color texture analysis based on fractal descriptors

Color texture classification is an important step in image segmentation and recognition. The color information is especially important in textures of natural scenes, such as leaves surfaces, terrains models, etc. In this paper, we propose a novel approach based on the fractal dimension for color texture analysis. The proposed approach investigates the complexity in R, G and B color channels to characterize a texture sample. We also propose to study all channels in combination, taking into consideration the correlations between them. Both these approaches use the volumetric version of the Bouligand-Minkowski Fractal Dimension method. The results show a advantage of the proposed method over other color texture analysis methods. (C) 2011 Elsevier Ltd. All rights reserved.

Self-Organizing Maps of Molecular Descriptors for Sesquiterpene Lactones and Their Application to the Chemotaxonomy of the Asteraceae Family

The Asteraceae, one of the largest families among angiosperms, is chemically characterised by the production of sesquiterpene lactones (SLs). A total of 1,111 SLs, which were extracted from 658 species, 161 genera, 63 subtribes and 15 tribes of Asteraceae, were represented and registered in two dimensions in the SISTEMATX, an in-house software system, and were associated with their botanical sources. The respective 11 block of descriptors: Constitutional, Functional groups, BCUT, Atom-centred, 2D autocorrelations, Topological, Geometrical, RDF, 3D-MoRSE, GETAWAY and WHIM were used as input data to separate the botanical occurrences through self-organising maps. Maps that were generated with each descriptor divided the Asteraceae tribes, with total index values between 66.7% and 83.6%. The analysis of the results shows evident similarities among the Heliantheae, Helenieae and Eupatorieae tribes as well as between the Anthemideae and Inuleae tribes. Those observations are in agreement with systematic classifications that were proposed by Bremer, which use mainly morphological and molecular data, therefore chemical markers partially corroborate with these classifications. The results demonstrate that the atom-centred and RDF descriptors can be used as a tool for taxonomic classification in low hierarchical levels, such as tribes. Descriptors obtained through fragments or by the two-dimensional representation of the SL structures were sufficient to obtain significant results, and better results were not achieved by using descriptors derived from three-dimensional representations of SLs. Such models based on physico-chemical properties can project new design SLs, similar structures from literature or even unreported structures in two-dimensional chemical space. Therefore, the generated SOMs can predict the most probable tribe where a biologically active molecule can be found according Bremer classification.

Analyzing the Complexity and Reliability of Switch-Frequency-Reconfigurable Antennas Using Graph Models

This paper addresses the functional reliability and the complexity of reconfigurable antennas using graph models. The correlation between complexity and reliability for any given reconfigurable antenna is defined. Two methods are proposed to reduce failures and improve the reliability of reconfigurable antennas. The failures are caused by the reconfiguration technique or by the surrounding environment. These failure reduction methods proposed are tested and examples are given which verify these methods.

Theoretical chemistry: current applications to photochemistry and thermochemistry

A historical perspective is given contrasting challenges and advances in theoretical chemistry at the time the first issue of Theoretical Chemistry Accounts appeared in 1962 and the progress achieved since then as expressed in current state-of-the-art applications in photochemistry and thermochemistry.

Connections between the Sznajd model with general confidence rules and graph theory

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabasi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Theoretical luminescence spectra in p-type superlattices based on InGaAsN

In this work, we present a theoretical photoluminescence (PL) for p-doped GaAs/InGaAsN nanostructures arrays. We apply a self-consistent method in the framework of the effective mass theory. Solving a full 8 x 8 Kane's Hamiltonian, generalized to treat different materials in conjunction with the Poisson equation, we calculate the optical properties of these systems. The trends in the calculated PL spectra, due to many-body effects within the quasi-two-dimensional hole gas, are analyzed as a function of the acceptor doping concentration and the well width. Effects of temperature in the PL spectra are also investigated. This is the first attempt to show theoretical luminescence spectra for GaAs/InGaAsN nanostructures and can be used as a guide for the design of nanostructured devices such as optoelectronic devices, solar cells, and others.

Correlation Between Molecular Conformation, Packing, and Dynamics in Oligofluorenes: A Theoretical/Experimental Study

Fluorene-based systems have shown great potential as components in organic electronics and optoelectronics (organic photovoltaics, OPVs, organic light emitting diodes, OLEDs, and organic transistors, OTFTs). These systems have drawn attention primarily because they exhibit strong blue emission associated with relatively good thermal stability. It is well-known that the electronic properties of polymers are directly related to the molecular conformations and chain packing of polymers. Here, we used three oligofluorenes (trimer, pentamer, and heptamer) as model systems to theoretically investigate the conformational properties of fluorene molecules, starting with the identification of preferred conformations. The hybrid exchange correlation functional, OPBE, and ZINDO/S-CI showed that each oligomer exhibits a tendency to adopt a specific chain arrangement, which could be distinguished by comparing their UV/vis electronic absorption and C-13 NMR spectra. This feature was used to identify the preferred conformation of the oligomer chains in chloroform-cast films by comparing experimental and theoretical UV/vis and C-13 NMR spectra. Moreover, the oligomer chain packing and dynamics in the films were studied by DSC and several solid state NMR techniques, which indicated that the phase behavior of the films may be influenced by the tendency that each oligomeric chain has to adopt a given conformation.

Riverbed: A Novel User-Steered Image Segmentation Method Based on Optimum Boundary Tracking

This paper presents an optimum user-steered boundary tracking approach for image segmentation, which simulates the behavior of water flowing through a riverbed. The riverbed approach was devised using the image foresting transform with a never-exploited connectivity function. We analyze its properties in the derived image graphs and discuss its theoretical relation with other popular methods such as live wire and graph cuts. Several experiments show that riverbed can significantly reduce the number of user interactions (anchor points), as compared to live wire for objects with complex shapes. This paper also includes a discussion about how to combine different methods in order to take advantage of their complementary strengths.

Modeling the emergence of HIV-1 drug resistance resulting from antiretroviral therapy: Insights from theoretical and numerical studies

The use of antiretroviral therapy has proven to be remarkably effective in controlling the progression of human immunodeficiency virus (HIV) infection and prolonging patient's survival. Therapy however may fail and therefore these benefits can be compromised by the emergence of HIV strains that are resistant to the therapy. In view of these facts, the question of finding the reason for which drug-resistant strains emerge during therapy has become a worldwide problem of great interest. This paper presents a deterministic HIV-1 model to examine the mechanisms underlying the emergence of drug-resistance during therapy. The aim of this study is to determine whether, and how fast, antiretroviral therapy may determine the emergence of drug resistance by calculating the basic reproductive numbers. The existence, feasibility and local stability of the equilibriums are also analyzed. By performing numerical simulations we show that Hopf bifurcation may occur. The model suggests that the individuals with drug-resistant infection may play an important role in the epidemic of HIV. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Fractal descriptors based on Fourier spectrum applied to texture analysis

This work proposes the development and study of a novel technique lot the generation of fractal descriptors used in texture analysis. The novel descriptors are obtained from a multiscale transform applied to the Fourier technique of fractal dimension calculus. The power spectrum of the Fourier transform of the image is plotted against the frequency in a log-log scale and a multiscale transform is applied to this curve. The obtained values are taken as the fractal descriptors of the image. The validation of the proposal is performed by the use of the descriptors for the classification of a dataset of texture images whose real classes are previously known. The classification precision is compared to other fractal descriptors known in the literature. The results confirm the efficiency of the proposed method. (C) 2012 Elsevier B.V. All rights reserved.