Graph theory reveals dysconnected hubs in 22q11DS and altered nodal efficiency in patients with hallucinations.

Schizophrenia is postulated to be the prototypical dysconnection disorder, in which hallucinations are the core symptom. Due to high heterogeneity in methodology across studies and the clinical phenotype, it remains unclear whether the structural brain dysconnection is global or focal and if clinical symptoms result from this dysconnection. In the present work, we attempt to clarify this issue by studying a population considered as a homogeneous genetic sub-type of schizophrenia, namely the 22q11.2 deletion syndrome (22q11.2DS). Cerebral MRIs were acquired for 46 patients and 48 age and gender matched controls (aged 6-26, respectively mean age = 15.20 ± 4.53 and 15.28 ± 4.35 years old). Using the Connectome mapper pipeline (connectomics.org) that combines structural and diffusion MRI, we created a whole brain network for each individual. Graph theory was used to quantify the global and local properties of the brain network organization for each participant. A global degree loss of 6% was found in patients' networks along with an increased Characteristic Path Length. After identifying and comparing hubs, a significant loss of degree in patients' hubs was found in 58% of the hubs. Based on Allen's brain network model for hallucinations, we explored the association between local efficiency and symptom severity. Negative correlations were found in the Broca's area (p < 0.004), the Wernicke area (p < 0.023) and a positive correlation was found in the dorsolateral prefrontal cortex (DLPFC) (p < 0.014). In line with the dysconnection findings in schizophrenia, our results provide preliminary evidence for a targeted alteration in the brain network hubs' organization in individuals with a genetic risk for schizophrenia. The study of specific disorganization in language, speech and thought regulation networks sharing similar network properties may help to understand their role in the hallucination mechanism.

EEG-based functional brain networks: does the network size matter?

Functional connectivity in human brain can be represented as a network using electroencephalography (EEG) signals. These networks--whose nodes can vary from tens to hundreds--are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which various graph metrics depend upon the network size. To this end, EEGs from 32 normal subjects were recorded and functional networks of three different sizes were extracted. A state-space based method was used to calculate cross-correlation matrices between different brain regions. These correlation matrices were used to construct binary adjacency connectomes, which were assessed with regards to a number of graph metrics such as clustering coefficient, modularity, efficiency, economic efficiency, and assortativity. We showed that the estimates of these metrics significantly differ depending on the network size. Larger networks had higher efficiency, higher assortativity and lower modularity compared to those with smaller size and the same density. These findings indicate that the network size should be considered in any comparison of networks across studies.

Structural prediction of peptides bound to MHC class I.

An ab initio structure prediction approach adapted to the peptide-major histocompatibility complex (MHC) class I system is presented. Based on structure comparisons of a large set of peptide-MHC class I complexes, a molecular dynamics protocol is proposed using simulated annealing (SA) cycles to sample the conformational space of the peptide in its fixed MHC environment. A set of 14 peptide-human leukocyte antigen (HLA) A0201 and 27 peptide-non-HLA A0201 complexes for which X-ray structures are available is used to test the accuracy of the prediction method. For each complex, 1000 peptide conformers are obtained from the SA sampling. A graph theory clustering algorithm based on heavy atom root-mean-square deviation (RMSD) values is applied to the sampled conformers. The clusters are ranked using cluster size, mean effective or conformational free energies, with solvation free energies computed using Generalized Born MV 2 (GB-MV2) and Poisson-Boltzmann (PB) continuum models. The final conformation is chosen as the center of the best-ranked cluster. With conformational free energies, the overall prediction success is 83% using a 1.00 Angstroms crystal RMSD criterion for main-chain atoms, and 76% using a 1.50 Angstroms RMSD criterion for heavy atoms. The prediction success is even higher for the set of 14 peptide-HLA A0201 complexes: 100% of the peptides have main-chain RMSD values &lt; or =1.00 Angstroms and 93% of the peptides have heavy atom RMSD values &lt; or =1.50 Angstroms. This structure prediction method can be applied to complexes of natural or modified antigenic peptides in their MHC environment with the aim to perform rational structure-based optimizations of tumor vaccines.

Structural Analysis of Networks

Network analysis naturally relies on graph theory and, more particularly, on the use of node and edge metrics to identify the salient properties in graphs. When building visual maps of networks, these metrics are turned into useful visual cues or are used interactively to filter out parts of a graph while querying it, for instance. Over the years, analysts from different application domains have designed metrics to serve specific needs. Network science is an inherently cross-disciplinary field, which leads to the publication of metrics with similar goals; different names and descriptions of their analytics often mask the similarity between two metrics that originated in different fields. Here, we study a set of graph metrics and compare their relative values and behaviors in an effort to survey their potential contributions to the spatial analysis of networks.

Quantifying network properties in multi-electrode recordings: spatiotemporal characterization and inter-trial variation of evoked gamma oscillations in mouse somatosensory cortex in vitro.

Linking the structural connectivity of brain circuits to their cooperative dynamics and emergent functions is a central aim of neuroscience research. Graph theory has recently been applied to study the structure-function relationship of networks, where dynamical similarity of different nodes has been turned into a "static" functional connection. However, the capability of the brain to adapt, learn and process external stimuli requires a constant dynamical functional rewiring between circuitries and cell assemblies. Hence, we must capture the changes of network functional connectivity over time. Multi-electrode array data present a unique challenge within this framework. We study the dynamics of gamma oscillations in acute slices of the somatosensory cortex from juvenile mice recorded by planar multi-electrode arrays. Bursts of gamma oscillatory activity lasting a few hundred milliseconds could be initiated only by brief trains of electrical stimulations applied at the deepest cortical layers and simultaneously delivered at multiple locations. Local field potentials were used to study the spatio-temporal properties and the instantaneous synchronization profile of the gamma oscillatory activity, combined with current source density (CSD) analysis. Pair-wise differences in the oscillation phase were used to determine the presence of instantaneous synchronization between the different sites of the circuitry during the oscillatory period. Despite variation in the duration of the oscillatory response over successive trials, they showed a constant average power, suggesting that the rate of expenditure of energy during the gamma bursts is consistent across repeated stimulations. Within each gamma burst, the functional connectivity map reflected the columnar organization of the neocortex. Over successive trials, an apparently random rearrangement of the functional connectivity was observed, with a more stable columnar than horizontal organization. This work reveals new features of evoked gamma oscillations in developing cortex.

Intégration de méthodes de data mining dans le renseignement criminel : analyse par des structures issues de la théorie des graphes dans le profilage des stupéfiants

Data mining can be defined as the extraction of previously unknown and potentially useful information from large datasets. The main principle is to devise computer programs that run through databases and automatically seek deterministic patterns. It is applied in different fields of application, e.g., remote sensing, biometry, speech recognition, but has seldom been applied to forensic case data. The intrinsic difficulty related to the use of such data lies in its heterogeneity, which comes from the many different sources of information. The aim of this study is to highlight potential uses of pattern recognition that would provide relevant results from a criminal intelligence point of view. The role of data mining within a global crime analysis methodology is to detect all types of structures in a dataset. Once filtered and interpreted, those structures can point to previously unseen criminal activities. The interpretation of patterns for intelligence purposes is the final stage of the process. It allows the researcher to validate the whole methodology and to refine each step if necessary. An application to cutting agents found in illicit drug seizures was performed. A combinatorial approach was done, using the presence and the absence of products. Methods coming from the graph theory field were used to extract patterns in data constituted by links between products and place and date of seizure. A data mining process completed using graphing techniques is called ``graph mining''. Patterns were detected that had to be interpreted and compared with preliminary knowledge to establish their relevancy. The illicit drug profiling process is actually an intelligence process that uses preliminary illicit drug classes to classify new samples. Methods proposed in this study could be used \textit{a priori} to compare structures from preliminary and post-detection patterns. This new knowledge of a repeated structure may provide valuable complementary information to profiling and become a source of intelligence.

The evolution of helping and harming on graphs: the return of the inclusive fitness effect.

Evolutionary graph theory has been proposed as providing new fundamental rules for the evolution of co-operation and altruism. But how do these results relate to those of inclusive fitness theory? Here, we carry out a retrospective analysis of the models for the evolution of helping on graphs of Ohtsuki et al. [Nature (2006) 441, 502] and Ohtsuki & Nowak [Proc. R. Soc. Lond. Ser. B Biol. Sci (2006) 273, 2249]. We show that it is possible to translate evolutionary graph theory models into classical kin selection models without disturbing at all the mathematics describing the net effect of selection on helping. Model analysis further demonstrates that costly helping evolves on graphs through limited dispersal and overlapping generations. These two factors are well known to promote relatedness between interacting individuals in spatially structured populations. By allowing more than one individual to live at each node of the graph and by allowing interactions to vary with the distance between nodes, our inclusive fitness model allows us to consider a wider range of biological scenarios leading to the evolution of both helping and harming behaviours on graphs.

Synchronizability of EEG-Based Functional Networks in Early Alzheimer's Disease.

Recently graph theory and complex networks have been widely used as a mean to model functionality of the brain. Among different neuroimaging techniques available for constructing the brain functional networks, electroencephalography (EEG) with its high temporal resolution is a useful instrument of the analysis of functional interdependencies between different brain regions. Alzheimer's disease (AD) is a neurodegenerative disease, which leads to substantial cognitive decline, and eventually, dementia in aged people. To achieve a deeper insight into the behavior of functional cerebral networks in AD, here we study their synchronizability in 17 newly diagnosed AD patients compared to 17 healthy control subjects at no-task, eyes-closed condition. The cross-correlation of artifact-free EEGs was used to construct brain functional networks. The extracted networks were then tested for their synchronization properties by calculating the eigenratio of the Laplacian matrix of the connection graph, i.e., the largest eigenvalue divided by the second smallest one. In AD patients, we found an increase in the eigenratio, i.e., a decrease in the synchronizability of brain networks across delta, alpha, beta, and gamma EEG frequencies within the wide range of network costs. The finding indicates the destruction of functional brain networks in early AD.

Extreme prematurity and intra uterine growth restriction effects in brain network topology at school age

Higher risk for long-term behavioral and emotional sequelae, with attentional problems (with or without hyperactivity) is now becoming one of the hallmarks of extreme premature (EP) birth and birth after pregancy conditions leading to poor intra uterine growth restriction (IUGR) [1,2]. However, little is know so far about the neurostructural basis of these complexe brain functional abnormalities that seem to have their origins in early critical periods of brain development. The development of cortical axonal pathways happens in a series of sequential events. The preterm phase (24-36 post conecptional weeks PCW) is known for being crucial for growth of the thalamocortical fiber bundles as well as for the development of long projectional, commisural and projectional fibers [3]. Is it logical to expect, thus, that being exposed to altered intrauterine environment (altered nutrition) or to extrauterine environment earlier that expected, lead to alterations in the structural organization and, consequently, alter the underlying white matter (WM) structure. Understanding rate and variability of normal brain development, and detect differences from typical development may offer insight into the neurodevelopmental anomalies that can be imaged at later stages. Due to its unique ability to non-invasively visualize and quantify in vivo white matter tracts in the brain, in this study we used diffusion MRI (dMRI) tractography to derive brain graphs [4,5,6]. This relatively simple way of modeling the brain enable us to use graph theory to study topological properties of brain graphs in order to study the effects of EP and IUGR on childrens brain connectivity at age 6 years old.

Implementing statistical learning methods through Bayesian networks. Part 1: a guide to Bayesian parameter estimation using forensic science data

As a thorough aggregation of probability and graph theory, Bayesian networks currently enjoy widespread interest as a means for studying factors that affect the coherent evaluation of scientific evidence in forensic science. Paper I of this series of papers intends to contribute to the discussion of Bayesian networks as a framework that is helpful for both illustrating and implementing statistical procedures that are commonly employed for the study of uncertainties (e.g. the estimation of unknown quantities). While the respective statistical procedures are widely described in literature, the primary aim of this paper is to offer an essentially non-technical introduction on how interested readers may use these analytical approaches - with the help of Bayesian networks - for processing their own forensic science data. Attention is mainly drawn to the structure and underlying rationale of a series of basic and context-independent network fragments that users may incorporate as building blocs while constructing larger inference models. As an example of how this may be done, the proposed concepts will be used in a second paper (Part II) for specifying graphical probability networks whose purpose is to assist forensic scientists in the evaluation of scientific evidence encountered in the context of forensic document examination (i.e. results of the analysis of black toners present on printed or copied documents).

EEG-based functional networks in schizophrenia.

Schizophrenia is often considered as a dysconnection syndrome in which, abnormal interactions between large-scale functional brain networks result in cognitive and perceptual deficits. In this article we apply the graph theoretic measures to brain functional networks based on the resting EEGs of fourteen schizophrenic patients in comparison with those of fourteen matched control subjects. The networks were extracted from common-average-referenced EEG time-series through partial and unpartial cross-correlation methods. Unpartial correlation detects functional connectivity based on direct and/or indirect links, while partial correlation allows one to ignore indirect links. We quantified the network properties with the graph metrics, including mall-worldness, vulnerability, modularity, assortativity, and synchronizability. The schizophrenic patients showed method-specific and frequency-specific changes especially pronounced for modularity, assortativity, and synchronizability measures. However, the differences between schizophrenia patients and normal controls in terms of graph theory metrics were stronger for the unpartial correlation method.

Using Pareto optimality to explore the topology and dynamics of the human connectome.

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain's topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an 'economical' small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

Intrahemispheric cortico-cortical connections of the human auditory cortex.

The human auditory cortex comprises the supratemporal plane and large parts of the temporal and parietal convexities. We have investigated the relevant intrahemispheric cortico-cortical connections using in vivo DSI tractography combined with landmark-based registration, automatic cortical parcellation and whole-brain structural connection matrices in 20 right-handed male subjects. On the supratemporal plane, the pattern of connectivity was related to the architectonically defined early-stage auditory areas. It revealed a three-tier architecture characterized by a cascade of connections from the primary auditory cortex to six adjacent non-primary areas and from there to the superior temporal gyrus. Graph theory-driven analysis confirmed the cascade-like connectivity pattern and demonstrated a strong degree of segregation and hierarchy within early-stage auditory areas. Putative higher-order areas on the temporal and parietal convexities had more widely spread local connectivity and long-range connections with the prefrontal cortex; analysis of optimal community structure revealed five distinct modules in each hemisphere. The pattern of temporo-parieto-frontal connectivity was partially asymmetrical. In conclusion, the human early-stage auditory cortical connectivity, as revealed by in vivo DSI tractography, has strong similarities with that of non-human primates. The modular architecture and hemispheric asymmetry in higher-order regions is compatible with segregated processing streams and lateralization of cognitive functions.