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PubMed2006

Disturbed functional connectivity in brain tumour patients: evaluation by graph analysis of synchronization matrices.

OBJECTIVE: Cerebral functions are based on the functional interactions between multiple distinct specialized regions of the brain. Functional interactions require anatomical connections as well as the synchronization of brain oscillations. The present work aims at evaluating the impact of brain tumours on spatial patterns of functional connectivity of the brain measured at rest by MEG. METHODS: We analyzed the statistical dependency (by computing the synchronization likelihood (SL, a measure of generalized synchronization)) between MEG signals at rest, in 17 patients with a brain tumour and in 15 healthy controls. Following an approach that derives from graph theory, we also analyzed the architectural properties of the networks by computing two parameters from the SL matrix, the cluster coefficient C and the characteristic path length L. RESULTS: Alterations in synchronization levels were found in the patients and were not focal but involved intra-hemispheric connectivity. Effects were different considering the frequencies sub-bands, predominating in a decrease in high frequencies bands for long-distance connections and an increase in slower bands for local connectivity. In addition, graph analysis reveals changes in the normal "small-world" network architecture in addition to changes in synchronization levels with some differences according to the studied frequency sub-bands. CONCLUSIONS: Brain tumours alter the functional connectivity and the "network" architecture of the brain. These alterations are not focal and effects are different considering the frequencies sub-bands. SIGNIFICANCE: These neurophysiological changes may contribute to the cognitive alterations observed in patients with brain tumours.

Adult↗

PubMed2004

Discriminative topological features reveal biological network mechanisms.

BACKGROUND: Recent genomic and bioinformatic advances have motivated the development of numerous network models intending to describe graphs of biological, technological, and sociological origin. In most cases the success of a model has been evaluated by how well it reproduces a few key features of the real-world data, such as degree distributions, mean geodesic lengths, and clustering coefficients. Often pairs of models can reproduce these features with indistinguishable fidelity despite being generated by vastly different mechanisms. In such cases, these few target features are insufficient to distinguish which of the different models best describes real world networks of interest; moreover, it is not clear a priori that any of the presently-existing algorithms for network generation offers a predictive description of the networks inspiring them. RESULTS: We present a method to assess systematically which of a set of proposed network generation algorithms gives the most accurate description of a given biological network. To derive discriminative classifiers, we construct a mapping from the set of all graphs to a high-dimensional (in principle infinite-dimensional) "word space". This map defines an input space for classification schemes which allow us to state unambiguously which models are most descriptive of a given network of interest. Our training sets include networks generated from 17 models either drawn from the literature or introduced in this work. We show that different duplication-mutation schemes best describe the E. coli genetic network, the S. cerevisiae protein interaction network, and the C. elegans neuronal network, out of a set of network models including a linear preferential attachment model and a small-world model. CONCLUSIONS: Our method is a first step towards systematizing network models and assessing their predictability, and we anticipate its usefulness for a number of communities.

Animals↗

PubMed2006

Comments on "the 1993 DIMACS graph coloring challenge" and "energy function-based approaches to graph coloring".

Since all graphs in the 1993 DIMACS graph coloring challenge are undirected, each edge should be only counted once. However, in some files each edge is counted once, whereas in others each edge is counted twice; so a systematical check on the DIMACS challenge is made to eliminate the inconsistencies. Besides, the experimental results of a previous paper by Blas et al. counted each violated edges twice and neglected the inconsistencies in the DIMACS challenge. So the correct experimental results of a previous paper by Blas et al are also given.

Algorithms↗

PubMed2006

Assessing self organizing maps via contiguity analysis.

Contiguity analysis is a straightforward generalization of linear discriminant analysis in which the partition of elements is replaced by a more general graph structure. Applied to the graph induced by a Self Organizing Map (SOM), contiguity analysis provides a set of linear projectors leading to a planar representation as close as possible to the SOM. As expected, such projectors may only concern local parts of the SOMs. They allow us to visualize the shapes of the clusters (convex hulls of the projections of the elements belonging to a cluster) and the pattern of the elements within each cluster. In some contexts, it is possible to project the bootstrap replicates of the elements, and therefore to produce confidence areas for elements via a standard partial bootstrap procedure.

Algorithms↗

PubMed2005

Qualitative modelling of regulated metabolic pathways: application to the tryptophan biosynthesis in E.coli.

MOTIVATION: The integrated dynamical modelling of mixed metabolic/genetic networks constitutes one of the challenges of systems biology. Furthermore, as most of available data about genetic and metabolic regulations are qualitative, there is a pressing need for rigorous qualitative mathematical approaches. RESULTS: On the basis of two established formalisms, the logical modelling of genetic regulatory networks and the Petri net modelling of metabolic networks, we propose a systematic approach for the modelling of regulated metabolic networks. This approach leans on previous work defining a systematic procedure to translate logical regulatory graphs into standard (discrete) Petri nets (PNs). This approach is illustrated by the qualitative modelling of the biosynthesis of tryptophan (Trp) in Escherichia coli, taking into account two types of regulatory feedbacks: the direct inhibition of the first enzyme of the pathway by the final product of the pathway, and the transcriptional inhibition of the Trp operon by the Trp-repressor complex. On the basis of this integrated PN model, we further indicate how available dynamical analysis tools can be applied to obtain significant insights in the behaviour of the system. AVAILABILITY: The software GINsim for the logical modelling of genetic regulatory networks together with the PN model of the regulated Trp biosynthesis pathway are available at: http://gin.univ-mrs.fr/GINsim.

Computer Simulation↗

PubMed1999

Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems.

The purpose of this article is to stress the implications that the consideration of nonlinearity has upon the extension and strength of connectivity, if this is understood as a characterization of the degree of interrelation between parts of the system. This objective is reached within the QP formalism for non-linear ODEs. The formalism is developed in a graph-theoretic setting, with the help of which the connectionist aspect of non-linearity becomes apparent. Topology-preserving transformations involve an exchange between the degree of non-linearity and the strengths of interactions, thus assembling systems of apparently different nature into classes of equivalence. We argue that, if we have in mind a classification of systems according to behavior, these classes of equivalence should be given their proper singularity. We characterize globally the connectivity of a class with an index, although we point out during the discussion that the mathematical conception of the complex idea of connectivity is still incomplete.

Linear Models↗

PubMed2006

A methodology for the structural and functional analysis of signaling and regulatory networks.

BACKGROUND: Structural analysis of cellular interaction networks contributes to a deeper understanding of network-wide interdependencies, causal relationships, and basic functional capabilities. While the structural analysis of metabolic networks is a well-established field, similar methodologies have been scarcely developed and applied to signaling and regulatory networks. RESULTS: We propose formalisms and methods, relying on adapted and partially newly introduced approaches, which facilitate a structural analysis of signaling and regulatory networks with focus on functional aspects. We use two different formalisms to represent and analyze interaction networks: interaction graphs and (logical) interaction hypergraphs. We show that, in interaction graphs, the determination of feedback cycles and of all the signaling paths between any pair of species is equivalent to the computation of elementary modes known from metabolic networks. Knowledge on the set of signaling paths and feedback loops facilitates the computation of intervention strategies and the classification of compounds into activators, inhibitors, ambivalent factors, and non-affecting factors with respect to a certain species. In some cases, qualitative effects induced by perturbations can be unambiguously predicted from the network scheme. Interaction graphs however, are not able to capture AND relationships which do frequently occur in interaction networks. The consequent logical concatenation of all the arcs pointing into a species leads to Boolean networks. For a Boolean representation of cellular interaction networks we propose a formalism based on logical (or signed) interaction hypergraphs, which facilitates in particular a logical steady state analysis (LSSA). LSSA enables studies on the logical processing of signals and the identification of optimal intervention points (targets) in cellular networks. LSSA also reveals network regions whose parametrization and initial states are crucial for the dynamic behavior. We have implemented these methods in our software tool CellNetAnalyzer (successor of FluxAnalyzer) and illustrate their applicability using a logical model of T-Cell receptor signaling providing non-intuitive results regarding feedback loops, essential elements, and (logical) signal processing upon different stimuli. CONCLUSION: The methods and formalisms we propose herein are another step towards the comprehensive functional analysis of cellular interaction networks. Their potential, shown on a realistic T-cell signaling model, makes them a promising tool.

Animals↗

PubMedDate not supplied

Stability of generalized topographic mappings between cell layers through correlational learning.

We propose a simple topographic mapping formation model from a cell layer to a cell layer. Our model is a discrete one in that the state value of input and output cells takes 0 or 1 and input and output layers are represented by undirected graphs. A binary input pattern can be given to the network consisting of input and output cell layers. Such an input pattern can be represented by a subset of input cells. That is, a state value of an input cell takes 1 if a cell belongs to the subset, otherwise, a state value of an input cell is 0. Such a definition of an input pattern does not necessarily assume a short-range excitatory mechanism in an input layer. Thus, a topographic mapping described in this model is a map, which preserves the input pattern relation. By using the concept of input pattern separability, we showed an existence condition of certain learning rules, which are correlational. We have paid special attention to such correlational type learning rules, and have shown under the rules that topographic mappings are the only stable ones. As to the non-correlational learning rules, we also investigate the stability of generated mappings.

Algorithms↗

PubMed2000

[Prediction and estimation on molar response values of alkanes by using molecular path vector].

A new method based on a novel molecular topological index vector, called the molecular path vector (MPV), of alkane molecules is proposed and employed for estimation and prediction of the molar response values of various alkanes. The novel MPV, p = (P1, P2, P3, P4, P5, P6, P7, P8, P9, P10)', which derived directly from the interaction terms of molecular graph, is used to characterize well molecular structures of all alkanes from one through ten or eleven carbon atoms. It showed that there exists very good correlation between the MPV elements and molar response values on both FID and TCD detectors in classical gas chromatography. Based on the given calibration set with different sample numbers and by using the practical multiple linear regression, the quantitative structure-response relationship (QSRR) equations, for the molar response values (SM) on both FID and TCD, are respectively given as follows: SM(FID) = 15.4004881 + 17.9905995 X1 - 0.1652116 X2 - 0.6974103 X3 - 0.8452390 X4 - 0.2671000 X5 - 1.5657273 X6 + 0.0944440 X7, n = 50, m = 7, r = 0.9976, ST = 26.132, SR = 1.965 1, Ev = 99.72%, RMS = 1.801, F = 1231.71 SM(TCD) = 11.9946996 + 29.1490916 X1 - 4.7451669 X2 - 3.7673385 X3 - 1.4948330 X4 - 1.6278831 X5 - 0.7934611 X6 - 3.0566093 X7, n = 32, m = 7, r = 0.9968, ST = 15.72, SR = 1.4310, Ev = 99.59%, RMS = 1.239, F = 531.227 where the independent descriptor variables, X1-X7, refer to the elements, P1, P2, P3, P4, P5, P6, P7 in the molecular path vector for all samples in both FID and TCD training sets; n, r, ST, SR, Ev, RMS and F are the sample number, regression coefficient, total standard deviation, standard residual deviation, explained variance, rooted mean squared error and F-statistic value, respectively. To test both models by using back-propagation neural network (BPNN) with the topological structure NN(7-4-2) and the cross validation through leave-one-out (LOO) procedure, the correlation coefficient of cross validation is over 0.96. Because there exists a quite good linear relationship between the molar responses and molecular path parameters, BPNN (r = 0.989 and 0.968) does not show its nonlinear advantage over multiple linear regression(MLR) (r = 0.9976 and 0.9968) in both presently examined cases, FID and TCD in the GC technique, for molecular modelling and quantitative prediction.

Alkanes↗

PubMed2006

A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs.

Small-world properties have been demonstrated for many complex networks. Here, we applied the discrete wavelet transform to functional magnetic resonance imaging (fMRI) time series, acquired from healthy volunteers in the resting state, to estimate frequency-dependent correlation matrices characterizing functional connectivity between 90 cortical and subcortical regions. After thresholding the wavelet correlation matrices to create undirected graphs of brain functional networks, we found a small-world topology of sparse connections most salient in the low-frequency interval 0.03-0.06 Hz. Global mean path length (2.49) was approximately equivalent to a comparable random network, whereas clustering (0.53) was two times greater; similar parameters have been reported for the network of anatomical connections in the macaque cortex. The human functional network was dominated by a neocortical core of highly connected hubs and had an exponentially truncated power law degree distribution. Hubs included recently evolved regions of the heteromodal association cortex, with long-distance connections to other regions, and more cliquishly connected regions of the unimodal association and primary cortices; paralimbic and limbic regions were topologically more peripheral. The network was more resilient to targeted attack on its hubs than a comparable scale-free network, but about equally resilient to random error. We conclude that correlated, low-frequency oscillations in human fMRI data have a small-world architecture that probably reflects underlying anatomical connectivity of the cortex. Because the major hubs of this network are critical for cognition, its slow dynamics could provide a physiological substrate for segregated and distributed information processing.

Adult↗

PubMedDate not supplied

Synaptic weight normalization effects for topographic mapping formation.

We propose a simple topographic mapping formation model between cell layers with weight normalization. In our model, each cell layer can have an arbitrary neighborhood relation between the cells represented by an undirected graph. Thus, a topographic mapping described in this model is a map which preserves the adjacency relation. We define several learning rules, input and output type weight normalization methods. Then, we not only concentrate on a Hebbean weight modification but also investigate the effects of normalization under a non-Hebbean weight modification. We first show that when an input type normalization is adopted or without normalization, a topographic mapping is stable under the correlational type learning rule, but when an output type normalization is adopted a topographic mapping is stable under not only the correlational type learning rule but also the non-correlational one. Next, we show by computer simulations that when an output type normalization is considered we have more learning rules which yield topographic mappings than the cases when an input type normalization is adopted or without normalization.

Algorithms↗

PubMed2006

Evaluation of the GTRACT diffusion tensor tractography algorithm: a validation and reliability study.

Fiber tracking, based on diffusion tensor imaging (DTI), is the only approach available to non-invasively study the three-dimensional structure of white matter tracts. Two major obstacles to this technique are partial volume artifacts and tracking errors caused by image noise. In this paper, a novel fiber tracking algorithm called Guided Tensor Restore Anatomical Connectivity Tractography (GTRACT) is presented. This algorithm utilizes a multi-pass approach to fiber tracking. In the first pass, a 3D graph search algorithm is utilized. The second pass incorporates anatomical connectivity information generated in the first pass to guide the tracking in this stage. This approach improves the ability to reconstruct complex fiber paths as well as the tracking accuracy. Validation and reliability studies using this algorithm were performed on both synthetic phantom data and clinical human brain data. A method is also proposed for the evaluating reliability of fiber tract generation based both on the position of the fiber tracts, as well the anisotropy values along the path. The results demonstrate that the GTRACT algorithm is less sensitive to image noise and more capable of handling areas of complex fiber crossing, compared to conventional streamline methods.

Algorithms↗

PubMed2006

Prediction of the main cortical areas and connections involved in the tactile function of the visual cortex by network analysis.

We explored the cortical pathways from the primary somatosensory cortex to the primary visual cortex (V1) by analysing connectional data in the macaque monkey using graph-theoretical tools. Cluster analysis revealed the close relationship of the dorsal visual stream and the sensorimotor cortex. It was shown that prefrontal area 46 and parietal areas VIP and 7a occupy a central position between the different clusters in the visuo-tactile network. Among these structures all the shortest paths from primary somatosensory cortex (3a, 1 and 2) to V1 pass through VIP and then reach V1 via MT, V3 and PO. Comparison of the input and output fields suggested a larger specificity for the 3a/1-VIP-MT/V3-V1 pathways among the alternative routes. A reinforcement learning algorithm was used to evaluate the importance of the aforementioned pathways. The results suggest a higher role for V3 in relaying more direct sensorimotor information to V1. Analysing cliques, which identify areas with the strongest coupling in the network, supported the role of VIP, MT and V3 in visuo-tactile integration. These findings indicate that areas 3a, 1, VIP, MT and V3 play a major role in shaping the tactile information reaching V1 in both sighted and blind subjects. Our observations greatly support the findings of the experimental studies and provide a deeper insight into the network architecture underlying visuo-tactile integration in the primate cerebral cortex.

Algorithms↗

PubMed2026

Beyond one-to-one mappings: Modelling distributed lesion-symptom relationships with multilayer networks.

Lesion-symptom mapping is widely used to identify causal relationships between brain structures and behaviour, and has played a central role in neuropsychologically informed network models of cognition. However, even recent approaches remain constrained by a one-to-one mapping framework, which oversimplifies the complex relationships between network-level damage and cognitive deficits. In addition, the non-orthogonality of cortical and white matter damage makes it difficult to disentangle their distinct contributions. Here, we used graph-based multilayer network analysis to address these limitations and evaluate clinical relevance. Using neuroanatomical and longitudinal neuropsychological data from 252 patients who underwent awake neurosurgery for low-grade glioma, we constructed interactive, three-layer networks for each hemisphere. Layer 1 comprised neuropsychological tasks (NT), layer 2 structural disconnections (SD), and layer 3 cortical damage (CD). Nodes represented tasks, white matter tracts, and cortical parcels, respectively, whereas within-layer edges captured correlations in performance or co-occurring damage patterns. Multilayer community detection identified domain- and hemisphere-specific brain-behaviour motifs linking executive, language, and spatial functions to distinct combinations of cortical and white matter disruption, a pattern confirmed by two spatial embedding approaches. Centrality analyses revealed a continuum of mapping relationships, ranging from one-to-one to one-to-many associations, indicating that tasks such as verbal fluency are better explained by multiple disconnection mechanisms. Additional analyses uncovered many-to-one and many-to-many relationships and highlighted tracts and cortical regions with domain-general relevance. Together, these findings support a neurobiologically grounded, network-oriented account of how structural brain damage gives rise to cognitive deficits, with implications for clinical care.

Humans↗

PubMed2004

Chaotic dynamics of a behavior-based miniature mobile robot: effects of environment and control structure.

To study the regularity and complexity of autonomous behavior, the flow of sensory information obtained in autonomous mobile robots under various conditions was analyzed as a complex system. Sensory information time series Xn was collected from a miniature mobile robot during free navigation, and plotted on the return map, the graph of X(n+tau) vs. Xn. The plot exhibited a characteristic trajectory, representing the regularity of the time series. Correlation integral and Lyapunov exponent analysis also showed properties of deterministic chaos; the presence of fractal dimension and positive Lyapunov exponent. Analysis of sensory information obtained in the robot with three different neural controllers revealed that the autonomous robot behaves in such a way that the flow of sensory information is governed by a deterministic rule, and this pattern is unique to each controller. Furthermore, the analysis in various environments exhibited that transitions from one trajectory to another on the return map occur during the course of autonomous behavior. The fractal and Lyapunov dimensions calculated in various conditions indicate that these dimension could be utilized to quantify the complexity of autonomous behavior and the relative difficulty of tasks. Analyses at different evolutionary stage revealed that behavioral performance correlates with fractal dimension. These studies using a miniature mobile robot that allowed to idealize the experimental conditions demonstrated firmly that the complex analysis could be utilized in evaluation and optimization of autonomous systems and the behavior.

Behavior↗

PubMed1991

The principle of interval constraints: a generalization of the symmetric Dirichlet distribution.

A structure for representing problems in decision analysis and in expert systems, which reason under uncertainty, is the influence diagram or causal network. A causal network consists of an underlying joint probability distribution and a directed acyclic graph in which a propositional variable that represents a marginal distribution is stored at each vertex in the graph. This paper is concerned with two of the problems in applications that use causal networks. The first problem is the determination of the conditional probabilities of the values of remaining propositional variables in the network given that certain variables are instantiated for particular values. This is called probability propagation. The second problem is the determination of the most probable, second most probable, third most probable, and so on sets of values of a particular set of variables (called the explanation set) given that certain variables are instantiated for particular values. This problem is called abductive inference. There exists a class of causal networks in which each variable has only two parents, for which the time is required, by any known method, for probability propagation is exponential relative to the number of vertices in the network. The determination of a new method that would be efficient for all causal networks appears unlikely, because probability propagation has been shown to be #P-complete. In many medical applications, networks are often large and not sparsely connected. Therefore a method for the exact determination of probability values appears unlikely for such applications, and the development of approximation methods seems to be the best solution. The current approximation methods obtain interval bounds for the probability values. When such intervals are obtained, it is not possible in general to rank the alternatives. In this paper, a method is developed for obtaining expected values for the point probabilities from interval constraints on the probabilities. The method is based on an application of the principle of indifference to the probability values themselves. The distributions obtained with the principle of indifference are a generalization of the symmetric Dirichlet distribution in which prior ignorance is assumed.

Decision Making↗

PubMed2005

Undirected graphs of frequency-dependent functional connectivity in whole brain networks.

We explored properties of whole brain networks based on multivariate spectral analysis of human functional magnetic resonance imaging (fMRI) time-series measured in 90 cortical and subcortical subregions in each of five healthy volunteers studied in the (no-task) resting state. We note that undirected graphs representing conditional independence between multivariate time-series can be more readily approached in the frequency domain than the time domain. Estimators of partial coherency and normalized partial mutual information phi, an integrated measure of partial coherence over an arbitrary frequency band, are applied. Using these tools, we replicate the prior observations that bilaterally homologous brain regions tend to be strongly connected and functional connectivity is generally greater at low frequencies [0.0004, 0.1518 Hz]. We also show that long-distance intrahemispheric connections between regions of prefrontal and parietal cortex were more salient at low frequencies than at frequencies greater than 0.3 Hz, whereas many local or short-distance connections, such as those comprising segregated dorsal and ventral paths in posterior cortex, were also represented in the graph of high-frequency connectivity. We conclude that the partial coherency spectrum between a pair of human brain regional fMRI time-series depends on the anatomical distance between regions: long-distance (greater than 7 cm) edges represent conditional dependence between bilaterally symmetric neocortical regions, and between regions of prefrontal and parietal association cortex in the same hemisphere, are predominantly subtended by low-frequency components.

Brain↗

PubMed1998

Periodically-modulated inhibition of living pacemaker neurons--III. The heterogeneity of the postsynaptic spike trains, and how control parameters affect it.

Codings involving spike trains at synapses with inhibitory postsynaptic potentials on pacemakers were examined in crayfish stretch receptor organs by modulating presynaptic instantaneous rates periodically (triangles or sines; frequencies, slopes and depths under, respectively, 5.0 Hz, 40.0/s/s and 25.0/s). Timings were described by interspike and cross-intervals ("phases"); patterns (dispersions, sequences) and forms (timing classes) were identified using pooled graphs (instant along the cycle when a spike occurs vs preceding interval) and return maps (plots of successive intervals). A remarkable heterogeneity of postsynaptic intervals and phases characterizes each modulation. All cycles separate into the same portions: each contains a particular form and switches abruptly to the next. Forms differ in irregularity and predictability: they are (see text) "p:q alternations", "intermittent", "phase walk-throughs", "messy erratic" and "messy stammering". Postsynaptic cycles are asymmetric (hysteresis). This contrasts with the presynaptic homogeneity, smoothness and symmetry. All control parameters are, individually and jointly, strongly influential. Presynaptic slopes, say, act through a postsynaptic sensitivity to their magnitude and sign; when increasing, hysteresis augments and forms change or disappear. Appropriate noise attenuates between-train contrasts, providing modulations are under 0.5 Hz. Postsynaptic natural intervals impose critical time bases, separating presynaptic intervals (around, above or below them) with dissimilar consequences. Coding rules are numerous and have restricted domains; generalizations are misleading. Modulation-driven forms are trendy pacemaker-driven forms. However, dissimilarities, slight when patterns are almost pacemaker, increase as inhibition departs from pacemaker and incorporate unpredictable features. Physiological significance-(1) Pacemaker-driven forms, simple and ubiquitous, appear to be elementary building blocks of synaptic codings, present always but in each case distorted typically. (2) Synapses are prototype: similar behaviours should be widespread, and networks simulations benefit by nonlinear units generating all forms. (3) Relevant to periodic functions are that few variables need be involved in form selection, that distortions are susceptible to noise levels and, if periods are heterogeneous, that simple input cycles impose heterogeneous outputs. (4) Slow Na inactivations are necessary for obtaining complex forms and hysteresis. Formal significance--(1) Pacemaker-driven forms and presumably their modulation-driven counterparts, pertain to universal periodic, intermittent, quasiperiodic and chaotic categories whose formal properties carry physiological connotations. (2) Only relatively elaborate, nonlinear geometric models show all forms; simpler ones, show only alternations and walk-throughs. (3) Bifurcations resemble those of simple maps that can provide useful guidelines. (4) Heterogeneity poses the unanswered question of whether or not the entire cycle and all portions have the same behaviours: therefore, whether trajectories are continuous or have discontinuities and/or singular points.

Action Potentials↗