Parametric construction of episode networks from pseudoperiodic time series based on mutual information

Recently, the construction of networks from time series data has gained widespread interest. In this paper, we develop this area further by introducing a network construction procedure for pseudoperiodic time series. We call such networks episode networks, in which an episode corresponds to a temporal interval of a time series, and which defines a node in the network. Our model includes a number of features which distinguish it from current methods. First, the proposed construction procedure is a parametric model which allows it to adapt to the characteristics of the data; the length of an episode being the parameter. As a direct consequence, networks of minimal size containing the maximal information about the time series can be obtained. In this paper, we provide an algorithm to determine the optimal value of this parameter. Second, we employ estimates of mutual information values to define the connectivity structure among the nodes in the network to exploit efficiently the nonlinearities in the time series. Finally, we apply our method to data from electroencephalogram (EEG) experiments and demonstrate that the constructed episode networks capture discriminative information from the underlying time series that may be useful for diagnostic purposes.     

A Multivariate Granger Causality Concept towards Full Brain Functional Connectivity

Detecting changes of spatially high-resolution functional connectivity patterns in the brain is crucial for improving the fundamental understanding of brain function in both health and disease, yet still poses one of the biggest challenges in computational neuroscience. Currently, classical multivariate Granger Causality analyses of directed interactions between single process components in coupled systems are commonly restricted to spatially low- dimensional data, which requires a pre-selection or aggregation of time series as a preprocessing step. In this paper we propose a new fully multivariate Granger Causality approach with embedded dimension reduction that makes it possible to obtain a representation of functional connectivity for spatially high-dimensional data. The resulting functional connectivity networks may consist of several thousand vertices and thus contain more detailed information compared to connectivity networks obtained from approaches based on particular regions of interest. Our large scale Granger Causality approach is applied to synthetic and resting state fMRI data with a focus on how well network community structure, which represents a functional segmentation of the network, is preserved. It is demonstrated that a number of different community detection algorithms, which utilize a variety of algorithmic strategies and exploit topological features differently, reveal meaningful information on the underlying network module structure.     

The Problem of Thresholding in Small-World Network Analysis

Graph theory deterministically models networks as sets of vertices, which are linked by connections. Such mathematical representation of networks, called graphs are increasingly used in neuroscience to model functional brain networks. It was shown that many forms of structural and functional brain networks have small-world characteristics, thus, constitute networks of dense local and highly effective distal information processing. Motivated by a previous small-world connectivity analysis of resting EEG-data we explored implications of a commonly used analysis approach. This common course of analysis is to compare small-world characteristics between two groups using classical inferential statistics. This however, becomes problematic when using measures of inter-subject correlations, as it is the case in commonly used brain imaging methods such as structural and diffusion tensor imaging with the exception of fibre tracking. Since for each voxel, or region there is only one data point, a measure of connectivity can only be computed for a group. To empirically determine an adequate small-world network threshold and to generate the necessary distribution of measures for classical inferential statistics, samples are generated by thresholding the networks on the group level over a range of thresholds. We believe that there are mainly two problems with this approach. First, the number of thresholded networks is arbitrary. Second, the obtained thresholded networks are not independent samples. Both issues become problematic when using commonly applied parametric statistical tests. Here, we demonstrate potential consequences of the number of thresholds and non-independency of samples in two examples (using artificial data and EEG data). Consequently alternative approaches are presented, which overcome these methodological issues.     

Altered Functional Connectivity between Emotional and Cognitive Resting State Networks in Euthymic Bipolar I Disorder Patients

Bipolar disorder is characterized by a functional imbalance between hyperactive ventral/limbic areas and hypoactive dorsal/cognitive brain regions potentially contributing to affective and cognitive symptoms. Resting-state studies in bipolar disorder have identified abnormal functional connectivity between these brain regions. However, most of these studies used a seed-based approach, thus restricting the number of regions that were analyzed. Using data-driven approaches, researchers identified resting state networks whose spatial maps overlap with frontolimbic areas such as the default mode network, the frontoparietal networks, the salient network, and the meso/paralimbic network. These networks are specifically engaged during affective and cognitive tasks and preliminary evidence suggests that functional connectivity within and between some of these networks is impaired in bipolar disorder. The present study used independent component analysis and functional network connectivity approaches to investigate functional connectivity within and between these resting state networks in bipolar disorder. We compared 30 euthymic bipolar I disorder patients and 35 age- and gender-matched healthy controls. Inter-network connectivity analysis revealed increased functional connectivity between the meso/paralimbic and the right frontoparietal network in bipolar disorder. This abnormal connectivity pattern did not correlate with variables related to the clinical course of the disease. The present finding may reflect abnormal integration of affective and cognitive information in ventral-emotional and dorsal-cognitive networks in euthymic bipolar patients. Furthermore, the results provide novel insights into the role of the meso/paralimbic network in bipolar disorder.     

WNP: a novel algorithm for gene products annotation from weighted functional networks

Predicting the biological function of all the genes of an organism is one of the fundamental goals of computational system biology. In the last decade, high-throughput experimental methods for studying the functional interactions between gene products (GPs) have been combined with computational approaches based on Bayesian networks for data integration. The result of these computational approaches is an interaction network with weighted links representing connectivity likelihood between two functionally related GPs. The weighted network generated by these computational approaches can be used to predict annotations for functionally uncharacterized GPs. Here we introduce Weighted Network Predictor (WNP), a novel algorithm for function prediction of biologically uncharacterized GPs. Tests conducted on simulated data show that WNP outperforms other 5 state-of-the-art methods in terms of both specificity and sensitivity and that it is able to better exploit and propagate the functional and topological information of the network. We apply our method to Saccharomyces cerevisiae yeast and Arabidopsis thaliana networks and we predict Gene Ontology function for about 500 and 10000 uncharacterized GPs respectively.     

Bayesian Hierarchical Functional Data Analysis Via Contaminated Informative Priors

Summary .  A variety of flexible approaches have been proposed for functional data analysis, allowing both the mean curve and the distribution about the mean to be unknown. Such methods are most useful when there is limited prior information. Motivated by applications to modeling of temperature curves in the menstrual cycle, this article proposes a flexible approach for incorporating prior information in semiparametric Bayesian analyses of hierarchical functional data. The proposed approach is based on specifying the distribution of functions as a mixture of a parametric hierarchical model and a nonparametric contamination. The parametric component is chosen based on prior knowledge, while the contamination is characterized as a functional Dirichlet process. In the motivating application, the contamination component allows unanticipated curve shapes in unhealthy menstrual cycles. Methods are developed for posterior computation, and the approach is applied to data from a European fecundability study.     

A method for the estimation of functional brain connectivity from time-series data

A central issue in cognitive neuroscience is which cortical areas are involved in managing information processing in a cognitive task and to understand their temporal interactions. Since the transfer of information in the form of electrical activity from one cortical region will in turn evoke electrical activity in other regions, the analysis of temporal synchronization provides a tool to understand neuronal information processing between cortical regions. We adopt a method for revealing time-dependent functional connectivity. We apply statistical analyses of phases to recover the information flow and the functional connectivity between cortical regions for high temporal resolution data. We further develop an evaluation method for these techniques based on two kinds of model networks. These networks consist of coupled Rössler attractors or of coupled stochastic Ornstein–Uhlenbeck systems. The implemented time-dependent coupling includes uni- and bi-directional connectivities as well as time delayed feedback. The synchronization dynamics of these networks are analyzed using the mean phase coherence, based on averaging over phase-differences, and the general synchronization index. The latter is based on the Shannon entropy. The combination of these with a parametric time delay forms the basis of a connectivity pattern, which includes the temporal and time lagged dynamics of the synchronization between two sources. We model and discuss potential artifacts. We find that the general phase measures are remarkably stable. They produce highly comparable results for stochastic and periodic systems. Moreover, the methods proves useful for identifying brief periods of phase coupling and delays. Therefore, we propose that the method is useful as a basis for generating potential functional connective models.     

Learning genetic regulatory network connectivity from time series data

Recent experimental advances facilitate the collection of time series data that indicate which genes in a cell are expressed. This information can be used to understand the genetic regulatory network that generates the data. Typically, Bayesian analysis approaches are applied which neglect the time series nature of the experimental data, have difficulty in determining the direction of causality, and do not perform well on networks with tight feedback. To address these problems, this paper presents a method to learn genetic network connectivity which exploits the time series nature of experimental data to achieve better causal predictions. This method first breaks up the data into bins. Next, it determines an initial set of potential influence vectors for each gene based upon the probability of the gene's expression increasing in the next time step. These vectors are then combined to form new vectors with better scores. Finally, these influence vectors are competed against each other to determine the final influence vector for each gene. The result is a directed graph representation of the genetic network's repression and activation connections. Results are reported for several synthetic networks with tight feedback showing significant improvements in recall and runtime over Yu's dynamic Bayesian approach. Promising preliminary results are also reported for an analysis of experimental data for genes involved in the yeast cell cycle.     

Reconstructing gene regulatory networks: from random to scale-free connectivity

The manipulation of organisms using combinations of gene knockout, RNAi and drug interaction experiments can be used to reveal regulatory interactions between genes. Several algorithms have been proposed that try to reconstruct the underlying regulatory networks from gene expression data sets arising from such experiments. Often these approaches assume that each gene has approximately the same number of interactions within the network, and the methods rely on prior knowledge, or the investigator's best guess, of the average network connectivity. Recent evidence points to scale-free properties in biological networks, however, where network connectivity follows a power-law distribution. For scale-free networks, the average number of regulatory interactions per gene does not satisfactorily characterise the network. With this in mind, a new reverse engineering approach is introduced that does not require prior knowledge of network connectivity and its performance is compared with other published algorithms using simulated gene expression data with biologically relevant network structures. Because this new approach does not make any assumptions about the distribution of network connections, it is suitable for application to scale-free networks.     

Information maintenance and statistical dependence reduction in simple neural networks

This study compares the ability of excitatory, feed-forward neural networks to construct good transformations on their inputs. The quality of such a transformation is judged by the minimization of two information measures: the information loss of the transformation and the statistical dependency of the output. The networks that are compared differ from each other in the parametric properties of their neurons and in their connectivity. The particular network parameters studied are output firing threshold, synaptic connectivity, and associative modification of connection weights. The network parameters that most directly affect firing levels are threshold and connectivity. Networks incorporating neurons with dynamic threshold adjustment produce better transformations. When firing threshold is optimized, sparser synaptic connectivity produces a better transformation than denser connectivity. Associative modification of synaptic weights confers only a slight advantage in the construction of optimal transformations. Additionally, our research shows that some environments are better suited than others for recoding. Specifically, input environments high in statistical dependence, i.e. those environments most in need of recoding, are more likely to undergo successful transformations.     

Modelling paired survival data with covariates

The objective of this paper is to consider the parametric analysis of paired censored survival data when additional covariate information is available, as in the Diabetic Retinopathy Study, which assessed the effectiveness of laser photocoagulation in delaying loss of visual acuity. Our first approach is to extend the fully parametric model of Clayton (1978, Biometrika 65, 141-151) to incorporate covariate information. Our second approach is to obtain parameter estimates from an independence working model together with robust variance estimates. The approaches are compared in terms of efficiency and computational considerations. A fundamental consideration in choosing a strategy for the analysis of paired survival data is whether the correlation within a pair is a nuisance parameter or a parameter of intrinsic scientific interest. The approaches are illustrated with the Diabetic Retinopathy Study.     

Decoding lifespan changes of the human brain using resting-state functional connectivity MRI

The development of large-scale functional brain networks is a complex, lifelong process that can be investigated using resting-state functional connectivity MRI (rs-fcMRI). In this study, we aimed to decode the developmental dynamics of the whole-brain functional network in seven decades (8-79 years) of the human lifespan. We first used parametric curve fitting to examine linear and nonlinear age effect on the resting human brain, and then combined manifold learning and support vector machine methods to predict individuals' "brain ages" from rs-fcMRI data. We found that age-related changes in interregional functional connectivity exhibited spatially and temporally specific patterns. During brain development from childhood to senescence, functional connections tended to linearly increase in the emotion system and decrease in the sensorimotor system; while quadratic trajectories were observed in functional connections related to higher-order cognitive functions. The complex patterns of age effect on the whole-brain functional network could be effectively represented by a low-dimensional, nonlinear manifold embedded in the functional connectivity space, which uncovered the inherent structure of brain maturation and aging. Regression of manifold coordinates with age further showed that the manifold representation extracted sufficient information from rs-fcMRI data to make prediction about individual brains' functional development levels. Our study not only gives insights into the neural substrates that underlie behavioral and cognitive changes over age, but also provides a possible way to quantitatively describe the typical and atypical developmental progression of human brain function using rs-fcMRI.     

Connectivity matrix method for analyses of biological networks and its application to atom-level analysis of a model network of carbohydrate metabolism

An approach for analysis of biological networks is proposed. In this approach, named the connectivity matrix (CM) method, all the connectivities of interest are expressed in a matrix. Then, a variety of analyses are performed on GNU Octave or Matlab. Each node in the network is expressed as a row vector or numeral that carries information defining or characterising the node itself. Information about connectivity itself is also expressed as a row vector or numeral. Thus, connection of node n1 to node n2 through edge e is expressed as [n1, n2, e], a row vector formed by the combination of three row vectors or numerals, where n1, n2 and e indicate two different nodes and one connectivity, respectively. All the connectivities in any given network are expressed as a matrix, CM, each row of which corresponds to one connectivity. Using this CM method, intermetabolite atom-level connectivity is investigated in a model metabolic network composed of the reactions for glycolysis, oxidative decarboxylation of pyruvate, citric acid cycle, pentose phosphate pathway and gluconeogenesis.     

Metabolic network discovery through reverse engineering of metabolome data

Reverse engineering of high-throughput omics data to infer underlying biological networks is one of the challenges in systems biology. However, applications in the field of metabolomics are rather limited. We have focused on a systematic analysis of metabolic network inference from in silico metabolome data based on statistical similarity measures. Three different data types based on biological/environmental variability around steady state were analyzed to compare the relative information content of the data types for inferring the network. Comparing the inference power of different similarity scores indicated the clear superiority of conditioning or pruning based scores as they have the ability to eliminate indirect interactions. We also show that a mathematical measure based on the Fisher information matrix gives clues on the information quality of different data types to better represent the underlying metabolic network topology. Results on several datasets of increasing complexity consistently show that metabolic variations observed at steady state, the simplest experimental analysis, are already informative to reveal the connectivity of the underlying metabolic network with a low false-positive rate when proper similarity-score approaches are employed. For experimental situations this implies that a single organism under slightly varying conditions may already generate more than enough information to rightly infer networks. Detailed examination of the strengths of interactions of the underlying metabolic networks demonstrates that the edges that cannot be captured by similarity scores mainly belong to metabolites connected with weak interaction strength.     

Intra- and Inter-Frequency Brain Network Structure in Health and Schizophrenia

Empirical studies over the past two decades have provided support for the hypothesis that schizophrenia is characterized by altered connectivity patterns in functional brain networks. These alterations have been proposed as genetically mediated diagnostic biomarkers and are thought to underlie altered cognitive functions such as working memory. However, the nature of this dysconnectivity remains far from understood. In this study, we perform an extensive analysis of functional connectivity patterns extracted from MEG data in 14 subjects with schizophrenia and 14 healthy controls during a 2-back working memory task. We investigate uni-, bi- and multivariate properties of sensor time series by computing wavelet entropy of and correlation between time series, and by constructing binary networks of functional connectivity both within and between classical frequency bands (, , , and ). Networks are based on the mutual information between wavelet time series, and estimated for each trial window separately, enabling us to consider both network topology and network dynamics. We observed significant decreases in time series entropy and significant increases in functional connectivity in the schizophrenia group in comparison to the healthy controls and identified an inverse relationship between these measures across both subjects and sensors that varied over frequency bands and was more pronounced in controls than in patients. The topological organization of connectivity was altered in schizophrenia specifically in high frequency and band networks as well as in the - cross-frequency networks. Network topology varied over trials to a greater extent in patients than in controls, suggesting disease-associated alterations in dynamic network properties of brain function. Our results identify signatures of aberrant neurophysiological behavior in schizophrenia across uni-, bi- and multivariate scales and lay the groundwork for further clinical studies that might lead to the discovery of new intermediate phenotypes.     

Validation of Network Communicability Metrics for the Analysis of Brain Structural Networks

Computational network analysis provides new methods to analyze the brain''s structural organization based on diffusion imaging tractography data. Networks are characterized by global and local metrics that have recently given promising insights into diagnosis and the further understanding of psychiatric and neurologic disorders. Most of these metrics are based on the idea that information in a network flows along the shortest paths. In contrast to this notion, communicability is a broader measure of connectivity which assumes that information could flow along all possible paths between two nodes. In our work, the features of network metrics related to communicability were explored for the first time in the healthy structural brain network. In addition, the sensitivity of such metrics was analysed using simulated lesions to specific nodes and network connections. Results showed advantages of communicability over conventional metrics in detecting densely connected nodes as well as subsets of nodes vulnerable to lesions. In addition, communicability centrality was shown to be widely affected by the lesions and the changes were negatively correlated with the distance from lesion site. In summary, our analysis suggests that communicability metrics that may provide an insight into the integrative properties of the structural brain network and that these metrics may be useful for the analysis of brain networks in the presence of lesions. Nevertheless, the interpretation of communicability is not straightforward; hence these metrics should be used as a supplement to the more standard connectivity network metrics.     

Synaptic information transfer in computer models of neocortical columns

Understanding the direction and quantity of information flowing in neuronal networks is a fundamental problem in neuroscience. Brains and neuronal networks must at the same time store information about the world and react to information in the world. We sought to measure how the activity of the network alters information flow from inputs to output patterns. Using neocortical column neuronal network simulations, we demonstrated that networks with greater internal connectivity reduced input/output correlations from excitatory synapses and decreased negative correlations from inhibitory synapses, measured by Kendall’s τ correlation. Both of these changes were associated with reduction in information flow, measured by normalized transfer entropy (nTE). Information handling by the network reflected the degree of internal connectivity. With no internal connectivity, the feedforward network transformed inputs through nonlinear summation and thresholding. With greater connectivity strength, the recurrent network translated activity and information due to contribution of activity from intrinsic network dynamics. This dynamic contribution amounts to added information drawn from that stored in the network. At still higher internal synaptic strength, the network corrupted the external information, producing a state where little external information came through. The association of increased information retrieved from the network with increased gamma power supports the notion of gamma oscillations playing a role in information processing.     

Model guided trait-specific co-expression network estimation as a new perspective for identifying molecular interactions and pathways

A wide variety of 1) parametric regression models and 2) co-expression networks have been developed for finding gene-by-gene interactions underlying complex traits from expression data. While both methodological schemes have their own well-known benefits, little is known about their synergistic potential. Our study introduces their methodological fusion that cross-exploits the strengths of individual approaches via a built-in information-sharing mechanism. This fusion is theoretically based on certain trait-conditioned dependency patterns between two genes depending on their role in the underlying parametric model. Resulting trait-specific co-expression network estimation method 1) serves to enhance the interpretation of biological networks in a parametric sense, and 2) exploits the underlying parametric model itself in the estimation process. To also account for the substantial amount of intrinsic noise and collinearities, often entailed by expression data, a tailored co-expression measure is introduced along with this framework to alleviate related computational problems. A remarkable advance over the reference methods in simulated scenarios substantiate the method’s high-efficiency. As proof-of-concept, this synergistic approach is successfully applied in survival analysis, with acute myeloid leukemia data, further highlighting the framework’s versatility and broad practical relevance.     

Network modeling of dynamic brain interactions predicts emergence of neural information that supports human cognitive behavior

How cognitive task behavior is generated by brain network interactions is a central question in neuroscience. Answering this question calls for the development of novel analysis tools that can firstly capture neural signatures of task information with high spatial and temporal precision (the “where and when”) and then allow for empirical testing of alternative network models of brain function that link information to behavior (the “how”). We outline a novel network modeling approach suited to this purpose that is applied to noninvasive functional neuroimaging data in humans. We first dynamically decoded the spatiotemporal signatures of task information in the human brain by combining MRI-individualized source electroencephalography (EEG) with multivariate pattern analysis (MVPA). A newly developed network modeling approach—dynamic activity flow modeling—then simulated the flow of task-evoked activity over more causally interpretable (relative to standard functional connectivity [FC] approaches) resting-state functional connections (dynamic, lagged, direct, and directional). We demonstrate the utility of this modeling approach by applying it to elucidate network processes underlying sensory–motor information flow in the brain, revealing accurate predictions of empirical response information dynamics underlying behavior. Extending the model toward simulating network lesions suggested a role for the cognitive control networks (CCNs) as primary drivers of response information flow, transitioning from early dorsal attention network-dominated sensory-to-response transformation to later collaborative CCN engagement during response selection. These results demonstrate the utility of the dynamic activity flow modeling approach in identifying the generative network processes underlying neurocognitive phenomena.

How is cognitive task behavior generated by brain network interactions? This study describes a novel network modeling approach and applies it to source electroencephalography data. The model accurately predicts future information dynamics underlying behavior and (via simulated lesioning) suggests a role for cognitive control networks as key drivers of response information flow.