To expand the toolbox available to network science, we study the isomorphism between distance and Fuzzy (proximity or strength) graphs. Distinct transitive closures in Fuzzy graphs lead to closures of their isomorphic distance graphs with widely different structural properties. For instance, the All Pairs Shortest Paths (APSP) problem, based on the Dijkstra algorithm, is equivalent to a metric closure, which is only one of the possible ways to calculate shortest paths in weighted graphs. We show that different closures lead to different distortions of the original topology of weighted graphs. Therefore, complex network analyses that depend on the calculation of shortest paths on weighted graphs should take into account the closure choice and associated topological distortion. We characterise the isomorphism using the max-min and Dombi disjunction/conjunction pairs. This allows us to: (1) study alternative distance closures, such as those based on diffusion, metric, and ultra-metric distances; (2) identify the operators closest to the metric closure of distance graphs (the APSP), but which are logically consistent; and (3) propose a simple method to compute alternative distance closures using existing algorithms for the APSP. In particular, we show that a specific diffusion distance is promising for community detection in complex networks, and is based on desirable axioms for logical inference or approximate reasoning on networks; it also provides a simple algebraic means to compute diffusion processes on networks. Based on these results, we argue that choosing different distance closures can lead to different conclusions about indirect associations on network data, as well as the structure of complex networks, and are thus important to consider.

Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that includes all possible measures of path length for weighted graphs. The result, without breaking the graph into smaller components, is a distance backbone subgraph sufficient to compute all shortest paths. This is important for understanding the dynamics of spread and communication phenomena in real-world networks. The general methodology we formally derive yields a principled graph reduction technique and provides a finer characterization of the triangular geometry of all edges—those that contribute to shortest paths and those that do not but are involved in other network phenomena. We demonstrate that the distance backbone is very small in large networks across domains ranging from air traffic to the human brain connectome, revealing that network robustness to attacks and failures seems to stem from surprisingly vast amounts of redundancy.

We describe a network approach to building recommendation systems for a Web service. We employ two different types of weighted graphs in our analysis and development: Proximity graphs, a type of Fuzzy Graphs based on a cooccurrence probability, and semi-metric distance graphs, which do not observe the triangle inequality of Euclidean distances. Both types of graphs are used to develop intelligent recommendation and collaboration systems for the MyLibrary@LANL web service, a user-centered front-end to the Los Alamos National Laboratory's digital library collections and Web resources.

IntroductionThe human functional connectome is a graphical representation, consisting of nodes connected by edges, of the inter-relationships of blood oxygenation-level dependent (BOLD) time-series measured by MRI from regions encompassing the cerebral cortices and, often, the cerebellum. Semi-metric analysis of the weighted, undirected connectome distinguishes an edge as either direct (metric), such that there is no alternative path that is accumulatively stronger, or indirect (semi-metric), where one or more alternative paths exist that have greater strength than the direct edge. The sensitivity and specificity of this method of analysis is illustrated by two case-control analyses with independent, matched groups of adolescents with autism spectrum conditions (ASC) and major depressive disorder (MDD).ResultsSignificance differences in the global percentage of semi-metric edges was observed in both groups, with increases in ASC and decreases in MDD relative to controls. Furthermore, MDD was associated with regional differences in left frontal and temporal lobes, the right limbic system and cerebellum. In contrast, ASC had a broadly increased percentage of semi-metric edges with a more generalised distribution of effects and some areas of reduction. In summary, MDD was characterised by localised, large reductions in the percentage of semi-metric edges, whilst ASC is characterised by more generalised, subtle increases. These differences were corroborated in greater detail by inspection of the semi-metric backbone for each group; that is, the sub-graph of semi-metric edges present in >90% of participants, and by nodal degree differences in the semi-metric connectome.ConclusionThese encouraging results, in what we believe is the first application of semi-metric analysis to neuroimaging data, raise confidence in the methodology as potentially capable of detection and characterisation of a range of neurodevelopmental and psychiatric disorders.

ObjectiveThere is little understanding of the neural system abnormalities subserving adolescent major depressive disorder (MDD). In a cross-sectional study we compare currently unipolar depressed with healthy adolescents to determine if group differences in grey matter volume (GMV) were influenced by age and illness severity.MethodStructural neuroimaging was performed on 109 adolescents with current MDD and 36 healthy controls, matched for age, gender, and handedness. GMV differences were examined within the anterior cingulate cortex (ACC) and across the whole-brain. The effects of age and self-reported depressive symptoms were also examined in regions showing significant main or interaction effects.ResultsWhole-brain voxel based morphometry revealed no significant group differences. At the whole-brain level, both groups showed a main effect of age on GMV, although this effect was more pronounced in controls. Significant group-by-age interactions were noted: A significant regional group-by-age interaction was observed in the ACC. GMV in the ACC showed patterns of age-related differences that were dissimilar between adolescents with MDD and healthy controls. GMV in the thalamus showed an opposite pattern of age-related differences in adolescent patients compared to healthy controls. In patients, GMV in the thalamus, but not the ACC, was inversely related with self-reported depressive symptoms.ConclusionsThe depressed adolescent brain shows dissimilar age-related and symptom-sensitive patterns of GMV differences compared with controls. The thalamus and ACC may comprise neural markers for detecting these effects in youth. Further investigations therefore need to take both age and level of current symptoms into account when disaggregating antecedent neural vulnerabilities for MDD from the effects of MDD on the developing brain.

Background: We participated in the BioCreAtIvE Task 2, which addressed the annotation of proteins into the Gene Ontology (GO) based on the text of a given document and the selection of evidence text from the document justifying that annotation. We approached the task utilizing several combinations of two distinct methods: an unsupervised algorithm for expanding words associated with GO nodes, and an annotation methodology which treats annotation as categorization of terms from a protein's document neighborhood into the GO.

Imaging studies have implicated altered functional connectivity in adults with major depressive disorder (MDD). Whether similar dysfunction is present in adolescent patients is unclear. The degree of resting-state functional connectivity (rsFC) may reflect abnormalities within emotional (‘hot’) and cognitive control (‘cold’) neural systems. Here, we investigate rsFC of these systems in adolescent patients and changes following cognitive behavioral therapy (CBT). Functional Magnetic Resonance Imaging (fMRI) was acquired from adolescent patients before CBT, and 24-weeks later following completed therapy. Similar data were obtained from control participants. Cross-sectional Cohort: From 82 patients and 34 controls at baseline, rsFC of the amygdala, anterior cingulate cortex (ACC), and pre-frontal cortex (PFC) was calculated for comparison. Longitudinal Cohort: From 17 patients and 30 controls with longitudinal data, treatment effects were tested on rsFC. Patients demonstrated significantly greater rsFC to left amygdala, bilateral supragenual ACC, but not with PFC. Treatment effects were observed in right insula connected to left supragenual ACC, with baseline case-control differences reduced. rsFC changes were significantly correlated with changes in depression severity. Depressed adolescents exhibited heightened connectivity in regions of ‘hot’ emotional processing, known to be associated with depression, where treatment exposure exerted positive effects, without concomitant differences in areas of ‘cold’ cognition.

Understanding brain connectivity is one of the most important issues in neuroscience. Nonetheless, connectivity data can reflect either functional relationships of brain activities or anatomical connections between brain areas. Although both representations should be related, this relationship is not straightforward. We have devised a powerful method that allows different operations between networks that share the same set of nodes, by embedding them in a common metric space, enforcing transitivity to the graph topology. Here, we apply this method to construct an aggregated network from a set of functional graphs, each one from a different subject. Once this aggregated functional network is constructed, we use again our method to compare it with the structural connectivity to identify particular brain regions that differ in both modalities (anatomical and functional). Remarkably, these brain regions include functional areas that form part of the classical resting state networks. We conclude that our method -based on the comparison of the aggregated functional network- reveals some emerging features that could not be observed when the comparison is performed with the classical averaged functional network.