Spectral goodness of fit for network models

We introduce a new statistic, 'spectral goodness of fit' (SGOF) to measure how well a network model explains the structure of an observed network. SGOF provides an absolute measure of fit, analogous to the standard R-squared in linear regression. Additionally, as it takes advantage of the properties of the spectrum of the graph Laplacian, it is suitable for comparing network models of diverse functional forms, including both fitted statistical models and algorithmic generative models of networks. After introducing, defining, and providing guidance for interpreting SGOF, we illustrate the properties of the statistic with a number of examples and comparisons to existing techniques. We show that such a spectral approach to assessing model fit fills gaps left by earlier methods and can be widely applied

Network 'small-world-ness': a quantitative method for determining canonical network equivalence

Background: Many technological, biological, social, and information networks fall into the broad class of 'small-world' networks: they have tightly interconnected clusters of nodes, and a shortest mean path length that is similar to a matched random graph (same number of nodes and edges). This semi-quantitative definition leads to a categorical distinction ('small/not-small') rather than a quantitative, continuous grading of networks, and can lead to uncertainty about a network's small-world status. Moreover, systems described by small-world networks are often studied using an equivalent canonical network model-the Watts-Strogatz (WS) model. However, the process of establishing an equivalent WS model is imprecise and there is a pressing need to discover ways in which this equivalence may be quantified. Methodology/Principal Findings: We defined a precise measure of 'small-world-ness' S based on the trade off between high local clustering and short path length. A network is now deemed a 'small-world' if S. 1-an assertion which may be tested statistically. We then examined the behavior of S on a large data-set of real-world systems. We found that all these systems were linked by a linear relationship between their S values and the network size n. Moreover, we show a method for assigning a unique Watts-Strogatz (WS) model to any real-world network, and show analytically that the WS models associated with our sample of networks also show linearity between S and n. Linearity between S and n is not, however, inevitable, and neither is S maximal for an arbitrary network of given size. Linearity may, however, be explained by a common limiting growth process. Conclusions/Significance: We have shown how the notion of a small-world network may be quantified. Several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing

Intelligent modelling of bioprocesses: A comparison of structured and unstructured approaches

This contribution moves in the direction of answering some general questions about the most effective and useful ways of modelling bioprocesses. We investigate the characteristics of models that are good at extrapolating. We trained 3 fully predictive models with different representational structures (diff eqns, inheritance of rates, network of reactions) on Saccharopolyspora erythraea shake flask fermentation data using genetic programming. The models were then tested on unseen data outside the range of the training data and the resulting performances compared. It was found that constrained models with mathematical forms analogous to internal mass balancing and stoichiometric were superior to flexible unconstrained models even though no A priori knowledge of this fermentation was used

Being first matters: topographical representational similarity analysis of ERP signals reveals separate networks for audiovisual temporal binding depending on the leading sense

In multisensory integration, processing in one sensory modality is enhanced by complementary information from other modalities. Inter-sensory timing is crucial in this process as only inputs reaching the brain within a restricted temporal window are perceptually bound. Previous research in the audiovisual field has investigated various features of the temporal binding window (TBW), revealing asymmetries in its size and plasticity depending on the leading input (auditory-visual, AV; visual-auditory, VA). We here tested whether separate neuronal mechanisms underlie this AV-VA dichotomy in humans. We recorded high-density EEG while participants performed an audiovisual simultaneity judgment task including various AV/VA asynchronies and unisensory control conditions (visual-only, auditory-only) and tested whether AV and VA processing generate different patterns of brain activity. After isolating the multisensory components of AV/VA event-related potentials (ERPs) from the sum of their unisensory constituents, we run a time-resolved topographical representational similarity analysis (tRSA) comparing AV and VA ERP maps. Spatial cross-correlation matrices were built from real data to index the similarity between AV- and VA-maps at each time point (500ms window post-stimulus) and then correlated with two alternative similarity model matrices: AVmaps=VAmaps vs. AVmaps≠VAmaps. The tRSA results favored the AVmaps≠VAmaps model across all time points, suggesting that audiovisual temporal binding (indexed by synchrony perception) engages different neural pathways depending on the leading sense. The existence of such dual route supports recent theoretical accounts proposing that multiple binding mechanisms are implemented in the brain to accommodate different information parsing strategies in auditory and visual sensory systems