Functional Structure in Production Networks

Production networks are integral to economic dynamics, yet dis-aggregated network data on inter-firm trade is rarely collected and often proprietary. Here we situate company-level production networks within a wider space of networks that are different in nature, but similar in local connectivity structure. Through this lens, we study a regional and a national network of inferred trade relationships reconstructed from Dutch national economic statistics and re-interpret prior empirical findings. We find that company-level production networks have so-called functional structure, as previously identified in protein-protein interaction (PPI) networks. Functional networks are distinctive in their over-representation of closed squares, which we quantify using an existing measure called spectral bipartivity. Shared local connectivity structure lets us ferry insights between domains. PPI networks are shaped by complementarity, rather than homophily, and we use multi-layer directed configuration models to show that this principle explains the emergence of functional structure in production networks. Companies are especially similar to their close competitors, not to their trading partners. Our findings have practical implications for the analysis of production networks and give us precise terms for the local structural features that may be key to understanding their routine function, failure, and growth.

A developmental framework linking neurogenesis and circuit formation in the Drosophila CNS

The mechanisms specifying neuronal diversity are well-characterized, yet it remains unclear how or if these mechanisms regulate neural circuit assembly. To address this, we mapped the developmental origin of 160 interneurons from seven bilateral neural progenitors (neuroblasts), and identify them in a synapse-scale TEM reconstruction of the Drosophila larval CNS. We find that lineages concurrently build the sensory and motor neuropils by generating sensory and motor hemilineages in a Notch-dependent manner. Neurons in a hemilineage share common synaptic targeting within the neuropil, which is further refined based on neuronal temporal identity. Connectome analysis shows that hemilineage-temporal cohorts share common connectivity. Finally, we show that proximity alone cannot explain the observed connectivity structure, suggesting hemilineage/temporal identity confers an added layer of specificity. Thus, we demonstrate that the mechanisms specifying neuronal diversity also govern circuit formation and function, and that these principles are broadly applicable throughout the nervous system.

On Some Properties of Collaboration Graphs of Scientists in Math-Net.Ru

A study of two graphs of scientific cooperation based on co-authorship and citation according to the all-Russian mathematical portal was conducted Math-Net.Ru. A citation-based scientific collaboration graph is a directed graph without loops and multiple edges, whose vertices are the authors of publications, and arcs connect them when there is at least one publication of the first author that cites the publication of the second author. A co-authorship graph is an undirected graph in which the vertices are the authors, and the edges record the co-authorship of two authors in at least one article. The customary study of the main characteristics of both graphs is carried out: diameter and average distance, connectivity components and clustering. In both graphs, we observe a similar connectivity structure – the presence of a giant component and a large number of small components. The similarity and difference of scientific cooperation through co-authorship and citation is noted.

A bi-directional approach to comparing the modular structure of networks

Here we propose a new method to compare the modular structure of a pair of node-aligned networks. The majority of current methods, such as normalized mutual information, compare two node partitions derived from a community detection algorithm yet ignore the respective underlying network topologies. Addressing this gap, our method deploys a community detection quality function to assess the fit of each node partition with respect to the other network’s connectivity structure. Specifically, for two networks A and B, we project the node partition of B onto the connectivity structure of A. By evaluating the fit of B’s partition relative to A’s own partition on network A (using a standard quality function), we quantify how well network A describes the modular structure of B. Repeating this in the other direction, we obtain a two-dimensional distance measure, the bi-directional (BiDir) distance. The advantages of our methodology are three-fold. First, it is adaptable to a wide class of community detection algorithms that seek to optimize an objective function. Second, it takes into account the network structure, specifically the strength of the connections within and between communities, and can thus capture differences between networks with similar partitions but where one of them might have a more defined or robust community structure. Third, it can also identify cases in which dissimilar optimal partitions hide the fact that the underlying community structure of both networks is relatively similar. We illustrate our method for a variety of community detection algorithms, including multi-resolution approaches, and a range of both simulated and real world networks.

The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series

Many methods of Granger causality, or broadly termed connectivity, have been developed to assess the causal relationships between the system variables based only on the information extracted from the time series. The power of these methods to capture the true underlying connectivity structure has been assessed using simulated dynamical systems where the ground truth is known. Here, we consider the presence of an unobserved variable that acts as a hidden source for the observed high-dimensional dynamical system and study the effect of the hidden source on the estimation of the connectivity structure. In particular, the focus is on estimating the direct causality effects in high-dimensional time series (not including the hidden source) of relatively short length. We examine the performance of a linear and a nonlinear connectivity measure using dimension reduction and compare them to a linear measure designed for latent variables. For the simulations, four systems are considered, the coupled Hénon maps system, the coupled Mackey–Glass system, the neural mass model and the vector autoregressive (VAR) process, each comprising 25 subsystems (variables for VAR) at close chain coupling structure and another subsystem (variable for VAR) driving all others acting as the hidden source. The results show that the direct causality measures estimate, in general terms, correctly the existing connectivity in the absence of the source when its driving is zero or weak, yet fail to detect the actual relationships when the driving is strong, with the nonlinear measure of dimension reduction performing best. An example from finance including and excluding the USA index in the global market indices highlights the different performance of the connectivity measures in the presence of hidden source.

Structure-Aware Trail Bundling for Large DTI Datasets

Creating simplified visualizations of large 3D trail sets with limited occlusion and preservation of the main structures in the data is challenging. We address this challenge for the specific context of 3D fiber trails created by DTI tractography. For this, we propose to jointly simplify trails in both the geometric space (by extending and adapting an existing bundling method to handle 3D trails) and in the image space (by proposing several shading and rendering techniques). Our method can handle 3D datasets of hundreds of thousands of trails at interactive rate, has parameters for the most of which good preset values are given, and produces visualizations that have been found, in a small-scale user study involving five medical professionals, to be better in occlusion reduction, conveying the connectivity structure of the brain, and overall clarity than existing methods for the same data. We demonstrate our technique with several real-world public DTI datasets.

Joint estimation of neural sources and their functional connections from MEG data

Current techniques to estimate directed functional connectivity from magnetoencephalography (MEG) signals involve two sequential steps; 1) Estimation of the sources and their amplitude time series from the MEG data by solving the inverse problem, and 2) fitting a multivariate autoregressive (MVAR) model to these time series for the estimation of AR coefficients, which reflect the directed interactions between the sources. However, such a sequential approach is not optimal since i) source estimation algorithms typically assume that the sources are independent, ii) the information provided by the connectivity structure is not used to inform the estimation of source amplitudes, and iii) the limited spatial resolution of source estimates often leads to spurious connectivity due to spatial leakage.Here, we present an algorithm to jointly estimate the source and connectivity parameters using Bayesian filtering, which does not require anatomical constraints in form of structural connectivity or a-priori specified regions-of-interest. By formulating a state-space model for the locations and amplitudes of a given number of sources, we show that estimation of functional connectivity can be reduced to a system identification problem. We derive a solution to this problem using a variant of the expectation–maximization (EM) algorithm known as stochastic approximation EM (SAEM).Compared to the traditional two-step approach, the joint approach using the SAEM algorithm provides a more accurate reconstruction of connectivity parameters, which we show with a connectivity benchmark simulation as well as with an electrocorticography-based simulation of MEG data. Using real MEG responses to visually presented faces in 16 subjects, we also demonstrate that our method gives source and connectivity estimates that are both physiologically plausible and largely consistent across subjects. In conclusion, the proposed joint-estimation approach based on the SAEM algorithm outperforms the traditional two-step approach in determining functional connectivity structure in MEG data.

The connectome

The connectome refers to a comprehensive network map of the connectivity of the nervous system. Such network maps are composed of sets of neural elements, which may correspond to individual neurons or brain areas, and their interconnections, which may correspond to synaptic links or inter-areal pathways. Connectome maps, at a given level of scale, provide a complete and systematic account of brain connectivity that portrays a complete set of anatomical or physiological relationships. This chapter provides an overview of the origins and definitions of the concept and its application to structural and functional brain connectivity, brief surveys of the major findings on the topology of the human connectome and how its connectivity structure shapes dynamic brain activity, and a selection of current themes in the study of individual differences in development and clinical populations.