Slow Excitation Trapping in Quantum Transport with Long-Range Interactions

Long-range interactions slow down the excitation trapping in quantum transport processes on a one-dimensional chain with traps at both ends. This is counter intuitive and in contrast to the corresponding classical processes with long-range interactions, which lead to faster excitation trapping. We give a pertubation theoretical explanation of this effect.Comment: 4 pages, 3 figure

From Correlation to Causation: Estimation of Effective Connectivity from Continuous Brain Signals based on Zero-Lag Covariance

Knowing brain connectivity is of great importance both in basic research and for clinical applications. We are proposing a method to infer directed connectivity from zero-lag covariances of neuronal activity recorded at multiple sites. This allows us to identify causal relations that are reflected in neuronal population activity. To derive our strategy, we assume a generic linear model of interacting continuous variables, the components of which represent the activity of local neuronal populations. The suggested method for inferring connectivity from recorded signals exploits the fact that the covariance matrix derived from the observed activity contains information about the existence, the direction and the sign of connections. Assuming a sparsely coupled network, we disambiguate the underlying causal structure via $L^1$-minimization. In general, this method is suited to infer effective connectivity from resting state data of various types. We show that our method is applicable over a broad range of structural parameters regarding network size and connection probability of the network. We also explored parameters affecting its activity dynamics, like the eigenvalue spectrum. Also, based on the simulation of suitable Ornstein-Uhlenbeck processes to model BOLD dynamics, we show that with our method it is possible to estimate directed connectivity from zero-lag covariances derived from such signals. In this study, we consider measurement noise and unobserved nodes as additional confounding factors. Furthermore, we investigate the amount of data required for a reliable estimate. Additionally, we apply the proposed method on a fMRI dataset. The resulting network exhibits a tendency for close-by areas being connected as well as inter-hemispheric connections between corresponding areas. Also, we found that a large fraction of identified connections were inhibitory.Comment: 18 pages, 10 figure

Quantum transport on small-world networks: A continuous-time quantum walk approach

We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWN). The SWN are build from a one-dimensional ring of N nodes by randomly introducing B additional bonds between them. The exciton dynamics is modeled by continuous-time quantum walks and we evaluate numerically the ensemble averaged transition probability to reach any node of the network from the initially excited one. For sufficiently large B we find that the quantum mechanical transport through the SWN is, first, very fast, given that the limiting value of the transition probability is reached very quickly; second, that the transport does not lead to equipartition, given that on average the exciton is most likely to be found at the initial node.Comment: 8 pages, 8 figures (high quality figures available upon request

Discovering universal statistical laws of complex networks

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their generalisation power, which we identify with large structural variability and absence of constraints imposed by the construction scheme. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This allows, for instance, to infer global features from local ones using regression models trained on networks with high generalisation power. Our results confirm and extend previous findings regarding the synchronisation properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks with good approximation. Finally, we demonstrate on three different data sets (C. elegans' neuronal network, R. prowazekii's metabolic network, and a network of synonyms extracted from Roget's Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models

How Structure Determines Correlations in Neuronal Networks

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks

Long-Term Blocking of Calcium Channels in mdx Mice Results in Differential Effects on Heart and Skeletal Muscle

The disease mechanisms underlying dystrophin-deficient muscular dystrophy are complex, involving not only muscle membrane fragility, but also dysregulated calcium homeostasis. Specifically, it has been proposed that calcium channels directly initiate a cascade of pathological events by allowing calcium ions to enter the cell. The objective of this study was to investigate the effect of chronically blocking calcium channels with the aminoglycoside antibiotic streptomycin from onset of disease in the mdx mouse model of Duchenne muscular dystrophy (DMD)

Identification of regulatory variants associated with genetic susceptibility to meningococcal disease.

Non-coding genetic variants play an important role in driving susceptibility to complex diseases but their characterization remains challenging. Here, we employed a novel approach to interrogate the genetic risk of such polymorphisms in a more systematic way by targeting specific regulatory regions relevant for the phenotype studied. We applied this method to meningococcal disease susceptibility, using the DNA binding pattern of RELA - a NF-kB subunit, master regulator of the response to infection - under bacterial stimuli in nasopharyngeal epithelial cells. We designed a custom panel to cover these RELA binding sites and used it for targeted sequencing in cases and controls. Variant calling and association analysis were performed followed by validation of candidate polymorphisms by genotyping in three independent cohorts. We identified two new polymorphisms, rs4823231 and rs11913168, showing signs of association with meningococcal disease susceptibility. In addition, using our genomic data as well as publicly available resources, we found evidences for these SNPs to have potential regulatory effects on ATXN10 and LIF genes respectively. The variants and related candidate genes are relevant for infectious diseases and may have important contribution for meningococcal disease pathology. Finally, we described a novel genetic association approach that could be applied to other phenotypes