Geometry of River Networks I: Scaling, Fluctuations, and Deviations

This article is the first in a series of three papers investigating the detailed geometry of river networks. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description of river network structure, scaling laws are uniformly observed. Reported values of scaling exponents vary suggesting that no unique set of scaling exponents exists. To improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure, we report here a theoretical and empirical study of fluctuations about and deviations from scaling. We examine data for continent-scale river networks such as the Mississippi and the Amazon and draw inspiration from a simple model of directed, random networks. We center our investigations on the scaling of the length of sub-basin's dominant stream with its area, a characterization of basin shape known as Hack's law. We generalize this relationship to a joint probability density and show that fluctuations about scaling are substantial. We find strong deviations from scaling at small scales which can be explained by the existence of linear network structure. At intermediate scales, we find slow drifts in exponent values indicating that scaling is only approximately obeyed and that universality remains indeterminate. At large scales, we observe a breakdown in scaling due to decreasing sample space and correlations with overall basin shape. The extent of approximate scaling is significantly restricted by these deviations and will not be improved by increases in network resolution.Comment: 16 pages, 13 figures, Revtex4, submitted to PR

Complete trails of co-authorship network evolution

The rise and fall of a research field is the cumulative outcome of its intrinsic scientific value and social coordination among scientists. The structure of the social component is quantifiable by the social network of researchers linked via co-authorship relations, which can be tracked through digital records. Here, we use such co-authorship data in theoretical physics and study their complete evolutionary trail since inception, with a particular emphasis on the early transient stages. We find that the co-authorship networks evolve through three common major processes in time: the nucleation of small isolated components, the formation of a tree-like giant component through cluster aggregation, and the entanglement of the network by large-scale loops. The giant component is constantly changing yet robust upon link degradations, forming the network's dynamic core. The observed patterns are successfully reproducible through a new network model

Neuronal synchrony: peculiarity and generality

Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their “dynamical repertoire” includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale

Topological Fractionation of Resting-State Networks

Exploring topological properties of human brain network has become an exciting topic in neuroscience research. Large-scale structural and functional brain networks both exhibit a small-world topology, which is evidence for global and local parallel information processing. Meanwhile, resting state networks (RSNs) underlying specific biological functions have provided insights into how intrinsic functional architecture influences cognitive and perceptual information processing. However, topological properties of single RSNs remain poorly understood. Here, we have two hypotheses: i) each RSN also has optimized small-world architecture; ii) topological properties of RSNs related to perceptual and higher cognitive processes are different. To test these hypotheses, we investigated the topological properties of the default-mode, dorsal attention, central-executive, somato-motor, visual and auditory networks derived from resting-state functional magnetic resonance imaging (fMRI). We found small-world topology in each RSN. Furthermore, small-world properties of cognitive networks were higher than those of perceptual networks. Our findings are the first to demonstrate a topological fractionation between perceptual and higher cognitive networks. Our approach may be useful for clinical research, especially for diseases that show selective abnormal connectivity in specific brain networks

Significance Driven Hybrid 8T-6T SRAM for Energy-Efficient Synaptic Storage in Artificial Neural Networks

Multilayered artificial neural networks (ANN) have found widespread utility in classification and recognition applications. The scale and complexity of such networks together with the inadequacies of general purpose computing platforms have led to a significant interest in the development of efficient hardware implementations. In this work, we focus on designing energy efficient on-chip storage for the synaptic weights. In order to minimize the power consumption of typical digital CMOS implementations of such large-scale networks, the digital neurons could be operated reliably at scaled voltages by reducing the clock frequency. On the contrary, the on-chip synaptic storage designed using a conventional 6T SRAM is susceptible to bitcell failures at reduced voltages. However, the intrinsic error resiliency of NNs to small synaptic weight perturbations enables us to scale the operating voltage of the 6TSRAM. Our analysis on a widely used digit recognition dataset indicates that the voltage can be scaled by 200mV from the nominal operating voltage (950mV) for practically no loss (less than 0.5%) in accuracy (22nm predictive technology). Scaling beyond that causes substantial performance degradation owing to increased probability of failures in the MSBs of the synaptic weights. We, therefore propose a significance driven hybrid 8T-6T SRAM, wherein the sensitive MSBs are stored in 8T bitcells that are robust at scaled voltages due to decoupled read and write paths. In an effort to further minimize the area penalty, we present a synaptic-sensitivity driven hybrid memory architecture consisting of multiple 8T-6T SRAM banks. Our circuit to system-level simulation framework shows that the proposed synaptic-sensitivity driven architecture provides a 30.91% reduction in the memory access power with a 10.41% area overhead, for less than 1% loss in the classification accuracy.Comment: Accepted in Design, Automation and Test in Europe 2016 conference (DATE-2016

Hidden geometries in networks arising from cooperative self-assembly

Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and compatibility of the building blocks are decisive factors in each phase of growth. Therefore, a comprehensive understanding of these processes is essential for the design of large assemblies of desired properties. Here, we introduce a computational model for cooperative self-assembly with simultaneous attachment of structured groups of particles, which can be described by simplexes (connected pairs, triangles, tetrahedrons and higher order cliques) to a growing network, starting from a small seed. The model incorporates geometric rules that provide suitable nesting spaces for the new group and the chemical affinity $\nu$ of the system to accepting an excess number of particles. For varying chemical affinity, we grow different classes of assemblies by binding the cliques of distributed sizes. Furthermore, to characterise the emergent large-scale structures, we use the metrics of graph theory and algebraic topology of graphs, and 4-point test for the intrinsic hyperbolicity of the networks. Our results show that higher Q-connectedness of the appearing simplicial complexes can arise due to only geometrical factors, i.e., for $\nu = 0$, and that it can be effectively modulated by changing the chemical potential and the polydispersity of the size of binding simplexes. For certain parameters in the model we obtain networks of mono-dispersed clicks, triangles and tetrahedrons, which represent the geometrical descriptors that are relevant in quantum physics and frequently occurring chemical clusters.Comment: 9 pages, 8 figure