330,095 research outputs found
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 âdynamical repertoireâ 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 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 , 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
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