Towards efficient SimRank computation on large networks

SimRank has been a powerful model for assessing the similarity of pairs of vertices in a graph. It is based on the concept that two vertices are similar if they are referenced by similar vertices. Due to its self-referentiality, fast SimRank computation on large graphs poses significant challenges. The state-of-the-art work [17] exploits partial sums memorization for computing SimRank in O(Kmn) time on a graph with n vertices and m edges, where K is the number of iterations. Partial sums memorizing can reduce repeated calculations by caching part of similarity summations for later reuse. However, we observe that computations among different partial sums may have duplicate redundancy. Besides, for a desired accuracy ϵ, the existing SimRank model requires K = [logC ϵ] iterations [17], where C is a damping factor. Nevertheless, such a geometric rate of convergence is slow in practice if a high accuracy is desirable. In this paper, we address these gaps. (1) We propose an adaptive clustering strategy to eliminate partial sums redundancy (i.e., duplicate computations occurring in partial sums), and devise an efficient algorithm for speeding up the computation of SimRank to 0(Kdn2) time, where d is typically much smaller than the average in-degree of a graph. (2) We also present a new notion of SimRank that is based on a differential equation and can be represented as an exponential sum of transition matrices, as opposed to the geometric sum of the conventional counterpart. This leads to a further speedup in the convergence rate of SimRank iterations. (3) Using real and synthetic data, we empirically verify that our approach of partial sums sharing outperforms the best known algorithm by up to one order of magnitude, and that our revised notion of SimRank further achieves a 5X speedup on large graphs while also fairly preserving the relative order of original SimRank scores

Tidal Barrier and the Asymptotic Mass of Proto Gas-Giant Planets

Extrasolar planets found with radial velocity surveys have masses ranging from several Earth to several Jupiter masses. While mass accretion onto protoplanetary cores in weak-line T-Tauri disks may eventually be quenched by a global depletion of gas, such a mechanism is unlikely to have stalled the growth of some known planetary systems which contain relatively low-mass and close-in planets along with more massive and longer period companions. Here, we suggest a potential solution for this conundrum. In general, supersonic infall of surrounding gas onto a protoplanet is only possible interior to both of its Bondi and Roche radii. At a critical mass, a protoplanet's Bondi and Roche radii are equal to the disk thickness. Above this mass, the protoplanets' tidal perturbation induces the formation of a gap. Although the disk gas may continue to diffuse into the gap, the azimuthal flux across the protoplanets' Roche lobe is quenched. Using two different schemes, we present the results of numerical simulations and analysis to show that the accretion rate increases rapidly with the ratio of the protoplanet's Roche to Bondi radii or equivalently to the disk thickness. In regions with low geometric aspect ratios, gas accretion is quenched with relatively low protoplanetary masses. This effect is important for determining the gas-giant planets' mass function, the distribution of their masses within multiple planet systems around solar type stars, and for suppressing the emergence of gas-giants around low mass stars

Wind turbulence inputs for horizontal axis wind turbines

Wind turbine response characteristics in the presence of atmospheric turbulence was predicted using two major modeling steps. First, the important atmospheric sources for the force excitations felt by the wind turbine system were identified and characterized. Second, a dynamic model was developed which describes how these excitations are transmitted through the structure and power train. The first modeling step, that of quantifying the important excitations due to the atmospheric turbulence was established. The dynamic modeling of the second step was undertaken separately

Statistical Modelling of Information Sharing: Community, Membership and Content

File-sharing systems, like many online and traditional information sharing communities (e.g. newsgroups, BBS, forums, interest clubs), are dynamical systems in nature. As peers get in and out of the system, the information content made available by the prevailing membership varies continually in amount as well as composition, which in turn affects all peers' join/leave decisions. As a result, the dynamics of membership and information content are strongly coupled, suggesting interesting issues about growth, sustenance and stability. In this paper, we propose to study such communities with a simple statistical model of an information sharing club. Carrying their private payloads of information goods as potential supply to the club, peers join or leave on the basis of whether the information they demand is currently available. Information goods are chunked and typed, as in a file sharing system where peers contribute different files, or a forum where messages are grouped by topics or threads. Peers' demand and supply are then characterized by statistical distributions over the type domain. This model reveals interesting critical behaviour with multiple equilibria. A sharp growth threshold is derived: the club may grow towards a sustainable equilibrium only if the value of an order parameter is above the threshold, or shrink to emptiness otherwise. The order parameter is composite and comprises the peer population size, the level of their contributed supply, the club's efficiency in information search, the spread of supply and demand over the type domain, as well as the goodness of match between them.Comment: accepted in International Symposium on Computer Performance, Modeling, Measurements and Evaluation, Juan-les-Pins, France, October-200

Criticality in Formal Languages and Statistical Physics

We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a power law for a context-free grammar. This result about formal languages is closely related to a well-known result in classical statistical mechanics that there are no phase transitions in dimensions fewer than two. It is also related to the emergence of power-law correlations in turbulence and cosmological inflation through recursive generative processes. We elucidate these physics connections and comment on potential applications of our results to machine learning tasks like training artificial recurrent neural networks. Along the way, we introduce a useful quantity which we dub the rational mutual information and discuss generalizations of our claims involving more complicated Bayesian networks.Comment: Replaced to match final published version. Discussion improved, references adde

Depolarization-activated potentiation of the T fiber synapse in the blue crab

The blue crab T fiber synapse, associated with the stretch receptor of the swimming leg, has a nonspiking presynaptic element that mediates tonic transmission. This synapse was isolated and a voltage clamp circuit was used to control the membrane potential at the release sites. The dependence of transmitter release on extracellular calcium, [Ca]o, was studied over a range of 2.5-40 mM. A power relationship of 2.7 was obtained between excitatory postsynaptic potential (EPSP) rate of rise and [Ca]o. Brief presynaptic depolarizing steps, 5-10 ms, presented at 0.5 Hz activated EPSP's of constant amplitude. Inserting a 300-ms pulse (conditioning pulse) between these test pulses potentiated the subsequent test EPSPs. This depolarization-activated potentiation (DAP) lasted for 10-20 s and decayed with a single exponential time course. The decay time course remained invariant with test pulse frequencies ranging from 0.11 to 1.1 Hz. The magnitude and decay time course of DAP were independent of the test pulse amplitudes. The magnitude of DAP was a function of conditioning pulse amplitudes. Large conditioning pulses activated large potentiations, whereas the decay time constants were not changed. The DAP is a Ca-dependent process. When the amplitude of conditioning pulses approached the Ca equilibrium potential, the magnitude of potentiation decreased. Repeated application of conditioning pulses, at 2-s intervals, did not produce additional potentiation beyond the level activated by the first conditioning pulse. Comparison of the conditioning EPSP waveforms activated repetitively indicated that potentiation lasted transiently, 100 ms, during a prolonged release. Possible mechanisms of the potentiation are discussed in light of these new findings.The blue crab T fiber synapse, associated with the stretch receptor of the swimming leg, has a nonspiking presynaptic element that mediates tonic transmission. This synapse was isolated and a voltage clamp circuit was used to control the membrane potential at the release sites. The dependence of transmitter release on extracellular calcium, [Ca]o, was studied over a range of 2.5-40 mM. A power relationship of 2.7 was obtained between excitatory postsynaptic potential (EPSP) rate of rise and [Ca]o. Brief presynaptic depolarizing steps, 5-10 ms, presented at 0.5 Hz activated EPSP's of constant amplitude. Inserting a 300-ms pulse (conditioning pulse) between these test pulses potentiated the subsequent test EPSPs. This depolarization-activated potentiation (DAP) lasted for 10-20 s and decayed with a single exponential time course. The decay time course remained invariant with test pulse frequencies ranging from 0.11 to 1.1 Hz. The magnitude and decay time course of DAP were independent of the test pulse amplitudes. The magnitude of DAP was a function of conditioning pulse amplitudes. Large conditioning pulses activated large potentiations, whereas the decay time constants were not changed. The DAP is a Ca-dependent process. When the amplitude of conditioning pulses approached the Ca equilibrium potential, the magnitude of potentiation decreased. Repeated application of conditioning pulses, at 2-s intervals, did not produce additional potentiation beyond the level activated by the first conditioning pulse. Comparison of the conditioning EPSP waveforms activated repetitively indicated that potentiation lasted transiently, 100 ms, during a prolonged release. Possible mechanisms of the potentiation are discussed in light of these new findings.NS-07942 - NINDS NIH HHS; NS-13742 - NINDS NIH HH