115,904 research outputs found
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 Ï”, the existing SimRank model requires K = [logC Ï”] 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
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
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