3,469 research outputs found
Fully-dynamic Approximation of Betweenness Centrality
Betweenness is a well-known centrality measure that ranks the nodes of a
network according to their participation in shortest paths. Since an exact
computation is prohibitive in large networks, several approximation algorithms
have been proposed. Besides that, recent years have seen the publication of
dynamic algorithms for efficient recomputation of betweenness in evolving
networks. In previous work we proposed the first semi-dynamic algorithms that
recompute an approximation of betweenness in connected graphs after batches of
edge insertions.
In this paper we propose the first fully-dynamic approximation algorithms
(for weighted and unweighted undirected graphs that need not to be connected)
with a provable guarantee on the maximum approximation error. The transfer to
fully-dynamic and disconnected graphs implies additional algorithmic problems
that could be of independent interest. In particular, we propose a new upper
bound on the vertex diameter for weighted undirected graphs. For both weighted
and unweighted graphs, we also propose the first fully-dynamic algorithms that
keep track of such upper bound. In addition, we extend our former algorithm for
semi-dynamic BFS to batches of both edge insertions and deletions.
Using approximation, our algorithms are the first to make in-memory
computation of betweenness in fully-dynamic networks with millions of edges
feasible. Our experiments show that they can achieve substantial speedups
compared to recomputation, up to several orders of magnitude
Generalized Rosenfeld scalings for tracer diffusivities in not-so-simple fluids: Mixtures and soft particles
Rosenfeld [Phys. Rev. A 15, 2545 (1977)] noticed that casting transport
coefficients of simple monatomic, equilibrium fluids in specific dimensionless
forms makes them approximately single-valued functions of excess entropy. This
has predictive value because, while the transport coefficients of dense fluids
are difficult to estimate from first principles, excess entropy can often be
accurately predicted from liquid-state theory. Here, we use molecular
simulations to investigate whether Rosenfeld's observation is a special case of
a more general scaling law relating mobility of particles in mixtures to excess
entropy. Specifically, we study tracer diffusivities, static structure, and
thermodynamic properties of a variety of one- and two-component model fluid
systems with either additive or non-additive interactions of the hard-sphere or
Gaussian-core form. The results of the simulations demonstrate that the effects
of mixture concentration and composition, particle-size asymmetry and
additivity, and strength of the interparticle interactions in these fluids are
consistent with an empirical scaling law relating the excess entropy to a new
dimensionless (generalized Rosenfeld) form of tracer diffusivity, which we
introduce here. The dimensionless form of the tracer diffusivity follows from
knowledge of the intermolecular potential and the transport / thermodynamic
behavior of fluids in the dilute limit. The generalized Rosenfeld scaling
requires less information, and provides more accurate predictions, than either
Enskog theory or scalings based on the pair-correlation contribution to the
excess entropy. As we show, however, it also suffers from some limitations,
especially for systems that exhibit significant decoupling of individual
component tracer diffusivities.Comment: 15 pages, 10 figure
Mean first-passage times for an ac-driven magnetic moment of a nanoparticle
The two-dimensional backward Fokker-Planck equation is used to calculate the
mean first-passage times (MFPTs) of the magnetic moment of a nanoparticle
driven by a rotating magnetic field. It is shown that a magnetic field that is
rapidly rotating in the plane {\it perpendicular} to the easy axis of the
nanoparticle governs the MFPTs just in the same way as a static magnetic field
that is applied {\it along} the easy axis. Within this framework, the features
of the magnetic relaxation and net magnetization of systems composed of
ferromagnetic nanoparticles arising from the action of the rotating field are
revealed.Comment: 7 pages, 1 figur
Optimal discrete stopping times for reliability growth tests
Often, the duration of a reliability growth development test is specified in advance and the decision to terminate or continue testing is conducted at discrete time intervals. These features are normally not captured by reliability growth models. This paper adapts a standard reliability growth model to determine the optimal time for which to plan to terminate testing. The underlying stochastic process is developed from an Order Statistic argument with Bayesian inference used to estimate the number of faults within the design and classical inference procedures used to assess the rate of fault detection. Inference procedures within this framework are explored where it is shown the Maximum Likelihood Estimators possess a small bias and converges to the Minimum Variance Unbiased Estimator after few tests for designs with moderate number of faults. It is shown that the Likelihood function can be bimodal when there is conflict between the observed rate of fault detection and the prior distribution describing the number of faults in the design. An illustrative example is provided
Minerological aspects of lead sintering
A brief overview on lead sinter microstructure is presented. Characteristic micro-structural features of a good and bad sinter are highlighted and these are used in a case study involving use of a low grade and complex concentrate of lead (-40% Pb) in the sintering operation. The plant sinter produced exhibited low strength and its nticrostructural examination revealed non-uniform distribution of porosity along with unsintered galena and low melting lead silicate phase. Part replacement of limestone by lime helped in producing sinter with good physical properties and desirable microstructure. The sinter with modified feed chemistry had more uniform distribution of porosity and presence of primarily a Pb-Fe silicate phase characterised by a (Pb+Fe):Si mole ratio of 3:1. Ca-Pb-Zn-Fe-Al-silicate phase identified as hardysonite and a spine! phase of the type (Fe,Zn)O.(Fe,Al),OJ. Lead nietal/oxide/sulphide occurred in the sinter only rarely. The likely implications of lime addition to the sinter charge mix are discussed Key Words: Lead. Complex and low grade concentrate. Sintering. Process Mineralog
Effects of Noise on Ecological Invasion Processes: Bacteriophage-mediated Competition in Bacteria
Pathogen-mediated competition, through which an invasive species carrying and
transmitting a pathogen can be a superior competitor to a more vulnerable
resident species, is one of the principle driving forces influencing
biodiversity in nature. Using an experimental system of bacteriophage-mediated
competition in bacterial populations and a deterministic model, we have shown
in [Joo et al 2005] that the competitive advantage conferred by the phage
depends only on the relative phage pathology and is independent of the initial
phage concentration and other phage and host parameters such as the
infection-causing contact rate, the spontaneous and infection-induced lysis
rates, and the phage burst size. Here we investigate the effects of stochastic
fluctuations on bacterial invasion facilitated by bacteriophage, and examine
the validity of the deterministic approach. We use both numerical and
analytical methods of stochastic processes to identify the source of noise and
assess its magnitude. We show that the conclusions obtained from the
deterministic model are robust against stochastic fluctuations, yet deviations
become prominently large when the phage are more pathological to the invading
bacterial strain.Comment: 39 pages, 7 figure
Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka-Volterra Models
We study the general properties of stochastic two-species models for
predator-prey competition and coexistence with Lotka-Volterra type interactions
defined on a -dimensional lattice. Introducing spatial degrees of freedom
and allowing for stochastic fluctuations generically invalidates the classical,
deterministic mean-field picture. Already within mean-field theory, however,
spatial constraints, modeling locally limited resources, lead to the emergence
of a continuous active-to-absorbing state phase transition. Field-theoretic
arguments, supported by Monte Carlo simulation results, indicate that this
transition, which represents an extinction threshold for the predator
population, is governed by the directed percolation universality class. In the
active state, where predators and prey coexist, the classical center
singularities with associated population cycles are replaced by either nodes or
foci. In the vicinity of the stable nodes, the system is characterized by
essentially stationary localized clusters of predators in a sea of prey. Near
the stable foci, however, the stochastic lattice Lotka-Volterra system displays
complex, correlated spatio-temporal patterns of competing activity fronts.
Correspondingly, the population densities in our numerical simulations turn out
to oscillate irregularly in time, with amplitudes that tend to zero in the
thermodynamic limit. Yet in finite systems these oscillatory fluctuations are
quite persistent, and their features are determined by the intrinsic
interaction rates rather than the initial conditions. We emphasize the
robustness of this scenario with respect to various model perturbations.Comment: 19 pages, 11 figures, 2-column revtex4 format. Minor modifications.
Accepted in the Journal of Statistical Physics. Movies corresponding to
Figures 2 and 3 are available at
http://www.phys.vt.edu/~tauber/PredatorPrey/movies
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