6,923 research outputs found
Direct Counting Analysis on Network Generated by Discrete Dynamics
A detail study on the In-degree Distribution (ID) of Cellular Automata is
obtained by exact enumeration. The results indicate large deviation from
multiscaling and classification according to ID are discussed. We further
augment the transfer matrix as such the distributions for more complicated
rules are obtained. Dependence of In-degree Distribution on the lattice size
have also been found for some rules including R50 and R77.Comment: 8 pages, 11 figure
Interfacial mixing in heteroepitaxial growth
We investigate the growth of a film of some element B on a substrate made of
another substrance A in a model of molecular beam epitaxy. A vertical exchange
mechanism allows the A-atoms to stay on the growing surface with a certain
probability. Using kinetic Monte Carlo simulations as well as scaling
arguments, the incorporation of the A's into the growing B-layer is
investigated. Moreover we develop a rate equation theory for this process. In
the limit of perfect layer-by-layer growth, the density of A-atoms decays in
the B-film like the inverse squared distance from the interface. The power law
is cut off exponentially at a characteristic thickness of the interdiffusion
zone that depends on the rate of exchange of a B-adatom with an A-atom in the
surface and on the system size. Kinetic roughening changes the exponents. Then
the thickness of the interdiffusion zone is determined by the diffusion length.Comment: 11 pages, 11 figure
Universal statistical properties of poker tournaments
We present a simple model of Texas hold'em poker tournaments which retains
the two main aspects of the game: i. the minimal bet grows exponentially with
time; ii. players have a finite probability to bet all their money. The
distribution of the fortunes of players not yet eliminated is found to be
independent of time during most of the tournament, and reproduces accurately
data obtained from Internet tournaments and world championship events. This
model also makes the connection between poker and the persistence problem
widely studied in physics, as well as some recent physical models of biological
evolution, and extreme value statistics.Comment: Final longer version including data from Internet and WPT tournament
A Spectral Algorithm with Additive Clustering for the Recovery of Overlapping Communities in Networks
This paper presents a novel spectral algorithm with additive clustering
designed to identify overlapping communities in networks. The algorithm is
based on geometric properties of the spectrum of the expected adjacency matrix
in a random graph model that we call stochastic blockmodel with overlap (SBMO).
An adaptive version of the algorithm, that does not require the knowledge of
the number of hidden communities, is proved to be consistent under the SBMO
when the degrees in the graph are (slightly more than) logarithmic. The
algorithm is shown to perform well on simulated data and on real-world graphs
with known overlapping communities.Comment: Journal of Theoretical Computer Science (TCS), Elsevier, A Para\^itr
Effects of Contact Network Models on Stochastic Epidemic Simulations
The importance of modeling the spread of epidemics through a population has
led to the development of mathematical models for infectious disease
propagation. A number of empirical studies have collected and analyzed data on
contacts between individuals using a variety of sensors. Typically one uses
such data to fit a probabilistic model of network contacts over which a disease
may propagate. In this paper, we investigate the effects of different contact
network models with varying levels of complexity on the outcomes of simulated
epidemics using a stochastic Susceptible-Infectious-Recovered (SIR) model. We
evaluate these network models on six datasets of contacts between people in a
variety of settings. Our results demonstrate that the choice of network model
can have a significant effect on how closely the outcomes of an epidemic
simulation on a simulated network match the outcomes on the actual network
constructed from the sensor data. In particular, preserving degrees of nodes
appears to be much more important than preserving cluster structure for
accurate epidemic simulations.Comment: To appear at International Conference on Social Informatics (SocInfo)
201
Topological Quantum Glassiness
Quantum tunneling often allows pathways to relaxation past energy barriers
which are otherwise hard to overcome classically at low temperatures. However,
this is not always the case. In this paper we provide simple exactly solvable
examples where the barriers each system encounters on its approach to lower and
lower energy states become increasingly large and eventually scale with the
system size. If the environment couples locally to the physical degrees of
freedom in the system, tunnelling under large barriers requires processes whose
order in perturbation theory is proportional to the width of the barrier. This
results in quantum relaxation rates that are exponentially suppressed in system
size: For these quantum systems, no physical bath can provide a mechanism for
relaxation that is not dynamically arrested at low temperatures. The examples
discussed here are drawn from three dimensional generalizations of Kitaev's
toric code, originally devised in the context of topological quantum computing.
They are devoid of any local order parameters or symmetry breaking and are thus
examples of topological quantum glasses. We construct systems that have slow
dynamics similar to either strong or fragile glasses. The example with
fragile-like relaxation is interesting in that the topological defects are
neither open strings or regular open membranes, but fractal objects with
dimension .Comment: (18 pages, 4 figures, v2: typos and updated figure); Philosophical
Magazine (2011
Diffuse-Charge Dynamics in Electrochemical Systems
The response of a model micro-electrochemical system to a time-dependent
applied voltage is analyzed. The article begins with a fresh historical review
including electrochemistry, colloidal science, and microfluidics. The model
problem consists of a symmetric binary electrolyte between parallel-plate,
blocking electrodes which suddenly apply a voltage. Compact Stern layers on the
electrodes are also taken into account. The Nernst-Planck-Poisson equations are
first linearized and solved by Laplace transforms for small voltages, and
numerical solutions are obtained for large voltages. The ``weakly nonlinear''
limit of thin double layers is then analyzed by matched asymptotic expansions
in the small parameter , where is the
screening length and the electrode separation. At leading order, the system
initially behaves like an RC circuit with a response time of
(not ), where is the ionic diffusivity, but nonlinearity
violates this common picture and introduce multiple time scales. The charging
process slows down, and neutral-salt adsorption by the diffuse part of the
double layer couples to bulk diffusion at the time scale, . In the
``strongly nonlinear'' regime (controlled by a dimensionless parameter
resembling the Dukhin number), this effect produces bulk concentration
gradients, and, at very large voltages, transient space charge. The article
concludes with an overview of more general situations involving surface
conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference
Deep Multi-object Spectroscopy to Enhance Dark Energy Science from LSST
Community access to deep (i ~ 25), highly-multiplexed optical and
near-infrared multi-object spectroscopy (MOS) on 8-40m telescopes would greatly
improve measurements of cosmological parameters from LSST. The largest gain
would come from improvements to LSST photometric redshifts, which are employed
directly or indirectly for every major LSST cosmological probe; deep
spectroscopic datasets will enable reduced uncertainties in the redshifts of
individual objects via optimized training. Such spectroscopy will also
determine the relationship of galaxy SEDs to their environments, key
observables for studies of galaxy evolution. The resulting data will also
constrain the impact of blending on photo-z's. Focused spectroscopic campaigns
can also improve weak lensing cosmology by constraining the intrinsic
alignments between the orientations of galaxies. Galaxy cluster studies can be
enhanced by measuring motions of galaxies in and around clusters and by testing
photo-z performance in regions of high density. Photometric redshift and
intrinsic alignment studies are best-suited to instruments on large-aperture
telescopes with wider fields of view (e.g., Subaru/PFS, MSE, or GMT/MANIFEST)
but cluster investigations can be pursued with smaller-field instruments (e.g.,
Gemini/GMOS, Keck/DEIMOS, or TMT/WFOS), so deep MOS work can be distributed
amongst a variety of telescopes. However, community access to large amounts of
nights for surveys will still be needed to accomplish this work. In two
companion white papers we present gains from shallower, wide-area MOS and from
single-target imaging and spectroscopy.Comment: Science white paper submitted to the Astro2020 decadal survey. A
table of time requirements is available at
http://d-scholarship.pitt.edu/36036
Amplified biochemical oscillations in cellular systems
We describe a mechanism for pronounced biochemical oscillations, relevant to
microscopic systems, such as the intracellular environment. This mechanism
operates for reaction schemes which, when modeled using deterministic rate
equations, fail to exhibit oscillations for any values of rate constants. The
mechanism relies on amplification of the underlying stochasticity of reaction
kinetics within a narrow window of frequencies. This amplification allows
fluctuations to beat the central limit theorem, having a dominant effect even
though the number of molecules in the system is relatively large. The mechanism
is quantitatively studied within simple models of self-regulatory gene
expression, and glycolytic oscillations.Comment: 35 pages, 6 figure
Fitting a geometric graph to a protein-protein interaction network
Finding a good network null model for protein-protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay between network structure and biological function as well as into evolution. Also, network (graph) models are used to guide biological experiments and discover new biological features. It has been proposed that geometric random graphs are a good model for PPI networks. In a geometric random graph, nodes correspond to uniformly randomly distributed points in a metric space and edges (links) exist between pairs of nodes for which the corresponding points in the metric space are close enough according to some distance norm. Computational experiments have revealed close matches between key topological properties of PPI networks and geometric random graph models. In this work, we push the comparison further by exploiting the fact that the geometric property can be tested for directly. To this end, we develop an algorithm that takes PPI interaction data and embeds proteins into a low-dimensional Euclidean space, under the premise that connectivity information corresponds to Euclidean proximity, as in geometric-random graphs.We judge the sensitivity and specificity of the fit by computing the area under the Receiver Operator Characteristic (ROC) curve. The network embedding algorithm is based on multi-dimensional scaling, with the square root of the path length in a network playing the role of the Euclidean distance in the Euclidean space. The algorithm exploits sparsity for computational efficiency, and requires only a few sparse matrix multiplications, giving a complexity of O(N2) where N is the number of proteins.The algorithm has been verified in the sense that it successfully rediscovers the geometric structure in artificially constructed geometric networks, even when noise is added by re-wiring some links. Applying the algorithm to 19 publicly available PPI networks of various organisms indicated that: (a) geometric effects are present and (b) two-dimensional Euclidean space is generally as effective as higher dimensional Euclidean space for explaining the connectivity. Testing on a high-confidence yeast data set produced a very strong indication of geometric structure (area under the ROC curve of 0.89), with this network being essentially indistinguishable from a noisy geometric network. Overall, the results add support to the hypothesis that PPI networks have a geometric structure
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