4,703 research outputs found
Stretched Exponential Relaxation in the Biased Random Voter Model
We study the relaxation properties of the voter model with i.i.d. random
bias. We prove under mild condions that the disorder-averaged relaxation of
this biased random voter model is faster than a stretched exponential with
exponent , where depends on the transition rates
of the non-biased voter model. Under an additional assumption, we show that the
above upper bound is optimal. The main ingredient of our proof is a result of
Donsker and Varadhan (1979).Comment: 14 pages, AMS-LaTe
THE DECAY OF NEPTUNIUM-238
>A study was made of the energy levels of Pu/sup 238/ which are populated by Np/sup 238/ beta decay, by an examination of the Np/sup 238/ conversion electron spectrum in high-resolution beta spectrographs. The general features of the level scheme as previously given were unchanged but several new transitions were observed, with energies of 119.8, 871, 943, 989, and 1034 kev. Two new levels are postulated at 915 and 1034 kev which accommodate all but the 943-kev transition. A possible assignment of the 943-kev transition to the (0+.0) state of the beta vibrational band is discussed. In addition, the weak 885-kev transition from the 2+ state of the gamma -vibrational band to the 4+ state of the ground band was seen and its relative intensity determined. Comparisons were made of the experimental relative transition intensities of the three photons depopulating this band with those predicted from the rules of Alaga et al.; only fair agreement was noted. A discussion is given of the beta decay branchings and log ft values of Np/sup 238/ decay in terms of the postulated characters of the Pu/sup 238/ states and the measured spin of Np/sup 238/. (auth
The Potential of Restarts for ProbSAT
This work analyses the potential of restarts for probSAT, a quite successful
algorithm for k-SAT, by estimating its runtime distributions on random 3-SAT
instances that are close to the phase transition. We estimate an optimal
restart time from empirical data, reaching a potential speedup factor of 1.39.
Calculating restart times from fitted probability distributions reduces this
factor to a maximum of 1.30. A spin-off result is that the Weibull distribution
approximates the runtime distribution for over 93% of the used instances well.
A machine learning pipeline is presented to compute a restart time for a
fixed-cutoff strategy to exploit this potential. The main components of the
pipeline are a random forest for determining the distribution type and a neural
network for the distribution's parameters. ProbSAT performs statistically
significantly better than Luby's restart strategy and the policy without
restarts when using the presented approach. The structure is particularly
advantageous on hard problems.Comment: Eurocast 201
Trapping reactions with subdiffusive traps and particles characterized by different anomalous diffusion exponents
A number of results for reactions involving subdiffusive species all with the
same anomalous exponent gamma have recently appeared in the literature and can
often be understood in terms of a subordination principle whereby time t in
ordinary diffusion is replaced by t^gamma. However, very few results are known
for reactions involving different species characterized by different anomalous
diffusion exponents. Here we study the reaction dynamics of a (sub)diffusive
particle surrounded by a sea of (sub)diffusive traps in one dimension. We find
rigorous results for the asymptotic survival probability of the particle in
most cases, with the exception of the case of a particle that diffuses normally
while the anomalous diffusion exponent of the traps is smaller than 2/3.Comment: To appear in Phys. Rev.
Measuring degree-degree association in networks
The Pearson correlation coefficient is commonly used for quantifying the
global level of degree-degree association in complex networks. Here, we use a
probabilistic representation of the underlying network structure for assessing
the applicability of different association measures to heavy-tailed degree
distributions. Theoretical arguments together with our numerical study indicate
that Pearson's coefficient often depends on the size of networks with equal
association structure, impeding a systematic comparison of real-world networks.
In contrast, Kendall-Gibbons' is a considerably more robust measure
of the degree-degree association
Kinetics of diffusion-limited catalytically-activated reactions: An extension of the Wilemski-Fixman approach
We study kinetics of diffusion-limited catalytically-activated
reactions taking place in three dimensional systems, in which an annihilation
of diffusive particles by diffusive traps may happen only if the
encounter of an with any of the s happens within a special catalytic
subvolumen, these subvolumens being immobile and uniformly distributed within
the reaction bath. Suitably extending the classical approach of Wilemski and
Fixman (G. Wilemski and M. Fixman, J. Chem. Phys. \textbf{58}:4009, 1973) to
such three-molecular diffusion-limited reactions, we calculate analytically an
effective reaction constant and show that it comprises several terms associated
with the residence and joint residence times of Brownian paths in finite
domains. The effective reaction constant exhibits a non-trivial dependence on
the reaction radii, the mean density of catalytic subvolumens and particles'
diffusion coefficients. Finally, we discuss the fluctuation-induced kinetic
behavior in such systems.Comment: To appear in J. Chem. Phy
Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States
The study of systems with multiple (not necessarily degenerate) metastable
states presents subtle difficulties from the mathematical point of view related
to the variational problem that has to be solved in these cases. We introduce
the notion of relaxation height in a general energy landscape and we prove
sufficient conditions which are valid even in presence of multiple metastable
states. We show how these results can be used to approach the problem of
multiple metastable states via the use of the modern theories of metastability.
We finally apply these general results to the Blume--Capel model for a
particular choice of the parameters ensuring the existence of two multiple, and
not degenerate in energy, metastable states
7T functional MRI finds no evidence for distinct functional subregions in the subthalamic nucleus during a speeded decision-making task
The subthalamic nucleus (STN) is a small, subcortical brain structure. It is a target for deep brain stimulation, an invasive treatment that reduces motor symptoms of Parkinson’s disease. Side effects of DBS are commonly explained using the tripartite model of STN organization, which proposes three functionally distinct subregions in the STN specialized in cognitive, limbic, and motor processing. However, evidence for the tripartite model exclusively comes from anatomical studies and functional studies using clinical patients. Here, we provide the first experimental tests of the tripartite model in healthy volunteers using ultra-high field 7 Tesla (T) functional magnetic resonance imaging (fMRI). Thirty-four participants performed a random-dot motion decision-making task with a difficulty manipulation and a choice payoff manipulation aimed to differentially affect cognitive and limbic networks. Moreover, participants responded with their left and right index finger, differentially affecting motor networks. We analysed BOLD signal in three subregions of the STN along the dorsolateral-ventromedial axis, identified using manually delineated high resolution anatomical images and based on a previously published atlas. Using these paradigms, all segments responded equally to the experimental manipulations, and the tasks did not provide evidence for the tripartite model
Survival probability of a particle in a sea of mobile traps: A tale of tails
We study the long-time tails of the survival probability of an
particle diffusing in -dimensional media in the presence of a concentration
of traps that move sub-diffusively, such that the mean square
displacement of each trap grows as with .
Starting from a continuous time random walk (CTRW) description of the motion of
the particle and of the traps, we derive lower and upper bounds for and
show that for these bounds coincide asymptotically, thus
determining asymptotically exact results. The asymptotic decay law in this
regime is exactly that obtained for immobile traps. This means that for
sufficiently subdiffusive traps, the moving particle sees the traps as
essentially immobile, and Lifshitz or trapping tails remain unchanged. For
and the upper and lower bounds again coincide,
leading to a decay law equal to that of a stationary particle. Thus, in this
regime the moving traps see the particle as essentially immobile. For ,
however, the upper and lower bounds in this regime no longer coincide
and the decay law for the survival probability of the particle remains
ambiguous
Copolymer with pinning: variational characterization of the phase diagram
This paper studies a polymer chain in the vicinity of a linear interface
separating two immiscible solvents. The polymer consists of random monomer
types, while the interface carries random charges. Both the monomer types and
the charges are given by i.i.d. sequences of random variables. The
configurations of the polymer are directed paths that can make i.i.d.
excursions of finite length above and below the interface. The Hamiltonian has
two parts: a monomer-solvent interaction ("copolymer") and a monomer-interface
interaction ("pinning"). The quenched and the annealed version of the model
each undergo a transition from a localized phase (where the polymer stays close
to the interface) to a delocalized phase (where the polymer wanders away from
the interface). We exploit the approach developed in [5] and [3] to derive
variational formulas for the quenched and the annealed free energy per monomer.
These variational formulas are analyzed to obtain detailed information on the
critical curves separating the two phases and on the typical behavior of the
polymer in each of the two phases. Our main results settle a number of open
questions.Comment: 46 pages, 9 figure
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