686 research outputs found

### Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding Walk

The conjecture that the scaling limit of the two-dimensional self-avoiding
walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE)
with $\kappa=8/3$ leads to explicit predictions about the SAW. A remarkable
feature of these predictions is that they yield not just critical exponents,
but probability distributions for certain random variables associated with the
self-avoiding walk. We test two of these predictions with Monte Carlo
simulations and find excellent agreement, thus providing numerical support to
the conjecture that the scaling limit of the SAW is SLE$_{8/3}$.Comment: TeX file using APS REVTeX 4.0. 10 pages, 5 figures (encapsulated
postscript

### Discovery and Assessment of New Target Sites for Anti-HIV Therapies

Human immunodeficiency virus (HIV) infects cells by endocytosis and takes over parts of the cellâ€™s reaction pathways in order to reproduce itself and spread the infection. One such pathway taken over by HIV becomes the inflammatory pathway which uses Nuclear Factor ÎºB (NF-ÎºB) as the principal transcription factor. Therefore, knocking out the NF-ÎºB pathway would prevent HIV from reproducing itself. In this report, our goal is to produce a simple model for this pathway with which we can identify potential targets for anti-HIV therapies and test out various hypotheses. We present a very simple model with four coupled first-order ODEs and see what happens if we treat IÎºK concentration as a parameter that can be controlled (by some unspecified means). In Section 3, we augment this model to account for activation and deactivation of IÎºK, which is controlled (again, by some unspecified means) by TNF

### Surface Code Threshold in the Presence of Correlated Errors

We study the fidelity of the surface code in the presence of correlated
errors induced by the coupling of physical qubits to a bosonic environment. By
mapping the time evolution of the system after one quantum error correction
cycle onto a statistical spin model, we show that the existence of an error
threshold is related to the appearance of an order-disorder phase transition in
the statistical model in the thermodynamic limit. This allows us to relate the
error threshold to bath parameters and to the spatial range of the correlated
errors.Comment: 5 pages, 2 figure

### Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk

We consider a discrete-time random walk where the random increment at time
step $t$ depends on the full history of the process. We calculate exactly the
mean and variance of the position and discuss its dependence on the initial
condition and on the memory parameter $p$. At a critical value $p_c^{(1)}=1/2$
where memory effects vanish there is a transition from a weakly localized
regime (where the walker returns to its starting point) to an escape regime.
Inside the escape regime there is a second critical value where the random walk
becomes superdiffusive. The probability distribution is shown to be governed by
a non-Markovian Fokker-Planck equation with hopping rates that depend both on
time and on the starting position of the walk. On large scales the memory
organizes itself into an effective harmonic oscillator potential for the random
walker with a time-dependent spring constant $k = (2p-1)/t$. The solution of
this problem is a Gaussian distribution with time-dependent mean and variance
which both depend on the initiation of the process.Comment: 10 page

### Pattern theorems, ratio limit theorems and Gumbel maximal clusters for random fields

We study occurrences of patterns on clusters of size n in random fields on
Z^d. We prove that for a given pattern, there is a constant a>0 such that the
probability that this pattern occurs at most an times on a cluster of size n is
exponentially small. Moreover, for random fields obeying a certain Markov
property, we show that the ratio between the numbers of occurrences of two
distinct patterns on a cluster is concentrated around a constant value. This
leads to an elegant and simple proof of the ratio limit theorem for these
random fields, which states that the ratio of the probabilities that the
cluster of the origin has sizes n+1 and n converges as n tends to infinity.
Implications for the maximal cluster in a finite box are discussed.Comment: 23 pages, 2 figure

### Rigorous Non-Perturbative Ornstein-Zernike Theory for Ising Ferromagnets

We rigorously derive the Ornstein-Zernike asymptotics of the pair-correlation
functions for finite-range Ising ferromagnets in any dimensions and at any
temperature above critical

### Universal properties of knotted polymer rings

By performing Monte Carlo sampling of $N$-steps self-avoiding polygons
embedded on different Bravais lattices we explore the robustness of
universality in the entropic, metric and geometrical properties of knotted
polymer rings. In particular, by simulating polygons with $N$ up to $10^5$ we
furnish a sharp estimate of the asymptotic values of the knot probability
ratios and show their independence on the lattice type. This universal feature
was previously suggested although with different estimates of the asymptotic
values. In addition we show that the scaling behavior of the mean squared
radius of gyration of polygons depends on their knot type only through its
correction to scaling. Finally, as a measure of the geometrical
self-entanglement of the SAPs we consider the standard deviation of the writhe
distribution and estimate its power-law behavior in the large $N$ limit. The
estimates of the power exponent do depend neither on the lattice nor on the
knot type, strongly supporting an extension of the universality property to
some features of the geometrical entanglement.Comment: submitted to Phys.Rev.

### What is the maximum rate at which entropy of a string can increase?

According to Susskind, a string falling toward a black hole spreads
exponentially over the stretched horizon due to repulsive interactions of the
string bits. In this paper such a string is modeled as a self-avoiding walk and
the string entropy is found. It is shown that the rate at which
information/entropy contained in the string spreads is the maximum rate allowed
by quantum theory. The maximum rate at which the black hole entropy can
increase when a string falls into a black hole is also discussed.Comment: 11 pages, no figures; formulas (18), (20) are corrected (the quantum
constant is added), a point concerning a relation between the Hawking and
Hagedorn temperatures is corrected, conclusions unchanged; accepted by
Physical Review D for publicatio

### Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: a walk counting approach

We introduce a new method to efficiently approximate the number of infections
resulting from a given initially-infected node in a network of susceptible
individuals. Our approach is based on counting the number of possible infection
walks of various lengths to each other node in the network. We analytically
study the properties of our method, in particular demonstrating different forms
for SIS and SIR disease spreading (e.g. under the SIR model our method counts
self-avoiding walks). In comparison to existing methods to infer the spreading
efficiency of different nodes in the network (based on degree, k-shell
decomposition analysis and different centrality measures), our method directly
considers the spreading process and, as such, is unique in providing estimation
of actual numbers of infections. Crucially, in simulating infections on various
real-world networks with the SIR model, we show that our walks-based method
improves the inference of effectiveness of nodes over a wide range of infection
rates compared to existing methods. We also analyse the trade-off between
estimate accuracy and computational cost, showing that the better accuracy here
can still be obtained at a comparable computational cost to other methods.Comment: 6 page

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