2,052 research outputs found
Off-Critical SLE(2) and SLE(4): a Field Theory Approach
Using their relationship with the free boson and the free symplectic fermion,
we study the off-critical perturbation of SLE(4) and SLE(2) obtained by adding
a mass term to the action. We compute the off-critical statistics of the source
in the Loewner equation describing the two dimensional interfaces. In these two
cases we show that ratios of massive by massless partition functions,
expressible as ratios of regularised determinants of massive and massless
Laplacians, are (local) martingales for the massless interfaces. The
off-critical drifts in the stochastic source of the Loewner equation are
proportional to the logarithmic derivative of these ratios. We also show that
massive correlation functions are (local) martingales for the massive
interfaces. In the case of massive SLE(4), we use this property to prove a
factorisation of the free boson measure.Comment: 30 pages, 1 figures, Published versio
Relativistic diffusion processes and random walk models
The nonrelativistic standard model for a continuous, one-parameter diffusion
process in position space is the Wiener process. As well-known, the Gaussian
transition probability density function (PDF) of this process is in conflict
with special relativity, as it permits particles to propagate faster than the
speed of light. A frequently considered alternative is provided by the
telegraph equation, whose solutions avoid superluminal propagation speeds but
suffer from singular (non-continuous) diffusion fronts on the light cone, which
are unlikely to exist for massive particles. It is therefore advisable to
explore other alternatives as well. In this paper, a generalized Wiener process
is proposed that is continuous, avoids superluminal propagation, and reduces to
the standard Wiener process in the non-relativistic limit. The corresponding
relativistic diffusion propagator is obtained directly from the nonrelativistic
Wiener propagator, by rewriting the latter in terms of an integral over
actions. The resulting relativistic process is non-Markovian, in accordance
with the known fact that nontrivial continuous, relativistic Markov processes
in position space cannot exist. Hence, the proposed process defines a
consistent relativistic diffusion model for massive particles and provides a
viable alternative to the solutions of the telegraph equation.Comment: v3: final, shortened version to appear in Phys. Rev.
Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
The Langevin equation (LE) for the one-dimensional relativistic Brownian
motion is derived from a microscopic collision model. The model assumes that a
heavy point-like Brownian particle interacts with the lighter heat bath
particles via elastic hard-core collisions. First, the commonly known,
non-relativistic LE is deduced from this model, by taking into account the
non-relativistic conservation laws for momentum and kinetic energy.
Subsequently, this procedure is generalized to the relativistic case. There, it
is found that the relativistic stochastic force is still \gd-correlated
(white noise) but does \emph{no} longer correspond to a Gaussian white noise
process. Explicit results for the friction and momentum-space diffusion
coefficients are presented and discussed.Comment: v2: Eqs. (17c) and (28) corrected; v3: discussion extended, Eqs. (33)
added, thereby connection to earlier work clarified; v4: final version,
accepted for publication in Phys. Rev.
The Length of an SLE - Monte Carlo Studies
The scaling limits of a variety of critical two-dimensional lattice models
are equal to the Schramm-Loewner evolution (SLE) for a suitable value of the
parameter kappa. These lattice models have a natural parametrization of their
random curves given by the length of the curve. This parametrization (with
suitable scaling) should provide a natural parametrization for the curves in
the scaling limit. We conjecture that this parametrization is also given by a
type of fractal variation along the curve, and present Monte Carlo simulations
to support this conjecture. Then we show by simulations that if this fractal
variation is used to parametrize the SLE, then the parametrized curves have the
same distribution as the curves in the scaling limit of the lattice models with
their natural parametrization.Comment: 18 pages, 10 figures. Version 2 replaced the use of "nu" for the
"growth exponent" by 1/d_H, where d_H is the Hausdorff dimension. Various
minor errors were also correcte
Reconstitution of monoterpene indole alkaloid biosynthesis in genome engineered Nicotiana benthamiana
Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field
We obtain lower and upper bounds on the heat kernel and Green functions of
the Schroedinger operator in a random Gaussian magnetic field and a fixed
scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic
upper bounds and the Jensen inequality for the lower bound. We show that if the
covariance of the electromagnetic (vector) potential is increasing at large
distances then the lower bound is decreasing exponentially fast for large
distances and a large time.Comment: some technical improvements, new references, to appear in
Journ.Phys.
The structures of Hausdorff metric in non-Archimedean spaces
For non-Archimedean spaces and let and be the
ballean of (the family of the balls in ), the space of mappings from
to and the space of mappings from the ballen of to
respectively. By studying explicitly the Hausdorff metric structures related to
these spaces, we construct several families of new metric structures (e.g., ) on the corresponding spaces, and study their convergence,
structural relation, law of variation in the variable including
some normed algebra structure. To some extent, the class is a counterpart of the usual Levy-Prohorov metric in the
probability measure spaces, but it behaves very differently, and is interesting
in itself. Moreover, when is compact and is a complete
non-Archimedean field, we construct and study a Dudly type metric of the space
of valued measures on Comment: 43 pages; this is the final version. Thanks to the anonymous
referee's helpful comments, the original Theorem 2.10 is removed, Proposition
2.10 is stated now in a stronger form, the abstact is rewritten, the
Monna-Springer is used in Section 5, and Theorem 5.2 is written in a more
general for
Mechanism of activation of Agrobacterium virulence genes: identification of phenol-binding proteins.
The universal Glivenko-Cantelli property
Let F be a separable uniformly bounded family of measurable functions on a
standard measurable space, and let N_{[]}(F,\epsilon,\mu) be the smallest
number of \epsilon-brackets in L^1(\mu) needed to cover F. The following are
equivalent:
1. F is a universal Glivenko-Cantelli class.
2. N_{[]}(F,\epsilon,\mu)0 and every probability
measure \mu.
3. F is totally bounded in L^1(\mu) for every probability measure \mu.
4. F does not contain a Boolean \sigma-independent sequence.
It follows that universal Glivenko-Cantelli classes are uniformity classes
for general sequences of almost surely convergent random measures.Comment: 26 page
Diffusion of medication drop-boxes in North Carolina from 2007 to 2016
Introduction: A permanent drug donation box (“drop-box”) is one strategy implemented in communities across the United States to reduce the availability of excess controlled medications, including prescription opioids, for diversion. The objective of this study was to examine correlates of the diffusion and implementation of drop-boxes in North Carolina.Methods: We assessed the number and location of drop-boxes implemented in North Carolina. Cox proportional hazards models were used to examine covariates associated with drop-box implementation in NC counties (n?=?100) between 2007 and 2016.Results: There were 311 drop-boxes implemented in 91 (out of 100) counties. Most drop-boxes were in law enforcement agencies (78.8%) and a growing number were in pharmacies (14.5%). Counties with a higher percentage of whites, more educated residents, a substance abuse prevention coalition, higher rates of controlled medications dispensed and prescription opioid overdose, and that were Appalachian were more likely to be early adopters. Rural counties were less likely to have a drop-box. In the multivariate model, only higher rate of controlled medicines dispensed was significant.Conclusions: A growing number of drop-boxes are being implemented in law enforcement offices and pharmacies. Given that communities with higher rates of controlled medication dispensing likely have the highest need for disposal opportunities, it is promising that they are early adopters of drop-boxes. Future research should assess the effectiveness of drop-boxes as they become more widespread in a variety of locations
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