469,443 research outputs found
Weak violation of universality for Polyelectrolyte Chains: Variational Theory and Simulations
A variational approach is considered to calculate the free energy and the
conformational properties of a polyelectrolyte chain in dimensions. We
consider in detail the case of pure Coulombic interactions between the
monomers, when screening is not present, in order to compute the end-to-end
distance and the asymptotic properties of the chain as a function of the
polymer chain length . We find where
and is the exponent which characterize
the long-range interaction . The exponent is
shown to be non-universal, depending on the strength of the Coulomb
interaction. We check our findings, by a direct numerical minimization of the
variational energy for chains of increasing size . The
electrostatic blob picture, expected for small enough values of the interaction
strength, is quantitatively described by the variational approach. We perform a
Monte Carlo simulation for chains of length . The non universal
behavior of the exponent previously derived within the variational
method, is also confirmed by the simulation results. Non-universal behavior is
found for a polyelectrolyte chain in dimension. Particular attention is
devoted to the homopolymer chain problem, when short range contact interactions
are present.Comment: to appear in European Phys. Journal E (soft matter
Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
We construct the Baxter Q-operator and the representation of the Separated
Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the
diagrammatical approach, we calculate Sklyanin's integration measure in the
separated variables and obtain the solution to the spectral problem for the
model in terms of the eigenvalues of the Q-operator. We show that the
transition kernel to the SoV representation is factorized into the product of
certain operators each depending on a single separated variable. As a
consequence, it has a universal pyramid-like form that has been already
observed for various quantum integrable models such as periodic Toda chain,
closed SL(2,R) and SL(2,C) spin chains.Comment: 29 pages, 9 figures, Latex styl
Chains of Frobenius subalgebras of so(M) and the corresponding twists
Chains of extended jordanian twists are studied for the universal enveloping
algebras U(so(M)). The carrier subalgebra of a canonical chain F cannot cover
the maximal nilpotent subalgebra N(so(M)). We demonstrate that there exist
other types of Frobenius subalgebras in so(M) that can be large enough to
include N(so(M)). The problem is that the canonical chains F do not preserve
the primitivity on these new carrier spaces. We show that this difficulty can
be overcome and the primitivity can be restored if one changes the basis and
passes to the deformed carrier spaces. Finally the twisting elements for the
new Frobenius subalgebras are explicitly constructed. This gives rise to a new
family of universal R-matrices for orthogonal algebras. For a special case of g
= so(5) and its defining representation we present the corresponding matrix
solution of the Yang-Baxter equation.Comment: 17 pages, Late
Recovery from Linear Measurements with Complexity-Matching Universal Signal Estimation
We study the compressed sensing (CS) signal estimation problem where an input
signal is measured via a linear matrix multiplication under additive noise.
While this setup usually assumes sparsity or compressibility in the input
signal during recovery, the signal structure that can be leveraged is often not
known a priori. In this paper, we consider universal CS recovery, where the
statistics of a stationary ergodic signal source are estimated simultaneously
with the signal itself. Inspired by Kolmogorov complexity and minimum
description length, we focus on a maximum a posteriori (MAP) estimation
framework that leverages universal priors to match the complexity of the
source. Our framework can also be applied to general linear inverse problems
where more measurements than in CS might be needed. We provide theoretical
results that support the algorithmic feasibility of universal MAP estimation
using a Markov chain Monte Carlo implementation, which is computationally
challenging. We incorporate some techniques to accelerate the algorithm while
providing comparable and in many cases better reconstruction quality than
existing algorithms. Experimental results show the promise of universality in
CS, particularly for low-complexity sources that do not exhibit standard
sparsity or compressibility.Comment: 29 pages, 8 figure
Constrained spin dynamics description of random walks on hierarchical scale-free networks
We study a random walk problem on the hierarchical network which is a
scale-free network grown deterministically. The random walk problem is mapped
onto a dynamical Ising spin chain system in one dimension with a nonlocal spin
update rule, which allows an analytic approach. We show analytically that the
characteristic relaxation time scale grows algebraically with the total number
of nodes as . From a scaling argument, we also show the
power-law decay of the autocorrelation function C_{\bfsigma}(t)\sim
t^{-\alpha}, which is the probability to find the Ising spins in the initial
state {\bfsigma} after time steps, with the state-dependent non-universal
exponent . It turns out that the power-law scaling behavior has its
origin in an quasi-ultrametric structure of the configuration space.Comment: 9 pages, 6 figure
To found or not to found: that is the question
Aim of this paper is to confute two views, the first about Schr\"oder's
presumptive foundationalism, according to he founded mathematics on the
calculus of relatives; the second one mantaining that Schr\"oder only in his
last years (from 1890 onwards) focused on an universal and symbolic language
(by him called pasigraphy). We will argue that, on the one hand Schr\"oder
considered the problem of founding mathematics already solved by Dedekind,
limiting himself in a mere translation of the Chain Theory in the language of
the relatives. On the other hand, we will show that Schr\"oder's pasigraphy was
connaturate to himself and that it roots in his very childhood and in his love
for foreign languages.Comment: Next to be published in Logic and Logical Philosoph
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