1,782 research outputs found
On the susceptibility function of piecewise expanding interval maps
We study the susceptibility function Psi(z) associated to the perturbation
f_t=f+tX of a piecewise expanding interval map f. The analysis is based on a
spectral description of transfer operators. It gives in particular sufficient
conditions which guarantee that Psi(z) is holomorphic in a disc of larger than
one. Although Psi(1) is the formal derivative of the SRB measure of f_t with
respect to t, we present examples satisfying our conditions so that the SRB
measure is not Lipschitz.*We propose a new version of Ruelle's conjectures.* In
v2, we corrected a few minor mistakes and added Conjectures A-B and Remark 4.5.
In v3, we corrected the perturbation (X(f(x)) instead of X(x)), in particular
in the examples from Section 6. As a consequence, Psi(z) has a pole at z=1 for
these examples.Comment: To appear Comm. Math. Phy
Comments on the Links between su(3) Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards
We examine the proposal made recently that the su(3) modular invariant
partition functions could be related to the geometry of the complex Fermat
curves. Although a number of coincidences and similarities emerge between them
and certain algebraic curves related to triangular billiards, their meaning
remains obscure. In an attempt to go beyond the su(3) case, we show that any
rational conformal field theory determines canonically a Riemann surface.Comment: 56 pages, 4 eps figures, LaTeX, uses eps
Linear response formula for piecewise expanding unimodal maps
The average R(t) of a smooth function with respect to the SRB measure of a
smooth one-parameter family f_t of piecewise expanding interval maps is not
always Lipschitz. We prove that if f_t is tangent to the topological class of
f_0, then R(t) is differentiable at zero, and the derivative coincides with the
resummation previously proposed by the first named author of the (a priori
divergent) series given by Ruelle's conjecture.Comment: We added Theorem 7.1 which shows that the horizontality condition is
necessary. The paper "Smooth deformations..." containing Thm 2.8 is now
available on the arxiv; see also Corrigendum arXiv:1205.5468 (to appear
Nonlinearity 2012
Structures of Malcev Bialgebras on a simple non-Lie Malcev algebra
Lie bialgebras were introduced by Drinfeld in studying the solutions to the
classical Yang-Baxter equation. The definition of a bialgebra in the sense of
Drinfeld (D-bialgebra), related with any variety of algebras, was given by
Zhelyabin. In this work, we consider Malcev bialgebras. We describe all
structures of a Malcev bialgebra on a simple non-Lie Malcev algebra
Pre-logarithmic and logarithmic fields in a sandpile model
We consider the unoriented two-dimensional Abelian sandpile model on the
half-plane with open and closed boundary conditions, and relate it to the
boundary logarithmic conformal field theory with central charge c=-2. Building
on previous results, we first perform a complementary lattice analysis of the
operator effecting the change of boundary condition between open and closed,
which confirms that this operator is a weight -1/8 boundary primary field,
whose fusion agrees with lattice calculations. We then consider the operators
corresponding to the unit height variable and to a mass insertion at an
isolated site of the upper half plane and compute their one-point functions in
presence of a boundary containing the two kinds of boundary conditions. We show
that the scaling limit of the mass insertion operator is a weight zero
logarithmic field.Comment: 18 pages, 9 figures. v2: minor corrections + added appendi
Generalized nonuniform dichotomies and local stable manifolds
We establish the existence of local stable manifolds for semiflows generated
by nonlinear perturbations of nonautonomous ordinary linear differential
equations in Banach spaces, assuming the existence of a general type of
nonuniform dichotomy for the evolution operator that contains the nonuniform
exponential and polynomial dichotomies as a very particular case. The family of
dichotomies considered allow situations for which the classical Lyapunov
exponents are zero. Additionally, we give new examples of application of our
stable manifold theorem and study the behavior of the dynamics under
perturbations.Comment: 18 pages. New version with minor corrections and an additional
theorem and an additional exampl
Modelling quasicrystals at positive temperature
We consider a two-dimensional lattice model of equilibrium statistical
mechanics, using nearest neighbor interactions based on the matching conditions
for an aperiodic set of 16 Wang tiles. This model has uncountably many ground
state configurations, all of which are nonperiodic. The question addressed in
this paper is whether nonperiodicity persists at low but positive temperature.
We present arguments, mostly numerical, that this is indeed the case. In
particular, we define an appropriate order parameter, prove that it is
identically zero at high temperatures, and show by Monte Carlo simulation that
it is nonzero at low temperatures
Scaling behavior of interactions in a modular quantum system and the existence of local temperature
We consider a quantum system of fixed size consisting of a regular chain of
-level subsystems, where is finite. Forming groups of subsystems
each, we show that the strength of interaction between the groups scales with
. As a consequence, if the total system is in a thermal state with
inverse temperature , a sufficient condition for subgroups of size
to be approximately in a thermal state with the same temperature is , where is the width of the occupied
level spectrum of the total system. These scaling properties indicate on what
scale local temperatures may be meaningfully defined as intensive variables.
This question is particularly relevant for non-equilibrium scenarios such as
heat conduction etc.Comment: 7 pages, accepted for publication in Europhysics Letter
Transmission of primary resistance mutation K103N in a cluster of Belgian young patients from different risk groups
Background: We analysed the distribution of an HIV-1 subtype B strain resistant to efavirenz and nevirapine among incident infections in the Belgian population.
Method: The Belgian AIDS reference laboratories searched their databases for HIV-1 subtype B sequences harbouring the K103N mutation in the reverse transcriptase (RT) or the C67S and V77I mutations in the protease (PR). We included the earliest RT sequence available of drug-naïve patients as well as sequences related to treatment failure. Fifty sequences were aligned omitting the codon 103 and submitted to phylogenetic analysis. Epidemiological data were collected through the Institute of Public Health national database. In addition, three sequences from the cluster were analysed by deep sequencing using the Roche GS Junior platform.
Results: Phylogenetic analysis revealed the presence of a 24 virus sequences cluster. All except one of those sequences resulted from patients who were ARV-naïve at the time of sampling, and 21 had the K103N mutation. Two thirds of the clustered patients were infected through homosexual or bisexual contacts while the others were heterosexuals. No case was related to migrants contaminated abroad. Fifteen of the clustered patients were diagnosed between January 2011 and June 2012; 87% of them were aged between 20 and 29 at the time of diagnosis. Interestingly, 60% of them reside in the province of Namur. Deep sequencing analysis of 3 individuals sampled near seroconversion revealed no other resistance mutations at a frequency > 1% than those already picked up by Sanger sequencing (RT A98S, K103N; PR V77I), except the RT V90I.
Conclusion: We identified a transmission cluster of drug resistant HIV-1 variants mainly including homo- and heterosexual young adults. Most individuals are of Belgian origin and are living around the city of Namur (Belgium). The K103N mutation had no apparent impact on transmission fitness as its spread raised during the last years. These observations may impact on local prevention and ARV prophylaxis strategies
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