First passage and arrival time densities for L\'evy flights and the failure of the method of images

We discuss the first passage time problem in the semi-infinite interval, for homogeneous stochastic Markov processes with L{\'e}vy stable jump length distributions $\lambda(x)\sim\ell^{\alpha}/|x|^{1+\alpha}$ ($|x|\gg\ell$), namely, L{\'e}vy flights (LFs). In particular, we demonstrate that the method of images leads to a result, which violates a theorem due to Sparre Andersen, according to which an arbitrary continuous and symmetric jump length distribution produces a first passage time density (FPTD) governed by the universal long-time decay $\sim t^{-3/2}$. Conversely, we show that for LFs the direct definition known from Gaussian processes in fact defines the probability density of first arrival, which for LFs differs from the FPTD. Our findings are corroborated by numerical results.Comment: 8 pages, 3 figures, iopart.cls style, accepted to J. Phys. A (Lett

Design of Sequences with Good Folding Properties in Coarse-Grained Protein Models

Background: Designing amino acid sequences that are stable in a given target structure amounts to maximizing a conditional probability. A straightforward approach to accomplish this is a nested Monte Carlo where the conformation space is explored over and over again for different fixed sequences, which requires excessive computational demand. Several approximate attempts to remedy this situation, based on energy minimization for fixed structure or high-$T$ expansions, have been proposed. These methods are fast but often not accurate since folding occurs at low $T$. Results: We develop a multisequence Monte Carlo procedure, where both sequence and conformation space are simultaneously probed with efficient prescriptions for pruning sequence space. The method is explored on hydrophobic/polar models. We first discuss short lattice chains, in order to compare with exact data and with other methods. The method is then successfully applied to lattice chains with up to 50 monomers, and to off-lattice 20-mers. Conclusions: The multisequence Monte Carlo method offers a new approach to sequence design in coarse-grained models. It is much more efficient than previous Monte Carlo methods, and is, as it stands, applicable to a fairly wide range of two-letter models.Comment: 23 pages, 7 figure

Solving package dependencies: from EDOS to Mancoosi

Mancoosi (Managing the Complexity of the Open Source Infrastructure) is an ongoing research project funded by the European Union for addressing some of the challenges related to the "upgrade problem" of interdependent software components of which Debian packages are prototypical examples. Mancoosi is the natural continuation of the EDOS project which has already contributed tools for distribution-wide quality assurance in Debian and other GNU/Linux distributions. The consortium behind the project consists of several European public and private research institutions as well as some commercial GNU/Linux distributions from Europe and South America. Debian is represented by a small group of Debian Developers who are working in the ranks of the involved universities to drive and integrate back achievements into Debian. This paper presents relevant results from EDOS in dependency management and gives an overview of the Mancoosi project and its objectives, with a particular focus on the prospective benefits for Debian

The decay of unstable k-strings in SU(N) gauge theories at zero and finite temperature

Sources in higher representations of SU(N) gauge theory at T=0 couple with apparently stable strings with tensions depending on the specific representation rather than on its N-ality. Similarly at the deconfining temperature these sources carry their own representation-dependent critical exponents. It is pointed out that in some instances one can evaluate exactly these exponents by fully exploiting the correspondence between the 2+1 dimensional critical gauge theory and the 2d conformal field theory in the same universality class. The emerging functional form of the Polyakov-line correlators suggests a similar form for Wilson loops in higher representations which helps in understanding the behaviour of unstable strings at T=0. A generalised Wilson loop in which along part of its trajectory a source is converted in a gauge invariant way into higher representations with same N-ality could be used as a tool to estimate the decay scale of the unstable strings.Comment: 18 pages, 4 figures v2: typos correcte