Improving non-linear fits

In this notes we describe an algorithm for non-linear fitting which incorporates some of the features of linear least squares into a general minimum $\chi^2$ fit and provide a pure Python implementation of the algorithm. It consists of the variable projection method (varpro), combined with a Newton optimizer and stabilized using the steepest descent with an adaptative step. The algorithm includes a term to account for Bayesian priors. We performed tests of the algorithm using simulated data. This method is suitable, for example, for fitting with sums of exponentials as often needed in Lattice Quantum Chromodynamics

Probabilistic data flow analysis: a linear equational approach

Speculative optimisation relies on the estimation of the probabilities that certain properties of the control flow are fulfilled. Concrete or estimated branch probabilities can be used for searching and constructing advantageous speculative and bookkeeping transformations. We present a probabilistic extension of the classical equational approach to data-flow analysis that can be used to this purpose. More precisely, we show how the probabilistic information introduced in a control flow graph by branch prediction can be used to extract a system of linear equations from a program and present a method for calculating correct (numerical) solutions.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Process chain approach to high-order perturbation calculus for quantum lattice models

A method based on Rayleigh-Schroedinger perturbation theory is developed that allows to obtain high-order series expansions for ground-state properties of quantum lattice models. The approach is capable of treating both lattice geometries of large spatial dimensionalities d and on-site degrees of freedom with large state space dimensionalities. It has recently been used to accurately compute the zero-temperature phase diagram of the Bose-Hubbard model on a hypercubic lattice, up to arbitrary large filling and for d=2, 3 and greater [Teichmann et al., Phys. Rev. B 79, 100503(R) (2009)].Comment: 11 pages, 6 figure

Quantifying Timing Leaks and Cost Optimisation

We develop a new notion of security against timing attacks where the attacker is able to simultaneously observe the execution time of a program and the probability of the values of low variables. We then show how to measure the security of a program with respect to this notion via a computable estimate of the timing leakage and use this estimate for cost optimisation.Comment: 16 pages, 2 figures, 4 tables. A shorter version is included in the proceedings of ICICS'08 - 10th International Conference on Information and Communications Security, 20-22 October, 2008 Birmingham, U

Molecular junctions for thermal transport between graphene nanoribbons: covalent bonding vs. interdigitated chains

Proper design and manufacturing thermal bridges based on molecular junctions at the contact between graphene platelets or other thermally conductive nanoparticles would provide a fascinating way to produce efficient heat transport networks for the exploitation in heat management applications. In this work, using Non Equilibrium Molecular Dynamics, we calculated thermal conductance of alkyl chains used as molecular junctions between two graphene nanoribbons, both as covalently bound and Van der Waals interdigitated chains. Effect of chain length, grafting density, temperature and chain interdigitation were systematically studied. A clear reduction of conductivity was found with increasing chain length and decreasing grafting density, while lower conductivity was observed for Van der Waals interdigitated chains compared to covalently bound ones. The importance of molecular junctions in enhancing thermal conductance at graphene nanoribbons contacts was further evidenced by calculating the conductance equivalence between a single chain and an overlapping of un-functionalized graphene sheets. As an example, one single pentyl covalently bound chain was found to have a conductance equivalent to the overlapping of an area corresponding to about 152 carbon atoms. These results contribute to the understanding of thermal phenomena occurring within networks of thermally conductive nanoparticles, including graphene nanopapers and graphene-based polymer nanocomposites, which are or high interest for the heat management application in electronics and generally in low-temperature heat exchange and recovery