7,039 research outputs found
Irrational Conformal Field Theory
This is a review of irrational conformal field theory, which includes
rational conformal field theory as a small subspace. Central topics of the
review include the Virasoro master equation, its solutions and the dynamics of
irrational conformal field theory. Discussion of the dynamics includes the
generalized Knizhnik-Zamolodchikov equations on the sphere, the corresponding
heat-like systems on the torus and the generic world- sheet action of
irrational conformal field theory.Comment: 195 pages, Latex, 12 figures, to appear in Physics Reports. Typos
corrected in Sections 13 and 14, and a footnote added in Section 1
Finding long cycles in graphs
We analyze the problem of discovering long cycles inside a graph. We propose
and test two algorithms for this task. The first one is based on recent
advances in statistical mechanics and relies on a message passing procedure.
The second follows a more standard Monte Carlo Markov Chain strategy. Special
attention is devoted to Hamiltonian cycles of (non-regular) random graphs of
minimal connectivity equal to three
A statistical mechanics approach to autopoietic immune networks
The aim of this work is to try to bridge over theoretical immunology and
disordered statistical mechanics. Our long term hope is to contribute to the
development of a quantitative theoretical immunology from which practical
applications may stem. In order to make theoretical immunology appealing to the
statistical physicist audience we are going to work out a research article
which, from one side, may hopefully act as a benchmark for future improvements
and developments, from the other side, it is written in a very pedagogical way
both from a theoretical physics viewpoint as well as from the theoretical
immunology one.
Furthermore, we have chosen to test our model describing a wide range of
features of the adaptive immune response in only a paper: this has been
necessary in order to emphasize the benefit available when using disordered
statistical mechanics as a tool for the investigation. However, as a
consequence, each section is not at all exhaustive and would deserve deep
investigation: for the sake of completeness, we restricted details in the
analysis of each feature with the aim of introducing a self-consistent model.Comment: 22 pages, 14 figur
Approximating random quantum optimization problems
We report a cluster of results regarding the difficulty of finding
approximate ground states to typical instances of the quantum satisfiability
problem -QSAT on large random graphs. As an approximation strategy, we
optimize the solution space over `classical' product states, which in turn
introduces a novel autonomous classical optimization problem, PSAT, over a
space of continuous degrees of freedom rather than discrete bits. Our central
results are: (i) The derivation of a set of bounds and approximations in
various limits of the problem, several of which we believe may be amenable to a
rigorous treatment. (ii) A demonstration that an approximation based on a
greedy algorithm borrowed from the study of frustrated magnetism performs well
over a wide range in parameter space, and its performance reflects structure of
the solution space of random -QSAT. Simulated annealing exhibits
metastability in similar `hard' regions of parameter space. (iii) A
generalization of belief propagation algorithms introduced for classical
problems to the case of continuous spins. This yields both approximate
solutions, as well as insights into the free energy `landscape' of the
approximation problem, including a so-called dynamical transition near the
satisfiability threshold. Taken together, these results allow us to elucidate
the phase diagram of random -QSAT in a two-dimensional
energy-density--clause-density space.Comment: 14 pages, 9 figure
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