Understanding the complexity of #SAT using knowledge compilation

Two main techniques have been used so far to solve the #P-hard problem #SAT. The first one, used in practice, is based on an extension of DPLL for model counting called exhaustive DPLL. The second approach, more theoretical, exploits the structure of the input to compute the number of satisfying assignments by usually using a dynamic programming scheme on a decomposition of the formula. In this paper, we make a first step toward the separation of these two techniques by exhibiting a family of formulas that can be solved in polynomial time with the first technique but needs an exponential time with the second one. We show this by observing that both techniques implicitely construct a very specific boolean circuit equivalent to the input formula. We then show that every beta-acyclic formula can be represented by a polynomial size circuit corresponding to the first method and exhibit a family of beta-acyclic formulas which cannot be represented by polynomial size circuits corresponding to the second method. This result shed a new light on the complexity of #SAT and related problems on beta-acyclic formulas. As a byproduct, we give new handy tools to design algorithms on beta-acyclic hypergraphs

Collective Phenomena and Non-Finite State Computation in a Human Social System

We investigate the computational structure of a paradigmatic example of distributed social interaction: that of the open-source Wikipedia community. We examine the statistical properties of its cooperative behavior, and perform model selection to determine whether this aspect of the system can be described by a finite-state process, or whether reference to an effectively unbounded resource allows for a more parsimonious description. We find strong evidence, in a majority of the most-edited pages, in favor of a collective-state model, where the probability of a "revert" action declines as the square root of the number of non-revert actions seen since the last revert. We provide evidence that the emergence of this social counter is driven by collective interaction effects, rather than properties of individual users.Comment: 23 pages, 4 figures, 3 tables; to appear in PLoS ON

Altered structural and effective connectivity in anorexia and bulimia nervosa in circuits that regulate energy and reward homeostasis.

Anorexia and bulimia nervosa are severe eating disorders that share many behaviors. Structural and functional brain circuits could provide biological links that those disorders have in common. We recruited 77 young adult women, 26 healthy controls, 26 women with anorexia and 25 women with bulimia nervosa. Probabilistic tractography was used to map white matter connectivity strength across taste and food intake regulating brain circuits. An independent multisample greedy equivalence search algorithm tested effective connectivity between those regions during sucrose tasting. Anorexia and bulimia nervosa had greater structural connectivity in pathways between insula, orbitofrontal cortex and ventral striatum, but lower connectivity from orbitofrontal cortex and amygdala to the hypothalamus (P<0.05, corrected for comorbidity, medication and multiple comparisons). Functionally, in controls the hypothalamus drove ventral striatal activity, but in anorexia and bulimia nervosa effective connectivity was directed from anterior cingulate via ventral striatum to the hypothalamus. Across all groups, sweetness perception was predicted by connectivity strength in pathways connecting to the middle orbitofrontal cortex. This study provides evidence that white matter structural as well as effective connectivity within the energy-homeostasis and food reward-regulating circuitry is fundamentally different in anorexia and bulimia nervosa compared with that in controls. In eating disorders, anterior cingulate cognitive-emotional top down control could affect food reward and eating drive, override hypothalamic inputs to the ventral striatum and enable prolonged food restriction