Comparing Beliefs, Surveys and Random Walks

Survey propagation is a powerful technique from statistical physics that has been applied to solve the 3-SAT problem both in principle and in practice. We give, using only probability arguments, a common derivation of survey propagation, belief propagation and several interesting hybrid methods. We then present numerical experiments which use WSAT (a widely used random-walk based SAT solver) to quantify the complexity of the 3-SAT formulae as a function of their parameters, both as randomly generated and after simplification, guided by survey propagation. Some properties of WSAT which have not previously been reported make it an ideal tool for this purpose -- its mean cost is proportional to the number of variables in the formula (at a fixed ratio of clauses to variables) in the easy-SAT regime and slightly beyond, and its behavior in the hard-SAT regime appears to reflect the underlying structure of the solution space that has been predicted by replica symmetry-breaking arguments. An analysis of the tradeoffs between the various methods of search for satisfying assignments shows WSAT to be far more powerful that has been appreciated, and suggests some interesting new directions for practical algorithm development.Comment: 8 pages, 5 figure

Minimally Allowed Neutrinoless Double Beta Decay Rates From Approximate Flavor Symmetries

Neutrinoless double beta decay ($\beta\beta0\nu$) is among the only realistic probes of Majorana neutrinos. In the standard scenario, dominated by light neutrino exchange, the process amplitude is proportional to $m_{ee}$, the $e-e$ element of the Majorana mass matrix. Naively, current data allows for vanishing $m_{ee}$, but this should be protected by an appropriate flavor symmetry. All such symmetries lead to mass matrices inconsistent with oscillation phenomenology. I perform a spurion analysis to break all possible Abelian symmetries that guarantee vanishing $\beta\beta0\nu$ rates and search for minimally allowed values. I survey 230 broken structures to yield $m_{ee}$ values and current phenomenological constraints under a variety of scenarios. This analysis also extracts predictions for both neutrino oscillation parameters and kinematic quantities. Assuming reasonable tuning levels, I find that $m_{ee}>4\times 10^{-6}$ eV at 99% confidence. Bounds below this value might indicate the Dirac neutrino nature or the existence of new light (eV-MeV scale) degrees of freedom that can potentially be probed elsewhere.Comment: 19 Pages, 4 .eps Figures, 3 Table

Non-detection of a statistically anisotropic power spectrum in large-scale structure

We search a sample of photometric luminous red galaxies (LRGs) measured by the Sloan Digital Sky Survey (SDSS) for a quadrupolar anisotropy in the primordial power spectrum, in which P(\vec{k}) is an isotropic power spectrum P(k) multiplied by a quadrupolar modulation pattern. We first place limits on the 5 coefficients of a general quadrupole anisotropy. We also consider axisymmetric quadrupoles of the form P(\vec{k}) = P(k){1 + g_*[(\hat{k}\cdot\hat{n})^2-1/3]} where \hat{n} is the axis of the anisotropy. When we force the symmetry axis \hat{n} to be in the direction (l,b)=(94 degrees,26 degrees) identified in the recent Groeneboom et al. analysis of the cosmic microwave background, we find g_*=0.006+/-0.036 (1 sigma). With uniform priors on \hat{n} and g_* we find that -0.41<g_*<+0.38 with 95% probability, with the wide range due mainly to the large uncertainty of asymmetries aligned with the Galactic Plane. In none of these three analyses do we detect evidence for quadrupolar power anisotropy in large scale structure.Comment: 23 pages; 10 figures; 3 tables; replaced with version published in JCAP (added discussion of scale-varying quadrupolar anisotropy

Symmetry Breaking Constraints: Recent Results

Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful cases: symmetry breaking constraints for row and column symmetry, and symmetry breaking constraints for eliminating value symmetryComment: To appear in Proceedings of Twenty-Sixth Conference on Artificial Intelligence (AAAI-12

Integration of first-principles methods and crystallographic database searches for new ferroelectrics: Strategies and explorations

In this concept paper, the development of strategies for the integration of first-principles methods with crystallographic database mining for the discovery and design of novel ferroelectric materials is discussed, drawing on the results and experience derived from exploratory investigations on three different systems: (1) the double perovskite Sr(Sb$_{1/2}$Mn$_{1/2}$)O$_3$ as a candidate semiconducting ferroelectric; (2) polar derivatives of schafarzikite $M$Sb$_2$O$_4$; and (3) ferroelectric semiconductors with formula $M_2$P$_2$(S,Se)$_6$. A variety of avenues for further research and investigation are suggested, including automated structure type classification, low-symmetry improper ferroelectrics, and high-throughput first-principles searches for additional representatives of structural families with desirable functional properties.Comment: 13 pages, 5 figures, 4 table