Phenomenological Analysis of pppp and pˉp\bar{p}p Elastic Scattering Data in the Impact Parameter Space

We use an almost model-independent analytical parameterization for $pp$ and $\bar{p}p$ elastic scattering data to analyze the eikonal, profile, and inelastic overlap functions in the impact parameter space. Error propagation in the fit parameters allows estimations of uncertainty regions, improving the geometrical description of the hadron-hadron interaction. Several predictions are shown and, in particular, the prediction for $pp$ inelastic overlap function at $\sqrt{s}=14$ TeV shows the saturation of the Froissart-Martin bound at LHC energies.Comment: 15 pages, 16 figure

Is Comprehensive Education Really Free? A Study of the Effects of Secondary School Admissions Policies on House Prices.

This paper reports on a study that tests the anecdotal hypothesis that the prices of houses near popular comprehensive schools carry a premium. Since local education authorities use admissions policies based on catchment areas and places in popular schools are very hard to obtain from outside these areas - but easy from within them - parents have an incentive to move house for the sake of their children's education. This would be expected to be reflected in house prices. The study uses a cross sectional sample based on two popular schools in Coventry.PRICES ; SCHOOLS ; EDUCATION

A novel evolutionary formulation of the maximum independent set problem

We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph's independence number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph and its acyclic orientations. The resulting heuristic has been tested on some of the Second DIMACS Implementation Challenge benchmark graphs, and has been found to be competitive when compared to several of the other heuristics that have also been tested on those graphs

The age-metallicity dependence for white dwarfs

We present a theoretical study on the metallicity dependence of the initial$-$to$-$final mass relation and its influence on white dwarf age determinations. We compute a grid of evolutionary sequences from the main sequence to $\sim 3\, 000$ K on the white dwarf cooling curve, passing through all intermediate stages. During the thermally-pulsing asymptotic giant branch no third dredge-up episodes are considered and thus the photospheric C/O ratio is below unity for sequences with metallicities larger than $Z=0.0001$. We consider initial metallicities from $Z=0.0001$ to $Z=0.04$, accounting for stellar populations in the galactic disk and halo, with initial masses below $\sim 3M_{\odot}$. We found a clear dependence of the shape of the initial$-$to$-$final mass relation with the progenitor metallicity, where metal rich progenitors result in less massive white dwarf remnants, due to an enhancement of the mass loss rates associated to high metallicity values. By comparing our theoretical computations with semi empirical data from globular and old open clusters, we found that the observed intrinsic mass spread can be accounted for by a set of initial$-$to$-$final mass relations characterized by different metallicity values. Also, we confirm that the lifetime spent before the white dwarf stage increases with metallicity. Finally, we estimate the mean mass at the top of the white dwarf cooling curve for three globular clusters NGC 6397, M4 and 47 Tuc, around $0.53 M_{\odot}$, characteristic of old stellar populations. However, we found different values for the progenitor mass, lower for the metal poor cluster, NGC 6397, and larger for the younger and metal rich cluster 47 Tuc, as expected from the metallicity dependence of the initial$-$to$-$final mass relation.Comment: Accepted for publication in MNRA

Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks

We discuss the computational complexity of approximating maximum a posteriori inference in sum-product networks. We first show NP-hardness in trees of height two by a reduction from maximum independent set; this implies non-approximability within a sublinear factor. We show that this is a tight bound, as we can find an approximation within a linear factor in networks of height two. We then show that, in trees of height three, it is NP-hard to approximate the problem within a factor $2^{f(n)}$ for any sublinear function $f$ of the size of the input $n$. Again, this bound is tight, as we prove that the usual max-product algorithm finds (in any network) approximations within factor $2^{c \cdot n}$ for some constant $c < 1$. Last, we present a simple algorithm, and show that it provably produces solutions at least as good as, and potentially much better than, the max-product algorithm. We empirically analyze the proposed algorithm against max-product using synthetic and realistic networks.Comment: 18 page