The Predictability of Punitive Damages

Using one year of jury trial outcomes from 45 of the nation\u27s most populous counties, this article shows a strong and statistically significant correlation between compensatory and punitive damages. These findings are replicated in 25 years of punitive damages awards from Cook County, Illinois, and California. In addition, we find no evidence that punitive damages awards are more likely when individuals sue businesses than when individuals sue individuals. With respect to award frequency, juries rarely award punitive damages and appear to be especially reluctant to do so in the areas of law that have captured the most attention, products liability and medical malpractice. Punitive damages are most frequently awarded in business/contract cases and intentional tort cases. The frequency-of-award findings are consistent with all major studies of punitive damages

The survival and disruption of CDM micro-haloes: implications for direct and indirect detection experiments

If the dark matter particle is a neutralino then the first structures to form are cuspy cold dark matter (CDM) haloes collapsing after redshifts z ~ 100 in the mass range 10^{-6} - 10^{-3} Msun. We carry out a detailed study of the survival of these micro-haloes in the Galaxy as they experience tidal encounters with stars, molecular clouds, and other dark matter substructures. We test the validity of analytic impulsive heating calculations using high resolution N-body simulations. A major limitation of analytic estimates is that mean energy inputs are compared to mean binding energies, instead of the actual mass lost from the system. This energy criterion leads to an overestimate of the stripped mass and underestimate of the disruption timescale since CDM haloes are strongly bound in their inner parts. We show that a significant fraction of material from CDM micro-haloes can be unbound by encounters with Galactic substructure and stars, however the cuspy central regions remain relatively intact. Furthermore, the micro-haloes near the solar radius are those which collapse significantly earlier than average and will suffer very little mass loss. Thus we expect a fraction of surviving bound micro-haloes, a smooth component with narrow features in phase space, which may be uncovered by direct detection experiments, as well as numerous surviving cuspy cores with proper motions of arc-minutes per year, which can be detected indirectly via their annihilation into gamma-rays.Comment: 9 pages, 12 figures, submitted to MNRAS, v2: references adde

Tricritical Points in Random Combinatorics: the (2+p)-SAT case

The (2+p)-Satisfiability (SAT) problem interpolates between different classes of complexity theory and is believed to be of basic interest in understanding the onset of typical case complexity in random combinatorics. In this paper, a tricritical point in the phase diagram of the random $2+p$-SAT problem is analytically computed using the replica approach and found to lie in the range $2/5 \le p_0 \le 0.416$. These bounds on $p_0$ are in agreement with previous numerical simulations and rigorous results.Comment: 7 pages, 1 figure, RevTeX, to appear in J.Phys.

The formation of ultra-compact dwarf galaxies and nucleated dwarf galaxies

Ultra compact dwarf galaxies (UCDs) have similar properties as massive globular clusters or the nuclei of nucleated galaxies. Recent observations suggesting a high dark matter content and a steep spatial distribution within groups and clusters provide new clues as to their origins. We perform high-resolution N-body / smoothed particle hydrodynamics simulations designed to elucidate two possible formation mechanisms for these systems: the merging of globular clusters in the centre of a dark matter halo, or the massively stripped remnant of a nucleated galaxy. Both models produce density profiles as well as the half light radii that can fit the observational constraints. However, we show that the first scenario results to UCDs that are underluminous and contain no dark matter. This is because the sinking process ejects most of the dark matter particles from the halo centre. Stripped nuclei give a more promising explanation, especially if the nuclei form via the sinking of gas, funneled down inner galactic bars, since this process enhances the central dark matter content. Even when the entire disk is tidally stripped away, the nucleus stays intact and can remain dark matter dominated even after severe stripping. Total galaxy disruption beyond the nuclei only occurs on certain orbits and depends on the amount of dissipation during nuclei formation. By comparing the total disruption of CDM subhaloes in a cluster potential we demonstrate that this model also leads to the observed spatial distribution of UCDs which can be tested in more detail with larger data sets.Comment: 8 pages, 8 figures, final version accepted for publication in MNRA

Phase coexistence and finite-size scaling in random combinatorial problems

We study an exactly solvable version of the famous random Boolean satisfiability problem, the so called random XOR-SAT problem. Rare events are shown to affect the combinatorial ``phase diagram'' leading to a coexistence of solvable and unsolvable instances of the combinatorial problem in a certain region of the parameters characterizing the model. Such instances differ by a non-extensive quantity in the ground state energy of the associated diluted spin-glass model. We also show that the critical exponent $\nu$, controlling the size of the critical window where the probability of having solutions vanishes, depends on the model parameters, shedding light on the link between random hyper-graph topology and universality classes. In the case of random satisfiability, a similar behavior was conjectured to be connected to the onset of computational intractability.Comment: 10 pages, 5 figures, to appear in J. Phys. A. v2: link to the XOR-SAT probelm adde

Simplest random K-satisfiability problem

We study a simple and exactly solvable model for the generation of random satisfiability problems. These consist of $\gamma N$ random boolean constraints which are to be satisfied simultaneously by $N$ logical variables. In statistical-mechanics language, the considered model can be seen as a diluted p-spin model at zero temperature. While such problems become extraordinarily hard to solve by local search methods in a large region of the parameter space, still at least one solution may be superimposed by construction. The statistical properties of the model can be studied exactly by the replica method and each single instance can be analyzed in polynomial time by a simple global solution method. The geometrical/topological structures responsible for dynamic and static phase transitions as well as for the onset of computational complexity in local search method are thoroughly analyzed. Numerical analysis on very large samples allows for a precise characterization of the critical scaling behaviour.Comment: 14 pages, 5 figures, to appear in Phys. Rev. E (Feb 2001). v2: minor errors and references correcte

Diffuse Lyman Alpha Haloes around Lyman Alpha Emitters at z=3: Do Dark Matter Distributions Determine the Lyman Alpha Spatial Extents?

Using stacks of Ly-a images of 2128 Ly-a emitters (LAEs) and 24 protocluster UV-selected galaxies (LBGs) at z=3.1, we examine the surface brightness profiles of Ly-a haloes around high-z galaxies as a function of environment and UV luminosity. We find that the slopes of the Ly-a radial profiles become flatter as the Mpc-scale LAE surface densities increase, but they are almost independent of the central UV luminosities. The characteristic exponential scale lengths of the Ly-a haloes appear to be proportional to the square of the LAE surface densities (r(Lya) \propto Sigma(LAE)^2). Including the diffuse, extended Ly-a haloes, the rest-frame Ly-a equivalent width of the LAEs in the densest regions approaches EW_0(Lya) ~ 200 A, the maximum value expected for young (< 10^7 yr) galaxies. This suggests that Ly-a photons formed via shock compression by gas outflows or cooling radiation by gravitational gas inflows may partly contribute to illuminate the Ly-a haloes; however, most of their Ly-a luminosity can be explained by photo-ionisation by ionising photons or scattering of Ly-a photons produced in HII regions in and around the central galaxies. Regardless of the source of Ly-a photons, if the Ly-a haloes trace the overall gaseous structure following the dark matter distributions, it is not surprising that the Ly-a spatial extents depend more strongly on the surrounding Mpc-scale environment than on the activities of the central galaxies.Comment: 7 pages, 4 figures, accepted for publication in MNRA

Central Powering of the Largest Lyman-alpha Nebula is Revealed by Polarized Radiation

High-redshift Lyman-alpha blobs are extended, luminous, but rare structures that appear to be associated with the highest peaks in the matter density of the Universe. Their energy output and morphology are similar to powerful radio galaxies, but the source of the luminosity is unclear. Some blobs are associated with ultraviolet or infrared bright galaxies, suggesting an extreme starburst event or accretion onto a central black hole. Another possibility is gas that is shock excited by supernovae. However some blobs are not associated with galaxies, and may instead be heated by gas falling into a dark matter halo. The polarization of the Ly-alpha emission can in principle distinguish between these options, but a previous attempt to detect this signature returned a null detection. Here we report on the detection of polarized Ly-alpha from the blob LAB1. Although the central region shows no measurable polarization, the polarized fraction (P) increases to ~20 per cent at a radius of 45 kpc, forming an almost complete polarized ring. The detection of polarized radiation is inconsistent with the in situ production of Ly-alpha photons, and we conclude that they must have been produced in the galaxies hosted within the nebula, and re-scattered by neutral hydrogen.Comment: Published in the August 18 issue of Nature. 1750 words, 3 figures, and full Supplementary Information. Version has not undergone proofing. Reduced and processed data products are available here: http://obswww.unige.ch/people/matthew.hayes/LymanAlpha/LabPol

The dark halo of the Hydra I galaxy cluster: core, cusp, cosmological? Dynamics of NGC 3311 and its globular cluster system

NGC 3311 is the central cD galaxy of the Hydra I cluster. We use globular clusters around NGC 3311, combined with kinematical data of the galaxy itself, to investigate the dark matter distribution in the central region of Hydra I. Radial velocities of 118 bright globular clusters, based on VLT/VIMOS mask spectroscopy, are used to calculate velocity dispersions which are well defined out to 100 kpc. NGC 3311 is the most distant galaxy for which this kind of study has been performed. We also determine velocity dispersions of the stellar component from long slit spectroscopy out to 20 kpc. Moreover, we present a new photometric model for NGC 3311 in the V-band. We search for a dark halo which in the context of a spherical Jeans model. We also compare the radial velocity distributions of globular clusters and planetary nebulae. The projected stellar velocity dispersion rises from 185 km/s to 350 km/s at a radius of 20 kpc. The globular cluster dispersion rises as well from 500 km/s at 10 kpc to about 800 km/s at 100 kpc, comparable to the velocity dispersion of the cluster galaxies. A dark matter halo with a core reproduces well the velocity dispersions of stars and globular clusters simultaneously under isotropy. The central stellar velocity dispersions predicted by cosmological NFW halos are less good representations, while the globular clusters allow a wide range of halo parameters. A suspected radial anisotropy of the stellar population aggravates the deviations. However, we find discrepancies with previous kinematical data, which we cannot resolve and may indicate a more complicated velocity pattern. Although one cannot conclusively demonstrate that the dark matter halo of NGC 3311 has a core rather than a cusp, a core seems to be preferred by the present data. A more complete velocity field and an analysis of the anisotropy is required to reach firm conclusions.Comment: 8 pages, 5 figures, abstract abridged, accepted for publication in A&