Swap Bribery

In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of change that the voter is asked to implement. Specifically, in our model the briber can change a voter's preference list by paying for a sequence of swaps of consecutive candidates. Each swap may have a different price; the price of a bribery is the sum of the prices of all swaps that it involves. We prove complexity results for this model, which we call swap bribery, for a broad class of election systems, including variants of approval and k-approval, Borda, Copeland, and maximin.Comment: 17 page

The Carina-Near Moving Group

We identify a group of ~20 co-moving, mostly southern hemisphere, ~200 Myr old stars near Earth. Of the stars likely to be members of this Carina-Near Moving Group, in either its nucleus (~30 pc from Earth) or surrounding stream, all but 3 are plausible members of a multiple star system. The nucleus is (coincidentally) located quite close to the nucleus of the AB Doradus moving group notwithstanding that the two groups have substantially different ages and Galactic space motions, UVW.Comment: 9 pages, 1 table, 2 figures. Accepted in ApJ

A note on anti-coordination and social interactions

This note confirms a conjecture of [Bramoull\'{e}, Anti-coordination and social interactions, Games and Economic Behavior, 58, 2007: 30-49]. The problem, which we name the maximum independent cut problem, is a restricted version of the MAX-CUT problem, requiring one side of the cut to be an independent set. We show that the maximum independent cut problem does not admit any polynomial time algorithm with approximation ratio better than $n^{1-\epsilon}$, where $n$ is the number of nodes, and $\epsilon$ arbitrarily small, unless P=NP. For the rather special case where each node has a degree of at most four, the problem is still MAXSNP-hard.Comment: 7 page

On k-Column Sparse Packing Programs

We consider the class of packing integer programs (PIPs) that are column sparse, i.e. there is a specified upper bound k on the number of constraints that each variable appears in. We give an (ek+o(k))-approximation algorithm for k-column sparse PIPs, improving on recent results of $k^2\cdot 2^k$ and $O(k^2)$. We also show that the integrality gap of our linear programming relaxation is at least 2k-1; it is known that k-column sparse PIPs are $\Omega(k/ \log k)$-hard to approximate. We also extend our result (at the loss of a small constant factor) to the more general case of maximizing a submodular objective over k-column sparse packing constraints.Comment: 19 pages, v3: additional detail

Randomisation and Derandomisation in Descriptive Complexity Theory

We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic L, which is defined from L in a similar way as the complexity class BPP, bounded error probabilistic polynomial time, is defined from PTIME. Our main focus lies on questions of derandomisation, and we prove that there is a query which is definable in BPFO, the probabilistic version of first-order logic, but not in Cinf, finite variable infinitary logic with counting. This implies that many of the standard logics of finite model theory, like transitive closure logic and fixed-point logic, both with and without counting, cannot be derandomised. Similarly, we present a query on ordered structures which is definable in BPFO but not in monadic second-order logic, and a query on additive structures which is definable in BPFO but not in FO. The latter of these queries shows that certain uniform variants of AC0 (bounded-depth polynomial sized circuits) cannot be derandomised. These results are in contrast to the general belief that most standard complexity classes can be derandomised. Finally, we note that BPIFP+C, the probabilistic version of fixed-point logic with counting, captures the complexity class BPP, even on unordered structures

Asymmetric Primitive-Model Electrolytes: Debye-Huckel Theory, Criticality and Energy Bounds

Debye-Huckel (DH) theory is extended to treat two-component size- and charge-asymmetric primitive models, focussing primarily on the 1:1 additive hard-sphere electrolyte with, say, negative ion diameters, a--, larger than the positive ion diameters, a++. The treatment highlights the crucial importance of the charge-unbalanced ``border zones'' around each ion into which other ions of only one species may penetrate. Extensions of the DH approach which describe the border zones in a physically reasonable way are exact at high $T$ and low density, $\rho$, and, furthermore, are also in substantial agreement with recent simulation predictions for \emph{trends} in the critical parameters, $T_c$ and $\rho_c$, with increasing size asymmetry. Conversely, the simplest linear asymmetric DH description, which fails to account for physically expected behavior in the border zones at low $T$, can violate a new lower bound on the energy (which applies generally to models asymmetric in both charge and size). Other recent theories, including those based on the mean spherical approximation, have predicted trends in the critical parameters quite opposite to those established by the simulations.Comment: to appear in Physical Review

The "weighted ensemble" path sampling method is statistically exact for a broad class of stochastic processes and binning procedures

The "weighted ensemble" method, introduced by Huber and Kim, [G. A. Huber and S. Kim, Biophys. J. 70, 97 (1996)], is one of a handful of rigorous approaches to path sampling of rare events. Expanding earlier discussions, we show that the technique is statistically exact for a wide class of Markovian and non-Markovian dynamics. The derivation is based on standard path-integral (path probability) ideas, but recasts the weighted-ensemble approach as simple "resampling" in path space. Similar reasoning indicates that arbitrary nonstatic binning procedures, which merely guide the resampling process, are also valid. Numerical examples confirm the claims, including the use of bins which can adaptively find the target state in a simple model.Comment: Minor refinements to previou

XHIP-II: Clusters and associations

Context. In the absence of complete kinematic data it has not previously been possible to furnish accurate lists of member stars for all moving groups. There has been an unresolved dispute concerning the apparent inconsistency of the Hipparcos parallax distance to the Pleiades. Aims. To find improved candidate lists for clusters and associations represented among Hipparcos stars, to establish distances, and to cast light on the Pleiades distance anomaly. Methods. We use a six dimensional fitting procedure to identify candidates, and plot CMDs for 20 of the nearest groups. We calculate the mean parallax distance for all groups. Results. We identify lists of candidates and calculated parallax distances for 42 clusters and 45 associations represented within the Hipparcos catalogue. We find agreement between parallax distance and photometric distances for the most important clusters. For single stars in the Pleiades we find mean parallax distance 125.6 \pm 4.2 pc and photometric distance 132 \pm 3 pc calibrated to nearby groups of similar in age and composition. This gives no reason to doubt either the Hipparcos database or stellar evolutionary theory.Comment: Accepted for publication in Astronomy Letters, 10 pages, 2 fig

A Multivariate Genetic Analysis of Sensation Seeking

The genetic architecture of sensation seeking was analyzed in 1591 adolescent twin pairs. Individual differences in sensation seeking were best explained by a simple additive genetic model. Between 48 and 63 % of the total variance in sensation seeking subscales was attributable to genetic factors. There were no sex differences in the magnitude of the genetic and environmental effects. The different dimensions of sensation seeking were moderately correlated. The strongest correlations were between the subscales Thrill and Adventure Seeking and Experience Seeking (r = 0.4) and between Boredom Susceptibility and Disinhibition (r = 0.4 in males, r = 0.5 in females). A triangular decomposition showed that the correlations between the sensation seeking subscales were induced mainly by correlated genetic factors and, to a smaller extent, by correlated unique enviromnental factors. The genetic and environmental correlation structures differed between males and females. For females, higher genetic correlations for Experience Seeking with Boredom Susceptibility and Disinhibition and higher correlations among the unique environmental factors were found. There was no evidence that sex-specific genes influenced sensation seeking behavior in males and females. KEY WORDS: Sensation seeking; adolescent twins; multivariate genetic analysis

Infrared Imaging of GRB 970508

We have observed the field of the gamma-ray burst GRB 970508 at infrared wavelengths (2.2 μm) and have found a variable source coincident with the visible transient thought to be associated with the burst. The source was decaying in brightness with Ks magnitudes of 18.2±0.1, 18.8±0.1, and 19.0±0.3 mag on May 13.25, 16.25, and 20.21 UT, respectively. A 1 σ upper limit of K=21.3 mag was obtained for the brightness of the source on June 14.27 UT. The infrared light curve during this period is consistent with a ~t^(-1.2) power law, similar to the visible light curve. We do not find evidence for extended structure around the burst, as has been claimed for GRB 970228, and we obtain an upper limit of 0.04L_* for the luminosity of an underlying galaxy at the position of the infrared transient