Ensuring an Impartial Jury in the Age of Social Media

The explosive growth of social networking has placed enormous pressure on one of the most fundamental of American institutions—the impartial jury. Through social networking services like Facebook and Twitter, jurors have committed significant and often high-profile acts of misconduct. Just recently, the Arkansas Supreme Court reversed a death sentence because a juror Tweeted about the case during deliberations. In light of the significant risks to a fair trial that arise when jurors communicate through social media during trial, judges must be vigilant in monitoring for potential outside influences and in deterring misconduct. In this Article, we present informal survey data from actual jurors on their use of social networking during trial. We discuss the rise of web-based social networks like Facebook and Twitter, and the concerns that arise when jurors communicate about a case through social media before returning a verdict. After surveying how courts have responded to jurors’ social media use, we describe the results of the informal survey. The results support a growing consensus in the legal profession that courts should frequently, as a matter of course, instruct jurors not to use social media to communicate about trial. Although others have stressed the importance of jury instructions in this area, we hope that the informal survey data will further the dialogue by providing an important perspective—that of actual jurors

Simple estimation of absolute free energies for biomolecules

One reason that free energy difference calculations are notoriously difficult in molecular systems is due to insufficient conformational overlap, or similarity, between the two states or systems of interest. The degree of overlap is irrelevant, however, if the absolute free energy of each state can be computed. We present a method for calculating the absolute free energy that employs a simple construction of an exactly computable reference system which possesses high overlap with the state of interest. The approach requires only a physical ensemble of conformations generated via simulation, and an auxiliary calculation of approximately equal central-processing-unit (CPU) cost. Moreover, the calculations can converge to the correct free energy value even when the physical ensemble is incomplete or improperly distributed. As a "proof of principle," we use the approach to correctly predict free energies for test systems where the absolute values can be calculated exactly, and also to predict the conformational equilibrium for leucine dipeptide in implicit solvent.Comment: To appear in J. Chem. Phys., 10 pages, 6 figure

Hardness of approximation for quantum problems

The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the second level of this quantum hierarchy, but that these problems are in fact hard to approximate. Using these techniques, we also obtain hardness of approximation for the class QCMA. Our approach is based on the use of dispersers, and is inspired by the classical results of Umans regarding hardness of approximation for the second level of the classical polynomial hierarchy [Umans, FOCS 1999]. The problems for which we prove hardness of approximation for include, among others, a quantum version of the Succinct Set Cover problem, and a variant of the local Hamiltonian problem with hybrid classical-quantum ground states.Comment: 21 pages, 1 figure, extended abstract appeared in Proceedings of the 39th International Colloquium on Automata, Languages and Programming (ICALP), pages 387-398, Springer, 201

Batalin-Vilkovisky Integrals in Finite Dimensions

The Batalin-Vilkovisky method (BV) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological Perturbation Theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangian system with symmetries. Localization (illustrated in terms of Duistermaat-Heckman localization) as well as anomalous symmetries are discussed in the framework of BV.Comment: 35 page

The complexity of 3-colouring H-colourable graphs.

We study the complexity of approximation on satisfiable instances for graph homomorphism problems. For a fixed graph $H$, the $H$-colouring problem is to decide whether a given graph has a homomorphism to $H$. By a result of Hell and Ne\v{s}et\v{r}il, this problem is NP-hard for any non-bipartite graph $H$. In the context of promise constraint satisfaction problems, Brakensiek and Guruswami conjectured that this hardness result extends to promise graph homomorphism as follows: fix any non-bipartite graph $H$ and another graph $G$ with a homomorphism from $H$ to $G$, it is NP-hard to find a homomorphism to $G$ from a given $H$-colourable graph. Arguably, the two most important special cases of this conjecture are when $H$ is fixed to be the complete graph on 3 vertices (and $G$ is any graph with a triangle) and when $G$ is the complete graph on 3 vertices (and $H$ is any 3-colourable graph). The former case is equivalent to the notoriously difficult approximate graph colouring problem. In this paper, we confirm the Brakensiek-Guruswami conjecture for the latter case. Our proofs rely on a novel combination of the universal-algebraic approach to promise constraint satisfaction, that was recently developed by Barto, Bul\'in and the authors, with some ideas from algebraic topology.Comment: To appear in FOCS 201

A Covariant Approach To Ashtekar's Canonical Gravity

A Lorentz and general co-ordinate co-variant form of canonical gravity, using Ashtekar's variables, is investigated. A co-variant treatment due to Crnkovic and Witten is used, in which a point in phase space represents a solution of the equations of motion and a symplectic functional two form is constructed which is Lorentz and general co-ordinate invariant. The subtleties and difficulties due to the complex nature of Ashtekar's variables are addressed and resolved.Comment: 18 pages, Plain Te

A Dusty Disk Around GD 362, a White Dwarf With a Uniquely High Photospheric Metal Abundance

Eighteen years after an infrared excess was discovered associated with the white dwarf G29-38, we report ground-based measurements (JHKL'N') with mJy-level sensitivity of GD 362 that show it to be a second single white dwarf with an infrared excess. As a first approximation, the excess around GD 362, which amounts to about 3% of the total stellar luminosity, can be explained by emission from a passive, flat, opaque dust disk that lies within the Roche radius of the white dwarf. The dust may have been produced by the tidal disruption of a large parent body such as an asteroid. Accretion from this circumstellar disk could account for the remarkably high abundance of metals in the star's photosphere.Comment: 12 pages, 2 figures. ApJ Letters, in pres

Counting Giant Gravitons in AdS_3

We quantize the set of all quarter BPS brane probe solutions in global AdS_3 \times S^3 \times T^4/K3 found in arxiv:0709.1168 [hep-th]. We show that, generically, these solutions give rise to states in discrete representations of the SL(2,R) WZW model on AdS_3. Our procedure provides us with a detailed description of the low energy 1/4 and 1/2 BPS sectors of string theory on this background. The 1/4 BPS partition function jumps as we move off the point in moduli space where the bulk theta angle and NS-NS fields vanish. We show that generic 1/2 BPS states are protected because they correspond to geodesics rather than puffed up branes. By exactly quantizing the simplest of the probes above, we verify our description of 1/4 BPS states and find agreement with the known spectrum of 1/2 BPS states of the boundary theory. We also consider the contribution of these probes to the elliptic genus and discuss puzzles, and their possible resolutions, in reproducing the elliptic genus of the symmetric product.Comment: 47 pages; (v2) references and minor clarifications adde