The inefficiency of re-weighted sampling and the curse of system size in high order path integration

Computing averages over a target probability density by statistical re-weighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we present a very general analysis of the accuracy and efficiency of this approach, highlighting some of its weaknesses. We then give an example of how our results can be used, specifically to assess the feasibility of high-order path integral methods. We demonstrate that the most promising of these techniques -- which is based on re-weighted sampling -- is bound to fail as the size of the system is increased, because of the exponential growth of the statistical uncertainty in the re-weighted average

A New Generalized Harmonic Evolution System

A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially suppresses all small short-wavelength constraint violations. Physical and constraint-preserving boundary conditions are derived for this system, and numerical tests that demonstrate the effectiveness of the constraint suppression properties and the constraint-preserving boundary conditions are presented.Comment: Updated to agree with published versio

Specific recognition of a multiply phosphorylated motif in the DNA repair scaffold XRCC1 by the FHA domain of human PNK.

Short-patch repair of DNA single-strand breaks and gaps (SSB) is coordinated by XRCC1, a scaffold protein that recruits the DNA polymerase and DNA ligase required for filling and sealing the damaged strand. XRCC1 can also recruit end-processing enzymes, such as PNK (polynucleotide kinase 3'-phosphatase), Aprataxin and APLF (aprataxin/PNK-like factor), which ensure the availability of a free 3'-hydroxyl on one side of the gap, and a 5'-phosphate group on the other, for the polymerase and ligase reactions respectively. PNK binds to a phosphorylated segment of XRCC1 (between its two C-terminal BRCT domains) via its Forkhead-associated (FHA) domain. We show here, contrary to previous studies, that the FHA domain of PNK binds specifically, and with high affinity to a multiply phosphorylated motif in XRCC1 containing a pSer-pThr dipeptide, and forms a 2:1 PNK:XRCC1 complex. The high-resolution crystal structure of a PNK-FHA-XRCC1 phosphopeptide complex reveals the basis for this unusual bis-phosphopeptide recognition, which is probably a common feature of the known XRCC1-associating end-processing enzymes

Verifying continuous variable entanglement of intense light pulses

Three different methods have been discussed to verify continuous variable entanglement of intense light beams. We demonstrate all three methods using the same set--up to facilitate the comparison. The non--linearity used to generate entanglement is the Kerr--effect in optical fibres. Due to the brightness of the entangled pulses, standard homodyne detection is not an appropriate tool for the verification. However, we show that by using large asymmetric interferometers on each beam individually, two non-commuting variables can be accessed and the presence of entanglement verified via joint measurements on the two beams. Alternatively, we witness entanglement by combining the two beams on a beam splitter that yields certain linear combinations of quadrature amplitudes which suffice to prove the presence of entanglement.Comment: 11 pages, 7 figures, to appear in Phys. Rev.

A pelagic thresher shark (Alopias pelagicus) gives birth at a cleaning station in the Philippines

The final publication is available at Springer via http://dx.doi.org/10.1007/s00338-014-1249-8This article discusses photographic evidence captured on April 4, 2013, as the first record of a thresher shark giving birth

Quantum gravity and the Coulomb potential

We apply a singularity resolution technique utilized in loop quantum gravity to the polymer representation of quantum mechanics on R with the singular -1/|x| potential. On an equispaced lattice, the resulting eigenvalue problem is identical to a finite difference approximation of the Schrodinger equation. We find numerically that the antisymmetric sector has an energy spectrum that converges to the usual Coulomb spectrum as the lattice spacing is reduced. For the symmetric sector, in contrast, the effect of the lattice spacing is similar to that of a continuum self-adjointness boundary condition at x=0, and its effect on the ground state is significant even if the spacing is much below the Bohr radius. Boundary conditions at the singularity thus have a significant effect on the polymer quantization spectrum even after the singularity has been regularized.Comment: 10 pages, 5 figures. v2: Minor presentational changes. One data point added in Table

Solving Einstein's Equations With Dual Coordinate Frames

A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the way fields are projected onto an orthonormal tetrad basis. These field components are then determined as functions of a second independent coordinate system. The transformation to the second coordinate system can be thought of as a mapping from the original ``inertial'' coordinate system to the computational domain. This dual-coordinate method is used to perform stable numerical evolutions of a black-hole spacetime using the generalized harmonic form of Einstein's equations in coordinates that rotate with respect to the inertial frame at infinity; such evolutions are found to be generically unstable using a single rotating coordinate frame. The dual-coordinate method is also used here to evolve binary black-hole spacetimes for several orbits. The great flexibility of this method allows comoving coordinates to be adjusted with a feedback control system that keeps the excision boundaries of the holes within their respective apparent horizons.Comment: Updated to agree with published versio

The Polyakov Loop and its Relation to Static Quark Potentials and Free Energies

It appears well accepted in the literature that the correlator of Polyakov loops in a finite temperature system decays with the "average" free energy of the static quark-antiquark system, and can be decomposed into singlet and adjoint (or octet for QCD) contributions. By fixing a gauge respecting the transfer matrix, attempts have been made to extract those contributions separately. In this paper we point out that the "average" and "adjoint" channels of Polyakov loop correlators are misconceptions. We show analytically that all channels receive contributions from singlet states only, and give a corrected definition of the singlet free energy. We verify this finding by simulations of the 3d SU(2) pure gauge theory in the zero temperature limit, which allows to cleanly extract the ground state exponents and the non-trivial matrix elements. The latter account for the difference between the channels observed in previous simulations.Comment: 14 pages, 3 figures, 1 table; note and reference adde