Specific heat anomaly in a supercooled liquid with amorphous boundary conditions

We study the specific heat of a model supercooled liquid confined in a spherical cavity with amorphous boundary conditions. We find the equilibrium specific heat has a cavity-size-dependent peak as a function of temperature. The cavity allows us to perform a finite-size scaling (FSS) analysis, which indicates that the peak persists at a finite temperature in the thermodynamic limit. We attempt to collapse the data onto a FSS curve according to different theoretical scenarios, obtaining reasonable results in two cases: a "not-so-simple" liquid with nonstandard values of the exponents {\alpha} and {\nu}, and random first-order theory, with two different length scales.Comment: Includes Supplemental Materia

The gauge structure of generalised diffeomorphisms

We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show that the gauge algebra is infinitely reducible, i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised diffeomorphisms gives such a reducibility transformation. We give a concrete description of the ghost structure, and demonstrate that the infinite sums give the correct (regularised) number of degrees of freedom. The ghost towers belong to the sequences of rep- resentations previously observed appearing in tensor hierarchies and Borcherds algebras. All calculations rely on the section condition, which we reformulate as a linear condition on the cotangent directions. The analysis holds for n < 8. At n = 8, where the dual gravity field becomes relevant, the natural guess for the gauge parameter and its reducibility still yields the correct counting of gauge parameters.Comment: 24 pp., plain tex, 1 figure. v2: minor changes, including a few added ref

Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method.

Recent advances in selected configuration interaction methods have made them competitive with the most accurate techniques available and, hence, creating an increasingly powerful tool for solving quantum Hamiltonians. In this work, we build on recent advances from the adaptive sampling configuration interaction (ASCI) algorithm. We show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The ASCI search algorithm can be used in several different modes, which includes an integral driven search and a coefficient driven search. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques, we present ASCI results applied to a large range of systems and basis sets to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-ζ benchmark data for the G1 data set. The largest of these calculations is Si2H6 which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets

Statistical modelling of transcript profiles of differentially regulated genes

Background: The vast quantities of gene expression profiling data produced in microarray studies, and the more precise quantitative PCR, are often not statistically analysed to their full potential. Previous studies have summarised gene expression profiles using simple descriptive statistics, basic analysis of variance (ANOVA) and the clustering of genes based on simple models fitted to their expression profiles over time. We report the novel application of statistical non-linear regression modelling techniques to describe the shapes of expression profiles for the fungus Agaricus bisporus, quantified by PCR, and for E. coli and Rattus norvegicus, using microarray technology. The use of parametric non-linear regression models provides a more precise description of expression profiles, reducing the "noise" of the raw data to produce a clear "signal" given by the fitted curve, and describing each profile with a small number of biologically interpretable parameters. This approach then allows the direct comparison and clustering of the shapes of response patterns between genes and potentially enables a greater exploration and interpretation of the biological processes driving gene expression. Results: Quantitative reverse transcriptase PCR-derived time-course data of genes were modelled. "Splitline" or "broken-stick" regression identified the initial time of gene up-regulation, enabling the classification of genes into those with primary and secondary responses. Five-day profiles were modelled using the biologically-oriented, critical exponential curve, y(t) = A + (B + Ct)Rt + ε. This non-linear regression approach allowed the expression patterns for different genes to be compared in terms of curve shape, time of maximal transcript level and the decline and asymptotic response levels. Three distinct regulatory patterns were identified for the five genes studied. Applying the regression modelling approach to microarray-derived time course data allowed 11% of the Escherichia coli features to be fitted by an exponential function, and 25% of the Rattus norvegicus features could be described by the critical exponential model, all with statistical significance of p < 0.05. Conclusion: The statistical non-linear regression approaches presented in this study provide detailed biologically oriented descriptions of individual gene expression profiles, using biologically variable data to generate a set of defining parameters. These approaches have application to the modelling and greater interpretation of profiles obtained across a wide range of platforms, such as microarrays. Through careful choice of appropriate model forms, such statistical regression approaches allow an improved comparison of gene expression profiles, and may provide an approach for the greater understanding of common regulatory mechanisms between genes

Theoretical uncertainty in baryon oscillations

We discuss the systematic uncertainties in the recovery of dark energy properties from the use of baryon acoustic oscillations as a standard ruler. We demonstrate that while unknown relativistic components in the universe prior to recombination would alter the sound speed, the inferences for dark energy from low-redshift surveys are unchanged so long as the microwave background anisotropies can measure the redshift of matter-radiation equality, which they can do to sufficient accuracy. The mismeasurement of the radiation and matter densities themselves (as opposed to their ratio) would manifest as an incorrect prediction for the Hubble constant at low redshift. In addition, these anomalies do produce subtle but detectable features in the microwave anisotropies.Comment: 4 pages, REVTeX, 1 figure. Submitted to PR

Ionized Gas Motions and the Structure of Feedback Near a Forming Globular Cluster in NGC 5253

We observed Brackett $\alpha$ 4.05$\mu$m emission towards the supernebula in NGC 5253 with NIRSPEC on Keck II in adaptive optics mode, NIRSPAO, to probe feedback from its exciting embedded super star cluster (SSC). NIRSPEC's Slit-Viewing Camera was simultaneously used to image the K-band continuum at $\sim$$0.1''$ resolution. We register the IR continuum with HST imaging, and find that the visible clusters are offset from the K-band peak, which coincides with the Br $\alpha$ peak of the supernebula and its associated molecular cloud. The spectra of the supernebula exhibit Br $\alpha$ emission with a strong, narrow core. The linewidths are 65-76 km s$^{-1}$, FWHM, comparable to those around individual ultra-compact HII regions within our Galaxy. A weak, broad (FWHM$\simeq$150-175 km s$^{-1}$) component is detected on the base of the line, which could trace a population of sources with high-velocity winds. The core velocity of Br $\alpha$ emission shifts by +13 km s$^{-1}$ from NE to SW across the supernebula, possibly indicating a bipolar outflow from an embedded object, or linked to a foreground redshifted gas filament. The results can be explained if the supernebula comprises thousands of ionized wind regions around individual massive stars, stalled in their expansion due to critical radiative cooling and unable to merge to drive a coherent cluster wind. Based on the absence of an outflow with large mass loss, we conclude that feedback is currently ineffective at dispersing gas, and the SSC retains enriched material out of which it may continue to form stars.Comment: 24 pages, 9 figure

Predicting the outcomes of treatment to eradicate the latent reservoir for HIV-1

Massive research efforts are now underway to develop a cure for HIV infection, allowing patients to discontinue lifelong combination antiretroviral therapy (ART). New latency-reversing agents (LRAs) may be able to purge the persistent reservoir of latent virus in resting memory CD4+ T cells, but the degree of reservoir reduction needed for cure remains unknown. Here we use a stochastic model of infection dynamics to estimate the efficacy of LRA needed to prevent viral rebound after ART interruption. We incorporate clinical data to estimate population-level parameter distributions and outcomes. Our findings suggest that approximately 2,000-fold reductions are required to permit a majority of patients to interrupt ART for one year without rebound and that rebound may occur suddenly after multiple years. Greater than 10,000-fold reductions may be required to prevent rebound altogether. Our results predict large variation in rebound times following LRA therapy, which will complicate clinical management. This model provides benchmarks for moving LRAs from the lab to the clinic and can aid in the design and interpretation of clinical trials. These results also apply to other interventions to reduce the latent reservoir and can explain the observed return of viremia after months of apparent cure in recent bone marrow transplant recipients and an immediately-treated neonate.Comment: 8 pages main text (4 figures). In PNAS Early Edition http://www.pnas.org/content/early/2014/08/05/1406663111. Ancillary files: SI, 24 pages SI (7 figures). File .htm opens a browser-based application to calculate rebound times (see SI). Or, the .cdf file can be run with Mathematica. The most up-to-date version of the code is available at http://www.danielrosenbloom.com/reboundtimes