Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation

We propose a new formulation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statististical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each velocity direction occupied by many particles. We show that the most probable state of this model corresponds to the usual equilibrium distribution of the lattice Boltzmann equation. Thermal fluctuations about this equilibrium are controlled by the mean number of particles at a lattice site. Stochastic collision rules are described by a Monte Carlo process satisfying detailed balance. This allows for a straightforward derivation of discrete Langevin equations for the fluctuating modes. It is shown that all non-conserved modes should be thermalized, as first pointed out by Adhikari et al.; any other choice violates the condition of detailed balance. A Chapman-Enskog analysis is used to derive the equations of fluctuating hydrodynamics on large length and time scales; the level of fluctuations is shown to be thermodynamically consistent with the equation of state of an isothermal, ideal gas. We believe this formalism will be useful in developing new algorithms for thermal and multiphase flows.Comment: Submitted to Physical Review E-11 pages Corrected Author(s) field on submittal for

A symplectic integration method for elastic filaments

A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin

A comparison of the static and dynamic properties of a semi-flexible polymer using lattice-Boltzmann and Brownian dynamics simulations

The aim of this paper is to compare results from lattice-Boltzmann and Brownian dynamics simulations of linear chain molecules. We have systematically varied the parameters that may affect the accuracy of the lattice-Boltzmann simulations, including grid resolution, temperature, polymer mass, and fluid viscosity. The effects of the periodic boundary conditions are minimized by an analytic correction for the different long-range interactions in periodic and unbounded systems. Lattice-Boltzmann results for the diffusion coefficient and Rouse mode relaxation times were found to be insensitive to temperature, which suggests that effects of hydrodynamic retardation are small. By increasing the resolution of the lattice-Boltzmann grid with respect to the polymer size, convergent results for the diffusion coefficient and relaxation times were obtained; these results agree with Brownian dynamics to within 1--2%.Comment: Corrected LB reduced time step ($\Delta t/t_0$) in Fig. 1 and Table

Experimental realisation of Shor's quantum factoring algorithm using qubit recycling

Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer. However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations. Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol. Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N=21. The algorithmic output is distinguishable from noise, in contrast to previous demonstrations. These results point to larger-scale implementations of Shor's algorithm by harnessing scalable resource reductions applicable to all physical architectures.Comment: 7 pages, 3 figure

Enhancement and suppression effects resulting from information structuring in sentences

Information structuring through the use of cleft sentences increases the processing efficiency of references to elements within the scope of focus. Furthermore, there is evidence that putting certain types of emphasis on individual words not only enhances their subsequent processing, but also protects these words from becoming suppressed in the wake of subsequent information, suggesting mechanisms of enhancement and suppression. In Experiment 1, we showed that clefted constructions facilitate the integration of subsequent sentences that make reference to elements within the scope of focus, and that they decrease the efficiency with reference to elements outside of the scope of focus. In Experiment 2, using an auditory text-change-detection paradigm, we showed that focus has similar effects on the strength of memory representations. These results add to the evidence for enhancement and suppression as mechanisms of sentence processing and clarify that the effects occur within sentences having a marked focus structure

AMI-LA radio continuum observations of Spitzer c2d small clouds and cores: Serpens region

We present deep radio continuum observations of the cores identified as deeply embedded young stellar objects in the Serpens molecular cloud by the Spitzer c2d programme at a wavelength of 1.8cm with the Arcminute Microkelvin Imager Large Array (AMI-LA). These observations have a resolution of ~30arcsec and an average sensitivity of 19microJy/beam. The targets are predominantly Class I sources, and we find the detection rate for Class I objects in this sample to be low (18%) compared to that of Class 0 objects (67%), consistent with previous works. For detected objects we examine correlations of radio luminosity with bolometric luminosity and envelope mass and find that these data support correlations found by previous samples, but do not show any indiction of the evolutionary divide hinted at by similar data from the Perseus molecular cloud when comparing radio luminosity with envelope mass. We conclude that envelope mass provides a better indicator for radio luminosity than bolometric luminosity, based on the distribution of deviations from the two correlations. Combining these new data with archival 3.6cm flux densities we also examine the spectral indices of these objects and find an average spectral index of 0.53+/-1.14, consistent with the canonical value for a partially optically thick spherical or collimated stellar wind. However, we caution that possible inter-epoch variability limits the usefulness of this value, and such variability is supported by our identification of a possible flare in the radio history of Serpens SMM 1.Comment: accepted MNRA

A correlation with exon expression approach to identify cis-regulatory elements for tissue-specific alternative splicing

Correlation of motif occurrences with gene expression intensity is an effective strategy for elucidating transcriptional cis-regulatory logic. Here we demonstrate that this approach can also identify cis-regulatory elements for alternative pre-mRNA splicing. Using data from a human exon microarray, we identified 56 cassette exons that exhibited higher transcript-normalized expression in muscle than in other normal adult tissues. Intron sequences flanking these exons were then analyzed to identify candidate regulatory motifs for muscle-specific alternative splicing. Correlation of motif parameters with gene-normalized exon expression levels was examined using linear regression and linear splines on RNA words and degenerate weight matrices, respectively. Our unbiased analysis uncovered multiple candidate regulatory motifs for muscle-specific splicing, many of which are phylogenetically conserved among vertebrate genomes. The most prominent downstream motifs were binding sites for Fox1- and CELF-related splicing factors, and a branchpoint-like element acuaac; pyrimidine-rich elements resembling PTB-binding sites were most significant in upstream introns. Intriguingly, our systematic study indicates a paucity of novel muscle-specific elements that are dominant in short proximal intronic regions. We propose that Fox and CELF proteins play major roles in enforcing the muscle-specific alternative splicing program, facilitating expression of unique isoforms of cytoskeletal proteins critical to muscle cell function

Genomic Relationships, Novel Loci, and Pleiotropic Mechanisms across Eight Psychiatric Disorders

Genetic influences on psychiatric disorders transcend diagnostic boundaries, suggesting substantial pleiotropy of contributing loci. However, the nature and mechanisms of these pleiotropic effects remain unclear. We performed analyses of 232,964 cases and 494,162 controls from genome-wide studies of anorexia nervosa, attention-deficit/hyper-activity disorder, autism spectrum disorder, bipolar disorder, major depression, obsessive-compulsive disorder, schizophrenia, and Tourette syndrome. Genetic correlation analyses revealed a meaningful structure within the eight disorders, identifying three groups of inter-related disorders. Meta-analysis across these eight disorders detected 109 loci associated with at least two psychiatric disorders, including 23 loci with pleiotropic effects on four or more disorders and 11 loci with antagonistic effects on multiple disorders. The pleiotropic loci are located within genes that show heightened expression in the brain throughout the lifespan, beginning prenatally in the second trimester, and play prominent roles in neurodevelopmental processes. These findings have important implications for psychiatric nosology, drug development, and risk prediction.Peer reviewe