Anomalous aging phenomena caused by drift velocities

We demonstrate via several examples that a uniform drift velocity gives rise to anomalous aging, characterized by a specific form for the two-time correlation functions, in a variety of statistical-mechanical systems far from equilibrium. Our first example concerns the oscillatory phase observed recently in a model of competitive learning. Further examples, where the proposed theory is exact, include the voter model and the Ohta-Jasnow-Kawasaki theory for domain growth in any dimension, and a theory for the smoothing of sandpile surfaces.Comment: 7 pages, 3 figures. To appear in Europhysics Letter

Models of competitive learning: complex dynamics, intermittent conversions and oscillatory coarsening

We present two models of competitive learning, which are respectively interfacial and cooperative learning. This learning is outcome-related, so that spatially and temporally local environments influence the conversion of a given site between one of two different types. We focus here on the behavior of the models at coexistence, which yields new critical behavior and the existence of a phase involving a novel type of coarsening which is oscillatory in nature.Comment: 23 pages, 11 figures. To appear in Phys. Rev.

A second-order class-D audio amplifier

Class-D audio amplifiers are particularly efficient, and this efficiency has led to their ubiquity in a wide range of modern electronic appliances. Their output takes the form of a high-frequency square wave whose duty cycle (ratio of on-time to off-time) is modulated at low frequency according to the audio signal. A mathematical model is developed here for a second-order class-D amplifier design (i.e., containing one second-order integrator) with negative feedback. We derive exact expressions for the dominant distortion terms, corresponding to a general audio input signal, and confirm these predictions with simulations. We also show how the observed phenomenon of “pulse skipping” arises from an instability of the analytical solution upon which the distortion calculations are based, and we provide predictions of the circumstances under which pulse skipping will take place, based on a stability analysis. These predictions are confirmed by simulations

Large-scale compression of genomic sequence databases with the Burrows-Wheeler transform

Motivation The Burrows-Wheeler transform (BWT) is the foundation of many algorithms for compression and indexing of text data, but the cost of computing the BWT of very large string collections has prevented these techniques from being widely applied to the large sets of sequences often encountered as the outcome of DNA sequencing experiments. In previous work, we presented a novel algorithm that allows the BWT of human genome scale data to be computed on very moderate hardware, thus enabling us to investigate the BWT as a tool for the compression of such datasets. Results We first used simulated reads to explore the relationship between the level of compression and the error rate, the length of the reads and the level of sampling of the underlying genome and compare choices of second-stage compression algorithm. We demonstrate that compression may be greatly improved by a particular reordering of the sequences in the collection and give a novel `implicit sorting' strategy that enables these benefits to be realised without the overhead of sorting the reads. With these techniques, a 45x coverage of real human genome sequence data compresses losslessly to under 0.5 bits per base, allowing the 135.3Gbp of sequence to fit into only 8.2Gbytes of space (trimming a small proportion of low-quality bases from the reads improves the compression still further). This is more than 4 times smaller than the size achieved by a standard BWT-based compressor (bzip2) on the untrimmed reads, but an important further advantage of our approach is that it facilitates the building of compressed full text indexes such as the FM-index on large-scale DNA sequence collections.Comment: Version here is as submitted to Bioinformatics and is same as the previously archived version. This submission registers the fact that the advanced access version is now available at http://bioinformatics.oxfordjournals.org/content/early/2012/05/02/bioinformatics.bts173.abstract . Bioinformatics should be considered as the original place of publication of this article, please cite accordingl

A Bayesian Analogue of Gleason's Theorem

We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these generalised probabilities as partially ordered notions of preference and we introduce a tentative generalised notion of Shannon entropy. A Bayesian approach to probability theory is adopted throughout, thus the axioms we use will be minimal criteria of rationality rather than ad hoc mathematical axioms.Comment: 14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published versio

On the Adjoint Operator in Photoacoustic Tomography

Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from coupled physics" technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.Comment: submitted to "Inverse Problems

Multiple Molecular H2 Outflows in AFGL 618

We report high spatial (0.5 arcsec) and high spectral (9 km/s) resolution spectro-imaging of the 2.12 micron H2 1-0 S(1) line in the proto-planetary nebula AFGL 618 using BEAR at the CFHT. The observations reveal the presence of multiple, high-velocity, molecular outflows that align with the remarkable optical jets seen in HST images. The structure and kinematics of the outflows show how jets interact with circumstellar gas and shape the environment in which planetary nebulae form.Comment: 14 pages, 5 figures. To appear in The Astrophysical Journal Letter

An approach to model interest for planetary rover through Dezert–Smarandache theory

In this paper, we propose an approach for assigning an interest level to the goals of a planetary rover. Assigning an interest level to goals allows the rover autonomously to transform and reallocate the goals. The interest level is defined by data-fusing payload and navigation information. The fusion yields an "interest map" that quantifies the level of interest of each area around the rover. In this way the planner can choose the most interesting scientific objectives to be analyzed, with limited human intervention, and reallocates its goals autonomously. The Dezert-Smarandache Theory of Plausible and Paradoxical Reasoning was used for information fusion: this theory allows dealing with vague and conflicting data. In particular, it allows us directly to model the behavior of the scientists that have to evaluate the relevance of a particular set of goals. The paper shows an application of the proposed approach to the generation of a reliable interest map

Getting the Measure of the Flatness Problem

The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of probability for such problems and stress the connection between probability and information which this approach makes explicit. This connection is important even when information is ``minimal'' or, in other words, when we need to argue from a state of maximum ignorance. We use the transformation group method of Jaynes to assign minimally--informative prior probability measure for cosmological parameters in the simple example of a dust Friedman model, showing that the usual statements of the cosmological flatness problem are based on an inappropriate choice of prior. We further demonstrate that, in the framework of a classical cosmological model, there is no flatness problem.Comment: 11 pages, submitted to Classical and Quantum Gravity, Tex source file, no figur