Unifying Optimization Algorithms to Aid Software System Users: optimx for R

R users can often solve optimization tasks easily using the tools in the optim function in the stats package provided by default on R installations. However, there are many other optimization and nonlinear modelling tools in R or in easily installed add-on packages. These present users with a bewildering array of choices. optimx is a wrapper to consolidate many of these choices for the optimization of functions that are mostly smooth with parameters at most bounds-constrained. We attempt to provide some diagnostic information about the function, its scaling and parameter bounds, and the solution characteristics. optimx runs a battery of methods on a given problem, thus facilitating comparative studies of optimization algorithms for the problem at hand. optimx can also be a useful pedagogical tool for demonstrating the strengths and pitfalls of different classes of optimization approaches including Newton, gradient, and derivative-free methods

Approximate Well-supported Nash Equilibria below Two-thirds

In an epsilon-Nash equilibrium, a player can gain at most epsilon by changing his behaviour. Recent work has addressed the question of how best to compute epsilon-Nash equilibria, and for what values of epsilon a polynomial-time algorithm exists. An epsilon-well-supported Nash equilibrium (epsilon-WSNE) has the additional requirement that any strategy that is used with non-zero probability by a player must have payoff at most epsilon less than the best response. A recent algorithm of Kontogiannis and Spirakis shows how to compute a 2/3-WSNE in polynomial time, for bimatrix games. Here we introduce a new technique that leads to an improvement to the worst-case approximation guarantee

Thermal emission from large area chemical vapor deposited graphene devices

Copyright © 2013 AIP PublishingThe spatial variation of thermal emission from large area graphene grown by chemical vapor deposition, transferred onto SiO2/Si substrates and fabricated into field effect transistor structures, has been investigated using infra-red microscopy. A peak in thermal emission occurs, the position of which can be altered by reversal of the current direction. The experimental results are compared with a one dimensional finite element model, which accounts for Joule heating and electrostatic effects, and it is found that the thermal emission is governed by the charge distribution in the graphene and maximum Joule heating occurs at the point of minimum charge density.This research was supported by the Engineering and Physical Sciences Research Council, and the European Union under the FET-open grant GOSFELEngineering and Physical Sciences Research Council (EPSRC)European Unio

A new approach for the analysis of bacterial microarray-based Comparative Genomic Hybridization: insights from an empirical study

BACKGROUND: Microarray-based Comparative Genomic Hybridization (M-CGH) has been used to characterize the extensive intraspecies genetic diversity found in bacteria at the whole-genome level. Although conventional microarray analytical procedures have proved adequate in handling M-CGH data, data interpretation using these methods is based on a continuous character model in which gene divergence and gene absence form a spectrum of decreasing gene conservation levels. However, whereas gene divergence may yet be accompanied by retention in gene function, gene absence invariably leads to loss of function. This distinction, if ignored, leads to a loss in the information to be gained from M-CGH data. We present here results from experiments in which two genome-sequenced strains of C. jejuni were compared against each other using M-CGH. Because the gene content of both strains was known a priori, we were able to closely examine the effects of sequence divergence and gene absence on M-CGH data in order to define analytical parameters for M-CGH data interpretation. This would facilitate the examination of the relative effects of sequence divergence or gene absence in comparative genomics analyses of multiple strains of any species for which genome sequence data and a DNA microarray are available. RESULTS: As a first step towards improving the analysis of M-CGH data, we estimated the degree of experimental error in a series of experiments in which identical samples were compared against each other by M-CGH. This variance estimate was used to validate a Log Ratio-based methodology for identification of outliers in M-CGH data. We compared two genome strains by M-CGH to examine the effect of probe/target identity on the Log Ratios of signal intensities using prior knowledge of gene divergence and gene absence to establish Log Ratio thresholds for the identification of absent and conserved genes. CONCLUSION: The results from this empirical study validate the Log Ratio thresholds that have been used in other studies to establish gene divergence/absence. Moreover, the analytical framework presented here enhances the information content derived from M-CGH data by shifting the focus from divergent/absent gene detection to accurate detection of conserved and absent genes. This approach closely aligns the technical limitations of M-CGH analysis with practical limitations on the biological interpretation of comparative genomics data

Comparative genomic assessment of Multi-Locus Sequence Typing: rapid accumulation of genomic heterogeneity among clonal isolates of Campylobacter jejuni

<p>Abstract</p> <p>Background</p> <p>Multi-Locus Sequence Typing (MLST) has emerged as a leading molecular typing method owing to its high ability to discriminate among bacterial isolates, the relative ease with which data acquisition and analysis can be standardized, and the high portability of the resulting sequence data. While MLST has been successfully applied to the study of the population structure for a number of different bacterial species, it has also provided compelling evidence for high rates of recombination in some species. We have analyzed a set of <it>Campylobacter jejuni </it>strains using MLST and Comparative Genomic Hybridization (CGH) on a full-genome microarray in order to determine whether recombination and high levels of genomic mosaicism adversely affect the inference of strain relationships based on the analysis of a restricted number of genetic loci.</p> <p>Results</p> <p>Our results indicate that, in general, there is significant concordance between strain relationships established by MLST and those based on shared gene content as established by CGH. While MLST has significant predictive power with respect to overall genome similarity of isolates, we also found evidence for significant differences in genomic content among strains that would otherwise appear to be highly related based on their MLST profiles.</p> <p>Conclusion</p> <p>The extensive genomic mosaicism between closely related strains has important implications in the context of establishing strain to strain relationships because it suggests that the exact gene content of strains, and by extension their phenotype, is less likely to be "predicted" based on a small number of typing loci. This in turn suggests that a greater emphasis should be placed on analyzing genes of clinical interest as we forge ahead with the next generation of molecular typing methods.</p

2+1 Dimensional QED and a Novel Phase Transition

We investigate the chiral phase transition in 2+1 dimensional QED. Previous gap equation and lattice Monte-Carlo studies of symmetry breaking have found that symmetry breaking ceases to occur when the number of fermion flavors exceeds a critical value. Here we focus on the order of the transition. We find that there are no light scalar degrees of freedom present as the critical number of flavors is approached from above (in the symmetric phase). Thus the phase transition is not second order, rendering irrelevant the renormalization group arguments for a fluctuation induced transition. However, the order parameter vanishes continuously in the broken phase, so this transition is also unlike a conventional first order phase transition.Comment: 11 pages, Late

Aram Dorsum: an extensive mid-Noachian age fluvial depositional system in Arabia Terra, Mars

A major debate in Mars science is the nature of the early Mars climate, and the availability of precipitation and runoff. Observations of relict erosional valley networks have been proposed as evidence for extensive surface run‐off around the Noachian‐Hesperian boundary. However, these valley networks only provide a time‐integrated record of landscape evolution and thus the timing, relative timescales and intensity of aqueous activity required to erode the valleys remain unknown. Here, we investigate an ancient fluvial sedimentary system in western Arabia Terra, now preserved in positive relief. This ridge, ‘Aram Dorsum’, is flat‐topped, branching, ~ 85 km long, and particularly well‐preserved. We show that Aram Dorsum was an aggradational alluvial system and that the existing ridge was once a large river channel‐belt set in extensive flood plains, many of which are still preserved. Smaller, palaeochannel‐belts feed the main system; their setting and network pattern suggest a distributed source of water. The alluvial succession is up to 60 m thick, suggesting a formation time of 105 to 107 years by analogy to Earth. Our observations are consistent with Aram Dorsum having formed by long‐lived flows of water, sourced both locally, and regionally as part of a wider alluvial system in Arabia Terra. This suggests frequent or seasonal precipitation as the source of water. Correlating our observations with previous regional‐scale mapping shows that Aram Dorsum formed in the mid‐Noachian, making it one of the oldest fluvial systems described on Mars and indicating climatic conditions that sustained surface river flows on early Mars

Shape selection in non-Euclidean plates

We investigate isometric immersions of disks with constant negative curvature into $\mathbb{R}^3$, and the minimizers for the bending energy, i.e. the $L^2$ norm of the principal curvatures over the class of $W^{2,2}$ isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls in $\mathbb{H}^2$ into $\mathbb{R}^3$. In elucidating the connection between these immersions and the non-existence/singularity results of Hilbert and Amsler, we obtain a lower bound for the $L^\infty$ norm of the principal curvatures for such smooth isometric immersions. We also construct piecewise smooth isometric immersions that have a periodic profile, are globally $W^{2,2}$, and have a lower bending energy than their smooth counterparts. The number of periods in these configurations is set by the condition that the principal curvatures of the surface remain finite and grows approximately exponentially with the radius of the disc. We discuss the implications of our results on recent experiments on the mechanics of non-Euclidean plates