Symmetric bilinear forms and vertices in characteristic 2

Let $G$ be a finite group and let $k$ be an algebraically closed field of characteristic $2$ and let $M$ be an indecomposable $kG$-module which affords a non-degenerate $G$-invariant symmetric bilinear form. We introduce the symmetric vertices of $M$. Each of these is a $2$-subgroup of $G$ which contains a Green vertex of $M$ with index at most $2$. If $M$ is irreducible then its symmetric vertices are determined up to $G$-conjugacy. If $B$ is the real $2$-block of $G$ containing $M$, we show that each symmetric vertex of $M$ is contained in an extended defect group of $B$. Moreover, we characterise the extended defect groups in terms of symmetric vertices. In order to prove these results, we develop the theory of involutary $G$-algebras. This allows us to translate questions about symmetric $kG$-modules into questions about projective modules of quadratic type.Comment: Changes from v2: erroneous Lemma 2.3 (on lifting idempotents) corrected. Consequent minor changes made to the rest of the paper. Table of contents remove

Bioinspired auditory sound localisation for improving the signal to noise ratio of socially interactive robots

In this paper we describe a bioinspired hybrid architecture for acoustic sound source localisation and tracking to increase the signal to noise ratio (SNR) between speaker and background sources for a socially interactive robot's speech recogniser system. The model presented incorporates the use of Interaural Time Differ- ence for azimuth estimation and Recurrent Neural Net- works for trajectory prediction. The results are then pre- sented showing the difference in the SNR of a localised and non-localised speaker source, in addition to presenting the recognition rates between a localised and non-localised speaker source. From the results presented in this paper it can be seen that by orientating towards the sound source of interest the recognition rates of that source can be in- creased

Optimal stopping times for estimating Bernoulli parameters with applications to active imaging

We address the problem of estimating the parameter of a Bernoulli process. This arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. We introduce a framework within which to minimize the mean-squared error (MSE) subject to an upper bound on the mean number of trials. This optimization has several simple and intuitive properties when the Bernoulli parameter has a beta prior. In addition, by exploiting typical spatial correlation using total variation regularization, we extend the developed framework to a rectangular array of Bernoulli processes representing the pixels in a natural scene. In simulations inspired by realistic active imaging scenarios, we demonstrate a 4.26 dB reduction in MSE due to the adaptive acquisition, as an average over many independent experiments and invariant to a factor of 3.4 variation in trial budget.Accepted manuscrip

Nested sampling for Potts models

Nested sampling is a new Monte Carlo method by Skilling [1] intended for general Bayesian computation. Nested sampling provides a robust alternative to annealing-based methods for computing normalizing constants. It can also generate estimates of other quantities such as posterior expectations. The key technical requirement is an ability to draw samples uniformly from the prior subject to a constraint on the likelihood. We provide a demonstration with the Potts model, an undirected graphical model

The Formation and Evolution of Planetary Systems: Description of the Spitzer Legacy Science Database

We present the science database produced by the Formation and Evolution of Planetary Systems (FEPS) Spitzer Legacy program. Data reduction and validation procedures for the IRAC, MIPS, and IRS instruments are described in detail. We also derive stellar properties for the FEPS sample from available broad-band photometry and spectral types, and present an algorithm to normalize Kurucz synthetic spectra to optical and near-infrared photometry. The final FEPS data products include IRAC and MIPS photometry for each star in the FEPS sample and calibrated IRS spectra.Comment: 64 pages, 12 figures, 5 tables; accepted for publication in ApJ

Strength of Headed Shear Studs in Cold-formed Steel Deck

Results from 57 push-out tests of headed shear studs in cold-formed steel deck are presented. The results are compared to predicted strengths using the American Institute of Steel Construction Load and Resistance Factor Design Specification. The results indicate that the AISC specification does not accurately predict the strength of the shear studs placed in steel deck