Essential dimension of algebraic groups,including bad characteristic

Let A and G be finite groups of relatively prime orders and assume that A acts on G via automorphisms. We study how certain conditions on G imply its solvability when we assume the existence of a unique A-invariant Sylow p-subgroup for p equal to 2 or 3.     

Asymptotic distribution for the birthday problem with multiple coincidences,via an embedding of the collision process

We study the random variable B(c, n), which counts the number of balls that must be thrown into n equally‐sized bins in order to obtain c collisions. The asymptotic expected value of B(1, n) is the well‐known appearing in the solution to the birthday problem; the limit distribution and asymptotic moments of B(1, n) are also well known. We calculate the distribution and moments of B(c, n) asymptotically as n goes to ∞ and c = O(n). We have two main tools: an embedding of the collision process — realizing the process as a deterministic function of the standard Poisson process — and a central limit result by Rényi. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 480–502, 2016     

Unramified cohomology of classifying varieties for exceptional simply connected groups

Let be a classifying variety for an exceptional simple simply connected algebraic group . We compute the degree 3 unramified Galois cohomology of with values in over an arbitrary field . Combined with a paper by Merkurjev, this completes the computation of these cohomology groups for semisimple simply connected over all fields.

These computations provide another family of examples of simple simply connected groups such that is not stably rational.

     

Scaling tests of the cross section for deeply virtual Compton scattering

We present the first measurements of the e[over -->]p-->epgamma cross section in the deeply virtual Compton scattering (DVCS) regime and the valence quark region. The Q(2) dependence (from 1.5 to 2.3 GeV(2)) of the helicity-dependent cross section indicates the twist-2 dominance of DVCS, proving that generalized parton distributions (GPDs) are accessible to experiment at moderate Q(2). The helicity-independent cross section is also measured at Q(2)=2.3 GeV(2). We present the first model-independent measurement of linear combinations of GPDs and GPD integrals up to the twist-3 approximation.     

Supervised machine learning algorithms for protein structure classification

We explore automation of protein structural classification using supervised machine learning methods on a set of 11,360 pairs of protein domains (up to 35% sequence identity) consisting of three secondary structure elements. Fifteen algorithms from five categories of supervised algorithms are evaluated for their ability to learn for a pair of protein domains, the deepest common structural level within the SCOP hierarchy, given a one-dimensional representation of the domain structures. This representation encapsulates evolutionary information in terms of sequence identity and structural information characterising the secondary structure elements and lengths of the respective domains. The evaluation is performed in two steps, first selecting the best performing base learners and subsequently evaluating boosted and bagged meta learners. The boosted random forest, a collection of decision trees, is found to be the most accurate, with a cross-validated accuracy of 97.0% and F-measures of 0.97, 0.85, 0.93 and 0.98 for classification of proteins to the Class, Fold, Super-Family and Family levels in the SCOP hierarchy. The meta learning regime, especially boosting, improved performance by more accurately classifying the instances from less populated classes.     

Description of Some Ground States by Puiseux Techniques

Let \((\Sigma^{+}_{G}, \sigma)\) be a one-sided transitive subshift of finite type, where symbols are given by a finite spin set S, and admissible transitions are represented by an irreducible directed graph G?S×S. Let \(H : \Sigma^{+}_{G}\to\mathbb{R}\) be a locally constant function (that corresponds with a local observable which makes finite-range interactions). Given β>0, let μ _βH be the Gibbs-equilibrium probability measure associated with the observable ?βH. It is known, by using abstract considerations, that {μ _βH } _β>0 converges as β→+∞ to a H-minimizing probability measure \(\mu_{\min}^{H}\) called zero-temperature Gibbs measure. For weighted graphs with a small number of vertices, we describe here an algorithm (similar to the Puiseux algorithm) that gives the explicit form of \(\mu_{\min}^{H}\) on the set of ground-state configurations.