Second cohomology groups for algebraic groups and their Frobenius kernels

Let $G$ be a simple simply connected algebraic group scheme defined over an algebraically closed field of characteristic $p > 0$. Let $T$ be a maximal split torus in $G$, $B \supset T$ be a Borel subgroup of $G$ and $U$ its unipotent radical. Let $F: G \rightarrow G$ be the Frobenius morphism. For $r \geq 1$ define the Frobenius kernel, $G_r$, to be the kernel of $F$ iterated with itself $r$ times. Define $U_r$ (respectively $B_r$) to be the kernel of the Frobenius map restricted to $U$ (respectively $B$). Let $X(T)$ be the integral weight lattice and $X(T)_+$ be the dominant integral weights. The computations of particular importance are \h^2(U_1,k), \h^2(B_r,\la) for \la \in X(T), \h^2(G_r,H^0(\la)) for \la \in X(T)_+, and \h^2(B,\la) for \la \in X(T). The above cohomology groups for the case when the field has characteristic 2 one computed in this paper. These computations complete the picture started by Bendel, Nakano, and Pillen for $p \geq 3$ \cite{BNP2}.Comment: 49 pages, 4 appendices, 6 table

Packing ellipsoids with overlap

The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact spheres. Convergence results are proved and computational experience is described and illustrated. The motivating application - chromosome organization in the human cell nucleus - is discussed briefly, and some illustrative results are presented

A Collection of Recipes for Students of English as a Second Language

A collection of recipes for students of English as a second language at an intermediate level. Included are basic American recipes with simple, detailed directions. There is also a supplement of more complex recipes gathered from American and foreign students at the School for International Training. There is a glossary of terms needed for a knowledge of food preparation. A conversion table of measurements is included as well as a dictionary of food names in English, Spanish, French, Arabic and Japanese

Conceptual issues for screening in the genomic era – time for an update?

screening from clinical testing remains strangely elusive. Although numerous definitions of screening have been suggested, there is considerable variation amongst them, leading to confusion and disagreement amongst clinicians and public health professionals alike. In light of developments in genomics, we emphasise the need to differentiate between opportunistic screening and clinical testing because of the differing prior probability of disease and thus ethical burden of responsibility placed upon the physician in each scenario. Screening requires higher standards, first because screening tests are performed in asymptomatic individuals, and second because these tests are generally offered to individuals who otherwise believe themselves to be healthy. All the other characteristics commonly invoked to describe screening – including the systematic use of a rapid test for risk stratification within a particular population – can be better categorised as either practical requirements or by-products of screening programmes rather than screening tests. Physicians need to appreciate the shifting moral burden placed upon them relating to clinical testing versus screening, and the differing legal obligations that may ensue

Objective measurement of cough frequency during COPD exacerbation convalescence

Chronic obstructive pulmonary disease (COPD) is a major cause of morbidity and mortality worldwide. Cough and sputum production are associated with adverse outcomes in COPD and are common during COPD exacerbation (AE-COPD). This study of objective cough monitoring using the Hull Automated Cough Counter and Leicester Cough Monitor software confirms that this system has the ability to detect a significant decrease in cough frequency during AE-COPD convalescence. The ability to detect clinically meaningful change indicates a potential role in home monitoring of COPD patients

Distinguishing low frequency mutations from RT-PCR and sequence errors in viral deep sequencing data

There is a high prevalence of coronary artery disease (CAD) in patients with left bundle branch block (LBBB); however there are many other causes for this electrocardiographic abnormality. Non-invasive assessment of these patients remains difficult, and all commonly used modalities exhibit several drawbacks. This often leads to these patients undergoing invasive coronary angiography which may not have been necessary. In this review, we examine the uses and limitations of commonly performed non-invasive tests for diagnosis of CAD in patients with LBBB

Urban Vertebrate Pest Management: A Practical Approach

Urban vertebrate pest management is influenced by a variety of factors. Public perceptions of wildlife limit control specialists in their methods of operation. Population density, costs of operation and timing of control are considered. Suggestions are made for operational mode, methods, baits, traps and disposal. Two new trapping concepts are described and experimental data on attractants are given. Computer-summarized data on urban wild life conflicts from one state (Texas) show that most complaints can be handled by extension methods supplemented with direct control by the public and wild life damage control specialists

Urban Vertebrate Pest Management: A Practical Approach

Urban vertebrate pest management is influenced by a variety of factors. Public perceptions of wildlife limit control specialists in their methods of operation. Population density, costs of operation and timing of control are considered. Suggestions are made for operational mode, methods, baits, traps and disposal. Two new trapping concepts are described and experimental data on attractants are given. Computer-summarized data on urban wild life conflicts from one state (Texas) show that most complaints can be handled by extension methods supplemented with direct control by the public and wild life damage control specialists