Efficient simple groups

We prove that the simple group L-3(5) which has order 372000 is efficient by providing an efficient presentation for it. This leaves one simple group with order less than one million, S-4(4) which has order 979200, whose efficiency or otherwise remains to be determined.

Symmetry breaking in the genetic code: Finite groups

We investigate the possibility of interpreting the degeneracy of the genetic code, i.e., the feature that different codons (base triplets) of DNA are transcribed into the same amino acid, as the result of a symmetry breaking process, in the context of finite groups. In the first part of this paper, we give the complete list of all codon representations (64-dimensional irreducible representations) of simple finite groups and their satellites (central extensions and extensions by outer automorphisms). In the second part, we analyze the branching rules for the codon representations found in the first part by computational methods, using a software package for computational group theory. The final result is a complete classification of the possible schemes, based on finite simple groups, that reproduce the multiplet structure of the genetic code. (C) 2010 Elsevier Ltd. All rights reserved.

Factorizations of some Groups of Lie Type of Lie Rank 4

Еленка Генчева, Цанко Генчев В настоящата работа се разглеждат крайни прости групи G , които могат да се представят като произведение на две свои собствени неабелеви прости подгрупи A и B. Всяко такова представяне G = AB е прието да се нарича факторизация на G, а тъй като множителите A и B са избрани да бъдат прости подгрупи на G, то разглежданите факторизации са известни още като прости факторизации на G. Тук се предполага, че G е проста група от лиев тип и лиев ранг 4 над крайно поле GF (q). Ключови думи: крайни прости групи, групи от лиев тип, факторизации на групи.

Prognostic value of the modified American College of Cardiology/American Heart Association lesion morphology classification for clinical outcome after sirolimus-eluting stent placement (results of the prospective multicenter German Cypher Registry)

The modified American College of Cardiology/American Heart Association (ACC/AHA) lesion morphology classification scheme has prognostic impact for early and late outcomes when bare-metal stents are used. Its value after drug-eluting stent placement is unknown. The predictive value of this lesion morphology classification system in patients treated using sirolimus-eluting stents included in the German Cypher Registry was prospectively examined. The study population included 6,755 patients treated for 7,960 lesions using sirolimus-eluting stents. Lesions were classified as type A, B1, B2, or C. Lesion type A or B1 was considered simple (35.1%), and type B2 or C, complex (64.9%). The combined end point of all deaths, myocardial infarction, or target vessel revascularization was seen in 2.6% versus 2.4% in the complex and simple groups, respectively (p = 0.62) at initial hospital discharge, with a trend for higher rates of myocardial infarction in the complex group. At the 6-month clinical follow-up and after adjusting for other independent factors, the composite of cumulative death, myocardial infarction, and target vessel revascularization was nonsignificantly different between groups (11.4% vs 11.2% in the complex and simple groups, respectively; odds ratio 1.08, 95% confidence interval 0.8 to 1.46). This was also true for target vessel revascularization alone (8.3% of the complex group, 9.0% of the simple group; odds ratio 0.87, 95% confidence interval 0.72 to 1.05). In conclusion, the modified ACC/AHA lesion morphology classification system has some value in determining early complications after sirolimus-eluting stent implantation. Clinical follow-up results at 6 months were generally favorable and cannot be adequately differentiated on the basis of this lesion morphology classification scheme.

Aurifeuillian factorization

The Cunningham project seeks to factor numbers of the form bn±1 with b = 2, 3, . . . small. One of the most useful techniques is Aurifeuillian Factorization whereby such a number is partially factored by replacing bn by a polynomial in such a way that polynomial factorization is possible. For example, by substituting y = 2k into the polynomial factorization (2y2)2+1 = (2y2−2y+1)(2y2+2y+1) we can partially factor 24k+2+1. In 1962 Schinzel gave a list of such identities that have proved useful in the Cunningham project; we believe that Schinzel identified all numbers that can be factored by such identities and we prove this if one accepts our definition of what “such an identity” is. We then develop our theme to similarly factor f(bn) for any given polynomial f, using deep results of Faltings from algebraic geometry and Fried from the classification of finite simple groups.

TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

Free groups in central simple algebras without Tits` theorem

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality \k\ (which need not be open).

Controllability of control systems on complex simple lie groups and the topology of flag manifolds

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

How bright is your child? A book of simple tests for age groups 2 to 14.

Mode of access: Internet.

Clustering Of Water Bodies In Unpolluted And Polluted Environments Based On Escherichia Coli Phylogroup Abundance Using A Simple Interaction Database.

Different types of water bodies, including lakes, streams, and coastal marine waters, are often susceptible to fecal contamination from a range of point and nonpoint sources, and have been evaluated using fecal indicator microorganisms. The most commonly used fecal indicator is Escherichia coli, but traditional cultivation methods do not allow discrimination of the source of pollution. The use of triplex PCR offers an approach that is fast and inexpensive, and here enabled the identification of phylogroups. The phylogenetic distribution of E. coli subgroups isolated from water samples revealed higher frequencies of subgroups A1 and B23 in rivers impacted by human pollution sources, while subgroups D1 and D2 were associated with pristine sites, and subgroup B1 with domesticated animal sources, suggesting their use as a first screening for pollution source identification. A simple classification is also proposed based on phylogenetic subgroup distribution using the w-clique metric, enabling differentiation of polluted and unpolluted sites.

Copper salt-catalyzed homo-coupling reaction of potassium alkynyltrifluoroborates: a simple and efficient synthesis of symmetrical 1,3-diynes

The copper-catalyzed dimerization of alkynyltrifluoroborates proceeds readily with good yields. The homo-coupling reaction can be effected in DMSO, in the open air, using Cu(OAc)(2) as catalyst in the absence of any other additives. A variety of functional groups are tolerated. (C) 2008 Elsevier Ltd. All rights reserved.

Do simple prudent health behaviours protect men from myocardial infarction?

Background We tested whether behaviours such as discarding obvious fat on meat, cessation of smoking, avoidance of passive smoking, habitual use of reduced fat milk, prudent consumption of alcohol and regular but moderate physical exercise are associated with a reduction of cardiovascular risk. Methods This was a population-based case-control study done in Perth, Western Australia. The cases (n = 336) were men aged 27-64 years with a first-ever acute myocardial infarction (AMI) during the period 1992-1993, and who survived at least 28 days. The controls (n = 735) were participants in a population-based survey of cardiovascular risk factors conducted during May-November 1994. Both groups completed the same questionnaire and the data were analysed with multiple logistic regression using backward elimination technique. Results Among men aged 27-64 years simple measures such as participation in non-vigorous exercise (odds ratio [OR] = 0.5, 95% CI : 0.4-0.7), and avoidance of added salt (OR = 0.6, 95% CI : 0.4-0.9) are associated with significant and Important protection from AMI. Conclusion After 25 years of falling mortality in Australia, lifestyles can still be significantly improved to reduce heart disease even further.

A simple, inexpensive and easily reproducible model of spinal cord injury in mice: Morphological and functional assessment

Spinal cord injury (SCI) causes motor and sensory deficits that impair functional performance, and significantly impacts life expectancy and quality. Animal models provide a good opportunity to test therapeutic strategies in vivo. C57BL/6 mice were subjected to laminectomy at T9 and compression with a vascular clip (30 g force, 1 min). Two groups were analyzed: injured group (SCI, n = 33) and laminectomy only (Sham, n = 15). Locomotor behavior (Basso mouse scale-BMS and global mobility) was assessed weekly. Morphological analyses were performed by LM and EM. The Sham group did not show any morphofunctional alteration. All SCI animals showed flaccid paralysis 24 h after injury. with subsequent improvement. The BMS score of the SCI group improved until the intermediate phase (2.037 +/- 1.198): the Sham animals maintained the highest BMS score (8.981 +/- 0.056). p < 0.001 during the entire time. The locomotor speed was slower in the SCI animals (5.581 +/- 0.871) than in the Sham animals (15.80 +/- 1.166), p < 0.001. Morphological analysis of the SCI group showed, in the acute phase, edema, hemorrhage, multiple cavities, fiber degeneration, cell death and demyelination. In the chronic phase we observed glial scarring, neuron death, and remyelination of spared axons by oligodendrocytes and Schwann cells. In conclusion, we established a simple, reliable, and inexpensive clip compression model in mice, with functional and morphological reproducibility and good validity. The availability of producing reliable injuries with appropriate outcome measures represents great potential for studies involving cellular mechanisms of primary injury and repair after traumatic SCI. (C) 2008 Elsevier B.V. All rights reserved.

Rating corporate groups a modelling experience

This paper aims to provide a model that allows BPI to measure the credit risk, through its rating scale, of the subsidiaries included in the corporate groups who are their clients. This model should be simple enough to be applied in practice, accurate, and must give consistent results in comparison to what have been the ratings given by the bank. The model proposed includes operational, strategic, and financial factors and ends up giving one of three results: no support, partial support, or full support from the holding to the subsidiary, and each of them translates in adjustments in each subsidiary’s credit rating. As it would be expectable, most of the subsidiaries should have the same credit rating of its parent company.