Practical parallel coset enumeration

Coset enumeration is a most important procedure for investigating finitely presented groups. We present a practical parallel procedure for coset enumeration on shared memory processors. The shared memory architecture is particularly interesting because such parallel computation is both faster and cheaper. The lower cost comes when the program requires large amounts of memory, and additional CPU's. allow us to lower the time that the expensive memory is being used. Rather than report on a suite of test cases, we take a single, typical case, and analyze the performance factors in-depth. The parallelization is achieved through a master-slave architecture. This results in an interesting phenomenon, whereby the CPU time is divided into a sequential and a parallel portion, and the parallel part demonstrates a speedup that is linear in the number of processors. We describe an early version for which only 40% of the program was parallelized, and we describe how this was modified to achieve 90% parallelization while using 15 slave processors and a master. In the latter case, a sequential time of 158 seconds was reduced to 29 seconds using 15 slaves.

Some challenging group presentations

We study some challenging presentations which arise as groups of deficiency zero. In four cases we settle finiteness: we show that two presentations are for finite groups while two are fur infinite groups. Thus we answer three explicit questions in the literature and we provide the first published deficiency zero presentation for a group with derived length seven. The tools we use are coset enumeration and Knuth-Bendix rewriting, which are well-established as methods for proving finiteness or otherwise of a finitely presented group. We briefly comment on their capabilities and compare their performance.

On the efficiency of some finite groups

We describe a new technique for finding efficient presentations for finite groups. We use it to answer three previously unresolved questions about the efficiency of group and semigroup presentations.

On the asymptotic enumeration of accessible automata

We simplify the known formula for the asymptotic estimate of the number of deterministic and accessible automata with n states over a k-letter alphabet. The proof relies on the theory of Lagrange inversion applied in the context of generalized binomial series.

Evaluation of culture media for enumeration of Lactobacillus acidophilus, Lactobacillus casei and Bifidobacterium animalis in the presence of Lactobacillus delbrueckii subsp bulgaricus and Streptococcus thermophilus

The study compared the growth capability of probiotic (Lactobacillus acidophilus La05, Lactobacillus casei Lc01 and Bifidobacterium animalis Bb12) and non-probiotic (Lactobacillus delbrueckii subsp bulgaricus and Streptococcus thermophilus) cultures on twenty-one culture media grouped according to selectivity: nonselective agars, selective agars without antibiotics and MRS agars containing different combinations of lithium chloride, cystein, bile salts and antibiotics. Four of these media were selected for quantitative enumeration of L acidophilus La05, L casei Lc01, and B. animalis Bb12. The best culture media and incubation conditions for enumeration of the probiotic cultures were: B. animalis: MRS agar with dicloxacillin, 37 degrees C or 42 degrees C, anaerobiosis; L acidophilus: MRS agar with bile salts, 37 degrees C or 42 degrees C, aerobiosis; L casei: MRS agar with lithium chloride and sodium propionate, 37 degrees C or 42 degrees C, aerobiosis or anaerobiosis. Plating on MRS with glucose replaced by maltose, 37 degrees C or 42 degrees C, anaerobiosis, will distinguish probiotic from non-probiotic cultures. For enumeration of each probiotic in a mixed culture, the following media and incubation conditions were recommended: B. animalis: 4ABC-MRS, 42 degrees C, anaerobiosis, L acidophilus: LC medium, 42 degrees C, aerobiosis or anaerobiosis and L casei: LP-MRS, 42 degrees C, aerobiosis or anaerobiosis. In all experiments, differences in counts using pour plating or surface plating were not significant (P <= 0.05). (C) 2008 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved.

Performance of Petrifilm Aerobic Count plates on enumeration of lactic acid bacteria in fermented milks

This study aimed to compare Petrifilm Aerobic Count (AC) plates and the conventional pour plate methodology using the de Man-Rogosa-Sharpe (MRS) agar for the enumeration of lactic acid bacteria (LAB) in fermented milks (FMs), with different starter cultures added. FM samples (n = 66) were collected and plated on both methodologies, with incubation under anaerobic conditions at 35C for 48 h. The count results were compared by analysis of variance (P <= 0.05) and regression analysis. No differences between the mean counts obtained by both methodologies were observed, even when distinct FMs were compared. Considering all samples, a high correlation level was obtained between Petrifilm AC and MRS agar (r = 0.92), but these indexes were lower in FMs with Streptococcus thermophilus and Lactobacillus delbrueckii subsp. bulgaricus (r = 0.90) and Lactobacillus fortis (r = 0.81). Despite some slight interferences, Petrifilm AC has proven to be a convenient methodology on enumerating LAB in FM.

Parallel improved Schnorr-Euchner enumeration SE++ for the CVP and SVP

The Closest Vector Problem (CVP) and the Shortest Vector Problem (SVP) are prime problems in lattice-based cryptanalysis, since they underpin the security of many lattice-based cryptosystems. Despite the importance of these problems, there are only a few CVP-solvers publicly available, and their scalability was never studied. This paper presents a scalable implementation of an enumeration-based CVP-solver for multi-cores, which can be easily adapted to solve the SVP. In particular, it achieves super-linear speedups in some instances on up to 8 cores and almost linear speedups on 16 cores when solving the CVP on a 50-dimensional lattice. Our results show that enumeration-based CVP-solvers can be parallelized as effectively as enumeration-based solvers for the SVP, based on a comparison with a state of the art SVP-solver. In addition, we show that we can optimize the SVP variant of our solver in such a way that it becomes 35%-60% faster than the fastest enumeration-based SVP-solver to date.

Plantae Wilsonianae :an enumeration of the woody plants collected in western China for the Arnold arboretum of Harvard university during the years 1907, 1908, and 1910 /by E. H. Wilson, ed. by Charles Sprague Sargent.

1916 v.2

Plantae Wilsonianae :an enumeration of the woody plants collected in western China for the Arnold arboretum of Harvard university during the years 1907, 1908, and 1910 /by E. H. Wilson, ed. by Charles Sprague Sargent.

1917 v.3

Plantae Wilsonianae :an enumeration of the woody plants collected in western China for the Arnold arboretum of Harvard university during the years 1907, 1908, and 1910 /by E. H. Wilson, ed. by Charles Sprague Sargent.

1913 v.1