Minimal generating sets of non-modular invariant rings of finite groups

It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case. Apart from very few explicit computations of Groebner bases, the algorithm only involves very basic operations, and is thus rather fast. As a test bed for comparative benchmarks, we use transitive permutation groups on 7 and 8 variables. In most examples, our algorithm implemented in Singular works much faster than the one used in Magma, namely by factors between 50 and 1000. We also compute some further examples on more than 8 variables, including a minimal generating set for the natural action of the cyclic group of order 11 in characteristic 0 and of order 15 in characteristic 2. We also apply our algorithm to the computation of irreducible secondary invariants.Comment: 14 pages v3: Timings updated. One example adde

The Crustacean Fauna (Branchiopoda, Copepoda) of Shallow Freshwater Bodies in Iceland

A survey of shallow freshwaters of Iceland was conducted in June and July 1996. The 34 stations prospected were rainpools, ditches, wetlands. The composition of their crustacean communities, investigated by qualitative net samples, is discussed in relation to water characteristics. One notostracan, Lepidurus arcticus (Pallas, 1793), 17 cladoceran species (5 Daphniidae, 10 Chydoridae, 1 Macrothricidae, 1 Polyphemidae), and 12 copepods (2 Diaptomidae, 7 Cyclopidae, 3 Canthocamptidae) were identified. Two species are reported for the first time from Iceland: the diaptomid Diaptomus (Chaetodiaptomus) rostripes Herbst, 1955 and the chydorid Alona rustica Scott, 1895. Taxonomical comments about different species are added, and their ecological pecularities are given. The species richness as well as the biogeographical features of the freshwater zooplankton of Iceland are discussed in relation to neighbouring Greenland and Northern Europe.Обследование мелких пресных водоемов Исландии проведено в июне-июле 1996 г. Материал собирался в дождевых и талых лужах, канавах, болотах. Среди 30 обнаруженных видов отмечены 1 вид щитней Lepidurus arcticus (Pallas, 1793), 17 видов ветвистоусых ракообразных (5 представителей сем. Daphnidae, 10 Chydoridae, 1 Macrothricidae, 1 Polyphemidae), 12 видов веслоногих ракобразных (2 вида сем. Diaptomidae, 7 Cyclopidae, 3 Canthocamptidae). Два вида указаны впервые для фауны Исландии: Diaptomus (Chaetodiatomus) rostripes Herbst, 1955 и Alona rustica Scott, 1895. Состав ракообразных в водоемах обсуждается в связи с экологической характеристикой последних. Для отдельных видов представлены краткие таксономические и экологические замечания. Обсуждаются видовое разнообразие и биогеографические особенности Исландии в связи с фаунистическими контактами с Гренландией и северной Европой

A new integrative assessment indicator for damage caused by major pests and diseases in the vineyard

An original and integrative evaluation indicator has been developed to quantify the cumulated damage from major pests and diseases affecting grape bunches: downy mildew, powdery mildew, gray mould and tortricid moths. It made it possible to estimate the associated crop losses and to relate them to the plant protection strategy in different modes of production (organic farming, in-transition, conventional). Thus, overall plant losses were higher in 2012 than in 2011. The in-transition growers’ strategy, with reduced copper doses but increased numbers of sprays, led to a 20% increase in average severity on bunches (essentially due to Downy mildew). The more pragmatic approach of experienced organic growers and conventional ones (higher doses and fewer sprays) reduced the yield losses. The proposed indicator is used for two purposes, i) evaluating the quantitative losses due to pest attacks and ii) differentiating them from other non-pest ones. A more detailed analysis including the impact on performance will be achieved and published soon

Turnover rate of cerebrospinal fluid in female sheep: changes related to different light-dark cycles

<p>Abstract</p> <p>Background</p> <p>Sheep are seasonal breeders. The key factor governing seasonal changes in the reproductive activity of the ewe is increased negative feedback of estradiol at the level of the hypothalamus under long-day conditions. It has previously been demonstrated that when gonadotropin secretions are inhibited during long days, there is a higher concentration of estradiol in the cerebrospinal fluid (CSF) than during short days. This suggests an involvement of the CSF and choroid plexus in the neuroendocrine regulatory loop, but the mechanisms underlying this phenomenon remain unknown. One possible explanation of this difference in hormonal content is an effect of concentration or dilution caused by variations in CSF secretion rate. The aim of this study was thus to investigate changes in the CSF turnover rate related to light-dark cycles.</p> <p>Methods</p> <p>The turnover rate of the CSF was estimated by measuring the time taken for the recovery of intraventricular pressure (IVP) after removal of a moderate volume (0.5 to 2 ml) of CSF (slope in mmHg/min). The turnover rate was estimated three times in the same group of sheep: during a natural period of decreasing day-length corresponding to the initial period when gonadotropin activity is stimulated (SG1), during a long-day inhibitory period (IG), and finally during a short-day stimulatory period (SG2).</p> <p>Results</p> <p>The time taken and the speed of recovery of initial IVP differed between groups: 8 min 30 sec, 0.63 ± 0.07 mmHg/min(SG1), 11 min 1 sec, 0.38 ± 0.06 mmHg/min (IG) and 9 min 0 sec, 0.72 ± 0.15 mmHg/min (SG2). Time changes of IVP differed between groups (ANOVA, p < 0.005, SG1 different from IG, <it>p </it>< 0.05). The turnover rate in SG2: 183.16 ± 23.82 μl/min was not significantly different from SG1: 169. 23 ± 51.58 μl/min (Mann-Whitney test, <it>p </it>= 0.41), but was significantly different from IG: 71.33 ± 16.59 μl/min (<it>p </it>= 0.016).</p> <p>Conclusion</p> <p>This study shows that the turnover rate of CSF in ewes changes according to the light-dark cycle; it is increased during short day periods and reduced in long day periods. This phenomenon could account for differences in hormonal concentrations in the CSF in this seasonal species.</p

On the uniqueness of promotion operators on tensor products of type A crystals

The affine Dynkin diagram of type $A_n^{(1)}$ has a cyclic symmetry. The analogue of this Dynkin diagram automorphism on the level of crystals is called a promotion operator. In this paper we show that the only irreducible type $A_n$ crystals which admit a promotion operator are the highest weight crystals indexed by rectangles. In addition we prove that on the tensor product of two type $A_n$ crystals labeled by rectangles, there is a single connected promotion operator. We conjecture this to be true for an arbitrary number of tensor factors. Our results are in agreement with Kashiwara's conjecture that all `good' affine crystals are tensor products of Kirillov-Reshetikhin crystals.Comment: 31 pages; 8 figure

OCT-GAN: single step shadow and noise removal from optical coherence tomography images of the human optic nerve head

Speckle noise and retinal shadows within OCT B-scans occlude important edges, fine textures and deep tissues, preventing accurate and robust diagnosis by algorithms and clinicians. We developed a single process that successfully removed both noise and retinal shadows from unseen single-frame B-scans within 10.4ms. Mean average gradient magnitude (AGM) for the proposed algorithm was 57.2% higher than current state-of-the-art, while mean peak signal to noise ratio (PSNR), contrast to noise ratio (CNR), and structural similarity index metric (SSIM) increased by 11.1%, 154% and 187% respectively compared to single-frame B-scans. Mean intralayer contrast (ILC) improvement for the retinal nerve fiber layer (RNFL), photoreceptor layer (PR) and retinal pigment epithelium (RPE) layers decreased from 0.362 ± 0.133 to 0.142 ± 0.102, 0.449 ± 0.116 to 0.0904 ± 0.0769, 0.381 ± 0.100 to 0.0590 ± 0.0451 respectively. The proposed algorithm reduces the necessity for long image acquisition times, minimizes expensive hardware requirements and reduces motion artifacts in OCT images