On the Complexity of Solving Zero-Dimensional Polynomial Systems via Projection

Given a zero-dimensional polynomial system consisting of n integer polynomials in n variables, we propose a certified and complete method to compute all complex solutions of the system as well as a corresponding separating linear form l with coefficients of small bit size. For computing l, we need to project the solutions into one dimension along O(n) distinct directions but no further algebraic manipulations. The solutions are then directly reconstructed from the considered projections. The first step is deterministic, whereas the second step uses randomization, thus being Las-Vegas. The theoretical analysis of our approach shows that the overall cost for the two problems considered above is dominated by the cost of carrying out the projections. We also give bounds on the bit complexity of our algorithms that are exclusively stated in terms of the number of variables, the total degree and the bitsize of the input polynomials

Application de certains indices diatomiques à un cours d'eau marocain : Oued Hassar

Les eaux de l'Oued Hassar (Maroc) sont caractérisées par une forte minéralisation. La conductivité, variant entre 3470 et 7210 µS.cm-1, est due essentiellement aux fortes teneurs en chlorures. L'examen de l'Indice de Pollution Organique (IPO) montre que l'effluent d'eaux usées provenant de la ville de Mediouna constitue la principale source de pollution des eaux de l'Oued Hassar.Concernant l'étude des diatomées épilithiques, 61 espèces et variétés de diatomées ont été inventoriées. Ces taxons sont liés particulièrement à la salinité (Pleurosira laevis, Fragilaria pulchella,…) et à la charge organique (Nitzschia palea, Gomphonema parvulum,…).Quatre indices diatomiques ont été testés pour l'évaluation de la qualité des eaux de l'Oued Hassar : l'Indice Diatomique Pratique (IDP), l'Indice Diatomique Générique (IDG), l'Indice de Sládecek (SLA) et l'Indice Diatomique Trophique (IDT). La variation spatio-temporelle de ces indices reflète bien la dégradation de la qualité de ce cours d'eau, particulièrement en aval du rejet de la ville de Mediouna (IDP=3,86 ± 1,84 ; IDG=6,05 ± 1,95 ; SLA=4,35 ± 1,93 ; IDT=5,80 ± 1,31). Parmi ces indices testés, seul l'IDP présente une corrélation significative (0,63 ; α<5%) avec l'IPO (indice de référence) tandis que l'IDG, le SLA et l'IDT montrent des corrélations non significatives avec cet indice (0,38 ; 0,27 et -0,11 respectivement).The water quality in Moroccan rivers and streams becomes more and more injured because of the important amount of pollutants discharged in these aquatic ecosystems without any treatment in the most cases. A physical, chemical and microbiological analyses are regularly done by public institutions (office national des eaux potables, direction de l'hydrolique). However, these analyses become insufficient facing the big diversity of chemicals and the intermittence of pollution sources at the time. So, methods using a biotic indicators as a complement of the chemical analyses become a requirement in the water quality assessment. In the present study, besides the physical and chemical analyses, we have tested the use of benthic diatoms as indicators of the oued Hassar water quality and diatom indices as a tool for the evaluation of this quality.Oued Hassar is a canalized stream situated on the valley of oued Mellah river. It drains a part of the Berrechid groundwater as sources. Its main source (station SC) is situated to 3 km in the Northeast of Mediouna (155 m). Along this water course, in sections of various degrees of water pollution, six sites (SC, SB, HP, OM, SH and CA) were sampled on four different dates (august 1997 and january, june and august 1998). The station OM belongs to oued Mouileh stream which is a unique tributary of oued Hassar. The main source of pollution; the wastewater effluent of Médiouna agglomeration entered the stream between The oued Hassar source and the station SB (Sidi Brahim). This region has a Mediterranean semi-aride bioclimate. The influence of the ocean results in a summer temperatures generally varying between 25 and 30°C and winter temperatures varying between 12 and 19°C.The physical and chemical analysis data of the oued Hassar waters show particularly elevated values of water conductivity essentially due to the high contents in chlorides. These values were understood between a minimal value recorded at station SH in August 1998 (3470 mS.cm-1) and a maximal value signalled at station OM in January of the same year (7210 mS.cm-1). Concentrations in sulphates vary according to stations. The most elevated values were recorded in january 1998 at stations SC and OM (231 and 218 mg.l-1 respectively). The hardness values are very important especially at the source of oued Hassar (SC) where the concentration reaches 25,2 meq.l-1. This excessive mineralization of waters, particularly at stations SC and OM, is essentially due to the Permo-triasique saliferous sedimentary layers which crop out in the area.The oued Hassar stream receives, to 100 ms downstream the station SC, the wastewater effluent of Médiouna agglomeration, highly loaded with organic matters, ammonia, orthophosphates and suspended matters. The impact of this effluent results on the elevated values of these parameters downstream the wastewater input (SB). On January 1998 (rainy period), the important contents in orthophosphates and sulphates recorded at all stations were essentially due to the high amounts of superphosphates and ammonia sulphates used as amendment of the cultivated lands situated a long the sides of oued Hassar stream.Outside of this period, contents in orthophosphates and ammonia at stations SC and OM are very low. However, the elevated content in nitrates at the oued Hassar's source (maximal value: 93,3 mg.l-1) gives an idea on the deterioration of the groundwater quality.To put in evidence the evolution of the global organic pollution of waters, the "Indice de Pollution Organique" (IPO) have been calculated. The exam of this index shows that the wastewater effluent constitutes the main source of pollution. Indeed, water quality goes from a mean pollution state (3,88 ± 0,14) at the oued Hassar's source to a very strong pollution state (1,96 ± 0,31) at the station SB. Downstream the swampy zone, at the station HP, the water quality of oued Hassar improves remarkably (3,50 ± 0,74) due to the auto-purification phenomenon and the dilution of these waters by those coming from the secondary sources situated between stations SB and HP. At the stations SH and CA, the IPO mean values (3,50 ± 0,79 and 3,75 ± 0,41 respectively) show that the water quality remains rather identical as at the station HP.Concerning the survey of epilithic diatoms, 61 species and varieties of diatoms have been inventoried. These taxa are bound especially to the salinity (Amphora coffeaeformis, Fragilaria fasciculata, Fragilaria pulchella, Pleurosira laevis,…) and to the organic load (Gomphonema parvulum, Navicula subminuscula, Nitzschia palea,…). In the most collected samples, particularly at the stations SB, SH and CA, diatom communities are essentially dominated by N. palea and the complex N. inconspicua / N. frustulum. At the station SB, the relative abundance of N. palea reaches 71% in august 1997 and august 1998, and goes beyond 45% in January and june 1998. giving evidence of the important organic pollution. this species is substituted, at stations SH and CA, essentially by Navicula subminuscula, N. veneta and Nitzschia inconspicua / N. frustulum complex. Diatom communities at the stations SC, HP and OM don't show an exclusive dominance of one or two species, but several species dominate and form a more varied communities.Four diatom indices have been tested to assess the water quality in Oued Hassar (Morocco) : the "Indice Diatomique Pratique" (IDP), the "Indice Diatomique Générique" (IDG), the Sládecek Index (SLA) and the Trophic Diatom Index (TDI). These indices are different by the assigned indicative values and pollution sensitivity coefficients relative to every species and by the taxonomic list integrated in the calculation of every index. The spatio-temporal variation of these indices reflects clearly the deterioration of water quality downstream the wastewater input of Mediouna agglomeration (IDP=3,86 ± 2,30; IDG=6,05 ± 2,31; SLA=4,35 ± 2,62; IDT=5,80 ± 1,85) and its recovery after the swampy zone at the station HP (IDP=9,37 ± 2,35; IDG=11,83 ± 1,77 ; SLA=7,19 ± 3,05 ; IDT=6,76 ± 2,48). Among these indices, only the IDP presents a significant correlation (0,63 ; α<5%) with the IPO (reference index). While the IDG, the SLA and the TDI don't show a significant correlation with this index (0,38 ; 0,27 and -0,11 respectively). The IDT shows nearly the same water quality in the different stations and rather inform on the high level of eutrophication in these water courses.The physical and chemical analyses, the composition of diatom communities as well as the relative results of diatom indices, show that the oued Hassar stream is submitted to an important pollution, particularly downstream the wastewater input. Among the tested indices, the IDP appears more adapted to the assessment of water quality in oued Hassar. However, more work is required in order to finalize a new diatom index which is more adapted to characteristics of the Moroccan water courses

Syringomatous carcinoma: Case report of a rare tumor entity

Syringomatous carcinoma is a rare cutaneous neoplasm, most frequently situated on the face and scalp and histologically characterised by aninfiltrative pattern of basaloid or squamous cells, a desmoplastic stromal reaction and keratin filled cysts. We report the case of a 76-year-oldwoman who presented an ulcerative interscapular lesion measuring 3x4cm. After resection, the histological examinations of the specimens haveidentified a basal cell carcinoma. However, a local recurrence was observed 18 months later; histopathological findings showed a syringomatouspattern and neoplastic epithelial cells arranged in interconnecting cords with microcystic areas. Nests, cords, and tubules of the tumour extendedinto the dermis and into the adjacent muscle. Sclerosis of stroma around the cords was present. Tumour cells were not connected to the epidermis. The immunohistochemical analysis showed positivity for anti-CK7, AE1/AE3 and negativity for anti CEA and anti CK20. These histological and immunohistochemical analyses were consistent with the diagnosis of syringomatous eccrine carcinoma. Syringomatous carcinoma is an extremely invasive tumor, locally destructive and slowly growing adnexal tumour, derived from eccrine sweat glands. It is often mistaken, both clinically and microscopically, for other benign and malignant entities. The tumour recurrence is high due to extensive perineural invasion, butregional or distant metastases are rare. The local aggressive nature of the tumour and the high recurrence rate may necessitate mutilating procedures. Optimal treatment consists of a complete microscopically controlled surgical excision with clear surgical margins. Key words: Syringomatous carcinoma, histopathology, immunohistochemistry, differential diagnosi

Switched reluctance motor design for electric vehicles based on harmonics and back EMF analysis

Permanent magnet synchronous motors are widely accepted in automotive applications. The high torque density, high rotational speed with maximum efficiency in electric vehicle applications is technically challenging for motor design. However, these machines are expensive and difficult to work at high-temperature harsh environment due to permanent magnets demagnetisation features. Alternatively, switched reluctance motors can provide similar output characteristics and a wider speed. Thus these are considered to be more fault tolerant and more reliable. This study proposes a 20 kW, three-phase switched reluctance motor and analyse its overall performance and harmonic contents. The study is conducted by optimising the slot filling factor, excitation voltage and switching sequence of an asymmetrical half bridge converter. A finite element model is used to predict the core and copper losses and other influencing parameters. Simulation results are presented and analysed the effectiveness of the proposed switched reluctance motor (SRM)

Lattice Boltzmann simulations of soft matter systems

This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview over the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures, 76 page

Hepatitis delta virus testing, epidemiology and management: A multicentre cross-sectional study of patients in London

Department of Health’s NIHR Biomedical Research Centres funding scheme

Current-induced microwave excitation of a domain wall confined in a magnetic wire with bi-axial anisotropy

We studied the current-induced magnetization dynamics of a domain wall confined in a magnetic wire with bi-axial anisotropy. We showed that above the threshold current density, breathing-mode excitation, where the thickness of the domain wall oscillates, is induced by spin-transfer torque. We found that the breathing-mode can be applied as a source of microwave oscillation because the resistance of the domain wall is a function of the domain wall thickness. In a current sweep simulation, the frequency of the breathing-mode exhibits hysteresis because of the confinement.Comment: 5 pages 4 figure

Detection and quantification of antibody to SARS CoV 2 receptor binding domain provides enhanced sensitivity, specificity and utility

Accurate and sensitive detection of antibody to SARS-CoV-2 remains an essential component of the pandemic response. Measuring antibody that predicts neutralising activity and the vaccine response is an absolute requirement for laboratory-based confirmatory and reference activity. The viral receptor binding domain (RBD) constitutes the prime target antigen for neutralising antibody. A double antigen binding assay (DABA), providing the most sensitive format has been exploited in a novel hybrid manner employing a solid-phase S1 preferentially presenting RBD, coupled with a labelled RBD conjugate, used in a two-step sequential assay for detection and measurement of antibody to RBD (anti-RBD). This class and species neutral assay showed a specificity of 100% on 825 pre COVID-19 samples and a potential sensitivity of 99.6% on 276 recovery samples, predicting quantitatively the presence of neutralising antibody determined by pseudo-type neutralisation and by plaque reduction. Anti-RBD is also measurable in ferrets immunised with ChadOx1 nCoV-19 vaccine and in humans immunised with both AstraZeneca and Pfizer vaccines. This assay detects anti-RBD at presentation with illness, demonstrates its elevation with disease severity, its sequel to asymptomatic infection and its persistence after the loss of antibody to the nucleoprotein (anti-NP). It also provides serological confirmation of prior infection and offers a secure measure for seroprevalence and studies of vaccine immunisation in human and animal populations. The hybrid DABA also displays the attributes necessary for the detection and quantification of anti-RBD to be used in clinical practice. An absence of detectable anti-RBD by this assay predicates the need for passive immune prophylaxis in at-risk patients

In vivo assembly of the axon initial segment in motor neurons

International audienceThe axon initial segment (AIS) is responsible for both the modulation of action potentials and the maintenance of neuronal polarity. Yet, the molecular mechanisms controlling its assembly are incompletely understood. Our study in single electroporated motor neurons in mouse embryos revealed that AnkyrinG (AnkG), the AIS master organizer, is undetectable in bipolar migrating motor neurons, but is already expressed at the beginning of axonogenesis at E9.5 and initially distributed homogeneously along the entire growing axon. Then, from E11.5, a stage when AnkG is already apposed to the membrane, as observed by electron microscopy, the protein progressively becomes restricted to the proximal axon. Analysis on the global motor neurons population indicated that Neurofascin follows an identical spatio-temporal distribution, whereas sodium channels and beta 4-spectrin only appear along AnkG(+) segments at E11.5. Early patch-clamp recordings of individual motor neurons indicated that at E12.5 these nascent AISs are already able to generate spikes. Using knock-out mice, we demonstrated that neither beta 4-spectrin nor Neurofascin control the distal-to-proximal restriction of AnkG

Genomic Diversity in Two Related Plant Species with and without Sex Chromosomes - Silene latifolia and S. vulgaris

Genome size evolution is a complex process influenced by polyploidization, satellite DNA accumulation, and expansion of retroelements. How this process could be affected by different reproductive strategies is still poorly understood.We analyzed differences in the number and distribution of major repetitive DNA elements in two closely related species, Silene latifolia and S. vulgaris. Both species are diploid and possess the same chromosome number (2n = 24), but differ in their genome size and mode of reproduction. The dioecious S. latifolia (1C = 2.70 pg DNA) possesses sex chromosomes and its genome is 2.5× larger than that of the gynodioecious S. vulgaris (1C = 1.13 pg DNA), which does not possess sex chromosomes. We discovered that the genome of S. latifolia is larger mainly due to the expansion of Ogre retrotransposons. Surprisingly, the centromeric STAR-C and TR1 tandem repeats were found to be more abundant in S. vulgaris, the species with the smaller genome. We further examined the distribution of major repetitive sequences in related species in the Caryophyllaceae family. The results of FISH (fluorescence in situ hybridization) on mitotic chromosomes with the Retand element indicate that large rearrangements occurred during the evolution of the Caryophyllaceae family.Our data demonstrate that the evolution of genome size in the genus Silene is accompanied by the expansion of different repetitive elements with specific patterns in the dioecious species possessing the sex chromosomes