On the Pierce-Birkhoff Conjecture

International audienceThis paper represents a step in our program towards the proof of the Pierce--Birkhoff conjecture. In the nineteen eighties J. Madden proved that the Pierce-Birkhoff conjecture for a ring A$is equivalent to a statement about an arbitrary pair of points$\alpha,\beta\in\sper\ A$and their separating ideal$$; we refer to this statement as the Local Pierce-Birkhoff conjecture at$\alpha,\beta$. In this paper, for each pair$(\alpha,\beta)$with$ht()=\dim A$, we define a natural number, called complexity of$(\alpha,\beta)$. Complexity 0 corresponds to the case when one of the points$\alpha,\beta$is monomial; this case was already settled in all dimensions in a preceding paper. Here we introduce a new conjecture, called the Strong Connectedness conjecture, and prove that the strong connectedness conjecture in dimension n-1 implies the connectedness conjecture in dimension n in the case when$ht()$is less than n-1. We prove the Strong Connectedness conjecture in dimension 2, which gives the Connectedness and the Pierce--Birkhoff conjectures in any dimension in the case when$ht()$less than 2. Finally, we prove the Connectedness (and hence also the Pierce--Birkhoff) conjecture in the case when dimension of A is equal to$ht()=3$, the pair$(\alpha,\beta)$is of complexity 1 and$A$ is excellent with residue field the field of real numbers

Molecular diversity and distribution of marine fungi across 130 European environmental samples.

Journal ArticleEnvironmental DNA and culture-based analyses have suggested that fungi are present in low diversity and in low abundance in many marine environments, especially in the upper water column. Here, we use a dual approach involving high-throughput diversity tag sequencing from both DNA and RNA templates and fluorescent cell counts to evaluate the diversity and relative abundance of fungi across marine samples taken from six European near-shore sites. We removed very rare fungal operational taxonomic units (OTUs) selecting only OTUs recovered from multiple samples for a detailed analysis. This approach identified a set of 71 fungal 'OTU clusters' that account for 66% of all the sequences assigned to the Fungi. Phylogenetic analyses demonstrated that this diversity includes a significant number of chytrid-like lineages that had not been previously described, indicating that the marine environment encompasses a number of zoosporic fungi that are new to taxonomic inventories. Using the sequence datasets, we identified cases where fungal OTUs were sampled across multiple geographical sites and between different sampling depths. This was especially clear in one relatively abundant and diverse phylogroup tentatively named Novel Chytrid-Like-Clade 1 (NCLC1). For comparison, a subset of the water column samples was also investigated using fluorescent microscopy to examine the abundance of eukaryotes with chitin cell walls. Comparisons of relative abundance of RNA-derived fungal tag sequences and chitin cell-wall counts demonstrate that fungi constitute a low fraction of the eukaryotic community in these water column samples. Taken together, these results demonstrate the phylogenetic position and environmental distribution of 71 lineages, improving our understanding of the diversity and abundance of fungi in marine environments.Gordon and Betty Moore FoundationDeutsche ForschungsgemeinschaftMarie Curie International Outgoing FellowshipMarie Curie Intra-European FellowshipEMBO Long-Term fellowshi

Current correlations of an on-demand electron source as an evidence of single particle emission

In analogy with quantum optics, short time correlations of the current fluctuations are used to characterize an on-demand electron source consisting of a quantum dot connected to a conductor via a tunable tunnel barrier. We observe a new fundamental noise for electrons associated with the quantum fluctuations of the electron emission time, which we call quantum jitter. In optimum operating conditions of the source, the noise reduces to the quantum jitter limit, which demonstrates single particle emission. Combined with the coherent manipulations of single electrons in a quantum conductor, this electron quantum optics experiment opens the way to explore new problems including quantum statistics and interactions at the single electron level

Ivermectin safety in infants and children under 15 kg treated for scabies: A multicentric Observational study

BACKGROUND: Scabies is a frequent condition in infants and children. Only topical treatments have been approved in infants but some of them are poorly tolerated. Oral ivermectin is approved for the treatment of scabies in several countries but its use in infants and children weighing < 15 kg is off-label. OBJECTIVES: To assess the safety of ivermectin in infants and young children and to collect data on ivermectin efficacy in these age groups. METHODS: This study was performed in the Dermatology and Paediatric Dermatology departments of 28 French centres between July 2012 and November 2015. Physicians treating an infant or child weighing < 15 kg for scabies with oral ivermectin were asked to send back a completed standardised and anonymous questionnaire. The data were subsequently analysed. RESULTS: Data were collected on 170 infants and children ranging in age from 1 to 64 months, with body weight of 4 to 14·5 kg, who were treated with oral ivermectin. The mean received dose was 223 μg/kg and 89% of the patients received a systematic second dose. Concomitant topical treatment was administered to 73% of patients. Adverse events were reported in seven patients (4%) and were not severe. At the follow-up visit, 139 (85%) patients had achieved healing. Factors significantly associated with healing were an ivermectin dose > 200 μg/kg (p=0·0005), and a delay between those two doses of < 10 days (p=0·0247). CONCLUSIONS: Our findings suggest the safety and efficacy of ivermectin for the treatment of scabies in infants and young children. This article is protected by copyright. All rights reserved

Motion-Aware Mosaicing for Confocal Laser Endomicroscopy

Probe-based Confocal Laser Endomicroscopy (pCLE) pro- vides physicians with real-time access to histological information during standard endoscopy procedures, through high-resolution cellular imaging of internal tissues. Earlier work on mosaicing has enhanced the potential of this imaging modality by meeting the need to get a complete representation of the imaged region. However, with approaches, the dynamic information, which may be of clinical interest, is lost. In this study, we propose a new mosaic construction algorithm for pCLE sequences based on a min-cut optimization and gradient-domain composition. Its main advantage is that the motion of some structures within the tissue such as blood cells in capillaries, is taken into account. This allows physicians to get both a sharper static representation and a dynamic representation of the imaged tissue. Results on 16 sequences acquired in vivo on six different organs demonstrate the clinical relevance of our approach

Antitumour necrosis factor-α therapy for hidradenitis suppurativa: results from a national cohort study between 2000 and 2013

International audienceHidradenitis suppurativa (HS) is a frequent chronic inflammatory skin disease typically characterized by recurrent painful, deep inflammatory nodules of the axillary, breast, groin and gluteal areas. European recommendations are mainly based on expert opinion. Drug treatments are heterogenous (e.g., antibiotics, corticosteroids, retinoids) and lack consensus among expert centres. The most severe disease forms or those failing to respond to conventional drugs may be associated with worsened functional prognosis. Anti-tumor necrosis factor α (anti-TNFα) drugs have been prescribed in these cases. The results of randomized controlled trials (RCTs) are discordant. Three RCTs concluded to the efficacy of adalimumab (ADA), and two others did not detect any difference between infliximab (IFX) or etanercept (ETA) and placebo. Finally, data from the literature and reported experiences do not conclude on the efficacy of anti-TNFα drugs for HS. This article is protected by copyright. All rights reserve