An Avoidance Principle with an Application to the Asymptotic Behaviour of Graded Local Cohomology

We present an Avoidance Principle for certain graded rings. As an application we fill a gap in the proof of a result by Brodmann, Rohrer and Sazeedeh about the antipolynomiality of the Hilbert-Samuel multiplicity of the graded components of the local cohomology modules of a finitely generated module over a Noetherian homogeneous ring with two-dimensional local base ring.Comment: 6 pages; to appear in Journal of Pure and Applied Algebra; corrected typo

On varieties of almost minimal degree I: Secant loci of rational normal scrolls

To complete the classification theory and the structure theory of varieties of almost minimal degree, that is of non-degenerate irreducible projective varieties whose degree exceeds the codimension by precisely 2, a natural approach is to investigate simple projections of varieties of minimal degree. Let $\tilde X \subset {\mathbb P}^{r+1}_K$ be a variety of minimal degree and of codimension at least 2, and consider $X_p = \pi_p (\tilde X) \subset {\mathbb P}^r_K$ where $p \in {\mathbb P}^{r+1}_K \backslash \tilde X$. By \cite{B-Sche}, it turns out that the cohomological and local properties of $X_p$ are governed by the secant locus $\Sigma_p (\tilde X)$ of $\tilde X$ with respect to $p$. Along these lines, the present paper is devoted to give a geometric description of the secant stratification of $\tilde X$, that is of the decomposition of ${\mathbb P}^{r+1}_K$ via the types of secant loci. We show that there are exactly six possibilities for the secant locus $\Sigma_p (\tilde X)$, and we precisely describe each stratum of the secant stratification of $\tilde X$, each of which turns out to be a quasi-projective variety. As an application, we obtain the classification of all non-normal Del Pezzo varieties by providing a complete list of pairs $(\tilde X, p)$ where $\tilde X \subset {\mathbb P}^{r+1}_K$ is a variety of minimal degree, $p$ is a closed point in $\mathbb P^{r+1}_K \setminus \tilde X$ and $X_p \subset {\mathbb P}^r _K$ is a Del Pezzo variety.Comment: 20 page

On projective curves of maximal regularity

Let C ⊆ Pr K be a non-degenerate projective curve of degree d > r + 1 of maximal regularity so that C has an extremal secant line L. We show that C ∪ L is arithmetically Cohen Macaulay if d < 2r − 1 and we study the Betti numbers and the Hartshorne-Rao module of the curve C

Towards Mixed Gr{\"o}bner Basis Algorithms: the Multihomogeneous and Sparse Case

One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of unmixed polynomial systems, that is systems with polynomials having the same support, using the approach of Faug{\`e}re, Spaenlehauer, and Svartz [ISSAC'14]. We present two algorithms for sparse Gr{\"o}bner bases computations for mixed systems. The first one computes with mixed sparse systems and exploits the supports of the polynomials. Under regularity assumptions, it performs no reductions to zero. For mixed, square, and 0-dimensional multihomogeneous polynomial systems, we present a dedicated, and potentially more efficient, algorithm that exploits different algebraic properties that performs no reduction to zero. We give an explicit bound for the maximal degree appearing in the computations

Using DHS and MICS data to complement or replace NGO baseline health data: An exploratory study

Background: Non-government organizations (NGOs) spend substantial time and resources collecting baseline data in order to plan and implement health interventions with marginalized populations. Typically interviews with households, often mothers, take over an hour, placing a burden on the respondents. Meanwhile, estimates of numerous health and social indicators in many countries already exist in publicly available datasets, such as the Demographic and Health Surveys (DHS) and the Multiple Indicator Cluster Surveys (MICS), and it is worth considering whether these could serve as estimates of baseline conditions. The objective of this study was to compare indicator estimates from non-governmental organizations (NGO) health projects' baseline reports with estimates calculated using the Demographic and Health Surveys (DHS) or the Multiple Indicator Cluster Surveys (MICS), matching for location, year, and season of data collection. / Methods: We extracted estimates of 129 indicators from 46 NGO baseline reports, 25 DHS datasets and three MICS datasets, generating 1,996 pairs of matched DHS/MICS and NGO indicators. We subtracted NGO from DHS/MICS estimates to yield difference and absolute difference, exploring differences by indicator. We partitioned variance of the differences by geographical level, year, and season using ANOVA. / Results: Differences between NGO and DHS/MICS estimates were large for many indicators but 33% fell within 5% of one another. Differences were smaller for indicators with prevalence 85%. Difference between estimates increased with increasing year and geographical level differences. However, <1% of the variance of the differences was explained by year, geographical level, and season. / Conclusions: There are situations where publicly available data could complement NGO baseline survey data, most importantly when the NGO has tolerance for estimates of low or unknown accuracy

Monomial ideals whose depth function has any given number of strict local maxima

We construct monomial ideals with the property that their depth function has any given number of strict local maxima

Mobilizable Plasmids for Tunable Gene Expression in Francisella novicida.

Francisella tularensis is the causative agent of the life-threatening disease tularemia. However, the molecular tools to study Francisella are limited. Especially, expression plasmids are sparse and difficult to use, as they are unstable and prone to spontaneous loss. Most Francisella expression plasmids lack inducible promoters making it difficult to control gene expression levels. In addition, available expression plasmids are mainly designed for F. tularensis, however, genetic differences including restriction-modification systems impede the use of these plasmids in F. novicida, which is often used as a model organism to study Francisella pathogenesis. Here we report construction and characterization of two mobilizable plasmids (pFNMB1 and pFNMB2) designed for regulated gene expression in F. novicida. pFNMB plasmids contain a tetracycline inducible promoter to control gene expression levels and oriT for RP4 mediated mobilization. We show that both plasmids are stably maintained in bacteria for more than 40 generations over 4 days of culturing in the absence of selection against plasmid loss. Expression levels are dependent on anhydrotetracycline concentration and homogeneous in a bacterial population. pFNMB1 and pFNMB2 plasmids differ in the sequence between promoter and translation start site and thus allow to reach different maximum levels of protein expression. We used pFNMB1 and pFNMB2 for complementation of Francisella Pathogenicity Island mutants ΔiglF, ΔiglI, and ΔiglC in-vitro and pFNMB1 to complement ΔiglI mutant in bone marrow derived macrophages

Paclitaxel-Coated Balloon for the Treatment of Infrainguinal Disease: 12-Month Outcomes in the All-Comers Cohort of BIOLUX P-III Global Registry

Purpose: To further investigate the safety and performance of the Passeo-18 Lux drug-coated balloon (DCB) for the treatment of atherosclerotic infrainguinal disease under real-world conditions. Materials and Methods: BIOLUX P-III is an international, prospective, observational registry (ClinicalTrials.gov identifier NCT02276313) conducted at 41 centers in Europe, Asia, and Australia with follow-up visits at 6, 12, and 24 months. Of 700 patients (mean age 70.0\ub110.2 years; 439 men) with 863 lesions in the all-comers cohort, 330 (47.1%) patients had diabetes and 234 (37.7%) had chronic limb-threatening ischemia. The majority (79.3%) of lesions were in the femoropopliteal segment; of all lesions, 645 (74.9%) were calcified and 99 (11.5%) had in-stent restenosis (ISR). The mean lesion length was 84.7\ub173.3 mm. The primary clinical endpoint was major adverse events (MAEs) within 6 months, a composite of device- and procedure-related mortality through 30 days, major target limb amputation, and clinically-driven target lesion revascularization (TLR). The primary performance endpoint was clinically-driven TLR within 12 months. Results: At 6 and 12 months, freedom from MAEs was 94.0% and 89.5% in the all-comers cohort: 95.0% and 91.2% in the femoropopliteal group and 95.3% and 88.0% in the ISR subgroup, respectively. Freedom from clinically-driven TLR at 12 months was 93.1% in the all-comers cohort, 93.9% in the femoropopliteal lesions, and 89.4% for ISR lesions. All-cause mortality was 6.1% in the all-comers cohort: 5.9% in both the femoropopliteal and ISR subgroups. There were no device- or procedure-related deaths at up to 12 months. The Rutherford category improved in &gt;80% of all subgroups at 12 months. Conclusion: In a real-world patient population, the safety and performance of the Passeo-18 Lux DCB for the treatment of atherosclerotic infrainguinal lesions are maintained, with good performance outcomes and low complication rates at 12 months

“Less is more”: A dose-response account of intranasal oxytocin pharmacodynamics in the human brain

Intranasal oxytocin is attracting attention as a potential treatment for several brain disorders due to promising preclinical results. However, translating findings to humans has been hampered by remaining uncertainties about its pharmacodynamics and the methods used to probe its effects in the human brain. Using a dose-response design (9, 18 and 36 IU), we demonstrate that intranasal oxytocin-induced changes in local regional cerebral blood flow (rCBF) in the amygdala at rest, and in the covariance between rCBF in the amygdala and other key hubs of the brain oxytocin system, follow a dose-response curve with maximal effects for lower doses. Yet, the effects on local rCBF might vary by amygdala subdivision, highlighting the need to qualify dose-response curves within subregion. We further link physiological changes with the density of the oxytocin receptor gene mRNA across brain regions, strengthening our confidence in intranasal oxytocin as a valid approach to engage central targets. Finally, we demonstrate that intranasal oxytocin does not disrupt cerebrovascular reactivity, which corroborates the validity of haemodynamic neuroimaging to probe the effects of intranasal oxytocin in the human brain. Data availability: Participants did not consent for open sharing of the data. Therefore, data can only be accessed from the corresponding author upon reasonable reques