851 research outputs found
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 be a variety of minimal degree and
of codimension at least 2, and consider where . By
\cite{B-Sche}, it turns out that the cohomological and local properties of
are governed by the secant locus of with
respect to .
Along these lines, the present paper is devoted to give a geometric
description of the secant stratification of , that is of the
decomposition of via the types of secant loci. We show
that there are exactly six possibilities for the secant locus , and we precisely describe each stratum of the secant stratification of
, 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 where is a variety of minimal degree, is a closed
point in and 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 >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
Coarsening of graded local cohomology
Some criteria for graded local cohomology to commute with coarsening functors
are proven, and an example is given where graded local cohomology does not
commute with coarsening.Comment: minor correction
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