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

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

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

Data and methods to calculate cut-off values for serum potassium and core temperature at hospital admission for extracorporeal rewarming of avalanche victims in cardiac arrest.

The data and estimation methods presented in this article are associated with the research article, "Cut-off values of serum potassium and core temperature at hospital admission for extracorporeal rewarming of avalanche victims in cardiac arrest: a retrospective multi-centre study" [1]. In this article we estimate recommended cut-off values for in-hospital triage with respect to extracorporeal rewarming. With only 6 survivors of 103 patients collected over a period of 20 years the ability to estimate reliable threshold values is limited. In addition, because the number of avalanche victims is also limited, a significantly larger dataset is unlikely to be obtained. We have therefore adapted two non-parametric estimation methods (bootstrapping and exact binomial distribution) to our specific needs and performed a simulations to confirm validity and reliability

Detection of triplex PCR for the modified qualitative soybean and maize genetically

A molecular screening method based on multiplex PCR that involves amplification of specific soybean or maize sequences from plant DNA (lectin or zein) and the amplification of 35S promoter and NOS terminator,for the detection of genetically modified soybean and maize was developed. The new method is proposed,for the simulicmeous cletcctimt of tree genetic elements in the.same run as reliable method for rapid detection of genetically, modified plants with sensitivity of 0.1%

Decomposition of semigroup algebras

Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case of a finite extension of positive affine semigroup rings we obtain an algorithm computing the decomposition. When R[A] is a polynomial ring over a field we explain how to compute many ring-theoretic properties of R[B] in terms of this decomposition. In particular we obtain a fast algorithm to compute the Castelnuovo-Mumford regularity of homogeneous semigroup rings. As an application we confirm the Eisenbud-Goto conjecture in a range of new cases. Our algorithms are implemented in the Macaulay2 package MonomialAlgebras.Comment: 12 pages, 2 figures, minor revisions. Package may be downloaded at http://www.math.uni-sb.de/ag/schreyer/jb/Macaulay2/MonomialAlgebras/html

Exceptional collections and D-branes probing toric singularities

We demonstrate that a strongly exceptional collection on a singular toric surface can be used to derive the gauge theory on a stack of D3-branes probing the Calabi-Yau singularity caused by the surface shrinking to zero size. A strongly exceptional collection, i.e., an ordered set of sheaves satisfying special mapping properties, gives a convenient basis of D-branes. We find such collections and analyze the gauge theories for weighted projective spaces, and many of the Y^{p,q} and L^{p,q,r} spaces. In particular, we prove the strong exceptionality for all p in the Y^{p,p-1} case, and similarly for the Y^{p,p-2r} case.Comment: 49 pages, 6 figures; v2 refs added; v3 published versio