Rational Ehrhart quasi-polynomials

Ehrhart's famous theorem states that the number of integral points in a rational polytope is a quasi-polynomial in the integral dilation factor. We study the case of rational dilation factors and it turns out that the number of integral points can still be written as a rational quasi-polynomial. Furthermore the coefficients of this rational quasi-polynomial are piecewise polynomial functions and related to each other by derivation.Comment: 15 pages, several changes in the expositio

Cone-volume measures of polytopes

The cone-volume measure of a polytope with centroid at the origin is proved to satisfy the subspace concentration condition. As a consequence a conjectured (a dozen years ago) fundamental sharp affine isoperimetric inequality for the U-functional is completely established -- along with its equality conditions.Comment: Slightly revised version thanks to the suggestions of the referees and other readers; two figures adde

Integer Points in Knapsack Polytopes and s-covering Radius

Given an integer matrix A satisfying certain regularity assumptions, we consider for a positive integer s the set F_s(A) of all integer vectors b such that the associated knapsack polytope P(A,b)={x: Ax=b, x non-negative} contains at least s integer points. In this paper we investigate the structure of the set F_s(A) sing the concept of s-covering radius. In particular, in a special case we prove an optimal lower bound for the s-Frobenius number

Notes on lattice points of zonotopes and lattice-face polytopes

Minkowski's second theorem on successive minima gives an upper bound on the volume of a convex body in terms of its successive minima. We study the problem to generalize Minkowski's bound by replacing the volume by the lattice point enumerator of a convex body. In this context we are interested in bounds on the coefficients of Ehrhart polynomials of lattice polytopes via the successive minima. Our results for lattice zonotopes and lattice-face polytopes imply, in particular, that for 0-symmetric lattice-face polytopes and lattice parallelepipeds the volume can be replaced by the lattice point enumerator.Comment: 16 pages, incorporated referee remarks, corrected proof of Theorem 1.2, added new co-autho

Lattice points in vector-dilated polytopes

For $A\in\mathbb{Z}^{m\times n}$ we investigate the behaviour of the number of lattice points in $P_A(b)=\{x\in\mathbb{R}^n:Ax\leq b\}$, depending on the varying vector $b$. It is known that this number, restricted to a cone of constant combinatorial type of $P_A(b)$, is a quasi-polynomial function if b is an integral vector. We extend this result to rational vectors $b$ and show that the coefficients themselves are piecewise-defined polynomials. To this end, we use a theorem of McMullen on lattice points in Minkowski-sums of rational dilates of rational polytopes and take a closer look at the coefficients appearing there.Comment: 16 page

Development of the innovative credit-based degree program "Bachelor IT business management" and derivation of findings for the stabilization of organizational learning processes of universities

Digitalization in combination with the shortage of skilled workers is a significant challenge that has to be faced. Especially the IT sector is characterized by agile and complex developments. In this context, academic further training of IT specialists is crucial to meet the requirements of the IT labor market. The University of Applied Science Weserbergland in Hamelin (Germany) (Hochschule Weserbergland) developed different IT study programs within the research project “Open IT” against the background of the described developments. The study programs “Bachelor of Business Informatics” and “Master IT Business Management” are designed for IT specialists and IT experts with initial and advanced training. These study programs are the first of its kind for the IT sector in Germany due to the recognition of previous professional qualifications. The study programs and their development process are described in this paper. The Deutero concept in terms of organizational learning is the theoretical basis for this article. Single-loop learning and double-loop learning are applied to the research project

Targeting the MYC interaction network in B-cell lymphoma via histone deacetylase 6 inhibition

Overexpression of MYC is a genuine cancer driver in lymphomas and related to poor prognosis. However, therapeutic targeting of the transcription factor MYC remains challenging. Here, we show that inhibition of the histone deacetylase 6 (HDAC6) using the HDAC6 inhibitor Marbostat-100 (M-100) reduces oncogenic MYC levels and prevents lymphomagenesis in a mouse model of MYC-induced aggressive B-cell lymphoma. M-100 specifically alters protein-protein interactions by switching the acetylation state of HDAC6 substrates, such as tubulin. Tubulin facilitates nuclear import of MYC, and MYC-dependent B-cell lymphoma cells rely on continuous import of MYC due to its high turn-over. Acetylation of tubulin impairs this mechanism and enables proteasomal degradation of MYC. M-100 targets almost exclusively B-cell lymphoma cells with high levels of MYC whereas non-tumor cells are not affected. M-100 induces massive apoptosis in human and murine MYC-overexpressing B-cell lymphoma cells. We identified the heat-shock protein DNAJA3 as an interactor of tubulin in an acetylation-dependent manner and overexpression of DNAJA3 resulted in a pronounced degradation of MYC. We propose a mechanism by which DNAJA3 associates with hyperacetylated tubulin in the cytoplasm to control MYC turnover. Taken together, our data demonstrate a beneficial role of HDAC6 inhibition in MYC-dependent B-cell lymphoma

Complete genome sequence and lifestyle of black-pigmented Corynebacterium aurimucosum ATCC 700975 (formerly C. nigricans CN-1) isolated from a vaginal swab of a woman with spontaneous abortion

Trost E, Götker S, Schneider J, et al. Complete genome sequence and lifestyle of black-pigmented Corynebacterium aurimucosum ATCC 700975 (formerly C. nigricans CN-1) isolated from a vaginal swab of a woman with spontaneous abortion. BMC Genomics. 2010;11(1): 91.Background Corynebacterium aurimucosum is a slightly yellowish, non-lipophilic, facultative anaerobic member of the genus Corynebacterium and predominantly isolated from human clinical specimens. Unusual black-pigmented variants of C. aurimucosum (originally named as C. nigricans) continue to be recovered from the female urogenital tract and they are associated with complications during pregnancy. C. aurimucosum ATCC 700975 (C. nigricans CN-1) was originally isolated from a vaginal swab of a 34-year-old woman who experienced a spontaneous abortion during month six of pregnancy. For a better understanding of the physiology and lifestyle of this potential urogenital pathogen, the complete genome sequence of C. aurimucosum ATCC 700975 was determined. Results Sequencing and assembly of the C. aurimucosum ATCC 700975 genome yielded a circular chromosome of 2,790,189 bp in size and the 29,037-bp plasmid pET44827. Specific gene sets associated with the central metabolism of C. aurimucosum apparently provide enhanced metabolic flexibility and adaptability in aerobic, anaerobic and low-pH environments, including gene clusters for the uptake and degradation of aromatic amines, L-histidine and L-tartrate as well as a gene region for the formation of selenocysteine and its incorporation into formate dehydrogenase. Plasmid pET44827 codes for a non-ribosomal peptide synthetase that plays the pivotal role in the synthesis of the characteristic black pigment of C. aurimucosum ATCC 700975. Conclusions The data obtained by the genome project suggest that C. aurimucosum could be both a resident of the human gut and possibly a pathogen in the female genital tract causing complications during pregnancy. Since hitherto all black-pigmented C. aurimucosum strains have been recovered from female genital source, biosynthesis of the pigment is apparently required for colonization by protecting the bacterial cells against the high hydrogen peroxide concentration in the vaginal environment. The location of the corresponding genes on plasmid pET44827 explains why black-pigmented (formerly C. nigricans) and non-pigmented C. aurimucosum strains were isolated from clinical specimens

Exercise training and high-sensitivity cardiac troponin T in patients with heart failure with reduced ejection fraction

Plasma cell disorders (PCDs) are identified in the clinical lab by detecting the monoclonal immunoglobulin (M-protein) which they produce. Traditionally, serum protein electrophoresis methods have been utilized to detect and isotype Mproteins. Increasing demands to detect low-level disease and new therapeutic monoclonal immunoglobulin treatments have stretched the electrophoretic methods to their analytical limits. Newer techniques based on mass spectrometry (MS) are emerging which have improved clinical and analytical performance. MS is gaining traction into clinical laboratories, and has replaced immunofixation electrophoresis (IFE) in routine practice at one institution. The International Myeloma Working Group (IMWG) Mass Spectrometry Committee reviewed the literature in order to summarize current data and to make recommendations regarding the role of mass spectrometric methods in diagnosing and monitoring patients with myeloma and related disorders. Current literature demonstrates that immune-enrichment of immunoglobulins coupled to intact light chain MALDI-TOF MS has clinical characteristics equivalent in performance to IFE with added benefits of detecting additional risk factors for PCDs, differentiating Mprotein from therapeutic antibodies, and is a suitable replacement for IFE for diagnosing and monitoring multiple myeloma and related PCDs. In this paper we discuss the IMWG recommendations for the use of MS in PCDs.publishedVersio

Moderate continuous or high intensity interval exercise in heart failure with reduced ejection fraction : Differences between ischemic and non-ischemic etiology

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