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

Skúšanie opakovanej presnosti polohovania plazmovej rezacej hlavy

Článok stručne opisuje experimentov zameraných na overenie vybraných technologických parametrov plazmového rezacieho stroja. Konštrukčné riešenie tohto stroja predstavuje komplexnú kinematickú štruktúru s deviatimi stupňami voľnosti. Jedným z najdôležitejších parametrov, ktoré sa od stroja požadujú, je dosiahnutie predpísanej opakovanej presnosti polohovania. Úplný návrh experimentov si vyžaduje viac ako tisíc experimentov. preto sa pripravil redukovaný návrh experimentov, ktorý s vyžaduje vykonanie iba 32 experimentov. Predpokladáme pritom iba jedno opakovanie každého experimentu. Ak sa má sledovať aj rozptyl nameraných údajov, vyžaduje sa najmenej päť opakovaní každého experimentu, čo vedie k značnému nárastu ich počtu.Paper briefly describes design of experiments aimed at verification of selected technological parameters of the plasma cutting machine. Design solution of the plasma cutting machine represents a complex kinematic structure with 9 DOF. Reaching the prescribed repeated accuracy of the positioning is one of the main parameters that is required from the machine. Full experiment design covers more than thousands experiments. Therefore reduced experiment design was prepared tehat requires only 32 experiments. We consider only one execution of each experiment. When thae data variability should be observed, five repeating of each experiment is required, resulting in respective increase of the number of experiments

Linking educational leadership styles to the HR architecture for new teachers in primary education

This study aims to gain insight in the relationship between principals’ leadership styles and the configuration of different HR practices for new teachers in primary education. Besides the longstanding interest in educational leadership as a key element in teacher and student performance, there is a growing interest in strategic human resource management (SHRM) in the educational sector. However, few educational studies link educational leadership to SHRM. In particular, this study examines the relationship between principals’ instructional and transformational leadership style and principals’ strategic and HR orientation in configuring HR practices for new teachers. Data were gathered using a mixed methods approach, including interviews with 75 principals as well as an online survey of 1058 teachers in Flemish primary education. Qualitative interview data were transformed and analysed together with the quantitative survey data using logistic regression and ANOVA analyses. The results indicate that both instructional and transformational leadership is associated with the strategic orientation of principals. The HR orientation, on the other hand, is not reflected in the principals’ leadership style. Recommendations for further research in this area are discussed

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

Bias-Reduction in Variational Regularization

The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on an appropriate set, the so-called model manifold. The latter is defined by Bregman distances or infimal convolutions thereof, using the (uniquely defined) subgradient appearing in the optimality condition of the variational method. For particular settings, such as anisotropic $\ell^1$ and TV-type regularization, previously used debiasing techniques are shown to be special cases. The proposed approach is however easily applicable to a wider range of regularizations. The two-step debiasing is shown to be well-defined and to optimally reduce bias in a certain setting. In addition to visual and PSNR-based evaluations, different notions of bias and variance decompositions are investigated in numerical studies. The improvements offered by the proposed scheme are demonstrated and its performance is shown to be comparable to optimal results obtained with Bregman iterations.Comment: Accepted by JMI