A5040119486- Point processes and geometric inequalities
- Computational Geometry and Mesh Generation
- Advanced Combinatorial Mathematics
- Optimization and Packing Problems
- Mathematics and Applications
- graph theory and CDMA systems
- Commutative Algebra and Its Applications
- Complexity and Algorithms in Graphs
- Prion Diseases and Protein Misfolding
- Algebraic Geometry and Number Theory
- Optimization and Search Problems
- Digital Image Processing Techniques
- Polynomial and algebraic computation
- Diffusion and Search Dynamics
- X-ray Diffraction in Crystallography
- Crystallography and molecular interactions
- Graph theory and applications
- Crystallization and Solubility Studies
- Advanced Optimization Algorithms Research
- Advanced Graph Theory Research
- Geometric Analysis and Curvature Flows
- Mathematical Dynamics and Fractals
- Advanced Algebra and Geometry
- Pharmacological Effects of Medicinal Plants
- Limits and Structures in Graph Theory
Technische Universität Berlin
2016-2025
Cardiff University
2013-2023
Wales Institute of Social and Economic Research, Data and Methods
2021
Otto-von-Guericke University Magdeburg
1999-2014
University Hospital Magdeburg
1999-2010
Klinikum Magdeburg
2005
TU Wien
2000-2002
Freie Universität Berlin
2002
Zuse Institute Berlin
1997-1998
University of Siegen
1990-1995
We prove a tight subspace concentration inequality for the dual curvature measures of symmetric convex body.
Abstract We obtain new transference bounds that connect the additive integrality gap and sparsity of solutions for integer linear programs. Specifically, we consider programs $$\min \{{\varvec{c}}\cdot {\varvec{x}}: {\varvec{x}}\in P\cap \mathbb {Z}^n\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>min</mml:mo> <mml:mo>{</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> <mml:mo>·</mml:mo> <mml:mi>x</mml:mi> <mml:mo>:</mml:mo> <mml:mo>∈</mml:mo> <mml:mi>P</mml:mi>...
We investigate the Ehrhart polynomial for class of 0-symmetric convex lattice polytopes in Euclidean $n$-space $\mathbb{R}^n$. It turns out that roots and Minkowski's successive minima are closely related by their geometric arithmetic mean. also show $n$-polytopes with or without interior points differ essentially. Furthermore, we study structure planar case. Here it distribution reflects basic properties polygons.
is called an integral polyhedral cone generated by {z1, . , zk}. It pointed if the origin a vertex of C and it unimodular set generators zk} forms part basis lattice Z. By Gordan’s lemma semigroup ∩ Z finitely for any C, i.e., there exist many vectors h, h such that every z ∈ has representation form = ∑m i=1mih mi Z≥0. was out van der Corput [Cor31] exists uniquely determined minimal (w.r.t. inclusions) finite generating system H(C) ∩Zn which may be characterized as all irreducible contained...
We give an optimal upper bound for the $$\ell _{\infty }$$-distance from a vertex of knapsack polyhedron to its nearest feasible lattice point. In randomised setting, we show that can be significantly improved on average. As corollary, obtain additive integrality gap integer problems and "typical" problem is drastically smaller than occurs in worst case scenario. also prove that, generic case, programming admits natural lower bound.
The main purpose of this note is to prove an upper bound on the number lattice points a centrally symmetric convex body in terms successive minima body. This improves former bounds and narrows gap towards point analogue Minkowski's second theorem minima. proof his rather lengthy it was also criticised as obscure. We present short minima, which, however, based ideas proof.
The largest integer that cannot be represented as a nonnegative integral combination of given set positive integers is called the Frobenius number these integers. We show asymptotic growth on average significantly slower than maximum number.
The second theorem of Minkowski establishes a relation between the successive minima and volume 0-symmetric convex body. Here we show corresponding inequalities for arbitrary bodies, where are replaced by certain diameters widths. We further give some applications these results to radii, intrinsic volumes lattice point enumerator