The mixing time of the Dikin walk in a polytope-A simple proof
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The extension complexity xc(P) of a polytope P is the minimum number of facets of a polytope that affinely projects to P. Let G be a bipartite graph with n vertices, m edges, and no isolated vertices. Let STAB(G) be the convex hull of the stable sets of G. ...
We study mixing and diffusion properties of passive scalars driven by generic rough shear flows. Genericity is here understood in the sense of prevalence, and (ir)regularity is measured in the Besov-Nikolskii scale B\alpha 1,\infty, \alpha \in (0,1). We pr ...
We answer several questions posed by Beck, Cox, Delgado, Gubeladze, Haase, Hibi, Higashitani, and Maclagan in [Cox et al. 14, Question 3.5 (1),(2), Question 3.6], [Beck et al. 15, Conjecture 3.5(a),(b)], and [Hasse et al. 07, Open question 3 (a),(b) p. 231 ...
We present the design of a motion planning algorithm that ensures safety for an autonomous vehicle. In particular, we consider a multimodal distribution over uncertainties; for example, the uncertain predictions of future trajectories of surrounding vehicl ...
An integer program (IP) is a problem of the form min{f(x):Ax=b,l≤x≤u,x∈Zn}, where A∈Zm×n, b∈Zm, l,u∈Zn, and f:Zn→Z is a separable convex objective function.
The problem o ...
2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arisi ...
2-level polytopes naturally appear in several areas of mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. We investigate upper bounds on the product of the number of facets and the number ...
In the first part, we first introduce steganography (in chapter 1) not in the usual context of information security, but as a method to piggyback data on top of some content. We then focus on audio steganography and propose a new steganographic scheme in c ...
In this thesis we investigate a number of problems related to 2-level polytopes, in particular from the point of view of the combinatorial structure and the extension complexity. 2-level polytopes were introduced as a generalization of stable set polytopes ...
Deterministic protocols are well-known tools to obtain extended formulations, with many applications to polytopes arising in combinatorial optimization. Although constructive, those tools are not output-efficient, since the time needed to produce the exten ...
