Sebastian Heinz

Sebastian Heinz
Zalando SE · Zalando Research

PhD

About

13
Publications
1,226
Reads
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181
Citations
Additional affiliations
October 2014 - June 2016
Zalando SE
Position
  • Analyst
April 2008 - September 2014
Weierstrass Institute for Applied Analysis and Stochastics
Position
  • PostDoc Position
April 2005 - March 2008
Humboldt-Universität zu Berlin
Position
  • PhD Student

Publications

Publications (13)
Article
Full-text available
Online fashion sales present a challenging use case for personalized recommendation: Stores offer a huge variety of items in multiple sizes. Small stocks, high return rates, seasonality, and changing trends cause continuous turnover of articles for sale on all time scales. Customers tend to shop rarely, but often buy multiple items at once. We repo...
Article
Full-text available
We design an algorithm for computations of quasiconvex hulls of isotropic compact sets in in the space of 2×2 real matrices. Our approach uses a recent result by the first author [17] on quasiconvex hulls of isotropic compact sets in the space of 2×2 real matrices. We show that our algorithm has the time complexity of O(N logN) where N is the numbe...
Conference Paper
Full-text available
We present a method to determine Fashion DNA, coordinate vectors locating fashion items in an abstract space. Our approach is based on a deep neural network architecture that ingests curated article information such as tags and images, and is trained to predict sales for a large set of frequent customers. In the process, a dual space of customer st...
Article
We revisit the model for a two-well phase transformation in a linearly elastic body that was introduced and studied in Mielke et al. (2002 Arch. Ration. Mech. Anal. 162, 137-177). This energetic rate-independent system is posed in terms of the elastic displacement and an internal variable that gives the phase portion of the second phase. We use a n...
Technical Report
Full-text available
We design an algorithm for computations of quasiconvex hulls of isotropic compact sets in in the space of 2 × 2 real matrices. Our approach uses a recent result by the first author [Adv.] on quasiconvex hulls of isotropic compact sets in the space of 2 × 2 real matrices. We show that our algorithm has the time complexity of O(N log N) where N is th...
Article
Let K1 and K2 be compact sets of real 2×2 matrices with positive determinant. Suppose that both sets are frame invariant, meaning invariant under the left action of the special orthogonal group. Then we give an algebraic characterization for K1 and K2 to be incompatible for homogeneous gradient Young measures. This result can be used to determine t...
Article
Let K be a given compact set of real 2×2 matrices that is isotropic, meaning invariant under the left and right action of the special orthogonal group. Then we show that the quasiconvex hull of K coincides with the lamination convex hull of order 2. In particular, there is no difference between quasiconvexity, rank-one convexity and lamination conv...
Article
We study the time evolution in elastoplasticity within the rate-independent framework of generalized standard materials. Our particular interest is the formation and the evolution of microstructure. Providing models where existence proofs are possible is a challenging task since the presence of microstructure comes along with a lack of convexity an...
Article
We study a polycrystalline material that undergoes a rigid-plastic rate-independent evolution. Of our particular interest is the creation of texture and the resulting qualitative change in the macroscopic material response: from isotropic to anisotropic. Texture is represented by a crystal orientation distribution function, which associates every s...
Article
We study the time evolution of a generalized standard material in elastoplasticity. Of our particular interest are the formation and the evolution of microstructure. Our aim is to prove the existence of solutions. This is a challenging task, since the presence of microstructure comes along with a lack of convexity and, hence, compactness arguments...
Article
Let $W$ be a function from the real m$\times$n-matrices to the real numbers. If $W$ is quasiconvex in the sense of the calculus of variations, then we show that $W$ can be approximated locally uniformly by quasiconvex polynomials.
Thesis
Die vorliegende Arbeit beschäftigt sich mit drei Klassen ausgewählter nichtlinearer Probleme, die Forschungsgegenstand der angewandten Mathematik sind. Diese Probleme behandeln die Minimierung von Integralen in der Variationsrechnung (Kapitel 3), das Lösen partieller Differentialgleichungen (Kapitel 4) und das Lösen nichtlinearer Optimierungsaufgab...
Article
We study a particular case of integer polynomial optimization: Minimize a polynomial F^ on the set of integer points described by an inequality system F1⩽0,…,Fs⩽0, where F^,F1,…,Fs are quasiconvex polynomials in n variables with integer coefficients.We design an algorithm solving this problem that belongs to the time-complexity class O(s)·lO(1)·dO(...

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