### Department of Mathematics and Systems Analysis

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* Dates within the next 7 days are marked by a star.

Professor Vitaly Skachek (University of Tartu)**Constructing Asynchronous Batch Codes using Hypergraphs***** ** Tuesday 23 April 2019, 15:15, M1 (M232)

Batch codes were first proposed by Ishai et al. as a means for balancing load in distributed storage systems. They are also of potential use in private information retrieval. In this talk, we present a new variant of batch codes termed "asynchronous batch codes", which are designed for parallel recovery of information symbols from the coded database, where different requests take different service time (i.e. the requests are served in an asynchronous manner).
It turns out that the graph-based batch codes studied by Rawat et al. are asynchronous. By building on the ideas therein, we show that hypergraphs of Berge girth at least 4 yield graph-based asynchronous batch codes. We prove the hypergraph-theoretic proposition that the maximum number of hyperedges in a hypergraph of a fixed Berge girth equals the quantity in a certain generalization of the hypergraph-theoretic (6,3)-problem. We then apply the constructions and bounds by Erdos, Frankl and Rodl to obtain batch code constructions and bounds on the optimal redundancy of the graph-based asynchronous batch codes.
We show that the optimal redundancy $\rho(k)$ of graph-based asynchronous batch codes of dimension $k$ with the query size $t=3$ is $2\sqrt{k}$. Moreover, for a general fixed value of $t \ge 4$, $\rho(k) = O\left({k}^{1/(2-\epsilon)}\right)$ for any small $\epsilon > 0$. For a general value of $t \ge 4$, $\lim_{k \rightarrow \infty} \rho(k)/\sqrt{k} = \infty$.
(Joint work with Ago-Erik Riet and Eldho K. Thomas)

Department Colloquium

Prof Thomas Banchoff (Brown University)**TBA**

Thursday 02 May 2019, 15:15, Aalto hall

Mathematics and Arts Colloquium

Ida Keskimäki**Tason symmetriat (kandiesitelmä)**

Tuesday 07 May 2019, 16:15, M3 (M234)

Nicolas Dietrich (University of Salzburg)**TBA**

Thursday 09 May 2019, 14:15, M2 (M233)

Seminar on analysis and geometry

Giovanni Comi (Scuola Normale Superiore di Pisa)**TBA**

Wednesday 15 May 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

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