### Algebraic sums and products of univoque bases

Karma Dajani
Given $x\in(0, 1]$, let ${\mathcal U}(x)$ be the set of bases $\beta\in(1,2]$ for which there exists a unique sequence $(d_i)$ of zeros and ones such that $x=\sum_{i=1}^{\infty}{{d_i}/{\beta^i}}$. In 2014, Lü, Tan and Wu proved that ${\mathcal U}(x)$ is a Lebesgue null set of full Hausdorff dimension. In this talk, we will show that the algebraic sum ${\mathcal U}(x)+\lambda {\mathcal U}(x)$, and the product ${\mathcal U}(x)\cdot {\mathcal U}(x)^{\lambda}$ contain an interval for all $x\in (0, 1]$...

### Statistical inverse problems and geometric "wavelet" construction

Gérard Kerkyacharian
In the fist part of the talk, we will look to some statistical inverse problems for which the natural framework is no more an Euclidian one. In the second part we will try to give the initial construction of (not orthogonal) wavelets -of the 80 - by Frazier, Jawerth,Weiss, before the Yves Meyer ORTHOGONAL wavelets theory. In the third part we will propose a construction of a geometric wavelet theory. In the Euclidian case, Fourier...

### Optimal rates for $k$-NN density and mode estimation

Samory Kpotufe
We present two related contributions of independent interest: high-probability finite sample rates for $k$-NN density estimation, and practical mode estimators – based on $k$-NN – which attain minimax-optimal rates under surprisingly general distributional conditions. $k$-nearest neighbor ($k$-NN) - $k$-NN density rates - mode estimation

Anne De Roton

### Reconstruction methods for ill-posed inverse problems - Part 2

Samuli Siltanen
inverse problem - reconstruction - regularization - tomography - computation

### Towards static analysis of functional programs using term rewriting and tree automata

Thomas Genet
Tree Automata Completion is an algorithm computing, or approximating, terms reachable by a term rewriting system. For many classes of term rewriting systems whose set of reachable terms is known to be regular, this algorithm is exact. Besides, the same algorithm can handle ²²any²² left-linear term rewriting system, in an approximated way, using equational 2 abstractions. Thanks to those two properties, we will see that regular languages and tree automata completion provide a promising alternative...

• 2017
948

• Audiovisual
948