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The saying has it that if you plan a talk for graduate students, then a few professors might understand it. Therefore we suggest that you plan your talk so that even undergraduates will understand it, and then maybe most of the audience will actually do so.

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2018-2019 Schedule

17.713:15Shill Fan (Central China Normal University)Stationary determinantal point processes: ψ-mixing property, correlation dimensions and g-conformal propertyLet $f$ be a Borel function from the unit circle to the closed unit interval. It determines a translate invariant measure on $\{0,1\}^{\mathbb{Z}}$.  We will first introduce the construction of these measures  and then discuss some properties of  these measures.
22.514:15 (MA342)Juho Kontio (Research plan seminar)Scalable non-parametric pre-screening method for searching higher-order genetic interactions underlying quantitative traitsThe Gaussian process (GP) based automatic relevance determination (ARD) is known to be an efficient technique for identifying determinants of gene-by-gene interactions important to trait variation. However, the estimation of GP models is feasible only for low-dimensional datasets ($\sim$ 200 variables) which severely prevents the GP-based ARD method to be applied for high-throughput sequencing data. We have developed a non-parametric pre-screening method that transforms the input variable space via an appropriate kernel function to reduce the GP-based ARD method into a linear similarity regression problem. The proposed method preserves virtually all the major benefits of the GP-based ARD method and extends its scalability to typical high-dimensional datasets used in practice. We present several simulated test scenarios to show that the proposed method compares superiorly with existing non-parametric pre-screening methods suitable for higher-order interaction search.  Methodological extensions and straightforward applications will be briefly discussed.
7.5

14:15

(MA342)

Jukka KemppainenScaling Limits for Continuous Time Random Walks with Heavy-Tailed DistributionsWe discuss the scaling limits for continuous time random walks, when the jumps or waiting times have heavy-tailed distributions. We will outline how the probability distribution functions of the limiting processes are connected to anomalous diffusion equations.
23.414:15 (MA342)Xiang GAO (Hubei University, Wuhan)On Fourier decay of some fractal measures 
17.414:15 (IT137)Sebastian Lunz (University of Cambridge)Adversarial Regularizers in Inverse ProblemsIn the past years, machine learning algorithms and in particular deep learning have been providing new tools to the inverse problems community, that have been used to greatly improve reconstruction quality. In this talk, we will give a brief overview of recent approaches to inverse problems using machine learning and will then discuss adversarial regularizers, an approach based on learning a regularization functional, in detail. As applications, we consider traditional imaging problems like computed tomography as well as single particle analysis as a novel application.
5.2.12:15 (IT137)Han Yu (University of St. Andrews)

Numbers with restricted digits and Furstenberg slicing problem

Furstenberg posed a problem on intersections between Cantor sets. In this talk, I will talk about Shmerkin-Wu's breakthrough towards this problem as well as a tiny improvement made by myself. It turns out that this tiny improvement can be used to show some intriguing results in number theory on numbers with restricted digits which I will also state in the talk. If time permits, I will briefly mention some key steps of the proofs and some potential future works.

14.1213:15 (L9)Andreas Hauptmann (University College, London)Learned image reconstruction for high-resolution tomographic imaging

Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up of reconstruction time. In this talk I will discuss two common approaches to combine deep learning methods, in particular convolutional neural networks (CNN), with model-based reconstruction techniques. I will illustrate these approaches with two conceptually different imaging modalities: For accelerated dynamic cardiovascular magnetic resonance we can train a CNN to remove noise and aliasing artefacts from an initial reconstruction to obtain clinically useful information. For the more challenging problem of limited-view photoacoustic tomography, we rather need to train a network that performs an iterative reconstruction which feeds back the model information into the reconstruction algorithm to successively negate limited-view artefacts.

4.1213:15 (MA341)Ruxi ShiFuglede's spectral set conjecture on some finite abelian groupsFor a locally compact abelian group $G$, Fuglede's spectral set conjecture states that a Borel set is spectral if and only if it tiles the group $G$ by translation. In the case $G=\mathbb{R}^n$, it have been studied for long time since Fuglede formulated this conjecture in 1974. It is proved to be false for $n\ge 3$ but it is still open for $n=1, 2$. Actually, Fuglede's conjecture on $\mathbb{R}$ and $\mathbb{R}^2$  is strongly related to the one on finite abelian groups, which is connected with number theory and combination. In this talks, I will present some recent results about Fuglede's spectral set conjecture on some finite abelian groups.
27.914:15 (MA342)Hua Qiu (Nanjing University)

The spectrum of the Laplacian on a family of domains in the Sierpinski gasket

 

 

For a certain domain $\Omega$ in the Sierpinski gasket $\mathcal{SG}$ whose boundary is a line segment, a complete description of the eigenvalues of the Laplacian, with an exact count of dimensions of eigenspaces, under the Dirichlet and Neumann boundary conditions is presented.  Let $\rho^\Omega(x)$ be the eigenvalue counting function of the Laplacian on  $\Omega$. We prove that $\rho^\Omega(x)=g(\log x)x^{\log 3/\log5}+O(x^{\log2/\log5}\log x)$ as $x\rightarrow\infty$ for some (right-continuous, discontinuous) $\log 5$-periodic function $g:\mathbb{R}\rightarrow\mathbb{R}$ with $0<\inf_{\mathbb{R}}g<\sup_\mathbb{R}g<\infty$. Moreover, we explain that the asymptotic expansion of $\rho^\Omega(x)$ should admit a second term of  order $\log2/\log5$, that becomes apparent from the experimental data. This is  analogous to the conjectures of Weyl and Berry. We will also talk about some other related boundary value problems on subdomains in the Sierpinski gasket. 

14.914:15 (TA101)Ruxi Shi

Chowla sequences in $(S^1\cup \{0\})^\mathbb{N}$}

 

The Chowla sequences and Sarnak sequences taking values in $\{-1,0,1\}$ was introduced by El Houcein el Abdalaoui, Joanna Kułaga-Przymus, Mariusz Lemańczyk and Thierry De La Rue for studying Chowla's conjecture and Sarnak's conjecture  from ergodic theory point of view. One of their results is that Chowla sequences are always Sarnak sequences, and consequently orthogonal to all topological dynamical systems of zero entropy. In this talk, I will explain how to generalize Chowla sequences from $\{-1,0,1\}^\mathbb{N}$ to $(S^1\cup \{0\})^\mathbb{N}$. I will also show that for almost all $\beta>1$, the sequences $(e^{2\pi i \beta^n})_{n\in \mathbb{N}}$ are Chowla sequences and consequently orthogonal to all topological dynamical systems of zero entropy
14.913:15 (TA101)Wen Wu (South China Unversity of Technology)

On the abelian complexity of the Rudin-Shapiro sequence

In this talk, we study the abelian complexity of the Rudin-Shapiro sequence. We show the regularity and some asymptotic property of its abelian complexity function.

14.911:15 (SÄ105)Amir Algom (The Hebrew University of Jerusalem)Slicing Theorems and rigidity in the class of Bedford-McMullen carpets

Let F be a Bedford-McMullen carpet, with algebraically independent defining integer exponents. Let L be an affine line in the plane that is not parallel to the principal axis  We prove that the upper-box dimension of F\cap L is bounded by max{ dim^* (F) - 1, 0}, where dim^* (F) is the star-dimension of F (which is the maximal Hausdorff dimension of a microset of F).

To prove this, we first reduce the problem to that of bounding the dimension of non-principal slices in a product set of two Cantor sets. Each Cantor set is assumed to be a non-stationary deleted digit set for some integer base, and the two bases are independent. To bound the dimension of these slices , we adapt Wu's ergodic-theoretic proof of Furstenberg's slicing conjecture to this situation.

Time permitting, we will explain how this slicing Theorem for products of Cantor sets can be applied to obtain various rigidity results in the class of Bedford-McMullen carpets. For example, we find explicit combinatorial upper bounds for the dimension of the intersection of two Bedford-McMullen carpets, under the assumption that all defining exponents are independent. 

14.910:15 (SÄ105)Bing Li (South China University of Technology)Simultaneous shrinking target problems for $\times 2$ and $\times 3$

We consider the simultaneous shrinking target problems for ×2 and ×3. We obtain the Haisdorff dimensions of the intersection of two well approximable sets and also of the set of points whose orbits approach a given point simultaneously for these two dynamical systems. It is a joint work with Lingmin Liao.

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