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Aalto Stochastics and Statistics Seminar is organized by Kalle Kytölä, Lasse Leskelä, and Pauliina Ilmonen. Feel free to contact one of us if you are interested in giving a talk. You may also earn credit points by active participation.
The objective of this talk is to propose a full discretization for the stochastic wave equation. More specifically, the discontinuous Galerkin finite element method is used in space and analyzed in a semigroup framework, and an explicit stochastic position Verlet scheme is used for the temporal approximation. Numerical experiments illustrate our theoretical results on strong convergence rates. Further, we analyze and bound the expected energy and numerically show excellent agreement with the energy of the exact solution. Join Zoom Meeting https://aalto.zoom.us/j/68911259210 Meeting ID: 689 1125 9210
The seminar is intended for epidemiological modellers. I will present a set SEIR models used by THL to model the COVID outbreak in Finland. I will analyse particular model features, discussing whatever they there useful for inference. I will describe different questions which we tried to answer with these models, and wherever modelling was able to provide useful insight. For any questions, contact Mikhail (Mikhail.shubin@thl.fi https://teams.microsoft.com/l/meetup-join/19%3ameeting_NjE4MDVkYWUtOGQ5MS00YWIxLWIwNDYtMzUxZjQyNmExOTE5%40thread.v2/0?context=%7b%22Tid%22%3a%2281d1db0d-c492-4225-a66c-3c3a9e4b8360%22%2c%22Oid%22%3a%221373e033-bd9e-4fa9-898a-a07b58e1f61e%22%7d
The six-vertex model is a planar random model for the crystalline structure of water ice. It has recently given important insights to the connection of Conformal field theory and critical 2D random models, due to its natural representation as a random field, called the height function, and due to couplings to several other important random models (e.g. FK cluster model, Ising and Potts models, dimers, random graph homomorphisms) We prove that the six-vertex height function has a localization/delocalization phase transition. Delocalization means roughly speaking that the model is not sensitive to a boundary condition far away; indeed our result for instance implies that there exists a unique whole-plane six-vertex model in the delocalized phase. The main tools of the proof are an explicit solution of the free energy of the model, and RSW and FKG inequalities similar as in the study of various percolation models. (Based on ongoing work with Hugo Duminil-Copin, Ioan Manolescu, and Mendes Oulamara.) Zoom-link: https://aalto.zoom.us/j/66281157229
The traditional methods for detecting community structure in a network are based on selecting dense subgraphs inside the network. Here we propose to use the methods of coalitional game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we propose an approach which is based on hedonic coalitional games. This approach allows to find clusters with various resolution. Furthermore, the modularity-based approach and its generalizations as well as ratio cut and normalized cut methods can be viewed as particular cases of the hedonic games. Finally, for methods based on potential hedonic games we suggest a very efficient computational scheme using Gibbs sampling. Bio: Konstantin Avrachenkov received the masters degree in control theory from St. Petersburg State Polytechnic University in 1996, the Ph.D. degree in mathematics from the University of South Australia in 2000, and the Habilitation (Doctor of Science) degree from the University of Nice Sophia Antipolis in 2010. Currently, K. Avrachenkov is Director of Research at Inria Sophia Antipolis. His main research interests are Markov chains, Markov decision processes, stochastic games and singular perturbations. He applies these methodological tools to the modelling and control of telecommunication systems and to design data mining and machine learning algorithms. He has won 5 best paper awards. He is an Associate Editor of the International Journal of Performance Evaluation, Probability in the Engineering and InformationalSciences, ACM TOMPECS and Stochastic Models.
Typically, in the functional context, data depth approaches heavily emphasize the location of the functions in the distribution, therefore often missing important shape or roughness features. Commonly, these depth approaches either integrate pointwise depth values to achieve a global value, or measure the expected distance from a function to the distribution. In this talk, we introduce a new class of functional depths, based on the distribution of depth values along the domain, and discuss their properties. We study the asymptotic properties of these $J$th order $k$th moment integrated depths, and illustrate their usefulness in supervised functional classification. In particular, we demonstrate the importance of receptivity to shape variations, and show that, similarly to existing depth notions, the new class of depth functions takes into account the variation in location, while remaining receptive to variations in shape and roughness.
Prostate cancer incidence rate is extremely high and on the rise, counting over 1.2 million new cases annually and causing 350 000 deaths in 2018. While the prognosis is typically good, approximately 20% of the new cases classifies as high-risk prostate cancer with dire consequences. Moreover, the initial prostate cancer diagnosis always reflects as worry and quality of life impairment. The initial prostate cancer determination is based on prostate specific antigen (PSA) measure, which cannot distinguish between low-risk and high-risk cases. After the PSA determination, the tumor state is characterized with various invasive methods such as Gleason score and T-stage classification. However, both methods display inaccuracy and puts patient under infection risk. Our take on this challenge is to use inflammation-related gene single nucleotide polymorphisms (SNP) as predictors of high-risk prostate cancer. SNP is a low-cost, non-invasive, and stable biomarker. We have explored inflammation SNP association with high-risk prostate cancer in a genotyped part of Finnish Randomized Screening for Prostate Cancer cohort (n = 2715) and found several statistically significant associations. Furthermore, our validation model using unknown prostate cancer cohort collected during hospital visits (n = 888) is in concordance with our discovery model. Remarkably, few SNPs increase early high-risk prostate cancer detection over PSA alone.
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