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2017/18 semester 1 events in Mathematics

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Mon 11/09/17 15:00
Fulton G20
Mathematics Seminar
Prof. Alexander Gorban (University of Leicester)
Stochastic Separation Theorems
abstract

Abstract

The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples where the system works properly. We demonstrate that in (moderately) high dimension this separation could be achieved with probability close to one by linear discriminants. Based on fundamental properties of measure concentration, we show that for M< aexp(bn) random M-element sets in Rn are linearly separable with probability p, p > 1−ϑ, where 1>ϑ>0 is a given small constant. Exact values of a,b>0 depend on the probability distribution that determines how the random M-element sets are drawn, and on the constant ϑ. Classical measure concentration theorems state that random points are concentrated in a thin layer near a surface (a sphere, an average or median level set of energy or another function, etc.). The stochastic separation theorems describe thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set even for exponentially large random sets. These stochastic separation theorems provide a new instrument for the development, analysis, and assessment of machine learning methods and algorithms in high dimension. Theoretical statements are illustrated with numerical examples. e-print: https://arxiv.org/abs/1703.01203

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Mon 18/09/17 15:00
Fulton G20
Mathematics Seminar
Dr. Theodosios Papathanasiou (Brunel University London)
Finite Elements for the Hydroelastic Response of Very Large Floating Structures under Long Wave Excitation
abstract

Abstract

The study of wave action on large, elastic floating bodies has received considerable attention, finding applications in both geophysics and marine engineering problems. Pontoon-type Very Large Floating Structures (VLFSs) share the same hydroelastic characteristics with ice floes and as a result the methodologies developed for their study bear great resemblance. Among these methodologies, efficient Finite Element schemes for the simulation of hydroelastic interactions in shallow water environments have been recently proposed. These numerical procedures, based on the vertical method of lines, will be presented and analysed. The talk will cover issues regarding (i) weak forms, properties and stability characteristics of the governing equations, (ii) Finite Element approximation and suitable time integration techniques, (iii) Energy norm error estimates and (iv) numerical examples of hydroelastic interactions in variable bathymetry regions.

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