Past Seminars

22 October 2021
15:00
Pablo Camara

Further Information: 

Pablo G. Cámara is an Assistant Professor of Genetics at the University of Pennsylvania and a faculty member of the Penn Institute for Biomedical Informatics. He received a Ph.D. in Theoretical Physics in 2006 from Universidad Autónoma de Madrid. He performed research in string theory for several years, with postdoctoral appointments at Ecole Polytechnique, the European Organization for Nuclear Research (CERN), and University of Barcelona. Fascinated by the extremely interesting and fundamental open questions in biology, in 2014 he shifted his research focus into problems in quantitative biology, and joined the groups of Dr. Rabadan, at Columbia University, and Dr. Levine, at the Institute for Advanced Study (Princeton). Building upon techniques from applied topology and statistics, he has devised novel approaches to the inference of ancestral recombination, human recombination mapping, the study of cancer heterogeneity, and the analysis of single-cell RNA-sequencing data from dynamic and heterogeneous cellular populations.

Abstract

One of the prevailing paradigms in data analysis involves comparing groups of samples to statistically infer features that discriminate them. However, many modern applications do not fit well into this paradigm because samples cannot be naturally arranged into discrete groups. In such instances, graph techniques can be used to rank features according to their degree of consistency with an underlying metric structure without the need to cluster the samples. Here, we extend graph methods for feature selection to abstract simplicial complexes and present a general framework for clustering-independent analysis. Combinatorial Laplacian scores take into account the topology spanned by the data and reduce to the ordinary Laplacian score when restricted to graphs. We show the utility of this framework with several applications to the analysis of gene expression and multi-modal cancer data. Our results provide a unifying perspective on topological data analysis and manifold learning approaches to the analysis of point clouds.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • Applied Topology Seminar
22 October 2021
14:00
James Timmins
Abstract

The Krull dimension is an ideal-theoretic invariant of an algebra. It has an important meaning in algebraic geometry: the Krull dimension of a commutative algebra is equal to the dimension of the corresponding affine variety/scheme. In my talk I'll explain how this idea can be transformed into a tool for measuring non-commutative rings. I'll illustrate this with important examples and techniques, and describe what is known for Iwasawa algebras of compact $p$-adic Lie groups.

  • Junior Algebra and Representation Theory Seminar
22 October 2021
14:00
Dr Richard Earl, Dr Neil Laws, and Dr Vicky Neale
Abstract

What should you expect in intercollegiate classes?  What can you do to get the most out of them?  In this session, experienced class tutors will share their thoughts, including advice about online classes. 

All undergraduate and masters students welcome, especially Part B and MSc students attending intercollegiate classes. 

22 October 2021
14:00
Abstract

Manipulation of the genome function is important for understanding the underlying genetics for sophisticated phenotypes and developing gene therapy. Beyond gene editing, there is a major need for high-precision and quantitative technologies that allow controlling and studying gene expression and epigenetics in the genome. Towards this goal, we develop the concept and technologies for the use of the nuclease-deactivated CRISPR-Cas (dCas) system, repurposed from the Cas nuclease, for programmable transcription regulation, epigenetic modifications, and the 3D genome organization. We combine genome engineering and mathematical modeling to understand the noncoding DNA function including ultralong-distance enhancers and repetitive elements. We actively explore new tools that allow precise manipulation of the large-scale chromatin as a novel gene therapy. In this talk, I will highlight our works at the interface between genome engineering and chromatin biology for studying the noncoding genome and related applications.

  • Mathematical Biology and Ecology Seminar
21 October 2021
16:00
Abstract

We introduce a method for estimating the roughness of a function based on a discrete sample, using the concept of normalized p-th variation along a sequence of partitions. We discuss the consistency of this estimator in a pathwise setting under high-frequency asymptotics. We investigate its finite sample performance for measuring the roughness of sample paths of stochastic processes using detailed numerical experiments based on sample paths of Fractional Brownian motion and other fractional processes.
We then apply this method to estimate the roughness of realized volatility signals based on high-frequency observations.
Through a detailed numerical experiment based on a stochastic volatility model, we show that even when instantaneous volatility has diffusive dynamics with the same roughness as Brownian motion, the realized volatility exhibits rougher behaviour corresponding to a Hurst exponent significantly smaller than 0.5. Similar behaviour is observed in financial data, which suggests that the origin of the roughness observed in realized volatility time-series lies in the `microstructure noise' rather than the volatility process itself.

 

 

 

  • Mathematical and Computational Finance Internal Seminar
21 October 2021
14:00
Abstract

I will discuss recent advances in sampling methods for positive semidefinite (PSD) matrix approximation. In particular, I will show how new techniques based on recursive leverage score sampling yield a surprising algorithmic result: we give a method for computing a near optimal k-rank approximation to any n x n PSD matrix in O(n * k^2) time. When k is not too large, our algorithm runs in sublinear time -- i.e. it does not need to read all entries of the matrix. This result illustrates the ability of randomized methods to exploit the structure of PSD matrices and go well beyond what is possible with traditional algorithmic techniques. I will discuss a number of current research directions and open questions, focused on applications of randomized methods to sublinear time algorithms for structured matrix problems.

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A link for this talk will be sent to our mailing list a day or two in advance.  If you are not on the list and wish to be sent a link, please contact trefethen@maths.ox.ac.uk.

  • Computational Mathematics and Applications Seminar
21 October 2021
12:00
Eric Rawdon

Further Information: 

Eric Rawdon is a Professor in Mathematics & Data Analytics at the University of St. Thomas, Minnesota.

Research interests

Physical knot theory

Publications

Please see google scholar

Abstract

Some proteins (in their folded form) are classified as being knotted.

The function of the knotting is mysterious since knotting seemingly

would make the folding process unnecessarily complicated.  To

function, proteins need to fold quickly and reproducibly, and

misfolding can have catastrophic results.  For example, Mad Cow

disease and the human analog, Creutzfeldt-Jakob disease, come from

misfolded proteins.

 

Traditionally, knotting is only defined for closed curves, where the

topology is trapped in the loop.  However, proteins have free ends, as

well as most of the objects that humans consider as being knotted

(like shoelaces and strings of lights).  Defining knotting in open

curves is tricky and ambiguous.  We consider some definitions of

knotting in open curves and see how one of these definitions is used

to characterize the knotting in proteins.

  • Industrial and Applied Mathematics Seminar

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