Tue, 07 Mar 2023

14:00 - 15:00
Virtual

A loglog step towards the Erdős-Hajnal conjecture

Paul Seymour
(Princeton)
Further Information

Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

Abstract

In 1977, Erdős and Hajnal made the conjecture that, for every graph $H$, there exists $c>0$ such that every $H$-free graph $G$ has a clique or stable set of size at least $|G|^c$; and they proved that this is true with $|G|^c$ replaced by $2^{c\sqrt{\log |G|}}$. Until now, there has been no improvement on this result (for general $H$). We recently proved a strengthening: that for every graph $H$, there exists $c>0$ such that every $H$-free graph $G$ with $|G|\ge 2$ has a clique or stable set of size at least $2^{c\sqrt{\log |G| \log\log|G|}}$. This talk will outline the proof. Joint work with Matija Bucić, Tung Nguyen and Alex Scott.

Tue, 07 Feb 2023

15:30 - 16:30
Virtual

Bounds for subsets of $\mathbb{F}_{p}^{n} \times \mathbb{F}_{p}^{n}$ without L-shaped configurations

Sarah Peluse
(Princeton/IAS)
Further Information

Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

Abstract

I will discuss the difficult problem of proving reasonable bounds in the multidimensional generalization of Szemerédi's theorem and describe a proof of such bounds for sets lacking nontrivial configurations of the form (x,y), (x,y+z), (x,y+2z), (x+z,y) in the finite field model setting.

Fri, 10 Mar 2023

14:00 - 15:00
Virtual

CRISPR-based decoding of disease-associated genomic variants

Prof Richard Sherwood
(Brigham and Womens Hospital Harvard Medical School)
Abstract

The overall goal of the Sherwood lab is to advance genomic and precision medicine applications through high-throughput, multi-disciplinary science. In a shortened talk this past autumn, I described our recent efforts using combined analysis of rare coding variants from the UK Biobank and genome-scale CRISPR-Cas9 knockout and activation screening to improve the identification of genes, coding variants, and non-coding variants whose alteration impacts serum LDL cholesterol (LDL-C) levels.

In this talk, I will discuss our emerging efforts to optimize and employ precision CRISPR techniques such as base editing and prime editing to better understand the impacts of coding and non-coding variation on serum LDL-C levels and coronary artery disease risk. This work involves the development of novel high-throughput screening platforms and computational analysis approaches that have wide applicability in dissecting complex human disease genetics.

Fri, 03 Mar 2023

14:00 - 15:00
Virtual

An agent-based model of the tumour microenvironment

Dr Cicely Macnamara
(School of Mathematics and Statistics University of Glasgow)
Abstract

The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Cancer cells can arise from any type of cell in the body; cancers can grow in or around any tissue or organ making the disease highly complex. My research is focused on understanding the specific mechanisms that occur in the tumour microenvironment via mathematical and computational modelling. In this talk I shall present a 3D individual-based force-based model for tumour growth and development in which we simulate the behaviour of, and spatio-temporal interactions between, cells, extracellular matrix fibres and blood vessels. Each agent is fully realised, for example, cells are described as viscoelastic sphere with radius and centre given within the off-lattice model. Interactions are primarily governed by mechanical forces between elements. However, as well as he mechanical interactions we also consider chemical interactions, by coupling the code to a finite element solver to model the diffusion of oxygen from blood vessels to cells, as well as intercellular aspects such as cell phenotypes. 

Fri, 27 Jan 2023

14:00 - 15:00
Virtual

Digital twin models for the precision diagnosis and therapy of cancer

Prof Walter Kolch
(School of Medicine University College Dublin)
Abstract

Approaches to personalized diagnosis and treatment in oncology are heavily reliant on computer models that use molecular and clinical features to
characterize an individual patient’s disease. Most of these models use genome and/or gene expression sequences to develop classifiers of a patient’s
tumor. However, in order to fully model the behavior and therapy response of a tumor, dynamic models are desirable that can act like a Digital Twin of
the cancer patient allowing prognostic and predictive simulations of disease progression, therapy responses and development of resistance. We are
constructing Digital Twins of cancer patients in order to perform dynamic and predictive simulations that improve patient stratification and
facilitate the design of individualized therapeutic strategies. Using a hybrid approach that combines artificial intelligence / machine learning
with dynamic mechanistic modelling we are developing a computational framework for generating Digital Twins. This framework can integrate
different types of data (multiomics, clinical, and existing knowledge) and produces personalized computational models of a patient’s tumor. The
computational models are validated and refined by experimental work and in retrospective patient studies. We present some of the results of the dynamic
Digital Twins simulations in neuroblastoma. They include (i) identification on non-MYCN amplified high risk patients; (ii) prediction of individual
patients’ responses to chemotherapy; and (iii) identification of new drug targets for personalized therapy. Digital Twin models allow the dynamic and
mechanistic simulation of disease progression and therapy response. They are useful for the stratification of patients and the design of personalized
therapies.

Thu, 01 Dec 2022
16:00
Virtual

Particle filters for Data Assimilation

Dan Crisan
(Imperial College London)

Note: we would recommend to join the meeting using the Teams client for best user experience.

Further Information
Abstract

Modern Data Assimilation (DA) can be traced back to the sixties and owes a lot to earlier developments in linear filtering theory. Since then, DA has evolved independently of Filtering Theory. To-date it is a massively important area of research due to its many applications in meteorology, ocean prediction, hydrology, oil reservoir exploration, etc. The field has been largely driven by practitioners, however in recent years an increasing body of theoretical work has been devoted to it. In this talk, In my talk, I will advocate the interpretation of DA through the language of stochastic filtering. This interpretation allows us to make use of advanced particle filters to produce rigorously validated DA methodologies. I will present a particle filter that incorporates three additional add-on procedures: nudging, tempering and jittering. The particle filter is tested on a two-layer quasi-geostrophic model with O(10^6) degrees of freedom out of which only a minute fraction are noisily observed.

Thu, 24 Nov 2022
16:00
Virtual

The Legendre Memory Unit: A neural network with optimal time series compression

Chris Eliasmith
(University of Waterloo)

Note: we would recommend to join the meeting using the Teams client for best user experience.

Further Information
Abstract

We have recently proposed a new kind of neural network, called a Legendre Memory Unit (LMU) that is provably optimal for compressing streaming time series data. In this talk, I describe this network, and a variety of state-of-the-art results that have been set using the LMU. I will include recent results on speech and language applications that demonstrate significant improvements over transformers. I will discuss variants of the original LMU that permit effective scaling on current GPUs and hold promise to provide extremely efficient edge time series processing.

Tue, 22 Nov 2022

17:00 - 18:00
Virtual

Percolation on finite transitive graphs

Philip Easo
(Caltech)
Further Information

Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

Abstract

Tom Hutchcroft and I have been working to develop a general theory of percolation on arbitrary finite transitive graphs. This extends from percolation on local approximations to infinite graphs, such as a sequence of tori, to percolation on the complete graphs - the Erdős-Rényi model. I will summarise our progress on the basic questions: When is there a phase transition for the emergence of a giant cluster? When is the giant cluster unique? How does this relate to percolation on infinite graphs? I will then sketch our proof that for finite transitive graphs with uniformly bounded vertex degrees, the supercritical giant cluster is unique, verifying a conjecture of Benjamini from 2001.

Tue, 22 Nov 2022

15:30 - 16:30
Virtual

Hypergraph Matchings Avoiding Forbidden Submatchings

Michelle Delcourt
(Toronto Metropolitan University)
Further Information

Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

Abstract

In 1973, Erdős conjectured the existence of high girth $(n,3,2)$-Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erdős' conjecture. Just this year, Kwan, Sah, Sawhney, and Simkin proved Erdős' conjecture. As for Steiner systems with more general parameters, Glock, Kühn, Lo, and Osthus conjectured the existence of high girth $(n,q,r)$-Steiner systems. We prove the approximate version of their conjecture. This result follows from our general main results which concern finding perfect or almost perfect matchings in a hypergraph $G$ avoiding a given set of submatchings (which we view as a hypergraph $H$ where $V(H)=E(G)$). Our first main result is a common generalization of the classical theorems of Pippenger (for finding an almost perfect matching) and Ajtai, Komlós, Pintz, Spencer, and Szemerédi (for finding an independent set in girth five hypergraphs). More generally, we prove this for coloring and even list coloring, and also generalize this further to when $H$ is a hypergraph with small codegrees (for which high girth designs is a specific instance). A number of applications in various areas follow from our main results including: Latin squares, high dimensional permutations, and rainbow matchings. This is joint work with Luke Postle.

Tue, 25 Oct 2022

17:00 - 18:00
Virtual

A tale of two balloons

Yinon Spinka
(UBC)
Further Information

Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

Abstract

From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law, and generalize bounds on independent sets that are factors of IID on trees. Joint work with Omer Angel and Gourab Ray.

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