L3

Cell-to-cell variability is often a primary source of variability in experimental data. Yet, it is common for mathematical analysis of biological systems to neglect biological variability by assuming that model parameters remain fixed between measurements. In this two-part talk, I present new mathematical and statistical tools to identify cell-to-cell variability from experimental data, based on mathematical models with random parameters. First, I identify variability in the internalisation of material by cells using approximate Bayesian computation and noisy flow cytometry measurements from several million cells. Second, I develop a computationally efficient method for inference and identifiability analysis of random parameter models based on an approximate moment-matched solution constructed through a multivariate Taylor expansion. Overall, I show how analysis of random parameter models can provide more precise parameter estimates and more accurate predictions with minimal additional computational cost compared to traditional modelling approaches.

Building computationally capable biological systems has long been an aim of synthetic biology. The potential utility of bio-computing devices ranges from biosafety and environmental applications to diagnosis and personalised medicine. Here we present work on the design of bacterial computers which use spatial patterning to process information. A computer is composed of a number of bacterial colonies which, inspired by patterning in embryo development, communicate using diffusible morphogen-like signals. A computation is programmed into the overall physical arrangement of the system by arranging colonies such that the resulting diffusion field encodes the desired function, and the output is represented in the spatial pattern displayed by the colonies. We first mathematically demonstrate the simple digital logic capability of single bacterial colonies and show how additional structure is required to build complex functions. Secondly, inspired by electronic design automation, an algorithm for designing optimal spatial circuits computing two-level digital logic functions is presented, extending the capability of our system to complex digital functions without significantly increasing the biological complexity. We implement experimentally a proof-of-principle system using engineered Escherichia coli interpreting diffusion fields formed from droplets of an inducer molecule. Our approach will open up new ways to perform biological computation, with applications in synthetic biology, bioengineering and biosensing. Ultimately, these computational bacterial communities will help us explore information processing in natural biological systems.

The overall goal of the Sherwood lab is to advance genomic and precision medicine applications through high-throughput, multi-disciplinary science. In this talk, I will review a suite of high-throughput genomic and cellular perturbation platforms using CRISPR-based genome editing that the lab has developed to improve our understanding of genetic disease, gene regulation, and genome editing outcomes.

This talk will focus on 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. Through these efforts, we show that dysfunction of the RAB10 vesicle transport pathway leads to hypercholesterolemia in humans and mice by impairing surface LDL receptor levels. Further, we demonstrate that loss of function of OTX2 leads to robust reduction in serum LDL-C levels in mice and humans by increasing cellular LDL-C uptake. Finally, we unveil an activity-normalized base editing screening framework to better understand the impacts of coding and non-coding variation on serum LDL-C levels, altogether providing a roadmap for further efforts to dissect complex human disease genetics.

Cell fate decision-making is responsible for development and homeostasis, and is dysregulated in disease. Despite great promise, we are yet to harness the high-resolution cell state information that is offered by single-cell genomics data to understand cell fate decision-making as it is controlled by gene regulatory networks. We describe how we leveraged joint dynamics + genomics measurements in single cells to develop a new framework for single-cell-informed Bayesian parameter inference of Ca2+ pathway dynamics in single cells. This work reveals a mapping from transcriptional state to dynamic cell fate. But no cell is an island: cell-internal gene regulatory dynamics act in concert with external signals to control cell fate. We developed a multiscale model to study the effects of cell-cell communication on gene regulatory network dynamics controlling cell fates in hematopoiesis. Specifically, we couple cell-internal ODE models with a cell signaling model defined by a Poisson process. We discovered a profound role for cell-cell communication in controlling the fates of single cells, and show how our results resolve a controversy in the literature regarding hematopoietic stem cell differentiation. Overall, we argue for the need to consider single-cell-resolved models to understand and predict the fates of cells.

We formulate and sketch the proof of the K-theoretic Farrell-Jones Conjecture for
for the Hecke algebras of reductive p-adic groups. This is the first time that
a version of the farrell-Jones Conjecture for topological groups is formulated. It implies that
the reductive projective class group of the Hecke algebra of a reductive p-adic group
is the colimit of these for all compact open subgroups. This has been proved rationally by
Bernstein and Dat using representation theory. The main applications of our result
will concern the theory of smooth representations
In particular we will prove a conjecture of Dat.

The proof is much more involved than the one for instance for discrete CAT(0)-groups.
We will only give a very brief sketch of it and the new problems occurring in the setting of
totally disconnected groups. Most of the talk will be devoted
an introduction to the Farrell-Jones Conjecture and the theory of
smooth representations of reductive p-adic groups, and
discussion of  applications.

This is a joint project with Arthur Bartels.

Solving sparse linear systems is omnipresent in scientific computing. Direct approaches based on matrix factorization are very robust, and since they can be used as a black-box, it is easy for other software to use them. However, the memory requirement of direct approaches scales poorly with the problem size, and the algorithms underpinning sparse direct solvers software are poorly suited to parallel computation. Multilevel Domain decomposition (MDD) methods are among the most efficient iterative methods for solving sparse linear systems. One of the main technical difficulties in using efficient MDD methods (and most other efficient preconditioners) is that they require information from the underlying problem which prohibits them from being used as a black-box. This was the motivation to develop the widely used algebraic multigrid for example. I will present a series of recently developed robust and fully algebraic MDD methods, i.e., that can be constructed given only the coefficient matrix and guarantee a priori prescribed convergence rate. The series consists of preconditioners for sparse least-squares problems, sparse SPD matrices, general sparse matrices, and saddle-point systems. Numerical experiments illustrate the effectiveness, wide applicability, scalability of the proposed preconditioners. A comparison of each one against state-of-the-art preconditioners is also presented.

I discuss the set of rates of growth of a finitely generated 
group with respect to all its finite generating sets. In a joint work 
with Sela, for a hyperbolic group, we showed that the set is 
well-ordered, and that each number can be the rate of growth of at most 
finitely many generating sets up to automorphism of the group. I may 
discuss its generalization to acylindrically hyperbolic groups.

Tensors, also known as multiway arrays, have become ubiquitous as representations for operators or as convenient schemes for storing data. Yet, when it comes to compressing these objects or analyzing the data stored in them, the tendency is to ``flatten” or ``matricize” the data and employ traditional linear algebraic tools, ignoring higher dimensional correlations/structure that could have been exploited. Impediments to the development of equivalent tensor-based approaches stem from the fact that familiar concepts, such as rank and orthogonal decomposition, have no straightforward analogues and/or lead to intractable computational problems for tensors of order three and higher.

In this talk, we will review some of the common tensor decompositions and discuss their theoretical and practical limitations. We then discuss a family of tensor algebras based on a new definition of tensor-tensor products. Unlike other tensor approaches, the framework we derive based around this tensor-tensor product allows us to generalize in a very elegant way all classical algorithms from linear algebra. Furthermore, under our framework, tensors can be decomposed in a natural (e.g. ‘matrix-mimetic’) way with provable approximation properties and with provable benefits over traditional matrix approximation. In addition to several examples from recent literature illustrating the advantages of our tensor-tensor product framework in practice, we highlight interesting open questions and directions for future research.

PDE Workshop in Stability Analysis for Nonlinear PDEs will be running Monday 15th - Friday 19th August.

Location: L3, AWB

Our goal was to bring together leading experts in the stability analysis of nonlinear partial differential equations across multi-scale applications. Some of the topics to be addressed include: 

• Stability analysis of shock wave patterns of reflections/diffraction.
• Stability analysis of vortex sheets, contact discontinuities, and other characteristic discontinuities for multidimensional hyperbolic systems of conservation laws.
• Stability analysis of particle to continuum limits including the quantifying asymptotic/mean-field/large-time limits for pairwise interactions and particle limits for general interactions among multi-agent systems
• Stability analysis of asymptotic limits with emphasis on the vanishing viscosity limit of solutions from multidimensional compressible viscous to inviscid flows with large initial data.