Most of the talk will be about the Farrell-Jones conjecture from the point of view of an outsider. I'll try to explain what the conjecture is about, why one wants to know it, and how to prove it in some cases. The motivation for the talk is my recent work with Fujiwara and Wigglesworth where we prove this conjecture for (virtually torsion-free hyperbolic)-by-cyclic groups. If there is time I will outline the proof of this result.

We investigate theoretical and numerical properties of sparse sketching for both dense and sparse Linear Least Squares (LLS) problems. We show that, sketching with hashing matrices --- with one nonzero entry per column and of size proportional to the rank of the data matrix --- generates a subspace embedding with high probability, provided the given data matrix has low coherence; thus optimal residual values are approximately preserved when the LLS matrix has similarly important rows. We then show that using $s-$hashing matrices, with $s>1$ nonzero entries per column, satisfy similarly good sketching properties for a larger class of low coherence data matrices. Numerically, we introduce our solver Ski-LLS for solving generic dense or sparse LLS problems. Ski-LLS builds upon the successful strategies employed in the Blendenpik and LSRN solvers, that use sketching to calculate a preconditioner before applying the iterative LLS solver LSQR. Ski-LLS significantly improves upon these sketching solvers by judiciously using sparse hashing sketching while also allowing rank-deficiency of input; furthermore, when the data matrix is sparse, Ski-LLS also applies a sparse factorization to the sketched input. Extensive numerical experiments show Ski-LLS is also competitive with other state-of-the-art direct and preconditioned iterative solvers for sparse LLS, and outperforms them in the significantly over-determined regime.

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We propose a randomized algorithm for solving a linear system $Ax = b$ with a highly numerically rank-deficient coefficient matrix $A$ with nearly consistent right-hand side possessing a small-norm solution. Our algorithm finds a small-norm solution with small residual in $O(N_r + nrlogn + r^3 )$ operations, where $r$ is the numerical rank of $A$ and $N_r$ is the cost of multiplying an $n\times r$ matrix to $A$. 

Joint work with Marcus Webb (Manchester). 

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Our society is witnessing an exponential growth of data being generated. Among the various data types being routinely collected, event logs are available in a wide variety of domains. Despite historical and structural digitalisation challenges, healthcare is an example where the analysis of event logs might bring a new revolution.

In this talk, I will present our recent efforts in analysing and exploring temporal event data sequences extracted from event logs. Our visual analytics approach is able to summarise and seamlessly explore large volumes of complex event data sequences. We are able to easily derive observations and findings that otherwise would have required significant investment of time and effort.  To facilitate the identification of findings, we use a hierarchical clustering approach to cluster sequences according to time and a novel visualisation environment.  To control the level of detail presented to the analyst, we use a hierarchical aggregation tree and an Align-Score-Simplify strategy based on an information score.   To show the benefits of this approach, I will present our results in three real world case studies: CUREd, Outpatient clinics and MIMIC-III. These will respectively cover the analysis of calls and responses of emergency services, the efficiency of operation of two outpatient clinics, and the evolution of patients with atrial fibrillation hospitalised in an acute and critical care unit. To finalise the talk, I will share our most recent work in the analysis of clinical events extracted from Electronic Health Records for the study of multimorbidity.

Natural killer (NK) cells are part of the innate immune system and are capable of killing diseased cells. As a result, NK cells are being used for adoptive cell therapies for cancer patients. The activation of NK cell stimulatory receptors leads to a cascade of intracellular phosphorylation reactions, which activates key signaling species that facilitate the secretion of cytolytic molecules required for cell killing. Strategies that maximize the activation of such intracellular species can increase the likelihood of NK cell killing upon contact with a cancer cell and thereby improve efficacy of NK cell-based therapies. However, NK cell exhaustion, a phenotype characterized by reduced effector functionality, can limit the NK cell’s capacity for cell lysis. Due to the complexity of intracellular signaling, it is difficult to deduce a priori which strategies can enhance species activation.  

To aid in the development of strategies to enhance NK cell activation and limit the NK cell exhaustion, we constructed a mechanistic model of the signaling pathways activated by stimulatory receptors in NK cells. We then extended the model to describe the dynamics of the cytolytic molecules granzyme B (GZMB) and perforin-1 (PRF1). We implemented an information-theoretic approach to perform a global sensitivity analysis and optimal control theory to investigate strategies to enhance intracellular signaling and maximize GZMB and PRF1 secretion. We recently expanded the modeling to investigate the role of NK cell heterogeneity on tumor cell killing. In total, we developed a theoretical framework that provides actionable insight into engineering robust NK cells for clinical applications.