Biomedical research and clinical practice rely on complex and multimodality

datasets for the characterisation of human organs in health and disease. In

computational biomedicine, we often argue that multiscale computational

models are and will be increasingly required as tools for data integration,

for probing the established knowledge of physiological systems, and for

predictions of the effects of therapies and disease. But what has

computational biomedicine delivered so far? This presentation will describe

successes, failures and future directions of computational models in

cardiac research from basic to translational science.

All data intelligence processes are designed for processing a finite amount of data within a time period. In practice, they all encounter
some difficulties, such as the lack of adequate techniques for extracting meaningful information from raw data; incomplete, incorrect 
or noisy data; biases encoded in computer algorithms or biases of human analysts; lack of computational resources or human resources; urgency in 
making a decision; and so on. While there is a great enthusiasm to develop automated data intelligence processes, it is also known that
many of such processes may suffer from the phenomenon of data processing inequality, which places a fundamental doubt on the credibility of these 
processes. In this talk, the speaker will discuss the recent development of an information-theoretic measure (by Chen and Golan) for optimizing 
the cost-benefit ratio of a data intelligence process, and will illustrate its applicability using examples of data analysis and 
visualization processes including some in bioinformatics.

The management of natural resources, from fisheries and climate change to gut bacteria colonies, all require the development of ecological models that represent the full spectrum of population interactions, from competition, through mixotrophy and mutualism, to predation.

Mixotrophic plankton, that both photosynthesise and eat other plankton, underpin all marine food webs and help regulate climate by facilitating gas exchange between the ocean and atmosphere. We show the recent discovery that their feeding preferences change with increasing temperature implies climate change could dramatically alter the structure of marine food webs.

We describe a theoretical framework that reveals the key role of mixotrophy in facilitating transitions between trophic interactions. Mixotrophy smoothly and stably links competition to predation, and extends this linkage to include mutualism in both facultative and obligate forms. Such smooth stable transitions further allow the development of eco-evolutionary theory at the population level through quantitative trait modelling.

Gauss invented Gaussian quadrature following an approach entirely different from the one we now find in textbooks. I will describe leisurely the contents of Gauss's original memoir on quadrature, an impressive piece of mathematics, based on continued fractions, Padé approximation, generating functions, the hypergeometric series and more.

The talk will describe accelerated algorithms for computing full or partial matrix factorizations such as the eigenvalue decomposition, the QR factorization, etc. The key technical novelty is the use of  randomized projections to reduce the effective dimensionality of  intermediate steps in the computation. The resulting algorithms execute faster on modern hardware than traditional algorithms, and are particularly well suited for processing very large data sets.

The algorithms described are supported by a rigorous mathematical analysis that exploits recent work in random matrix theory. The talk will briefly review some representative theoretical results.

Abstract: We study nonuniform sampling in shift-invariant spaces whose generator is a totally positive function. For a subclass of such generators the sampling theorems can be formulated in analogy to the theorems of Beurling and Landau for bandlimited functions. These results are  optimal and validate  the  heuristic reasonings in the engineering literature. In contrast to the cardinal series, the reconstruction procedures for sampling in a shift-invariant space with a totally positive generator  are local and thus accessible to numerical linear algebra.

A subtle  connection between sampling in shift-invariant spaces and the theory of Gabor frames leads to new and optimal  results for Gabor frames.  We show that the set of phase-space shifts of  $g$ (totally positive with a Gaussian part) with respect to a rectangular lattice forms a frame, if and only if the density of the lattice  is strictly larger than 1. This solves an open problem going backto Daubechies in 1990 for the class of totally positive functions of Gaussian type.
 

Almost all real-world applications involve a degree of uncertainty. This may be the result of noisy measurements, restrictions on observability, or simply unforeseen events. Since many models in both engineering and the natural sciences make use of partial differential equations (PDEs), it is natural to consider PDEs with random inputs. In this context, passing from modelling and simulation to optimization or control results in stochastic PDE-constrained optimization problems. This leads to a number of theoretical, algorithmic, and numerical challenges.

 From a mathematical standpoint, the solution of the underlying PDE is a random field, which in turn makes the quantity of interest or the objective function an implicitly defined random variable. In order to minimize this distributed objective, one can use, e.g., stochastic order constraints, a distributionally robust approach, or risk measures. In this talk, we will make use of risk measures.

After motivating the approach via a model for the mitigation of an airborne pollutant, we build up an analytical framework and introduce some useful risk measures. This allows us to prove the existence of solutions and derive optimality conditions. We then present several approximation schemes for handling non-smooth risk measures in order to leverage existing numerical methods from PDE-constrained optimization. Finally, we discuss solutions techniques and illustrate our results with numerical examples.