Catheter ablation and antiarrhythmic drug therapy approaches for treatment of atrial fibrillation are sub-optimal. This is in part because it is challenging to predict long-term response to therapy from short-term measurements, which makes it difficult to select optimal patient-specific treatment approaches. Clinical trials identify patient demographics that provide prediction of long-term response to standard treatments across populations. Patient-specific biophysical models can be used to assess novel treatment approaches but are typically applied in small cohorts to investigate the acute response to therapies. Our overall aim is to use machine learning approaches together with patient-specific biophysical simulations to predict long-term atrial fibrillation recurrence after ablation or drug therapy in large populations.

In this talk I will present our methodology for constructing personalised atrial models from patient imaging and electrical data; present results from biophysical simulations of ablation treatment; and finally explain how we are combining these methodologies with machine learning techniques for predicting long-term treatment outcomes.

In this talk, I will give an overview of our multi-scale models that we have developed to study a number of aspects of the immune response to infection.  Scales that we explore range from molecular to the whole-host scale.  We are also able to study virtual populations and perform simulated clinical trials. We apply these approaches to study Tuberculosis, the disease caused by inhalation of the bacteria, Mycobacterium tuberculosis. It has infected 2 billion people in the world today, and kills 1-2 million people each year, even more than COVID-19. Our goal is to aid in understanding infection dynamics, treatment and vaccines to improve outcomes for this global health burden. I will discuss our frameworks for multi-scale modeling, and the analysis tools and statistical approaches that we have honed to better understand different outcomes at different scales.

This presentation will focus on the role of mathematical modelling and predictive toxicology in the safety assessment of chemicals and consumer products. The starting point will be regulatory assessment of chemicals based on their potential for harming human health or the environment. This will set the scene for describing current practices in the development and application of mathematical and computational models. A wide variety of methodological approaches are employed, ranging from relatively simple statistical models to more advanced machine learning approaches. The modelling context also ranges from discovering the underlying mechanisms of chemical toxicity to the safe and sustainable design of chemical products. The main modelling approaches will be reviewed, along with the challenges and opportunities associated with their use.  The presentation will conclude by identifying current research needs, including progress towards a Unified Theory of Chemical Toxicology.

Many scientific questions in biology can be formulated as a direct problem:

given a biochemical system, can one deduce some of its properties? 

For example, one might be interested in deducing equilibria of a given intracellular network.  On the other hand, one might instead be interested in designing an intracellular network with specified equilibria. Such scientific tasks take the form of inverse problems:
given a property, can one design a biochemical system that displays this property? 

Given a biochemical system, can one embed additional molecular species and reactions into the original system to control some of its properties?
These questions are at the heart of the emerging field of synthetic biology, where it has recently become possible to systematically realize dynamical systems using molecules.  Furthermore, addressing these questions for man-made synthetic systems may also shed light on how evolution has overcome similar challenges for natural systems.  In this talk, I will focus on the inverse problems, and outline some of the results and challenges which are important when biochemical systems are designed and controlled.

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.

Actin filaments are polymers that interact with myosin motor
proteins and play important roles in cell motility, shape, and
development. Depending on its function, this dynamic network of
interacting proteins reshapes and organizes in a variety of structures,
including bundles, clusters, and contractile rings. Motivated by
observations from the reproductive system of the roundworm C. elegans,
we use an agent-based modeling framework to simulate interactions
between actin filaments and myosin motor proteins inside cells. We also
develop tools based on topological data analysis to understand
time-series data extracted from these filament network interactions. We
use these tools to compare the filament organization resulting from
myosin motors with different properties. We have also recently studied
how myosin motor regulation may regulate actin network architectures
during cell cycle progression. This work also raises questions about how
to assess the significance of topological features in common topological
summary visualizations.
 

It is a well-known fact that Boolean rings, those rings in which $x^2 = x$ for all $x$, are necessarily commutative. There is a short and completely elementary proof of this. One may wonder what the situation is for rings in which $x^n = x$ for all $x$, where $n > 2$ is some positive integer. Jacobson and Herstein proved a very general theorem regarding these rings, and the proof follows a widely applicable strategy that can often be used to reduce questions about general rings to more manageable ones. We discuss this strategy, but will also focus on a different approach: can we also find ''elementary'' proofs of some special cases of the theorem? We treat a number of these explicit computations, among which a few new results.

Although a multidimensional data array can be very large, it may contain coherence patterns much smaller in size. For example, we may need to detect a subset of genes that co-express under a subset of conditions. In this presentation, we discuss our recently developed co-clustering algorithms for the extraction and analysis of coherent patterns in big datasets. In our method, a co-cluster, corresponding to a coherent pattern, is represented as a low-rank tensor and it can be detected from the intersection of hyperplanes in a high dimensional data space. Our method has been used successfully for DNA and protein data analysis, disease diagnosis, drug therapeutic effect assessment, and feature selection in human facial expression classification. Our method can also be useful for many other real-world data mining, image processing and pattern recognition applications.