The Hardy-Littlewood generalised twin prime conjecture states an asymptotic formula for the number of primes $p\le X$ such that $p+h$ is prime for any non-zero even integer $h$. While this conjecture remains wide open, Matom\"{a}ki, Radziwi{\l}{\l} and Tao proved that it holds on average over $h$, improving on a previous result of Mikawa. In this talk we will discuss an almost prime analogue of the Hardy-Littlewood conjecture for which we can go beyond what is known for primes. We will describe some recent work in which we prove an asymptotic formula for the number of almost primes $n=p_1p_2 \le X$ such that $n+h$ has exactly two prime factors which holds for a very short average over $h$.

Over the past decades, the morbidity and mortality associated with cardiovascular disease have reduced due to advancements in patient care. However, cardiovascular disease remains the world’s leading cause of death, and the prevalence of myocardial pathologies remains significant. Continued advancements in diagnostics and therapeutics are needed to further drive down the social and economic burden of cardiac disease in both developed and developing countries. 

Routine clinical evaluation of patients with cardiovascular disease includes non-invasive imaging, such as echocardiography (echo), cardiac magnetic resonance imaging (MRI), and/or CT, and where appropriate, invasive investigation with cardiac catheterisation However, little clinical information is available regarding the linkage between structural and function remodelling of the heart and the intrinsic biomechanical properties of heart muscle which cannot be measured in patients with cardiovascular diseases. 

The lack of detailed mechanistic understanding about the change in biomechanical properties of heart muscle may play a significant role in non-specific diagnosis and patient management. Bioengineering approaches, such as computational modelling tools, provide the perfect platform to analyze a wealth of clinical data of individual patients in an objective and consistent manner to augment and enrich existing personalized clinical diagnoses and precise treatment planning by building 3D computational model of the patient's heart. 

In my presentation, I will present my research efforts in 1) developing integrative 3D computational modeling platform to enable model-based analysis of medical images of the heart; 2) studying the biomechanical mechanisms underpinning various forms of heart failure using pre-clinica experimental data; 3) applying personalized modeling pipeline to clinical heart failure patient data to non-invasively estimate mechanical properties of the heart muscle on a patient-specific basis; 4) performing in silico simulation of cardiac surgical procedures to evaluate efficacy of mitral clip in treating ischemic mitral regurgitation. 

My presentation aims to showcase the power of combining computational modeling and bioengineering technologies with medical imaging to enrich and enhance precision and personalized medicine. 

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.