L3

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.

In this talk, I will argue how the observation that four-dimensional N=2 superconformal field theories are interconnected via the operation of Higgsing can be turned into an effective method to construct such SCFTs. A fundamental role is played by the (generalized) free field realization of the associated VOAs.

We present a simple algorithm that successfully re-constructs a sine wave, sampled vastly below the Nyquist rate, but with sampling time intervals having small random perturbations. We show how the fact that it works is just common sense, but then go on to discuss how the procedure relates to Compressed Sensing. It is not exactly Compressed Sensing as traditionally stated because the sampling transformation is not linear.  Some published results do exist that cover non-linear sampling transformations, but we would like a better understanding as to what extent the relevant CS properties (of reconstruction up to probability) are known in certain relatively simple but non-linear cases that could be relevant to industrial applications.

I will describe work exploring the spectrum of two-dimensional unitary conformal field theories(CFT) with no extended chiral algebra and central charge larger than one. I will revisit a classical result from analytic number theory by Rademacher, which provides an exact formula for the Fourier coefficients of modular forms of non-positive weight. Generalizing this, I will explain how we employed Rademacher's idea to study the spectral density of two-dimensional CFT of our interest. The expression is given in terms of a Rademacher expansion, which converges for nonzero spin. The implications of our spectral density to the pure gravity in AdS3 will be discussed.

String sigma-models relevant in the AdS/CFT correspondence are highly non-trivial two-dimensional field theories for which predictions at finite coupling exist, assuming integrability and/or the duality itself.  I will discuss general features of the perturbative approach to these models, and present progress on how to go extract finite coupling information in the most possibly general way, namely via the use of lattice field theory techniques. I will also present new results on certain ``defect-CFT’' correlators  at strong coupling.