Georgia Institute of Technology College of Sciences

The type VI secretion system (T6SS) is a bacterial subcellular structure that has been likened to a molecular syringe, capable of directly injecting toxins into neighboring cells. Bacteria use T6SS to kill competitor cells, gaining limited space and resources, such as a niche in a host. T6SS has been found in about 25% of Gram negative bacteria, including some human pathogens. Thus, understanding regulation, control, and function of T6SS, as well as the role of T6SS in interbacterial competition, has far-reaching ramifications. However, there are many open questions in this active research area, especially since bacteria have evolved diverse ways in producing and engaging this lethal weapon.

In a multidisciplinary collaboration, we combine experiments and applied mathematics to address a central question about T6SS’s role in interbacterial competition: what is the connection between the subcellular dynamics of T6SS and the competitive strength of the population as a whole? Based on detailed microscopy data, we develop a model on the scale of individual T6SS structures, which is then integrated with an agent-based model (ABM) to enable multi-scale simulations. In this talk, we present the experimental data, the subcellular T6SS model, and findings about T6SS-dependent competitions obtained by simulating the ABM.

Recording link: https://bluejeans.com/s/6fzcqvzTQ5m

Recent research on solving partial differential equations with deep neural networks (DNNs) has demonstrated that spatiotemporal-function approximators defined by auto-differentiation are effective    for approximating nonlinear problems. However, it remains a challenge to resolve discontinuities in nonlinear conservation laws using forward methods with DNNs without beginning with part of the solution. In this study, we incorporate first-order numerical schemes into DNNs to set up the loss function approximator instead of auto-differentiation from traditional deep learning framework such as the TensorFlow package, thereby improving the effectiveness of capturing discontinuities in Riemann problems. We introduce a novel neural network method.  A local low-cost solution is first used as the input of a neural network to predict the high-fidelity solution at a space-time location. The challenge lies in the fact that there is no way to distinguish a smeared discontinuity from a steep smooth solution in the input, thus resulting in “multiple predictions” of the neural network. To overcome the difficulty, two solutions of the conservation laws from a converging sequence, computed from low-cost numerical schemes, and in a local domain of dependence of the space-time location, serve as the input. Despite smeared input solutions, the output provides sharp approximations to solutions containing shocks and contact surfaces, and the method is efficient to use, once trained. It works not only for discontinuities, but also for smooth areas of the solution, implying broader applications for other differential equations.

Suppose that $M$ is a closed isotropic Riemannian manifold and that $R_1,...,R_m$ generate the isometry group of $M$. Let $f_1,...,f_m$ be smooth perturbations of these isometries. We show that the $f_i$ are simultaneously conjugate to isometries if and only if their associated uniform Bernoulli random walk has all Lyapunov exponents zero. This extends a linearization result of Dolgopyat and Krikorian from $S^n$ to real, complex, and quaternionic projective spaces.

We will discuss Akbulut's construction of two smooth, contractible four-manifolds whose boundaries are diffeomorphic and extend to a homeomorphism but not to a diffeomorphism of the manifolds.