Georgia Institute of Technology College of Sciences

The complex connectivity structure unique to the brain network is believed to underlie its robust and efficient coding capability. Specifically, neuronal networks at multiple scales utilize their structural complexities to achieve different computational goals. In this talk, I will discuss functional implications that can be inferred from the architecture of brain networks.

The first part of the talk will focus on a generalized problem of linking structure and dynamics of the whole-brain network. By simulating large-scale brain dynamics using a data-driven network of phase oscillators, we show that complexities added to the spatially embedded brain connectome by idiosyncratic long-range connections, enable rapid transitions between local and global synchronizations. In addition to the spatial dependence, I will also discuss hierarchical structure of the brain network. Based on the data-driven layer-specific connectivity patterns, we developed an unsupervised method to find the hierarchical organization of the mouse cortical and thalamic network. The uncovered hierarchy provides insights into the direction of information flow in the mouse brain, which has been less well-defined compared to the primate brain.

Finally, I will discuss computational implications of the hierarchical organization of the brain network. I will focus on a specific type of computation – discrimination of partially occluded objects— carried out by a small cortical circuitry composed of an intermediate visual cortical area V4 and its efferent prefrontal cortex. I will explore how distinct feedforward and feedback signals promote robust encoding of visual stimuli by leveraging predictive coding, a Bayesian inference theory of cortical computation which has been proposed as a method to create efficient neural codes. We implement a predictive coding model of V4 and prefrontal cortex to investigate possible computational roles of feedback signals in the visual system and their potential significance in robust encoding of nosy visual stimuli.

In sum, our results reveal the close link between structural complexity and computational versatility found in brain networks, which may be useful for developing more efficient artificial neural networks and neuromorphic devices.

A major challenge in clinical and biomedical research is on translating in-vitro and in- vivo model findings to humans. Translation success rate of all new compounds going through different clinical trial phases is generally about 10%. (i) This field is challenged by a lack of robust methods that can be used to translate model findings to humans (or interpret preclinical finds to accurately design successful patient regimens), hence providing a platform to evaluate a plethora of agents before they are channeled in clinical trials. Using set theory principles of mapping morphisms, we recently developed a novel translational framework that can faithfully map experimental results to clinical patient results. This talk will demonstrate how this method was used to predict outcomes of anti-TB drug clinical trials. (ii) Translation failure is deeply rooted in the dissimilarities between humans and experimental models used; wide pathogen isolates variation, patient population genetic diversities and geographic heterogeneities. In TB, bacteria phenotypic heterogeneity shapes differential antibiotic susceptibility patterns in patients. This talk will also demonstrate the application of dynamical systems in Systems Biology to model (a) gene regulatory networks and how gene programs influence Mycobacterium tuberculosis bacteria metabolic/phenotypic plasticity. (b) And then illustrate how different bacteria phenotypic subpopulations influence treatment outcomes and the translation of preclinical TB therapeutic regimens. In general, this talk will strongly showcase how mathematical modeling can be used to critically analyze experimental and patient data.

It is anticipated that chaotic regimes (characterized by, e.g., sensitivity with respect to initial conditions and loss of memory) arise in a wide variety of dynamical systems, including those arising from the study of ensembles of gas particles and fluid mechanics. However, in most cases the problem of rigorously verifying asymptotic chaotic regimes is notoriously difficult. For volume-preserving systems (e.g., incompressible fluid flow or Hamiltonian systems), these issues are exemplified by coexistence phenomena: even in quite simple models which should be chaotic, e.g. the Chirikov standard map, completely opposite dynamical regimes (elliptic islands vs. hyperbolic sets) can be tangled together in phase space in a convoluted way.

Recent developments have indicated, however, that verifying chaos is tractable for systems subjected to a small amount of noise— from the perspective of modeling, this is not so unnatural, as the real world is inherently noisy. In this talk, I will discuss two recent results: (1) a large positive Lyapunov exponent for (extremely small) random perturbations of the Chirikov standard map, and (2) a positive Lyapunov exponent for the Lagrangian flow corresponding to various incompressible stochastic fluids models, including stochastic 2D Navier-Stokes and 3D hyperviscous Navier-Stokes on the periodic box. The work in this talk is joint with Jacob Bedrossian, Samuel Punshon-Smith, Jinxin Xue and Lai-Sang Young.