Microtornadoes and Oscillations in Vapor-to-Particle Reaction Zones
DateThursday, March 15, 2018 - 12:30pm
AbstractIn topochemically organized, nanoparticulate experimental systems, vapor diffuses and convects to form spatially defined reaction zones. In these zones, a complex sequence of catalyzed proton-transfer, nucleation, growth, aggregation, hydration, charging processes, and turbulence produce rings, tubes, spirals, pulsing crystals, oscillating fronts and patterns such as Liesegang rings. We call these beautiful 3-dimensional structures “microtornadoes”, “microstalagtites”, and “microhurricanes” and make progress towards understanding the mechanisms of their formation with the aid of mathematical models.
Multilevel Monte Carlo for spiking neuronal networks
DateThursday, March 22, 2018 - 12:30pm
AbstractLarge network dynamics is the main concern in many computational neuroscience studies. A common task in simulating such dynamics is to estimate dynamical statistics like firing rates and correlations elicited by stimuli. These computational tasks are potentially expensive for classical Monte Carlo method. One possible solution is multilevel Monte Carlo method(MLMC). MLMC has been widely used to reduce variance and accelerate estimation for stochastic differential equations. For spiking neuron networks, however, it was unknown whether MLMC would be effective. Our work reveals that the applicability of MLMC heavily relies on the type of dynamics. In this study, we focused on networks of leaky-integrate-and-fire neuron and investigated the utility of MLMC for such networks. By analyzing an associated Fokker-Planck equation and by numerical tests, we found that 1. MLMC is effective for single cells under broad conditions. Thus, by induction, it could be extended to all feed-forward networks. 2. When applying MLMC to randomly-connected recurrent networks, MLMC turns out effective for systems operating in a homogeneous, "mean-field"-like regime in which cells are only weakly correlated. On the contrary, for networks operating in partially-synchronous regimes, the behavior of MLMC is poor, since any small numerical deviation could possibly lead to totally different dynamics of the network.
Trans-disciplinary modeling of mosquito-borne diseases
DateThursday, March 29, 2018 - 12:30pm
AbstractThis talk will focus on a trans-disciplinary approach to the modeling and spread of mosquito-borne diseases. I will first discuss a vector abundance model that takes into account how meteorological data (temperature, precipitation, relative humidity) affect mosquito development and survival, and will describe its calibration for Aedes aegypti mosquitoes against surveillance data in Puerto Rico. Then, I will present a simple nonlinear growth model that is able to capture trends in disease incidence reports at the level of a country, and illustrate its efficacy in predicting the 2014-15 chikungunya epidemic in the Caribbean and the Americas. Time-permitting, I will turn to data describing the spread of chikungunya and Zika in the small island nation of Dominica, and present preliminary work on a network-based approach to understand these phenomena. Throughout the talk, I will emphasize our goal to develop a suite of data-driven models that have predictive ability. I will also take advantage of this presentation to describe our trans-disciplinary team as well as its current and future research directions.