Title: TBA
Abstract: TBA

Title: Control of a consumer-resource agent-based model using partial differential equation approximation
Abstract: Agent-based models (ABMs) are increasing in popularity as tools to simulate and explore many biological systems. Successes in simulation lead to deeper investigations, from designing systems to optimizing performance. The typically stochastic, rule-based structure of ABMs, however, does not lend itself to analytic and numerical techniques of optimization the way traditional dynamical systems models do. The goal of this work is to illustrate a technique for approximating ABMs with a partial differential equation (PDE) system to design some management strategies on the ABM. We propose a surrogate modeling approach, using differential equations that admit direct means of determining optimal controls, with a particular focus on environmental heterogeneity in the ABM. We implement this program with both PDE and ordinary differential equation (ODE) approximations on the well-known rabbits and grass ABM, in which a pest population consumes a resource. The control problem addressed is the reduction of this pest population through an optimal control formulation. After fitting the ODE and PDE models to ABM simulation data in the absence of control, we compute optimal controls using the ODE and PDE models, which we them apply to the ABM. The results show promise for approximating ABMs with differential equations in this context.

Title: Accurate angular integration with only a handful of neurons
Abstract: To flexibly navigate, many animals rely on neural activity that tracks the animal’s movements relative to its surroundings. In mammals, this signal is carried by large populations of cells (N ~ O(10^4) – O(10^6)) that maintain a persistent internal representation of the animal’s head direction when standing still and accurately integrate the animal’s angular velocity when turning. Such neural dynamics can be realized by ring attractor networks: a class of networks that generate a continuum of marginally stable states along a ring-like manifold. Although there are many variants of ring attractor networks, they all rely on large numbers of neurons as the ring attractor solution emerges in the limit as network size becomes infinite. Surprisingly, in the fruit fly, Drosophila Melanogaster, a head direction representation is maintained by a much smaller number of neurons whose dynamics and connectivity resemble those of a ring attractor network. These findings challenge our understanding of ring attractors and their putative implementation in neural circuits. Here, we analyze the ability of small systems to integrate an angular velocity input using threshold linear networks (though simulations suggest our results hold for more general nonlinear systems as well). We construct an energy function to determine the system’s encoding ability in the absence of input and find that certain parameterizations lead to perfect encodings (i.e., ring attractors) and hence perfect integration as well. Such optimal parameterizations correspond to singularities in the above threshold subsystems, suggesting that ring attractors emerge in small systems as a discrete set of line attractors “stitched together”. We then analyze the network dynamics away from these optimal parameterizations and calculate the rate at which the system’s ability to integrate accurately degrades. This work shows how even small networks can accurately track an animal’s movements to guide navigation, and it informs our understanding of the functional capabilities of discrete systems more broadly.