Georgia Institute of Technology College of Sciences

One of the most challenging aspects of designing human sensitive systems is in designing systems that assist decision makers in applying an effective intervention to a large group of individuals. This design challenge becomes especially difficult when the decision maker must operate under scarce resources and only partial knowledge of how each individual will react to the intervention.

In this talk, I will consider this problem from the perspective of a clinician that is designing a personalized weight loss program. Despite this focus, the precision analytics framework I propose for designing these interventions is quite general and can apply to many settings where a single coordinator must influence agents who make decisions by maximizing utility functions that depend on prior system states, inputs, and other parameters that are initially unknown. This precision analytics framework involves three steps: first, a predictive model that effectively captures the decision-making process of an agent; second, an optimization algorithm to estimate this model’s parameters for each agent and predict their future decisions; and third, an optimization model that uses these predictions to optimize a set of incentives that will be provided to each agent. A key advantage of this framework is that the calculated incentives are adapted as new information is collected. In the case of personalized weight loss interventions, this means that the framework can leverage patient level data from mobile and wearable sensors over the course of the intervention to personalize the recommended treatment for each individual.

  I will present theoretical results that show that the incentives computed by this approach are asymptotically optimal with respect to a loss function that describes the coordinator's objective.  I will also present an effective decomposition scheme to optimize the agent incentives, where each sub-problem solves the coordinator's problem for a single agent, and the master problem is a pure integer program. To validate this method I will present a numerical study that shows this proposed framework is more cost efficient and clinically effective than simple heuristics in a simulated environment. I will conclude by discussing the results of a randomized control trial (RCT) and pilot study where this precision analytics framework was applied for personalizing exercise goals for UC Berkeley staff and students. The results of these trials show that using personalized step goals calculated by the precision analytics algorithm result in a significant improvement over existing state of the art approaches in a real world setting.

The Liouville equation is a semi-linear elliptic equation of exponential non-linearity. Its non-local version is a steady state of the Keller-Segel equation representing the distribution of living cells, such as slime molds. I will represent an extension of this equation to multi-agent systems and discuss some associated critical phenomena, and recent results with Debabrata Karmakar on the parabolic Keller segel system and its asymptotics in both critical and non-critical cases.

Adaptive control problems arise in many engineering applications in which one needs to design feedback controllers that ensure tracking of desired reference trajectories while at the same time identify unknown parameters such as control gains. This talk will summarize the speaker's work on adaptive tracking and parameter identification, including an application to curve tracking problems in robotics. The talk will be understandable to those familiar with the basic theory of ordinary differential equations. No prerequisite background in systems and control will be needed to understand and appreciate this talk.

An afternoon of public engagement of mathematics through puzzles, games, and the arts, including:  magic (by Matt Baker), juggling and other circus arts, music, dance, an art gallery, and a live construction of a Fibonacci-based sculpture (by Akio Hizume).  It is free and open to the public, but our partner the Julia Robinson Mathematics Festival recommends registering at https://jrmf.org/event-details/mathapalooza .  If you want to get involved, please contact Evans Harrell directly.