- Challenges: Stress reduction, emotion regulation, attention (ADHD), mood disorders (depression, bipolar illness).
- Mathematics/computational: Mathematical modeling of mood disorders, emotion regulation, mindfulness, attention; computational analysis, model validation, evolutionary analysis. Feedback control and optimization methods. Stability analysis.
- Sensors: EEG and heart rate variability (HRV) signals.
- Actuators: Auto-generation of music and video.
- Technology goals: Apps/web sites, psychoeducation and bio-signal driven virtual reality treatments.
- Financial: Financial advisors for low-income people. View as a feedback control problem, use methods of PID, model-predictive, and adaptive control. Interested in implementations in apps or cell phones.
- Environmental: Modeling and analysis of the tragedy of the commons, environmental policy, and sustainability.
- Social Justice: Modeling and analysis of wealth distribution policies based on ideas from social justice. Modeling and analysis of democracy.
- Poverty Traps: Modeling and analysis, economic models, sensitivity analysis, optimization methods for allocation decisions, impact of technology diffusion, breaking poverty traps.
- Participation: Models and analysis, cooperation perspective.
- Cooperative Management of Community Technology: control and optimization approaches, implementation.
- Sustainable Community Development: Models, measures of development, computational analysis of the impact of technology on development.
Overview of Some Past Research
(some relevant to the above research)
Distributed control, decision-making, and optimization...
- Research Topics: Much past work focusds on the impact of local agent sensing/decision making, dynamical agent interactions/communications, and resulting group-level dynamics and behavior (and hence falls under the area of "biocomplexity" and "complex systems" across multiple spatio-temporal scales). The work lies in the general areas of intelligent and multiagent systems and draws heavily from (Lyapunov) stability analysis of complex systems, (distributed) optimization theory, and game theory (conventional and evolutionary). Since in many cases the focus is on distributed and networked systems, the theory of parallel and distributed algorithms/computing is used. Specific areas include:
- Swarms and coordinated motion (or cognitive variables) of multiagent systems: The main focus is on mathematical modeling and stability analysis of how individual sensing and movement decisions create emergent group motion in three (or higher) dimensional space (e.g., group cohesion/dispersal properties characterized as an invariant set). "Motion" can mean the change of cognitive variables (as in distibuted agreement) as opposed to physical motion. Study the impact of agent dynamics, external objectives (e.g., simultaneous foraging or task completion activities), continuous and discrete-time formulations (ODEs, difference equations, and asynchronous distributed discrete event system models), sensing noise, and information flow constraints (e.g., delays in sensing and sensing network topology constraints). Applications studied include swarms of honey bees, Apis mellifera (including experimental work with T. Seeley, a biologist at Cornell Univ.), groups of air/ground vehicles, and bacterial chemotaxis. Now, interested in applications to human group dynamics and decision making.
- Solitary and social foraging: (i) Solitary agents: Classical prey and patch models including predation, speed, sensor imperfections, and risk-sensitive aspects. Applications studied include autonomous vehicle decision-making system design (foraging for tasks) and distributed temperature control (foraging for temperature error). Irrational choice and the state-predation trade-off with applications to gray jays, Persoreus Canadenis (with experimental work done by my collaborator T. Waite, a biologist). (ii) Social agents: (a) modeling and analysis of honey bee social foraging (with experimental work done by my collaborator T. Seeley at Cornell); (b) social foraging theory (e.g., via evolutionary game theory) for cooperate/no-cooperate decisions, group size design, and heterogenous agent mix design for multiagent systems. Applications studied include multizone temperature control, and cooperative control for multiple autonomous air vehicles. Now, interested in applications in human individuals/groups.
- Cooperative task scheduling and resource allocation: Modeling and analysis of strategies for distributed and networked agents performing scheduling, resource allocation, load balancing, and task assignment (several approaches extend methods from parallel and distributed computing), with the special challenges presented by the need for mobile agents (task processors) to process spatially-distributed tasks. Cooperative task processing networks and the automatic tuning of cooperation parameters (willingness to volunteer) to achieve a Nash equilibrium. Multiagent task choice/allocation/scheduling problems with mathematical analysis of emergent agent spatial distributions (e.g., "ideal free distributions") and applications have been studied for honey bee social foraging, groups of autonomous vehicles, and multizone temperature control. Impact of delays and information flow constraints has been considered (e.g., via a computer network). Now, interested in evolution of complex task networks (including topology) in biology, particularly for human individuals/groups.
- Cooperative choice and "swarm cognition": Mathematical modeling and analysis of the speed vs. accuracy trade-off in the distributed (and low information flow) decision-making (choice) process with application to nest site selection by honey bees (with experimental work done by my collaborator T. Seeley at Cornell Univ.). Relationships to neurobiological cognition for choice processes, and psychological tests, especially mathematical models and analysis for such systems. Now, interested in mathematical modeling and analysis of stochastic biological/technological group choice processes, with interest in human individual/group decision making.
- Experimental research: (i) Experimental biomimicry projects: Biomimicry of solitary and social foraging for multizone temperature control (temperature error distribution is analogous to nutrient distribution), distributed attentional systems (electromechanical arcade), distributed sychronization (mimic fire flies); and (ii) Experimental engineering projects: Multizone temperature control over a network, distributed control for smart lights, distributed dynamic resource allocation (for temperature, balls in tubes), cooperative control (electromechanical arcade). See our Distributed Dynamical Systems Laboratory for more information.
Now, interested in mobile devices/apps and web-based programs for humans and human groups.
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