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I am a professor of mathematics and public health at the University of Arizona. This site describes my work as a member of an international community of researchers and educators. The menus at the top contain information about me and my professional activities. Some of the blog items below tell professional stories; others summarize information I have collected on important academic issues, or point to interesting work that I have seen in the recent literature. Collectively, the pages in this site illustrate my passion for curiosity-driven research, for elegant applications, and for discovering and sharing knowledge.Show Less
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Courses
- EISExplorations in Integrated Science
- RAOVReal Analysis of One Variable
- FMRWFormal Mathematical Reasoning and Writing
- MMMathematical Modeling
Grants
- RAPID: Networked Data-Driven Modelling of the COVID-19 Outbreak with a Performativity-Aware Calibration Learning Algorithm
Co-Investigator (COI)
2020
$156.4K
Active - DARPA Chikungunya Challenge Prize
Principal Investigator (PI)
2015
$150.0K
Active - The Sixth International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems
Co-Investigator (COI)
2017
$18.0K
- Simulation Modeling of Public Health Interventions on Dengue Vector Abundance: Current and Future Estimations
Key Personnel (KP)
2014
$573.6K
- Intel Math National Training Agency: Revision of the Intel Math Curriculum
Principal Investigator (PI)
2012
$50.0K
- Intel Math National Training Agency
Principal Investigator (PI)
2011
$65.0K
- "New: GK-12" Graduate Students and Teacher Engaging in Mathematical Sciences (G-Teams)
Principal Investigator (PI)
2009
$3.0M
- Proposal to Implement the Intel Math Program in the United States
Principal Investigator (PI)
2009
$182.4K
Technologies / Patents
News
- 6 From UA Recognized in New Class of Fellows by AAAS
2017
- Students Use CyVerse to Help Predict Mosquito-Borne Diseases
2017
- 2 From UA Solve Public Health Issue, Win Competition
2015
- UA Program Working to Improve Math Instruction, Learning
2009
Publications (61)
Recent
- Multiple Scale Asymptotics of Map Enumeration
2023
- Epidemics from the Eye of the Pathogen
2022
- Dynamics of Non-polar Solutions to the Discrete Painlevé I Equation
2022
- Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States
2022
- The United States COVID-19 Forecast Hub dataset
2022
- Non-recursive Counts of Graphs on Surfaces
2022
- Aedes-AI: Neural network models of mosquito abundance
2021
- Parameter Estimation from ICC curves
2021
- A 70% Reduction in Mosquito Populations Does Not Require Removal of 70% of Mosquitoes
2020
- Collaborative efforts to forecast seasonal influenza in the United States, 2015–2016
2019
- A new gravity model for spatial interaction
2019
- On collisions times of `self-sorting' interacting particles in one-dimension with random initial positions and velocities
2018
- The Phase Structure of Grain Boundaries
2018
- Summary Results of the 2014-2015 DARPA Chikungunya Challenge
2018
- Effect of temperature thresholds on modeled Aedes aegypti population dynamics
2017
- Aedes aegypti (Diptera: Culicidae) abundance model improved with relative humidity and precipitation-driven egg hatching
2017
- Data-driven outbreak forecasting with a simple nonlinear growth model
2016
- Capillary induced deformations of a thin elastic sheet
2016
- Two-dimensional capillary origami
2016
- Two-dimensional capillary origami with pinned contact line
2015
- Projection of Climate Change Influences on U.S. West Nile Virus Vectors
2015
- Regularized Model of Post-Touchdown Configurations in Electrostatic MEMS: Interface Dynamics
2015
- Explorations in integrated science
2014
- Regularized model of post-touchdown configurations in electrostatic MEMS: Equilibrium analysis
2014
- Erratum: Collective behaviors in two-dimensional systems of interacting particles (SIAM Journal on Applied Dynamical Systems (2011) 10 (1213-1231))
2013
- Effect of disjoining pressure in a thin film equation with non-uniform forcing
2013
- The quenching set of a MEMS capacitor in two-dimensional geometries
2013
- Multiple quenching solutions of a fourth order parabolic PDE with a singular nonlinearity modeling a mems capacitor
2012
- Collective behaviors in two-dimensional systems of interacting particles
2011
- Reduced models for the pacemaker dynamics of cardiac cells
2011
- Instability of local deformations of an elastic rod: Numerical evaluation of the evans function
2011
- Reverse draining of a magnetic soap film - Analysis and simulation of a thin film equation with non-uniform forcing
2009
- Hydrodynamics of bacterial colonies
2007
- Spectral stability of local deformations of an elastic rod: Hamiltonian formalism
2005
- Hydrodynamics of bacterial colonies: Phase diagrams
2004
- Inverse cascade and energy transfer in forced low-Reynolds number two-dimensional turbulence
2004
- Hydrodynamics of bacterial colonies: A model
2003
- Instability of local deformations of an elastic rod
2003
- Traveling hole solutions of the complex Ginzburg-Landau equation: A review
2001
- Pulses, fronts and oscillations of an elastic rod
1999
- Control-parameter-dependent Swift-Hohenberg equation as a model for bioconvection patterns
1999
- A complex pattern of traveling stripes is produced by swimming cells of Bacillus subtilis
1998
- Pulses of tunable size near a subcritical bifurcation
1998
- Traveling hole solutions to the complex Ginzburg-Landau equation as perturbations of nonlinear Schrödinger dark solitons
1997
- Loss-induced transverse effects in lasers
1997
- Controlling optical turbulence
1997
- Measuring disorder with correlation functions of averaged patterns
1996
- Temporal forcing of traveling wave patterns
1996
- Travelling wave patterns in lasers with curved mirrors
1996
- Correlation functions in the presence of optical vortices
1994
- Spatio-temporal intermittency in a 1D convective pattern: Theoretical model and experiments
1992
- Localized phase jumps in wave trains
1992
- Dynamics of Bloch Walls in a Rotating Magnetic Field: A Model
1991
- Statistical properties of defect-mediated turbulence
1990
- Breaking chirality in nonequilibrium systems
1990
- Defects in Roll-Hexagon competition
1990
- Defect-mediated turbulence
1989
- Une forme de turbulence associ eacute;e aux d eacute;fauts topologiques
1989
- A form of turbulence associated with defects
1989
- Defect-mediated turbulence in wave patterns
1988
- Topological defects of wave patterns
1987