Courses
- ASPApplied Stochastic Processes
- ILAIntroduction to Linear Algebra
- MAEMathematical Analysis for Engineers
- LADLinear Algebra for Data Science
- CIICalculus II
- TAMTopics in Applied Mathematics
- TPTheory of Probability
- DSCDynamical Systems and Chaos
- PMAPrinciples and Methods of Applied Mathematics
- ISBIntroduction to Statistics and Biostatistics
- IODIntroduction to Ordinary Differential Equations
Student Thesis/Dissertation
- A Nonparametric Test for Equality of Distributions
2021
masters - Extension of the Group Invariance Theorem for Perceptrons
2020
bachelors - A Bayesian Approach to Spike Sorting of Neural Data via Source Localization
2018
doctoral - Constraining frisbee tracking methods through Bayesian analysis of flying disc models
2018
bachelors - Monte Carlo Methods for Stochastic Differential Equations and their Applications
2017
doctoral - An Investigation of In-Silico Evolving Networks
2017
bachelors - SYMMETRIZED IMPLICIT SAMPLING FOR PARTLICE FILTER
2016
Bachelors
Grants
- RTG: Applied Mathematics and Statistics for Data-Driven Discovery
Principal Investigator (PI)
2020
$1.7MActive - CDS&E-MSS: Predictive Modeling and Data-Driven Closure of Chaotic and Noisy Dynamics in Discrete Time
Principal Investigator (PI)
2018
$200.0KActive - Computational Nonlinear Dynamics: Variance Reduction Methods and Numerical Studies of Large, Chaotic, and Noisy Systems
Principal Investigator (PI)
2014
$220.0K - Computational Analysis of Large Dynamical Systems
Principal Investigator (PI)
2009
$249.3K
News
- Playing the Odds to Your Favor
2012
Publications (45)
Recent
- A comparison of probe geometries for neuronal localization
2022
- Data-driven model reduction, Wiener projections, and the Mori-Zwanzig formalism
2021
- Conjunctive reward-place coding properties of dorsal distal CA1 hippocampus cells
2020
- Multilevel Monte Carlo for Cortical Circuit Models
2020
- Data assimilation with stochastic reduced models quantifying model error
2018
- Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation
2017
- Symmetrized importance samplers for stochastic differential equations
2017
- Symmetrized Importance Samplers for Uncertainty Quantification and Data Assimilation
2016
- Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems
2016
- Revisiting chaos in stimulus-driven spiking networks: signal encoding and discrimination
2016
- A discrete-time approach to stochastic model reduction for spatiotemporally chaotic systems
2016
- Encoding in balanced networks: revisiting spike patterns and chaos in stimulus-driven systems
2016
- Small‐Noise Analysis and Symmetrization of Implicit Monte Carlo Samplers
2016
- Data-driven stochastic parameterization and dimension reduction in nonlinear dynamics
2016
- Control theory and experimental design in diffusion processes
2014
- Small-noise analysis and symmetrization of implicit Monte Carlo samplers
2014
- A Global Approach to the Identification of Model Noise
2014
- Stimulus-response reliability of biological networks
2013
- Limitations of perturbative techniques in the analysis of rhythms and oscillations
2013
- Chaos and reliability in balanced spiking networks with temporal drive
2013
- Phase-amplitude descriptions of neural oscillator models
2013
- The influence of multiple firing events on the formation and stability of activity patterns in continuous attractor networks
2013
- Spatial scale and place field stability in a grid-to-place cell model of the dorsoventral axis of the hippocampus.
2013
- Modeling temporal networks using random itineraries
2013
- Reliability of Driven Oscillator Networks
2012
- Coding, stability, and non-spatial inputs in a modular grid-to-place cell model
2012
- Dynamics of periodically kicked oscillators
2010
- Nonequilibrium steady states for certain Hamiltonian models
2010
- Reliability of layered neural oscillator networks
2009
- Coupling control variates for Markov chain Monte Carlo
2009
- Ergodicity and energy distributions for some boundary driven integrable Hamiltonian chains
2009
- Reliability of coupled oscillators
2009
- Reliability of coupled oscillators II: Larger networks
2007
- Correlations in nonequilibrium steady states of random halves models
2007
- Reliability of coupled oscillators I: Two-oscillator systems
2007
- Entrainment and chaos in a pulse-driven hodgkin-huxley oscillator
2006
- Propagating coalitions in networks of nonlinear oscillators
2006
- Reliable and unreliable dynamics in driven coupled oscillators
2006
- The Mori-Zwanzig Equation
2005
- Convergence of invariant densities in the small-noise limit
2004
- The Selberg Zeta Function for Convex Co-Compact Schottky Groups
2004
- Random perturbations of SRB measures and numerical studies of chaotic dynamics
2003
- Numerical study of quantum resonances in chaotic scattering
2002
- Quantum resonances in chaotic scattering
2002
- Coordinate-independent computations on differential equations
1997
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