##### KMap

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 - Modeling inhibition-mediated neural dynamics in the rodent spatial navigation system
2014

doctoral

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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