Sunday, July 24, 2016
We consider the application of Koopman theory to nonlinear partial differential equations
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Wednesday, July 6, 2016
Given a network, we would like to determine which subset of nodes should be measured by limited sensing facilities to maximize information about the entire network.
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Friday, May 13, 2016
A stochastic collocation method coupled with an analytical expansion of the canonical epidemiological master equation is used to analyze the effects of both extrinsic and intrinsic noise.
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Thursday, March 31, 2016
A novel method is presented to compute the exit time for the stochastic simulation alogrithm. The method is based on the addition of random variables and is derived using the convolution theorem.
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Thursday, January 28, 2016
This publication examines new stochastic simulations of a prototypical infection on the dense, highly-connected United States air travel network.
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Tuesday, January 26, 2016
This publication explores a new method, called Dynamic Mode Decomposition with control (DMDc), which extends DMD to incorporate the effect of inputs and control.
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Saturday, January 16, 2016
We explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. ​
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Sunday, October 11, 2015
Koopman spectral analysis provides an operator-theoretic perspective to dynamical systems rather than the more standard geometric and probabilistic perspectives.
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Friday, September 11, 2015
Extracting physical laws from data is a central challenge in many diverse areas of science and engineering.
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Sunday, March 1, 2015
The development and application of quantitative methods to understand disease dynamics and plan interventions is becoming increasingly important in the push toward eradication of human infectious dise
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