159 citations · 234 across the 10 of their papers we have counts for
14 papers
Robustness of solutions of almost every system of equations
Sana Jahedi, Timothy Sauer, James A. Yorke
In mathematical modeling, it is common to have an equation where the exact form of is not known. This article shows that there are large classes of where almost al…
A Generalized Unscented Transformation for Probability Distributions
Donald Ebeigbe, Tyrus Berry, Michael M. Norton +4
The unscented transform uses a weighted set of samples called sigma points to propagate the means and covariances of nonlinear transformations of random variables. However, unscent…
A Poisson Kalman filter for disease surveillance
Donald Ebeigbe, Tyrus Berry, Steven J. Schiff +1
An optimal filter for Poisson observations is developed as a variant of the traditional Kalman filter. Poisson distributions are characteristic of infectious diseases, which model…
Limits on reconstruction of dynamical networks
Jiajing Guan, Tyrus Berry, Timothy Sauer
An observability condition number is defined for physical systems modeled by network dynamics. Assuming the dynamical equations of the network are known and a noisy trajectory is o…
Correcting Observation Model Error in Data Assimilation
Franz Hamilton, Tyrus Berry, Timothy Sauer
Standard methods of data assimilation assume prior knowledge of a model that describes the system dynamics and an observation function that maps the model state to a predicted outp…
Changes in Ugandan Climate Rainfall at the Village and Forest Level
Paddy Ssentongo, Abraham J. B. Muwanguzi, Uri Eden +7
In 2013, the US National Oceanographic and Atmospheric Agency refined the historical rainfall estimates over the African Continent and produced the African Rainfall Climate version…
Kalman-Takens filtering in the presence of dynamical noise
Franz Hamilton, Tyrus Berry, Timothy Sauer
The use of data assimilation for the merging of observed data with dynamical models is becoming standard in modern physics. If a parametric model is known, methods such as Kalman f…
Consistent Manifold Representation for Topological Data Analysis
Tyrus Berry, Timothy Sauer
For data sampled from an arbitrary density on a manifold embedded in Euclidean space, the Continuous k-Nearest Neighbors (CkNN) graph construction is introduced. It is shown that C…
Density Estimation on Manifolds with Boundary
Tyrus Berry, Timothy Sauer
Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant…
Local Kernels and the Geometric Structure of Data
Tyrus Berry, Timothy Sauer
We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local ke…
Observability and Controllability of Nonlinear Networks: The Role of Symmetry
Andrew J. Whalen, Sean N. Brennan, Timothy D. Sauer +1
Observability and controllability are essential concepts to the design of predictive observer models and feedback controllers of networked systems. For example, noncontrollable mat…
Convergence of Periodically-Forced Rank-Type Equations
Tyrus Berry, Timothy Sauer
Consider a difference equation which takes the k-th largest output of m functions of the previous m terms of the sequence. If the functions are also allowed to change periodically…
Functional dissipation microarrays for classification
D. Napoletani, D. C. Struppa, T. Sauer +3
In this article, we describe a new method of extracting information from signals, called functional dissipation, that proves to be very effective for enhancing classification of hi…
Prevalence: an addendum
Brian R. Hunt, Tim Sauer, James A. Yorke
The authors mention work of Christensen, Mycielski, Tsujii, and others which is closely related to a survey article by the first author [math.FA/9210220].