33 citations · 72 across the 20 of their papers we have counts for
22 papers
Random and mean Lyapunov exponents for
Diego Armentano, Gautam Chinta, Siddhartha Sahi +1
We consider orthogonally invariant probability measures on and compare the mean of the logs of the moduli of eigenvalues of the matrices to the Lyapunov…
Cusp Bifurcation in Metastatic Breast Cancer Cells
Brenda Delamonica, Gabor Balazsi, Michael Shub
Ordinary differential equations (ODEs) can model the transition of cell states over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior…
Disease Prediction with a Maximum Entropy Method
Michael Shub, Qing Xu, Xiaohua +1
In this paper, we propose a maximum entropy method for predicting disease risks. It is based on a patient's medical history with diseases coded in ICD-10 which can be used in vario…
Stable and non-symmetric pitchfork bifurcations
Enrique Pujals, Michael Shub, Yun Yang
In this paper, we present a criterion for pitchfork bifurcation of smooth vector fields based on a topological argument. Our result expands Rajapakse and Smale's result \cite{RS2}…
A theory of NP-completeness and ill-conditioning for approximate real computations
Gregorio Malajovich, Mike Shub
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition…
Computing the Homology of Real Projective Sets
Felipe Cucker, Teresa Krick, Michael Shub
We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here numerical means that the algori…