PHCpack is a software package for Polynomial Homotopy Continuation to numerically solve polynomial systems. In the past five years, the package has been extended with tools to compute a numerical irreducible decomposition. Other features include deflation for isolated singularities and an equation-by-equation solver.Most recently, PHCpack has be...
Creator:
Verschelde, Jan (University of Illinois, Chicago)
Created:
2006-10-24
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The edge-triangle exponential random graph model has been a topic of continued research interest. We review recent developments in the study of this classic model and concentrate on the phenomenon of phase transitions. We first describe the asymptotic feature of the model along general straight lines. We show that as we continuously vary the slo...
Creator:
Yin, Mei (Brown University)
Created:
2014-04-28
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The study of phase transitions in random graphs was initiated by Erdos and Renyi in 1960. They proved among other things that a uniform random graph undergoes a drastic change in the size and structure of the largest component, caused by altering a critical edge density. Since the seminal work of Erdos and Renyi, various random graph models have...
Creator:
Kang, Mihyun (Technische Universität Graz)
Created:
2014-09-12
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In manifold learning, one wishes to infer geometric and topological features of an unknown manifold, embedded in a d-dimensional Euclidean space, from a finite (random) point cloud. One topological invariant of a considerable interest is the homology of the underlying space. A common method for recovering the homology of a manifold from a set of...
Creator:
Bobrowski, Omer (Duke University)
Created:
2013-10-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We study generic properties of high-dimensional quantum states. Specifically, for a random state on H=C^d otimes C^d obtained by partial tracing a random pure state on H otimes C^s, we consider the problem whether it is typically separable or typically entangled. We show that a threshold occurs when the ancilla dimension s is of order roughly d^...
Created:
2011-09-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Non-convex heuristics have been used to solve phase retrieval problems for decades, but only recently have convergence guarantees been obtained for some non-convex algorithms, mostly in the case where the sensing vectors are random. Algorithms for which such guarantees were established typically have a particular form: they consist in finding a ...
Creator:
Waldspurger, Irene (Université Paris-Dauphine)
Created:
2017-08-15
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk we analyze the topology of critical points of systems of polynomial equations, and bifurcation diagrams of parametric systems. In particular, in the case of the phase retrieval problem, the analysis of systems of cubic multivariate polynomial equations produces a homotopy/continuation method that numerically achieves the Cramer-Rao ...
Creator:
Balan, Radu V. (University of Maryland)
Created:
2017-08-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
