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.
