scholarly journals Random aspects of high-dimensional convex bodies

2000 ◽  
pp. 169-190 ◽  
Author(s):  
A. E. Litvak ◽  
N. Tomczak-Jaegermann
Keyword(s):  
Convex Bodies ◽  
High Dimensional

scholarly journals High dimensional random sections of isotropic convex bodies

2010 ◽  
Vol 361 (2) ◽  
pp. 431-439
Author(s):  
David Alonso-Gutiérrez ◽  
Jesús Bastero ◽  
Julio Bernués ◽  
Grigoris Paouris
Keyword(s):  
Convex Bodies ◽  
High Dimensional ◽  
Random Sections

scholarly journals Over-relaxed hit-and-run Monte Carlo for the uniform sampling of convex bodies with applications in metabolic network biophysics

2015 ◽  
Vol 26 (01) ◽  
pp. 1550010
Author(s):  
G. De Concini ◽  
D. De Martino
Keyword(s):  
Monte Carlo ◽  
High Dimension ◽  
Metabolic Networks ◽  
Convex Bodies ◽  
Point Of View ◽  
High Dimensional ◽  
Inference Problem ◽  
Uniform Sampling ◽  
Monte Carlo Algorithms ◽  
Hit And Run

The uniform sampling of convex regions in high dimension is an important computational issue, both from theoretical and applied point of view. The hit-and-run Monte Carlo algorithms are the most efficient methods known to perform it and one of their bottlenecks relies in the difficulty of escaping from tight corners in high dimension. Inspired by optimized Monte Carlo methods used in statistical mechanics, we define a new algorithm by over-relaxing the hit-and-run dynamics. We made numerical simulations on high-dimensional simplexes and hypercubes in order to test its performances, pointing out its improved ability to escape from angles and finally apply it to an inference problem in the steady state dynamics of metabolic networks.

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