This book presents an enticing introduction to tropical circuits and their use as a rigorous mathematical model for dynamic programming (DP), which is one of the most fundamental algorithmic paradigms for solving combinatorial, discrete optimization problems.
In DP, an optimization problem is broken up into smaller subproblems that are solved recursively. Many classical DP algorithms are pure in that they only use the basic (min,+) or (max,+) operations in their recursion equations. In tropical circuits, these operations are used as gates. Thanks to the...
This book presents an enticing introduction to tropical circuits and their use as a rigorous mathematical model for dynamic programming (DP), whi...
This book serves as an introductory asset for learning metric geometry by delivering an in-depth examination of key constructions and providing an analysis of universal spaces, injective spaces, the Gromov-Hausdorff convergence, and ultralimits. This book illustrates basic examples of domestic affairs of metric spaces, this includes Alexandrov geometry, geometric group theory, metric-measure spaces and optimal transport.
Researchers in metric geometry will find this book appealing and helpful, in addition to graduate students in mathematics, and advanced undergraduate students in...
This book serves as an introductory asset for learning metric geometry by delivering an in-depth examination of key constructions and providing an ...
This book develops limit theorems for a natural class of long range random walks on finitely generated torsion free nilpotent groups. The limits in these limit theorems are Lévy processes on some simply connected nilpotent Lie groups. Both the limit Lévy process and the limit Lie group carrying this process are determined by and depend on the law of the original random walk. The book offers the first systematic study of such limit theorems involving stable-like random walks and stable limit Lévy processes in the context of (non-commutative) nilpotent groups.
This book develops limit theorems for a natural class of long range random walks on finitely generated torsion free nilpotent groups. The limits...
This book investigates homogenisation problems for divergence form equations with rapidly sign-changing coefficients. Focusing on problems with piecewise constant, scalar coefficients in a (d-dimensional) crosswalk type shape, we will provide a limit procedure in order to understand potentially ill-posed and non-coercive settings.
Depending on the integral mean of the coefficient and its inverse, the limits can either satisfy the usual homogenisation formula for stratified media, be entirely degenerate or be a non-local differential operator of 4th order. In order to mark the drastic...
This book investigates homogenisation problems for divergence form equations with rapidly sign-changing coefficients. Focusing on problems with pie...
