We consider convex contact spheres Y Y all of whose Reeb orbits are closed. Any such admits a stratification by the periods closed orbi...

The main purpose of this work is to study and apply generalized contact distributions of (inhomogeneous) Boolean models Z with values in the extended convex ring. Given a convex body L ⊂ Rd and a gauge body B ⊂ Rd such a generalized contact distribution is the conditional distribution of the random vector (dB(L,Z), uB(L,Z), pB(L,Z), lB(L,Z)) given that Z ∩L = ∅, where Z is a Boolean model, dB(L...

The conic structure of the convex cone of non-negative operator convex functions on (0,∞) (also on (−1, 1)) is clarified. We completely determine the extreme rays, the closed faces, and the simplicial closed faces of this convex cone.

In order to get estimates on the solutions of the equation ∂̄u = ω on Stein manifold, we introduce a new method the ”raising steps method”, to get global results from local ones. In particular it allows us to transfer results form open sets in C to open sets in a Stein manifold. Using it we get L − L results for solutions of equation ∂̄u = ω with a gain, s > r, in strictly pseudo convex domains i...

In several applications, underestimation of functions has proven to be a helpful tool for global optimization. In protein-ligand docking problems as well as in protein structure prediction, single convex quadratic underestimators have been used to approximate the location of the global minimum point. While this approach has been successful for basin-shaped functions, it is not suitable for ener...

Parsimony, including sparsity and low-rank, has shown great importance for data mining in social networks, particularly in tasks such as segmentation and recognition. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with convex l₁-norm or nuclear norm constraints. However, the obtained results by convex optimization are usually suboptim...

We analyze minimization algorithms for L\-convex functions in discrete convex analysis, and establish exact bounds for the number of iterations required by the steepest descent algorithm and its variants.