Mixed semicontinuous perturbations of nonconvex sweeping processes

In this paper we prove a theorem on the existence of a global solution of a differential inclusion governed by a class of nonconvex sweeping processes with unbounded pertubations. The perturbations are not required to be convex valued.     

Sub differential Monotonicity as Characterization of Convex Functions

We prove that a lower semicontinuous function defined on a Banach space is convex if and only if its subdifferential ismonotone.     

The Flip-Graph of the 4-Dimensional Cube is Connected

Flip-graph connectedness is established here for the vertex set of the 4-dimensional cube. It is found as a consequence that this vertex set has 92,487,256 triangulations, partitioned into 247,451 symmetry classes.     

A Turning-Band Method for the Simulation of Anisotropic Fractional Brownian Fields

In this article, we propose a method for simulating realizations of two-dimensional anisotropic fractional Brownian fields (AFBF) introduced by Bonami and Estrade. The method is adapted from a generic simulation method called the turning-band method (TBM) due to Matheron. The TBM reduces the problem of simulating a field in two dimensions by combining independent processes simulated on oriented bands. In the AFBF context, the simulation fields are constructed by discretizing an integral equation arising from the application of the TBM to nonstationary anisotropic fields. This guarantees the convergence of simulations as the step of discretization is decreased. The construction is followed by a theoretical study of the convergence rate (the detailed proofs are available in the online supplementary materials). Another key feature of this work is the simulation of band processes. Using self-similarity properties, processes are simulated exactly on bands with a circulant embedding method, so that simulation errors are exclusively due to the field approximation. Moreover, we design a dynamic programming algorithm that selects band orientations achieving the optimal trade-off between computational cost and precision. Finally, we conduct a numerical study showing that the approximation error does not significantly depend on the regularity of the fields to be simulated, nor on their degree of anisotropy. Experiments also suggest that simulations preserve the statistical properties of the original field.     

Weakly Regular Subdivisions

It is shown that 2-dimensional subdivisions can be made regular by moving their vertices within parallel 1-dimensional spaces. As a consequence, any 2-dimensional subdivision is projected from the boundary complex of a 4-polytope.     

Mixed Semicontinuous Perturbation of Nonconvex State-Dependent Sweeping Process

In this paper we prove a result on the existence of solutions of a first-order differential inclusion governed by a class of nonconvex sweeping process. The moving set involved in the process is prox-regular and depends both on the time and on the state.     

Primal-Lower-Nice Property of Value Functions in Optimization and Control Problems

The paper studies value functions associated with optimization problems and with Mayer-type control problems. Using methods belonging to proximal analysis and control theory, we establish new results for the primal-lower-nice (pln) property of the value functions for these problems.     

Distance Function Associated to a Prox-regular set

Set-Valued and Variational Analysis - In this paper, we provide in a general Hilbert space new characterizations of uniform prox-regularity involving outside but sufficiently close points of...     

Methylerythritol Phosphate Pathway: Enzymatic Evidence for a Rotation in the LytB/IspH-Catalyzed Reaction

IspH/LytB, an oxygen-sensitive [4Fe-4S] enzyme, catalyzes the last step of the methylerythritol phosphate (MEP) pathway, a target for the development of new antimicrobial agents. This metalloenzyme converts (E)-4-hydroxy-3-methylbut-2-en-1-yl diphosphate (HMBPP) into the two isoprenoid precursors: isopentenyl diphosphate (IPP) and dimethylallyl diphosphate (DMAPP). Here, the synthesis of (S)-[4-²H₁]HMBPP and (R)-[4-²H₁]HMBPP is reported together with a detailed NMR analysis of the products formed after their respective incubation with E. coli IspH/LytB in the presence of the biological reduction system used by E. coli to reduce the [4Fe-4S] center. (S)-[4-²H₁]HMBPP was converted into [4-²H₁]DMAPP and (E)-[4-²H₁]IPP, whereas (R)-[4-²H₁]HMBPP yielded [4-²H₁]DMAPP and (Z)-[4-²H₁]IPP, hence providing the direct enzymatic evidence that the mechanism catalyzed by IspH/LytB involves a rotation of the CH₂OH group of the substrate to display it away from the [4Fe-4S].