Calderón-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we introduce a new approach for general which admit Markov semigroup purely algebraic assumptions. We shall construct an abstract form ‘Markov metric’ governing process and naturally associated BMO spaces, interpolate with Lp-scale endpoint ...

Suppose that we have the unit Euclidean ball in R and construct new bodies using three operations linear transformations, closure in the radial metric and multiplicative summation defined by ‖x‖K+0L = p ‖x‖K‖x‖L. We prove that in dimension 3 this procedure gives all origin symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of ...

We consider the task of obtaining the maximum a posteriori estimate of discrete pairwise random fields with arbitrary unary potentials and semimetric pairwise potentials. For this problem, we propose an accurate hierarchical move making strategy where each move is computed efficiently by solving an st-MINCUT problem. Unlike previous move making approaches, e.g. the widely used α-expansion algor...

We give a new randomized LP-rounding 1.725-approximation algorithm for the metric Fault-Tolerant Uncapacitated Facility Location problem. This improves on the previously best known 2.076-approximation algorithm of Swamy & Shmoys. To the best of our knowledge, our work provides the first application of a dependent-rounding technique in the domain of facility location. The analysis of our algorit...

In this work, we analyse the chicken production in a poultry network composed of set farms that serves slaughterhouse city Tlemcen. Each farm has house dedicated to breeding, and each three breeding modes: manual semi-automatic automatic breeding. And mode consumes an appropriate energy level depending on degree automation used, which directly affects quality chicken. The objective study is det...

In the FPGA (Field Programmable Gate Arrays) design flow, one of the most time-consuming step is the routing of nets. Therefore, there is a need to accelerate it. In [2], the authors have developed a Linear Programming (LP) based framework that parallelizes this routing process to achieve significant speedups (the resulting algorithm is termed as ParaLaR). However, this approach has certain wea...

Finding the exact integrality gap α for the LP relaxation of the metric Travelling Salesman Problem (TSP) has been an open problem for over thirty years, with little progress made. It is known that 4/3 ≤ α ≤ 3/2, and a famous conjecture states α = 4/3. For this problem, essentially two “fundamental” classes of instances have been proposed. This fundamental property means that in order to show t...