Combined scanning probe microscopy and x-ray scattering instrument for in situ catalysis investigations

Catalysis and Surface Chemistr

Error bounds for monomial convexification in polynomial optimization

Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. However, there has been no study of the error in the global optimum from such approaches. We give bounds on the worst-case error for convexifying a monomial over subsets of $[0,1]^n$. This implies additive error bounds for relaxing a polynomial optimization problem by convexifying each monomial separately. Our main error bounds depend primarily on the degree of the monomial, making them easy to compute. Since monomial convexification studies depend on the bounds on the associated variables, in the second part, we conduct an error analysis for a multilinear monomial over two different types of box constraints. As part of this analysis, we also derive the convex hull of a multilinear monomial over $[-1,1]^n$.Comment: 33 pages, 2 figures, to appear in journa

Local search heuristics for the multidimensional assignment problem

The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate that a combination of two neighborhoods may yield a heuristics which is superior to both of its components

Jeune syndrome: description of 13 cases and a proposal for follow-up protocol

Jeune syndrome (asphyxiating thoracic dystrophy, ATD) is a rare autosomal recessive skeletal dysplasia characterized by a small, narrow chest and variable limb shortness with a considerable neonatal mortality as a result of respiratory distress. Renal, hepatic, pancreatic and ocular complications may occur later in life. We describe 13 cases with ages ranging from 9 months to 22 years. Most patients experienced respiratory problems in the first years of their life, three died, one experienced renal complications, and one had hepatic problems. With age, the thoracic malformation tends to become less pronounced and the respiratory problems decrease. The prognosis of ATD seems better than described in literature and in our opinion this justifies long term intensive treatment in the first years. We also propose a follow-up protocol for patients with ATD

Real-time polymerase chain reaction in the diagnosis of acute postoperative endophthalmitis

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