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Between 2012 and 2014, ABYS study recorded antibiotic use, detection and resistance data for 23 organic and 35 conventional pig farms. Antibiotic contents of farm-made fertilizers were assessed by LC/MS-MS. Phenotypic antimicrobial resistance was investigated in Escherichia (E.) coli (indicator bacteria); antimicrobial resistance genes of the total bacterial microbiota (sul(II), tet(A), tet(B), tet(M); marker Measured in nUDD (number of animals treated multiplied by treatment days), colistin was the most frequently used antibiotic, in organic farms followed by tylosin, doxycycline and amoxicillin. Antibiotic residues were rarely detected; however, manure contained up to 10^8 antimicrobial resistance genes per gram; concentrations were higher when the antibiotic had been used on farm. In six farms, antimicrobial resistant E. coli were tracked from the moment when pigs were placed on farm. Some isolates carried a broad variety of resistances from the very beginning that were maintained until slaughter, despite the fact that partly no antibiotics were applied during fattening. Approaches for reducing carry-over of antimicrobial resistant bacteria will be discussed

We describe the links existing between a recently introduced semidefinite relaxation for the max-cut problem and the well known semidefinite relaxation for the stable set problem underlying the Lovász's theta function. It turns out that the connection between the convex bodies defining the semidefinite relaxations mimicks the connection existing between the corresponding polyhedra. We also show how the semidefinite relaxations can be combined with the classical linear relaxations in order to obtain tighter relaxations.

We study the facial structure of the set ${cal E_{ntimes n$ of correlation matrices (i.e., the positive semidefinite matrices with diagonal entries equal to 1). In particular, we determine the possible dimensions for a face, as well as for a polyhedral face of ${cal E_{ntimes n$. It turns out that the spectrum of face dimensions is lacunary and that ${cal E_{ntimes n$ has polyhedral faces of dimension up to $approx sqrt {2n$. As an application, we describe in detail the faces of ${cal E_{4times 4$. We also discuss results related to optimization over ${cal E_{ntimes n$.

We study the facial structure of the set ${cal E_{ntimes n$ of correlation matrices (i.e., the positive semidefinite matrices with diagonal entries equal to 1). In particular, we determine the possible dimensions for a face, as well as for a polyhedral face of ${cal E_{ntimes n$. It turns out that the spectrum of face dimensions is lacunary and that ${cal E_{ntimes n$ has polyhedral faces of dimension up to $approx sqrt {2n$. As an application, we describe in detail the faces of ${cal E_{4times 4$. We also discuss results related to optimization over ${cal E_{ntimes n$.

We describe the links existing between a recently introduced semidefinite relaxation for the max-cut problem and the well known semidefinite relaxation for the stable set problem underlying the Lovász's theta function. It turns out that the connection between the convex bodies defining the semidefinite relaxations mimicks the connection existing between the corresponding polyhedra. We also show how the semidefinite relaxations can be combined with the classical linear relaxations in order to obtain tighter relaxations.