Wall-crossing, open BPS counting and matrix models

We consider wall-crossing phenomena associated to the counting of D2-branes attached to D4-branes wrapping lagrangian cycles in Calabi-Yau manifolds, both from M-theory and matrix model perspective. Firstly, from M-theory viewpoint, we review that open BPS generating functions in various chambers are given by a restriction of the modulus square of the open topological string partition functions. Secondly, we show that these BPS generating functions can be identified with integrands of matrix models, which naturally arise in the free fermion formulation of corresponding crystal models. A parameter specifying a choice of an open BPS chamber has a natural, geometric interpretation in the crystal model. These results extend previously known relations between open topological string amplitudes and matrix models to include chamber dependence.Comment: 25 pages, 8 figures, published versio

Instantons on ALE spaces and orbifold partitions

We consider N=4 theories on ALE spaces of $A_{k-1}$ type. As is well known, their partition functions coincide with $A_{k-1}$ affine characters. We show that these partition functions are equal to the generating functions of some peculiar classes of partitions which we introduce under the name 'orbifold partitions'. These orbifold partitions turn out to be related to the generalized Frobenius partitions introduced by G. E. Andrews some years ago. We relate the orbifold partitions to the blended partitions and interpret explicitly in terms of a free fermion system.Comment: 28 pages, 10 figures; reference adde

KnotProt: a database of proteins with knots and slipknots.

The protein topology database KnotProt, http://knotprot.cent.uw.edu.pl/, collects information about protein structures with open polypeptide chains forming knots or slipknots. The knotting complexity of the cataloged proteins is presented in the form of a matrix diagram that shows users the knot type of the entire polypeptide chain and of each of its subchains. The pattern visible in the matrix gives the knotting fingerprint of a given protein and permits users to determine, for example, the minimal length of the knotted regions (knot's core size) or the depth of a knot, i.e. how many amino acids can be removed from either end of the cataloged protein structure before converting it from a knot to a different type of knot. In addition, the database presents extensive information about the biological functions, families and fold types of proteins with non-trivial knotting. As an additional feature, the KnotProt database enables users to submit protein or polymer chains and generate their knotting fingerprints

The influence of doxycycline on articular cartilage in experimental osteoarthrosis induced by iodoacetate

The experiment was performed on 36 Wistar rats. On the first day of the experiment iodoacetate was administered to the left posterior knee joint of the 18 rats which composed Group I. The second group of 18 rats received additionally doxycycline (doxy) through the gastric tube in doses comparable with those of doxycycline used in humans. The experiment lasted 21 days. The animals were sacrificed after 7, 14 and 21 days in groups of 6 rats each. In sections stained with Safranin 0 semiquantitative histochemical intensity tests were performed on articular cartilage glycosaminoglycans (GAG) using a four-point scale (0–3). In the first group examined destructive lesions in the articular cartilage and weak reactivity on GAG were noted at all stages of the experiment. The intensity of GAG staining was higher in the second group after 14 and especially after 21 days, which may suggest a protective action of doxy on articular cartilage