An adaptive prefix-assignment technique for symmetry reduction

This paper presents a technique for symmetry reduction that adaptively assigns a prefix of variables in a system of constraints so that the generated prefix-assignments are pairwise nonisomorphic under the action of the symmetry group of the system. The technique is based on McKay's canonical extension framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the technique are (i) adaptability---the prefix sequence can be user-prescribed and truncated for compatibility with the group of symmetries; (ii) parallelizability---prefix-assignments can be processed in parallel independently of each other; (iii) versatility---the method is applicable whenever the group of symmetries can be concisely represented as the automorphism group of a vertex-colored graph; and (iv) implementability---the method can be implemented relying on a canonical labeling map for vertex-colored graphs as the only nontrivial subroutine. To demonstrate the practical applicability of our technique, we have prepared an experimental open-source implementation of the technique and carry out a set of experiments that demonstrate ability to reduce symmetry on hard instances. Furthermore, we demonstrate that the implementation effectively parallelizes to compute clusters with multiple nodes via a message-passing interface.Comment: Updated manuscript submitted for revie

On the crossing relation in the presence of defects

The OPE of local operators in the presence of defect lines is considered both in the rational CFT and the $c>25$ Virasoro (Liouville) theory. The duality transformation of the 4-point function with inserted defect operators is explicitly computed. The two channels of the correlator reproduce the expectation values of the Wilson and 't Hooft operators, recently discussed in Liouville theory in relation to the AGT conjecture.Comment: TEX file with harvmac; v3: JHEP versio

Defect loops in gauged Wess-Zumino-Witten models

We consider loop observables in gauged Wess-Zumino-Witten models, and study the action of renormalization group flows on them. In the WZW model based on a compact Lie group G, we analyze at the classical level how the space of renormalizable defects is reduced upon the imposition of global and affine symmetries. We identify families of loop observables which are invariant with respect to an affine symmetry corresponding to a subgroup H of G, and show that they descend to gauge-invariant defects in the gauged model based on G/H. We study the flows acting on these families perturbatively, and quantize the fixed points of the flows exactly. From their action on boundary states, we present a derivation of the "generalized Affleck-Ludwig rule, which describes a large class of boundary renormalization group flows in rational conformal field theories.Comment: 43 pages, 2 figures. v2: a few typos corrected, version to be published in JHE

Defect Perturbations in Landau-Ginzburg Models

Perturbations of B-type defects in Landau-Ginzburg models are considered. In particular, the effect of perturbations of defects on their fusion is analyzed in the framework of matrix factorizations. As an application, it is discussed how fusion with perturbed defects induces perturbations on boundary conditions. It is shown that in some classes of models all boundary perturbations can be obtained in this way. Moreover, a universal class of perturbed defects is constructed, whose fusion under certain conditions obey braid relations. The functors obtained by fusing these defects with boundary conditions are twist functors as introduced in the work of Seidel and Thomas.Comment: 46 page

Protection from ultraviolet damage and photocarcinogenesis by vitamin d compounds

© Springer Nature Switzerland AG 2020. Exposure of skin cells to UV radiation results in DNA damage, which if inadequately repaired, may cause mutations. UV-induced DNA damage and reactive oxygen and nitrogen species also cause local and systemic suppression of the adaptive immune system. Together, these changes underpin the development of skin tumours. The hormone derived from vitamin D, calcitriol (1,25-dihydroxyvitamin D3) and other related compounds, working via the vitamin D receptor and at least in part through endoplasmic reticulum protein 57 (ERp57), reduce cyclobutane pyrimidine dimers and oxidative DNA damage in keratinocytes and other skin cell types after UV. Calcitriol and related compounds enhance DNA repair in keratinocytes, in part through decreased reactive oxygen species, increased p53 expression and/or activation, increased repair proteins and increased energy availability in the cell when calcitriol is present after UV exposure. There is mitochondrial damage in keratinocytes after UV. In the presence of calcitriol, but not vehicle, glycolysis is increased after UV, along with increased energy-conserving autophagy and changes consistent with enhanced mitophagy. Reduced DNA damage and reduced ROS/RNS should help reduce UV-induced immune suppression. Reduced UV immune suppression is observed after topical treatment with calcitriol and related compounds in hairless mice. These protective effects of calcitriol and related compounds presumably contribute to the observed reduction in skin tumour formation in mice after chronic exposure to UV followed by topical post-irradiation treatment with calcitriol and some, though not all, related compounds

MRI following severe perinatal asphyxia: preliminary experience.

In 30 children suffering from severe perinatal asphyxia an attempt was made to determine the early prognostic signs of severe hypoxic-ischemic brain injury with magnetic resonance imaging (MRI). Ten early (1-4 days of age), 16 intermediate (2-4 weeks of age), and 38 late MRI (older than 1 month of age) procedures were performed on a 2.35 T MR-system. Severe cerebral necrosis was suspected by T2 hyperintensity of the white matter, with blurred limits to the cortex in early MRI, and was confirmed by T1 hyperintensity of the cortex in intermediate MRI. Severe cerebral necrosis was established at 3 months of age. Of the 11 children with this pattern (group A), 8 had severe and 3 had moderate cerebral palsy on subsequent examination. Thirteen children (group B) had normal late MRI scans; none developed severe cerebral palsy or marked mental retardation. Two children (group C) had focal ischemic lesions. Four children had intracranial hemorrhage (group D). Groups A and B did not differ in the severity of their perinatal histories and findings, suggesting that MRI during the first 3 months is of significant prognostic value