Pairs of Bloch electrons and magnetic translation groups

A product of irreducible representations of magnetic translation group is considered. It leads to irreducible representations which were previously rejected as nonphysical. A very simple example indicates a possible application of these representations. In particular, they are important in descriptions of pairs of electrons in a magnetic field and a periodic potential. The periodicity of some properties with respect to the charge of a particle is briefly discussed.Comment: 4 pages, RevTex. Latex2.09, amsfont

Neel probability and spin correlations in some nonmagnetic and nondegenerate states of hexanuclear antiferromagnetic ring Fe6: Application of algebraic combinatorics to finite Heisenberg spin systems

The spin correlations \omega^z_r, r=1,2,3, and the probability p_N$ of finding a system in the Neel state for the antiferromagnetic ring Fe(III)6 (the so-called `small ferric wheel') are calculated. States with magnetization M=0, total spin 0<=S<=15 and labeled by two (out of four) one-dimensional irreducible representations (irreps) of the point symmetry group D_6 are taken into account. This choice follows from importance of these irreps in analyzing low-lying states in each S-multiplet. Taking into account the Clebsch--Gordan coefficients for coupling total spins of sublattices (SA=SB=15/2) the global Neel probability p*_N can be determined. Dependencies of these quantities on state energy (per bond and in the units of exchange integral J) and the total spin S are analyzed. Providing we have determined p_N(S) etc. for other antiferromagnetic rings (Fe10, for instance) we could try to approximate results for the largest synthesized ferric wheel Fe18. Since thermodynamic properties of Fe6 have been investigated recently, in the present considerations they are not discussed, but only used to verify obtained values of eigenenergies. Numerical results re calculated with high precision using two main tools: (i) thorough analysis of symmetry properties including methods of algebraic combinatorics and (ii) multiple precision arithmetic library GMP. The system considered yields more than 45 thousands basic states (the so-called Ising configurations), but application of the method proposed reduces this problem to 20-dimensional eigenproblem for the ground state (S=0). The largest eigenproblem has to be solved for S=4; its dimension is 60. These two facts (high precision and small resultant eigenproblems) confirm efficiency and usefulness of such an approach, so it is briefly discussed here.Comment: 13 pages, 7 figs, 5 tabs, revtex

Diazepam and its metabolites in the mothers' and newborns' hair as a biomarker of prenatal exposure

Pregnant women are exposed to benzodiazepines for therapeutic purposes during gestation. The goal of this study was to evaluate prenatal exposure to benzodiazepines. Time of exposure during course of pregnancy is a significant aspect of fetal exposure to drugs. Benzodiazepine concentration assay in hair of mothers and newborns exposed prenatally to these drugs was performed in the studies. Development, validation and evaluation of benzodiazepine determination method in mothers and their newborns enables assessment of health risks for the child and implementation of adequate therapeutic procedures. We used A LC-ESI-MS/MS method that allowed determination of diazepam (the main benzodiazepine used by pregnant women was diazepam) and its metabolites (nordazepam, oxazepam) in hair of mothers and newborns. LOQ 10 pg/mg of hair was used in the study. Results: concentration of nordazepam was higher than parent drug (diazepam) and higher in newborns’ hair when compared to mothers’. The mean concentrations of diazepam in mothers’ hair were 31.6±36.0 and 34.1±42.4 pg/mg in the second and third trimester of pregnancy respectively. The mean concentration of diazepam in newborns’ hair was higher and reached levels of 53.3±36.5 pg/mg. The mean concentration of nordazepam in the mothers’ hair corresponding to the second and third trimester was 52.9±48.1 and 89.9±122.8 pg/mg, respectively. Nordazepam in the newborns’ hair was detected at the mean level of 108.1±144.2 pg/mg. It was concluded that diazepam and nordazepam are permanently incorporated into the hair structure. Presence of diazepam and its metabolites in newborn’s hair confirms that these benzodiazepines permeate placental barrier. Segmental analysis of mothers’ hair enabled the assessment of drug administration time. Diazepam and its metabolites determined in hair of newborns may serve as biomarkers of prenatal exposure to these drugs. The performed LC-MS/MS analysis was accurate enough to determine even low concentrations of benzodiazepines, at the level of few pg/mg of hair. Levels of diazepam detected in hair of newborns were higher than levels determined in mothers. This may confirm the fact, that fetus’s ability to metabolize diazepam is scarce. Nordazepam was found in higher concentrations in hair of newborns than in hair of mothers, which may suggest that it is cumulated in child’s organism. Other metabolites of diazepam - oxazepam and temazepam - were detected in very few cases, in low concentrations

Magnetic translation groups in an n-dimensional torus

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG on an n-dimensional torus is isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG on a three-torus and apply the representation theory to three examples. We shortly describe a representation theory for a general n-torus. The MTG on an n-torus can be regarded as a generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in Journal of Mathematical Physic

Geometric entropy, area, and strong subadditivity

The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed, previous calculations in the context of quantum field theory, where the result is actually ultraviolet divergent, have shown that the geometric entropy is proportional to the area for a very special type of subsets. In this work we show that the area law follows in general from simple considerations based on quantum mechanics and relativity. An essential ingredient of our approach is the strong subadditive property of the quantum mechanical entropy.Comment: Published versio

Implementation of U.K. Earth system models for CMIP6

We describe the scientific and technical implementation of two models for a core set of experiments contributing to the sixth phase of the Coupled Model Intercomparison Project (CMIP6). The models used are the physical atmosphere-land-ocean-sea ice model HadGEM3-GC3.1 and the Earth system model UKESM1 which adds a carbon-nitrogen cycle and atmospheric chemistry to HadGEM3-GC3.1. The model results are constrained by the external boundary conditions (forcing data) and initial conditions.We outline the scientific rationale and assumptions made in specifying these. Notable details of the implementation include an ozone redistribution scheme for prescribed ozone simulations (HadGEM3-GC3.1) to avoid inconsistencies with the model's thermal tropopause, and land use change in dynamic vegetation simulations (UKESM1) whose influence will be subject to potential biases in the simulation of background natural vegetation.We discuss the implications of these decisions for interpretation of the simulation results. These simulations are expensive in terms of human and CPU resources and will underpin many further experiments; we describe some of the technical steps taken to ensure their scientific robustness and reproducibility

Analysis of Agglomerative Clustering

The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes a hierarchy of approximate solutions to this problem (for all values of $k$) is the agglomerative clustering algorithm with the complete linkage strategy. For decades, this algorithm has been widely used by practitioners. However, it is not well studied theoretically. In this paper, we analyze the agglomerative complete linkage clustering algorithm. Assuming that the dimension $d$ is a constant, we show that for any $k$ the solution computed by this algorithm is an $O(\log k)$-approximation to the diameter $k$-clustering problem. Our analysis does not only hold for the Euclidean distance but for any metric that is based on a norm. Furthermore, we analyze the closely related $k$-center and discrete $k$-center problem. For the corresponding agglomerative algorithms, we deduce an approximation factor of $O(\log k)$ as well.Comment: A preliminary version of this article appeared in Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS '11), March 2011, pp. 308-319. This article also appeared in Algorithmica. The final publication is available at http://link.springer.com/article/10.1007/s00453-012-9717-

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

Custom Made Candy Plug for Distal False Lumen Occlusion in Aortic Dissection: International Experience

Objective: To evaluate early and midterm outcomes of the Candy Plug (CP) technique for distal false lumen (FL) occlusion in thoracic endovascular aortic repair for aortic dissection (AD) in a more real world cohort of patients from an international multicentre registry. Methods: A multicentre retrospective study was conducted of all consecutive patients from the contributing centres with subacute and chronic AD treated with the CP technique from October 2013 to April 2020 at 18 centres. Results: A custom made CP was used in 155 patients (92 males, mean age 62 ± 11 years). Fourteen (9%) presented with ruptured false lumen aneurysms. Technical success was achieved in all patients (100%). Clinical success was achieved in 138 patients (89%). The median hospital stay was 7 days (1 – 77). The 30 day mortality rate was 3% (n = 5). Stroke occurred in four patients (3%). Spinal cord ischaemia occurred in three patients (2%). The 30 day computed tomography angiogram (CTA) confirmed successful CP placement at the intended level in all patients. Early complete FL occlusion was achieved in 120 patients (77%). Early (30 day) CP related re-intervention was required in four patients (3%). The early (30 day) stent graft related re-intervention rate was 8% (n = 12). Follow up CTA was available in 142 patients (92%), with a median follow up of 23 months (6 – 87). Aneurysmal regression was achieved in 68 of 142 patients (47%); the aneurysm diameter remained stable in 69 of 142 patients (49%) and increased in five of 142 patients (4%). A higher rate of early FL occlusion was detected in the largest volume centre patients (50 [88%] vs. 70 [71%] from other centres; p = .019). No other differences in outcome were identified regarding volume of cases or learning curve. Conclusion: This international CP technique experience confirmed its feasibility and low mortality and morbidity rates. Aortic remodelling and false lumen thrombosis rates were high and support the concept of distal FL occlusion in AD using the CP technique