238 research outputs found

    Block Spin Density Matrix of the Inhomogeneous AKLT Model

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    We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outside the block. It is diagonalized and shown to be a projector onto a subspace. We prove that for large block the density matrix behaves as the identity in the subspace. The von Neumann entropy coincides with Renyi entropy and is equal to the saturated value.Comment: 20 page

    Entanglement and Density Matrix of a Block of Spins in AKLT Model

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    We study a 1-dimensional AKLT spin chain, consisting of spins SS in the bulk and S/2S/2 at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension (S+1)2(S+1)^{2}. This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to ln(S+1)2\ln(S+1)^{2}.Comment: Revised version, typos corrected, references added, 31 page

    Prevalence and predictors of complementary and alternative medicine modalities in patients with chronic hepatitis B

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    Background & Aims The use of complementary and alternative medicine (CAM) in patients with chronic hepatitis B (CHB) can interact with antiviral treatment or influence health‐seeking behaviour. We aimed to study the use of individual CAM modalities in CHB and explore determinants of use, particularly migration‐related, socio‐economic and clinical factors. Methods A total of 436 CHB outpatients who attended the Toronto Centre for Liver Disease in 2015‐2016 were included in this cross‐sectional study. Using the comprehensive I‐CAM questionnaire and health records, data were collected on socio‐demographic and clinical variables and on usage of 16 CAM modalities in the last year. Results Sixty percent of patients were male, 74% were Asian and 46% were using antiviral treatment. Three‐hundred and nine (71%) patients used CAM. Vitamin/mineral preparations (45% of patients) were most commonly used. Overall CAM use and the specific use of potentially injurious CAM, such as green tea extract (9.2%) and St. John's wort (0.2%), were not associated with liver disease severity. Female sex, family history of CHB, lower serum HBV DNA, and higher socio‐economic status were independently associated with bio‐holistic CAM use, the clinically most‐relevant CAM group (P < 0.05); ethnicity, antiviral therapy use and liver disease severity were not. Conclusions CAM use among CHB patients was extensive, especially use of vitamin and mineral preparations, but without direct influence on liver disease severity. Bio‐holistic CAM use appeared to be associated with socio‐economic status rather than with ethnicity or liver disease severity. Despite the rare use of hepatotoxins, physicians should actively inquire about it

    Physical activity attenuates the influence of FTO variants on obesity risk: A meta-analysis of 218,166 adults and 19,268 children

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    Background: The FTO gene harbors the strongest known susceptibility locus for obesity. While many individual studies have suggested that physical activity (PA) may attenuate the effect of FTO on obesity risk, other studies have not been able to confirm this interaction. To confirm or refute unambiguously whether PA attenuates the association of FTO with obesity risk, we meta-analyzed data from 45 studies of adults (n = 218,166) and nine studies of children and adolescents (n = 19,268). Methods and Findings: All studies identified to have data on the FTO rs9939609 variant (or any proxy [r2>0.8]) and PA were invited to participate, regardless of ethnicity or age of the participants. PA was standardized by categorizing it into a dichotomous variable (physically inactive versus active) in each study. Overall, 25% of adults and 13% of children were categorized as inactive. Interaction analyses were performed within each study by including the FTO×PA interaction term in an additive model, adjusting for age and sex. Subsequently, random effects meta-analysis was used to pool the interaction terms. In adults, the minor (A-) allele of rs9939609 increased the odds of obesity by 1.23-fold/allele (95% CI 1.20-1.26), but PA attenuated this effect (pinteraction= 0.001). More specifically, the minor allele of rs9939609 increased the odds of obesity less in the physically active group (odds ratio = 1.22/allele, 95% CI 1.19-1.25) than in the inactive group (odds ratio = 1.30/allele, 95% CI 1.24-1.36). No such interaction was found in children and adolescents. Concl

    Loss-of-function mutations in UDP-Glucose 6-Dehydrogenase cause recessive developmental epileptic encephalopathy

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    Developmental epileptic encephalopathies are devastating disorders characterized by intractable epileptic seizures and developmental delay. Here, we report an allelic series of germline recessive mutations in UGDH in 36 cases from 25 families presenting with epileptic encephalopathy with developmental delay and hypotonia. UGDH encodes an oxidoreductase that converts UDP-glucose to UDP-glucuronic acid, a key component of specific proteoglycans and glycolipids. Consistent with being loss-of-function alleles, we show using patients’ primary fibroblasts and biochemical assays, that these mutations either impair UGDH stability, oligomerization, or enzymatic activity. In vitro, patient-derived cerebral organoids are smaller with a reduced number of proliferating neuronal progenitors while mutant ugdh zebrafish do not phenocopy the human disease. Our study defines UGDH as a key player for the production of extracellular matrix components that are essential for human brain development. Based on the incidence of variants observed, UGDH mutations are likely to be a frequent cause of recessive epileptic encephalopathy
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