Comments on nonunitary conformal field theories

As is well-known, nonunitary RCFTs are distinguished from unitary ones in a number of ways, two of which are that the vacuum 0 doesn't have minimal conformal weight, and that the vacuum column of the modular S matrix isn't positive. However there is another primary field, call it o, which has minimal weight and has positive S column. We find that often there is a precise and useful relationship, which we call the Galois shuffle, between primary o and the vacuum; among other things this can explain why (like the vacuum) its multiplicity in the full RCFT should be 1. As examples we consider the minimal WSU(N) models. We conclude with some comments on fractional level admissible representations of affine algebras. As an immediate consequence of our analysis, we get the classification of an infinite family of nonunitary WSU(3) minimal models in the bulk.Comment: 24 page

Residential exposure to solar ultraviolet radiation and incidence of childhood hematological malignancies in France

Few studies have investigated the relationship between solar ultraviolet radiation (UV) and childhood hematological malignancies (CHM). This study addresses the associations between residential UV exposure at diagnosis and the incidence of types and subtypes of CHM, by age and gender, in France, over a long period, on the fine scale of the 36,326 Communes that constitute mainland France. The 9,082 cases of acute leukemia and 3,563 cases of lymphoma diagnosed before the age of 15 years from 1990 to 2009 were provided by the French National Registry of Childhood Hematological Malignancies. The incidence of CHM was calculated by Commune, year, age and gender and expressed as the standardized incidence ratio (SIR). UV data from 1988 to 2007 were extracted from the EUROSUN database. The annual daily average UV exposure of the children ranged from 85.5 to 137.8 J/cm2. For each additional 25 J/cm2, there was a significant increase in precursor B-cell acute lymphoblastic leukemia (PBC-ALL) in children aged less than 5 years (SIR 1.18; 95 % CI 1.10–1.27). Further analysis of PBC-ALL in the young children suggested a better fit of models with a threshold, with the risk increasing above 100 J/cm2, for which the SIR was 1.24 (95 % CI 1.14–1.36) for a 25 J/cm2 increase. The results remained stable in analyses stratifying by deprivation index or degree of urbanization of the Communes. The study suggests that higher residential UV exposure may be positively associated with a higher incidence of PBC-ALL in early childhood

The W_N minimal model classification

We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) W_N(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten theories at level (p-N,q-N). This permits considerable simplifications to the proof of the Cappelli-Itzykson-Zuber classification of Virasoro minimal models. More important, we obtain from this the complete classification of all modular invariants for the W_3(p,q) minimal models. All should be realised by rational conformal field theories. Previously, only those for the unitary models, i.e. W_3(p,p+1), were classified. For all N our correspondence yields for free an extensive list of W_N(p,q) modular invariants. The W_3 modular invariants, like the Virasoro minimal models, all factorise into SU(3) modular invariants, but this fails in general for larger N. We also classify the SU(3)xSU(3) modular invariants, and find there a new infinite series of exceptionals.Comment: 25 page

Metastable states, quasi-stationary distributions and soft measures

We establish metastability in the sense of Lebowitz and Penrose under practical and simple hypothesis for (families of) Markov chains on finite configuration space in some asymptotic regime, including the case of configuration space size going to infinity. By comparing restricted ensemble and quasi-stationary measures, we study point-wise convergence velocity of Yaglom limits and prove asymptotic exponential exit law. We introduce soft measures as interpolation between restricted ensemble and quasi-stationary measure to prove an asymptotic exponential transition law on a generally different time scale. By using potential theoretic tools, we prove a new general Poincar\'e inequality and give sharp estimates via two-sided variational principles on relaxation time as well as mean exit time and transition time. We also establish local thermalization on a shorter time scale and give mixing time asymptotics up to a constant factor through a two-sided variational principal. All our asymptotics are given with explicit quantitative bounds on the corrective terms.Comment: 41 page

The Logarithmic Sobolev Constant of The Lamplighter

We give estimates on the logarithmic Sobolev constant of some finite lamplighter graphs in terms of the spectral gap of the underlying base. Also, we give examples of application

J Clin Med

Background/Objectives: The aim of the study was to compare dacryocystectomy (DCT) versus dacryocystorhinostomy (DCR) in patients with dacryocystitis in terms of tearing complaints. Methods: We conducted a retrospective and comparative study on 19 patients. The main outcome measure was defined as an improvement by 1 point of the Munk score postoperatively. Results: A total of 19 patients were included with 10 in the DCR group and 9 in the DCT group. The primary endpoint was reached in 7 (70%) and in 6 (67%) patients in the DCR and DCT groups, respectively (p > 0.999). All DCR procedures were performed under general anesthesia (GA), while almost all DCT procedures were performed under local anesthesia (LA) (p < 0.001). There was a higher need for hospitalization in the DCR group (p < 0.001). Conclusions: Our preliminary results indicate that DCR is not always the solution in the case of dacryocystitis. DCT is a viable surgical procedure, especially in elderly patients without any tearing complaint and with underlying dry eye disease

Nrf2-interacting nutrients and COVID-19 : time for research to develop adaptation strategies

There are large between- and within-country variations in COVID-19 death rates. Some very low death rate settings such as Eastern Asia, Central Europe, the Balkans and Africa have a common feature of eating large quantities of fermented foods whose intake is associated with the activation of the Nrf2 (Nuclear factor (erythroid-derived 2)-like 2) anti-oxidant transcription factor. There are many Nrf2-interacting nutrients (berberine, curcumin, epigallocatechin gallate, genistein, quercetin, resveratrol, sulforaphane) that all act similarly to reduce insulin resistance, endothelial damage, lung injury and cytokine storm. They also act on the same mechanisms (mTOR: Mammalian target of rapamycin, PPAR gamma:Peroxisome proliferator-activated receptor, NF kappa B: Nuclear factor kappa B, ERK: Extracellular signal-regulated kinases and eIF2 alpha:Elongation initiation factor 2 alpha). They may as a result be important in mitigating the severity of COVID-19, acting through the endoplasmic reticulum stress or ACE-Angiotensin-II-AT(1)R axis (AT(1)R) pathway. Many Nrf2-interacting nutrients are also interacting with TRPA1 and/or TRPV1. Interestingly, geographical areas with very low COVID-19 mortality are those with the lowest prevalence of obesity (Sub-Saharan Africa and Asia). It is tempting to propose that Nrf2-interacting foods and nutrients can re-balance insulin resistance and have a significant effect on COVID-19 severity. It is therefore possible that the intake of these foods may restore an optimal natural balance for the Nrf2 pathway and may be of interest in the mitigation of COVID-19 severity

Cabbage and fermented vegetables : From death rate heterogeneity in countries to candidates for mitigation strategies of severe COVID-19

Large differences in COVID-19 death rates exist between countries and between regions of the same country. Some very low death rate countries such as Eastern Asia, Central Europe, or the Balkans have a common feature of eating large quantities of fermented foods. Although biases exist when examining ecological studies, fermented vegetables or cabbage have been associated with low death rates in European countries. SARS-CoV-2 binds to its receptor, the angiotensin-converting enzyme 2 (ACE2). As a result of SARS-CoV-2 binding, ACE2 downregulation enhances the angiotensin II receptor type 1 (AT(1)R) axis associated with oxidative stress. This leads to insulin resistance as well as lung and endothelial damage, two severe outcomes of COVID-19. The nuclear factor (erythroid-derived 2)-like 2 (Nrf2) is the most potent antioxidant in humans and can block in particular the AT(1)R axis. Cabbage contains precursors of sulforaphane, the most active natural activator of Nrf2. Fermented vegetables contain many lactobacilli, which are also potent Nrf2 activators. Three examples are: kimchi in Korea, westernized foods, and the slum paradox. It is proposed that fermented cabbage is a proof-of-concept of dietary manipulations that may enhance Nrf2-associated antioxidant effects, helpful in mitigating COVID-19 severity.Peer reviewe

Promoting physical activity toward children and their parents : a pilot study of the « Grand Défi Vivez Bougez »

International audienc