A Unified Scheme for Modular Invariant Partition Functions of WZW Models

We introuduce a unified method which can be applied to any WZW model at arbitrary level to search systematically for modular invariant physical partition functions. Our method is based essentially on modding out a known theory on group manifold $G$ by a discrete group $\Gamma$. We apply our method to $\widehat {su(n)}$ with $n=2,3,4,5,6$, and to $\widehat {g_2}$ models, and obtain all the known partition functions and some new ones, and give explicit expressions for all of them.Comment: 30 page ,SUTDP/11/93/72 Department of Physics, Sharif University of Technolog

Coined quantum walks on percolation graphs

Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well-studied on regular structures and also shown to be sensitive to defects and imperfections in the lattice. As a simple example of a disordered system, we consider percolation lattices, in which edges or sites are randomly missing, interrupting the progress of the quantum walk. We use numerical simulation to study the properties of coined quantum walks on these percolation lattices in one and two dimensions. In one dimension (the line) we introduce a simple notion of quantum tunneling and determine how this affects the properties of the quantum walk as it spreads. On two-dimensional percolation lattices, we show how the spreading rate varies from linear in the number of steps down to zero, as the percolation probability decreases to the critical point. This provides an example of fractional scaling in quantum walk dynamics.Comment: 25 pages, 14 figures; v2 expanded and improved presentation after referee comments, added extra figur

Prophet Inequalities for IID Random Variables from an Unknown Distribution

A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: given a sequence of random variables X1, . . . , Xn drawn independently from a distribution F , the goal is to choose a stopping time τ so as to maximize α such that for all distributions F we have E[Xτ ] ≥ α · E[maxt Xt ]. What makes this problem challenging is that the decision whether τ = t may only depend on the values of the random variables X1, . . . , Xt and on the distribution F . For a long time the best known bound for the problem had been α ≥ 1 − 1/e ≈ 0.632, but quite recently a tight bound of α ≈ 0.745 was obtained. The case where F is unknown, such that the decision whether τ = t may depend only on the values of the random variables X1, . . . , Xt , is equally well motivated but has received much less attention. A straightforward guarantee for this case of α ≥ 1/e ≈ 0.368 can be derived from the solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F , and show that even with o(n) samples α ≤ 1/e. On the other hand, n samples allow for a significant improvement, while O(n2) samples are equivalent to knowledge of the distribution: specifically, with n samples α ≥ 1 − 1/e ≈ 0.632 and α ≤ ln(2) ≈ 0.693, and with O(n2) samples α ≥ 0.745 − ε for any ε > 0

The Heterogeneous Pathogenesis of Selective Immunoglobulin A Deficiency

Selective immunoglobulin A deficiency (SIgAD) is the most prevalent type of primary immunodeficiency disorder. The phenotypic feature of SIgAD is related to a defect in B lymphocyte differentiation into plasma cell-producing immunoglobulin A (IgA). In this review, we summarize the recent advances in this regard. Genetic (including major histocompatibility complex MHC and non-MHC genes), immunologic (including B and T lymphocyte subsets abnormality), cytokines/chemokines and their related receptors, apoptosis and microbiota defects are reviewed. The mechanisms leading to SIgAD are most likely multifactorial and it can be speculated that several pathways controlling B cells functions or regulating epigenetic of the IGHA gene encoding constant region of IgA heavy chain and long-term survival of IgA switched memory B cells and plasma cells may be defective in different SIgAD patients. © 2019 S. Karger AG, Basel. Copyright: All rights reserved

Substitutional doping of Cu in diamond: Mott physics with pp orbitals

Discovery of superconductivity in the impurity band formed by heavy doping of boron into diamond (C:B) as well as doping of boron into silicon (Si:B) has provided a rout for the possibility of new families of superconducting materials. Motivated by the special role played by copper atoms in high temperature superconducting materials where essentially Cu $d$ orbitals are responsible for a variety of correlation induced phases, in this paper we investigate the effect of substitutional doping of Cu into diamond. Our extensive first principle calculations averaged over various geometries based on density functional theory, indicates the formation of a mid-gap band, which mainly arises from the $t_{2g}$ and $4p$ states of Cu. For impurity concentrations of more than $\sim 1$2p$bands of neighboring carbon atoms can be ignored. Based on our detailed analysis, we suggest a two band model for the mid-gap states consisting of a quarter-filled hole like$t_{2g}$band, and a half-filled band of$4p$states. Increasing the concentration of the Cu impurity beyond$\sim 5%, completely closes the spectral gap of the host diamond.Comment: 5 figure

Ephemeris Updates for Seven Selected HATNet Survey Transiting Exoplanets

We refined the ephemeris of seven transiting exoplanets HAT-P-6b, HAT-P-12b, HAT-P-18b, HAT-P-22b, HAT-P-32b, HAT-P-33b, and HAT-P-52b. We observed 11 transits from eight observatories in different filters for HAT-P-6b and HAT-P-32b. Also, the Exoplanet Transit Database (ETD) observations for each of the seven exoplanets were analyzed, and the light curves of five systems were studied using Transiting light Exoplanet Survey Satellite (TESS) data. We used Exofast-v1 to simulate these ground- and space-based light curves and estimate mid-transit times. We obtained a total of 11, 175 and 67 mid-transit times for these seven exoplanets from our observations, ETD and TESS data, respectively, along with 155 mid-transit times from the literature. Then, we generated transit timing variation (TTV) diagrams for each using derived mid-transit times as well as those found in the literature. The systems' linear ephemeris was then refined and improved using the Markov Chain Monte Carlo (MCMC) method. All of the studied exoplanets, with the exception of the HAT-P-12b system, displayed an increasing trend in the orbital period in the TTV diagrams.Comment: 11 Pages, submitted to the Astrophysics journa

Expanding clinical phenotype and novel insights into the pathogenesis of ICOS deficiency

Background: Inducible T cell co-stimulator (ICOS) deficiency has been categorized as a combined immunodeficiency often complicated by enteropathies, autoimmunity, lymphoproliferation, and malignancy. We report seven new patients and four novel ICOS mutations resulting in a common variable immunodeficiency (CVID)–like phenotype and show that dysregulated IL-12 release, reduced cytotoxic T lymphocyte–associated protein 4 (CTLA4) expression, and skewing towards a Th1-dominant phenotype are all associated with inflammatory complications in this condition. Methods: A combination of whole exome and Sanger sequencing was used to identify novel mutations. Standard clinical and immunological evaluation was performed. FACS and ELISA-based assays were used to study cytokine responses and ICOS/ICOSL/CTLA4 expression following stimulation of whole blood and PBMCs with multiple TLR ligands, anti-CD3, and PHA. Results: Four novel ICOS mutations included homozygous c.323_332del, homozygous c.451C>G, and compound heterozygous c.58+1G>A/c.356T>C. The predominant clinical phenotype was that of antibody deficiency associated with inflammatory complications in 4/7 patients. Six out of seven patients were treated with immunoglobulin replacement and one patient died from salmonella sepsis. All patients who were tested showed reduced IL-10 and IL-17 cytokine responses, normal IL-1β, IL6, and TNF release following LPS stimulation and highly elevated IL-12 production in response to combined LPS/IFNγ stimulation. This was associated with skewing of CD4+ T cells towards Th1 phenotype and increased expression of ICOSL on monocytes. Lastly, reduced CTLA4 expression was found in 2 patients. One patient treated with ustekinumab for pancytopenia due to granulomatous bone marrow infiltration failed to respond to this targeted therapy. Conclusions: ICOS deficiency is associated with defective T cell activation, with simultaneously enhanced stimulation of monocytes. The latter is likely to result from a lack of ICOS/ICOSL interaction which might be necessary to provide negative feedback which limits monocytes activation