Density of defects and the scaling law of the entanglement entropy in quantum phase transition of one dimensional spin systems induced by a quench

We have studied quantum phase transition induced by a quench in different one dimensional spin systems. Our analysis is based on the dynamical mechanism which envisages nonadiabaticity in the vicinity of the critical point. This causes spin fluctuation which leads to the random fluctuation of the Berry phase factor acquired by a spin state when the ground state of the system evolves in a closed path. The two-point correlation of this phase factor is associated with the probability of the formation of defects. In this framework, we have estimated the density of defects produced in several one dimensional spin chains. At the critical region, the entanglement entropy of a block of $L$ spins with the rest of the system is also estimated which is found to increase logarithmically with $L$. The dependence on the quench time puts a constraint on the block size $L$. It is also pointed out that the Lipkin-Meshkov-Glick model in point-splitting regularized form appears as a combination of the XXX model and Ising model with magnetic field in the negative z-axis. This unveils the underlying conformal symmetry at criticality which is lost in the sharp point limit. Our analysis shows that the density of defects as well as the scaling behavior of the entanglement entropy follows a universal behavior in all these systems.Comment: 4 figures, Accepted in Phys. Rev.

Quantum Cournot equilibrium for the Hotelling-Smithies model of product choice

This paper demonstrates the quantization of a spatial Cournot duopoly model with product choice, a two stage game focusing on non-cooperation in locations and quantities. With quantization, the players can access a continuous set of strategies, using continuous variable quantum mechanical approach. The presence of quantum entanglement in the initial state identifies a quantity equilibrium for every location pair choice with any transport cost. Also higher profit is obtained by the firms at Nash equilibrium. Adoption of quantum strategies rewards us by the existence of a larger quantum strategic space at equilibrium.Comment: 13 pages, 6 tables, 8 figure

A statistical method for excluding non-variable CpG sites in high-throughput DNA methylation profiling

<p>Abstract</p> <p>Background</p> <p>High-throughput DNA methylation arrays are likely to accelerate the pace of methylation biomarker discovery for a wide variety of diseases. A potential problem with a standard set of probes measuring the methylation status of CpG sites across the whole genome is that many sites may not show inter-individual methylation variation among the biosamples for the disease outcome being studied. Inclusion of these so-called "non-variable sites" will increase the risk of false discoveries and reduce statistical power to detect biologically relevant methylation markers.</p> <p>Results</p> <p>We propose a method to estimate the proportion of non-variable CpG sites and eliminate those sites from further analyses. Our method is illustrated using data obtained by hybridizing DNA extracted from the peripheral blood mononuclear cells of 311 samples to an array assaying 1505 CpG sites. Results showed that a large proportion of the CpG sites did not show inter-individual variation in methylation.</p> <p>Conclusions</p> <p>Our method resulted in a substantial improvement in association signals between methylation sites and outcome variables while controlling the false discovery rate at the same level.</p

Searching for VHE gamma-ray emission associated with IceCube neutrino alerts using FACT, H.E.S.S., MAGIC, and VERITAS

The realtime follow-up of neutrino events is a promising approach to searchfor astrophysical neutrino sources. It has so far provided compelling evidencefor a neutrino point source: the flaring gamma-ray blazar TXS 0506+056 observedin coincidence with the high-energy neutrino IceCube-170922A detected byIceCube. The detection of very-high-energy gamma rays (VHE, $\mathrm{E} >100\,\mathrm{GeV}$) from this source helped establish the coincidence andconstrained the modeling of the blazar emission at the time of the IceCubeevent. The four major imaging atmospheric Cherenkov telescope arrays (IACTs) -FACT, H.E.S.S., MAGIC, and VERITAS - operate an active follow-up program oftarget-of-opportunity observations of neutrino alerts sent by IceCube. Thisprogram has two main components. One are the observations of known gamma-raysources around which a cluster of candidate neutrino events has been identifiedby IceCube (Gamma-ray Follow-Up, GFU). Second one is the follow-up of singlehigh-energy neutrino candidate events of potential astrophysical origin such asIceCube-170922A. GFU has been recently upgraded by IceCube in collaborationwith the IACT groups. We present here recent results from the IACT follow-upprograms of IceCube neutrino alerts and a description of the upgraded IceCubeGFU system.<br

Haplotype Analysis of Genomic Polymorphisms in and Around the Myotonic Dystrophy Locus in Diverse Populations of India

The frequencies of haplotypes based upon the (CTG)n repeat and three other biallelic markers in and around the myotonic dystrophy (DM) locus were estimated in 13 ethnically, linguistically and geographically diverse sub-populations of India. The range of CTG repeats in caste populations was 5–31, while in tribal populations the range was shorter (5–23). Extensive variation in frequencies of large (CTG)n alleles (≥18 repeats) was found in Indian populations. The implications of this finding on DM epidemiology are discussed. Haplotype diversity was found to be very high in most populations. The majority of the Indian DM patients carried a haplotype that is commonly found among DM patients globally; this is the most common haplotype in the class of large (≥18 repeats) CTG alleles. However, one haplotype was found to be present in particularly high frequency in Indian populations; this haplotype was also found among Indian DM patients. This haplotype may be a characteristic of Indian and possibly of other East Asian populations

Structure-Based Energetics of Stop Codon Recognition by Eukaryotic Release Factor

In translation termination, the eukaryotic release factor (eRF1) recognizes mRNA stop codons (UAA, UAG, or UGA) in a ribosomal A site and triggers release of the nascent polypeptide chain from P-site tRNA. eRF1 is highly selective for U in the first position and a combination of purines (except two consecutive guanines, i.e., GG) in the second and third positions. Eukaryotes decode all three stop codons with a single release factor eRF1, instead of two (RF1 and RF2), in bacteria. Furthermore, unlike bacterial RF1/RF2, eRF1 stabilizes the compact U-turn mRNA configuration in the ribosomal A site by accommodating four nucleotides instead of three. Despite the available cryo-EM structures (resolution ∼3.5–3.8 Å), the energetic principle for eRF1 selectivity toward a stop codon remains a fundamentally unsolved problem. Using cryo-EM structures of eukaryotic translation termination complexes as templates, we carried out molecular dynamics free energy simulations of cognate and near-cognate complexes to quantitatively address the energetics of stop codon recognition by eRF1. Our results suggest that eRF1 has a higher discriminatory power against sense codons, compared to that reported earlier for RF1/RF2. The compact mRNA formed specific intra-mRNA interactions, which itself contributed to stop codon specificity. Furthermore, the specificity is enhanced by the loss of protein–mRNA interactions and, most importantly, by desolvation of the incorrect codons in the near-cognate complexes. Our work provides a clue to how eRF1 discriminates between cognate and near-cognate codons during protein synthesis