Dynamics of multipartite quantum correlations under decoherence

Quantum discord is an optimal resource for the quantification of classical and non-classical correlations as compared to other related measures. Geometric measure of quantum discord is another measure of quantum correlations. Recently, the geometric quantum discord for multipartite states has been introduced by Jianwei Xu [arxiv:quant/ph.1205.0330]. Motivated from the recent study [Ann. Phys. 327 (2012) 851] for the bipartite systems, I have investigated global quantum discord (QD) and geometric quantum discord (GQD) under the influence of external environments for different multipartite states. Werner-GHZ type three-qubit and six-qubit states are considered in inertial and non-inertial settings. The dynamics of QD and GQD is investigated under amplitude damping, phase damping, depolarizing and flipping channels. It is seen that the quantum discord vanishes for p>0.75 in case of three-qubit GHZ states and for p>0.5 for six qubit GHZ states. This implies that multipartite states are more fragile to decoherence for higher values of N. Surprisingly, a rapid sudden death of discord occurs in case of phase flip channel. However, for bit flip channel, no sudden death happens for the six-qubit states. On the other hand, depolarizing channel heavily influences the QD and GQD as compared to the amplitude damping channel. It means that the depolarizing channel has the most destructive influence on the discords for multipartite states. From the perspective of accelerated observers, it is seen that effect of environment on QD and GQD is much stronger than that of the acceleration of non-inertial frames. The degradation of QD and GQD happens due to Unruh effect. Furthermore, QD exhibits more robustness than GQD when the multipartite systems are exposed to environment.Comment: 15 pages, 4 figures, 4 table

Author Correction: Discovery of 42 genome-wide significant loci associated with dyslexia

Correction to: Nature Genetics https://doi.org/10.1038/s41588-022-01192-y. Published online 20 October 2022. In the version of this article originally published, a paragraph was omitted in the Methods section, reading “Genomic control. Top SNPs are reported from the more conservative GWAS results adjusted for genomic control (Fig. 1, Extended Data Figs. 1–4, and Supplementary Tables 1, 2, 9 and 10), whereas downstream analyses (including gene-set analysis, enrichment and heritability partitioning, genetic correlations, polygenic prediction, candidate gene replication) are based on GWAS results without genomic control.” The paragraph has now been included in the HTML and PDF versions of the article

On the Estimation and Application of Max-Stable Processes

Modeling extreme observations in multivariate time series is a di#cult exercise. Classical treatments of multivariate extremes use certain multivariate extreme value distributions to model the dependencies between components. An alternative approach based on multivariate max-stable processes enables the simultaneous modeling of dependence within and between time series. We propose a specific class of max-stable processes, known as multivariate maxima of moving maxima (M4 processes for short), and present procedures to estimate their coe#cients. To illustrate the methods, some examples are given for modeling jumps in returns in multivariate financial time series. We introduce a new measure to quantify and predict the extreme co-movements in price returns. Keywords: multivariate extremes, multivariate maxima of moving maxima, extreme value distribution, empirical distribution, estimation, extreme dependence, extreme co-movement.

MONITORING THE CHANGES OF LAKES IN THE SOURCE REGION OF THREE RIVERS WITH REMOTE SENSING DATA FROM 1976 TO 2009

As the birthplace of Yangtze River, the Yellow River and Lancang Rive, Source Region of Three Rivers (SRTR) is an important resource for fresh water supplement in China. SRTR also has very obvious ecological function which forms ecological security barrier for China's Qinghai-Tibet plateau. The inland lakes here play an important role for the water cycle in the plateau. The monitoring results were extracted with TM data from 1976 to 2009. The results show that from 1976 to 2009 the lakes' area in SRTR dropped first and then expanded with 2000 as sector. The lakes area was 6778 km2 in 2009, about 1.90% of the whole region, and increased than 1976 by 133.15 km2. Most of the large lakes above 80 km2 have the same change trend. The expanded lakes increased in number gradually, while the changes in the amplitude and time characteristics were different. From 1976 to 2000, the number of new lakes increased while died lakes dropped; and from 2000 to 2009 it is just on the contrary. In the study the index of lake change trend (ILCT) was adopted to contrast lake atrophy condition. With ILCT 24.55 there is an expansion trend for the lakes in SRTR during the last 35 years. The lakes with ILCT's absolute value greater than 1 were those merged with or disconnected from surrounding smaller lakes. Here the precipitation and snow melt are main supplies for the lakes. The change of lakes' area has well correlated with precipitation, and weak correlated with temperature from 1976 to 2009. But from 2000 to 2009, there has a strong correlation with precipitation, temperature. All these show from the side that the precipitation and snow melt are important factors to influence the lakes’ change. The lakes have the coordination function for the good ecological environment in the region. The conclusions from the study can provide references in response to climate change research and rational utilization of water resources in SRTR

The Behavior of Multivariate Maxima of Moving Maxima Processes

In the characterization of multivariate extreme indices of multivariate stationary processes, multivariate maxima of moving maxima processes, or M4 processes for short, have been introduced by Smith and Weissman. Central to the introduction of M4 processes is that the extreme observations of multivariate stationary processes may be characterized in terms of a limiting max-stable process under quite general conditions and a max-stable process can be arbitrarily closely approximated by a M4 process. In this paper, we derive some additional basic probabilistic properties for a finite class of M4 processes of which each contains finite range clustered moving patterns, called signature patterns, when extreme events occur. We use these properties to construct statistical estimation schemes for model parameters