Brownian Integrated Covariance Functions for Gaussian Process Modeling: Sigmoidal Versus Localized Basis Functions

<p>Gaussian process modeling, or kriging, is a popular method for modeling data from deterministic computer simulations, and the most common choices of covariance function are Gaussian, power exponential, and Matérn. A characteristic of these covariance functions is that the basis functions associated with their corresponding response predictors are localized, in the sense that they decay to zero as the input location moves away from the simulated input sites. As a result, the predictors tend to revert to the prior mean, which can result in a bumpy fitted response surface. In contrast, a fractional Brownian field model results in a predictor with basis functions that are nonlocalized and more sigmoidal in shape, although it suffers from drawbacks such as inability to represent smooth response surfaces. We propose a class of Brownian integrated covariance functions obtained by incorporating an integrator (as in the white noise integral representation of a fractional Brownian field) into any stationary covariance function. Brownian integrated covariance models result in predictor basis functions that are nonlocalized and sigmoidal, but they are capable of modeling smooth response surfaces. We discuss fundamental differences between Brownian integrated and other covariance functions, and we illustrate by comparing Brownian integrated power exponential with regular power exponential kriging models in a number of examples. Supplementary materials for this article are available online.</p

SOiCISCF: Combining SOiCI and iCISCF for Variational Treatment of Spin–Orbit Coupling

It has recently been shown that the SOiCI approach [Zhang, N.; J. Phys.: Condens. Matter 2022, 34, 224007], in conjunction with the spin-separated exact two-component relativistic Hamiltonian, can provide very accurate fine structures of systems containing heavy elements by treating electron correlation and spin–orbit coupling (SOC) on an equal footing. Nonetheless, orbital relaxations/polarizations induced by SOC are not yet fully accounted for due to the use of scalar relativistic orbitals. This issue can be resolved by further optimizing the still real-valued orbitals self-consistently in the presence of SOC, as done in the spin–orbit coupled CASSCF approach [Ganyushin, D.; et al. J. Chem. Phys. 2013, 138, 104113] but with the iCISCF algorithm [Guo, Y.; J. Chem. Theory Comput. 2021, 17, 7545–7561] for large active spaces. The resulting SOiCISCF employs both double group and time reversal symmetries for computational efficiency and the assignment of target states. The fine structures of p-block elements are taken as showcases to reveal the efficacy of SOiCISCF

79genes_concatenated

79 coding gene

Additional file 1: Figure S1. of The prognosis of invasive micropapillary carcinoma compared with invasive ductal carcinoma in the breast: a meta-analysis

(A) Funnel plot to detect publication bias for overall survival (OS). (B) Funnel plot to detect publication bias for disease-specific survival (DSS). (TIFF 304 kb

Estimating publication bias by <i>Begg's</i> test (A) and <i>Harbord's weighted linear regression</i> test (B).

<p><i>Begg's</i> test (A) was adopted for measuring publication bias and showed a non-significant publication bias (<i>P</i> = 0.917). <i>Harbord's weighted linear regression</i> (B) also indicated a non-significant publication bias (<i>P</i> = 0.173).</p

Air pollution and tourism development: An interplay

We empirically examine the interplay between air pollution and tourism development based on a fine-grained dataset covering monthly-level tourism information of 58 major cities in China from October 2013 to December 2017. We adopt an empirical strategy utilizing wind speed as an instrumental variable for air pollution to deal with the endogeneity caused by the reverse causality. We control for individual city fixed effects, month fixed effects, meteorological conditions and other social factors of tourism destinations. We find the interplay between air pollution and tourism development. Our study offers significant empirical evidence for policy makers to design policies that can mitigate the consequences of air pollution in the tourism sector and manage the development of the tourism economy

174_coding_noncoding_genes

174 regions including 79 coding genes and 95 non-coding region

Paired data of different detection fragments of EBV DNA.

<p>Paired data of different detection fragments of EBV DNA.</p

Different primers used for detecting EBV prevalence in PCR analyses.

<p><i>95% CI:</i> confidence interval, <i>OR:</i> odds ratio.</p>a<p>: One study <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031656#pone.0031656-Fina1" target="_blank">[10]</a> was divided into six parts because samples from six different countries were tested. Three studies <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031656#pone.0031656-Bonnet1" target="_blank">[11]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031656#pone.0031656-Kulka1" target="_blank">[22]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031656#pone.0031656-Cristina1" target="_blank">[30]</a> were excluded because one <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031656#pone.0031656-Bonnet1" target="_blank">[11]</a> could not offer the EBV DNA prevalence detected by each primer, respectively, and the others <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031656#pone.0031656-Kulka1" target="_blank">[22]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031656#pone.0031656-Cristina1" target="_blank">[30]</a> only included 1 case.</p>b<p>: adjusted by normalizing the constituent ratio of region and DNA specimen of the <i>Bam H1W</i> group.</p>c<p>: one-sided, 97.5% confidence interval.</p>d<p>: exact confidence levels not possible with zero count cells.</p

concatenated_non_coding_95genes

95 non-coding region