Stochastic embedding DFT: theory and application to p-nitroaniline

Over this past decade, we combined the idea of stochastic resolution of identity with a variety of electronic structure methods. In our stochastic Kohn-Sham DFT method, the density is an average over multiple stochastic samples, with stochastic errors that decrease as the inverse square root of the number of sampling orbitals. Here we develop a stochastic embedding density functional theory method (se-DFT) that selectively reduces the stochastic error (specifically on the forces) for a selected sub-system(s). The motivation, similar to that of other quantum embedding methods, is that for many systems of practical interest the properties are often determined by only a small sub-system. In stochastic embedding DFT two sets of orbitals are used: a deterministic one associated with the embedded subspace, and the rest which is described by a stochastic set. The method is exact in the limit of large number of stochastic samples. We apply se-DFT to study a p-nitroaniline molecule in water, where the statistical errors in the forces on the system (the p-nitroaniline molecule) are reduced by an order of magnitude compared with non-embedding stochastic DFT

Tunable superlattice p-i-n photodetectors: characteristics, theory, and application

Extended measurements and theory on the recently developed monolithic wavelength demultiplexer consisting of voltage-tunable superlattice p-i-n photodetectors in a waveguide confirmation are discussed. It is shown that the device is able to demultiplex and detect two optical signals with a wavelength separation of 20 nm directly into different electrical channels at a data rate of 1 Gb/s and with a crosstalk attenuation varying between 20 and 28 dB, depending on the polarization. The minimum acceptable crosstalk attenuation at a data rate of 100 Mb/s is determined to be 10 dB. The feasibility of using the device as a polarization angle sensor for linearly polarized light is also demonstrated. A theory for the emission of photogenerated carriers out of the quantum wells is included, since this is potentially a speed limiting mechanism in these detectors. It is shown that a theory of thermally assisted tunneling by polar optical phonon interaction is able to predict emission times consistent with the observed temporal response

Ferrocene-derived P,N ligands : synthesis and application in enantioselective catalysis

Due to their unique steric and electronic properties, air-stability and modular structure, chiral hybrid P,N-ferrocenyl ligands play a prominent role in the field of asymmetric catalysis. This report aims to give a concise introduction to the syntheses of chiral hybrid P,N-ferrocenyl ligands and presents an overview of their application in enantioselective catalysis. This review is of special interest to chemists working on ligand design and asymmetric catalysis, as well as to the broader organic and inorganic community

Stochastic embedding DFT: Theory and application to p-nitroaniline in water.

Over this past decade, we combined the idea of stochastic resolution of identity with a variety of electronic structure methods. In our stochastic Kohn-Sham density functional theory (DFT) method, the density is an average over multiple stochastic samples, with stochastic errors that decrease as the inverse square root of the number of sampling orbitals. Here, we develop a stochastic embedding density functional theory method (se-DFT) that selectively reduces the stochastic error (specifically on the forces) for a selected subsystem(s). The motivation, similar to that of other quantum embedding methods, is that for many systems of practical interest, the properties are often determined by only a small subsystem. In stochastic embedding DFT, two sets of orbitals are used: a deterministic one associated with the embedded subspace and the rest, which is described by a stochastic set. The method agrees exactly with deterministic calculations in the limit of a large number of stochastic samples. We apply se-DFT to study a p-nitroaniline molecule in water, where the statistical errors in the forces on the system (the p-nitroaniline molecule) are reduced by an order of magnitude compared with nonembedding stochastic DFT

R(p,q)- analogs of discrete distributions: general formalism and application

In this paper, we define and discuss $\mathcal{R}(p,q)$- deformations of basic univariate discrete distributions of the probability theory. We mainly focus on binomial, Euler, P\'olya and inverse P\'olya distributions. We discuss relevant $\mathcal{R}(p,q)-$ deformed factorial moments of a random variable, and establish associated expressions of mean and variance. Futhermore, we derive a recursion relation for the probability distributions. Then, we apply the same approach to build main distributional properties characterizing the generalized $q-$ Quesne quantum algebra, used in physics. Other known results in the literature are also recovered as particular cases

Imputation of truncated p-values for meta-analysis methods and its genomic application

Microarray analysis to monitor expression activities in thousands of genes simultaneously has become routine in biomedical research during the past decade. A tremendous amount of expression profiles are generated and stored in the public domain and information integration by meta-analysis to detect differentially expressed (DE) genes has become popular to obtain increased statistical power and validated findings. Methods that aggregate transformed $p$-value evidence have been widely used in genomic settings, among which Fisher's and Stouffer's methods are the most popular ones. In practice, raw data and $p$-values of DE evidence are often not available in genomic studies that are to be combined. Instead, only the detected DE gene lists under a certain $p$-value threshold (e.g., DE genes with $p$-value${}<0.001$) are reported in journal publications. The truncated $p$-value information makes the aforementioned meta-analysis methods inapplicable and researchers are forced to apply a less efficient vote counting method or na\"{i}vely drop the studies with incomplete information. The purpose of this paper is to develop effective meta-analysis methods for such situations with partially censored $p$-values. We developed and compared three imputation methods - mean imputation, single random imputation and multiple imputation - for a general class of evidence aggregation methods of which Fisher's and Stouffer's methods are special examples. The null distribution of each method was analytically derived and subsequent inference and genomic analysis frameworks were established. Simulations were performed to investigate the type I error, power and the control of false discovery rate (FDR) for (correlated) gene expression data. The proposed methods were applied to several genomic applications in colorectal cancer, pain and liquid association analysis of major depressive disorder (MDD). The results showed that imputation methods outperformed existing na\"{i}ve approaches. Mean imputation and multiple imputation methods performed the best and are recommended for future applications.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS747 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org