Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity

This paper is concerned with the inhomogeneous nonlinear Shrödinger equation (INLS-equation)iu_t + Δu + V(Єx)│u│^pu = 0, x Є R^N. In the critical and supercritical cases p ≥ 4/N, with N ≥ 2, it is shown here that standing-wave solutions of (INLS-equation) on H^1(R^N) perturbation are nonlinearly unstable or unstable by blow-up under certain conditions on the potential term V with a small Є > 0

Norms of commutators of self-adjoint operators

AbstractIn this note, the estimate of norms of commutators of self-adjoint operators is established

Statistical Modeling of MicroRNA Expression with Human Cancers

MicroRNAs (miRNAs) are small non-coding RNAs (containing about 22 nucleotides) that regulate gene expression. MiRNAs are involved in many different biological processes such as cell proliferation, differentiation, apoptosis, fat metabolism, and human cancer genes; while miRNAs may function as candidates for diagnostic and prognostic biomarkers and predictors of drug response. This paper emphasizes the statistical methods in the analysis of the associations of miRNA gene expression with human cancers and related clinical phenotypes: 1) simple statistical methods include chi-square test, correlation analysis, t-test and one-way ANOVA; 2) regression models include linear and logistic regression; 3) survival analysis approaches such as non-parametric Kaplan-Meier method and log-rank test as well as semi-parametric Cox proportional hazards models have been used for time to event data; 4) multivariate method such as cluster analysis has been used for clustering samples and principal component analysis (PCA) has been used for data mining; 5) Bayesian statistical methods have recently made great inroads into many areas of science, including the assessment of association between miRNA expression and human cancers; and 6) multiple testing

Bayesian Survival Analysis of Genetic Variants in PTPRN2 Gene for Age at Onset of Cancer

Background: The protein tyrosine phosphatase, receptor type, N polypeptide 2 (PTPRN2) gene may play a role in cancer; however, no study has focused on the associations of genetic variants within the PTPRN2 gene with age at onset (AAO) of cancer. Methods: This study examined 220 single nucleotide polymorphisms (SNPs) within the PTPRN2 gene in the Marshfield sample with 716 cancer cases (any diagnosed cancer, excluding minor skin cancer) and 2,848 non-cancer controls. Multiple logistic regression model and linear regression model in PLINK software were used to examine the association of each SNP with the risk of cancer and AAO, respectively. For survival analysis of AAO, both classic Cox regression and Bayesian survival analysis using the Cox proportional hazards model in SAS v. 9.4 were applied to detect the association of each SNP with AAO. The hazards ratios (HRs) with 95% confidence intervals (CIs) were estimated. Results: Single marker analysis identified 10 SNPs associated with the risk of cancer and 9 SNPs associated with AAO (p \u3c 0.05). SNP rs7783909 revealed the strongest association with cancer (p = 6.52x10-3); while the best signal for AAO was rs4909140 (p = 6.18x10-4), which was also associated with risk of cancer (p = 0.0157). Classic Cox regression model showed that 11 SNPs were associated with AAO (top SNP rs4909140 with HR = 1.38, 95%CI = 1.11-1.71, p = 3.3x10-3). Bayesian Cox regression model showed similar results to those using the classic Cox regression (top SNP rs4909140 with HR = 1.39, 95%CI = 1.1-1.69). Conclusions: This study provides evidence of several genetic variants within the PTPRN2 gene influencing the risk of cancer and AAO, and will serve as a resource for replication in other populations

Two-dimensional thermoelastic contact problem of functionally graded materials involving frictional heating

AbstractThe two-dimensional thermoelastic sliding frictional contact of functionally graded material (FGM) coated half-plane under the plane strain deformation is investigated in this paper. A rigid punch is sliding over the surface of the FGM coating with a constant velocity. Frictional heating, with its value proportional to contact pressure, friction coefficient and sliding velocity, is generated at the interface between the punch and the FGM coating. The material properties of the coating vary exponentially along the thickness direction. In order to solve the heat conduction equation analytically, the homogeneous multi-layered model is adopted for treating the graded thermal diffusivity coefficient with other thermomechanical properties being kept as the given exponential forms. The transfer matrix method and Fourier integral transform technique are employed to convert the problem into a Cauchy singular integral equation which is then solved numerically to obtain the unknown contact pressure and the in-plane component of the surface stresses. The effects of the gradient index, Peclet number and friction coefficient on the thermoelastic contact characteristics are discussed in detail. Numerical results show that the distribution of the contact stress can be altered and therefore the thermoelastic contact damage can be modified by adjusting the gradient index, Peclet number and friction coefficient

A search for massive young stellar objects towards 98 CH3_{3}OH maser sources

Using the 13.7 m telescope of Purple Mountain Observatory (PMO), a survey of J=1-0 lines of CO and its isotopes was carried out towards 98 methanol maser sources in January 2008. Eighty-five sources have infrared counterparts within one arcmin. In the survey, except 43 sources showing complex or multiple-peak profiles, almost all the $^{13}$CO line profiles of the other 55 sources have large line widths of 4.5 km s$^{-1}$ on average and are usually asymmetric. Fifty corresponding Infrared Astronomical Satellite (IRAS) sources of these 55 sources are with $L_{bol}$ larger than $10^{3}L_{\odot}$, which can be identified as possible high-mass young stellar sources. Statistics show that the $^{13}$CO line widths correlate with the bolometric luminosity of the associated IRAS sources. We also report the mapping results of two sources: IRAS 06117+1350 and IRAS 07299-1651 here. Two cores were found in IRAS 06117+1350 and one core was detected in IRAS 07299-1651. The northwest core in IRAS 06117+1350 and the core in IRAS 07299-1651 can be identified as precursors of UC\simH{\sc ii} regions or high-mass protostellar objects (HMPOs). The southeast core of IRAS 06117+1350 has no infrared counterpart, seeming to be on younger stages than pre-UC\simH{\sc ii} phase.Comment: A search for massive young stellar objects. Accepted to RAA in 201

Robust measurement selection design for experimental systems with input uncertainty

Input uncertainty in experimental implementation deteriorates data quality for parameter estimation. This work aims to examine the influence of input uncertainty, in particular the inaccurate setting of initial states, to parameter estimation and explore methods to mitigate the effects. First, a Monte-Carlo method is employed to generate input-output data. The input uncertainty is assumed to follow Gaussian distribution. Samples are taken from the uncertainty region and used to produce output through the dynamic system. Statistical characteristics are utilised to quantify uncertainty in outputs. Then a robust experimental design (RED) is proposed, in which the states that are less affected by input uncertainty are selected as measurement state variables. In addition, two different residual functions are used in parameter estimation to compare the estimation robustness against data uncertainty. Simulation studies are conducted using a benchmark enzyme reaction system. Compared to the nondesigned experimental settings, improved parameter estimation is achieved via robust design

Common Genetic Variants in the HNF1B Gene Contribute to Diabetes and Multiple Cancers

Diabetes and cancers are major public health problems in the United States and in the world. Epidemiological studies have clearly demonstrated the associations and co morbidity between Type 2 Diabetes (T2D) and multiple cancers such as endometrial and prostate cancers. However, the mechanism of such associations has not been elucidated. Genetic variation is proposed to contribute to these diseases, and common genetic variants may explain part of the associations among these diseases. Single Nucleotide Polymorphisms (SNPs) rs4430796 and rs7501939 within the HNF1B/TCF2 gene (Gene ID: 6928) have been observed to be associated with T2D and endometrial and prostate cancers in several studies (pleiotropic effects). Future work is needed to assess additional genetic loci sharing among these diseases. To better understand the genetic etiology of disease comorbidity it will be useful to combine the results of Genome-Wide Association Studies (GWAS), gene-gene and gene-environment interactions, with the recent rapid advances in Next Generation Sequencing (NGS) technologies

Positive and unlabeled learning for user behavior analysis based on mobile internet traffic data

With the rapid development of wireless communication and mobile Internet, mobile phone becomes ubiquitous and functions as a versatile and smart system, on which people frequently interact with various mobile applications (Apps). Understanding human behaviors using mobile phone is significant for mobile system developers, for human-centered system optimization and better service provisioning. In this paper, we focus on mobile user behavior analysis and prediction based on mobile Internet traffic data. Real traffic flow data is collected from the public network of Internet Service Providers (ISPs), by high-performance network traffic monitors.We construct User-App bipartite network to represent the traffic interaction pattern between users and App servers. After mining the explicit and implicit features from User-App bipartite network, we propose two positive and unlabeled learning (PU learning) methods, including Spy-based PU learning and K-means-based PU learning, for App usage prediction and mobile video traffic identification. We firstly use the traffic flow data of QQ, a very famous messaging and social media application possessing high market share in China, as the experimental dataset for App usage prediction task. Then we use the traffic flow data from six popular Apps, including video intensive Apps (Youku, Baofeng, LeTV, Tudou) and other Apps (Meituan, Apple), as the experimental dataset for mobile video traffic identification task. Experimental results show that our proposed PU learning methods perform well in both tasks