The monotonicity results and sharp inequalities for some power-type means of two arguments

For $a,b>0$ with $a\neq b$, we define M_{p}=M^{1/p}(a^{p},b^{p})\text{if}p\neq 0 \text{and} M_{0}=\sqrt{ab}, where $M=A,He,L,I,P,T,N,Z$ and $Y$ stand for the arithmetic mean, Heronian mean, logarithmic mean, identric (exponential) mean, the first Seiffert mean, the second Seiffert mean, Neuman-S\'{a}ndor mean, power-exponential mean and exponential-geometric mean, respectively. Generally, if $M$ is a mean of $a$ and $b$, then $M_{p}$ is also, and call "power-type mean". We prove the power-type means $P_{p}$, $T_{p}$, $N_{p}$, $Z_{p}$ are increasing in $p$ on $\mathbb{R}$ and establish sharp inequalities among power-type means $A_{p}$, $He_{p}$, $L_{p}$, $I_{p}$, $P_{p}$, $N_{p}$, $Z_{p}$, $Y_{p}$% . From this a very nice chain of inequalities for these means L_{2}<P<N_{1/2}<He<A_{2/3}<I<Z_{1/3}<Y_{1/2} follows. Lastly, a conjecture is proposed.Comment: 11 page

Fast kinetic Monte Carlo simulation of strained heteroepitaxy in three dimensions

Accelerated algorithms for simulating the morphological evolution of strained heteroeptiaxy based on a ball and spring lattice model in three dimensions are explained. We derive exact Green's function formalisms for boundary values in the associated lattice elasticity problems. The computational efficiency is further enhanced by using a superparticle surface coarsening approximation. Atomic hoppings simulating surface diffusion are sampled using a multi-step acceptance-rejection algorithm. It utilizes quick estimates of the atomic elastic energies from extensively tabulated values modulated by the local strain. A parameter controls the compromise between accuracy and efficiency of the acceptance-rejection algorithm.Comment: 10 pages, 4 figures, submitted to Proceedings of Barrett Lectures 2007, Journal of Scientific Computin

Capillary-based multiplexed isothermal nucleic acid-based test for sexually transmitted diseases in patients

We demonstrate a multiplexed loop mediated isothermal amplification (LAMP) assay for infectious disease diagnostics, where the analytical process flow of target pathogens genomic DNA is performed manually by moving magnetic beads through a series of plugs in a capillary. Heat is provided by a water bath and the results read by the naked eye, enabling applications in low resource settings

Competing roughening mechanisms in strained heteroepitaxy: a fast kinetic Monte Carlo study

We study the morphological evolution of strained heteroepitaxial films using kinetic Monte Carlo simulations in two dimensions. A novel Green's function approach, analogous to boundary integral methods, is used to calculate elastic energies efficiently. We observe island formation at low lattice misfit and high temperature that is consistent with the Asaro-Tiller-Grinfeld instability theory. At high misfit and low temperature, islands or pits form according to the nucleation theory of Tersoff and LeGoues.Comment: 4 pages, 4 figures, ReVTe

Universal condition for critical percolation thresholds of kagome-like lattices

Lattices that can be represented in a kagome-like form are shown to satisfy a universal percolation criticality condition, expressed as a relation between P_3, the probability that all three vertices in the triangle connect, and P_0, the probability that none connect. A linear approximation for P_3(P_0) is derived and appears to provide a rigorous upper bound for critical thresholds. A numerically determined relation for P_3(P_0) gives thresholds for the kagome, site-bond honeycomb, (3-12^2), and "stack-of-triangle" lattices that compare favorably with numerical results.Comment: Several new figures and small change

Systematic Analysis of Impact of Sampling Regions and Storage Methods on Fecal Gut Microbiome and Metabolome Profiles.

The contribution of human gastrointestinal (GI) microbiota and metabolites to host health has recently become much clearer. However, many confounding factors can influence the accuracy of gut microbiome and metabolome studies, resulting in inconsistencies in published results. In this study, we systematically investigated the effects of fecal sampling regions and storage and retrieval conditions on gut microbiome and metabolite profiles from three healthy children. Our analysis indicated that compared to homogenized and snap-frozen samples (standard control [SC]), different sampling regions did not affect microbial community alpha diversity, while a total of 22 of 176 identified metabolites varied significantly across different sampling regions. In contrast, storage conditions significantly influenced the microbiome and metabolome. Short-term room temperature storage had a minimal effect on the microbiome and metabolome profiles. Sample storage in RNALater showed a significant level of variation in both microbiome and metabolome profiles, independent of the storage or retrieval conditions. The effect of RNALater on the metabolome was stronger than the effect on the microbiome, and individual variability between study participants outweighed the effect of RNALater on the microbiome. We conclude that homogenizing stool samples was critical for metabolomic analysis but not necessary for microbiome analysis. Short-term room temperature storage had a minimal effect on the microbiome and metabolome profiles and is recommended for short-term fecal sample storage. In addition, our study indicates that the use of RNALater as a storage medium of stool samples for microbial and metabolomic analyses is not recommended.IMPORTANCE The gastrointestinal microbiome and metabolome can provide a new angle to understand the development of health and disease. Stool samples are most frequently used for large-scale cohort studies. Standardized procedures for stool sample handling and storage can be a determining factor for performing microbiome or metabolome studies. In this study, we focused on the effects of stool sampling regions and stool sample storage conditions on variations in the gut microbiome composition and metabolome profile

Electron and Ion Acceleration in Relativistic Shocks with Applications to GRB Afterglows

We have modeled the simultaneous first-order Fermi shock acceleration of protons, electrons, and helium nuclei by relativistic shocks. By parameterizing the particle diffusion, our steady-state Monte Carlo simulation allows us to follow particles from particle injection at nonthermal thermal energies to above PeV energies, including the nonlinear smoothing of the shock structure due to cosmic-ray (CR) backpressure. We observe the mass-to-charge (A/Z) enhancement effect believed to occur in efficient Fermi acceleration in non-relativistic shocks and we parameterize the transfer of ion energy to electrons seen in particle-in-cell (PIC) simulations. For a given set of environmental and model parameters, the Monte Carlo simulation determines the absolute normalization of the particle distributions and the resulting synchrotron, inverse-Compton, and pion-decay emission in a largely self-consistent manner. The simulation is flexible and can be readily used with a wide range of parameters typical of gamma-ray burst (GRB) afterglows. We describe some preliminary results for photon emission from shocks of different Lorentz factors and outline how the Monte Carlo simulation can be generalized and coupled to hydrodynamic simulations of GRB blast waves. We assume Bohm diffusion for simplicity but emphasize that the nonlinear effects we describe stem mainly from an extended shock precursor where higher energy particles diffuse further upstream. Quantitative differences will occur with different diffusion models, particularly for the maximum CR energy and photon emission, but these nonlinear effects should be qualitatively similar as long as the scattering mean free path is an increasing function of momentum.Comment: Accepted for publication in MNRA