Search Results (8)

The exponential dispersion model (EDM) generated by the Landau distribution, denoted by EDM-EVF (exponential variance function), belongs to the Tweedie scale with power infinity. Its density function does not have an explicit form and, as of yet, has not been used for statistical aspects. Out of all EDMs belonging to the Tweedie scale, only two EDMs are steep and supported on the whole real line: the normal EDM with constant variance function and the EDM-EVF. All other absolutely continuous steep EDMs in the Tweedie scale are supported on the positive real line. This paper aims to accomplish an overall picture of all generalized linear model (GLM) applications belonging to the Tweedie scale by including the EDM-EVF. This paper introduces all GLM ingredients needed for its analysis, including the respective link function and total and scaled deviance. We study its analysis of deviance, derive the asymptotic properties of the maximum likelihood estimation (MLE) of the covariate parameters, and obtain the asymptotic distribution of deviance, using saddlepoint approximation. We provide numerical studies, which include estimation algorithm, simulation studies, and applications to three real datasets, and demonstrate that GLM using the EDM-EVF performs better than the linear model based on the normal EDM. An R package accompanies all of these. Full article

Asymptotic analysis for an elastic layer under light fluid loading was developed. The ratio of fluid and solid densities was chosen as the main small parameter determining a novel scaling. The leading- and next-order approximations were derived from the full dispersion relation corresponding to long-wave, low-frequency, antisymmetric motions. The asymptotic plate models, including the equations of motion and the impenetrability condition, motivated by the aforementioned shortened dispersion equations, were derived for a plane-strain setup. The key findings included, in particular, the necessity of taking into account transverse plate inertia at the leading order, which is not the case for heavy fluid loading. In addition, the transverse shear deformation, rotation inertia, and a number of other corrections appeared at the next order, contrary to the previous asymptotic developments for fluid-loaded plates not assuming a light fluid loading scenario. Full article

Solute transport in rivers is controlled by mixing processes that occur over a wide spectrum of spatial and temporal scales. Deviations from the classic advection–dispersion model observed in tracer test studies are known to be generated by the temporary trapping of solutes in storage zones where velocities and mixing rates are relatively small. In this work, the relation between the early and late-time behavior of solute breakthrough curves (BTCs) and the key parameters of the Transient Storage Model (TSM) is analyzed using non-asymptotic approximations of the model equations. Two main slopes are identified corresponding to the rising and decreasing limbs of the BTCs which are linked by specific relationships to transport and storage parameters. The validity of the proposed approximations is demonstrated with both synthetic and experimental data. Consistent with the TSM assumptions, the range of validity of the proposed approximations represents the limit of separability between surface dispersion and transient storage and can be expressed as a function of a nondimensional parameter. The results of this work can help environmental scientists identify solute transport and transient storage parameters and support the design of enhanced field tracer experiments. Full article

The atmosphere of Venus exhibits equatorial planetary-scale waves that are suspected to play an important role in its complex atmospheric circulation. Due to its particularly long sidereal day (243 terrestrial days against 24 h for the Earth), the Venusian waves must be described with the momentum equations for a cyclostrophic regime, but efforts to derive analytical wave solutions have been scarce. Following a classic approach for the terrestrial quasi-geostrophic regime, I present analytical solutions for equatorial waves in the atmosphere of Venus, assuming a single layer of a homogeneous incompressible fluid with a free surface and focusing on two asymptotic cases described by the ratio of their non-dimensional frequency and zonal wavenumber. One of the dispersion relations that has been obtained describes waves on a small spatial scale propagating upstream relative to the zonal flow, which is associated with a Rossby-type wave called “centrifugal”. The solutions for the other asymptotic case were interpreted as inertio-surface waves, which describe planetary-scale waves that can propagate “upstream” and “downstream” relative to the zonal winds and have null group velocity. These new wave solutions stress relevant differences between waves in geostrophic and cyclostrophic regimes and may be applicable to Saturn’s moon, Titan, and Venus-like exoplanets. Full article

In this work, a novel workflow has been proposed, validated and applied to interpret the early time transient pressure data in tight oil reservoirs with physical constraints. More specifically, the theoretical model was developed to obtain the transient pressure response for a vertical well in tight oil reservoirs with consideration of pseudo threshold pressure gradient (TPG). Then, a physical constraint between the skin factor and formation permeability has been proposed based on the physical meaning of percolation theory. This physical constraint can be applied to determine the lower limit of the skin factor which can reduce the uncertainty during the interpretation process. It is found that the influence range of the skin factor and permeability may partially overlap during the interpretation process without consideration of physical constraints. Additionally, it is found that the equivalent wellbore radius is more reasonable by considering the skin factor constraints. Furthermore, the short-time asymptotic method was applied to separate the small pressure signal at the early time period and a novel type curve was proposed to better analyze the early time pressure response. Subsequently, sensitivity analyses were conducted to investigate the influence of different parameters on the new type curves. It is found that the new type curves are more dispersed and sensitive to the parameters at the early time period which can be beneficial for the early time transient pressure analysis in a tight formation. The proposed method has been validated and then extended to a field application, demonstrating that the transient pressure for a vertical well in a tight formation can be analyzed in a reasonable and accurate manner with only early time transient pressure data. Full article

The single-cell RNA-seq allows exploring the transcriptome for one cell at a time. By doing so, cellular regulation is pictured. One limitation is the dropout events phenomenon, where a gene is observed at a low or moderate expression level in one cell but not detected in another. Dropouts obscure legitimate biological heterogeneity leading to the description of a small fraction of the meaningful relations. We used a stochastic approach to model the Reverse Transcription Polymerase Chain Reaction (RT-PCR) kinetic, in which we contemplated the temperature profile, RT-PCR duration, and reaction rates. By studying the underlying biochemical processes of RT-PCR, using a computational and analytical framework, we show a minimal amount of RNA to avoid dropout events. We further use this fact to characterize the limits in the dispersion reduction. Dispersion asymptotically decreases as the RNA initial value increases. Despite always being a basal dispersion, their decreasing speed is modulated mainly by the degradation rates, particularly for the RNA. We concluded that the critical step into the RT-PCR is the RT phase due to the fragile nature of the RNA. We propose that limiting RNA degradation might ensure that the portraited transcriptional landscape is unbiased by technical error. Full article

Non-Fickian diffusion has been increasingly documented in hydrology and modeled by promising time nonlocal transport models. While previous studies showed that most of the time nonlocal models are identical with correlated parameters, fundamental challenges remain in real-world applications regarding model selection and parameter definition. This study compared three popular time nonlocal transport models, including the multi-rate mass transfer (MRMT) model, the continuous time random walk (CTRW) framework, and the tempered time fractional advection–dispersion equation (tt-fADE), by focusing on their physical interpretation and feasibility in capturing non-Fickian transport. Mathematical comparison showed that these models have both related parameters defining the memory function and other basic-transport parameters (i.e., velocity v and dispersion coefficient D) with different hydrogeologic interpretations. Laboratory column transport experiments and field tracer tests were then conducted, providing data for model applicability evaluation. Laboratory and field experiments exhibited breakthrough curves with non-Fickian characteristics, which were better represented by the tt-fADE and CTRW models than the traditional advection–dispersion equation. The best-fit velocity and dispersion coefficient, however, differ significantly between the tt-fADE and CTRW. Fitting exercises further revealed that the observed late-time breakthrough curves were heavier than the MRMT solutions with no more than two mass-exchange rates and lighter than the MRMT solutions with power-law distributed mass-exchange rates. Therefore, the time nonlocal models, where some parameters are correlated and exchangeable and the others have different values, differ mainly in their quantification of pre-asymptotic transport dynamics. In all models tested above, the tt-fADE model is attractive, considering its small fitting error and the reasonable velocity close to the measured flow rate. Full article

The traditional approach with microarray data has been to apply transformations that approximately normalize them, with the drawback of losing the original scale. The alternative stand point taken here is to search for models that fit the data, characterized by the presence of negative values, preserving their scale; one advantage of this strategy is that it facilitates a direct interpretation of the results. A new family of distributions named gpower-normal indexed by p∈R is introduced and it is proven that these variables become normal or truncated normal when a suitable gpower transformation is applied. Expressions are given for moments and quantiles, in terms of the truncated normal density. This new family can be used to model asymmetric data that include non-positive values, as required for microarray analysis. Moreover, it has been proven that the gpower-normal family is a special case of pseudo-dispersion models, inheriting all the good properties of these models, such as asymptotic normality for small variances. A combined maximum likelihood method is proposed to estimate the model parameters, and it is applied to microarray and contamination data. Rcodes are available from the authors upon request. Full article