Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+\beta\log(1+t^\alpha)},00$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.Comment: 12 pages, LaTe

Determination of Grain-Size Distributions from Ultrasonic Attenuation

The overall research goal of this project is the nondestructive measurement of grain-size distribution parameters using ultrasonic attenuation. Ultrasonic attenuation α is dependent upon the sound wavelength (λ), the size of the grains (D), and in many cases elastic constants and sound velocities of the material. Assuming that multiple scattering can be ignored, the expression for the wavelength dependence of the attenuation is 1 α(λ)=∫0∞N(D)α(λ,D)dD where N(D) is the grain-size distribution. In previous work [1] the sizes were assumed to be distributed following a power-law with exponent γ: 2 N(D)=KD−γ,

Algebraic charge liquids

High temperature superconductivity emerges in the cuprate compounds upon changing the electron density of an insulator in which the electron spins are antiferromagnetically ordered. A key characteristic of the superconductor is that electrons can be extracted from them at zero energy only if their momenta take one of four specific values (the `nodal points'). A central enigma has been the evolution of the zero energy electrons in the metallic state between the antiferromagnet and the superconductor, and recent experiments yield apparently contradictory results. The oscillation of the resistance in this metal as a function of magnetic field indicate that the zero energy electrons carry momenta which lie on elliptical `Fermi pockets', while ejection of electrons by high intensity light indicates that the zero energy electrons have momenta only along arc-like regions. We present a theory of new states of matter, which we call `algebraic charge liquids', which arise naturally between the antiferromagnet and the superconductor, and reconcile these observations. Our theory also explains a puzzling dependence of the density of superconducting electrons on the total electron density, and makes a number of unique predictions for future experiments.Comment: 6+8 pages, 2 figures; (v2) Rewritten for broader accessibility; (v3) corrected numerical error in Eq. (5

Genetic variation in populations of the earthworm, Lumbricus rubellus, across contaminated mine sites

Background  Populations of the earthworm, Lumbricus rubellus, are commonly found across highly contaminated former mine sites and are considered to have under-gone selection for mitigating metal toxicity. Comparison of adapted populations with those found on less contaminated soils can provide insights into ecological processes that demonstrate the long-term effects of soil contamination. Contemporary sequencing methods allow for portrayal of demographic inferences and highlight genetic variation indicative of selection at specific genes. Furthermore, the occurrence of L. rubellus lineages across the UK allows for inferences of mechanisms associated with drivers of speciation and local adaptation.  Results  Using RADseq, we were able to define population structure between the two lineages through the use of draft genomes for each, demonstrating an absence of admixture between lineages and that populations over extensive geographic distances form discrete populations. Between the two British lineages, we were able to provide evidence for selection near to genes associated with epigenetic and morphological functions, as well as near a gene encoding a pheromone. Earthworms inhabiting highly contaminated soils bare close genomic resemblance to those from proximal control soils. We were able to define a number of SNPs that largely segregate populations and are indicative of genes that are likely under selection for managing metal toxicity. This includes calcium and phosphate-handling mechanisms linked to lead and arsenic contaminants, respectively, while we also observed evidence for glutathione-related mechanisms, including metallothionein, across multiple populations. Population genomic end points demonstrate no consistent reduction in nucleotide diversity, or increase in inbreeding coefficient, relative to history of exposure.   Conclusions  Though we can clearly define lineage membership using genomic markers, as well as population structure between geographic localities, it is difficult to resolve markers that segregate entirely between populations in response to soil metal concentrations. This may represent a highly variable series of traits in response to the heterogenous nature of the soil environment, but ultimately demonstrates the maintenance of lineage-specific genetic variation among local populations. L. rubellus appears to provide an exemplary system for exploring drivers for speciation, with a continuum of lineages coexisting across continental Europe, while distinct lineages exist in isolation throughout the UK

Winter wheat roots grow twice as deep as spring wheat roots, is this important for N uptake and N leaching losses?

Cropping systems comprising winter catch crops followed by spring wheat could reduce N leaching risks compared to traditional winter wheat systems in humid climates. We studied the soil mineral N (Ninorg) and root growth of winter- and spring wheat to 2.5 m depth during three years. Root depth of winter wheat (2.2 m) was twice that of spring wheat, and this was related to much lower amounts of Ninorg in the 1 to 2.5 m layer after winter wheat (81 kg Ninorg ha-1 less). When growing winter catch crops before spring wheat, N content in the 1 to 2.5 m layer after spring wheat was not different from that after winter wheat. The results suggest that by virtue of its deep rooting, winter wheat may not lead to high levels of leaching as it is often assumed in humid climates. Deep soil and root measurements (below 1 m) in this experiment were essential to answer the questions we posed

The dune effect on sand-transporting winds on Mars

Wind on Mars is a significant agent of contemporary surface change, yet the absence of in situ meteorological data hampers the understanding of surface–atmospheric interactions. Airflow models at length scales relevant to landform size now enable examination of conditions that might activate even small-scale bedforms (ripples) under certain contemporary wind regimes. Ripples have the potential to be used as modern ‘wind vanes’ on Mars. Here we use 3D airflow modelling to demonstrate that local dune topography exerts a strong influence on wind speed and direction and that ripple movement likely reflects steered wind direction for certain dune ridge shapes. The poor correlation of dune orientation with effective sand-transporting winds suggests that large dunes may not be mobile under modelled wind scenarios. This work highlights the need to first model winds at high resolution before inferring regional wind patterns from ripple movement or dune orientations on the surface of Mars today

Cognitive and Neuronal Link With Inflammation: A Longitudinal Study in People With and Without HIV Infection

BACKGROUND: Across many settings, lack of virologic control remains common in people with HIV (PWH) due to late presentation and lack of retention in care. This contributes to neuronal damage and neurocognitive impairment, which remain prevalent. More evidence is needed to understand these outcomes in both PWH and people without HIV (PWOH). METHODS: We recruited PWH initiating antiretroviral therapy (ART) as well as PWOH at two sites in the United States. 108 adults were enrolled (56 PWOH and 52 PWH), most of whom had a second assessment at least 24 weeks later (193 total assessments). Tumor necrosis factor alpha (TNFá), monocyte chemotactic protein-1 (MCP-1), neopterin, soluble CD14, and neurofilament light chain protein (NFL) were measured in plasma and cerebrospinal fluid (CSF). Using multivariate models including Bayesian Model Averaging (BMA), we analyzed factors associated with global neuropsychological (NP) performance (NPT-9) and CSF NFL at baseline and over time. RESULTS: At baseline, higher CSF MCP-1 and plasma sCD14 were associated with worse NPT-9 in PWH, while CSF HIV RNA decrease was the only marker associated with improved NPT-9 over time. Among PWH, higher CSF neopterin was most closely associated with higher NFL. Among PWOH, higher CSF MCP-1 was most closely associated with higher NFL. Following ART initiation, decrease in CSF MCP-1 was most closely associated with NFL decrease. CONCLUSION: Monocyte-associated CSF biomarkers are highly associated with neuronal damage in both PWH and PWOH. More research is needed to evaluate if therapies targeting monocyte-associated inflammation may ameliorate HIV-associated neurobehavioral diseases