Average trajectory of returning walks

We compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For uncorrelated random walks the average shape is semicircular, independently from the single increments distribution, as long as it is symmetric. Such universality extends to biased random walks and Levy flights, with the exception of a particular class of biased Levy flights. Adding a linear damping term destroys scaling and leads asymptotically to flat excursions. The introduction of short and long ranged noise correlations induces non trivial asymmetric shapes, which are studied numerically.Comment: 16 pages, 16 figures; accepted for publication in Phys. Rev.

Boundary-crossing identities for diffusions having the time-inversion property

We review and study a one-parameter family of functional transformations, denoted by (S (β)) β∈ℝ, which, in the case β<0, provides a path realization of bridges associated to the family of diffusion processes enjoying the time-inversion property. This family includes Brownian motions, Bessel processes with a positive dimension and their conservative h-transforms. By means of these transformations, we derive an explicit and simple expression which relates the law of the boundary-crossing times for these diffusions over a given function f to those over the image of f by the mapping S (β), for some fixed β∈ℝ. We give some new examples of boundary-crossing problems for the Brownian motion and the family of Bessel processes. We also provide, in the Brownian case, an interpretation of the results obtained by the standard method of images and establish connections between the exact asymptotics for large time of the densities corresponding to various curves of each family

Cr cluster characterization in Cu-Cr-Zr alloy after ECAP processing and aging using SANS and HAADF-STEM

International audienceThe precipitation of nano-sized Cr clusters was investigated in a commercial Cu-1Cr-0.1Zr (wt.%) alloy processed by Equal-Channel Angular Pressing (ECAP) and subsequent aging at 550 °C for 4 hours using small angle neutron scattering (SANS) measurements and high-angle annular dark-field-scanning transmission electron microscopy (HAADF-STEM). The size and volume fraction of nano-sized Cr clusters were estimated using both techniques. These parameters assessed from SANS (d~3.2 nm, Fv~1.1 %) agreed reasonably with those from HAADF-STEM (d ~2.5 nm, Fv~2.3%). Besides nano-sized Cr clusters, HAADF-STEM technique evidenced the presence of rare cuboid and spheroid sub-micronic Cr particles about 380-620 nm mean size. Both techniques did not evidence the presence of intermetallic CuxZry phases within the aging conditions

Sustainability of the Pension System in the Republic of Macedonia: Challenges and Solutions

The aim of the study is to create a forecasting model that will foresee the trend of the situation of the Pension, Insurance and Disability Fund of the Republic ofMacedonia. The methodology applied to evaluate the sustainability of pension system, and controlling the risk to pension funds, is forecast of all individual regressors through first order autoregressive model. This method will enable the assessment of the future uncertainty of the contributions and expenditures of pension insurance. The forecasted data show that in 2056, if no other reforms are undertaken, the increase in the percentage points of the number of employers is less than the increase in the number of pensioners for 3.9 percentage points. As per the natality and mortality, in the Republic of Macedonia natality will be only one third of its statistics in 2016, whereas mortality will double its value by 2056

Synthesis of eco-friendly ZnO-based heterophotocatalysts with enhanced properties under visible light in the degradation of organic pollutants

Abstract Heterogeneous photocatalysts have been widely used for the removal of various organic pollutants from wastewater. The main challenge so far resides in the sustainability of the process, with regard to the synthesis and the application under visible light. In this study the precipitated materials from the Moringa oleifera seed (MO), groundnut shells (GS) and apatite (A) agrowastes were functionalized with zinc oxide (ZnO) and silver (Ag) solution, to produce a novel bioheterophotocatalysts. Various analytical techniques such as scanning electron microscope (SEM), energy-dispersive X-ray spectroscopy (EDS), photoluminescence (PL) and X-ray diffraction (XRD) were used for the characterization of the novel photocatalysts. It was proven that agrowastes can also enhance the photocatalytic activity of a ZnO-based photocatalyst as pure metals. The combination of MO/GS/A/ZnO/Ag in a 1:1:1 ratio resulted in a lower band gap of 1.59 eV, as compared to the band gap of 2.96 eV for ZnO/Ag. These photocatalysts' efficiency was also tested on the photodegradation of polycyclic aromatic hydrocarbon (PAHs) derived from coal leaching in various water sources such as acidic mine drainage, alkaline mine drainage and sewage wastewater. From MO/GS/A/ZnO/Ag, the removal efficiency was found to be 69.59%, 61.07% and 61.68%, compared to 52.62%, 37.96 and 44.30% using ZnO/Ag in acidic mine drainage, alkaline mine drainage and sewage wastewater for 60 min under solar irradiation

American Step-Up and Step-Down Default Swaps under Levy Models

This paper studies the valuation of a class of default swaps with the embedded option to switch to a different premium and notional principal anytime prior to a credit event. These are early exercisable contracts that give the protection buyer or seller the right to step-up, step-down, or cancel the swap position. The pricing problem is formulated under a structural credit risk model based on Levy processes. This leads to the analytic and numerical studies of several optimal stopping problems subject to early termination due to default. In a general spectrally negative Levy model, we rigorously derive the optimal exercise strategy. This allows for instant computation of the credit spread under various specifications. Numerical examples are provided to examine the impacts of default risk and contractual features on the credit spread and exercise strategy.Comment: 35 pages, 5 figure

How to screen for non-adherence to antihypertensive therapy

The quality of assessment of non-adherence to treatment in hypertensive is poor. Within this review, we discuss the different methods used to assess adherence to blood-pressure-lowering medications in hypertension patients. Subjective reports such as physicians’ perceptions are inaccurate, and questionnaires completed by patients tend to overreport adherence and show a low diagnostic specificity. Indirect objective methods such as pharmacy database records can be useful, but they are limited by the robustness of the recorded data. Electronic medication monitoring devices are accurate but usually track adherence to only a single medication and can be expensive. Overall, the fundamental issue with indirect objective measures is that they do not fully confirm ingestion of antihypertensive medications. Detection of antihypertensive medications in body fluids using liquid chromatography–tandem mass spectrometry is currently, in our view, the most robust and clinically useful method to assess non-adherence to blood-pressure-lowering treatment. It is particularly helpful in patients presenting with resistant, refractory or uncontrolled hypertension despite the optimal therapy. We recommend using this diagnostic strategy to detect non-adherence alongside a no-blame approach tailoring support to address the perceptions (e.g. beliefs about the illness and treatment) and practicalities (e.g. capability and resources) influencing motivation and ability to adhere

Evidence of a causal and modifiable relationship between kidney function and circulating trimethylamine N-oxide

The host-microbiota co-metabolite trimethylamine N-oxide (TMAO) is linked to increased cardiovascular risk but how its circulating levels are regulated remains unclear. We applied "explainable" machine learning, univariate, multivariate and mediation analyses of fasting plasma TMAO concentration and a multitude of phenotypes in 1,741 adult Europeans of the MetaCardis study. Here we show that next to age, kidney function is the primary variable predicting circulating TMAO, with microbiota composition and diet playing minor, albeit significant, roles. Mediation analysis suggests a causal relationship between TMAO and kidney function that we corroborate in preclinical models where TMAO exposure increases kidney scarring. Consistent with our findings, patients receiving glucose-lowering drugs with reno-protective properties have significantly lower circulating TMAO when compared to propensity-score matched control individuals. Our analyses uncover a bidirectional relationship between kidney function and TMAO that can potentially be modified by reno-protective anti-diabetic drugs and suggest a clinically actionable intervention for decreasing TMAO-associated excess cardiovascular risk