Weighted-mean regions of a probability distribution

In this paper we investigate a new class of central regions for probability distributions on R^d, called weighted-mean regions. Their restrictions to an empirical distribution are the weighted-mean trimmed regions investigated by Dyckerhoff and Mosler (2011) for d-variate data. Furthermore a new class of stochastic orderings of variability, the weighted-mean orderings, is introduced.     

Region of variability for close-to-convex functions-II

For a complex number α with let be the class of analytic functions f in the unit disk with f(0)=0 satisfying in , for some convex univalent function in . For any fixed , and we shall determine the region of variability V(z₀,α,λ) for f(z₀) when f ranges over the class

In the final section we graphically illustrate the region of variability for several sets of parameters z₀ and α.     

New log-t-based CFAR detectors for a non-homogeneous Weibull Background

Based on new log-t-based detectors, we propose to improve the detection performances of the log-t-Constant False Alarm Rate (log-t-CFAR) detector for a non-homogeneous Weibull background. This paper is twofold. We first resort to the Automatic Constant False Censoring Rate (CFCR) algorithm, which guarantees an accurate rejection of an a priori unknown number of outliers. That is, we introduce two hybrid detectors by coupling the log-t-CFAR algorithm to the Maximum Likelihood-CFCR (MLE-CFCR) algorithm, yielding the H-MLE/log-t-CFAR detector, and to the Weber-Haykin Constant False Censoring Rate (WH-CFCR) algorithm, yielding the H-WH/log-t-CFAR detector. Then, based on the Variability Index (VI) as a background discriminator, we propose the Switching VI-log-t-CFAR (SVI-log-t-CFAR) detector. Thus, depending on the background heterogeneity, this detector has the capability to switch automatically to the appropriate detector; namely, the log-t-CFAR detector, in case of a homogeneous background, either one of the hybrid detectors, in case of the presence of outliers or the Automatic Edge Censoring log-t-CFAR (AEC-log-t-CFAR) detector, in case of the presence of a clutter edge. We assess the efficiency of these detectors through intensive Monte Carlo simulations. We show that, while no additional detection performances are observed in a homogeneous background, the new detectors exhibit a significant CFAR gain with respect to the log-t-CFAR detector in the presence of any inhomogeneity within the reference window.     

Modelling Fruit Characteristics During Apple Maturation: A Stochastic Approach

At present, mathematical models to predict the change of fruit quality attributes during apple maturation are deterministic and do not take into account the large natural variability of fruit quality attributes during the growing season. In this work a stochastic system approach was developed to describe the quality evolution of fruit. The basic dynamics of fruit quality evolution was represented by means of a stochastic system, in which the initial conditions and the model parameters were specified as random variables together with their probability density functions. A fundamental approach from stochastic systems theory was used to compute the propagation of the probability density functions of fruit quality attributes, which requires the numerical solution of the Fokker–Planck equation.     

Neural and vascular variability and the fMRI-BOLD response in normal aging

Neural, vascular and structural variables contributing to the blood oxygen level-dependent (BOLD) signal response variability were investigated in younger and older humans. Twelve younger healthy human subjects (six male and six female; mean age: 24 years; range: 19–27 years) and 12 older healthy subjects (five male and seven female; mean age: 58 years; range: 55–71 years) with no history of head trauma and neurological disease were scanned. Functional magnetic resonance imaging measurements using the BOLD contrast were made when participants performed a motor, cognitive or a breath hold (BH) task. Activation volume and the BOLD response amplitude were estimated for the younger and older at both group and subject levels. Mean activation volume was reduced by 45%, 40% and 38% in the elderly group during the motor, cognitive and BH tasks, respectively, compared to the younger. Reduction in activation volume was substantially higher compared to the reduction in the gray matter volume of 14% in the older compared to the younger. A significantly larger variability in the intersubject BOLD signal change occurred during the motor task, compared to the cognitive task. BH-induced BOLD signal change between subjects was significantly less-variable in the motor task-activated areas in the younger compared to older whereas such a difference between age groups was not observed during the cognitive task. Hemodynamic scaling using the BH signal substantially reduced the BOLD signal variability during the motor task compared to the cognitive task. The results indicate that the origin of the BOLD signal variability between subjects was predominantly vascular during the motor task while being principally a consequence of neural variability during the cognitive task. Thus, in addition to gray matter differences, the type of task performed can have different vascular variability weighting that can influence age-related differences in brain functional response.     

Development and evaluation of a diffusive gradients in a thin film technique for measuring ammonium in freshwaters

A new diffusive gradients in a thin film (DGT) technique, using Microlite PrCH cation exchange resin, was developed and evaluated for measuring NH₄–N in freshwaters. Microlite PrCH had high uptake (>92.5%) and elution efficiencies (87.2% using 2 mol L⁻¹ NaCl). Mass vs. time validation experiments over 24 h demonstrated excellent linearity (R² ≥ 0.996). PrCH-DGT binding layers had an extremely high intrinsic binding capacity for NH₄–N (∼3000 μg). NH₄–N uptake was quantitative over pH ranges 3.5–8.5 and ionic strength (up to 0.012 mol L⁻¹ as NaCl) typical of freshwater systems. Several cations (Na⁺, K⁺, Ca²⁺ and Mg²⁺) were found to compete with NH₄–N for uptake by PrCH-DGT, but NH₄–N uptake was quantitative over concentration ranges typical of freshwater (up to 0.012 mol L⁻¹ Na⁺, 0.006 mol L⁻¹ K⁺, 0.003 mol L⁻¹ Ca²⁺ and 0.004 mol L⁻¹ Mg²⁺). Effective diffusion coefficients determined from mass vs. time experiments changed non-linearly with electrical conductivity. Field deployments of DGT samplers with varying diffusive layer thicknesses validated the use of the technique in situ, allowed deployment times to be manipulated with respect to NH₄–N concentration, and enable the calculation of the diffusive boundary layer thickness. Daily grab sample NH₄–N concentrations were observed to vary considerably independent of major rainfall events, but good agreements were obtained between PrCH-DGT values and mean grab sample measurements of NH₄–N (C_DGT:C_SOLN 0.83–1.3). Reproducibility of DGT measurements in the field was good (relative standard deviation < 11%). Limit of detection was 0.63 μg L⁻¹ (equivalent to 0.045 μmol L⁻¹) based on 24 h deployments.     

On a family of risk measures based on proportional hazards models and tail probabilities

In this paper, we explore a class of tail variability measures based on distances among proportional hazards models. Tail versions of some well-known variability measures, such as the Gini mean difference, the Wang right tail deviation and the cumulative residual entropy are, up to a scale factor, in this class. These tail variability measures are combined with tail conditional expectation to generate premium principles that are especially useful to price heavy-tailed risks. We study their properties, including stochastic consistency and bounds, as well as the coherence of the associated premium principles.