On the convolution equivalence of tempered stable distributions on the real line

We show the convolution equivalence property of univariate tempered stable distributions in the sense of Rosi\'nsky (2007). This makes rigorous various classic heuristic arguments on the asymptotic similarity between the probability and L\'evy densities of such distributions. Some specific examples from the literature are discussed

Tempered positive Linnik processes and their representations

This paper analyzes various classes of processes associated with the tempered positive Linnik (TPL) distribution.We provide several subordinated representations of TPL Lévy processes and in particular establish a stochastic self-similarity property with respect to negative binomial subordination. In finite activity regimes we show that the explicit compound Poisson representations give raise to innovations following Mittag-Leffler type laws which are apparently new. We characterize two time-inhomogeneous TPL processes, namely the Ornstein-Uhlenbeck (OU) Lévy-driven processes with stationary distribution and the additive process determined by a TPL law. We finally illustrate how the properties studied come together in a multivariate TPL Lévy framework based on a novel negative binomial mixing methodology. Some potential applications are outlined in the contexts of statistical anti-fraud and financial modelling

Tempered positive Linnik processes and their representations

This paper analyzes various classes of processes associated with the tempered positive Linnik (TPL) distribution. We provide several subordinated representations of TPL Lévy processes and in particular establish a stochastic self-similarity property with respect to negative binomial subordination. In finite activity regimes we show that the explicit compound Poisson representations give raise to innovations following Mittag-Leffler type laws which are apparently new. We characterize two time-inhomogeneous TPL processes, namely the Ornstein-Uhlenbeck (OU) Lévy-driven processes with stationary distribution and the additive process determined by a TPL law. We finally illustrate how the properties studied come together in a multivariate TPL Lévy framework based on a novel negative binomial mixing methodology. Some potential applications are outlined in the contexts of statistical anti-fraud and financial modelling

Optical properties of developing pip and stone fruit reveal underlying structural changes

Analyzing the optical properties of fruits represents a powerful approach for non-destructive observations of fruit development. With classical spectroscopy in the visible and near-infrared wavelength ranges, the apparent attenuation of light results from its absorption or scattering. In horticultural applications, frequently, the normalized difference vegetation index (NDVI) is employed to reduce the effects of varying scattering properties on the apparent signal. However, this simple approach appears to be limited. In the laboratory, with time-resolved reflectance spectroscopy, the absorption coefficient, μa, and the reduced scattering coefficient, μs′, can be analyzed separately. In this study, these differentiated optical properties were recorded (540-940 nm), probing fruit tissue from the skin up to 2 cm depth in apple (Malus × domestica 'Elstar') and plum (Prunus domestica 'Tophit plus') harvested four times (65-145 days after full bloom). The μa spectra showed typical peak at 670 nm of the chlorophyll absorption. The μs′ at 670 nm in apple changed by 14.7% (18.2-15.5 cm-1), while in plum differences of 41.5% (8.5-5.0 cm-1) were found. The scattering power, the relative change of μs′, was zero in apple, but enhanced in plum over the fruit development period. This mirrors more isotropic and constant structures in apple compared with plum. For horticultural applications, the larger variability in scattering properties of plum explains the discrepancy between commercially assessed NDVI values or similar indices and the absolute μa values in plum (R < 0.05), while the NDVI approach appeared reasonable in apple (R ≥ 0.80)

Clinical trial of time-resolved scanning optical mammography at 4 wavelengths between 683 and 975 nm

The first time-resolved optical mammograph operating beyond 900 nm (683, 785, 913, and 975 nm) is presently being used in a clinical trial to test the diagnostic potential of the technique in detecting and characterizing breast lesions. Between November 2001 and October 2002, 101 patients with malignant and benign lesions were analyzed retrospectively. Scattering plots, as derived from a homogeneous model, and late gated intensity images, to monitor spatial changes in the absorption properties, are routinely used. The intensity images available at four wavelengths provide sensitivity to the main tissue constituents (oxy- and deoxyhemoglobin, water, and lipids), in agreement with expected tissue composition and physiology, while the scattering plots mirror structural changes. Briefly, tumors are usually identified due to the strong blood absorption at short wavelengths, cysts to the low scattering, and fibroadenomas to low absorption at 913 nm and high at 975 nm, even though the optical features of fibroadenomas seem not to be uniquely defined. The effectiveness of the technique in localizing and discriminating different lesion types is analyzed as a function of various parameters (lesion size, compressed breast thickness, and breast parenchymal pattern).

Time-resolved reflectance spectroscopy as a management tool for late-maturing nectarine supply chain

The absorption coefficient of the fruit flesh at 670 nm (mu(a)), measured at harvest by time-resolved reflectance spectroscopy (TRS) is a good maturity index for early nectarine cultivars. A kinetic model has been developed linking the mu(a), expressed as the biological shift factor to softening during ripening. This allows shelf life prediction for individual fruit from the value of mu(a) at harvest and the fruit categorization into predicted softening and usability classes. In this work, the predictive capacity of a kinetic model developed using mu(a) data at harvest and firmness data within 1-2 d after harvest for a late maturing nectarine cultivar ('Morsiani 90') was tested for prediction and classification ability. Compared to early maturing cultivars, mu(a) at harvest had low values and low variability, indicating advanced maturity, whereas firmness was similar. Hence, fruit were categorized into six usability classes (from 'transportable-hard' to 'ready-to-eat-very soft') basing on mu(a) limits established analyzing firmness data in shelf life after harvest. The model was tested by comparing the predicted firmness and class of usability to the actual ones measured during ripening and its performance compared to that of models based on data during the whole shelf life at 20 degrees C after harvest and after storage at 0 degrees C and 4 degrees C. The model showed a classification ability very close to that of models based on data of the whole shelf life, and was able to correctly segregate the 'ready-to-eat-transportable', 'transportable' and 'transportable-hard' classes for ripening at harvest and after storage at 0 degrees C, and the 'ready-to-eat-very soft' and 'ready-to-eat-soft' classes for ripening after storage at 4 degrees C, with lower performance of models for fruit after storage at 4 degrees C respect to those of the other two ripening