A note on inverses of non-decreasing Lévy processes

We show that, apart from deterministic processes, compound Poisson processes with exponential jumps are the only (shifted) non-decreasing Lévy processes whose inverses are also (shifted) non-decreasing Lévy processes

A goodness of fit statistic for the geometric distribution

We propose a goodness of fit statistic for the geometric distribution and compare it in terms of power, via simulation, with the chi-square statistic. The statistic is based on the Lau-Rao theorem and can be seen as a discrete analogue of the total time on test statistic. The results suggest that the test based on the new statistic is generally superior to the chi-square test

On the nonparametric prediction of conditionally stationary sequences

We prove the strong consistency of estimators of the conditional distribution function and conditional expectation of a future observation of a discrete time stochastic process given a fixed number of past observations. The results apply to conditionally stationary processes (a class of processes including Markov and stationary processes) satisfying a strong mixing condition, and they extend and bring together the work of several authors in the area of nonparametric estimation. One of our goals is to provide further justification for the growing practical application of estimators in non-stationary time series and in other `non i.i.d.'~settings. Some arguments as to why such estimators should work very generally in practice, often in a nearly `optimal' way, are given. Two numerical illustrations are included, one with simulated data and the other with oceanographic data

Design of few-mode fibers with M-modes and low differential mode delay

In this paper, we investigate the design of few-mode fibers (FMFs) guiding 2 to 12 linearly polarized (LP) modes with low differential mode delay (DMD) over the C-band, suitable for long-haul transmission. Two different types of refractive index profile have been considered: a graded-core with a cladding trench (GCCT) profile and a multi-step-index (MSI) profile. The profiles parameters are optimized in order to achieve: the lowest possible DMD and macro-bend losses (MBL) lower than the ITU-T standard recommendation. The optimization results show that the MSI profiles present lower DMD than the minimum achieved with a GCCT profile. Moreover, it is shown that the optimum DMD and the MBL scale with the number of modes for both profiles. The optimum DMD obtained for 12 LP modes is lower than 3 ps/km using a GCCT profile and lower than 2.5 ps/km using a MSI profile. The optimization results reveal that the most preponderant parameter of the GCCT profile is the refractive index relative difference at the core center, Δnco. Reducing Δn co, the DMD is reduced at the expense of increasing the MBL. Regarding the MSI profiles, it is shown that 64 steps are required to obtain a DMD improvement considering 12 LP modes. Finally, the impact of the fabrication margins on the optimum DMD is analyzed. The probability of having a manufactured FMF with 12 LP modes and DMD lower than 12 ps/km is approximately 68% using a GCCT profile and 16% using a MSI profile

A minimal set of top-Higgs anomalous couplings

We use the equations of motion to simplify the general form of fermion-fermion-Higgs interactions generated by dimension-six gauge-invariant effective operators. After removing redundant operators it is found that the most general H f_i f_j vertex for off-shell fermions f_i, f_j and an off-shell Higgs boson only involves scalar and pseudo-scalar terms, without derivatives. Examples are presented for the Htt and Htq interactions, where q=u,c, giving the explicit expressions of the vertices in terms of gauge-invariant operators. The new operator equalities obtained here also reduce the number of operators relevant for the Ztq vertices, although the general form of these interactions is not simplified with respect to previous results.Comment: LaTeX 16 pages, 2 PS figures. Typos corrected. Final version which appeared on the journa

Antioxidant potential of chestnut (Castanea sativa L.) and almond (Prunus dulcis L.) by-products.

The antioxidant properties of almond green husks (Cvs. Duro Italiano, Ferraduel, Ferranhês, Ferrastar and Orelha de Mula), chestnut skins and chestnut leaves (Cvs. Aveleira, Boa Ventura, Judia and Longal) were evaluated through several chemical and biochemical assays in order to provide a novel strategy to stimulate the application of waste products as new suppliers of useful bioactive compounds, namely antioxidants. All the assayed by-products revealed good antioxidant properties, with very low EC50 values (lower than 380 μg/mL), particularly for lipid peroxidation inhibition (lower than 140 μg/mL). The total phenols and flavonoids contents were also determined. The correlation between these bioactive compounds and DPPH (2,2-diphenyl-1-picrylhydrazyl) radical scavenging activity, reducing power, inhibition of β-carotene bleaching and inhibition of lipid peroxidation in pig brain tissue through formation of thiobarbituric acid reactive substances, was also obtained. Although, all the assayed by-products proved to have a high potential of application in new antioxidants formulations, chestnut skins and leaves demonstrated better results

Sugars profiles of different chestnut (Castanea sativa Mill.) and almond (Prunus dulcis) cultivars by HPLC-RI

Sugar profiles of different almond and chestnut cultivars were obtained by high-performance liquid chromatography (HPLC), by means of a refractive index (RI) detector. A solid-liquid extraction procedure was used in defatted and dried samples. The chromatographic separation was achieved using a Eurospher 100-5 NH2 column using an isocratic elution with acetonitrile/water (70:30, v/v) at a flow rate of 1.0 ml/min. All the compounds were separated in 16 min. The method was optimized and proved to be reproducible and accurate. Generally, more than 95% of sugars were identified for both matrixes. Sugars profiles were quite homogeneous for almond cultivars; sucrose was the main sugar (11.46±0.14 in Marcona to 22.23±0.59 in Ferragnes g/100 g of dried weight), followed by raffinose (0.71±0.05 in Ferraduel to 2.11±0.29 in Duro Italiano), glucose (0.42±0.12 in Pegarinhos two seeded to 1.47±0.19 in Ferragnes) and fructose (0.11±0.02 in Pegarinhos two seeded to 0.59±0.05 in Gloriette). Commercial cultivars proved to have higher sucrose contents, except in the case of Marcona. Nevertheless, chestnut cultivars revealed a high heterogeneity. Sucrose was the main sugar in Aveleira (22.05±1.48), Judia (23.30±0.83) and Longal (9.56± 0.91), while glucose was slightly prevalent in Boa Ventura (6.63±0.49). The observed variance could serve for intercultivar discrimination

Antioxidant activities of the extracts from chestnut flower, leaf, skins and fruit

In this study, the antioxidant properties of chestnut (flowers, leaves, skins and fruits) extracts were evaluated through several biochemical assays: DPPH (2,2-diphenyl-1-picrylhydrazyl) radical-scavenging activity, reducing power, inhibition of β-carotene bleaching, inhibition of oxidative hemolysis in erythrocytes, induced by 2,2′-azobis(2-amidinopropane)dihydrochloride (AAPH), and inhibition of lipid peroxidation in pig brain tissue through the formation of thiobarbituric acid-reactive substances (TBARS). These assays have been extensively studied as models for the peroxidative damage in biomembranes. The EC50 values were calculated for all the methods in order to evaluate the antioxidant efficiency of each chestnut extract. The phenol and flavonoid contents were also obtained. Chestnut skins revealed the best antioxidant properties, presenting much lower EC50 values, particularly for lipid peroxidation inhibition in the TBARS assay. Furthermore, the highest antioxidant contents (polyphenols and flavonoids) were found for these extracts