Smoothness of scale functions for spectrally negative Lévy processes

Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes and often appear in the context of martingale relations. These relations are often require excursion theory rather than Itô calculus. The reason for the latter is that standard Itô calculus is only applicable to functions with a sufficient degree of smoothness and knowledge of the precise degree of smoothness of scale functions is seemingly incomplete. The aim of this article is to offer new results concerning properties of scale functions in relation to the smoothness of the underlying Lévy measure. We place particular emphasis on spectrally negative Lévy processes with a Gaussian component and processes of bounded variation. An additional motivation is the very intimate relation of scale functions to renewal functions of subordinators. The results obtained for scale functions have direct implications offering new results concerning the smoothness of such renewal functions for which there seems to be very little existing literature on this topic.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

Multi‐method global sensitivity analysis (MMGSA) for modelling floodplain hydrological processes

When studying hydrological processes with a numerical model, global sensitivity analysis (GSA) is essential if one is to understand the impact of model parameters and model formulation on results. However, different definitions of sensitivity can lead to a difference in the ranking of importance of the different model factors. Here we combine a fuzzy performance function with different methods of calculating global sensitivity to perform a multi-method global sensitivity analysis (MMGSA). We use an application of a finite element subsurface flow model (ESTEL-2D) on a flood inundation event on a floodplain of the River Severn to illustrate this new methodology. We demonstrate the utility of the method for model understanding and show how the prediction of state variables, such as Darcian velocity vectors, can be affected by such a MMGSA. This paper is a first attempt to use GSA with a numerically intensive hydrological model.

Multi-method global sensitivity analysis (MMGSA) for modelling floodplain hydrological processes

When studying hydrological processes with a numerical model, global sensitivity analysis (GSA) is essential if one is to understand the impact of model parameters and model formulation on results. However, different definitions of sensitivity can lead to a difference in the ranking of importance of the different model factors. Here we combine a fuzzy performance function with different methods of calculating global sensitivity to perform a multi-method global sensitivity analysis (MMGSA). We use an application of a finite element subsurface flow model (ESTEL-2D) on a flood inundation event on a floodplain of the River Severn to illustrate this new methodology. We demonstrate the utility of the method for model understanding and show how the prediction of state variables, such as Darcian velocity vectors, can be affected by such a MMGSA. This paper is a first attempt to use GSA with a numerically intensive hydrological model

Focus on high energy particles and atmospheric processes

The letters published in the ‘Focus issue on high energy particles and atmospheric processes’ serve to broaden the discussion about the influence of high energy particles on the atmosphere beyond their possible effects on clouds and climate. These letters link climate and meteorological processes with atmospheric electricity, atmospheric chemistry, high energy physics and aerosol science from the smallest molecular cluster ions through to liquid droplets. Progress in such a disparate and complex topic is very likely to benefit from continued interdisciplinary interactions between traditionally distinct science areas.

Intrinsic flavor violation for massive neutrinos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Search for electroweak production of charginos and neutralinos using leptonic final states in pp collisions at root s=7 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Interleukin-8 expression associated with canine mammary tumors

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stochastic field processes in the mathematical modelling of damped transmission line vibrations

Wind-excited vibrations in the frequency range of 10 to 50 Hz due to vortex shedding often cause fatigue failures in the cables of overhead transmission lines. Damping devices, such as the Stockbridge dampers, have been in use for a long time for supressing these vibrations. The dampers are conveniently modelled by means of their driving point impedance, measured in the lab over the frequency range under consideration. The cables can be modelled as strings with additional small bending stiffness. The main problem in modelling the vibrations does however lay in the aerodynamic forces, which usually are approximated by the forces acting on a rigid cylinder in planar flow. In the present paper, the wind forces are represented by stochastic processes with arbitrary crosscorrelation in space; the case of a Kármán vortex street on a rigid cylinder in planar flow is contained as a limit case in this approach. The authors believe that this new view of the problem may yield useful results, particularly also concerning the reliability of the lines and the probability of fatigue damages. © 1987.

Treatment of developmental defect of upper lip with carbon dioxide laser radiation (CO2): First surgical time

With the exception of the cleft lip, developmental defects (DD) of the lip are rare. The upper lip originates from the ectomesenchyme and is formed by the merging of the nasal medial and lateral processes with the maxillary process. Disturbances during this formation period can cause DD with functional and/or esthetic repercussions. We present a case of DD of the upper lip in a patient with a history of progressive growth of the left lateral portion of the upper lip that occurred from the time of birth until the age of 22 years. Clinical examination revealed hypertrophy of the area from the left philtral columns to the left commissure of the lip, extending the portion of the surface mucosa creating a flaccid and asymptomatic tissue mass. All other buccal structures appeared to be within normal limits and without any evidence of defects or deformities. In the surgical planning we decided to carry out corrective surgery in two phases. The first phase accomplished a conservative excision of the total abnormal labial tissue mass with a CO2 laser radiation (5 W in continuous mode, bunch diameter φ = 0.6 mm with a power density of 768 W/cm2 and fluency of 0.231 J/cm2) being careful to preserve the vermilion portion of the lip. Postsurgical clinical evaluations were done every three days until the skin sutures were removed and then every seven days until two months post surgery. While the entire mass of excessive tissue could not be completely removed, the removal of the excessive mucosal tissue produced a very good outcome relative to lip function, with a good esthetic result without scarring, and good tissue mobility. The results showed that the CO2 laser is an extremely useful instrument that can provide excellent control of the surgical field and allow for healing that produces excellent functional and esthetic results. © 2005 Taylor & Francis.

First measurement of the underlying event activity at the LHC with √ = 0.9 TeV

A measurement of the underlying activity in scattering processes with pT scale in the GeV region is performed in proton-proton collisions at √ = 0.9 TeV, using data collected by the CMS experiment at the LHC. Charged particle production is studied with reference to the direction of a leading object, either a charged particle or a set of charged particles forming a jet. Predictions of several QCD-inspired models as implemented in PYTHIA are compared, after full detector simulation, to the data. The models generally predict too little production of charged particles with pseudorapidity {pipe}η{pipe} < 2, pT > 0.5 GeV/c, and azimuthal direction transverse to that of the leading object. © 2010 CERN for benefit of the CMS collaboration.

Interactive Processes among Babies at a Daycare Center

The paper presents a study regarding babies' interactive processes with peers, which aimed to apprehend some of their qualitative aspects, considering babies' peculiarities. An empirical work was conducted with video recording scenes and interviews, regarding the "Babies' Adaptation to a Daycare Center" project, which followed up 21 babies (4-13 months) at a daycare center. Data analysis was based on the Network of Meanings perspective. Five episodes are here presented regarding three focal subjects and their peers. Analysis indicates the occurrence of interactions; among them it can be highlighted the role of the glance, presence of triadic relations (even among babies younger than nine months old), abbreviation of communicative resources and empathy. Moreover, despite verbal language absence at this age, it was verified meaning processes. Some practical-theoretical implications are pointed out as well.

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Fermentative processes for environmental remediation

The growing interest in environmental protection has led to the development of emerging biotechnologies for environmental remediation also introducing the biorefinery concept. This work mainly aimed to evaluate the applicability of innovative biotechnologies for environmental remediation and bioenergy production, throught fermentative processes. The investigated biotechnologies for waste and wastewater treatment and for the valorisation of specific feedstocks and energy recovery, were mainly focused on four research lines. 1. Biotechnology for textile wastewater treatment and water reuse that involving anaerobic and aerobic processes in combination with membrane technologies. Combinations of different treatments were also implemented for water reuse in a textile company. 2. Biotechnology for the treatment of solid waste and leachate in landfill and for biogas production. Landfill operated as Bioreactor with recirculation of the generated leachate was proposed for organic matter biostabilisation and for ammonia removal from leachate by favouring the Anammox process. 3. An innovative two-stage anaerobic process for effective codigestion of waste from the dairy industry, as cheese whey and dairy manure, was studied by combining conventional fermentative processes with a simplified system design for enhancing biomethanisation. 4) The valorisation of the glycerol waste as surplus by-product of the biodiesel industry was investigated via microbial conversion to value-added chemicals, as 1,3-propanediol. The investigated fermentative processes have been successfully implemented and reached high yields of the produced bio-chemical. The studied biotechnological systems proved to be feasible for environmental remediation and bioenergy and chemicals production.