Noise recovery for L\'evy-driven CARMA processes and high-frequency behaviour of approximating Riemann sums

We consider high-frequency sampled continuous-time autoregressive moving average (CARMA) models driven by finite-variance zero-mean L\'evy processes. An L^2-consistent estimator for the increments of the driving L\'evy process without order selection in advance is proposed if the CARMA model is invertible. In the second part we analyse the high-frequency behaviour of approximating Riemann sum processes, which represent a natural way to simulate continuous-time moving average processes on a discrete grid. We shall compare their autocovariance structure with the one of sampled CARMA processes, where the rule of integration plays a crucial role. Moreover, new insight into the kernel estimation procedure of Brockwell et al. (2012a) is given.Comment: 26 pages, 2 figure

Does the somatosensory temporal discrimination threshold change over time in focal dystonia?

BACKGROUND: The somatosensory temporal discrimination threshold (STDT) is defined as the shortest interval at which an individual recognizes two stimuli as asynchronous. Some evidence suggests that STDT depends on cortical inhibitory interneurons in the basal ganglia and in primary somatosensory cortex. Several studies have reported that the STDT in patients with dystonia is abnormal. No longitudinal studies have yet investigated whether STDT values in different forms of focal dystonia change during the course of the disease. METHODS: We designed a follow-up study on 25 patients with dystonia (15 with blepharospasm and 10 with cervical dystonia) who were tested twice: upon enrolment and 8 years later. STDT values from dystonic patients at the baseline were also compared with those from a group of 30 age-matched healthy subjects. RESULTS: Our findings show that the abnormally high STDT values observed in patients with focal dystonia remained unchanged at the 8-year follow-up assessment whereas disease severity worsened. CONCLUSIONS: Our observation that STDT abnormalities in dystonia remain unmodified during the course of the disease suggests that the altered activity of inhibitory interneurons-either at cortical or at subcortical level-responsible for the increased STDT does not deteriorate as the disease progresses

High frequency sampling of a continuous-time ARMA process

Continuous-time autoregressive moving average (CARMA) processes have recently been used widely in the modeling of non-uniformly spaced data and as a tool for dealing with high-frequency data of the form $Y_{n\Delta}, n=0,1,2,...$, where $\Delta$ is small and positive. Such data occur in many fields of application, particularly in finance and the study of turbulence. This paper is concerned with the characteristics of the process (Y_{n\Delta})_{n\in\bbz}, when $\Delta$ is small and the underlying continuous-time process (Y_t)_{t\in\bbr} is a specified CARMA process.Comment: 13 pages, submitte

A Worldwide Overview of the Wellness Economy Market: The Technogym and Peloton Case Studies

A stressful and unbalanced lifestyle leadsto a marked decrease in wellbeing levels from a different point of view. The generation of baby boomers and generation X have suffered more and more from this modern style. Today, generation Y (Millennials) seems to be much more interested and sensitive in this field. They also proactively seek to find an adequate solution by investing one of the most precious personal assets which is their free time. Considering the growing demand for well-being, the wellness economy is becoming more and more popular. It is a market of about $ 4.5 trillion dollars, divided into well-defined segments or macro-areas market, steadily growing from 2015 onwards. The boundaries are difficult to define today due to its numerous cross-growth opportunities. After a wide description of the wellness economy, this paper focuses on introducing the role of connected fitness to analyze its component and dynamics. Using a case study methodology, supported by a SWOT analysis, two of the most relevant players in this market were analyzed based on strengths, weakness, and future developments. The results show a situation where the two competitors are balanced and have a clear strategy for their expansion, even though they cannot count on all customer groups

Reversible Supramolecular Noncovalent Self-Assembly Determines the Optical Properties and the Formation of Melanin-like Nanoparticles

The role of noncovalent supramolecular self-assembly in the formation of melanin-like NP, as well as the nature of the electronic transition at the basis of their unique optical properties, is strongly debated. Here we demonstrate that, during the first stage of formation of synthetic melanin, polydopamine (PDA), a small fraction of the molecular precursor dopamine (DA) is oxidized to quinone (Q) and a simple supramolecular charge-transfer (CT) adduct is formed thanks to the electron donor and electron acceptor properties of DA and Q, respectively. This adduct, also detectable by HPLC-MS, presents the broad absorption band in the red-NIR region typical of melanin-like materials. Importantly, its disaggregation upon dilution can be easily detected since it leads to the disappearance of the CT band, indicating the reversibility of the process. Moreover, the stability constant K of the CT adduct could be obtained using a simple association model

Five-Membered Nitrogen Heterocycle Derivatives as Core Structures for the Synthesis of Bioactive Compounds Classes

The research towards new cyclic isosteres of functional groups and the optimization of their synthesis have been one of the basis of this work. In particular, the attention was paid to three different heterocycles: isoxazolines, isoxazolidinones and 3,4-dehydro-beta-prolines. The synthetic protocols developed for them are based on the electrophylic properties of alkylidene acetoacetates, malonates, acetoacetamide esters and malonamides. Their preparation is found on Knöevenagel condensation and a microwaves-assisted protocol.For this last topic, two applications are microwave-assisted protocols for the Yonemitsu-type trimolecular condensation and for the one-pot two-steps synthesis of alkylidene acetoacetamide esters for the preparation of dehydropeptides. The reactivity towards indoles, amines and diprotected hydroxylamines is reported. 1,4-Michael addition of C- and N-nucleophyles to alpha,beta-unsaturated electrophyles is the ground for the synthesis of isoxazolines and isoxazolidinones, differently substituted. Then, the Luche-reduction of these unsaturated intermediates was investigated and the consequent enzymatic resolution for the enantioselective preparation of 3,4-dehydro-beta-prolines. Applications of the synthesized heterocycles in molecules with biological target are the synthesis of Linezolid analogues and peptidomimetic integrin ligands. Finally, the synthesis of red-shifted self-assembled nanoparticles as tools for bioimaging is reported