Ladders operators for general discrete Sobolev orthogonal polynomials

We consider a general discrete Sobolev inner product involving the Hahn difference operator, so this includes the well--known difference operators $\mathscr{D}_{q}$ and $\Delta$ and, as a limit case, the derivative operator. The objective is twofold. On the one hand, we construct the ladder operators for the corresponding nonstandard orthogonal polynomials and we obtain the second--order difference equation satisfied by these polynomials. On the other hand, we generalise some related results appeared in the literature as we are working in a more general framework. Moreover, we will show that all the functions involved in these constructions can be computed explicitly

Markov Chains and Multiple Orthogonality

In this work we survey on connections of Markov chains and the theory of multiple orthogonality. Here we mainly concentrate on give a procedure to generate stochastic tetra diagonal Hessenberg matrices, coming from some specific families of multiple orthogonal, such as the ones of Jacobi--Pi\~neiro and Hypergeometric Lima--Loureiro. We show that associated with a positive tetra diagonal nonnegative bounded Hessenberg matrix we can construct two stochastic tetra diagonal ones. These two stochastic tridiagonal nonnegative Hessenberg matrices are shown to be, enlightened by the Poincar\'e theorem, limit transpose of each other

Bidiagonal factorization of the recurrence matrix for the Hahn multiple orthogonal polynomials

This paper explores a factorization using bidiagonal matrices of the recurrence matrix of Hahn multiple orthogonal polynomials. The factorization is expressed in terms of ratios involving the generalized hypergeometric function ${}_3F_2$ and is proven using recently discovered contiguous relations. Moreover, employing the multiple Askey scheme, a bidiagonal factorization is derived for the Hahn descendants, including Jacobi-Pi\~neiro, multiple Meixner (kinds I and II), multiple Laguerre (kinds I and II), multiple Kravchuk, and multiple Charlier, all represented in terms of hypergeometric functions. For the cases of multiple Hahn, Jacobi-Pi\~neiro, Meixner of kind II, and Laguerre of kind I, where there exists a region where the recurrence matrix is nonnegative, subregions are identified where the bidiagonal factorization becomes a positive bidiagonal factorization.Comment: 14 pages, 2 figure

Strain Switching in van der Waals Heterostructures Triggered by a Spin-Crossover Metal-Organic Framework

Van der Waals heterostructures (vdWHs) provide the possibility of engineering new materials with emergent functionalities that are not accessible in another way. These heterostructures are formed by assembling layers of different materials used as building blocks. Beyond inorganic 2D crystals, layered molecular materials remain still rather unexplored, with only few examples regarding their isolation as atomically thin layers. Here, the family of van der Waals heterostructures is enlarged by introducing a molecular building block able to produce strain: the so-called spin-crossover (SCO). In these metal-organic materials, a spin transition can be induced by applying external stimuli like light, temperature, pressure, or an electric field. In particular, smart vdWHs are prepared in which the electronic and optical properties of the 2D material (graphene and WSe2) are clearly switched by the strain concomitant to the spin transition. These molecular/inorganic vdWHs represent the deterministic incorporation of bistable molecular layers with other 2D crystals of interest in the emergent fields of straintronics and band engineering in low-dimensional materials

ARIA 2016 : Care pathways implementing emerging technologies for predictive medicine in rhinitis and asthma across the life cycle

The Allergic Rhinitis and its Impact on Asthma (ARIA) initiative commenced during a World Health Organization workshop in 1999. The initial goals were (1) to propose a new allergic rhinitis classification, (2) to promote the concept of multi-morbidity in asthma and rhinitis and (3) to develop guidelines with all stakeholders that could be used globally for all countries and populations. ARIA-disseminated and implemented in over 70 countries globally-is now focusing on the implementation of emerging technologies for individualized and predictive medicine. MASK [MACVIA (Contre les Maladies Chroniques pour un Vieillissement Actif)-ARIA Sentinel NetworK] uses mobile technology to develop care pathways for the management of rhinitis and asthma by a multi-disciplinary group and by patients themselves. An app (Android and iOS) is available in 20 countries and 15 languages. It uses a visual analogue scale to assess symptom control and work productivity as well as a clinical decision support system. It is associated with an inter-operable tablet for physicians and other health care professionals. The scaling up strategy uses the recommendations of the European Innovation Partnership on Active and Healthy Ageing. The aim of the novel ARIA approach is to provide an active and healthy life to rhinitis sufferers, whatever their age, sex or socio-economic status, in order to reduce health and social inequalities incurred by the disease.Peer reviewe

Correlation between work impairment, scores of rhinitis severity and asthma using the MASK-air (R) App

Background In allergic rhinitis, a relevant outcome providing information on the effectiveness of interventions is needed. In MASK-air (Mobile Airways Sentinel Network), a visual analogue scale (VAS) for work is used as a relevant outcome. This study aimed to assess the performance of the work VAS work by comparing VAS work with other VAS measurements and symptom-medication scores obtained concurrently. Methods All consecutive MASK-air users in 23 countries from 1 June 2016 to 31 October 2018 were included (14 189 users; 205 904 days). Geolocalized users self-assessed daily symptom control using the touchscreen functionality on their smart phone to click on VAS scores (ranging from 0 to 100) for overall symptoms (global), nose, eyes, asthma and work. Two symptom-medication scores were used: the modified EAACI CSMS score and the MASK control score for rhinitis. To assess data quality, the intra-individual response variability (IRV) index was calculated. Results A strong correlation was observed between VAS work and other VAS. The highest levels for correlation with VAS work and variance explained in VAS work were found with VAS global, followed by VAS nose, eye and asthma. In comparison with VAS global, the mCSMS and MASK control score showed a lower correlation with VAS work. Results are unlikely to be explained by a low quality of data arising from repeated VAS measures. Conclusions VAS work correlates with other outcomes (VAS global, nose, eye and asthma) but less well with a symptom-medication score. VAS work should be considered as a potentially useful AR outcome in intervention studies.Peer reviewe