A mean square chain rule and its application in solving the random Chebyshev differential equation

[EN] In this paper a new version of the chain rule for calculat- ing the mean square derivative of a second-order stochastic process is proven. This random operational calculus rule is applied to construct a rigorous mean square solution of the random Chebyshev differential equation (r.C.d.e.) assuming mild moment hypotheses on the random variables that appear as coefficients and initial conditions of the cor- responding initial value problem. Such solution is represented through a mean square random power series. Moreover, reliable approximations for the mean and standard deviation functions to the solution stochastic process of the r.C.d.e. are given. Several examples, that illustrate the theoretical results, are included.This work was completed with the support of our TEX-pert.Cortés, J.; Villafuerte, L.; Burgos-Simon, C. (2017). A mean square chain rule and its application in solving the random Chebyshev differential equation. Mediterranean Journal of Mathematics. 14(1):14-35. https://doi.org/10.1007/s00009-017-0853-6S1435141Calbo, G., Cortés, J.C., Jódar, L., Villafuerte, L.: Analytic stochastic process solutions of second-order random differential equations. Appl. Math. Lett. 23(12), 1421–1424 (2010). doi: 10.1016/j.aml.2010.07.011El-Tawil, M.A., El-Sohaly, M.: Mean square numerical methods for initial value random differential equations. Open J. Discret. Math. 1(1), 164–171 (2011). doi: 10.4236/ojdm.2011.12009Khodabin, M., Maleknejad, K., Rostami, K., Nouri, M.: Numerical solution of stochastic differential equations by second order Runge Kutta methods. Math. Comp. Model. 59(9–10), 1910–1920 (2010). doi: 10.1016/j.mcm.2011.01.018Santos, L.T., Dorini, F.A., Cunha, M.C.C.: The probability density function to the random linear transport equation. Appl. Math. Comput. 216(5), 1524–1530 (2010). doi: 10.1016/j.amc.2010.03.001González Parra, G., Chen-Charpentier, B.M., Arenas, A.J.: Polynomial Chaos for random fractional order differential equations. Appl. Math. Comput. 226(1), 123–130 (2014). doi: 10.1016/j.amc.2013.10.51El-Beltagy, M.A., El-Tawil, M.A.: Toward a solution of a class of non-linear stochastic perturbed PDEs using automated WHEP algorithm. Appl. Math. Model. 37(12–13), 7174–7192 (2013). doi: 10.1016/j.apm.2013.01.038Nouri, K., Ranjbar, H.: Mean square convergence of the numerical solution of random differential equations. Mediterran. J. Math. 12(3), 1123–1140 (2015). doi: 10.1007/s00009-014-0452-8Villafuerte, L., Braumann, C.A., Cortés, J.C., Jódar, L.: Random differential operational calculus: theory and applications. Comp. Math. Appl. 59(1), 115–125 (2010). doi: 10.1016/j.camwa.2009.08.061Øksendal, B.: Stochastic differential equations: an introduction with applications, 6th edn. Springer, Berlin (2007)Soong, T.T.: Random differential equations in science and engineering. Academic Press, New York (1973)Wong, B., Hajek, B.: Stochastic processes in engineering systems. Springer Verlag, New York (1985)Arnold, L.: Stochastic differential equations. Theory and applications. John Wiley, New York (1974)Cortés, J.C., Jódar, L., Camacho, J., Villafuerte, L.: Random Airy type differential equations: mean square exact and numerical solutions. Comput. Math. Appl. 60(5), 1237–1244 (2010). doi: 10.1016/j.camwa.2010.05.046Calbo, G., Cortés, J.C., Jódar, L.: Random Hermite differential equations: mean square power series solutions and statistical properties. Appl. Math. Comp. 218(7), 3654–3666 (2011). doi: 10.1016/j.amc.2011.09.008Calbo, G., Cortés, J.C., Jódar, L., Villafuerte, L.: Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Comp. Math. Appl. 61(9), 2782–2792 (2010). doi: 10.1016/j.camwa.2011.03.045Cortés, J.C., Jódar, L., Company, R., Villafuerte, L.: Laguerre random polynomials: definition, differential and statistical properties. Utilit. Math. 98, 283–293 (2015)Cortés, J.C., Jódar, L., Villafuerte, L.: Mean square solution of Bessel differential equation with uncertainties. J. Comp. Appl. Math. 309, 383–395 (2017). doi: 10.1016/j.cam.2016.01.034Golmankhaneh, A.K., Porghoveh, N.A., Baleanu, D.: Mean square solutions of second-order random differential equations by using homotopy analysis method. Romanian Reports Physics 65(2), 1237–1244 (2013)Khalaf, S.L.: Mean square solutions of second-order random differential equations by using homotopy perturbation method. Int. Math. Forum 6(48), 2361–2370 (2011)Khudair, A.R., Ameen, A.A., Khalaf, S.L.: Mean square solutions of second-order random differential equations by using Adomian decomposition method. Appl. Math. Sci. 5(49), 2521–2535 (2011)Agarwal, R.P., O’Regan, D.: Ordinary and partial differential equations. Springer, New York (2009

Group motivational intervention in overweight/obese patients in primary prevention of cardiovascular disease in the primary healthcare area

Background The global mortality caused by cardiovascular disease increases with weight. The Framingham study showed that obesity is a cardiovascular risk factor independent of other risks such as type 2 diabetes mellitus, dyslipidemia and smoking. Moreover, the main problem in the management of weight-loss is its maintenance, if it is achieved. We have designed a study to determine whether a group motivational intervention, together with current clinical practice, is more efficient than the latter alone in the treatment of overweight and obesity, for initial weight loss and essentially to achieve maintenance of the weight achieved; and, secondly, to know if this intervention is more effective for reducing cardiovascular risk factors associated with overweight and obesity. Methods This 26-month follow up multi-centre trial, will include 1200 overweight/obese patients. Random assignment of the intervention by Basic Health Areas (BHA): two geographically separate groups have been created, one of which receives group motivational intervention (group intervention), delivered by a nurse trained by an expert phsychologist, in 32 group sessions, 1 to 12 fortnightly, and 13 to 32, monthly, on top of their standard program of diet, exercise, and the other (control group), receiving the usual follow up, with regular visits every 3 months. Discussion By addressing currently unanswered questions regarding the maintenance in weight loss in obesity/overweight, upon the expected completion of participant follow-up in 2012, the IMOAP trial should document, for the first time, the benefits of a motivational intervention as a treatment tool of weight loss in a primary care setting

A 'snip' in time: what is the best age to circumcise?

<p>Abstract</p> <p>Background</p> <p>Circumcision is a common procedure, but regional and societal attitudes differ on whether there is a need for a male to be circumcised and, if so, at what age. This is an important issue for many parents, but also pediatricians, other doctors, policy makers, public health authorities, medical bodies, and males themselves.</p> <p>Discussion</p> <p>We show here that infancy is an optimal time for clinical circumcision because an infant's low mobility facilitates the use of local anesthesia, sutures are not required, healing is quick, cosmetic outcome is usually excellent, costs are minimal, and complications are uncommon. The benefits of infant circumcision include prevention of urinary tract infections (a cause of renal scarring), reduction in risk of inflammatory foreskin conditions such as balanoposthitis, foreskin injuries, phimosis and paraphimosis. When the boy later becomes sexually active he has substantial protection against risk of HIV and other viral sexually transmitted infections such as genital herpes and oncogenic human papillomavirus, as well as penile cancer. The risk of cervical cancer in his female partner(s) is also reduced. Circumcision in adolescence or adulthood may evoke a fear of pain, penile damage or reduced sexual pleasure, even though unfounded. Time off work or school will be needed, cost is much greater, as are risks of complications, healing is slower, and stitches or tissue glue must be used.</p> <p>Summary</p> <p>Infant circumcision is safe, simple, convenient and cost-effective. The available evidence strongly supports infancy as the optimal time for circumcision.</p

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

Pan-cancer analysis of whole genomes

Cancer is driven by genetic change, and the advent of massively parallel sequencing has enabled systematic documentation of this variation at the whole-genome scale(1-3). Here we report the integrative analysis of 2,658 whole-cancer genomes and their matching normal tissues across 38 tumour types from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). We describe the generation of the PCAWG resource, facilitated by international data sharing using compute clouds. On average, cancer genomes contained 4-5 driver mutations when combining coding and non-coding genomic elements; however, in around 5% of cases no drivers were identified, suggesting that cancer driver discovery is not yet complete. Chromothripsis, in which many clustered structural variants arise in a single catastrophic event, is frequently an early event in tumour evolution; in acral melanoma, for example, these events precede most somatic point mutations and affect several cancer-associated genes simultaneously. Cancers with abnormal telomere maintenance often originate from tissues with low replicative activity and show several mechanisms of preventing telomere attrition to critical levels. Common and rare germline variants affect patterns of somatic mutation, including point mutations, structural variants and somatic retrotransposition. A collection of papers from the PCAWG Consortium describes non-coding mutations that drive cancer beyond those in the TERT promoter(4); identifies new signatures of mutational processes that cause base substitutions, small insertions and deletions and structural variation(5,6); analyses timings and patterns of tumour evolution(7); describes the diverse transcriptional consequences of somatic mutation on splicing, expression levels, fusion genes and promoter activity(8,9); and evaluates a range of more-specialized features of cancer genomes(8,10-18).Peer reviewe