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

A specification-based QoS-aware design framework for service-based applications

Effective and accurate service discovery and composition rely on complete specifications of service behaviour, containing inputs and preconditions that are required before service execution, outputs, effects and ramifications of a successful execution and explanations for unsuccessful executions. The previously defined Web Service Specification Language (WSSL) relies on the fluent calculus formalism to produce such rich specifications for atomic and composite services. In this work, we propose further extensions that focus on the specification of QoS profiles, as well as partially observable service states. Additionally, a design framework for service-based applications is implemented based on WSSL, advancing state of the art by being the first service framework to simultaneously provide several desirable capabilities, such as supporting ramifications and partial observability, as well as non-determinism in composition schemas using heuristic encodings; providing explanations for unexpected behaviour; and QoS-awareness through goal-based techniques. These capabilities are illustrated through a comparative evaluation against prominent state-of-the-art approaches based on a typical SBA design scenario

VISUAL PPINOT: A Graphical Notation for Process Performance Indicators

Process performance indicators (PPIs) allow the quantitative evaluation of business processes, providing essential information for decision making. It is common practice today that business processes and PPIs are usually modelled separately using graphical notations for the former and natural language for the latter. This approach makes PPI definitions simple to read and write, but it hinders maintenance consistency between business processes and PPIs. It also requires their manual translation into lower-level implementation languages for their operationalisation, which is a time-consuming, error-prone task because of the ambiguities inherent to natural language definitions. In this article, Visual ppinot, a graphical notation for defining PPIs together with business process models, is presented. Its underlying formal metamodel allows the automated processing of PPIs. Furthermore, it improves current state-of-the-art proposals in terms of expressiveness and in terms of providing an explicit visualisation of the link between PPIs and business processes, which avoids inconsistencies and promotes their co-evolution. The reference implementation, developed as a complete tool suite, has allowed its validation in a multiple-case study, in which five dimensions of Visual ppinot were studied: expressiveness, precision, automation, understandability, and traceability

Tolerance of sponge assemblages to temperature anomalies: resilience and proliferation of sponges following the 1997-8 El-Niño southern oscillation.

Coral reefs across the world are under threat from a range of stressors, and while there has been considerable focus on the impacts of these stressors on corals, far less is known about their effect on other reef organisms. The 1997-8 El-Niño Southern Oscillation (ENSO) had notable and severe impacts on coral reefs worldwide, but not all reef organisms were negatively impacted by this large-scale event. Here we describe how the sponge fauna at Bahia, Brazil was influenced by the 1997-8 ENSO event. Sponge assemblages from three contrasting reef habitats (reef tops, walls and shallow banks) at four sites were assessed annually from 1995 to 2011. The within-habitat sponge diversity did not vary significantly across the study period; however, there was a significant increase in density in all habitats. Multivariate analyses revealed no significant difference in sponge assemblage composition (ANOSIM) between pre- and post-ENSO years for any of the habitats, suggesting that neither the 1997-8 nor any subsequent smaller ENSO events have had any measurable impact on the reef sponge assemblage. Importantly, this is in marked contrast to the results previously reported for a suite of other taxa (including corals, echinoderms, bryozoans, and ascidians), which all suffered mass mortalities as a result of the ENSO event. Our results suggest that of all reef taxa, sponges have the potential to be resilient to large-scale thermal stress events and we hypothesize that sponges might be less affected by projected increases in sea surface temperature compared to other major groups of reef organisms

A genome-wide association study identifies new susceptibility loci for esophageal adenocarcinoma and Barrett's esophagus.

Esophageal adenocarcinoma is a cancer with rising incidence and poor survival. Most such cancers arise in a specialized intestinal metaplastic epithelium, which is diagnostic of Barrett's esophagus. In a genome-wide association study, we compared esophageal adenocarcinoma cases (n = 2,390) and individuals with precancerous Barrett's esophagus (n = 3,175) with 10,120 controls in 2 phases. For the combined case group, we identified three new associations. The first is at 19p13 (rs10419226: P = 3.6 × 10(-10)) in CRTC1 (encoding CREB-regulated transcription coactivator), whose aberrant activation has been associated with oncogenic activity. A second is at 9q22 (rs11789015: P = 1.0 × 10(-9)) in BARX1, which encodes a transcription factor important in esophageal specification. A third is at 3p14 (rs2687201: P = 5.5 × 10(-9)) near the transcription factor FOXP1, which regulates esophageal development. We also refine a previously reported association with Barrett's esophagus near the putative tumor suppressor gene FOXF1 at 16q24 and extend our findings to now include esophageal adenocarcinoma

Phytoplankton across Tropical and Subtropical Regions of the Atlantic, Indian and Pacific Oceans

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Interactive Effect of UVR and Phosphorus on the Coastal Phytoplankton Community of the Western Mediterranean Sea: Unravelling Eco- Physiological Mechanisms

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