Mean square solution of Bessel differential equation with uncertainties

[EN] This paper deals with the study of a Bessel-type differential equation where input parameters (coefficient and initial conditions) are assumed to be random variables. Using the so-called Lp-random calculus and assuming moment conditions on the random variables in the equation, a mean square convergent generalized power series solution is constructed. As a result of this convergence, the sequences of the mean and standard deviation obtained from the truncated power series solution are convergent as well. The results obtained in the random framework extend their deterministic counterpart. The theory is illustrated in two examples in which several distributions on the random inputs are assumed. Finally, we show through examples that the proposed method is computationally faster than Monte Carlo method.This work has been partially supported by the Spanish Ministerio de Economía y Competitividad grant MTM2013-41765-P and by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement No. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and Mexican Conacyt.Cortés, J.; Jódar Sánchez, LA.; Villafuerte, L. (2017). Mean square solution of Bessel differential equation with uncertainties. Journal of Computational and Applied Mathematics. 309:383-395. https://doi.org/10.1016/j.cam.2016.01.034S38339530

Solving Riccati time-dependent models with random quadratic coefficient

This paper deals with the construction of approximate solutions of a random logistic differential equation whose nonlinear coefficient is assumed to be an analytic stochastic process and the initial condition is a random variable. Applying p-mean stochastic calculus, the nonlinear equation is transformed into a random linear equation whose coefficients keep analyticity. Next, an approximate solution of the nonlinear problem is constructed in terms of a random power series solution of the associate linear problem. Approximations of the average and variance of the solution are provided. The proposed technique is illustrated through an example where comparisons with respect to Monte Carlo simulations are shown. © 2011 Elsevier Ltd. All rights reserved.This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-08587, DPI2010-20891-C02-01, Universitat Politecnica de Valencia grant PAID06-09-2588 and Mexican Conacyt.Cortés López, JC.; Jódar Sánchez, LA.; Company Rossi, R.; Villafuerte Altuzar, L. (2011). Solving Riccati time-dependent models with random quadratic coefficient. Applied Mathematics Letters. 24(12):2193-2196. https://doi.org/10.1016/j.aml.2011.06.024S21932196241

Bibliometric trends of health economic evaluation in Sub-Saharan Africa

Background: Collaboration between Sub-Saharan African researchers is important for the generation and transfer of health technology assessment (HTA) evidence, in order to support priority-setting in health. The objective of this analysis was to evaluate collaboration patterns between countries. Methods: We conducted a rapid evidence assessment that included a random sample of health economic evaluations carried out in 20 countries (Angola, Botswana, Congo, Lesotho, Madagascar, Malawi, Mauritius, Mozambique, Namibia, Seychelles, South Africa, Swaziland, Tanzania, Zambia, Zimbabwe, Ghana, Kenya, Nigeria, Ethiopia, Uganda). We conducted bibliometric network analysis based on all first authors with a Sub-Saharan African academic affiliation and their co-authored publications (“network-articles”). Then we produced a connection map of collaboration patterns among Sub-Saharan African researchers, reflecting the number of network-articles and the country of affiliation of the main co-authors. Results: The sample of 119 economic evaluations mostly related to treatments of communicable diseases, in particular HIV/AIDS (42/119, 35.29 %) and malaria (26/119, 21.85 %). The 39 first authors from Sub-Saharan African institutions together co-authored 729 network-articles. The network analysis showed weak collaboration between health economic researchers in Sub-Saharan Africa, with researchers being more likely to collaborate with Europe and North America than with other African countries. South Africa stood out as producing the highest number of health economic evaluations and collaborations. Conclusions: The development and evaluation of HTA research networks in Sub-Saharan Africa should be supported, with South Africa central to any such efforts. Organizations and institutions from high income countries interested in supporting priority setting in Sub-Saharan Africa should include promoting collaboration as part of their agendas, in order to take advantage of the potential transferability of results and methods of the available health economic analyses in Africa and internationally

Random differential operational calculus: theory and applications

In this article, we obtain a product rule and a chain rule for mean square derivatives. An application of the chain rule to the mean square solution of random differential equations is shown. However, to achieve such mean square differentiation rules, fourth order properties were needed and, therefore, we first studied a mean fourth order differential and integral calculus. Results are applied to solve random linear variable coefficient differential problems

Random differential operational calculus: Theory and applications

A product rule and a chain rule for mean square derivatives are obtained using fourth order properties. Applications to the mean square solution of random differential equations are shown

HIERARCHICAL CAPITALISM IN LATIN AMERICA: COMPARATIVE ANALYSIS WITH OTHER ECONOMIES

The Latin American capitalism is hierarchical (Schneider, 2009), due to the existence of monopolies and oligopolies and with high influence of multinationals and large national companies. That situation has an impact on several variables, both economic and social. The aim of this paper is to compare the three largest economies in Latin America (Brazil, Mexico and Argentina) with other economies that have another type of capitalism, in that way we can extract some effects of the hierarchical capitalism in Latin America. The comparison is based on the following variables: economic growth, innovation and democracy

Economies of scale and scope in publicly funded biomedical and health research: evidence from the literature

BACKGROUND: Publicly funded biomedical and health research is expected to achieve the best return possible for taxpayers and for society generally. It is therefore important to know whether such research is more productive if concentrated into a small number of ‘research groups’ or dispersed across many. METHODS: We undertook a systematic rapid evidence assessment focused on the research question: do economies of scale and scope exist in biomedical and health research? In other words, is that research more productive per unit of cost if more of it, or a wider variety of it, is done in one location? We reviewed English language literature without date restriction to the end of 2014. To help us to classify and understand that literature, we first undertook a review of econometric literature discussing models for analysing economies of scale and/or scope in research generally (not limited to biomedical and health research). RESULTS: We found a large and disparate literature. We reviewed 60 empirical studies of (dis-)economies of scale and/or scope in biomedical and health research, or in categories of research including or overlapping with biomedical and health research. This literature is varied in methods and findings. At the level of universities or research institutes, studies more often point to positive economies of scale than to diseconomies of scale or constant returns to scale in biomedical and health research. However, all three findings exist in the literature, along with inverse U-shaped relationships. At the level of individual research units, laboratories or projects, the numbers of studies are smaller and evidence is mixed. Concerning economies of scope, the literature more often suggests positive economies of scope than diseconomies, but the picture is again mixed. The effect of varying the scope of activities by a research group was less often reported than the effect of scale and the results were more mixed. CONCLUSIONS: The absence of predominant findings for or against the existence of economies of scale or scope implies a continuing need for case by case decisions when distributing research funding, rather than a general policy either to concentrate funding in a few centres or to disperse it across many

Solving a class of random non-autonomous linear fractional differential equations by means of a generalized mean square convergent power series

[EN] The aim of this paper is to solve a class of non-autonomous linear fractional differential equations with random inputs. A mean square convergent series solution is constructed in the case that the fractional order a of that Caputo derivative lies in ]0,1] using a random Frobenius approach. The analysis is conducted by using the so-called mean square random calculus. The mean square convergence of the series solution is established assuming mild conditions on random inputs (diffusion coefficient and initial condition). We show that these conditions are satisfied for a variety of unbounded random variables. In addition, explicit expressions to approximate the mean, the variance and the covariance functions of the random series solution are given. Two full illustrative examples are shown. (C) 2017 Elsevier Ltd. All rights reserved.Authors gratefully acknowledge the comments made by reviewers, which have greatly enriched the manuscript. This work has been partially supported by Ministerio de Economia y Competitividad grant MTM2013-41765-P.Burgos-Simon, C.; Calatayud-Gregori, J.; Cortés, J.; Villafuerte, L. (2018). Solving a class of random non-autonomous linear fractional differential equations by means of a generalized mean square convergent power series. Applied Mathematics Letters. 78:95-104. https://doi.org/10.1016/j.aml.2017.11.009S951047

Extending the deterministic Riemann-Liouville and Caputo operators to the random framework: A mean square approach with applications to solve random fractional differential equations

[EN] This paper extends both the deterministic fractional Riemann¿Liouville integral and the Caputo fractional derivative to the random framework using the mean square random calculus. Characterizations and sufficient conditions to guarantee the existence of both fractional random operators are given. Assuming mild conditions on the random input parameters (initial condition, forcing term and diffusion coefficient), the solution of the general random fractional linear differential equation, whose fractional order of the derivative is ¿ ¿ [0, 1], is constructed. The approach is based on a mean square chain rule, recently established, together with the random Fröbenius method. Closed formulae to construct reliable approximations for the mean and the covariance of the solution stochastic process are also given. Several examples illustrating the theoretical results are included.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2013-41765-P. The co-author Prof. L. Villafuerte acknowledges the support by Mexican Conacyt.Burgos, C.; Cortés, J.; Villafuerte, L.; Villanueva Micó, RJ. (2017). Extending the deterministic Riemann-Liouville and Caputo operators to the random framework: A mean square approach with applications to solve random fractional differential equations. Chaos, Solitons and Fractals. 102:305-318. https://doi.org/10.1016/j.chaos.2017.02.008S30531810

Exploring the interdependencies of research funders in the UK

Investment in medical research is vital to the continuing improvement of the UK's health and wealth. It is through research that we expand our understanding of disease and develop new treatments for patients. Medical research charities currently contribute over £1 billion annually to medical research in the UK, of which over £350 million is provided by Cancer Research UK. Many charities, including Cancer Research UK, receive no government funding for their research activity. Cancer Research UK is engaged in a programme of work in order to better understand the medical research funding environment and demonstrate the importance of sustained investment. A key part of that is the Office of Health Economics‟ (OHE) 2011 report “Exploring the interdependency between public and charitable medical research”. This study found that there are substantial benefits, both financial and qualitative, from the existence of a variety of funders and that reductions in the level of government financial support for medical research are likely to have broader negative effects. This contributed to other evidence which found that the activities and funding of the charity, public and private sectors respectively are complementary, i.e. mutually reinforcing, rather than duplicative or merely substituting for one another. “Exploring the interdependencies of research funders in the UK” by the Office of Health Economics (OHE) and SPRU: Science and Technology Policy Research at the University of Sussex, represents a continued effort to build the evidence base around the funding of medical research. This report uncovers the extent to which funders of cancer research are interdependent, nationally and internationally. Key figures show that two thirds of publications acknowledging external support have relied on multiple funders, while just under half benefited from overseas funding, and almost a fifth are also supported by industry. In addition the analysis shows that the general public would not want tax funding of cancer research to be reduced, but would not donate enough to charities to compensate for any such reduction