Integral transform solution of random coupled parabolic partial differential models

[EN] Random coupled parabolic partial differential models are solved numerically using random cosine Fourier transform together with non-Gaussian random numerical integration that captures the highly oscillatory behaviour of the involved integrands. Sufficient condition of spectral type imposed on the random matrices of the system is given so that the approximated stochastic process solution and its statistical moments are numerically convergent. Numerical experiments illustrate the results.Spanish Ministerio de Economia, Industria y Competitividad (MINECO); Agencia Estatal de Investigacion (AEI); Fondo Europeo de Desarrollo Regional (FEDER UE), Grant/Award Number: MTM2017-89664-PCasabán Bartual, MC.; Company Rossi, R.; Egorova, VN.; Jódar Sánchez, LA. (2020). Integral transform solution of random coupled parabolic partial differential models. Mathematical Methods in the Applied Sciences. 43(14):8223-8236. https://doi.org/10.1002/mma.6492S822382364314Bäck, J., Nobile, F., Tamellini, L., & Tempone, R. (2010). Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison. Spectral and High Order Methods for Partial Differential Equations, 43-62. doi:10.1007/978-3-642-15337-2_3Bachmayr, M., Cohen, A., & Migliorati, G. (2016). Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients. ESAIM: Mathematical Modelling and Numerical Analysis, 51(1), 321-339. doi:10.1051/m2an/2016045Ernst, O. G., Sprungk, B., & Tamellini, L. (2018). Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs). SIAM Journal on Numerical Analysis, 56(2), 877-905. doi:10.1137/17m1123079Sheng, D., & Axelsson, K. (1995). Uncoupling of coupled flows in soil—a finite element method. International Journal for Numerical and Analytical Methods in Geomechanics, 19(8), 537-553. doi:10.1002/nag.1610190804Mitchell, J. K. (1991). Conduction phenomena: from theory to geotechnical practice. Géotechnique, 41(3), 299-340. doi:10.1680/geot.1991.41.3.299Das, P. K. (1991). Optical Signal Processing. doi:10.1007/978-3-642-74962-9Ashkenazy, Y. (2017). Energy transfer of surface wind-induced currents to the deep ocean via resonance with the Coriolis force. Journal of Marine Systems, 167, 93-104. doi:10.1016/j.jmarsys.2016.11.019Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4), 500-544. doi:10.1113/jphysiol.1952.sp004764Galiano, G. (2012). On a cross-diffusion population model deduced from mutation and splitting of a single species. Computers & Mathematics with Applications, 64(6), 1927-1936. doi:10.1016/j.camwa.2012.03.045Casabán, M. C., Company, R., & Jódar, L. (2019). Numerical solutions of random mean square Fisher‐KPP models with advection. Mathematical Methods in the Applied Sciences, 43(14), 8015-8031. doi:10.1002/mma.5942Casabán, M. C., Company, R., & Jódar, L. (2019). Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness. Mathematics, 7(9), 853. doi:10.3390/math7090853Shampine, L. F. (2008). Vectorized adaptive quadrature in MATLAB. Journal of Computational and Applied Mathematics, 211(2), 131-140. doi:10.1016/j.cam.2006.11.021Iserles, A. (2004). On the numerical quadrature of highly-oscillating integrals I: Fourier transforms. IMA Journal of Numerical Analysis, 24(3), 365-391. doi:10.1093/imanum/24.3.365Ma, J., & Liu, H. (2018). On the Convolution Quadrature Rule for Integral Transforms with Oscillatory Bessel Kernels. Symmetry, 10(7), 239. doi:10.3390/sym10070239Jódar, L., & Goberna, D. (1996). Exact and analytic numerical solution of coupled diffusion problems in a semi-infinite medium. Computers & Mathematics with Applications, 31(9), 17-24. doi:10.1016/0898-1221(96)00038-7Jódar, L., & Goberna, D. (1998). A matrix D’Alembert formula for coupled wave initial value problems. Computers & Mathematics with Applications, 35(9), 1-15. doi:10.1016/s0898-1221(98)00052-2Ostrowski, A. M. (1959). A QUANTITATIVE FORMULATION OF SYLVESTER’S LAW OF INERTIA. Proceedings of the National Academy of Sciences, 45(5), 740-744. doi:10.1073/pnas.45.5.740Ashkenazy, Y., Gildor, H., & Bel, G. (2015). The effect of stochastic wind on the infinite depth Ekman layer model. EPL (Europhysics Letters), 111(3), 39001. doi:10.1209/0295-5075/111/3900

vCJD risk in the Republic of Ireland

BACKGROUND: The Republic of Ireland has the second highest incidence of BSE worldwide. Only a single case of vCJD has been identified to date. METHODS: We estimate the total future number of clinical cases of vCJD using an established mathematical model, and based on infectivity of bovine tissue calculated from UK data and on the relative exposure to BSE contaminated meat. RESULTS: We estimate 1 future clinical case (95% CI 0 – 15) of vCJD in the Republic of Ireland. Irish exposure is from BSE infected indigenous beef products and from imported UK beef products. Additionally, 2.5% of the Irish population was exposed to UK beef through residing in the UK during the 'at-risk' period. The relative proportion of risk attributable to each of these three exposures individually is 2:2:1 respectively. CONCLUSIONS: The low numbers of future vCJD cases estimated in this study is reassuring for the Irish population and for other countries with a similar level of BSE exposure

Cognitive networks: brains, internet, and civilizations

In this short essay, we discuss some basic features of cognitive activity at several different space-time scales: from neural networks in the brain to civilizations. One motivation for such comparative study is its heuristic value. Attempts to better understand the functioning of "wetware" involved in cognitive activities of central nervous system by comparing it with a computing device have a long tradition. We suggest that comparison with Internet might be more adequate. We briefly touch upon such subjects as encoding, compression, and Saussurean trichotomy langue/langage/parole in various environments.Comment: 16 page

Updated projections of future vCJD deaths in the UK

BACKGROUND: Past projections of the future course of the vCJD epidemic in the UK have shown considerable uncertainty, with wide confidence bounds. However, recent vCJD case data have indicated a decrease in the annual incidence of deaths over the past two years. METHODS: A detailed survival model is fitted to the 121 vCJD deaths reported by the end of 2002 stratified by age and calendar time to obtain projections of future incidence. The model is additionally fitted to recent results from a survey of appendix tissues. RESULTS: Our results show a substantial decrease in the uncertainty of the future course of the primary epidemic in the susceptible genotype (MM-homozygous at codon 129 of the prion protein gene), with a best estimate of 40 future deaths (95% prediction interval 9–540) based on fitting to the vCJD case data alone. Additional fitting of the appendix data increases these estimates (best estimate 100, 95% prediction interval 10–2,600) but remains lower than previous projections. CONCLUSIONS: The primary vCJD epidemic in the known susceptible genotype in the UK appears to be in decline

Barriers and opportunities for evidence-based health service planning: the example of developing a Decision Analytic Model to plan services for sexually transmitted infections in the UK

Decision Analytic Models (DAMs) are established means of evidence-synthesis to differentiate between health interventions. They have mainly been used to inform clinical decisions and health technology assessment at the national level, yet could also inform local health service planning. For this, a DAM must take into account the needs of the local population, but also the needs of those planning its services. Drawing on our experiences from stakeholder consultations, where we presented the potential utility of a DAM for planning local health services for sexually transmitted infections (STIs) in the UK, and the evidence it could use to inform decisions regarding different combinations of service provision, in terms of their costs, cost-effectiveness, and public health outcomes, we discuss the barriers perceived by stakeholders to the use of DAMs to inform service planning for local populations, including (1) a tension between individual and population perspectives; (2) reductionism; and (3) a lack of transparency regarding models, their assumptions, and the motivations of those generating models

Clean birth kits to improve birth practices: development and testing of a country level decision support tool

Background: Clean birth practices can prevent sepsis, one of the leading causes of both maternal and newborn mortality. Evidence suggests that clean birth kits (CBKs), as part of package that includes education, are associated with a reduction in newborn mortality, omphalitis, and puerperal sepsis. However, questions remain about how best to approach the introduction of CBKs in country. We set out to develop a practical decision support tool for programme managers of public health systems who are considering the potential role of CBKs in their strategy for care at birth. Methods: Development and testing of the decision support tool was a three-stage process involving an international expert group and country level testing. Stage 1, the development of the tool was undertaken by the Birth Kit Working Group and involved a review of the evidence, a consensus meeting, drafting of the proposed tool and expert review. In Stage 2 the tool was tested with users through interviews (9) and a focus group, with federal and provincial level decision makers in Pakistan. In Stage 3 the findings from the country level testing were reviewed by the expert group. Results: The decision support tool comprised three separate algorithms to guide the policy maker or programme manager through the specific steps required in making the country level decision about whether to use CBKs. The algorithms were supported by a series of questions (that could be administered by interview, focus group or questionnaire) to help the decision maker identify the information needed. The country level testing revealed that the decision support tool was easy to follow and helpful in making decisions about the potential role of CBKs. Minor modifications were made and the final algorithms are presented. Conclusion: Testing of the tool with users in Pakistan suggests that the tool facilitates discussion and aids decision making. However, testing in other countries is needed to determine whether these results can be replicated and to identify how the tool can be adapted to meet country specific needs

Molecular characterization of a Chinese variant of the Flury-LEP strain

The entire genome of rabies virus vaccine strain Flury-LEP-C, a Chinese variant of the rabies virus vaccine strain Flury-LEP, was sequenced. The overall length of the genome of Flury-LEP-C strain was 11 924 nucleotides (nt), comprising a leader sequence of 58 nt, nucleoprotein (N) gene of 1353 nt, phosphoprotein (P) gene of 894 nt, matrix protein (M) gene of 609 nt, glycoprotein (G) gene of 1575 nt, RNA-dependent RNA polymerase (RdRp, L) gene of 6384 nt, and a trailer region of 70 nt. There was TGAAAAAAA (TGA7) consensus sequence in the end of each gene in Flury-LEP-C genome, except G gene which had a GAGAAAAAAA sequence in the end of the non-coding G-L region. There were AACAYYYCT consensus start signal close to the TGA7. Flury-LEP-C has 310 nucleotides more than HEP-Flury in G-L intergenic region. The analysis showed that the residue at 333 of the mature G protein was Arg, which was reported to be related to pathogenicity. Compared with FluryLEP, there were 19 different amino acids (AAs) in five proteins of Flury-LEP-C, including 15 AAs which were identical with corresponding residues of Hep-Flury, and 4 AAs which were neither identical with the residues of FluryLEP nor with the residues of Hep-Flury. The results showed the topology of the phylogenetic trees generated by two protein sequences were similar. It was demonstrated that HN10, BD06, FJ009, FJ008, D02, D01, F04, F02 have a close relationship to CTN-1 and CTN181, and MRV was closely related to Flury-LEP, HEP-Flury and Flury-LEP-C

A Method of Drusen Measurement Based on the Geometry of Fundus Reflectance

BACKGROUND: The hallmarks of age-related macular degeneration, the leading cause of blindness in the developed world, are the subretinal deposits known as drusen. Drusen identification and measurement play a key role in clinical studies of this disease. Current manual methods of drusen measurement are laborious and subjective. Our purpose was to expedite clinical research with an accurate, reliable digital method. METHODS: An interactive semi-automated procedure was developed to level the macular background reflectance for the purpose of morphometric analysis of drusen. 12 color fundus photographs of patients with age-related macular degeneration and drusen were analyzed. After digitizing the photographs, the underlying background pattern in the green channel was leveled by an algorithm based on the elliptically concentric geometry of the reflectance in the normal macula: the gray scale values of all structures within defined elliptical boundaries were raised sequentially until a uniform background was obtained. Segmentation of drusen and area measurements in the central and middle subfields (1000 μm and 3000 μm diameters) were performed by uniform thresholds. Two observers using this interactive semi-automated software measured each image digitally. The mean digital measurements were compared to independent stereo fundus gradings by two expert graders (stereo Grader 1 estimated the drusen percentage in each of the 24 regions as falling into one of four standard broad ranges; stereo Grader 2 estimated drusen percentages in 1% to 5% intervals). RESULTS: The mean digital area measurements had a median standard deviation of 1.9%. The mean digital area measurements agreed with stereo Grader 1 in 22/24 cases. The 95% limits of agreement between the mean digital area measurements and the more precise stereo gradings of Grader 2 were -6.4 % to +6.8 % in the central subfield and -6.0 % to +4.5 % in the middle subfield. The mean absolute differences between the digital and stereo gradings 2 were 2.8 +/- 3.4% in the central subfield and 2.2 +/- 2.7% in the middle subfield. CONCLUSIONS: Semi-automated, supervised drusen measurements may be done reproducibly and accurately with adaptations of commercial software. This technique for macular image analysis has potential for use in clinical research