Applying the Random Variable Transformation method to solve a class of random linear differential equation with discrete delay

[EN] We randomize the following class of linear differential equations with delay, x(tau)' (t) = ax(tau) (t) bx(tau) (t -tau), t> 0, and initial condition, x(tau )(t) = g(t), -tau 0(+), to the first probability density function, say f(x, t), of the corresponding associated random linear problem without delay (tau = 0). The paper concludes with several numerical experiments illustrating our theoretical findings.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2017-89664-P and MTM2015-63723-P and Junta de Andalucia under Proyecto de Excelencia P12-FQM-1492. Ana Navarro Quiles acknowledges the Fundacio Ferran Sunyer i Balaguer and the Instituto de Estudios Catalanes for its contribution through the Borsa Ferran Sunyer i Balaguer. Ana Navarro Quiles acknowledges the postdoctoral contract financed by DyCon project funding from the European Research Council(ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No 694126-DYCON). The authors express their deepest thanks and respect to the editors and reviewers for their valuable comments.Caraballo, T.; Cortés, J.; Navarro-Quiles, A. (2019). Applying the Random Variable Transformation method to solve a class of random linear differential equation with discrete delay. Applied Mathematics and Computation. 356:198-218. https://doi.org/10.1016/j.amc.2019.03.048S19821835

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

Relationship between tissue retention efficiency and production traits in a slow-growing broiler population

An experiment was conducted using 96 individually caged male broilers between 49 and 77 d of age. One objective was to establish phenotypic relationships between some production traits [feed conversion ratio (FCR), feed consumption, residual feed consumption (RFC), relative weight gain (RWG), weight gain (WG) and live weight (LW)] and “tissue retention efficiency” (TRE) traits in a slow-growing broiler population. The other objective was the characterization of Campero-INTA broilers for TRE traits. Weight and feed consumption were recorded weekly. Forty four broilers were slaughtered at 44 d of age to estimate initial body composition while the remaining birds were slaughtered at 79 d of age. Ether extract and crude protein content of the carcasses were used to estimate TRE traits: Energy retained as protein (ERP), energy retained as fat (ERF), ERP/(ERP+ERF), ERF/(ERP+ERF), protein retention efficiency and lipid-protein ratio. Correlation coefficients between traits were obtained and regression analyses were done for the evaluation of the influence of production traits on TRE traits. The independent variable that best explained ERF was WG (R2 = 0.49). Inclusion of final LW and RWG raised the R2 to 0.58 and decreased the error term. The ERP was best explained by RWG (R2 = 0.37); lipid-protein ratio by final LW (R2 = 0.49); protein retention efficiency by FCR (R2 = 0.34) and fraction of retained energy (ERF-ERP/ERP+ERF) by WG (R2 = 0.29). The TRE traits were not well predicted by the measured production traits. The high phenotypic variability observed in some of the TRE traits suggested a need for further studies on these characteristics. Keywords: Broiler; tissue retention; efficiency; slow-growing stock South African Journal of Animal Science Vol. 37 (3) 2007: pp.164-16

Two S. pombe septation phases differ in ingression rate, septum structure, and response to F-actin loss

In fission yeast, cytokinesis requires a contractile actomyosin ring (CR) coupled to membrane and septum ingression. Septation proceeds in two phases. In anaphase B, the septum ingresses slowly. During telophase, the ingression rate increases, and the CR becomes dispensable. Here, we explore the relationship between the CR and septation by analyzing septum ultrastructure, ingression, and septation proteins in cells lacking F-actin. We show that the two phases of septation correlate with septum maturation and the response of cells to F-actin removal. During the first phase, the septum is immature and, following F-actin removal, rapidly loses the Bgs1 glucan synthase from the membrane edge and fails to ingress. During the second phase, the rapidly ingressing mature septum can maintain a Bgs1 ring and septum ingression without F-actin, but ingression becomes Cdc42 and exocyst dependent. Our results provide new insights into fungal cytokinesis and reveal the dual function of CR as an essential landmark for the concentration of Bgs1 and a contractile structure that maintains septum shape and synthesis

The evolution of acoustic size exaggeration in terrestrial mammals

Recent studies have revealed that some mammals possess adaptations that enable them to produce vocal signals with much lower fundamental frequency (F0) and formant frequency spacing (ΔF) than expected for their size. Although these adaptations are assumed to reflect selection pressures for males to lower frequency components and exaggerate body size in reproductive contexts, this hypothesis has not been tested across a broad range of species. Here we show that male terrestrial mammals produce vocal signals with lower ΔF (but not F0) than expected for their size in mating systems with greater sexual size dimorphism. We also reveal that males produce calls with higher than expected F0 and ΔF in species with increased sperm competition. This investigation confirms that sexual selection favours the use of ΔF as an acoustic size exaggerator, and supports the notion of an evolutionary trade-off between pre-copulatory signalling displays and sperm production

Merozoite release from Plasmodium falciparum-infected erythrocytes involves the transfer of DiIC16 from infected cell membrane to Maurer’s clefts

Merozoite release from infected erythrocytes is a complex process, which is still not fully understood. Such process was characterised at ultra-structural level in this work by labelling erythrocyte membrane with a fluorescent lipid probe and subsequent photo-conversion into an electron-dense precipitate. A lipophilic DiIC16 probe was inserted into the infected erythrocyte surface and the transport of this phospholipid analogue through the erythrocyte membrane was followed up during 48 h of the asexual erythrocyte cycle. The lipid probe was transferred from infected erythrocyte membranes to Maurer’s clefts during merozoite release, thereby indicating that these membranes remained inside host cells after parasite release. Fluorescent structures were never observed inside infected erythrocytes preceding merozoite exit and merozoites released from infected erythrocyte were not fluorescent. However, specific precipitated material was localised bordering the parasitophorous vacuole membrane and tubovesicular membranes when labelled non-infected erythrocytes were invaded by merozoites. It was revealed that lipids were interchangeable from one membrane to another, passing from infected erythrocyte membrane to Maurer’s clefts inside the erythrocyte ghost, even after merozoite release. Maurer’s clefts became photo-converted following merozoite release, suggesting that these structures were in close contact with infected erythrocyte membrane during merozoite exit and possibly played some role in malarial parasite exit from the host cell

Multilocus Bayesian Estimates of Intra-Oceanic Genetic Differentiation, Connectivity, and Admixture in Atlantic Swordfish (Xiphias gladius L.)

Versión del editor

Statistical colocalization of genetic risk variants for related autoimmune diseases in the context of common controls.

Determining whether potential causal variants for related diseases are shared can identify overlapping etiologies of multifactorial disorders. Colocalization methods disentangle shared and distinct causal variants. However, existing approaches require independent data sets. Here we extend two colocalization methods to allow for the shared-control design commonly used in comparison of genome-wide association study results across diseases. Our analysis of four autoimmune diseases--type 1 diabetes (T1D), rheumatoid arthritis, celiac disease and multiple sclerosis--identified 90 regions that were associated with at least one disease, 33 (37%) of which were associated with 2 or more disorders. Nevertheless, for 14 of these 33 shared regions, there was evidence that the causal variants differed. We identified new disease associations in 11 regions previously associated with one or more of the other 3 disorders. Four of eight T1D-specific regions contained known type 2 diabetes (T2D) candidate genes (COBL, GLIS3, RNLS and BCAR1), suggesting a shared cellular etiology.MF is funded by the Wellcome Trust (099772). CW and HG are funded by the Wellcome Trust (089989). This work was funded by the JDRF (9–2011–253), the Wellcome Trust (091157) and the National Institute for Health Research (NIHR) Cambridge Biomedical Research Centre. The Cambridge Institute for Medical Research (CIMR) is in receipt of a Wellcome Trust Strategic Award (100140). ImmunoBase.org is supported by Eli Lilly and Company. We thank the UK Medical Research Council and Wellcome Trust for funding the collection of DNA for the British 1958 Birth Cohort (MRC grant G0000934, WT grant 068545/Z/02). DNA control samples were prepared and provided by S. Ring, R. Jones, M. Pembrey, W. McArdle, D. Strachan and P. Burton. Biotec Cluster M4, the Fidelity Biosciences Research Initiative, Research Foundation Flanders, Research Fund KU Leuven, the Belgian Charcot Foundation, Gemeinntzige Hertie Stiftung, University Zurich, the Danish MS Society, the Danish Council for Strategic Research, the Academy of Finland, the Sigrid Juselius Foundation, Helsinki University, the Italian MS Foundation, Fondazione Cariplo, the Italian Ministry of University and Research, the Torino Savings Bank Foundation, the Italian Ministry of Health, the Italian Institute of Experimental Neurology, the MS Association of Oslo, the Norwegian Research Council, the South–Eastern Norwegian Health Authorities, the Australian National Health and Medical Research Council, the Dutch MS Foundation and Kaiser Permanente. Marina Evangelou is thanked for motivating the investigation of the FASLG association.This is the author accepted manuscript. The final version is available at http://www.nature.com/ng/journal/v47/n7/full/ng.3330.html

On-chip generation of high-dimensional entangled quantum states and their coherent control

Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science1. Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantum mechanics2, for increasing the sensitivity of quantum imaging schemes3, for improving the robustness and key rate of quantum communication protocols4, for enabling a richer variety of quantum simulations5, and for achieving more efficient and error-tolerant quantum computation6. Integrated photonics has recently become a leading platform for the compact, cost-efficient, and stable generation and processing of non-classical optical states7. However, so far, integrated entangled quantum sources have been limited to qubits (D = 2)8, 9, 10, 11. Here we demonstrate on-chip generation of entangled qudit states, where the photons are created in a coherent superposition of multiple high-purity frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions, formed by two entangled qudits with D = 10. Furthermore, using state-of-the-art, yet off-the-shelf telecommunications components, we introduce a coherent manipulation platform with which to control frequency-entangled states, capable of performing deterministic high-dimensional gate operations. We validate this platform by measuring Bell inequality violations and performing quantum state tomography. Our work enables the generation and processing of high-dimensional quantum states in a single spatial mode