Impedance-type approximations of the P-P elastic reflection coefficient: Modeling and AVO inversion

The normal-incidence elastic compressional reflection coefficient admits an exact, simple expression in terms of the acoustic impedance, namely the product of the P-wave velocity and density, at both sides of an interface. With slight modifications a similar expression can, also exactly, express the oblique-incidence acoustic reflection coefficient. A severe limitation on the use of these two reflection coefficients in analyzing seismic reflection data is that they provide no information on shearwave velocities that refer to the interface. We address the natural question of whether a suitable impedance concept can be introduced for which arbitrary P-P reflection coefficients can be expressed in a form analogous to their acoustic counterparts. Although no closed-form exact solution exists, our analysis provides a general framework for which, under suitable restrictions of the medium parameters, possible impedance functions can be derived. In particular, the well-established concept of elastic impedance and the recently introduced concept of reflection impedance can be better understood. Concerning these two impedances, we examine their potential for modeling and for estimating the AVO indicators of intercept and gradient. For typical synthetic examples, we show that the reflection impedance formulation provides consistently better results than those obtained using the elastic impedance.69259259

A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications

[EN] This paper provides a comprehensive probabilistic analysis of a full randomization of approximate SIR-type epidemiological models based on discrete-time Markov chain formulation. The randomization is performed by assuming that all input data (initial conditions, the contagion, and recovering rates involved in the transition matrix) are random variables instead of deterministic constants. In the first part of the paper, we determine explicit expressions for the so called first probability density function of each subpopulation identified as the corresponding states of the Markov chain (susceptible, infected, and recovered) in terms of the probability density function of each input random variable. Afterwards, we obtain the probability density functions of the times until a given proportion of the population remains susceptible, infected, and recovered, respectively. The theoretical analysis is completed by computing explicit expressions of important randomized epidemiological quantities, namely, the basic reproduction number, the effective reproduction number, and the herd immunity threshold. The study is conducted under very general assumptions and taking extensive advantage of the random variable transformation technique. The second part of the paper is devoted to apply our theoretical findings to describe the dynamics of the pandemic influenza in Egypt using simulated data excerpted from the literature. The simulations are complemented with valuable information, which is seldom displayed in epidemiological models. In spite of the nonlinear mathematical nature of SIR epidemiological model, our results show a strong agreement with the approximation via an appropriate randomized Markov chain. A justification in this regard is discussed.Spanish Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-P; Generalitat Valenciana, Grant/Award Number: APOSTD/2019/128; Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-PCortés, J.; El-Labany, S.; Navarro-Quiles, A.; Selim, MM.; Slama, H. (2020). A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications. Mathematical Methods in the Applied Sciences. 43(14):8204-8222. https://doi.org/10.1002/mma.6482S820482224314Hamra, G., MacLehose, R., & Richardson, D. (2013). Markov Chain Monte Carlo: an introduction for epidemiologists. International Journal of Epidemiology, 42(2), 627-634. doi:10.1093/ije/dyt043Becker, N. (1981). A General Chain Binomial Model for Infectious Diseases. Biometrics, 37(2), 251. doi:10.2307/2530415Allen, L. J. S. (2010). An Introduction to Stochastic Processes with Applications to Biology. doi:10.1201/b12537Hethcote, H. W. (2000). The Mathematics of Infectious Diseases. SIAM Review, 42(4), 599-653. doi:10.1137/s0036144500371907Brauer, F., & Castillo-Chávez, C. (2001). Mathematical Models in Population Biology and Epidemiology. Texts in Applied Mathematics. doi:10.1007/978-1-4757-3516-1Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., & Roselló, M.-D. (2018). Some results about randomized binary Markov chains: theory, computing and applications. International Journal of Computer Mathematics, 97(1-2), 141-156. doi:10.1080/00207160.2018.1440290Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., & Roselló, M.-D. (2017). Randomizing the parameters of a Markov chain to model the stroke disease: A technical generalization of established computational methodologies towards improving real applications. Journal of Computational and Applied Mathematics, 324, 225-240. doi:10.1016/j.cam.2017.04.040Casabán, M.-C., Cortés, J.-C., Romero, J.-V., & Roselló, M.-D. (2015). Probabilistic solution of random SI-type epidemiological models using the Random Variable Transformation technique. Communications in Nonlinear Science and Numerical Simulation, 24(1-3), 86-97. doi:10.1016/j.cnsns.2014.12.016Casabán, M.-C., Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., Roselló, M.-D., & Villanueva, R.-J. (2016). A comprehensive probabilistic solution of random SIS-type epidemiological models using the random variable transformation technique. Communications in Nonlinear Science and Numerical Simulation, 32, 199-210. doi:10.1016/j.cnsns.2015.08.009Slama, H., Hussein, A., El-Bedwhey, N. A., & Selim, M. M. (2019). An approximate probabilistic solution of a random SIR-type epidemiological model using RVT technique. Applied Mathematics and Computation, 361, 144-156. doi:10.1016/j.amc.2019.05.019Slama, H., El-Bedwhey, N. A., El-Depsy, A., & Selim, M. M. (2017). Solution of the finite Milne problem in stochastic media with RVT Technique. The European Physical Journal Plus, 132(12). doi:10.1140/epjp/i2017-11763-6Kegan, B., & West, R. W. (2005). Modeling the simple epidemic with deterministic differential equations and random initial conditions. Mathematical Biosciences, 195(2), 179-193. doi:10.1016/j.mbs.2005.02.004Dorini, F. A., Cecconello, M. S., & Dorini, L. B. (2016). On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Communications in Nonlinear Science and Numerical Simulation, 33, 160-173. doi:10.1016/j.cnsns.2015.09.009Van den Driessche, P. (2017). Reproduction numbers of infectious disease models. Infectious Disease Modelling, 2(3), 288-303. doi:10.1016/j.idm.2017.06.002Heffernan, J. ., Smith, R. ., & Wahl, L. . (2005). Perspectives on the basic reproductive ratio. Journal of The Royal Society Interface, 2(4), 281-293. doi:10.1098/rsif.2005.0042Khalil, K. M., Abdel-Aziz, M., Nazmy, T. T., & Salem, A.-B. M. (2012). An Agent-Based Modeling for Pandemic Influenza in Egypt. Intelligent Systems Reference Library, 205-218. doi:10.1007/978-3-642-25755-1_1

The yeast P5 type ATPase, Spf1, regulates manganese transport into the endoplasmic reticulum

The endoplasmic reticulum (ER) is a large, multifunctional and essential organelle. Despite intense research, the function of more than a third of ER proteins remains unknown even in the well-studied model organism Saccharomyces cerevisiae. One such protein is Spf1, which is a highly conserved, ER localized, putative P-type ATPase. Deletion of SPF1 causes a wide variety of phenotypes including severe ER stress suggesting that this protein is essential for the normal function of the ER. The closest homologue of Spf1 is the vacuolar P-type ATPase Ypk9 that influences Mn2+ homeostasis. However in vitro reconstitution assays with Spf1 have not yielded insight into its transport specificity. Here we took an in vivo approach to detect the direct and indirect effects of deleting SPF1. We found a specific reduction in the luminal concentration of Mn2+ in ∆spf1 cells and an increase following it’s overexpression. In agreement with the observed loss of luminal Mn2+ we could observe concurrent reduction in many Mn2+-related process in the ER lumen. Conversely, cytosolic Mn2+-dependent processes were increased. Together, these data support a role for Spf1p in Mn2+ transport in the cell. We also demonstrate that the human sequence homologue, ATP13A1, is a functionally conserved orthologue. Since ATP13A1 is highly expressed in developing neuronal tissues and in the brain, this should help in the study of Mn2+-dependent neurological disorders

Silicon particles as trojan horses for potential cancer therapy

[EN] Background: Porous silicon particles (PSiPs) have been used extensively as drug delivery systems, loaded with chemical species for disease treatment. It is well known from silicon producers that silicon is characterized by a low reduction potential, which in the case of PSiPs promotes explosive oxidation reactions with energy yields exceeding that of trinitrotoluene (TNT). The functionalization of the silica layer with sugars prevents its solubilization, while further functionalization with an appropriate antibody enables increased bioaccumulation inside selected cells. Results: We present here an immunotherapy approach for potential cancer treatment. Our platform comprises the use of engineered silicon particles conjugated with a selective antibody. The conceptual advantage of our system is that after reaction, the particles are degraded into soluble and excretable biocomponents. Conclusions: In our study, we demonstrate in particular, specific targeting and destruction of cancer cells in vitro. The fact that the LD50 value of PSiPs-HER-2 for tumor cells was 15-fold lower than the LD50 value for control cells demonstrates very high in vitro specificity. This is the first important step on a long road towards the design and development of novel chemotherapeutic agents against cancer in general, and breast cancer in particular.The authors acknowledge financial support from the following projects FIS2009-07812, MAT2012-35040, PROMETEO/2010/043, CTQ2011-23167, CrossSERS, FP7 MC-IEF 329131, and HSFP (project RGP0052/2012) and Medcom Tech SA. Xiang Yu acknowledges support by the Chinese government (CSC, Nr. 2010691036).Fenollosa Esteve, R.; Garcia-Rico, E.; Alvarez, S.; Alvarez, R.; Yu, X.; Rodriguez, I.; Carregal-Romero, S.... (2014). Silicon particles as trojan horses for potential cancer therapy. 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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

Targeting a Newly Established Spontaneous Feline Fibrosarcoma Cell Line by Gene Transfer

Fibrosarcoma is a deadly disease in cats and is significantly more often located at classical vaccine injections sites. More rare forms of spontaneous non-vaccination site (NSV) fibrosarcomas have been described and have been found associated to genetic alterations. Purpose of this study was to compare the efficacy of adenoviral gene transfer in NVS fibrosarcoma. We isolated and characterized a NVS fibrosarcoma cell line (Cocca-6A) from a spontaneous fibrosarcoma that occurred in a domestic calico cat. The feline cells were karyotyped and their chromosome number was counted using a Giemsa staining. Adenoviral gene transfer was verified by western blot analysis. Flow cytometry assay and Annexin-V were used to study cell-cycle changes and cell death of transduced cells. Cocca-6A fibrosarcoma cells were morphologically and cytogenetically characterized. Giemsa block staining of metaphase spreads of the Cocca-6A cells showed deletion of one of the E1 chromosomes, where feline p53 maps. Semi-quantitative PCR demonstrated reduction of p53 genomic DNA in the Cocca-6A cells. Adenoviral gene transfer determined a remarkable effect on the viability and growth of the Cocca-6A cells following single transduction with adenoviruses carrying Mda-7/IL-24 or IFN-γ or various combination of RB/p105, Ras-DN, IFN-γ, and Mda-7 gene transfer. Therapy for feline fibrosarcomas is often insufficient for long lasting tumor eradication. More gene transfer studies should be conducted in order to understand if these viral vectors could be applicable regardless the origin (spontaneous vs. vaccine induced) of feline fibrosarcomas