Solving the Random Pielou Logistic Equation with the Random Variable Transformation Technique: Theory and Applications

[EN] The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However, discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state, and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples: The first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data.This work has been partially supported by the Ministerio de Economía y Competitividad grant MTM2017-89664-PCortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2019). Solving the Random Pielou Logistic Equation with the Random Variable Transformation Technique: Theory and Applications. Mathematical Methods in the Applied Sciences. 42(17):5708-5717. https://doi.org/10.1002/mma.5440S570857174217Kwasnicki, W. (2013). Logistic growth of the global economy and competitiveness of nations. Technological Forecasting and Social Change, 80(1), 50-76. doi:10.1016/j.techfore.2012.07.007Chen-Charpentier, B. M., & Stanescu, D. (2011). Biofilm growth on medical implants with randomness. Mathematical and Computer Modelling, 54(7-8), 1682-1686. doi:10.1016/j.mcm.2010.11.075Wolfram Research Inc.Mathematica. Version 11.2 Champaign IL;2018.CNMC Comisión Nacional de los Mercados y la Competencia.http://data.cnmc.es/datagraph/jsp/inf_anual.jsp Accessed: 2018‐07‐24 (in Spanish)

Semi-active damping using a hybrid control approach

In this article, a hybrid control framework is used to design semi-active controllers for vibration reduction. It is shown that the semi-active skyhook damper, typically used for vibration reduction, can be recast in the framework of an event-driven intermittent controller. By doing this, we can then exploit the well-developed techniques associated with hybrid control theory to design the semi-active control system. Illustrative simulation examples are based on a 2 degree-of-freedom system, often used to model the dynamics of a quarter car body model. The simulation results demonstrate how hybrid control design techniques can improve the overall performance of the semi-active control system

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

On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments

"This is the peer reviewed version of the following article: Calatayud, J, Cortés, J-;C, Jornet, M. On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments. Comp and Math Methods. 2019; 1:e1045. https://doi.org/10.1002/cmm4.1045 , which has been published in final form at https://doi.org/10.1002/cmm4.1045. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] In this paper, we construct two linearly independent response processes to the random Legendre differential equation on (-1,1)U(1,3), consisting of Lp(omega) convergent random power series around the regular¿singular point 1. A theorem on the existence and uniqueness of Lp(omega) solution to the random Legendre differential equation on the intervals (-1,1) and (1,3) is obtained. The hypotheses assumed are simple: initial conditions in Lp(omega) and random input A in L infinite(omega) (this is equivalent to A having absolute moments that grow at most exponentially). Thus, this paper extends the deterministic theory to a random framework. Uncertainty quantification for the solution stochastic process is performed by truncating the random series and taking limits in Lp(omega). In the numerical experiments, we approximate its expectation and variance for certain forms of the differential equation. The reliability of our approach is compared with Monte Carlo simulations and generalized polynomial chaos expansions.Spanish Ministerio de Economía y Competitividad, Grant/Award Number: MTM2017-89664-P; Programa de Ayudas de Investigación y Desarrollo; Universitat Politècnica de ValènciaCalatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments. Computational and Mathematical Methods. 1(4):1-12. https://doi.org/10.1002/cmm4.1045S11214Calbo, G., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2011). Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Computers & Mathematics with Applications, 61(9), 2782-2792. doi:10.1016/j.camwa.2011.03.045Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Wong, E., & Hajek, B. (1985). Stochastic Processes in Engineering Systems. Springer Texts in Electrical Engineering. doi:10.1007/978-1-4612-5060-9Nouri, K., & Ranjbar, H. (2014). Mean Square Convergence of the Numerical Solution of Random Differential Equations. Mediterranean Journal of Mathematics, 12(3), 1123-1140. doi:10.1007/s00009-014-0452-8Lupulescu, V., O’Regan, D., & ur Rahman, G. (2014). Existence results for random fractional differential equations. Opuscula Mathematica, 34(4), 813. doi:10.7494/opmath.2014.34.4.813Villafuerte, L., & Chen-Charpentier, B. M. (2012). A random differential transform method: Theory and applications. Applied Mathematics Letters, 25(10), 1490-1494. doi:10.1016/j.aml.2011.12.033Licea, J. A., Villafuerte, L., & Chen-Charpentier, B. M. (2013). Analytic and numerical solutions of a Riccati differential equation with random coefficients. Journal of Computational and Applied Mathematics, 239, 208-219. doi:10.1016/j.cam.2012.09.040Lang, S. (1997). Undergraduate Analysis. Undergraduate Texts in Mathematics. doi:10.1007/978-1-4757-2698-5Cortés, J.-C., Romero, J.-V., Roselló, M.-D., Santonja, F.-J., & Villanueva, R.-J. (2013). Solving Continuous Models with Dependent Uncertainty: A Computational Approach. Abstract and Applied Analysis, 2013, 1-10. doi:10.1155/2013/983839Calatayud, J., Cortés, J. C., Jornet, M., & Villanueva, R. J. (2018). Computational uncertainty quantification for random time-discrete epidemiological models using adaptive gPC. Mathematical Methods in the Applied Sciences, 41(18), 9618-9627. doi:10.1002/mma.531

Numerical solutions of random mean square Fisher-KPP models with advection

[EN] This paper deals with the construction of numerical stable solutions of random mean square Fisher-Kolmogorov-Petrosky-Piskunov (Fisher-KPP) models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique transforms the original continuous problem into a nonlinear inhomogeneous system of random differential equations. Then, by extending to the random framework, the ideas of the exponential time differencing method, a full vector discretization of the problem addresses to a random vector difference scheme. A sample approach of the random vector difference scheme, the use of properties of Metzler matrices and the logarithmic norm allow the proof of stability of the numerical solutions in the mean square sense. In spite of the computational complexity, the results are illustrated by comparing the results with a test problem where the exact solution is known.Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-PCasabán Bartual, MC.; Company Rossi, R.; Jódar Sánchez, LA. (2020). Numerical solutions of random mean square Fisher-KPP models with advection. Mathematical Methods in the Applied Sciences. 43(14):8015-8031. https://doi.org/10.1002/mma.5942S801580314314FISHER, R. A. (1937). THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES. Annals of Eugenics, 7(4), 355-369. doi:10.1111/j.1469-1809.1937.tb02153.xBengfort, M., Malchow, H., & Hilker, F. M. (2016). The Fokker–Planck law of diffusion and pattern formation in heterogeneous environments. Journal of Mathematical Biology, 73(3), 683-704. doi:10.1007/s00285-016-0966-8Okubo, A., & Levin, S. A. (2001). Diffusion and Ecological Problems: Modern Perspectives. Interdisciplinary Applied Mathematics. doi:10.1007/978-1-4757-4978-6SKELLAM, J. G. (1951). RANDOM DISPERSAL IN THEORETICAL POPULATIONS. Biometrika, 38(1-2), 196-218. doi:10.1093/biomet/38.1-2.196Aronson, D. G., & Weinberger, H. F. (1975). Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. Partial Differential Equations and Related Topics, 5-49. doi:10.1007/bfb0070595Aronson, D. ., & Weinberger, H. . (1978). Multidimensional nonlinear diffusion arising in population genetics. Advances in Mathematics, 30(1), 33-76. doi:10.1016/0001-8708(78)90130-5Weinberger, H. F. (2002). On spreading speeds and traveling waves for growth and migration models in a periodic habitat. Journal of Mathematical Biology, 45(6), 511-548. doi:10.1007/s00285-002-0169-3Weinberger, H. F., Lewis, M. A., & Li, B. (2007). Anomalous spreading speeds of cooperative recursion systems. Journal of Mathematical Biology, 55(2), 207-222. doi:10.1007/s00285-007-0078-6Liang, X., & Zhao, X.-Q. (2006). Asymptotic speeds of spread and traveling waves for monotone semiflows with applications. Communications on Pure and Applied Mathematics, 60(1), 1-40. doi:10.1002/cpa.20154E. Fitzgibbon, W., Parrott, M. E., & Webb, G. (1995). Diffusive epidemic models with spatial and age dependent heterogeneity. Discrete & Continuous Dynamical Systems - A, 1(1), 35-57. doi:10.3934/dcds.1995.1.35Kinezaki, N., Kawasaki, K., & Shigesada, N. (2006). Spatial dynamics of invasion in sinusoidally varying environments. Population Ecology, 48(4), 263-270. doi:10.1007/s10144-006-0263-2Jin, Y., Hilker, F. M., Steffler, P. M., & Lewis, M. A. (2014). Seasonal Invasion Dynamics in a Spatially Heterogeneous River with Fluctuating Flows. Bulletin of Mathematical Biology, 76(7), 1522-1565. doi:10.1007/s11538-014-9957-3Faou, E. (2009). Analysis of splitting methods for reaction-diffusion problems using stochastic calculus. Mathematics of Computation, 78(267), 1467-1483. doi:10.1090/s0025-5718-08-02185-6Doering, C. R., Mueller, C., & Smereka, P. (2003). Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality. Physica A: Statistical Mechanics and its Applications, 325(1-2), 243-259. doi:10.1016/s0378-4371(03)00203-6Siekmann, I., Bengfort, M., & Malchow, H. (2017). Coexistence of competitors mediated by nonlinear noise. The European Physical Journal Special Topics, 226(9), 2157-2170. doi:10.1140/epjst/e2017-70038-6McKean, H. P. (1975). Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov. Communications on Pure and Applied Mathematics, 28(3), 323-331. doi:10.1002/cpa.3160280302Berestycki, H., & Nadin, G. (2012). Spreading speeds for one-dimensional monostable reaction-diffusion equations. Journal of Mathematical Physics, 53(11), 115619. doi:10.1063/1.4764932Cortés, J. C., Jódar, L., Villafuerte, L., & Villanueva, R. J. (2007). Computing mean square approximations of random diffusion models with source term. Mathematics and Computers in Simulation, 76(1-3), 44-48. doi:10.1016/j.matcom.2007.01.020Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Casabán, M.-C., Cortés, J.-C., & Jódar, L. (2016). Solving linear and quadratic random matrix differential equations: A mean square approach. Applied Mathematical Modelling, 40(21-22), 9362-9377. doi:10.1016/j.apm.2016.06.017Sarmin, E. N., & Chudov, L. A. (1963). On the stability of the numerical integration of systems of ordinary differential equations arising in the use of the straight line method. USSR Computational Mathematics and Mathematical Physics, 3(6), 1537-1543. doi:10.1016/0041-5553(63)90256-8Sanz-Serna, J. M., & Verwer, J. G. (1989). Convergence analysis of one-step schemes in the method of lines. Applied Mathematics and Computation, 31, 183-196. doi:10.1016/0096-3003(89)90118-5Calvo, M. P., de Frutos, J., & Novo, J. (2001). Linearly implicit Runge–Kutta methods for advection–reaction–diffusion equations. Applied Numerical Mathematics, 37(4), 535-549. doi:10.1016/s0168-9274(00)00061-1Cox, S. M., & Matthews, P. C. (2002). Exponential Time Differencing for Stiff Systems. Journal of Computational Physics, 176(2), 430-455. doi:10.1006/jcph.2002.6995De la Hoz, F., & Vadillo, F. (2016). Numerical simulations of time-dependent partial differential equations. Journal of Computational and Applied Mathematics, 295, 175-184. doi:10.1016/j.cam.2014.10.006Company, R., Egorova, V. N., & Jódar, L. (2018). Conditional full stability of positivity-preserving finite difference scheme for diffusion–advection-reaction models. Journal of Computational and Applied Mathematics, 341, 157-168. doi:10.1016/j.cam.2018.02.031Kaczorek, T. (2002). Positive 1D and 2D Systems. Communications and Control Engineering. doi:10.1007/978-1-4471-0221-2Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences. doi:10.1007/978-1-4612-5561-

Solving random boundary heat model using the finite difference method under mean square convergence

"This is the peer reviewed version of the following article: Cortés, J. C., Romero, J. V., Roselló, M. D., Sohaly, MA. Solving random boundary heat model using the finite difference method under mean square convergence. Comp and Math Methods. 2019; 1:e1026. https://doi.org/10.1002/cmm4.1026 , which has been published in final form at https://doi.org/10.1002/cmm4.1026. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] This contribution is devoted to construct numerical approximations to the solution of the one-dimensional boundary value problem for the heat model with uncertainty in the diffusion coefficient. Approximations are constructed via random numerical schemes. This approach permits discussing the effect of the random diffusion coefficient, which is assumed a random variable. We establish results about the consistency and stability of the random difference scheme using mean square convergence. Finally, an illustrative example is presented.Spanish Ministerio de Economía y Competitividad. Grant Number: MTM2017-89664-PCortés, J.; Romero, J.; Roselló, M.; Sohaly, M. (2019). Solving random boundary heat model using the finite difference method under mean square convergence. Computational and Mathematical Methods. 1(3):1-15. https://doi.org/10.1002/cmm4.1026S11513Han, X., & Kloeden, P. E. (2017). Random Ordinary Differential Equations and Their Numerical Solution. Probability Theory and Stochastic Modelling. doi:10.1007/978-981-10-6265-0Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Logan, J. D. (2004). Partial Differential Equations on Bounded Domains. Undergraduate Texts in Mathematics, 121-171. doi:10.1007/978-1-4419-8879-9_4Cannon, J. R. (1964). A Cauchy problem for the heat equation. Annali di Matematica Pura ed Applicata, 66(1), 155-165. doi:10.1007/bf02412441LinPPY.On The Numerical Solution of The Heat Equation in Unbounded Domains[PhD thesis].New York NY:New York University;1993.Li, J.-R., & Greengard, L. (2007). On the numerical solution of the heat equation I: Fast solvers in free space. Journal of Computational Physics, 226(2), 1891-1901. doi:10.1016/j.jcp.2007.06.021Han, H., & Huang, Z. (2002). Exact and approximating boundary conditions for the parabolic problems on unbounded domains. Computers & Mathematics with Applications, 44(5-6), 655-666. doi:10.1016/s0898-1221(02)00180-3Han, H., & Huang, Z. (2002). A class of artificial boundary conditions for heat equation in unbounded domains. Computers & Mathematics with Applications, 43(6-7), 889-900. doi:10.1016/s0898-1221(01)00329-7Strikwerda, J. C. (2004). Finite Difference Schemes and Partial Differential Equations, Second Edition. doi:10.1137/1.9780898717938Kloeden, P. E., & Platen, E. (1992). Numerical Solution of Stochastic Differential Equations. doi:10.1007/978-3-662-12616-5Øksendal, B. (2003). Stochastic Differential Equations. Universitext. doi:10.1007/978-3-642-14394-6Holden, H., Øksendal, B., Ubøe, J., & Zhang, T. (2010). Stochastic Partial Differential Equations. doi:10.1007/978-0-387-89488-1El-Tawil, M. A., & Sohaly, M. A. (2012). Mean square convergent three points finite difference scheme for random partial differential equations. Journal of the Egyptian Mathematical Society, 20(3), 188-204. doi:10.1016/j.joems.2012.08.017Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., Roselló, M.-D., & Sohaly, M. A. (2018). Solving the random Cauchy one-dimensional advection–diffusion equation: Numerical analysis and computing. Journal of Computational and Applied Mathematics, 330, 920-936. doi:10.1016/j.cam.2017.02.001Cortés, J. C., Jódar, L., Villafuerte, L., & Villanueva, R. J. (2007). Computing mean square approximations of random diffusion models with source term. Mathematics and Computers in Simulation, 76(1-3), 44-48. doi:10.1016/j.matcom.2007.01.020Cortés, J. C., Jódar, L., & Villafuerte, L. (2009). Random linear-quadratic mathematical models: Computing explicit solutions and applications. Mathematics and Computers in Simulation, 79(7), 2076-2090. doi:10.1016/j.matcom.2008.11.008Henderson, D., & Plaschko, P. (2006). Stochastic Differential Equations in Science and Engineering. doi:10.1142/580

The Impact of the Oncotype DX Breast Cancer Assay on Treatment Decisions for Women With Estrogen Receptor-Positive, Node-Negative Breast Carcinoma in Hong Kong

Background The Oncotype DX Breast Cancer Assay is validated to assess risk of distant recurrence and likelihood of chemotherapy (CT) benefit in estrogen receptor-positive ESBC in various populations. In Hong Kong, > 80% of breast cancers are early stage breast cancer (ESBC) and > 60% of these women receive CT. This prospective study measured changes in CT type and recommendations, as well as physician impression of assay impact in a homogenous Chinese population. Methods Consecutive patients with estrogen receptor-positive, T1-3 N0-1mi M0 ESBC were offered enrollment. After surgery, physicians discussed treatment options with patients, then ordered the assay, then reassessed treatment recommendation considering assay results. Changes in treatment recommendation, CT utilization, physician confidence, and physician rating of influence on their treatment recommendations were measured. Results A total of 146 evaluable patients received pre- and post-testing treatment recommendations. CT recommendations (including changes in intensity of CT) were changed for 34 of 146 patients (23.3%; 95% confidence interval, 16.7%-31.0%); change in intensity occurred in 7 of 146 (4.8%). There were 27 changes in treatment recommendations of adding or removing CT altogether (18.5% change; 95% confidence interval, 12.6%-25.8%). CT recommendations decreased from 52.1% to 37.7%, a net absolute reduction of 14.4% (P < .001; 27.6% net relative reduction). Pre-assay, 96% of physicians agreed/strongly agreed that they were confident in their treatment recommendation; post-assay, 90% of physicians agreed/strongly agreed with the same statement. Thirty percent of physicians agreed/strongly agreed that the test had influenced their recommendation, similar to the proportion of changed recommendations. Conclusions The Oncotype DX Assay appears to influence physician ESBC adjuvant treatment recommendations in Hong Kong.published_or_final_versio

An inerter-equipped vibrating barrier for non-invasive motion control of seismically excited structures

The Vibrating Barrier (ViBa) is a large-scale oscillating mass-spring-damper unit contained in the ground and tuned to mitigate the motion of surrounding structures under earthquakeinduced ground shaking, without being directly in contact to them, through a structure-soilstructure interaction mechanism. Previous research showed that ViBa achieves significant seismic structural response reductions but, in doing so, it requires excessive vibrating mass, equal to the mass of the structure that aims to control or more, which hinders its practical applicability. This paper considers coupling ViBa with a grounded inerter acting as a mass amplifier to reduce ViBa mass/weight in suppressing seismically induced structural response. Attention is focused on structures amenable to modelling as single-degree-of freedom (SDOF) damped oscillators by establishing equations of motion of a 5-DOF dynamical system of a grounded inerter-equipped ViBa (IViBa) fused with a SDOF structure and accounting for soil structure interaction (SSI) effects due to soil compliance. Optimal closed-form H∞ and numerical H2 IViBa tuning are addressed minimizing the response of SDOF structure subject to harmonic resonant and to broadband/white base excitation, respectively. Numerical results pertaining to a small-scale physical ViBa prototype specimen are furnished quantifying the trade-off between IViBa mass and inertance considering non-rigid/compliant inerter-to-ground connectivity. Monotonic IViBa mass/weight reduction trend is found for fixed targeted structural performance under white stationary as well as colored non-stationary seismic excitation for increasing inertance and for sufficiently rigid inerter-to-ground connection. It is concluded that careful engineering design of the inerter-to-ground connection minimizing compliance is most critical in fully exploiting the beneficial effects of grounded inerter for mass/weight IViBa reduction facilitating, thus, its practical implementation

Fail-safe optimization of viscous dampers for seismic retrofitting

This paper presents a new optimization approach for designing minimum-cost fail-safe distributions of fluid viscous dampers for seismic retrofitting. Failure is modeled as either complete damage of the dampers or partial degradation of the dampers' properties. In general, this leads to optimization problems with large number of constraints. Thus, the use of a working-set optimization algorithm is proposed. The main idea is to solve a sequence of relaxed optimization sub-problems with a small sub-set of all constraints. The algorithm terminates once a solution of a sub-problem is found that satisfies all the constraints of the problem. The retrofitting cost is minimized with constraints on the inter-story drifts at the peripheries of frame structures. The structures considered are subjected to a realistic ensemble of ground motions, and their response is evaluated with time-history analyses. The transient optimization problem is efficiently solved with a gradient-based sequential linear programming algorithm. The gradients of the response functions are calculated with a consistent adjoint sensitivity analysis procedure. Promising results attained for 3-D irregular frames are presented and discussed. The numerical results highlight the fact that the optimized layout and size of the dampers can change significantly even for moderate levels of damage

Application modeling for performance evaluation on event-triggered wireless sensor networks

This paper presents an approach for event-triggered wireless sensor network (WSN) application modeling, aiming to evaluate the performance of WSN configurations with regards to metrics that are meaningful to specific application domains and respective end-users. It combines application, environment-generated workload and computing/communication infrastructure within a high-level modeling simulation framework, and includes modeling primitives to represent different kind of events based on different probabilities distributions. Such primitives help end-users to characterize their application workload to capture realistic scenarios. This characterization allows the performance evaluation of specific WSN configurations, including dynamic management techniques as load balancing. Extensive experimental work shows that the proposed approach is effective in verifying whether a given WSN configuration can fulfill non-functional application requirements, such as identifying the application behavior that can lead a WSN to a break point after which it cannot further maintain these requirements. Furthermore, through these experiments, we discuss the impact of different distribution probabilities to model temporal and spatial aspects of the workload on WSNs performance, considering the adoption of dynamic and decentralized load balancing approaches