Bright and Gap Solitons in Membrane-Type Acoustic Metamaterials

We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schr\"odinger equation and obtain analytical expressions for bright and gap solitons. We also perform direct numerical simulations to study the dissipation-induced dynamics of the bright and gap solitons. Numerical and analytical results, relying on the analytical approximations and perturbation theory for solions, are found to be in good agreement

Validation of the cognitive structure of the test of signs by structural equation modeling

El objetivo de este trabajo es realizar un estudio de validación de los procesos cognitivos implicados en la resolución de ítems de un test de operaciones aritméticas básicas entre números enteros. La validación de la estructura cognitiva propuesta para la tarea se lleva a cabo mediante modelos de ecuaciones estructurales y triangulación. Los resultados muestran relaciones de subordinación fuertes y positivas entre los ítems en algunas de las rutas, apoyando solo parcialmente la estructura propuesta. Sin embargo, la triangulación aporta una mayor evidencia de validez.The present work is aimed to carry out a validation study of the cognitive operations required for the correct solution of items of a math test which includes basic arithmetic operations between integer numbers. The validation of the hypothesized cognitive structure is made by means of structural equation modeling and triangulation methods. Results show strong and positive cognitive subordination relationships between some items but the structural equation model fit only provides a partial support for the proposed structure. However, the triangulation procedure provides further evidence of validity.Este trabajo está financiado por el proyecto de la DGICYT (ref. SEJ2004-05872

Neuroimagen y neurobiología de la adicción:un estudio sobre los cambios funcionales cerebrales en personas adictas a las cocaína

Decenes Jornades de Foment de la Investigació de la FCHS (Any 2004-2005)El consumo crónica de cocaína produce una reducción de la dopamina en ciertas áreas cerebrales, provocando una alteración en este sistema. (Volkow y cols., 1999; Wu y cols., 1997). El objetivo de este trabajo es estudiar mediante Resonancia Magnética Funcional, los efectos que el consumo crónico de cocaína provoca sobre el procesamiento emocional. Los participantes (10 pacientes adictos a la cocaína y 10 personas no adictas) realizaron una tarea de procesamiento emocional en la que visualizaban fotografías con contenido emocional positivo, negativo y neutro (Adaptación española del International Affective Pictures System, IAPS, moltó y cols. 2001) como fondo en un tarea de discriminación de letras. Los resultados muestran una menor activación en el núcleo accumbens, giro cingulado anterior y cortex orbitofrontal en personas adictas a la cocaína en comparación al grupo control, ante la visión de imágenes positivas. Mientras que, se observa una menor activación del giro cingulado anterior en pacientes en comparación a los controles, para la visión de imágenes negativas. Estos resultados sugieren que la tarea del IAPS es una buena tarea para activar áreas específicas de recompensa (N.acc y giro orbitofrontal). Y que los pacientes presentan una disfunción en el sistema de recompensa, lugar donde actúa la cocaína tras su administración, liberando dopamina. Esto podría tener como consecuencia una menor sensibilidad de estas personas para los reforzadores naturales

Detection of Q-matrix misspecification using two criteria for validation of cognitive structures under the Least Squares Distance Model

Cognitive Diagnostic Models (CDMs) aim to provide information about the degree to which individuals have mastered specific attributes that underlie the success of these individuals on test items. The Q-matrix is a key element in the application of CDMs, because contains links item-attributes representing the cognitive structure proposed for solve the test. Using a simulation study we investigated the performance of two model-fit statistics (MAD and LSD) to detect misspecifications in the Q-matrix within the least squares distance modeling framework. The manipulated test design factors included the number of respondents (300, 500, 1000), attributes (1, 2, 3, 4), and type of model (conjunctive vs disjunctive). We investigated MAD and LSD behavior under correct Q-matrix specification, with Qmisspecifications and in a real data application. The results shows that the two model-fit indexes were sensitive to Q-misspecifications, consequently, cut points were proposed to use in applied context.Detección de errores de especificación en la matriz Q utilizando dos criterios de validación de estructuras cognitivas con el Modelo de las Distancias Mínimo Cuadráticas (LSDM). Los Modelos de Diagnóstico Cognitivo (MDC) tienen por objeto proporcionar información sobre el grado en que los individuos dominan atributos específicos para resolver correctamente los items de un test. La matriz Q es un elemento clave en la aplicación de los MDC porque contiene vínculos entre items y atributos que representan la estructura cognitiva propuesta para resolver la prueba. Por medio de un estudio de simulación, se determinó el rendimiento de dos estadísticos de ajuste (MAD y LSD) para detectar errores de especificación en la matriz Q dentro del marco del modelo de la distancia mínimo cuadrática. Los factores manipulados en el diseño del test incluyen: número de encuestados (300, 500, 1000), número de atributos (1, 2, 3, 4), y el tipo de modelo (conjuntivo vs. disyuntivo). Se investigó el comportamiento de los valores MAD y LSD bajo una correcta especificación de Q, con errores de especificación en Q y en una aplicación de datos reales. Los resultados muestran que los dos índices son sensibles a los errores de especificación de Q, por este motivo se proponen puntos de corte para usar en aplicaciones del modelo

Solving second-order linear differential equations with random analytic coefficients about ordinary points: A full probabilistic solution by the first probability density function

[EN] This paper deals with the approximate computation of the first probability density function of the solution stochastic process to second-order linear differential equations with random analytic coefficients about ordinary points under very general hypotheses. Our approach is based on considering approximations of the solution stochastic process via truncated power series solution obtained from the random regular power series method together with the so-called Random Variable Transformation technique. The validity of the proposed method is shown through several illustrative examples.This work has been partially supported by the Ministerio de Econom ia y Competitividad grant MTM2013-41765-P. Ana Navarro Quiles acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.Cortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2018). Solving second-order linear differential equations with random analytic coefficients about ordinary points: A full probabilistic solution by the first probability density function. Applied Mathematics and Computation. 331:33-45. https://doi.org/10.1016/j.amc.2018.02.051S334533

Solving fully randomized higher-order linear control differential equations: Application to study the dynamics of an oscillator

This is the peer reviewed version of the following article: Cortés, J-C, Navarro-Quiles, A, Romero, J-V, Roselló, M-D. Solving fully randomized higher-order linear control differential equations: Application to study the dynamics of an oscillator. Comp and Math Methods. 2021; 3:e1163, which has been published in final form at https://doi.org/10.1002/cmm4.1163. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.[EN] In this work, we consider control problems represented by a linear differential equation assuming that all the coefficients are random variables and with an additive control that is a stochastic process. Specifically, we will work with controllable problems in which the initial condition and the final target are random variables. The probability density function of the solution and the control has been calculated. The theoretical results have been applied to study, from a probabilistic standpoint, a damped oscillator.European Social Fund, Grant/Award Numbers: GJIDI/2018/A/009, GJIDI/2018/A/010; Spanish Ministerio de Economía, Industria y Competitividad (MINECO), the Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE), Grant/Award Number: MTM2017-89664-P.Cortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2021). Solving fully randomized higher-order linear control differential equations: Application to study the dynamics of an oscillator. Computational and Mathematical Methods. 3(6):1-15. https://doi.org/10.1002/cmm4.1163S1153

Solving second-order linear differential equations with random analytic coefficients about regular-singular points

[EN] In this contribution, we construct approximations for the density associated with the solution of second-order linear differential equations whose coefficients are analytic stochastic processes about regular-singular points. Our analysis is based on the combination of a random Fröbenius technique together with the random variable transformation technique assuming mild probabilistic conditions on the initial conditions and coefficients. The new results complete the ones recently established by the authors for the same class of stochastic differential equations, but about regular points. In this way, this new contribution allows us to study, for example, the important randomized Bessel differential equation.This work was partially funded by the Ministerio de Economia y Competitividad Grant MTM2017-89664-P. Ana Navarro Quiles acknowledges the funding received from Generalitat Valenciana through a postdoctoral contract (APOSTD/2019/128). Computations were carried out thanks to the collaboration of Raul San Julian Garces and Elena Lopez Navarro granted by the European Union through the Operational Program of the European Regional Development Fund (ERDF)/European Social Fund (ESF) of the Valencian Community 2014-2020, Grants GJIDI/2018/A/009 and GJIDI/2018/A/010, respectivelyCortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2020). Solving second-order linear differential equations with random analytic coefficients about regular-singular points. Mathematics. 8(2):1-20. https://doi.org/10.3390/math8020230S12082Hussein, A., & Selim, M. M. (2012). Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique. Applied Mathematics and Computation, 218(13), 7193-7203. doi:10.1016/j.amc.2011.12.088Dorini, 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.2015.09.009Santos, L. T., Dorini, F. A., & Cunha, M. C. C. (2010). The probability density function to the random linear transport equation. Applied Mathematics and Computation, 216(5), 1524-1530. doi:10.1016/j.amc.2010.03.001Hussein, A., & Selim, M. M. (2019). A complete probabilistic solution for a stochastic Milne problem of radiative transfer using KLE-RVT technique. Journal of Quantitative Spectroscopy and Radiative Transfer, 232, 54-65. doi:10.1016/j.jqsrt.2019.04.034Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., & Roselló, M.-D. (2018). Solving second-order linear differential equations with random analytic coefficients about ordinary points: A full probabilistic solution by the first probability density function. Applied Mathematics and Computation, 331, 33-45. doi:10.1016/j.amc.2018.02.051Cortés, J.-C., Jódar, L., Camacho, F., & Villafuerte, L. (2010). Random Airy type differential equations: Mean square exact and numerical solutions. Computers & Mathematics with Applications, 60(5), 1237-1244. doi:10.1016/j.camwa.2010.05.046Calbo, G., Cortés, J.-C., & Jódar, L. (2011). Random Hermite differential equations: Mean square power series solutions and statistical properties. Applied Mathematics and Computation, 218(7), 3654-3666. doi:10.1016/j.amc.2011.09.008Calbo, 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.2011.03.045Cortés, J.-C., Villafuerte, L., & Burgos, C. (2017). A Mean Square Chain Rule and its Application in Solving the Random Chebyshev Differential Equation. Mediterranean Journal of Mathematics, 14(1). doi:10.1007/s00009-017-0853-6Cortés, J.-C., Jódar, L., & Villafuerte, L. (2017). Mean square solution of Bessel differential equation with uncertainties. Journal of Computational and Applied Mathematics, 309, 383-395. doi:10.1016/j.cam.2016.01.034Khudair, A. R., Haddad, S. A. M., & Khalaf, S. L. (2016). Mean Square Solutions of Second-Order Random Differential Equations by Using the Differential Transformation Method. Open Journal of Applied Sciences, 06(04), 287-297. doi:10.4236/ojapps.2016.64028Qi, Y. (2018). A Very Brief Introduction to Nonnegative Tensors from the Geometric Viewpoint. Mathematics, 6(11), 230. doi:10.3390/math6110230Ragusa, M. A., & Tachikawa, A. (2016). Boundary regularity of minimizers of p(x)-energy functionals. Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 33(2), 451-476. doi:10.1016/j.anihpc.2014.11.003Ragusa, M. A., & Tachikawa, A. (2019). Regularity for minimizers for functionals of double phase with variable exponents. Advances in Nonlinear Analysis, 9(1), 710-728. doi:10.1515/anona-2020-0022Braumann, C. A., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2018). On the random gamma function: Theory and computing. Journal of Computational and Applied Mathematics, 335, 142-155. doi:10.1016/j.cam.2017.11.04

Some results about randomized binary Markov chains: Theory, computing and applications

[EN] This paper is addressed to give a generalization of the classical Markov methodology allowing the treatment of the entries of the transition matrix and initial condition as random variables instead of deterministic values lying in the interval [0,1]. This permits the computation of the first probability density function (1-PDF) of the solution stochastic process taking advantage of the so-called Random Variable Transformation technique. From the 1-PDF relevant probabilistic information about the evolution of Markov models can be calculated including all one-dimensional statistical moments. We are also interested in determining the computation of distribution of some important quantities related to randomized Markov chains (steady state, hitting times, etc.). All theoretical results are established under general assumptions and they are illustrated by modelling the spread of a technology using real data.This work has been partially supported by the Ministerio de Economía y Competitividad [grant MTM2017-89664-P]. Ana Navarro Quiles acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigación y Desarrollo (PAID), Universitat Politècnica de ValènciaCortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2020). Some results about randomized binary Markov chains: Theory, computing and applications. International Journal of Computer Mathematics. 97(1-2):141-156. https://doi.org/10.1080/00207160.2018.1440290S141156971-

Probabilistic analysis of random nonlinear oscillators subject to small perturbations via probability density functions: Theory and computing

[EN] We study a class of single-degree-of-freedom oscillators whose restoring function is affected by small nonlinearities and excited by stationary Gaussian stochastic processes. We obtain, via the stochastic perturbation technique, approximations of the main statistics of the steady state, which is a random variable, including the first moments, and the correlation and power spectral functions. Additionally, we combine this key information with the principle of maximum entropy to construct approximations of the probability density function of the steady state. We include two numerical examples where the advantages and limitations of the stochastic perturbation method are discussed with regard to certain general properties that must be preservedThis work has been supported by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI), and Fondo Europeo de Desarrollo Regional (FEDER UE) Grant PID2020-115270GB-I00. The authors express their deepest thanks and respect to the reviewers for their valuable commentsCortés, J.; López-Navarro, E.; Romero, J.; Roselló, M. (2021). Probabilistic analysis of random nonlinear oscillators subject to small perturbations via probability density functions: Theory and computing. European Physical Journal Plus. 136(7):1-23. https://doi.org/10.1140/epjp/s13360-021-01672-wS1231367W.L. Oberkampf, S.M. De Land, B.M. Rutherford, K.V. Diegert, K.F. Alvin, Error and uncertainty in modeling and simulation. Reliab. Eng. Syst. Saf. 75, 333–357 (2002)T. Soong, Random Differential Equations in Science and Engineering, vol. 103 (Academic Press, New York, 1973)Kloeden, P., Platen, E.: Numerical Solution of Stochastic Differential Equations, Ser. Stochastic Modelling and Applied Probability, vol. 23. Springer, Berlin Heidelberg (1992)J.L. Bogdanoff, J.E. Goldberg, M. Bernard, Response of a simple structure to a random earthquake-type disturbance. Bull. Seismol. Soc. Am. 51, 293–310 (1961)L. Su, G. Ahmadi, Earthquake response of linear continuous structures by the method of evolutionary spectra. Eng. Struct. 10, 47–56 (1988)X. Jin, Y. Tian, Y. Wang, Z. Huang, Explicit expression of stationary response probability density for nonlinear stochastic systems. Acta Mech. 232, 2101–2114 (2021)D. Lobo, T. Ritto, D. Castello, E. Cataldo, Dynamics of a Duffing oscillator with the stiffness modeled as a stochastic process. Int. J. Non-Linear Mech. 116, 273–280 (2019)Y. Lin, G. Cai, Probabilistic Structural Dynamics: Advanced Theory and Applications (McGraw-Hill, Cambridge, 1995)C. To, Nonlinear Random Vibration: Analytical Techniques and Applications (Swets & Zeitlinger, New York, 2000)M. Kaminski, The Stochastic Perturbation Method for Computational Mechanics (Wiley, New York, 2013)J.J. Stoker, Nonlinear Vibrations (Wiley (Interscience), New York, 1950)N. McLachlan, Laplace Transforms and Their Applications to Differential Equations, vol. 103 (Dover Publ. INc., New York, 2014)R.F. Steidel, An Introduction to Mechanical Vibrations (Wiley, New York, 1989)G. Casella, R. Berger, Statistical Inference (Cengage Learning, New Delhi, 2007)H.V. Storch, F.W. Zwiers, Statistical Analysis in Climate Research (Cambridge University Press, Cambridge, 2001)J.V. Michalowicz, J.M. Nichols, F. Bucholtz, Handbook of Differential Entropy (CRC Press, Boca Raton, 2018)H. Banks, H. Shuhua, W. Clayton Thompson, Modelling and Inverse Problems in the Presence of Uncertainty (Ser. Monographs and Research Notes in Mathematics. CRC Press, Boca Raton, 2001)Garg, V.K., Wang, Y.-C.: 1 - signal types, properties, and processes. In: Chen, W.-K. (ed.) The Electrical Engineering Handboo