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| Estudio teórico de terapias optimizadas y marcadores basados en imagen en gliomas: Un enfoque multidisciplinario utilizando un modelado matemático | |
| Descripción del proyecto de Investigación | Se pretende llevar a cabo un estudio retrospectivo observacional para estudiar desde un punto de vista teórico la optimización de terapias y marcadores basados en imagen usando modelos matemáticos. |
| Fuente de Financiamiento | Ninguna |
| Fecha (año) de inicio de la Investigación | Mayo 2023 |
| Co-autores | Dr. Raúl Allan Hernández Estrada Dr. Luis Armando Gallegos Infante Dra. Luz Fabiola Velázquez Fernández Dra. Alejandra Espinosa Garrido Dr. Raúl Gómez Gómez |
| Diseño, análisis y simulación de modelos matemáticos robustos para la propagación de enfermedades infecciosas. | |
| Descripción del proyecto de Investigación | Proponer y analizar modelos matemáticos basados en ecuaciones diferenciales parciales, que describan la propagación de enfermedades infecciosas, tales como el COVID-19. El modelo contará con fuerte análisis matemático, numérico y computacional. |
| Fuente de Financiamiento | CONAHCYT |
| Fecha (año) de inicio de la Investigación | Diciembre 2022 |
| Co-autores | Luis Romeo Martínez Jiménez Luis Armando Gallegos Infante Jorge Eduardo Macías Díaz |
| Efectos físicos en marcos de referencia arbitrarios. | |
| Descripción del proyecto de Investigación | En este proyecto investigamos diversos efectos físicos en las relatividades especial y general que se presentan cuando son estudiados desde el punto de vista de distintas familias de observadores, que poseen distintos estados de movimiento. En particular, en el caso de los campos electromagnéticos, nos interesa los efectos físicos medibles por aquellas familias de observadores para las cuales el vector de Poynting se anula; en el caso de los campos gravitacionales nos interesan los efectos gravito–eléctricos y gravito–magnéticos medidos por aquellas familias de observadores para las cuales el super-vector de Poynting se anula. Las herramientas matemáticas utilizadas en este proyecto son el cálculo tensorial, la geometría Riemanniana, la teoría de formas diferenciales de Cartan, la teoría de marcos de referencia y la relatividad general. |
| Fuente de Financiamiento | Ninguna |
| Fecha (año) de inicio de la Investigación | Diciembre 2023 |
| Co-autores | María Guadalupe Medina Guevara Héctor Vargas Rodríguez |
| Aplicación de herramientas matemáticas para la identificación de biomarcadores y de esquemas de tratamiento con mejores beneficios terapéuticos en gliomas. | |
| Descripción del proyecto de Investigación | Este proyecto busca aplicar diversas herramientas matemáticas en el campo de la medicina. Investigaciones recientes señalan la necesidad de la práctica médica de adoptar métodos cuantitativos más precisos para entender, diagnosticar y tratar de mejor manera las enfermedades. En primer lugar, se pretende caracterizar geométricamente los estudios de imagen de tumores gliales para estudiar la relación de su geometría con el tiempo de supervivencia y el pronóstico de la cirugía. Por otro lado, se desarrollarán modelos matemáticos, los cuales serán parametrizados con la información obtenida en la caracterización, para simular computacionalmente diferentes esquemas de administración de terapia con la intención de exponer los fundamentos que aportan la mayor calidad de vida para el paciente. |
| Fuente de Financiamiento | CONAHCYT |
| Fecha (año) de inicio de la Investigación | Septiembre 2023 |
| Co-autores | Luis Enrique Ayala Hernández Luis Armando Gallegos Infante Omar Jesús Díaz Cázares |
| A fractional tumor-growth model and the determination of the power law for different cancers based on data fitting | |
| Descripción del proyecto de Investigación | We study a fractional model for tumor growth and derive its general solution, the blow-up time and the radius of convergence. The model is simplified then to fit human data. The results show that there is a noticeable variation in the value of the scaling exponent depending on whether the model is fractional or integer. This supports the idea that the inclusion of memory effects may become relevant in the study of tumor growth via the scaling exponent. |
| Fecha (año) de inicio de la Investigación | 2023 |
| Fecha (año) de fin de la Investigación | 2024 |
| Co-autores | Romeo Martínez Armando Gallegos Jorge E. Macías-Díaz |
| On a deterministic mathematical model which efficiently predicts the protective effect of a plant extract mixture in cirrhotic rats | |
| Descripción del proyecto de Investigación | In this work, we propose a mathematical model that describes liver evolution and concentrations of alanine aminotransferase and aspartate aminotransferase in a group of rats damaged with carbon tetrachloride. Carbon tetrachloride was employed to induce cirrhosis. A second group damaged with carbon tetrachloride was exposed simultaneously to a plant extract as hepatoprotective agent. The model reproduces the data obtained in the experiment reported in [Rev. Cub. Plant. Med. 22(1),2017], and predicts that using the plants extract helps to get a better natural recovery after the treatment. Computer simulations show that the extract reduces the damage velocity but does not avoid it entirely. The present paper is the first report in the literature in which a mathematical model reliably predicts the protective effect of a plant extract mixture in rats with cirrhosis disease. The results reported in this manuscript could be used in the future to help in fighting cirrhotic conditions in humans, though more experimental and mathematical work is required in that case. |
| Fecha (año) de inicio de la Investigación | 2019 |
| Fecha (año) de fin de la Investigación | 2024 |
| Co-autores | Luis E. Ayala-Hernández, Gabriela Rosales-Muñoz, Armando Gallegos, María L. Miranda-Beltrán Jorge E. Macías-Díaz |
| Dynamics of coexisting rotating waves in unidirectional rings of bistable Duffing oscillators | |
| Descripción del proyecto de Investigación | We study the dynamics of multistable coexisting rotating waves that propagate along a unidirectional ring consisting of coupled double well Duffing oscillators with different numbers of oscillators. By employing time series analysis, phase portraits, bifurcation diagrams, and basins of attraction, we provide evidence of multistability on the route from coexisting stable equilibria to hyperchaos via a sequence of bifurcations, including the Hopf bifurcation, torus bifurcations, and crisis bifurcations, as the coupling strength is increased. The specific bifurcation route depends on whether the ring comprises an even or odd number of oscillators. In the case of an even number of oscillators, we observe the existence of up to 32 coexisting stable fixed points at relatively weak coupling strengths, while a ring with an odd number of oscillators exhibits 20 coexisting stable equilibria. As the coupling strength increases, a hidden amplitude death attractor is born in an inverse supercritical pitchfork bifurcation in the ring with an even number of oscillators, coexisting with various homoclinic and heteroclinic orbits. Additionally, for stronger coupling, amplitude death coexists with chaos. Notably, the rotating wave speed of all coexisting limit cycles remains approximately constant and undergoes an exponential decrease as the coupling strength is increased. At the same time, the wave frequency varies among different coexisting orbits, exhibiting an almost linear growth with the coupling strength. It is worth mentioning that orbits originating from stronger coupling strengths possess higher frequencies. |
| Fecha (año) de inicio de la Investigación | 2020 |
| Fecha (año) de fin de la Investigación | 2023 |
| Co-autores | J. J. Barba-Franco, A. Gallegos, R. Jaimes-Reátegui, J. Muñoz-Maciel, A. N. Pisarchik |
| Integral of motion and nonlinear dynamics of three Duffing oscillators with weak or strong bidirectional coupling | |
| Descripción del proyecto de Investigación | We present a system composed of three identical Duffing oscillators coupled bidirectionally. Starting from a Lagrangian that describes the system, an integral of motion is obtained by means of Noether’s theorem. The dynamics of the model is studied using bifurcation diagrams, Lyapunov exponents, time-series analysis, phase spaces, Poincaré sections, spatiotemporal and integral of motion planes. The analysis focuses on the monostable and bistable cases of the Duffing oscillator potential, in which a confined movement is guaranteed. In particular, it is observed that the system shows a chaotic behavior for small values of the coupling parameter for the bistable case. This is one of the first articles in the literature in which non-trivial integrals of motion are obtained for a system of three Duffing oscillators coupled bidirectionally. It is worth pointing out that there are some reports in the literature on integrals of motion for unidirectionally coupled nonlinear Duffing oscillators, but the study carried out in this work for bidirectionally coupled systems with more than two nonlinear Duffing oscillators is certainly one of the first |
| Fecha (año) de inicio de la Investigación | 2020 |
| Fecha (año) de fin de la Investigación | 2023 |
| Co-autores | Ernesto Urenda-Cázares José de Jesús Barba-Franco Armando Gallegos Jorge E. Macías-Díaz |
| Dynamics of a ring of three fractional-order Duffing oscillators | |
| Descripción del proyecto de Investigación | We investigate the dynamics of three ring-coupled double-well Duffing oscillators modeled by fractional- order differential equations. The analysis of time series, Fourier spectra, phase portraits, Poincaré sections, and Lyapunov exponents using the fractional order and the coupling strength as control parameters, shows that the dynamics of such a system is much richer than that of the system with integer order. We demonstrate the appearance of multistability and a rotating wave when either the fractional derivative index or the coupling strength is increased, on the route from a stable steady-state regime to hyperchaos through a Hopf bifurcation and a cascade of torus bifurcations. |
| Fecha (año) de inicio de la Investigación | 2020 |
| Fecha (año) de fin de la Investigación | 2022 |
| Co-autores | J.J. Barba-Franco, A. Gallegos, R. Jaimes-Reátegui, A.N. Pisarchik |
| Design and numerical analysis of a logarithmic scheme for nonlinear fractional diffusion-reaction equations | |
| Descripción del proyecto de Investigación | In this work, we consider a parabolic partial differential equation with fractional diffusion that generalizes the well-known Fisher’s and Hodgkin–Huxley equations. The spatial fractional derivatives are understood in the sense of Riesz, and initial–boundary conditions on a closed and bounded interval are considered here. The mathematical model is presented in an equivalent form, and a finite-difference discretization based on fractional-order centered differences is proposed. The scheme is the first explicit logarithmic model proposed in the literature to solve fractional diffusion–reaction equations. We rigorously establish the capability of the technique to preserve the positivity and the boundedness of the methodology. Moreover, we propose conditions under which the monotonicity of the numerical model is also preserved. The consistency, the stability and the convergence of the scheme are also proved mathematically, and some a priori bounds for the numerical solutions are proposed. We provide some numerical simulations in order to confirm that the method is capable of preserving the positivity and the boundedness of the approximations, and a numerical study of the convergence of the technique is carried out confirming, thus, the analytical results. |
| Fecha (año) de inicio de la Investigación | 2019 |
| Fecha (año) de fin de la Investigación | 2022 |
| Co-autores | J.E. Macías-Díaz, A. Gallegos |
| Vanishing Poynting observers and electromagnetic field classification in Kerr and Kerr-Newman spacetimes. | |
| Descripción del proyecto de Investigación | We consider electromagnetic fields having an angular momentum density in a locally non–rotating reference frame in Schwarzschild, Kerr, and Kerr-Newman spacetimes. The nature of such fields is assessed with two families of observers, the locally nonrotating ones and those of vanishing Poynting flux. The velocity fields of the vanishing-Poynting observers in the locally nonrotating reference frames are determined using the decomposition formalism. From a methodological point of view and considering a classification of the electromagnetic field based on its invariants, it is convenient to separate the consideration of the vanishing-Poynting observers into two cases corresponding to the pure and nonpure fields; additionally, if there are regions where the field rotates with the speed of light (light surfaces), it becomes necessary to split these observers into two subfamilies. We present several examples of relevance in astrophysics and general relativity, such as pure rotating dipolar-like magnetic fields and the electromagnetic field of the Kerr-Newman solution. For the latter example, we see that vanishing-Poynting observers also measure a vanishing super-Poynting vector, confirming recent results in the literature. Finally, for all nonnull electromagnetic fields, we present the 4-velocity fields of vanishing Poynting observers in an arbitrary spacetime. |
| Fecha (año) de inicio de la Investigación | 2021 |
| Fecha (año) de fin de la Investigación | 2022 |
| Co-autores | Héctor Vargas Rodríguez Haret Rosu María Guadalupe Medina Guevara Luis Armando Gallegos Infante Miguel Angel Muñiz Torres |
| TEMAS SELECTOS DE MODELACIÓN Y MATEMÁTICAS APLICADAS II | |
| Descripción del proyecto de Investigación | En el primer capítulo una breve introducción al cálculo tensorial y formas diferenciales de Cartan aplicados a campos electromagnéticos rotantes, este formalismo matemático resulta ser una herramienta extremadamente útil para describir la física de cualquier sistema físico en diferentes marcos de referencia, tanto inerciales como no inerciales, este último caso da pie a poder trabajar sin problemas en relatividad general. Sin embargo, sólo nos concentramos en su aplicación a la teoría electromagnética y su clasificación en campos eléctricos, magnéticos o nulos, o bien campos puros o no puros, todo esto en términos de los invariantes relativistas que pueden ser construidos. En el segundo capítulo, presentamos uno de los primeros trabajos que desarrollamos dentro de lo que se conoce como biología matemática, particularmente el modelado estocástico del crecimiento de un glioma a partir de los niveles de glucosa en suero y cerebro. Los gliomas son los tipos de cáncer cerebral más común y más letal, por lo que cualquier herramienta que permita hacer un diagnóstico temprano puede ser de gran utilidad. El modelo consiste en un sistema de ecuaciones diferenciales ordinarias no lineales de primer orden, cuyos parámetros son perturbados con ruido estocástico con la finalidad de visualizar un efecto más real en el modelo. Se puede observar una clara influencia del sistema inmune y de la ingesta de glucosa, tanto en individuos sanos y con tumor en crecimiento conforme transcurren los años. Como ya lo hemos mencionado, el modelado matemático ha llegado incluso a los ámbitos de la sociología y en el tercer capítulo es un ejemplo de ello. Este tiene como propósito precisar estructural y formalmente un modelo de dinámica de opinión de acuerdo relativo en una sociedad mixta en términos en lo que se conoce como el protocolo ODD (Visión general, Conceptos de diseño y Detalles por sus siglas en inglés), para su mejor comprensión y facilidad de replicación. La primera parte del capítulo consiste en describir el protocolo ODD como una metodología para estandarizar el modelado basado en agentes. En la segunda parte, presentamos la implementación de dicho protocolo en la dinámica de opinión de acuerdo relativo en una sociedad mixta. El propósito del modelo es modelar y simular las opiniones en una sociedad artificial, en la que los agentes tienen perfil psicológico e incertidumbre, con la finalidad de conocer y determinar las condiciones para llegar a consensos, polarización o fragmentación en la distribución media de opinión, controlando la incertidumbre y la mezcla de perfil psicológico. |
| Fecha (año) de inicio de la Investigación | 2020 |
| Fecha (año) de fin de la Investigación | 2022 |
| Co-autores | Norma Leticia Abrica Jacinto Antonio Aguilera Ontiveros Luis Enrique Ayala Hernández Luis Armando Gallegos Infante Ricardo Armando González Silva Héctor Vargas Rodríguez |
| Dynamics of Indoctrination in Small Groups around Three Options. | |
| Descripción del proyecto de Investigación | In this work, we consider the dynamics of opinion among three parties: two small groups of agents and one very persuasive agent, the indoctrinator. Each party holds a position different from that of the others. In this situation, the opinion space is required to be a circle, on which the agents express their position regarding three different options. Initially, each group supports a unique position, and the indoctrinator tries to convince them to adopt her or his position. The interaction between the agents is in pairs and is modeled through a system of non-linear difference equations. Agents, in both groups, give a high weight to the opinion of the indoctrinator, while they give the same weight to the opinion of their peers. Through several computational experiments, we investigate the times required by the indoctrinator to convince both groups. |
| Fecha (año) de inicio de la Investigación | Enero, 2022 |
| Fecha (año) de fin de la Investigación | Diciembre, 2022 |
| Co-autores | María Guadalupe Medina Guevara Evguenii Kourmyshev Héctor Vargas Rodriguez |
| Optimal Combinations of Chemotherapy and Radiotherapy in Low-Grade Gliomas: A Mathematical Approach | |
| Descripción del proyecto de Investigación | Low-grade gliomas (LGGs) are brain tumors characterized by their slow growth and infiltrative nature. Treatment options for these tumors are surgery, radiation therapy and chemotherapy. The optimal use of radiation therapy and chemotherapy is still under study. In this paper, we construct a mathematical model of LGG response to combinations of chemotherapy, specifically to the alkylating agent temozolomide and radiation therapy. Patient-specific parameters were obtained from longitudinal imaging data of the response of real LGG patients. Computer simulations showed that concurrent cycles of radiation therapy and temozolomide could provide the best therapeutic efficacy in-silico for the patients included in the study. The patient cohort was extended computationally to a set of 3000 virtual patients. This virtual cohort was subject to an in-silico trial in which matching the doses of radiotherapy to those of temozolomide in the first five days of each cycle improved overall survival over concomitant radio-chemotherapy according to RTOG 0424. Thus, the proposed treatment schedule could be investigated in a clinical setting to improve combination treatments in LGGs with substantial survival benefits. |
| Fecha (año) de inicio de la Investigación | 2019 |
| Fecha (año) de fin de la Investigación | 2021 |
| Co-autores | Luis E. Ayala-Hernández, Armando Gallegos, Philippe Schucht, Michael Murek, Luis Pérez-Romasanta, Juan Belmonte-Beitia Víctor M. Pérez-García |
| Dynamics of a ring of three unidirectionally coupled Duffing oscillators with time-dependent damping | |
| Descripción del proyecto de Investigación | We study dynamics of a ring of three unidirectionally coupled double-well Duffing oscillators for three different values of the damping coefficient: fixed, proportional to time, and inversely proportional to time. The system dynamics in all cases are analyzed using time series, Fourier and Hilbert transforms, Poincare sections, bifurcation diagrams, and Lyapunov exponents for various coupling strengths and damping coefficients. In the first case, we observe a well known route from a stable steady state to hyperchaos through Hopf bifurcation and a series of torus bifurcations, as the coupling strength is increased. In the second case, the system is highly dissipative and converges into one of the stable equilibria. Finally, in the third case, transient toroidal hyperchaos takes place. |
| Fecha (año) de inicio de la Investigación | 2019 |
| Fecha (año) de fin de la Investigación | 2021 |
| Co-autores | J. J. Barba-Franco, A. Gallegos, R. Jaimes-Reategui, S. A. Gerasimova, A. N. Pisarchik |
| Driven damped nth-power anharmonic oscillators with time-dependent coefficients and their integrals of motion | |
| Descripción del proyecto de Investigación | We derive integrals of motion for general anharmonic oscillators with damping and power law forcing. The model under investigation has time-dependent coefficients, and the determination of these physical quantities is carried out using Noether’s theorem. The solutions must satisfy appropriate analytical conditions for the proposed quantities to be true integrals of motion. In turn, these analytical conditions are associated with well known physical systems, including the Milne-Pinney and Ermakov-Lewis models. We provide various numerical solutions of our equations of motion and the associated integrals to verify the theoretical results. |
| Fecha (año) de inicio de la Investigación | 2019 |
| Fecha (año) de fin de la Investigación | 2021 |
| Co-autores | J.E. Macías-Díaz, E. Urenda-Cázares, A. Gallegos |
| Relativistic rotating electromagnetic fields. | |
| Descripción del proyecto de Investigación | In this work, we consider axially symmetric stationary electromagnetic fields in the framework of special relativity. These fields have an angular momentum density in the reference frame at rest with respect to the axis of symmetry; their Poynting vector form closed integral lines around the symmetry axis. In order to describe the state of motion of the electromagnetic field, two sets of observers are introduced: the inertial set, whose members are at rest with the symmetry axis; and the noninertial set, whose members are rotating around the symmetry axis. The rotating observers measure no Poynting vector, and they are considered as comoving with the electromagnetic field. Using explicit calculations in the covariant 3 + 1 splitting formalism, the velocity field of the rotating observers is determined and interpreted as that of the electromagnetic field. The considerations of the rotating observers split in two cases, for pure fields and impure fields, respectively. Moreover, in each case, each family of rotating observers splits in two subcases, due to regions where the electromagnetic field rotates with the speed of light. These regions are generalizations of the light cylinders found around magnetized neutron stars. In both cases, we give the explicit expressions for the corresponding velocity fields. Several examples of relevance in astrophysics and cosmology are presented, such as the rotating point magnetic dipoles and a superposition of a Coulomb electric field with the field of a point magnetic dipole. |
| Fecha (año) de inicio de la Investigación | 2017 |
| Fecha (año) de fin de la Investigación | 2020 |
| Co-autores | Héctor Vargas Rodríguez Luis Armando Gallegos Infante Miguel Angel Muñiz Torres Haret Rosu Paulino Javier Domínguez Chávez |
| Effects of multiplicative noise on the Duffing oscillator with variable coefficients and its integral of motion | |
| Descripción del proyecto de Investigación | In this work, we implement multiplicative noise to the Duffing oscillator with variable coefficients. The stochastic differential equations are solved using the fourth-order Runge–Kutta method with the Box-Müller algorithm and the corresponding integral of motion is obtained. Some numerical experiments are performed and the results show that the integral of motion is highly unaffected by the multiplicative noise. |
| Fecha (año) de inicio de la Investigación | 2018 |
| Fecha (año) de fin de la Investigación | 2020 |
| Co-autores | E. Urenda-Cazares, A. Gallegos R. Jaimes-Reátegui |
| A mathematical model that combines chemotherapy and oncolytic virotherapy as an alternative treatment against a glioma | |
| Descripción del proyecto de Investigación | In this paper, we propose a mathematical model that combines chemotherapy and oncolytic virotherapy as an alternative to treatment of a glioma. The main idea is to incorporate the virotherapy after the first or second chemotherapy session using a specialist virus that attacks only tumor cells. Some simulations are presented. Based on the results, we conclude that this combined therapy may reduce the number of chemotherapy sessions and may lead to obtain better results in the fight against gliomas. |
| Fecha (año) de inicio de la Investigación | 2018 |
| Fecha (año) de fin de la Investigación | 2020 |
| Co-autores | E. Urenda-Cázares A. Gallegos J. E. Macías-Díaz |
| An integral of motion for the damped cubic-quintic Duffing oscillator with variable coefficients | |
| Descripción del proyecto de Investigación | Integrals of motion for the undamped and damped cubic- quintic Duffing oscillators with time-dependent coefficients are obtained for the first time in the literature under appropriate analytical conditions. The integrals of motion are obtained using Noether’s theorem, and the conditions for their existence are directly related to the well-known Milne–Pinney equation, which is associated with the Ermakov-Lewis systems. We perform here some numerical simulations to illustrate the validity of our analytical results. |
| Fecha (año) de inicio de la Investigación | 2017 |
| Fecha (año) de fin de la Investigación | 2019 |
| Co-autores | E. Urenda-Cázares, A. Gallegos, J.E. Macías-Díaz, H. Vargas-Rodríguez |
| On a positivity-preserving numerical model for a linearized hyperbolic Fisher–Kolmogorov–Petrovski–Piscounov equation | |
| Descripción del proyecto de Investigación | We introduce a nonstandard finite-difference scheme to approximate positive solutions of a modified hyperbolic Fisher–Kolmogorov–Petrovski–Piscounov equation appearing in the investigation of the dynamics of some populations. The technique has a consistency of second order, and it provides nonnegative approximations for nonnegative initial profiles. The stability analysis of the method is carried out in detail, and the scheme is validated against known analytical solutions for some initial–boundary-value problems |
| Fecha (año) de inicio de la Investigación | 2017 |
| Fecha (año) de fin de la Investigación | 2019 |
| Co-autores | J.E. Macías-Díaz, Armando Gallegos |
| A mathematical model for the pre-diagnostic of glioma growth based on blood glucose levels | |
| Descripción del proyecto de Investigación | We propose a stochastic model in which the values of the factors involved in the development of a glioma vary randomly in a biologically congruent range. Stability analysis revealed three fixed points which allude to patients with a growing glioma, with an advanced stage glioma and without glioma, respectively. The graphics of the solutions and the diagrams of asymptotic behavior of some of the parameters are presented. We also show the order of influence of them. The results obtained show a decay in serum glucose levels in the presence of a glioma.Moreover, they indicate that the immune system is an important element in the prevention of the growth of glioma. |
| Fecha (año) de inicio de la Investigación | 2016 |
| Fecha (año) de fin de la Investigación | 2018 |
| Co-autores | L. E. Ayala-Hernández Armando Gallegos J. E. Macías-Díaz M. L. Miranda-Beltrán H. Vargas-Rodríguez |
| Evolution of electoral preferences for a regime of three political parties. | |
| Descripción del proyecto de Investigación | |
| Fecha (año) de inicio de la Investigación | octubre 2017 |
| Fecha (año) de fin de la Investigación | 24 de octubre de 2018 |
| Co-autores | Maria Guadalupe Medina Guevara Héctor Vargas Rodríguez Pedro Basilio Espinoza Padilla José Luis González Solís |
| Superenergy flux of Einstein–Rosen waves. | |
| Descripción del proyecto de Investigación | In this work, we consider the propagation speed of the superenergy flux associated to the Einstein–Rosen cylindrical waves propagating in vacuum and over the background of the gravitational field of an infinitely long mass line distribution. The velocity of the flux is determined considering the reference frame in which the super-Poynting vector vanishes. This reference frame is then considered as comoving with the flux. The explicit expressions for the velocities are given with respect to a reference frame at rest with the symmetry axis. |
| Fecha (año) de inicio de la Investigación | 2015 |
| Fecha (año) de fin de la Investigación | 2018 |
| Co-autores | Paulino Javier Dominguez Chávez Luis Armando Gallegos Infante Jorge Eduardo Macías Díaz Héctor Vargas Rodríguez |
| Comment on demystifying the constancy of the Ermakov Lewis invariant for a time-dependent oscillator | |
| Descripción del proyecto de Investigación | We show that a simple modification of the Lagrangian proposed by Padmanabhan in the paper [Mod. Phys. Lett. A 33, 1830005 (2018)] leads to the most general dynamical invariant in [Ray and Reid, Phys. Lett. A 71, 317 (1979)]. |
| Fecha (año) de inicio de la Investigación | 2018 |
| Fecha (año) de fin de la Investigación | 2018 |
| Co-autores | A. Gallegos H. C. Rosu |
| A finite‐difference model for indoctrination dynamics. | |
| Descripción del proyecto de Investigación | In this work, a system of non‐linear difference equations is employed to model the opinion dynamics between a small group of agents (the target group) and a very persuasive agent (the indoctrinator). Two scenarios are investigated: the indoctrination of a homogeneous target group, in which each agent grants the same weight to his (or her) partner's opinion and the indoctrination of a heterogenous target group, in which each agent may grant a different weight to his or her partner's opinion. Simulations are performed to study the required times by the indoctrinator to convince a group. Initially, these groups are in a consensus about a doctrine different to that of the ideologist. The interactions between the agents are pairwise. |
| Fecha (año) de inicio de la Investigación | Enero 2018 |
| Fecha (año) de fin de la Investigación | Noviembre 2018 |
| Co-autores | María Guadalupe Medina Guevara Héctor Vargas Rodríguez Pedro Basilio Espinoza Padilla |
| On S1 as an alternative continuous opinion space in a three-party regime. | |
| Descripción del proyecto de Investigación | In this work, we propose a discrete system to model the dynamics of individual opinions when the agents of a population have three equally likely choices. The social network consists of a finite number of agents with pairwise interactions at discrete times, and the opinion space is identified as a triangle in the plane. After a suitable homotopic transformation, one may convert the opinion space into the classical circle of the Cartesian plane. The opinion of each agent is updated following a general nonlinear law which considers individual parameters of the members. We establish conditions that guarantee the existence of attracting points (or strong consensus), and infer the existence of attracting intervals (identified here as weak consensus). Moreover, we notice that the conditions that lead to global consensuses are independent of the weight matrix and the number of agents in the network. The simulations obtained in this work confirm the validity of the analytical results. |
| Fecha (año) de inicio de la Investigación | Diciembre 2015 |
| Fecha (año) de fin de la Investigación | Septiembre de 2016 |
| Co-autores | María Guadalupe Medina Guevara Jorge Eduardo Macías Diáz Luis Armando Gallegos Infante Héctor Vargas Rodríguez |