Asymptotic behaviour of global solutions to a model of cell invasion

In this paper we analyze a mathematical model focusing on key events of the cells invasion process. Global well-possedness and asymptotic behaviour of nonnegative solutions to the corresponding coupled system of three nonlinear partial differential equations are studied.Comment: 29 page

Cálculo y predicción de coeficientes de fugacidad y actividad en mezclas binarias mediante el algoritmo de búsqueda armónica con ancho de banda autoajustable

El presente artículo de investigación propone el uso de la nueva variante del algoritmo hs (Harmony Search), esto es, el sfhs (Self-Regulated Fretwidth Harmony Search Algorithm) para el cálculo y predicción de coeficientes de fugacidad y actividad en mezclas binarias. La selección de los parámetros de ejecución del algoritmo sfhs se realizó con base en pruebas preliminares con diferentes funciones de prueba estándar. Se seleccionaron sistemas previamente reportados en la literatura, a 25 ºC y 40 ºC, y a presiones bajas y moderadas. Adicionalmente, se seleccionaron dos solutos diferentes: dióxido de carbono y etano. Se tomaron diferentes solventes, polares y no polares, con propósitos comparativos. Los coeficientes de actividad y fugacidad se calcularon utilizando la ecuación de estado Redlich-Kwong y la regla de Lewis, junto con el algoritmo sfhs para los dos solutos en fase vapor. La consistencia de los coeficientes de actividad se analizó mediante la estrategia de Redlich-Kister. Se obtuvieron resultados muy cercanos a los encontrados experimentalmente por otros autores y en su mayoría, no difirieron en más de una unidad porcentual.This research article proposes the use of a novel variant of the HS algorithm (harmony search), i.e. SFHS (self-regulated fret width harmony search algorithm), for calculating and predicting fugacity and activity coefficients in binary mixtures. Parameter selection was carried out based on preliminary results with different standard test functions. Different previously reported systems were selected, at 25 ° C and 40 ° C, and at low and moderate pressure levels. Moreover, two solutes were selected: carbon dioxide and ethane. Different solvents, both polar and nonpolar, were selected with comparative purposes. Activity and fugacity coefficients were calculated using the Redlich-Kwong state equation and Lewis rule, along with the sfhs algorithm, assuming both solutes in vapor phase. Consistency of the activity coefficients was analyzed by the Redlich-Kister strategy. Results were very close to those found experimentally by other authors, and most of them did not differ in more than one percentage unit

Local existence and uniqueness of regular solutions in a model of tissue invasion by solid tumours

In this paper we consider a nonlinear system of differential equations arising in tumour invasion which has been proposed in [1] M.A.J. Chaplain and A.R.A. Anderson, Mathematical modelling of tissue invasion, in Cancer Modelling and Simulation, ed., L. Preziosi (Chapman & Hall/CRT, 2003), pp. 269–297. The system consists of two PDEs describing the evolution of tumour cells and proteases and an ODE which models the concentration of the extracellular matrix. We prove local existence and uniqueness of solutions in the class of Hölder spaces. The proof of local existence is done by Schauder’s fixed point theorem and for the uniqueness we use an idea from [2] H. Gajewski, K. Zacharias, Global behaviour of a reaction-diffusion system modelling chemotaxis, Math. Nachr. 195 (1998) 77–114.Marie Curie Research Training Networ

On some models describing cellular movement: The macroscopic scale

Along this work we will consider several models of partial differential equations that describe cellular movement. We will introduce some mathematical techniques in order to describe the behaviour of the solutions of these models.Junta de Andalucí

How a General-Purpose Commonsense Ontology can Improve Performance of Learning-Based Image Retrieval

The knowledge representation community has built general-purpose ontologies which contain large amounts of commonsense knowledge over relevant aspects of the world, including useful visual information, e.g.: "a ball is used by a football player", "a tennis player is located at a tennis court". Current state-of-the-art approaches for visual recognition do not exploit these rule-based knowledge sources. Instead, they learn recognition models directly from training examples. In this paper, we study how general-purpose ontologies---specifically, MIT's ConceptNet ontology---can improve the performance of state-of-the-art vision systems. As a testbed, we tackle the problem of sentence-based image retrieval. Our retrieval approach incorporates knowledge from ConceptNet on top of a large pool of object detectors derived from a deep learning technique. In our experiments, we show that ConceptNet can improve performance on a common benchmark dataset. Key to our performance is the use of the ESPGAME dataset to select visually relevant relations from ConceptNet. Consequently, a main conclusion of this work is that general-purpose commonsense ontologies improve performance on visual reasoning tasks when properly filtered to select meaningful visual relations.Comment: Accepted in IJCAI-1

M-Learning in the development of speaking skills

This research with the name “M-Learning in the Development of English Speaking Skills in First Baccalaureate Students at Marco Aurelio Subía Martínez - Batalla De Panupali Educative Unit”. Has as the main objective to analyze Mobile learning in the development of speaking. The research was descriptive, qualitative, and not experimental. It was descriptive because it was described both variables (M-learning and speaking skills) in the theoretical framework, moreover, M-learning influences speaking skills. Besides, the research carried out a qualitative approach to analyze and describe the results obtained by the survey; the technique applied in this study, whose instrument was a questionnaire thus, it was identified the lack of use of mobile devices with educational purposes in English classes. To validate the proposal, which was a booklet entitled “M-learning to develop speaking skills”. It was applied a checklist as a technique and a questionnaire as an instrument to three experts and two users; the results affirmed that mobile applications could positively influence the development of speaking skills. Finally, the researcher socialized the proposal with his English colleagues. To conclude the four interactive applications used in the proposal and based on practicing, interacting, learning vocabulary and grammatical structures were very attractive and interesting for teachers, thus, being useful curricular tools in the teaching and learning of the English language in the classrooms.Esta investigación con el nombre “Aprendizaje móvil en el desarrollo de las destrezas del hablar inglés en los estudiantes de Primer año de Bachillerato de la Unidad Educativa Marco Aurelio Subía-Batalla de Panupali”, tiene como objetivo principal analizar el aprendizaje móvil en el desarrollo del habla. La investigación fue descriptiva, cualitativa y no experimental. Fue descriptiva porque se describió ambas variables (Aprendizaje móvil y destreza del habla) en la revisión literaria. Además, la investigación llevo a cabo un enfoque cualitativo para analizar y describir los resultados obtenidos en la encuesta, técnica aplicada en la investigación, cuyo instrumento fue un cuestionario así, se identificó la falta de uso de dispositivos móviles con fines educativos en las clases de inglés. Para validar la propuesta el cual fue un folleto titulado “Aprendizaje móvil para desarrollar el habla”, se aplicó una lista de cotejo como técnica y un cuestionario como instrumento a tres expertos y dos usuarios, los resultados afirmaron que las aplicaciones móviles pueden influenciar positivamente en el desarrollo del habla. Finalmente, el investigador socializó la propuesta con sus docentes colegas de Ingles. Para concluir las cuatro aplicaciones interactivas usadas en la propuesta y basadas en la práctica, interacción, aprendizaje de vocabulario y estructura gramatical fueron muy atractivas e interesantes para los docentes. Así, convirtiéndose en herramientas curriculares muy útiles en el proceso de enseñanza-aprendizaje de idioma inglés en las aulas

Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect. Existence and uniqueness of global-in-time solutions

A system of quasilinear non-uniformly parabolic-elliptic equations modelling chemotaxis and taking into account the volume filling effect is studied under no-flux boundary conditions. The proof of existence and uniqueness of a global-in-time weak solution is given. First the local solutions are constructed. This is done by the Schauder fixed point theorem. Uniqueness is proved with the use of the duality method. A priori estimates are stated either in the case when the Lyapunov functional is bounded from below or chemotactic forces are suitably weakened.Marie Curie Research Training Networ

Convergencia al equilibrio en un modelo simplificado de angiogénesis

En esta comunicación abordamos una clase general de modelos con origen en biología. En particular los modelos describen el movimiento de bacterias, procesos invasivos tumorales y el proceso de angiogénesis asociado a los tumores