First passages in bounded domains: When is the mean first passage time meaningful?

We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(\omega) distribution of the random variable \omega=\tau_1/(\tau_1+\tau_2), which is a measure for how similar the first passage times \tau_1 and \tau_2 are of two independent realisations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(\omega) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behaviour. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behaviour, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(\omega), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behaviour even in bounded domains, in which all moments of the first passage distribution exist.Comment: 9 pages, 6 figure

Gender Violence in the University: The Role of Higher Education Institutions in its Prevention

Talking about gender-based violence and sexual harassment at the Ecuadorian university has been considered by many as an uncomfortable subject, and for some years it has been silenced. It is only recently that this situation has become an essential topic to investigate, so that currently several universities have struggled to explore through studies the problems of gender violence, discrimination and sexual harassment in the university context. In this sense, the present study has tried to develop a review of all the investigations that have been carried out to identify cases or situations of gender violence in universities at international, national and local level, as well as to determine the role of education institutions superior in the prevention and eradication of this problem. Keywords: gender violence, sexual harassment, university. Resumen Hablar de violencia de género y acoso sexual en la universidad ecuatoriana ha sido considerado por muchos como un tema incómodo por lo que durante algunos años ha permanecido silenciado. No es sino hace poco que esta situación se ha vuelto una temática imprescindible de investigar, por lo que actualmente varias universidades se han esforzado en explorar a través de estudios los problemas de violencia de género, discriminación y acoso sexual en el contexto universitario. En este sentido, el presente estudio ha pretendido desarrollar una revisión de todas las investigaciones que se han realizado para identificar los casos o situaciones de violencia de género en universidades a nivel internacional, nacional y local, así como determinar el rol de las instituciones de educación superior en la prevención y erradicación de esta problemática. Palabras clave: violencia de género, acoso sexual, universidad

Nonequilibrium dynamics of a stochastic model of anomalous heat transport

We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A: Math. Theor. 42 (2009) 025001], we have studied the stationary state of this system with fixed boundary conditions, finding analytical exact expressions for the temperature profile and the heat current in the thermodynamic (continuum) limit. In this paper we extend the analysis to the evolution of the covariance matrix and to generic boundary conditions. Our main purpose is to construct a hydrodynamic description of the relaxation to the stationary state, starting from the exact equations governing the evolution of the correlation matrix. We identify and adiabatically eliminate the fast variables, arriving at a continuity equation for the temperature profile T(y,t), complemented by an ordinary equation that accounts for the evolution in the bulk. Altogether, we find that the evolution of T(y,t) is the result of fractional diffusion.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica

Optimal estimates of the diffusion coefficient of a single Brownian trajectory

Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way of extracting diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least squares estimate. Furthermore we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.Comment: 8 pages, 5 figure

Factors that promote positive attitudes towards mathematics in higher education students

The purpose of this review article is to explain the importance of understanding attitudes towards teaching and learning mathematics in higher education students. For that, we start from the premise that attitudes are related to performance towards learning mathematics, bearing in mind that what directly influences their success are the feelings of possessing competencies to understand their contents and not the feelings of difficulty towards them. In essence, at first, we describe the different attitudes towards mathematics. Next, we examine how attitudes influence math learning and finally identify the factors that foster positive attitudes toward math. From this, we suggest teaching practices that can be carried out to foster positive attitudes towards mathematics and propose new lines of research in this field

Impact of a basic mathematics course on the performance of college students in algebra subject

A common problem for universities is the lack of knowledge and mathematical skills of new students because this deficiency creates difficulties in their studies throughout their career, which can cause their dropout. The aim of this paper is to describe the impact of a basic mathematics course on the performance of college student in algebra subject. This is a 32-hour course which is developed in 16 sessions in parallel to the algebra classes and is mainly offered to students: a) identified with low performance on mathematics component of national highschool test, and b) remitted by the subject teacher. The main findings are: a) the pass rate for students who attended to more than half of the sessions of the course if 95%, and b) the average grade of the subject tends to increase as with the attendance level to the course of the students. Consequently, these results lead to the conclusion that the course has a positive effect on the students' performance

Nuevos tratamientos médicos para el cáncer medular de tiroides

Los pacientes con cáncer medular de tiroides avanzado tienen pocas opciones de tratamiento; las únicas terapias aceptadas a la fecha son el vandetanib y el cabozantinib. Sin embargo, al ser inhibidores multiquinasa tienen efectos adversos importantes, que pueden limitar su uso clínico. Con el vandetanib la prolongación del QT puede producir arritmias y requiere un uso cauteloso de medicamentos concomitantes. Con el cabozantinib, aparte de la hipertensión y el síndrome mano-pie, pueden aparecer fistulas y perforación gastrointestinal con riesgo de sangrado. Las alteraciones genéticas del proto-oncogén RET no solo están implicadas en el cáncer medular de tiroides, sino en otros tipos de cáncer, como el de pulmón. La inhibición específica del RET con los medicamentos LOXO-292 y BLU-677 es segura y no afecta otras tirosina quinasa. Por ende, su uso clínico parece ser prometedor, dado que tienen una buena respuesta clínica; además, tienen efectos adversos menos frecuentes y graves que los inhibidores de tirosina quinasa actuales

Ferromagnetic behavior of ultrathin manganese nanosheets

Ferromagnetic behaviour has been observed experimentally for the first time in nanostructured Manganese. Ultrathin ($\sim$ 0.6 nm) Manganese nanosheets have been synthesized inside the two dimensional channels of sol-gel derived Na-4 mica. The magnetic properties of the confined system are measured within 2K-300K temperature range. The confined structure is found to show a ferromagnetic behaviour with a nonzero coercivity value. The coercivity value remains positive throughout the entire temperature range of measurement. The experimental variation of susceptibility as a function of temperature has been satisfactorily explained on the basis of a two dimensional system with a Heisenberg Hamiltonian involving direct exchange interaction.Comment: 13 pages, 9 figure