Diffusion equations for nonhomogeneous media. Existence of similarity solutions

We study the invariance of the diffusion equation δP(x,t)/δt = (δ/δx)[D(x)δP(x,t)/δx] under continuous groups of transformations. We show the conditions which D(x) must satisfy for the existence of similarity solutions

On the equivalence between compromise programming and the use of composite compromise metrics.

This paper analyzes the relationship between Compromise Programming and a close relative called Composite Programming that is based on the use of composite metrics. More specifically, it focuses on the possibility that the results of Compromise Programming are equivalent to those obtained with a particular case of Composite Programming in which a linear combination between the two bounds of the compromise set is established. Several situations, depending on the number of criteria involved and the mathematical structure of the efficient set, are studied. The most relevant result is obtained when two criteria are involved and the efficient set is continuously differentiable. In this case, it is possible to find a unique equivalent value of the control parameter in Composite Programming for each metric in Compromise Programming. It is remarked that this particular case is very relevant in many economic scenarios. On the other hand, it turns out that the equivalence between both approaches can not be extended to the case with more than two criteria.Compromise programming, composite metric, p-norms, economic optimization.

El efecto de la publicidad en la norma

En la experiencia cotidiana las interpretaciones de lo que es el derecho son muy variadas; por ejemplo, caben, entre las más frecuentes: la de orden justo y equitativo; norma o conjunto de normas que regulan nuestra conducta social; garantía o protección, restricción o límite del ámbito de actuación de la libertad de cada uno; sanción de una conducta; disposición o mandato; orden, imposición, decisión; acuerdo, pacto o consenso de voluntades; resolución de conflictos y litigios; facultad y pretensión; modelo de ordenación y organización de la vida social; institución; ciencia… Pero, si focalizamos la concepción del derecho en la norma jurídica, es evidente que es una entidad lógica y, desde que se convierte en efectiva, socialización de comportamientos humanos.In daily experience, interpretations of what the Law is can be very varied; for example the most frequent include those of law and equitable order; norms or sets of social norms that regulate our conduct; guarantee or protection, restriction or limiting of the scope of freedom to perform each one; sanctioning of conduct; disposition or mandate; order, imposition, decision; agreement, pact or consensus of wills; resolution of conflicts and litigations; faculty and pretension; model of arrangement and organization of social life; institution; Science… But, if we focus the conception of the Law on legislative norms, it is evident that the organization is logical , and that once it becomes effective, it socializes human behaviours

Elements inherent to the dignity and free development of the personality from the Spanish legal approach to the bad uses in children of the new information technologies applied to the tourism

La irrupción masiva de las nuevas tecnologías de la información y comunicación han proyectado consecuencias jurídicas de primer orden en el ámbito turístico, especialmente en el turismo sexual, y en un segundo término en el denominado turismo de ferias y congresos que, en numerosas ocasiones, aparece vinculado al primero en concentraciones y eventos multitudinarios que se celebran en las grandes ciudades del planeta. La aparición del escenario virtual que conforma el ciberespacio ha afectado y afecta, sobre todo, a una minoría bastante desprotegida como son los menores en su rol de víctimas de las modalidades de explotación del siglo XXIThe massive emergence of new information and communication technologies have been projected legal consequences of first order in the tourism field, especially in sex tourism, and a second in the so-called tourism fairs and congresses that, on numerous occasions, it appears linked to the first in concentrations and multitudinous events that are held in big cities on the planet. The emergence of the virtual scenario that makes up cyberspace has affected and affects, above all, a fairly unprotected minority as they are minors in their role as victims of the modes of exploitation of the 21st centur

Multi-Level Batch Normalization In Deep Networks For Invasive Ductal Carcinoma Cell Discrimination In Histopathology Images

Breast cancer is the most diagnosed cancer and the most predominant cause of death in women worldwide. Imaging techniques such as the breast cancer pathology helps in the diagnosis and monitoring of the disease. However identification of malignant cells can be challenging given the high heterogeneity in tissue absorbotion from staining agents. In this work, we present a novel approach for Invasive Ductal Carcinoma (IDC) cells discrimination in histopathology slides. We propose a model derived from the Inception architecture, proposing a multi-level batch normalization module between each convolutional steps. This module was used as a base block for the feature extraction in a CNN architecture. We used the open IDC dataset in which we obtained a balanced accuracy of 0.89 and an F1 score of 0.90, thus surpassing recent state of the art classification algorithms tested on this public dataset.Comment: 4 pages, 5 figure

Diffusion in a class of exactly solvable non-harmonic potentials. Intrinsic effects induced by non-linearities

This paper deals with the problem of a particle that diffuses in a potential with a reflecting barrier and has a point of stable equilibrium and a point of unstable equilibrium. Based on the exact solutions obtained earlier for the Fokker-Planck equation of a class of these models, we analyze the behavior of the probability density, the mean path and the onset time which determines the transition from unimodal to bimodal probability densities. The study is made over different initial positions, two of them very close to the unstable point, which permits a clear comparison among the subsequent evolutions, and the observation of some intrinsic effects induced by non-linearities