Defensive alliances in graphs: a survey

A set $S$ of vertices of a graph $G$ is a defensive $k$-alliance in $G$ if every vertex of $S$ has at least $k$ more neighbors inside of $S$ than outside. This is primarily an expository article surveying the principal known results on defensive alliances in graph. Its seven sections are: Introduction, Computational complexity and realizability, Defensive $k$-alliance number, Boundary defensive $k$-alliances, Defensive alliances in Cartesian product graphs, Partitioning a graph into defensive $k$-alliances, and Defensive $k$-alliance free sets.Comment: 25 page

Distribution functions for a family of axially symmetric galaxy models

We present the derivation of distribution functions for the first four members of a family of disks, previously obtained in (MNRAS, 371, 1873, 2006), which represent a family of axially symmetric galaxy models with finite radius and well behaved surface mass density. In order to do this we employ several approaches that have been developed starting from the potential-density pair and, essentially using the method introduced by Kalnajs (Ap. J., 205, 751, 1976) we obtain some distribution functions that depend on the Jacobi integral. Now, as this method demands that the mass density can be properly expressed as a function of the gravitational potential, we can do this only for the first four discs of the family. We also find another kind of distribution functions by starting with the even part of the previous distribution functions and using the maximum entropy principle in order to find the odd part and so a new distribution function, as it was pointed out by Dejonghe (Phys. Rep., 133, 217, 1986). The result is a wide variety of equilibrium states corresponding to several self-consistent finite flat galaxy models.Comment: 12 pages, 7 figures, updated version, accepted for publication in Rev. Acad. Colomb. Cienc. Ex. Fis. Na

A free boundary model for oxygen diffusion in a spherical medium

The goal of this article is to find a correct approximated solution using a polynomial of sixth degree for the free boundary problem corresponding to the diffusion of oxygen in a spherical medium with simultaneous absorption at a constant rate, and to show some mistakes in previously published solutions.Comment: 10 pages, 6 figures and 2 tables. Paper accepted, in press in Journal of Biological Systems (2015

Cooperative cell motility during tandem locomotion of amoeboid cells.

Streams of migratory cells are initiated by the formation of tandem pairs of cells connected head to tail to which other cells subsequently adhere. The mechanisms regulating the transition from single to streaming cell migration remain elusive, although several molecules have been suggested to be involved. In this work, we investigate the mechanics of the locomotion ofDictyosteliumtandem pairs by analyzing the spatiotemporal evolution of their traction adhesions (TAs). We find that in migrating wild-type tandem pairs, each cell exerts traction forces on stationary sites (∼80% of the time), and the trailing cell reuses the location of the TAs of the leading cell. Both leading and trailing cells form contractile dipoles and synchronize the formation of new frontal TAs with ∼54-s time delay. Cells not expressing the lectin discoidin I or moving on discoidin I-coated substrata form fewer tandems, but the trailing cell still reuses the locations of the TAs of the leading cell, suggesting that discoidin I is not responsible for a possible chemically driven synchronization process. The migration dynamics of the tandems indicate that their TAs' reuse results from the mechanical synchronization of the leading and trailing cells' protrusions and retractions (motility cycles) aided by the cell-cell adhesions

Leonardo Polo: la persona humana como ser libre.

Si actiones sunt suppositorum, en cambio no todos los actos del hombre son humanos. La transformación de la sustancia en subjetividad se justifica como intento de comprensión de lo estrictamente humano. Polo apunta cómo entender la libertad para descubrir en ella la existencia personalAlthough actiones sunt suppositorum, not all the man's acts are human. The transformation of the substance in subjectivity is justified for understanding of the strictly human. Leonardo Polo points how to understand the freedom to discover in her the personal existence

Between Husserl and Heidegger: The articulation of time or the configuration of space; the appropriation of time and the facticity of experience

Pretendemos dar una visión de conjunto de la obra husserliana, que explique la evolución posterior a Ideas. Desde ella es hacedera una comparación con Heidegger, en particular en orden a precisar el carácter incorporado de la inteligencia humana. Estaremos en condiciones entonces de considerar la propuesta de Leonardo Polo sobre el estatuto del cuerpo humano latente bajo la intelección.We intend to give an overview of the Husserlian work, which explains the subsequent evolution to Ideas. From it a comparison with Heidegger is made, particularly in order to specify the built-in character of human intelligence. We will then be able to consider Leonardo Polo’s proposal on the status of the human body latent under intellection