The degree/diameter problem in maximal planar bipartite graphs

The (¿;D) (degree/diameter) problem consists of nding the largest possible number of vertices n among all the graphs with maximum degree ¿ and diameter D. We consider the (¿;D) problem for maximal planar bipartite graphs, that are simple planar graphs in which every face is a quadrangle. We obtain that for the (¿; 2) problem, the number of vertices is n = ¿+2; and for the (¿; 3) problem, n = 3¿¿1 if ¿ is odd and n = 3¿ ¿ 2 if ¿ is even. Then, we study the general case (¿;D) and obtain that an upper bound on n is approximately 3(2D + 1)(¿ ¿ 2)¿D=2¿ and another one is C(¿ ¿ 2)¿D=2¿ if ¿ D and C is a sufficiently large constant. Our upper bound improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on n for maximal planar bipartite graphs, which is approximately (¿ ¿ 2)k if D = 2k, and 3(¿ ¿ 3)k if D = 2k + 1, for ¿ and D sufficiently large in both cases.Postprint (published version

La memoria femenina en la narrativa Title: The Female Memory in Narrative

Nélida Piñon (1937-), condecorada novelista brasileña, autora de República de los sueños (1984), ganadora del Premio Juan Rulfo (1995), miembro y ex Presidenta de la Academia de Literatura.Culture & Arts, Nélida Piñon Centro Cultural Encuentros Nro. 35 La memoria femenina en la narrativa

The degree/diameter problem in maximal planar bipartite graphs

The (Δ,D)(Δ,D) (degree/diameter) problem consists of finding the largest possible number of vertices nn among all the graphs with maximum degree ΔΔ and diameter DD. We consider the (Δ,D)(Δ,D) problem for maximal planar bipartite graphs, that is, simple planar graphs in which every face is a quadrangle. We obtain that for the (Δ,2)(Δ,2) problem, the number of vertices is n=Δ+2n=Δ+2; and for the (Δ,3)(Δ,3) problem, n=3Δ−1n=3Δ−1 if ΔΔ is odd and n=3Δ−2n=3Δ−2 if ΔΔ is even. Then, we prove that, for the general case of the (Δ,D)(Δ,D) problem, an upper bound on nn is approximately 3(2D+1)(Δ−2)⌊D/2⌋3(2D+1)(Δ−2)⌊D/2⌋, and another one is C(Δ−2)⌊D/2⌋C(Δ−2)⌊D/2⌋ if Δ≥DΔ≥D and CC is a sufficiently large constant. Our upper bounds improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on nn for maximal planar bipartite graphs, which is approximately (Δ−2)k(Δ−2)k if D=2kD=2k, and 3(Δ−3)k3(Δ−3)k if D=2k+1D=2k+1, for ΔΔ and DD sufficiently large in both cases.Peer ReviewedPostprint (published version

El método socrático en los programas educativos actuales: una propuesta de Martha C. Nussbaum

A partir de la propuesta de Martha C. Nussbaum, se analizó la importancia del método socrático aplicado a la educación. Se enfatizó la necesidad de incluir en los programas escolares la enseñanza de las humanidades, las artes y las ciencias sociales a fin de desarrollar en los alumnos habilidades como la crítica, la imaginación, la reflexión, la creatividad y la empatía. Para que estas medidas tengan éxito se propuso que los gobiernos incrementen la inversión en materia educativa, la adecuada formación de los docentes, el aprendizaje de lenguas distintas a la materna y un enfoque plural y multicultural en los cursos

“ESTADO ACTUAL DE LOS BLOQUEADORES DE CANALES DE CALCIO “ (REVISIÓN DE LA LITERATURA)

Desde el siglo pasado nuestra población ha estado en una transición epidemiológica, es decir que las enfermedades que afectaban en el siglo pasado como las infecciones respiratorias agudas y enfermedades diarreicas agudas, se han visto desplazadas por la aparición de enfermedades crónico degenerativas como Diabetes Mellitus, Hipertensión Arterial, Enfermedades del Corazón, Obesidad y que esto a largo plazo conlleva a un aumento de la morbimortalidad ya sea por eventos cardiovasculares o cerebrovasculares con un desenlace fatal, por lo cual se ha cambiado desde entonces y se ha optado por una cultura preventiva que lleve consigo reducir la incidencia y prevalencia de estas enfermedades, de este modo es importante un diagnóstico oportuno y un tratamiento adecuad

Why the United States and Cuba Collaborate

This article examines Cuba\u27s upcoming oil exploration drilling program. It outlines some of the benefits of collaboration between the United States and Cuba given that the drilling will take place in the Gulf of Mexico. The article recommends an agreement between the two countries similar to the MEXUS Plan (1980) that the United States signed with Mexico

Enhancing dendritic cell immunotherapy for melanoma using a simple mathematical model

ABSTRACT Background: The immunotherapy using dendritic cells (DCs) against different varieties of cancer is an approach that has been previously explored which induces a specific immune response. This work presents a mathematical model of DCs immunotherapy for melanoma in mice based on work by Experimental Immunotherapy Laboratory of the Medicine Faculty in the Universidad Autonoma de Mexico (UNAM). Method: The model is a five delay differential equation (DDEs) which represents a simplified view of the immunotherapy mechanisms. The mathematical model takes into account the interactions between tumor cells, dendritic cells, naive cytotoxic T lymphocytes cells (inactivated cytotoxic cells), effector cells (cytotoxic T activated cytotoxic cells) and transforming growth factor β cytokine (TGF − β). The model is validated comparing the computer simulation results with biological trial results of the immunotherapy developed by the research group of UNAM. Results: The results of the growth of tumor cells obtained by the control immunotherapy simulation show a similar amount of tumor cell population than the biological data of the control immunotherapy. Moreover, comparing the increase of tumor cells obtained from the immunotherapy simulation and the biological data of the immunotherapy applied by the UNAM researchers obtained errors of approximately 10 %. This allowed us to use the model as a framework to test hypothetical treatments. The numerical simulations suggest that by using more doses of DCs and changing the infusion time, the tumor growth decays compared with the current immunotherapy. In addition, a local sensitivity analysis is performed; the results show that the delay in time “τ ”, the maximal growth rate of tumor “r” and the maximal efficiency of tumor cytotoxic cells rate “aT” are the most sensitive model parameters. Conclusion: By using this mathematical model it is possible to simulate the growth of the tumor cells with or without immunotherapy using the infusion protocol of the UNAM researchers, to obtain a good approximation of the biological trials data. It is worth mentioning that by manipulating the different parameters of the model the effectiveness of the immunotherapy may increase. This last suggests that different protocols could be implemented by the Immunotherapy Laboratory of UNAM in order to improve their results