Isidoro Gitler

Reseaux électriques planaires II.

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Blowup Algebras of Square-Free Monomial Ideals and Some Links to Combinatorial Optimization Problems

Let I = (x v 1 , . . . , x v q ) be a square-free monomial ideal of a polynomial ring K[x1, . . . , xn] over an arbitrary field K and let A be the incidence matrix with column vectors v1, . . . , vq. We will establish some connections between algebraic properties of certain graded algebras associated to I and combinatorial optimization properties of certain polyhedra and clutters associated to A and I respectively. Some applications to Rees algebras and combinatorial optimization are presented. We study a conjecture of Conforti and

Ring graphs and complete intersection toric ideals

We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs correspond to ring graphs and that these ideals are minimally generated by Grobner bases. We prove that any graph can be oriented such that its toric ideal is a complete intersection with a universal Grobner basis determined by the cycles. It turns out that bipartite ring graphs are exactly the bipartite graphs that have complete intersection toric ideals for any orientation.

Ring graphs and toric ideals

Abstract We study the family of simple graphs whose number of primitive cycles equals its cycle rank. Then we study toric ideals of simple and oriented graphs.

The crossing number of a projective graph is quadratic in the face{width

We show that for each integer g 0 there is a constant cg > 0 such that every graph that embeds in the projective plane with sucien tly large face{width r has crossing number at least cgr 2 in the orientable surface g of genus g. As a corollary, we give a polynomial time constant factor approximation algorithm for the crossing number of projective graphs with bounded degree.

Multiplicities of edge subrings

For a bipartite graph G we are able to characterize the complete intersection property of the edge subring in terms of the multiplicity and we give optimal bounds for this number. We give a method to obtain a regular sequence for the atomic ideal of G, when G is embedded on an orientable surface. We also give a graph theoretical condition for the edge subring associated with G to be Gorenstein. Finally we give a formula for the multiplicity of edge subrings, of arbitrary simple graphs.

Performance of a code migration for the simulation of supersonic ejector flow to SMP, MIC, and GPU using OpenMP, OpenMP+LEO, and OpenACC directives

A serial source code for simulating a supersonic ejector flow is accelerated using parallelization based on OpenMP and OpenACC directives. The purpose is to reduce the development costs and to simplify the maintenance of the application due to the complexity of the FORTRAN source code. This research follows well-proven strategies in order to obtain the best performance in both OpenMP and OpenACC. OpenMP has become the programming standard for scientific multicore software and OpenACC is one true alternative for graphics accelerators without the need of programming low level kernels. The strategies using OpenMP are oriented towards reducing the creation of parallel regions, tasks creation to handle boundary conditions, and a nested control of the loop time for the programming in offload mode specifically for the Xeon Phi. In OpenACC, the strategy focuses on maintaining the data regions among the executions of the kernels. Experiments for performance and validation are conducted here on a 12-core Xeon CPU, Xeon Phi 5110p, and Tesla C2070, obtaining the best performance from the latter. The Tesla C2070 presented an acceleration factor of 9.86X, 1.6X, and 4.5X compared against the serial version on CPU, 12-core Xeon CPU, and Xeon Phi, respectively.

CIO and ring graphs

We give a polynomial time algorithm that tests whether a graph is a theta-ring graph or equivalently if a graph has the ź ź ź Δ -property (each chorded-theta has a transversal triangle). It is known that G is a theta-ring graph if and only if G is a CI O graph (each toric ideal associated to an edge orientation of G is a binomial complete intersection). In particular ring graphs are theta-ring graphs. We prove that the forbidden induced subgraphs that characterize ring graphs are chorded-thetas and K 4 . We introduce a new graph invariant, the CI O deficiency. This invariant has the property that graphs with CI O deficiency zero are exactly CI O graphs.

Delta-Wye Transformations and the Efficient Reduction of Almost-Planar Graphs

Abstract A non-planar graph G is almost-planar if, for every edge e of G, either G \ e or G/e is planar. We provide an algorithmic proof of a theorem by D. K. Wagner, according to which every almost-planar graph can be reduced to the graph K 3 , 3 by some sequence of series/parallel reductions and delta-wye exchanges such that the reduction sequence is formed by almost-planar graphs. We study 3-connected almost-planar graphs on the projective plane and establish duality relations between the resulting families. We show that one family reduces to K 3 , 3 (with an added parallel edge) while the dual family reduces to K5. We also characterize 3-terminal delta-wye reducibility for almost-planar graphs.

A Network Model to Explore the Effect of the Micro-environment on Endothelial Cell Behavior during Angiogenesis

Angiogenesis is an important adaptation mechanism of the blood vessels to the changing requirements of the body during development, aging, and wound healing. Angiogenesis allows existing blood vessels to form new connections or to reabsorb existing ones. Blood vessels are composed of a layer of endothelial cells (ECs) covered by one or more layers of mural cells (smooth muscle cells or pericytes). We constructed a computational Boolean model of the molecular regulatory network involved in the control of angiogenesis. Our model includes the ANG/TIE, HIF, AMPK/mTOR, VEGF, IGF, FGF, PLCγ/Calcium, PI3K/AKT, NO, NOTCH, and WNT signaling pathways, as well as the mechanosensory components of the cytoskeleton. The dynamical behavior of our model recovers the patterns of molecular activation observed in Phalanx, Tip, and Stalk ECs. Furthermore, our model is able to describe the modulation of EC behavior due to extracellular micro-environments, as well as the effect due to loss- and gain-of-function mutations. These properties make our model a suitable platform for the understanding of the molecular mechanisms underlying some pathologies. For example, it is possible to follow the changes in the activation patterns caused by mutations that promote Tip EC behavior and inhibit Phalanx EC behavior, that lead to the conditions associated with retinal vascular disorders and tumor vascularization. Moreover, the model describes how mutations that promote Phalanx EC behavior are associated with the development of arteriovenous and venous malformations. These results suggest that the network model that we propose has the potential to be used in the study of how the modulation of the EC extracellular micro-environment may improve the outcome of vascular disease treatments.