Generalized hypercubes and (0,2)-graphs

AbstractA generalized hypercube Qd(S) (S ⊆ {1, 2, …, d}) has {0,1}d as vertex set and two vertices are joined whenever their mutual distance in Qd belongs to S. These graphs have been introduced in (Berrachedi and Mollard, 1996) where the notion mainly investigated there is graph embedding, especially, in the case where the host graph is a hypercube. A simple connected graph G is a (0, 2)-graph if any two vertices have 0 or exactly two common neighbors as introduced in (Mulder, 1980). We give first some results about the structure of generalized hypercubes, and then characterize those of which are (0, 2)-graphs. Using similar construction as in generalized hypercubes, we exhibit a class of (0, 2)-graphs which are not vertex transitive which contradicts again a conjecture of Mulder (1982) on the convexity of interval regular graphs

A characterization of the interval distance monotone graphs

AbstractA simple connected graph G is said to be interval distance monotone if the interval I(u,v) between any pair of vertices u and v in G induces a distance monotone graph. Aı¨der and Aouchiche [Distance monotonicity and a new characterization of hypercubes, Discrete Math. 245 (2002) 55–62] proposed the following conjecture: a graph G is interval distance monotone if and only if each of its intervals is either isomorphic to a path or to a cycle or to a hypercube. In this paper we verify the conjecture

On the chromatic number of cube-like graphs

AbstractA cube-like graph is a graph whose vertices are all 2n subsets of a set E of cardinality n, in which two vertices are adjacent if their symmetric difference is a member of a given specified collection of subsets of E. Many authors were interested in the chromatic number of such graphs and thought it was always a power of 2. Although this conjecture is false (we show a cube-like graph of chromatic number 7), we prove that there is no cube-like graph with chromatic number 3

Role of Computational Fluid Dynamics in the Analysis of Haemodynamic and Morphological Characteristics of Intracranial Aneurysms

Aneurysmal subarachnoid hemorrhage (SAH) carries a high morbidity and mortality. The current protocols used to treat the unruptured Intracranial Aneurysms (IAs) are inadequate underscoring the need of finding new descriptors. As demonstrated by the studies performed in this manuscript, haemodynamics plays an important role in the aetiopathogenesis of IAs. An evaluation of haemodynamic indices can provide a useful alternative to predict the behavior of an unruptured IA at an early stage. Studies performed by me demonstrate that Computational Fluid Dynamics (CFD) can be used successfully to predict haemodynamic indices where detailed in vivo measurement of haemodynamic flow variables is not possible owing to technical limitations. European Commission funded Project @neurIST was the first project of it’s kind that brought together a number of multidisciplinary professionals from 32 European institutions and made possible development of state-of-the-art tools for personalised risk assessment and treatment IAs using CFD. These tools have been constantly improved and amended in the light of feedback gathered from their controlled exposures conducted world over, as described in the manuscript. However, need of a well-designed Randomized Controlled Trial in this context cannot be overemphasized, before these tools can be accepted by clinicians and patients. In my study on the validation of different concepts used in CFD, I demonstrated that there is no added advantage of complex Womersley-flow-profile over the much simpler plug-flow profile. One of my studies on initiation and rupture of IAs showed that the haemodynamic patterns of IAs during these two phases are significantly different with values of supra-physiological Wall Shear Stress (WSS) being higher in initiation while lower in rupture phase. I also investigated the effects of pharmacological agents on the aetiopathogenesis of IAs and found that heparin induces significant derangements in the haemodynamics of both, pre-aneurysmal as well as ruptured IA. I propose that heparin (and its derivatives) can, on the one hand may facilitate the rupture of existing IAs, on the other hand they may suppress the formation of new IAs. I have also found significant differences in the results using patient-specific vs. Modeled Boundary Conditions and showed that the 1D circulation model adopted by @neurIST performs better than other approaches found in the literature. I also proposed a novel mechanism of increase in Blood Viscosity leading to high WSS as one of the important underlying mechanisms responsible for the increased incidence of IA formation in smokers and hypertensive patients. In my study on patients with pre-existing Coarctation of Aorta (CoA) and Intracranial Aneurysms, I demonstrated that the cerebral flow-rates in CoA patients were significantly higher when compared to average flow-rates in healthy population. It was also seen that the values and the area affected by supraphysiological WSS (>15Pa) were exponentially higher in patients with CoA indicating the possible role of increased haemodynamic WSS secondary to the increased flow-rates playing an important role in the pathogenesis and rupture of IAs in CoA patients

Espectrometría de masas para la identificación y cuantificación de biomarcadores metabolómicos en análisis clínico

La finalidad de la investigación desarrollada fue desarrollar estrategias de análisis metabolómico global y orientado para la identificación y cuantificación de metabolitos con potencial como biomarcadores en análisis clínico, para lo que se utilizó una técnica de detección clave como es la espectrometría de masas. Los objetivos perseguidos con la realización de la tesis fueron varios, todos con el denominador común de la metabolómica en el área clínica, y que pueden resumirse como sigue: (1) Desarrollar estrategias innovadores en análisis metabolómico global con aplicación en el área clínica para analizar una muestra escasamente estudiada como es el sudor y también para intentar solucionar algunas de las debilidades del análisis global como el número de metabolitos detectados en un análisis o el número de metabolitos identificados. (2) Identificar metabolitos con potencial como biomarcadores mediante el análisis global de biofluidos para su aplicación en estudios clínicos nutricionales y en el diagnóstico de enfermedades como la aterosclerosis y el cáncer de pulmón. (3) Optimizar métodos de análisis orientado confirmatorio y cuantitativo (absoluto y relativo) para la determinación de compuestos con potencial como marcadores en biofluidos y su aplicación en el diagnóstico de enfermedades