Long cycles in graphs with large degree sums and neighborhood unions

We present and prove several results concerning the length of longest cycles in 2-connected or 1-tough graphs with large degree sums. These results improve many known results on long cycles in these graphs. We also consider the sharpness of the results and discuss some possible strengthenings

Circumference of 3-connected claw-free graphs and large Eulerian subgraphs of 3-edge-connected graphs

AbstractThe circumference of a graph is the length of its longest cycles. Results of Jackson, and Jackson and Wormald, imply that the circumference of a 3-connected cubic n-vertex graph is Ω(n0.694), and the circumference of a 3-connected claw-free graph is Ω(n0.121). We generalize and improve the first result by showing that every 3-edge-connected graph with m edges has an Eulerian subgraph with Ω(m0.753) edges. We use this result together with the Ryjáček closure operation to improve the lower bound on the circumference of a 3-connected claw-free graph to Ω(n0.753). Our proofs imply polynomial time algorithms for finding large Eulerian subgraphs of 3-edge-connected graphs and long cycles in 3-connected claw-free graphs

Relationship between the Magnitude and Location of Thigh-Calf Contact Force in High Flexion and Anthropometric Measures

The soft-tissue contact between the thigh and calf during deep knee flexion results in tibiofemoral joint contact force reductions at angles beyond 134º of flexion (Caruntu et al., 2003; Zelle et al., 2009; Hirokawa et al., 2013). Many knee models that predict tibiofemoral joint contact forces in high flexion neglect to account for this force. Very few investigations have attempted to characterize thigh-calf contact force, and even fewer have directly measured thigh-calf contact or attempted to model thigh-calf contact force and contact force location on the tibia (Zelle et al. 2007; Zelle et al. 2009). This study focused on the following four thigh-calf contact parameters: (1) maximum total thigh-calf contact force, (2) the corresponding flexion angle, (3) the corresponding centre of pressure, and (4) the starting angle of thigh-calf contact (the flexion angle at the initiation of thigh-calf contact when transitioning into a kneeling or squatting posture). This study addresses limitations of previous work by investigating how the thigh-calf contact parameters are correlated to anthropometric measures after accounting for correlations between body mass and contact force (by normalizing thigh-calf contact force to body mass), comparing parameters between sexes and activities, and presenting an equation for the average thigh-calf contact force and location from 30 participants as a function of percent thigh-calf contact flexion range (this has only been done previously for a single participant as a function of flexion angle). Anthropometric measurements from 30 healthy participants (16 male and 14 female) were recorded. Instrumentation included opto-electronic markers to track dominant leg motion and an interface pressure mapping system to determine the thigh-calf contact force during three deep flexion movements: dorsi-flexed kneeling, plantar-flexed kneeling, and plantar-flexed squatting. Four two-way (3 activities x 2 sexes) ANOVAs were used to compare the mean values for maximum total thigh-calf contact force (in N/kg), centre of pressure at maximum total force (in cm), flexion angle at maximum total force (in degrees) and the starting angle of thigh-calf contact (in degrees) between sexes and between the three activities. Pearson product-moment correlation coefficients (R) were calculated in order to investigate the relationship between the anthropometric measures and the four outcome parameters. In cases where the R value exceeded 0.5 for one or more of the anthropometric measures for a given outcome parameter, predictive modeling of the outcome parameter based on anthropometric measures was pursued using multivariate linear regression with forward stepwise selection. A mean curve for thigh-calf contact force and a mean curve for centre of pressure were created for all participants for each activity. Equations were fit to the mean curves to express each of the measures as a function of percent range of flexion after contact. Based on the average thigh-calf contact force curve for 30 participants, the maximum thigh-calf contact force occurred at maximum flexion and was 1.1 N/kg (S.D. 0.6 N/kg) during squatting, 2.0 N/kg (S.D. 0.7 N/kg) during dorsi-flexed kneeling and 2.2 N/kg (S.D. 0.9 N/kg) during plantar-flexed kneeling. The average centre of pressure, corresponding to those maximum total thigh-calf contact force values, was found to be closer to the epicondylar axis during squatting (13.7 cm, S.D. 1.6cm) than for dorsi-flexed kneeling (14.9 cm, S.D. 1.7 cm) and plantar-flexed kneeling (14.6 cm, S.D. 1.9 cm). There was a significant difference in the maximum total thigh-calf contact force, centre of pressure at maximum total force, and starting angle of thigh-calf contact between squatting and each of the two kneeling activities, however, for all outcome parameters, dorsi-flexed and plantar-flexed kneeling were not significantly different. There was a significant main effect of sex on the starting angle of thigh-calf contact (p = 0.004), whereas, with all other outcome parameters, there was no sex main effect. Unlike the previous investigation that measured thigh-calf contact (Zelle et al., 2007), there was little correlation between anthropometric measures and maximum total thigh-calf contact force or location of centre of pressure at maximum total thigh-calf contact force. This discrepancy likely occurred because thigh-calf contact force was normalized to body mass in this study, whereas non-normalized contact force was used in the previous study. The joint reaction forces, net joint moment, and joint contact forces at the knee joint in the sagittal plane during static full flexion squatting were calculated for a single participant both with and without the addition of thigh-calf contact force. The addition of thigh-calf contact force into the model reduced the knee joint reaction forces by 101.09 N in the anterior-posterior direction and the net sagittal plane knee joint moment by 13.14 Nm at maximal flexion. Based on a single muscle equivalent estimate, the compressive tibiofemoral joint contact force decreased by 221.78 N in the longitudinal direction and 84.96 N in the anterior-posterior direction

Computational analysis of fluid dynamics at the asceding thoracic aorta in Marfan syndrome patients

Els aneurismes aòrtics són una dilatació progressiva i irreversible de la paret aòrtica, que pot causar la ruptura o dissecció dels vasos, el que resulta en una pèrdua catastròfica de sang que condueix a la mort. El tractament farmacològic inicial se centra en aturar el creixement per prevenir la ruptura, però requereix una reparació invasiva oberta o una reparació endovascular en pacients en risc. El maneig del pacient i l'estratificació de risc després del diagnòstic són crítics, especialment en l'aorta ascendent, ja que actualment no hi ha tractaments endovasculars disponibles. Segons les directrius actuals, el diàmetre aòrtic màxim és l'únic criteri geomètric o fluidodinàmic específic del pacient acceptat com a predictor clínic del risc de ruptura. No obstant això, l'anormal fluidodinàmica en l'aorta ascendent s'ha reportat àmpliament com una possible font d'aneurismes aòrtics i la seva comprensió podria millorar l'avaluació del risc del pacient. En aquest estudi, es va avaluar la fluidodinàmica en aortes de controls sans i pacients amb síndrome de Marfan. Per fer això, hem comparat el rendiment de les simulacions de dinàmica de fluids computacional i d'interacció fluid-estructura utilitzant imatges clíniques com a condicions específiques del pacient. També hem dissenyat un sistema in vitro que podria exposar les cèl·lules endotelials aòrtiques humanes a un entorn fluidodinàmic que imita el de les simulacions aòrtiques. L'estudi ha revelat, en pacients Marfan, que considerà l'elasticitat de la paret en les simulacions és essencial per obtenir amb precisió els valors fluidodinàmics que tenen el potencial d'estratificar aquests pacients. En aquest sentit, les simulacions d'interacció fluid-estructura han superat la fluidodinàmica computacional clàssica a un cost computacional moderat. Com a resultat d'aquest estudi, un paràmetre adimensional, la relació d'esforç tallant, ha determinat el seu potencial com a marcador de progressió d'aneurisma en pacients amb Marfan.Los aneurismas aórticos son una dilatación progresiva e irreversible de la pared aórtica, que puede causar la ruptura o disección de los vasos, lo que resulta en una pérdida catastrófica de sangre que conduce a la muerte. El tratamiento farmacológico inicial se centra en detener el crecimiento para prevenir la ruptura, pero se requiere una reparación invasiva abierta o una reparación endovascular en pacientes en riesgo. El manejo del paciente y la estratificación del riesgo después del diagnóstico son críticos, especialmente en la aorta ascendente, ya que actualmente no hay tratamientos endovasculares disponibles. Según las directrices actuales, el diámetro aórtico máximo es el único criterio geométrico o fluidodinámico específico del paciente aceptado como predictor clínico del riesgo de ruptura. Sin embargo, la anormal fluidodinámica en la aorta ascendente se ha reportado ampliamente como una posible fuente de aneurismas aórticos y su comprensión podría mejorar la evaluación del riesgo del paciente. En este estudio, se evaluó la fluidodinámica en aortas de controles sanos y pacientes con síndrome de Marfan. Para hacer esto, hemos comparado el rendimiento de las simulaciones de dinámica de fluidos computacional y de interacción fluido-estructura utilizando imágenes clínicas como condiciones específicas del paciente. También hemos diseñado un sistema in vitro que podría exponer las células endoteliales aórticas humanas a un entorno fluidodinámico que imita el de las simulaciones aórticas. El estudio ha revelado, en pacientes Marfan, que considerar la elasticidad de la pared en las simulaciones es esencial para obtener con precisión los valores dinámicos de los fluidos que tienen el potencial de estratificar a estos pacientes. En este sentido, las simulaciones de interacción fluido-estructura han superado la fluidodinámica computacional clásica a un costo computacional moderado. Como resultado de este estudio, un parámetro adimensional, la relación de esfuerzo cortante, ha demostrado su potencial como marcador de progresión de aneurisma en pacientes con Marfan.Aortic aneurysms are a progressive and irreversible dilation of the aortic wall, which can lead to vessel rupture or dissection, resulting in catastrophic blood loss leading to death. Initial pharmacological treatment is focused on growth arrest to prevent rupture, but invasive open repair or endovascular repair are required in patients at risk. Patient management and risk stratification after diagnosis are critical, especially in the ascending aorta since no endovascular treatments are currently available. According to current guidelines, maximum aortic diameter is the only patient-specific geometrical or fluidodynamic criterion accepted as clinical rupture risk predictor. However, abnormal fluid dynamics at the ascending aorta have been widely reported as potential origin of aortic aneurysms and their understanding could improve the risk assessment of patients. In this study, the fluid dynamics of aortae from healthy controls and patients with Marfan syndrome have been evaluated. To do so, we have compared the performance of computational fluid dynamics and fluid-structure interaction simulations using clinical imaging as patient-specific inputs. We have also designed an in vitro system that could expose human aortic endothelial cells to a fluidodynamic environment that mimics that of aortic simulations. The study has revealed, in Marfan patients, that considering the wall elasticity in simulations is critical to derive precisely fluid dynamic values that hold the potential to stratify such patients. In this sense, fluid-structure interaction simulations have outperformed classic computational fluid dynamics at a moderate computational cost. As a result of this study, a dimensionless parameter, the shear stress ratio, has shown its potential as marker of aneurysm progression in Marfan patients

Design and Optimization of Hybrid Foundation for Tall Wind Turbines and Development of New Foundation Through Biomimicry

This study presents a simplified geotechnical design, design optimization, and finite element modeling of the piled-raft foundation intended for a 130 m tall wind turbine for different site conditions. The sites considered are composed of multilayered soil, clayey soil, and sandy soil. The simplified geotechnical design includes the safety checks (vertical load, horizontal load, and bending moment capacities) and serviceability check (total vertical and differential settlements). The simplified design showed that the final design is controlled by differential settlement requirement. Subsequently, a parametric study was also conducted to investigate the effect of soil strength parameter (undrained cohesion for clay and friction angle for sand) and wind speed on the design. The major drawback of this parametric study is that only one variable is changed at a time. However, more than one variable can change at the same time. Therefore, a reliability-based robust design optimization was conducted using Non-dominated Sorting Genetic Algorithm – II (NSGA-II) coupled with Monte Carlo simulation. In the design optimization, the wind speed and soil strength parameter were considered as random variables, radius of raft, length of pile, and number of piles were considered as the design variables, and the total cost of the foundation and the standard deviation of differential settlement were considered as the two objectives to satisfy. This resulted in a set of acceptable designs forming a Pareto front which showed a trade-off relationship between the total cost and standard deviation of differential settlement which can be used to obtain the design as per the cost and safety requirement. The most optimum design can be obtained using the knee point concept. Further, a three-dimensional finite element model of the piled-raft foundation was developed and analyzed in ABAQUS and the response was compared with the simplified analytical design results. The stress-strain behavior of soil was represented by both linear and nonlinear constitutive models. The soil-structure interfaces were modeled by defining the interaction properties at the interfaces. It was observed that the analytical design resulted in a higher vertical settlement and the horizontal displacement and lower differential settlement and rotation compared to the finite element result. The parametric study conducted subsequently by varying the wind speed and undrained cohesion of soil showed that the difference between the predicted responses from two methods decreases when the load is large and/or soil is soft. Finally, a preliminary study on the development of a new foundation for wind turbine through biomimicry is also presented. Since wind turbine is comparable to a coconut tree, sabal palm tree, and Palmyra tree, the root of these trees is studied to develop simplified configurations with a different number of main roots and sub-roots. The results showed that the performance of the foundation under combined load improved with the increase in the number of main roots while the sub-roots had a negligible contribution to the performance of the foundation

General Dynamic Surface Reconstruction: Application to the 3D Segmentation of the Left Ventricle

Aquesta tesi descriu la nostra contribució a la reconstrucció tridimensional de les superfícies interna i externa del ventricle esquerre humà. La reconstrucció és un primer procés dins d'una aplicació global de Realitat Virtual dissenyada com una important eina de diagnòstic per a hospitals. L'aplicació parteix de la reconstrucció de les superfícies i proveeix a l'expert de manipulació interactiva del model en temps real, a més de càlculs de volums i de altres paràmetres d'interès. El procés de recuperació de les superfícies es caracteritza per la seva velocitat de convergència, la suavitat a les malles finals i la precisió respecte de les dades recuperades. Donat que el diagnòstic de patologies cardíaques requereix d'experiència, temps i molt coneixement professional, la simulació és un procés clau que millora la eficiència.Els nostres algorismes i implementacions han estat aplicats a dades sintètiques i reals amb diferències relatives a la quantitat de dades inexistents, casuístiques presents a casos patològics i anormals. Els conjunts de dades inclouen adquisicions d'instants concrets i de cicles cardíacs complets. La bondat del sistema de reconstrucció ha estat avaluada mitjançant paràmetres mèdics per a poder comparar els nostres resultats finals amb aquells derivats a partir de programari típic utilitzat pels professionals de la medicina.A més de l'aplicació directa al diagnòstic mèdic, la nostra metodologia permet reconstruccions de tipus genèric en el camp dels Gràfics 3D per ordinador. Les nostres reconstruccions permeten generar models tridimensionals amb un baix cost en quant a la interacció manual necessària i a la càrrega computacional associada. Altrament, el nostre mètode pot entendre's com un robust algorisme de triangularització que construeix superfícies partint de núvols de punts que poden obtenir-se d'escàners làser o sensors magnètics, per exemple.Esta tesis describe nuestra contribución a la reconstrucción tridimensional de las superficies interna y externa del ventrículo izquierdo humano. La reconstrucción es un primer proceso que forma parte de una aplicación global de Realidad Virtual diseñada como una importante herramienta de diagnóstico para hospitales. La aplicación parte de la reconstrucción de las superficies y provee al experto de manipulación interactiva del modelo en tiempo real, además de cálculos de volúmenes y de otros parámetros de interés. El proceso de recuperación de las superficies se caracteriza por su velocidad de convergencia, la suavidad en las mallas finales y la precisión respecto de los datos recuperados. Dado que el diagnóstico de patologías cardíacas requiere experiencia, tiempo y mucho conocimiento profesional, la simulación es un proceso clave que mejora la eficiencia.Nuestros algoritmos e implementaciones han sido aplicados a datos sintéticos y reales con diferencias en cuanto a la cantidad de datos inexistentes, casuística presente en casos patológicos y anormales. Los conjuntos de datos incluyen adquisiciones de instantes concretos y de ciclos cardíacos completos. La bondad del sistema de reconstrucción ha sido evaluada mediante parámetros médicos para poder comparar nuestros resultados finales con aquellos derivados a partir de programario típico utilizado por los profesionales de la medicina.Además de la aplicación directa al diagnóstico médico, nuestra metodología permite reconstrucciones de tipo genérico en el campo de los Gráficos 3D por ordenador. Nuestras reconstrucciones permiten generar modelos tridimensionales con un bajo coste en cuanto a la interacción manual necesaria y a la carga computacional asociada. Por otra parte, nuestro método puede entenderse como un robusto algoritmo de triangularización que construye superficies a partir de nubes de puntos que pueden obtenerse a partir de escáneres láser o sensores magnéticos, por ejemplo.This thesis describes a contribution to the three-dimensional reconstruction of the internal and external surfaces of the human's left ventricle. The reconstruction is a first process fitting in a complete VR application that will serve as an important diagnosis tool for hospitals. Beginning with the surfaces reconstruction, the application will provide volume and interactive real-time manipulation to the model. We focus on speed, precision and smoothness for the final surfaces. As long as heart diseases diagnosis requires experience, time and professional knowledge, simulation is a key-process that enlarges efficiency.The algorithms and implementations have been applied to both synthetic and real datasets with differences regarding missing data, present in cases where pathologies and abnormalities arise. The datasets include single acquisitions and complete cardiac cycles. The goodness of the reconstructions has been evaluated with medical parameters in order to compare our results with those retrieved by typical software used by physicians.Besides the direct application to medicine diagnosis, our methodology is suitable for generic reconstructions in the field of computer graphics. Our reconstructions can serve for getting 3D models at low cost, in terms of manual interaction and CPU computation overhead. Furthermore, our method is a robust tessellation algorithm that builds surfaces from clouds of points that can be retrieved from laser scanners or magnetic sensors, among other available hardware

Annual Report of Undergraduate Research Fellows, August 2008 to May 2009

Annual Report of Undergraduate Research Fellows from August 2008 to May 2009

Detecting Majorana Fermion Induced Crossed Andreev Reflection

This dissertation is devoted to a study of detecting the Majorana fermion induced crossed Andreev reflection. Majorana fermions are particles that constitute their own antiparticles. In condensed matter physics, Majorana fermions are zero energy modes that reside at edges or around vortices of topological superconductors. The special properties of Majorana fermions result in their potential to conduct topological quantum computation, which has been attracting a lot of current research. One of the most important issues in the field of the Majorana fermion physics now is to detect their existence in realistic systems. Among many classes of detecting methods, a transport experiment is the most direct one. The existence of Majorana fermions induces uncommon Andreev reflections that can happen at interfaces between normal regions and superconducting regions. There are two types of Andreev reflections: local Andreev reflection and crossed Andreev reflection. The Majorana fermion induced local Andreev reflection yields zero-bias conductance peaks that have been observed by many experimentalists. Nonetheless, the zero-bias peak alone cannot be taken as a conclusive evidence for the existence of Majorana fermions, because several other mechanisms can lead to analogous results. On the other hand, the Majorana fermion induced crossed Andreev reflection yields equal probabilities of electron tunneling and hole tunneling. It is thus usually believed that a direct measurement of the tunneling current is impossible and a measurement of the shot noise is necessary for the detection of the Majorana fermion induced crossed Andreev reflection. My main contribution is a new experimental proposal that is aimed at changing this opinion. In my proposal, a metallic ring structure is employed to separate the electron tunneling signals and the hole tunneling signals, and as a result the tunneling current is measurable. The key idea behind this proposal is that the constructive interference condition for the tunneling electrons in the metallic ring is different from that for the tunneling holes, utilizing the fact that their wave-vectors are different. The signature of the tunneling current in my intended set-up is that it changes sign from the electron tunneling dominated regime to the hole tunneling dominated regime, where the control parameter is the magnetic flux threading the ring