175 research outputs found
Spectral radius of graphs forbidden or
Let be the graph obtained from a cycle by adding a
new vertex connecting two adjacent vertices in . In this note, we obtain
the graph maximizing the spectral radius among all graphs with size and
containing no subgraph isomorphic to . As a byproduct, we will
show that if the spectral radius , then must
contains all the cycles for unless .Comment: 11 pages, 1 figur
Spectral extremal graphs for the bowtie
Let be the (friendship) graph obtained from triangles by sharing a
common vertex. The -free graphs of order which attain the maximal
spectral radius was firstly characterized by Cioab\u{a}, Feng, Tait and Zhang
[Electron. J. Combin. 27 (4) (2020)], and later uniquely determined by Zhai,
Liu and Xue [Electron. J. Combin. 29 (3) (2022)] under the condition that
is sufficiently large. In this paper, we get rid of the condition on being
sufficiently large if . The graph is also known as the bowtie. We
show that the unique -vertex -free spectral extremal graph is the
balanced complete bipartite graph adding an edge in the vertex part with
smaller size if , and the condition is tight. Our result is a
spectral generalization of a theorem of Erd\H{o}s, F\"{u}redi, Gould and
Gunderson [J. Combin. Theory Ser. B 64 (1995)], which states that
. Moreover, we
study the spectral extremal problem for -free graphs with given number of
edges. In particular, we show that the unique -edge -free spectral
extremal graph is the join of with an independent set of
vertices if , and the condition is tight.Comment: 22 pages, 6 figures. This is the published versio
Soft tissue modelling and facial movement simulation using the finite element method
This thesis presents a framework for soft tissue modelling, facial surgery simulation, and facial movement synthesis based on the volumetric finite element method. Assessment of facial appearance pre- and post-surgery is of major concern for both patients and clinicians. Pre-surgical planning is a prerequisite for successful surgical procedures and outcomes. Early computer-assisted facial models have been geometrically based. They are computationally efficient, but cannot give an accurate prediction for facial surgery simulation. Therefore, in this thesis, the emphasis is placed on physically-based methods, especially the finite element technique. To achieve realistic surgery simulation, soft tissue modelling is of crucial importance. Thus, in this thesis, considerable effort has been directed to develop constitutive equations for facial skeletal muscles. The skeletal muscle model subsequently developed is able to capture the complex mechanical properties of skeletal muscle, which are active, quasi-incompressible, fibre-reinforced and hyperelastic. In addition, to improve the characterisation of in-vivo muscle behaviour, a technique has been developed to visualise the internal fibre arrangement of skeletal muscle using the FEM-NURBS method, which is the combination of the finite element method and the non-uniform rational B-spline solid mathematical representation. Another principal contribution made in this thesis is the three-dimensional finite element facial model, which can be used for the simulations of facial surgery and facial movement. The procedure of one cranio-facial surgery is simulated by using this facial model and the numerical predictions show a good agreement with the patient post-surgical data. In addition, it would be very helpful to also simulate the facial movement and facial expressions. In this thesis, two facial expressions (smile and disgust) and the mouth opening are simulated to assess the post-surgical appearance and test the muscle-driven facial movement simulation method
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Finite element model of ocular adduction with unconstrained globe translation.
Details of the anatomy and behavior of the structures responsible for human eye movements have been extensively elaborated since the first modern biomechanical models were introduced. Based on these findings, a finite element model of human ocular adduction is developed based on connective anatomy and measured optic nerve (ON) properties, as well as active contractility of bilaminar extraocular muscles (EOMs), but incorporating the novel feature that globe translation is not otherwise constrained so that realistic kinematics can be simulated. Anatomy of the hemisymmetric model is defined by magnetic resonance imaging. The globe is modeled as suspended by anatomically realistic connective tissues, orbital fat, and contiguous ON. The model incorporates a material subroutine that implements active EOM contraction based on fiber twitch characteristics. Starting from the initial condition of 26° adduction, the medial rectus (MR) muscle was commanded to contract as the lateral rectus (LR) relaxed. We alternatively modeled absence or presence of orbital fat. During pursuit-like adduction from 26 to 32°, the globe translated 0.52 mm posteriorly and 0.1 mm medially with orbital fat present, but 1.2 mm posteriorly and 0.1 mm medially without fat. Maximum principal strains in the optic disk and peripapillary reached 0.05-0.06, and von-Mises stress 96 kPa. Tension in the MR orbital layer was ~ 24 g-force after 6° adduction, but only ~ 3 gm-f in the whole LR. This physiologically plausible simulation of EOM activation in an anatomically realistic globe suspensory system demonstrates that orbital connective tissues and fat are integral to the biomechanics of adduction, including loading by the ON
Three-dimensional multifractal analysis of trabecular bone under clinical computed tomography
Purpose: An adequate understanding of bone structural properties is critical for predicting fragility conditions caused by diseases such as osteoporosis, and in gauging the success of fracture prevention treatments. In this work we aim to develop multiresolution image analysis techniques to extrapolate high-resolution images predictive power to images taken in clinical conditions. Methods: We performed multifractal analysis (MFA) on a set of 17 ex vivo human vertebrae clinical CT scans. The vertebræ failure loads (FFailure) were experimentally measured. We combined bone mineral density (BMD) with different multifractal dimensions, and BMD with multiresolution statistics (e.g., skewness, kurtosis) of MFA curves, to obtain linear models to predict FFailure. Furthermore we obtained short- and long-term precisions from simulated in vivo scans, using a clinical CT scanner. Ground-truth data - high-resolution images - were obtained with a High-Resolution Peripheral Quantitative Computed Tomography (HRpQCT) scanner. Results: At the same level of detail, BMD combined with traditional multifractal descriptors (Lipschitz-Hölder exponents), and BMD with monofractal features showed similar prediction powers in predicting FFailure (87%, adj. R2). However, at different levels of details, the prediction power of BMD with multifractal features raises to 92% (adj. R2) of FFailure. Our main finding is that a simpler but slightly less accurate model, combining BMD and the skewness of the resulting multifractal curves, predicts 90% (adj. R2) of FFailure. Conclusions: Compared to monofractal and standard bone measures, multifractal analysis captured key insights in the conditions leading to FFailure. Instead of raw multifractal descriptors, the statistics of multifractal curves can be used in several other contexts, facilitating further research.Fil: Baravalle, Rodrigo Guillermo. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Thomsen, Felix Sebastian Leo. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentina. Universidad Nacional del Sur; ArgentinaFil: Delrieux, Claudio Augusto. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Lu, Yongtao. Dalian University of Technology; ChinaFil: Gómez, Juan Carlos. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: StoÅ¡ić, Borko. Universidade Federal Rural Pernambuco; BrasilFil: StoÅ¡ić, Tatijana. Universidade Federal Rural Pernambuco; Brasi
XGBoostPP:Tree-based Estimation of Point Process Intensity Functions
We propose a novel tree-based ensemble method, named XGBoostPP, to nonparametrically estimate the intensity of a point process as a function of covariates. It extends the use of gradient-boosted regression trees (Chen & Guestrin, 2016) to the point process literature via two carefully designed loss functions. The first loss is based on the Poisson likelihood, working for general point processes. The second loss is based on the weighted Poisson likelihood, where spatially dependent weights are introduced to further improve the estimation efficiency for clustered processes. An efficient greedy search algorithm is developed for model estimation, and the effectiveness of the proposed method is demonstrated through extensive simulation studies and two real data analyses. In particular, we report that XGBoostPP achieves superior performance to existing approaches when the dimension of the covariate space is high, revealing the advantages of tree-based ensemble methods in estimating complex intensity function
Relationship between the morphological, mechanical and permeability properties of porous bone scaffolds and the underlying microstructure
Bone scaffolds are widely used as one of the main bone substitute materials. However, many bone scaffold microstructure topologies exist and it is still unclear which topology to use when designing scaffold for a specific application. The aim of the present study was to reveal the mechanism of the microstructure-driven performance of bone scaffold and thus to provide guideline on scaffold design. Finite element (FE) models of five TPMS (Diamond, Gyroid, Schwarz P, Fischer-Koch S and F-RD) and three traditional (Cube, FD-Cube and Octa) scaffolds were generated. The effective compressive and shear moduli of scaffolds were calculated from the mechanical analysis using the FE unit cell models with the periodic boundary condition. The scaffold permeability was calculated from the computational fluid dynamics (CFD) analysis using the 4×4×4 FE models. It is revealed that the surface-to-volume ratio of the Fischer-Koch S-based scaffold is the highest among the scaffolds investigated. The mechanical analysis revealed that the bending deformation dominated structures (e.g., the Diamond, the Gyroid, the Schwarz P) have higher effective shear moduli. The stretching deformation dominated structures (e.g., the Schwarz P, the Cube) have higher effective compressive moduli. For all the scaffolds, when the same amount of change in scaffold porosity is made, the corresponding change in the scaffold relative shear modulus is larger than that in the relative compressive modulus. The CFD analysis revealed that the structures with the simple and straight pores (e.g., Cube) have higher permeability than the structures with the complex pores (e.g., Fischer-Koch S). The main contribution of the present study is that the relationship between scaffold properties and the underlying microstructure is systematically investigated and thus some guidelines on the design of bone scaffolds are provided, for example, in the scenario where a high surface-to-volume ratio is required, it is suggested to use the Fischer-Koch S based scaffold
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