the new upper bounds on the spectral radius of weighted graphs abstract let us consider weighted graphs where the weights of the edges are positive definite matrices the eigenvalues of a weighted graph are the eigenvalues of its adjacency matrix and the spectral radius of a weighted graph is also the spectral radius of its adjacency matrix in this paper we obtain two upper bounds for the spectral radius of weighted graphs and compare with a known upper bound we also characterize graphs for which the upper bounds are attained

connected graphs of fixed order and size with maximal index some spectral bounds the index or spectral radius of a simple graph is the largest eigenvalue of its adjacency matrix for connected graphs of fixed order and size the graphs with maximal index are not yet identified in the general case it is known for a long time that these graphs are nested split graphs or threshold graphs in this paper we use the eigenvector techniques for getting some new lower and upper bounds on the index of nested split graphs besides we give some computational results in order to compare these bounds

spectra of digraphs in this primarily expository paper we survey classical and some more recent results on the spectra of digraphs equivalently the spectra of 0 1 matrices with emphasis on the spectral radius

a bound on the spectral radius of graphs with e edges the spectral radius p a of the adjacency matrix a of a graph g with e edges satisfiesp a i l equalityoccnrsifandonlyif e i andgisa disjoint union of the complete graph k and isolated vertices 0

the spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices in this paper we determine graphs with the largest spectral radius among all the unicyclic and all the bicyclic graphs with n vertices and k pendant vertices respectively

prediction of the mechanical response of the femur with uncertain elastic properties abstract a mandatory requirement for any reliable prediction of the mechanical response of bones based on quantitative computer tomography is an accurate relationship between material properties usually young s modulus e and bone density many such e relationships are available based on different experiments on femur specimens with a large spread due to uncertainties the first goal of this study is to pool and analyze the relevant available experimental data and develop a stochastic e relationship this analysis highlights that there is no experimental data available to cover the entire density range of the human femur and that some popular e relationships are based on data that contains extreme scatter while others are based on a very limited amount of information the second goal is to use the newly developed stochastic e relationship in high order finite element analyses feas for the computation of strains and displacements in two human proximal femurs mimicking in vitro experiments when compared with the experimental observations the fea predictions using the median of the stochastic e relationship follow the underlying distribution of the stochastic e relationship thus most deviations of the fea predictions from experimental observations can possibly be explained by uncertain elastic properties of the femur

individual density elasticity relationships improve accuracy of subject specific finite element models of human femurs abstract in a previous study on subject specific finite element models we found that appropriate density elasticity relationships to compute the mechanical behavior of femurs seem to be subject specific the purpose of this study was to test the hypothesis that the predictive error of a cohort of subject specific finite element models is lower with subject specific density elasticity relationships than with a cohort specific density elasticity relationship finite element analysis and inverse optimization based on response surface methodology were employed to test the hypothesis subject specific fe models of 17 human femurs and corresponding experimental data from biomechanical tests were taken from a previous study a power function for the relation between radiological bone density and elastic modulus was set up with the optimization variables a and b e mpa a q c t b gk 2 hpo 4 cm 3 the goal of the optimization was to minimize the root mean square error in percent rmse between computational and experimental results a wilcoxon test p 0 05 was performed on all absolute relative errors between the two groups subject specific functions vs cohort specific function the subject specific functions resulted in a 6 lower overall prediction error and a 6 lower rmse than the cohort specific function p e mpa 12486 q c t 1 16 gk 2 hpo 4 cm 3 we conclude that individual density elasticity relationships improve the accuracy of subject specific finite element models future subject specific finite element analyses of bones should include the individuality of the elastic properties by a stochastic density elasticity relationship with mean and standard deviation of a and b

the least eigenvalue of a graph with cut vertices in this paper we characterize the unique graph whose least eigenvalue attains the minimum among all connected graphs of fixed order and given number of cut vertices and then obtain a lower bound for the least eigenvalue of a connected graph in terms of the number of cut vertices during the discussion we also get some results for the spectral radius of a connected bipartite graph and its upper bound

maximizing the spectral radius of graphs with fixed minimum degree and edge connectivity abstract the spectral radius g of a graph g is the largest eigenvalue of the adjacency matrix a g suppose a graph g 0 maximizes the spectral radius over the class of graphs of order n with fixed minimum degree and edge connectivity in this paper we mainly show that g 0 b n where b n is obtained by adding edges between k 1 and k n 1 a property of the adjacency matrix of g 0 is also obtained moreover graphs that maximize g over the class of graphs with minimum degree and edge connectivity for 0 1 2 3 are completely determined

assessing accuracy of mammography in the presence of verification bias and intrareader correlation la performance des tests diagnostiques medicaux est souvent evaluee en comparant le resultat du test au vrai etat de la maladie du patient l analyse des courbes de caracteristiques de fonctionnement roc peut etre utilisee pour resumer la precision du test cependant une telle analyse peut rencontrer plusieurs difficultes dans la pratique reelle une difficulte est la verification du biais c est a dire que l evaluation de l etat de la maladie peut etre partiellement disponible et la probabilite de determination de la maladie peut dependre aussi bien du resultat du test que des caracteristiques du sujet une deuxieme difficulte est que les tests interpretes par le meme lecteur peuvent ne pas etre independants a l aide des equations d estimation nous generalisons des methodes proposees pour prendre en compte ces problemes nous comparons la performance de differents estimateurs de la precision en utilisant les estimateurs robustes de la variance sandwich pour permettre une inference asymptotique valide nous montrons que dans le contexte d une cohorte d observation ou de bonnes informations sur les covariables sont disponibles une approche par des equations d estimations ponderees wee peut etre preferable pour sa robustesse a un modele mal specifie nous appliquons la methodologie a la mammographie comme realisee dans la communaute des radiologues

higher order multi resolution topology optimization using the finite cell method this article presents a detailed study on the potential and limitations of performing higher order multi resolution topology optimization with the finite cell method to circumvent stiffness overestimation in high contrast topologies a length scale is applied on the solution using filter methods the relations between stiffness overestimation the analysis system and the applied length scale are examined while a high resolution topology is maintained the computational cost associated with nested topology optimization is reduced significantly compared with the use of first order finite elements this reduction is caused by exploiting the decoupling of density and analysis mesh and by condensing the higher order modes out of the stiffness matrix

the spectral radius of trees on k pendant vertices abstract in this paper we consider the following problem of all trees of order n with k pendant vertices n k fixed which achieves the maximal spectral radius we show that the maximal spectral radius is obtained uniquely at t n k where t n k is a tree obtained from a star k 1 k and k paths of almost equal lengths by joining each pendant vertex of k 1 k to an end vertex of one path we also discuss the spectral radius of t n k and get some results

the majorization theorem of connected graphs abstract let d 1 d 2 d n and d 1 d 2 d n be two non increasing degree sequences we say is majorizated by denoted by if and only if i 1 n d i i 1 n d i and i 1 j d i i 1 j d i for all j 1 2 n if the degree of vertex v is resp not equal to 1 then we call v a pendant resp non pendant vertex of g we use c to denote the class of connected graphs with degree sequence suppose and are two non increasing c cyclic degree sequences let g and g be the graphs with greatest spectral radii in c and c respectively in this paper we shall prove that if g and g have the same number of pendant vertices and the degrees of all non pendant vertices of g are greater than c then g g

on the maximal index of graphs with a prescribed number of edges abstract among the graphs with a prescribed number of edges those with maximal index are determined the result confirms a conjecture of brualdi and hoffman

on the spectral radius of 0 1 matrices we determine the maximum spectral radius for 0 1 matrices with k2 andk2 1 1 s respectively and for symmetric 0 1 matrices with zero trace and e k21 s graphs with e edges in all cases equality is characterized

the finite cell method for three dimensional problems of solid mechanics this article presents a generalization of the recently proposed finite cell method to three dimensional problems of linear elasticity the finite cell method combines ideas from embedding or fictitious domain methods with the p version of the finite element method besides supporting a fast simple generation of meshes it also provides high convergence rates mesh generation for a boundary representation of solids and for voxel based data obtained from ct scans is addressed in detail in addition the implementation of non homogeneous neumann boundary conditions and the computation of cell matrices based on a composed integration is presented the performance of the proposed method is demonstrated by three numerical examples including the elastostatic computation of a human bone biopsy

likelihood approximation by numerical integration on sparse grids the calculation of likelihood functions of many econometric models requires the evaluation of integrals without analytical solutions approaches for extending gaussian quadrature to multiple dimensions discussed in the literature are either very specific or suffer from exponentially rising computational costs in the number of dimensions we propose an extension that is very general and easily implemented and does not suffer from the curse of dimensionality monte carlo experiments for the mixed logit model indicate the superior performance of the proposed method over simulation techniques

probabilistic finite element analysis of the uncemented hip replacement effect of femur characteristics and implant design geometry in the present study a probabilistic finite element tool was assessed using an uncemented total hip replacement model fully bonded and frictional interfaces were investigated for combinations of three proximal femurs and two implant designs the proxima short stem and the ips hip stem prostheses the monte carlo method was used with two performance indicators the percentage of bone volume that exceeded specified strain limits and the maximum nodal micromotion the six degrees of freedom of bone implant relative position magnitude of the hip contact force l and spatial direction of l were the random variables the distal portion of the proximal femurs was completely constrained and some of the main muscle forces acting in the hip were applied the coefficients of the linear approximation between the random variables and the output were used as the sensitivity values in all cases bone implant position related parameters were the most sensitive parameters the results varied depending on the femur the implant design and the interface conditions values of maximum nodal micromotion agreed with results from previous studies confirming the robustness of the implemented computational tool it was demonstrated that results from a single model study should not be generalised to the entire population of femurs and that bone variability is an important factor that should be investigated in such analyses

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

the greedy strategy for optimizing the perron eigenvalue we address the problems of minimizing and of maximizing the spectral radius over a compact family of non negative matrices those problems being hard in general can be efficiently solved for some special families we consider the so called product families where each matrix is composed of rows chosen independently from given sets a recently introduced greedy method works very fast however it is applicable mostly for strictly positive matrices for sparse matrices it often diverges and gives a wrong answer we present the selective greedy method that works equally well for all non negative product families including sparse ones for this method we prove a quadratic rate of convergence and demonstrate its efficiency in numerical examples the numerical examples are realised for two cases finite uncertainty sets and polyhedral uncertainty sets given by systems of linear inequalities in dimensions up to 2000 the matrices with minimal maximal spectral radii in product families are found within a few iterations applications to dynamical systems and to the graph theory are considered

stochastic description of the peak hip contact force during walking free and going upstairs abstract uncertainty quantification for the response of a patient specific femur is mandatory when advocating finite element fe models in clinical applications reliable stochastic descriptions of physiological hip contact forces are an essential prerequisite for such an endeavor we therefore analyze the in vivo available data of seven individuals from hip98 and orthoload with the objective of characterizing the variability of the peak hip contact force magnitude and two corresponding spatial angles in sagittal and frontal plane during walking free and going upstairs regression analyses with linear mixed effects models were performed resulting in six normal random variables one for each force component and activity importantly the statistical analysis accounts for the fact that same individuals performed both activities the mean of the peak force magnitude was found to be linearly dependent on the body weight with an additional activity specific intercept and all variances were dominated by the inter patient variability no distinct correlation was found between the two angles and the force magnitude the proposed stochastic description of the peak hip contact force during walking free and going upstairs contributes towards future uncertainty quantification of patient specific fe models

estimating disease prevalence from two phase surveys with non response at the second phase summary in this paper we compare several methods for estimating population disease prevalence from data collected by two phase sampling when there is non response at the second phase the traditional weighting type estimator requires the missing completely at random assumption and may yield biased estimates if the assumption does not hold we review two approaches and propose one new approach to adjust for non response assuming that the non response depends on a set of covariates collected at the first phase an adjusted weighting type estimator using estimated response probability from a response model a modelling type estimator using predicted disease probability from a disease model and a regression type estimator combining the adjusted weighting type estimator and the modelling type estimator these estimators are illustrated using data from an alzheimer s disease study in two populations simulation results are presented to investigate the performances of the proposed estimators under various situations

misspecified maximum likelihood estimates and generalised linear mixed models summary we investigate the impact of model violations on the estimate of a regression coefficient in a generalised linear mixed model specifically we evaluate the asymptotic relative bias that results from incorrect assumptions regarding the random effects we compare the impact of model violation for two parameterisations of the regression model substantial bias in the conditionally specified regression point estimators can result from using a simple random intercepts model when either the random effects distribution depends on measured covariates or there are autoregressive random effects a marginally specified regression structure that is estimated using maximum likelihood is much less susceptible to bias resulting from random effects model misspecification

roc curve estimation when covariates affect the verification process summary a receiver operating characteristic roc curve is commonly used to measure the accuracy of a medical test it is a plot of the true positive fraction sensitivity against the false positive fraction 1 specificity for increasingly stringent positivity criterion bias can occur in estimation of an roc curve if only some of the tested patients are selected for disease verification and if analysis is restricted only to the verified cases this bias is known as verification bias in this paper we address the problem of correcting for verification bias in estimation of an roc curve when the verification process and efficacy of the diagnostic test depend on covariates our method applies the em algorithm to ordinal regression models to derive ml estimates for roc curves as a function of covariates adjusted for covariates affecting the likelihood of being verified asymptotic variance estimates are obtained using the observed information matrix of the observed data these estimates are derived under the missing at random assumption which means that selection for disease verification depends only on the observed data i e the test result and the observed covariates we also address the issues of model selection and model checking finally we illustrate the proposed method on data from a two phase study of dementia disorders where selection for verification depends on the screening test result and age

to what extent can linear finite element models of human femora predict failure under stance and fall loading configurations proximal femur strength estimates from computed tomography ct based finite element fe models are finding clinical application published models reached a high in vitro accuracy yet many of them rely on nonlinear methodologies or internal best fitting of parameters the aim of the present study is to verify to what extent a linear fe modelling procedure fully based on independently determined parameters can predict the failure characteristics of the proximal femur in stance and sideways fall loading configurations fourteen fresh frozen cadaver femora were ct scanned seven femora were tested to failure in stance loading conditions and seven in fall fracture was monitored with high speed videos linear fe models were built from ct images according to a procedure already validated in the prediction of strains an asymmetric maximum principal strain criterion 0 73 tensile 1 04 compressive limit was used to define a node based risk factor rf fe predicted failure load mode tensile compressive and location were determined from the first node reaching rf 1 fe predicted and measured failure loads were highly correlated r 2 0 89 see 814n in all specimens fe models correctly identified the failure mode tensile in stance compressive in fall and the femoral region where fracture started supero lateral neck aspect the location of failure onset was accurately predicted in eight specimens in summary a simple fe model adaptable in the future to multiple loads e g including muscles was highly correlated with experimental failure in two loading conditions on specimens ranging from normal to osteoporotic thus it can be suitable for use in clinical studies

spectral radius of uniform hypergraphs abstract we prove a result concerning the behavior of the spectral radius of a hypergraph under relocations of edges we determine the unique hypergraphs with maximum spectral radius among connected k uniform hypergraphs with fixed number of pendant edges the unique k uniform hypertrees with respectively maximum second maximum and third maximum spectral radius the unique k uniform unicyclic hypergraphs k uniform linear unicyclic hypergraphs respectively with respectively maximum and second maximum spectral radius we also determine the unique hypergraphs with maximum spectral radius among k uniform unicyclic hypergraphs with given girth

spectral radius of bipartite graphs abstract let k p q be positive integers with k p q 1 we prove that the maximum spectral radius of a simple bipartite graph obtained from the complete bipartite graph k p q of bipartition orders p and q by deleting k edges is attained when the deleted edges are all incident on a common vertex which is located in the partite set of order q our method is based on new sharp upper bounds on the spectral radius of bipartite graphs in terms of their degree sequences

the signless laplacian spectral radius of tricyclic graphs and trees with k pendant vertices abstract in this paper we consider the following problem of all tricyclic graphs or trees of order n with k pendant vertices n k fixed which achieves the maximal signless laplacian spectral radius we determine the graph with the largest signless laplacian spectral radius among all tricyclic graphs with n vertices and k pendant vertices then we show that the maximal signless laplacian spectral radius among all trees of order n with k pendant vertices is obtained uniquely at t n k where t n k is a tree obtained from a star k 1 k and k paths of almost equal lengths by joining each pendant vertex to one end vertex of one path we also discuss the signless laplacian spectral radius of t n k and give some results

on the spectral radii and the signless laplacian spectral radii of c cyclic graphs with fixed maximum degree if g is a connected undirected simple graph on n vertices and n c 1 edges then g is called a c cyclic graph specially g is called a tricyclic graph if c 3 let g be the maximum degree of g in this paper we determine the structural characterizations of the c cyclic graphs which have the maximum spectral radii resp signless laplacian spectral radii in the class of c cyclic graphs on n vertices with fixed maximum degree n c 12 moreover we prove that the spectral radius of a tricyclic graph g strictly increases with its maximum degree when g 1 6 2n32 and identify the first six largest spectral radii and the corresponding graphs in the class of tricyclic graphs on n vertices

on the minimum spectral radius of matrices of zeros and ones abstract we consider the minimum spectral radius for an n n matrix of 0 s and 1 s having a specified number of 0 s we determine this minimum spectral radius when n 2 n 2 and bound it between two consecutive integers for all other values of

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

spectral simplex method we develop an iterative optimization method for finding the maximal and minimal spectral radius of a matrix over a compact set of nonnegative matrices we consider matrix sets with product structure i e all rows are chosen independently from given compact sets row uncertainty sets if all the uncertainty sets are finite or polyhedral the algorithm finds the matrix with maximal minimal spectral radius within a few iterations it is proved that the algorithm avoids cycling and terminates within finite time the proofs are based on spectral properties of rank one corrections of nonnegative matrices the practical efficiency is demonstrated in numerical examples and statistics in dimensions up to 500 some generalizations to non polyhedral uncertainty sets including euclidean balls are derived finally we consider applications to spectral graph theory mathematical economics dynamical systems and difference equations

modeling continuous diagnostic test data using approximate dirichlet process distributions there is now a large literature on the analysis of diagnostic test data in the absence of a gold standard test latent class analysis is most often used to estimate the prevalence of the condition of interest and the properties of the diagnostic tests when test results are measured on a continuous scale both parametric and nonparametric models have been proposed parametric methods such as the commonly used bi normal model may not fit the data well nonparametric methods developed to date have been relatively complex to apply in practice and their properties have not been carefully evaluated in the diagnostic testing context in this paper we propose a simple yet flexible bayesian nonparametric model which approximates a dirichlet process for continuous data we compare results from the nonparametric model with those from the bi normal model via simulations investigating both how much is lost in using a nonparametric model when the bi normal model is correct and how much can be gained in using a nonparametric model when normality does not hold we also carefully investigate the trade offs that occur between flexibility and identifiability of the model as different dirichlet process prior distributions are used motivated by an application to tuberculosis clustering we extend our nonparametric model to accommodate two additional dichotomous tests and proceed to analyze these data using both the continuous test alone as well as all three tests together copyright 2011 john wiley sons ltd

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

a bound on the spectral radius of graphs abstract let g be a simple connected graph with n vertices and m edges let a be the adjacency matrix of g the spectral radius a of a satisfies a 2m n 1 with equality if and only if g is isomorphic to one of the following two graphs a the star k1 n 1 b the complete graph kn

the maximal eigenvalue of 0 1 matrices with prescribed number of ones abstract we determine the maximum spectral radius for 0 1 matrices with m 2 l ones for l 2 m 2 m 3 for all m and for a fixed l and m m l similar results are obtained for symmetric 0 1 matrix with zero diagonal in all cases equality is characterized

the spectral radius of bicyclic graphs with prescribed degree sequences restricted to the bicyclic graphs with prescribed degree sequences we determine the unique graph with the largest spectral radius with respect to the adjacency matrix

spectral radius of 0 1 tensor with prescribed number of ones abstract for any r order 0 1 tensor a with e ones we prove that the spectral radius of a is at most e r 1 r with the equality holds if and only if e k r for some integer k and all ones forms a principal sub tensor 1 k k we also prove a stability result for general tensor a with e ones where e k r l with relatively small l using the stability result we completely characterized the tensors achieving the maximum spectral radius among all r order 0 1 tensor a with k r l ones for r 1 l r and k sufficiently large

imputation approaches for estimating diagnostic accuracy for multiple tests from partially verified designs interest often focuses on estimating sensitivity and specificity of a group of raters or a set of new diagnostic tests in situations in which gold standard evaluation is expensive or invasive various authors have proposed semilatent class modeling approaches for estimating diagnostic accuracy in this situation this article presents imputation approaches for this problem i show how imputation provides a simpler way of performing diagnostic accuracy and prevalence estimation than the use of semilatent modeling furthermore the imputation approach is more robust to modeling assumptions and in general there is only a moderate efficiency loss relative to a correctly specified semilatent class model i apply imputation to a study designed to estimate the diagnostic accuracy of digital radiography for gastric cancer the feasibility and robustness of imputation is illustrated with analysis asymptotic results and simulations

validation of subject specific automated p fe analysis of the proximal femur abstract background the use of subject specific finite element fe models in clinical practice requires a high level of automation and validation in yosibash et al 2007a reliable simulations of the human proximal femur by high order finite element analysis validated by experimental observations j biomechanics 40 3688 3699 a novel method for generating high order finite element p fe models from ct scans was presented and validated by experimental observations on two fresh frozen femurs harvested from a 30 year old male and 21 year old female herein we substantiate the validation process by enlarging the experimental database 54 year old female femur improving the method and examine its robustness under different ct scan conditions approach a fresh frozen femur of a 54 year old female was scanned under two different environments in air and immersed in water dry and wet ct thereafter the proximal femur was quasi statically loaded in vitro by a 1000 n load the two qct scans were manipulated to generate p fe models that mimic the experimental conditions we compared p fe displacements and strains of the wet ct model to the dry ct model and to the experimental results in addition the material assignment strategy was reinvestigated the inhomogeneous young s modulus was represented in the fe model using two different methods directly extracted from the ct data and using continuous spatial functions as in yosibash et al 2007a reliable simulations of the human proximal femur by high order finite element analysis validated by experimental observations j biomechanics 40 3688 3699 results excellent agreement between dry and wet fe models was found for both displacements and strains i e the method is insensitive to ct conditions and may be used in vivo good agreement was also found between fe results and experimental observations the spatial functions representing young s modulus are local and do not influence strains and displacements prediction finally the p fe results of all three fresh frozen human femurs compare very well to experimental observations exemplifying that the presented method may be in a mature stage to be used in clinical computer aided decision making

spectral radius and degree sequence of a graph abstract let g be a simple connected graph of order n with degree sequence d 1 d 2 d n in non increasing order the spectral radius g of g is the largest eigenvalue of its adjacency matrix for each positive integer l at most n we give a sharp upper bound for g by a function of d 1 d 2 d l which generalizes a series of previous results

on the maximal index of connected graphs abstract let h n e denote the set of all connected graphs having n vertices and e edges the graphs in h n n k with maximal index are determined for k of form r 2 1 and n arbitrary

incorporating uncertainty in mechanical properties for finite element based evaluation of bone mechanics finite element fe models of bone developed from computed tomography ct scan data are used to evaluate stresses and strains load transfer and fixation of implants and potential for fracture the experimentally derived relationships used to transform ct scan data in hounsfield unit to modulus and strength contain substantial scatter the scatter in these relationships has potential to impact the results and conclusions of bone studies the objectives of this study were to develop a computationally efficient probabilistic fe based platform capable of incorporating uncertainty in bone property relationships and to apply the model to a representative analysis variability in stresses and fracture risk was predicted in five proximal femurs under stance loading conditions based on published variability in strength and modulus relationships derived in the proximal femur the probabilistic analysis predicted the distributions of stress and risk for the five femurs analyzed the 1 and 99 percentile bounds varied by an average of 17 3 mpa for stress and by 0 28 for risk in each femur the predicted variability in risk was greater than 50 of the mean risk calculated with obvious implications for clinical assessment results using the advanced mean value amv method required only seven analysis trials 1 h and differed by less than 2 when compared to a 1000 trial monte carlo simulation 400 h the probabilistic modeling platform developed has broad applicability to bone studies and can be similarly implemented to investigate other loading conditions structures sources of uncertainty or output measures of interest r 2007 elsevier ltd all rights reserved

extremal graph characterization from the bounds of the spectral radius of weighted graphs abstract we consider weighted graphs where the edge weights are positive definite matrices the eigenvalues of a graph are the eigenvalues of its adjacency matrix we obtain a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained

connected graphs with maximal q index the one dominating vertex case abstract by the signless laplacian of a simple graph g we mean the matrix q g d g a g where a g d g denote respectively the adjacency matrix and the diagonal matrix of vertex degrees of g for every pair of positive integers n k it is proved that if 3 k n 3 then h n k the graph obtained from the star k 1 n 1 by joining a vertex of degree 1 to k 1 other vertices of degree 1 is the unique connected graph that maximizes the largest signless laplacian eigenvalue over all connected graphs with n vertices and n k edges

the signless laplacian spectral radius of graphs with a prescribed number of edges abstract the signless laplacian spectral radius of a graph is the largest eigenvalue of its signless laplacian matrix in the paper the graph with maximal signless laplacian spectral radius among all graphs with given size and clique number is characterized as applications we determine the graph with maximal signless laplacian spectral radius among all graphs with given size and characterize the graph with maximal signless laplacian spectral radius among all graphs with given size and chromatic number

new method and new results on the order of spectral radius this paper presents a simple method to order trees unicyclic graphs and bicyclic graphs according to their spectral radii which is based on the application of the majorization theorem of tree unicyclic and bicyclic graphs respectively moreover we obtain some new results on the order of spectral radii of unicyclic and bicyclic graphs by employing this new method

some upper bounds on the spectral radius of a graph abstract for a graph g the spectral radius g of g is the largest eigenvalue of its adjacency matrix the coalescence of two graphs h with a root v and k with a root w is obtained by identifying v and w from disjoint union of h and k in this paper we investigate the upper bounds of the spectral radius of the coalescence of two graphs which generalize some results by passbani and salemi in 2019 furthermore we show that if the graph g u v is obtained from a connected graph g by contracting the internal edge uv which not contained in any triangle of g then g g u v the corresponding extremal graphs are characterized completely and also extend a result of hoffman and smith as an application a new sharp upper bound on the spectral radius of a tree is provided

graphs with maximal signless laplacian spectral radius abstract by the signless laplacian of a simple graph g we mean the matrix q g d g a g where a g d g denote respectively the adjacency matrix and the diagonal matrix of vertex degrees of g it is known that connected graphs g that maximize the signless laplacian spectral radius q g over all connected graphs with given numbers of vertices and edges are degree maximal for a maximal graph g with n vertices and r distinct vertex degrees r r 1 1 it is proved that q g q h for some maximal graph h with n 1 respectively n vertices and the same number of edges as g if either g has precisely two dominating vertices or there exists an integer i 2 i r 2 respectively if there exist positive integers i l with l 2 i r 2 such that i r 1 i n 1 respectively i r 1 i l r l 1 graphs that maximize q g over the class of graphs with m edges and m k vertices for k 0 1 2 3 are completely determined

a new upper bound for the spectral radius of graphs with girth at least 5 let g be a simple connected graph with v g v1 v 2 v n and girth at least 5 let be the maximum degree of g in this paper we present a new sharp upper bound for the spectral radius of g as follows

bounds on the spectral radius of graphs with e edges abstract we give upper bounds for the spectral radius of a graph with e edges provided that there is no complete graph with e edges our bounds are sharp for i the complete graphs with one two or three edges removed ii the complete graph with one added vertex and edge

sharp upper bounds on the spectral radius of graphs abstract let g be a simple connected graph with n vertices m edges and degree sequence d 1 d 2 d n the spectral radius g of graph g is the largest eigenvalue of its adjacency matrix in this paper we present some sharp upper bounds of the spectral radius in terms of the degree sequence of graphs

optimal designs of two stage studies for estimation of sensitivity specificity and positive predictive value the cost efficiency of estimation of sensitivity specificity and positive predictive value from two stage sampling designs is considered assuming a relatively cheap test classifies first stage subjects into several categories and an expensive gold standard is applied at stage two simple variance formulae are derived and used to find optimal designs for a given cost ratio the utility of two stage designs is measured by the reduction in variances compared with one stage simple random designs separate second stage design is also compared with proportional allocation pa the maximum percentage reductions in variance from two stage designs for sensitivity specificity and positive predictive value estimation are p per cent 1 p per cent and w respectively where p is the population prevalence of disease and w the population percentage of test negatives the optimum allocation of stage two resources is not obvious the optimum proportion of true cases at stage two may even be less than under pa pa is near optimal for sensitivity estimation in most cases when prevalence is low but inefficient compared with the optimal scheme for specificity

uncertainty quantification for personalized analyses of human proximal femurs computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads which affect the simulation results to quantify the influence we developed a probabilistic framework based on polynomial chaos pc that propagates stochastic input variables through any computational model we considered a stochastic e relationship and a stochastic hip contact force representing realistic variability of experimental data their influence on the prediction of principal strains 1 and 3 was quantified for one human proximal femur including sensitivity and reliability analysis large variabilities in the principal strain predictions were found in the cortical shell of the femoral neck with coefficients of variation of 40 between 60 and 80 of the variance in 1 and 3 are attributable to the uncertainty in the e relationship while 10 are caused by the load magnitude and 5 30 by the load direction principal strain directions were unaffected by material and loading uncertainties the antero superior and medial inferior sides of the neck exhibited the largest probabilities for tensile and compression failure however all were very small pf 0 001 in summary uncertainty quantification with pc has been demonstrated to efficiently and accurately describe the influence of very different stochastic inputs which increases the credibility and explanatory power of personalized analyses of human proximal femurs

on linear combinations of biomarkers to improve diagnostic accuracy we consider combining multiple biomarkers to improve diagnostic accuracy su and liu derived the linear combinations that maximize the area under the receiver operating characteristic roc curves these linear combinations however may have unsatisfactory low sensitivity over a certain range of desired specificity in this paper we consider maximizing sensitivity over a range of specificity we first present a simpler proof for su and liu s main theorem and further investigate some other optimal properties of their linear combinations we then derive alternative linear combinations that have higher sensitivity over a range of high or low specificity the methods are illustrated using data from a study evaluating biomarkers for coronary heart disease

bounds on graph eigenvalues abstract upper and lower estimates are found for the maximum of the kth eigenvalue of a graph as a function of the number of vertices or edges

the majorization theorem of extremal pseudographs a pseudograph is a graph in which both loops and multiple edges are permitted suppose d1 d2 dn and d1 d2 dn are two positive non increasing degree sequences we write if and only if i 1ndi i 1ndi and i 1jdi i 1jdi for all j 1 2 n let be the class of connected undirected pseudographs with degree sequence let g and g be the spectral radius and signless laplacian spectral radius of g respectively in this paper the extremal pseudographs with the largest respectively signless laplacian spectral radii in are characterized furthermore we show that if g and g are the pseudographs with the largest respectively signless laplacian spectral radii in and respectively then g g and g g