direct numerical simulation of the glottal jet and vocal fold dynamics in a three dimensional laryngeal model an immersed boundary method based flow solver coupled with a finite element solid dynamics solver is employed in order to conduct direct numerical simulations of phonatory dynamics in a three dimensional model of the human larynx the computed features of the glottal flow including mean and peak flow rates and the open and skewness quotients are found to be within the normal physiological range the flow induced vibration pattern shows the classical convergent divergent glottal shape and the vibration amplitude is also found to be typical for human phonation the vocal fold motion is analyzed through the method of empirical eigenfunctions and this analysis indicates a 1 1 modal entrainment between the adduction abduction mode and the mucosal wave mode the glottal jet is found to exhibit noticeable cycle to cycle asymmetric deflections and the mechanism underlying this phenomenon is examined

a green s discrete transformation meshfree method for simulating transient diffusion problems this manuscript presents the formulation and application of the green s discrete transformation method gdtm for the meshfree simulation of transient diffusion problems including those with moving boundaries the gdtm implements a linear combination of time dependent green s basis functions defined on a set of source points to approximate the field in the form of a solution series a discrete transformation is implemented to evaluate unknown coefficients of this series which eliminates the need to use time integration schemes we will study the optimal number and location of the gdtm source points that yield the highest level of accuracy while maintaining a manageable condition number for the resulting linear system of equations the optimal values of these parameters which are inherently independent of the domain geometry are determined such that the basis functions have appropriate features for approximating the field a comprehensive convergence study is presented to show the precision and convergence rate of the gdtm for modeling various diffusion problems we also demonstrate the application of this method for simulating three diffusion problems with complex and evolving morphologies heat transfer in a turbine blade thermal response of a porous material and localized pitting corrosion in stainless steel copyright c 2015 john wiley sons ltd

modeling vocal fold motion with a hydrodynamic semicontinuum model vocal fold vf motion is a fundamental process in voice production and is also a challenging problem for numerical computation because the vf dynamics depend on nonlinear coupling of air flow with the response of elastic channels vf which undergo opening and closing and induce internal flow separation the traditional modeling approach makes use of quasisteady flow approximation or bernoulli s law which ignores air compressibility and is known to be invalid during vf opening a hydrodynamic semicontinuum system for vf motion is presented the airflow is modeled by a modified quasi one dimensional euler system with coupling to vf velocity the vf is modeled by a lumped two mass system with a built in geometric condition on flow separation the modified euler system contains the bernoulli s law as a special case and is derivable from the two dimensional compressible navier stokes equations in the inviscid limit the computational domain contains also solid walls next to vfs flexible walls it is shown numerically that several salient features of vfs are captured especially transients such as the double peaks of the driving subglottal pressures at the opening and the closing stages of vf motion consistent with fully resolved two dimensional direct simulations and experimental data the system is much simpler to compute than a vf model based on two dimensional navier stokes system

relaxation of an optimal control problem involving a perturbed sweeping process we establish first in the setting of infinite dimensional hilbert space a result concerning the existence of solutions for perturbed sweeping processes whose perturbations are lipschitz single valued maps then we use this result to extend to the infinite dimensional setting a relaxation result concerning optimal control problems involving such processes

subject specific computational modeling of human phonation a direct numerical simulation of flow structure interaction is carried out in a subject specific larynx model to study human phonation under physiological conditions the simulation results compare well to the established human data the resulting glottal flow and waveform are found to be within the normal physiological ranges the effects of realistic geometry on the vocal fold dynamics and the glottal flow are extensively examined it is found that the asymmetric anterior posterior laryngeal configuration produces strong anterior posterior asymmetries in both vocal fold vibration and glottal flow which has not been captured in the simplified models it needs to be pointed out that the observations from the current numerical simulation are only valid for the flow conditions investigated the limitations of the study are also discussed

optimal threshold for pareto tail modelling in the presence of outliers abstract the pareto distribution is widely applied in many areas of studies such as economics and sciences an important issues related to pareto tail modelling is to determine the optimal threshold of the pareto distribution one of the methods used for determining the optimal threshold of pareto distribution is by choosing the threshold that minimizes the goodness of fit statistics found based on empirical distribution function edf this study involves determination of the shape parameter of the pareto distribution using the maximum likelihood method and robust method based on the probability integral transform statistics in addition given the particular estimates of the shape parameter comparison of the performance of several edf statistics namely kolmogorov smirnov kuiper anderson darling cramer von misses and watson statistics in determining the optimal threshold in the presence of outliers is studied based on monte carlo simulation since the edf statistics are found smallest for kolmogorov smirnov or kuiper statistics these two edf statistics outperformed other edf statistics considered the findings are illustrated using a sample of household income data of the malaysian population the optimal threshold found can be used to classify the high income earners in malaysia since pareto distribution is one of the most frequently used model to describe the upper tail of income distribution

integration of subdifferentials of nonconvex functions in nonsmooth analysis and optimization subgradients come in many different flavors e g approximate dini proximal clarke generalized see 2 5 6 12 14 191 these subgradients are important and valuable tools however many questions remain unsolved concerning the exact link between the function and its subgradients for instance can two functions not differing by an additive constant have the same subgradients in this paper we study the fundamental problem of determining functions that can be recovered up to an additive constant from the knowledge of their subgradients this integration problem is not very well understood and very few functions or classes of functions are known to be recoverable from their subgradients in section 4 we show that if the basic constraint qualification holds at r then the composition of a closed i e lowersemicontinuous proper convex function with a twice continuously differentiable mapping is determined up to an additive constant by its generalized subgradients actually in this case all above mentioned subgradients are the same beside the obvious theoretical interest of this integration problem it is our hope or perhaps our long term goal that once this problem is better understood we can then tackle the question of uniqueness of solutions to generalized differential equations involving subgradients in place of partial derivatives an example of such an equation that well deserves study is the extended hamilton jacobi equation used in optimal control see clarke 2 let us also mention that a problem similar to the integration problem is the one of determining the set valued mappings that are in fact subgradient set valued mappings uniqueness is not mandatory for a contribution to this problem see janin 8 before we look at some of the known cases where the function can be recovered from its subgradients let us look at some negative examples it is clear that not every function can be recovered up to an additive constant from its subgradients we only need to look at the following two functions 0 x50 0 x10 f x 1 x o g x 2 x o

a constitutive model of the human vocal fold cover for fundamental frequency regulation the elastic as well as time dependent mechanical response of the vocal fold cover epithelium and superficial layer of the lamina propria under tension is one key variable in regulating the fundamental frequency this study examines the hyperelastic and time dependent tensile deformation behavior of a group of human vocal fold cover specimens six male and five female the primary goal is to formulate a constitutive model that could describe empirical trends in speaking fundamental frequency with reasonable confidence the constitutive model for the tissue mechanical behavior consists of a hyperelastic equilibrium network in parallel with an inelastic time dependent network and is combined with the ideal string model for phonation results showed that hyperelastic and time dependent parameters of the constitutive model can be related to observed age related and gender related differences in speaking fundamental frequency the implications of these findings on fundamental frequency regulation are described limitations of the current constitutive model are discussed

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

do wealth distributions follow power laws evidence from rich lists abstract we use data on the wealth of the richest persons taken from the rich lists provided by business magazines like forbes to verify if the upper tails of wealth distributions follow as often claimed a power law behaviour the data sets used cover the world s richest persons over 1996 2012 the richest americans over 1988 2012 the richest chinese over 2006 2012 and the richest russians over 2004 2011 using a recently introduced comprehensive empirical methodology for detecting power laws which allows for testing the goodness of fit as well as for comparing the power law model with rival distributions we find that a power law model is consistent with data only in 35 of the analysed data sets moreover even if wealth data are consistent with the power law model they are usually also consistent with some rivals like the log normal or stretched exponential distributions

size distribution of u s lower tail cities abstract studies that analyzed the size distribution of u s cities have mainly focused on the upper tail and showed that these cities adhere to zipf s law however even though a large number of cities are in the lower tail very few studies have examined the distribution of these small cities because of data limitations we apply reverse pareto and reverse general pareto distributions to analyze u s lower tail cities our results show the power law behavior of lower tail u s cities is accurately represented by both the reverse pareto and general pareto

clarke subgradients for directionally lipschitzian stratifiable functions using a geometric argument we show that under a reasonable continuity condition the clarke subdifferential of a semi algebraic or more generally stratifiable directionally lipschitzian function admits a simple form the normal cone to the domain and limits of gradients generate the entire clarke subdifferential the characterization formula we obtain unifies various apparently disparate results that have appeared in the literature our techniques also yield a simplified proof that closed semialgebraic functions on rn have a limiting subdifferential graph of uniform local dimension n

the power law distribution for the income of poor households abstract this study proposes a reverse pareto model to describe the power law behavior for the lower tail data of income distribution and illustrates an application on malaysian and italian household income data a robust method based on probability integral transform statistic is used for estimating the shape parameter of the reverse pareto model to allow for the existence of outlying observations in the lower tail data besides that the optimal threshold of reverse pareto is determined by using kolmogorov smirnov statistic it is found that the fitted reverse pareto adequately describes the lower tail data of both datasets suggesting that the power law behavior is obeyed in addition the estimated optimal threshold of reverse pareto model can be utilized as an alternative measure for the relative poverty line based on the reverse pareto model the lorenz curve gini and theil coefficients are determined and it is found that low income inequality is observed for the period of the study the fitted lorenz curve shows that nearly 80 of the total household income is owned by the bottom 80 whereas the remaining total household income is owned by the top 20 finally comparison of the reverse pareto model with some alternative distributions such as shifted reverse exponential shifted reverse stretched exponential and shifted reverse lognormal in terms of model fitting for the lower tail data is also conducted the results show that the reverse pareto model outperform all the other models

reducing the number of vocal fold mechanical tissue properties evaluation of the incompressibility and planar displacement assumptions the incompressibility and planar displacement assumptions were used to reduce the number of independent tissue parameters required for the characterization of a structural model of the vocal folds the influence of these simplifying assumptions on the vibratory properties of the model was investigated the purpose was to provide estimates of the error introduced by these assumptions the variability in human tissue properties was accounted for through systematic variation of several material parameters the modal properties of a vocal fold structural model were computed with each assumption and in turn were relaxed to determine their respective effects the results indicated that the incompressibility assumption introduces little error errors introduced by the planar displacement assumption were found to depend on the ratio of the longitudinal stiffness and the transverse stiffness criteria for determining the compatibility of tissue property values from independent studies are also presented

a 2d finite element scheme for fluid solid acoustic interactions and its application to human phonation abstract we present a recently developed approach for the modeling of fluid solid acoustic interaction problems for the efficient numerical solution of the coupled three field problem we apply the finite element method the mechanical and the acoustic fields are approximated by a standard galerkin scheme a residual based stabilization method is chosen for the fluid field the interaction of the eulerian fluid field with the lagrangian mechanical field is based on the arbitrary lagrangian eulerian ale method and is iteratively coupled in a strong sense the solid acoustic interaction is based on continuum mechanics and the fluid acoustic coupling on lighthill s analogy the new steps of our scheme are verified through validation examples finally a fluid solid acoustic simulation of the human phonation process is presented based on a realistic model

sensitivity of a continuum vocal fold model to geometric parameters constraints and boundary conditions the influence of key dimensional parameters motion constraints and boundary conditions on the modal properties of an idealized continuum model of the vocal folds was investigated the ritz method and the finite element method were used for the analysis the model s vibratory modes were determined to be most sensitive to changes in the anterior posterior length of the vocal fold model due to the influence of three dimensional stress components acting in the transverse plane anterior posterior boundary conditions were found to have a significant influence on the vibratory response overestimation of modal frequencies resulted when vibration of the structure was restricted to the transverse plane the overestimation of each modal frequency was proportional to the ratio of longitudinal to transverse young s modulus and was significant for ratio values less than 20

a nonsmooth maximum principle for a controlled nonconvex sweeping process abstract for an optimal control problem governed by a controlled nonconvex sweeping process we provide using an exponential penalization technique existence of solution and nonsmooth necessary conditions in the form of the pontryagin maximum principle our results generalize known theorems in the literature including those in 3 and 23 in several directions indeed the main feature in our sweeping process inclusion is the presence of the subdifferential of a function that is c 1 1 in the interior of its domain instead of the usual normal cone the subdifferential of the indicator function moreover no convexity is assumed on the function and its domain or on the set f t x u and our control mapping f is merely assumed to be lipschitz in x

optimal control of the sweeping process over polyhedral controlled sets abstract the paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given bolza type functional which depends on control and state variables as well as their velocities besides the highly non lipschitzian nature of the unbounded differential inclusion of the controlled sweeping process the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types all of this creates serious challenges for deriving necessary optimality conditions we develop here the method of discrete approximations and combine it with advanced tools of first order and second order variational analysis and generalized differentiation this approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions as a by product of the developed approach we prove the strong w 1 2 convergence of optimal solutions of discrete approximations to a given local minimizer of the continuous time system and derive necessary optimality conditions for the discrete counterparts the established necessary optimality conditions for the sweeping process are illustrated by several examples

a finite element model of vocal fold vibration a finite element model of the vocal fold is developed from basic laws of continuum mechanics to obtain the oscillatory characteristics of the vocal folds the model is capable of accommodating inhomogeneous anisotropic material properties and irregular geometry of the boundaries it has provisions for asymmetry across the midplane both from the geometric and tension point of view which enables one to simulate certain kinds of voice disorders due to vocal fold paralysis it employs the measured viscoelastic properties of the vocal fold tissues the detailed construction of the matrix differential equations of motion is presented followed by the solution scheme finally typical results are presented and validated using an eigenvalue method and a commercial finite element package abaqus

optimal control of a nonconvex perturbed sweeping process abstract the paper concerns optimal control of discontinuous differential inclusions of the normal cone type governed by a generalized version of the moreau sweeping process with control functions acting in both nonconvex moving sets and additive perturbations this is a new class of optimal control problems in comparison with previously considered counterparts where the controlled sweeping sets are described by convex polyhedra besides a theoretical interest a major motivation for our study of such challenging optimal control problems with intrinsic state constraints comes from the application to the crowd motion model in a practically adequate planar setting with nonconvex but prox regular sweeping sets based on a constructive discrete approximation approach and advanced tools of first order and second order variational analysis and generalized differentiation we establish the strong convergence of discrete optimal solutions and derive a complete set of necessary optimality conditions for discrete time and continuous time sweeping control systems that are expressed entirely via the problem data

computation of physiological human vocal fold parameters by mathematical optimization of a biomechanical model with the use of an endoscopic high speed camera vocal fold dynamics may be observed clinically during phonation however observation and subjective judgment alone may be insufficient for clinical diagnosis and documentation of improved vocal function especially when the laryngeal disease lacks any clear morphological presentation in this study biomechanical parameters of the vocal folds are computed by adjusting the corresponding parameters of a three dimensional model until the dynamics of both systems are similar first a mathematical optimization method is presented next model parameters such as pressure tension and masses are adjusted to reproduce vocal fold dynamics and the deduced parameters are physiologically interpreted various combinations of global and local optimization techniques are attempted evaluation of the optimization procedure is performed using 50 synthetically generated data sets the results show sufficient reliability including 0 07 normalized error 96 correlation and 91 accuracy the technique is also demonstrated on data from human hemilarynx experiments in which a low normalized error 0 16 and high correlation 84 values were achieved in the future this technique may be applied to clinical high speed images yielding objective measures with which to document improved vocal function of patients with voice disorders

anterior posterior biphonation in a finite element model of vocal fold vibration in this paper a finite element model is used to simulate anterior posterior biphonation neubauer et al j acoust soc am 110 6 3179 3192 2001 the anterior posterior stiffness asymmetric factor and the anterior posterior shape asymmetric factor describe the asymmetry properties of vocal folds spatiotemporal plot spectral analysis anterior posterior fundamental frequency ratio cross covariation function and correlation length quantitatively estimate the spatial asymmetry of vocal fold oscillations calculation results show that the anterior posterior stiffness asymmetry decreases the spatial coherence of vocal fold vibration when the stiffness asymmetry reaches a certain level the drop in spatial coherence desynchronizes the vibration modes the anterior and posterior sides of the vocal fold oscillate with two independent fundamental frequencies fa and fp the complex spectral characteristics of vocal fold vibration under biphonation conditions can be explained by the linear combination

pareto tails and lognormal body of us cities size distribution abstract we consider a distribution which consists of lower tail pareto lognormal body and upper tail pareto to estimate the size distribution of all us cities this distribution fits the data more accurately than a distribution that comprises of only lognormal and the upper tail pareto

a numerical scheme for a class of sweeping processes the aim of this paper is to study a whole class of first order differential inclusions which fit into the framework of perturbed sweeping process by uniformly prox regular sets after obtaining well posedness results we propose a numerical scheme based on a prediction correction algorithm and we prove its convergence finally we apply these results to a problem coming from the modelling of crowd motion

the size distributions of all indian cities abstract we apply five distributions lognormal double pareto lognormal lognormal upper tail pareto pareto tails lognormal and pareto tails lognormal with differentiability restrictions to estimate the size distribution of all indian cities since india contains numerous small cities it is important to explicitly model the lower tail behavior for studying the distribution of all indian cities our results rigorously confirm using both graphical and formal statistical tests that among these five distributions pareto tails lognormal is a better suited parametrization of the indian city size data verifying that the indian city size distribution exhibits a strong reverse pareto in the lower tail lognormal in the mid range body and pareto in the upper tail

regularization of differential variational inequalities with locally prox regular sets this paper studies for a differential variational inequality involving a locally prox regular set a regularization process with a family of classical differential equations whose solutions converge to the solution of the differential variational inequality the concept of local prox regularity will be termed in a quantified way as r alpha prox regularity

income distribution and inequality measurement the problem of extreme values we examine the statistical performance of inequality indices in the presence of extreme values in the data and show that these indices are very sensitive to the properties of the income distribution estimation and inference can be dramatically affected especially when the tail of the income distribution is heavy even when standard bootstrap methods are employed however use of appropriate semiparametric methods for modelling the upper tail can greatly improve the performance of even those inequality indices that are normally considered particularly sensitive to extreme values

existence of solutions to the nonconvex sweeping process abstract in this note we prove the existence of solutions for the sweeping process problem x t nc t x t a e x t c t x 0 x0 c 0 where c is an arbitrary hausdorff lipschitzean multifunction from i 0 t onto the set of nonempty closed subsets of r d this generalizes a well known result of j j moreau 1971 in sem d analyse convexe montpelier exp 15 in the convex case

normal modes in a continuum model of vocal fold tissues the ritz method is used to calculate eigenmodes and eigenfrequencies in a continuum model of the vocal folds the investigation represents a rectification and extension of previous studies emphasizing the indispensability of utilizing natural boundary conditions when computing the characteristic modes of a system concurring with previous assertions two of the lower order eigenmodes are theorized to play a major role in facilitating self oscillation of the folds during phonation one mode related to vertical phasing is shown to have a more direct control over glottal convergence divergence than indicated in previous calculations unlike lumped element models the continuum model predicts that the eigenfrequencies of the two modes are closely spaced over an extensive range of tissue sizes and stiffnesses this finding may help explain why the two modes entrain so naturally over a wide range of phonatory adjustments in human phonation

local differentiability of distance functions recently clarke stern and wolenski characterized in a hilbert space the closed subsets c for which the distance function dc is continuously differentiable everywhere on an open tube of uniform thickness around c here a corresponding local theory is developed for the property of dc being continuously differentiable outside of c on some neighborhood of a point x c this is shown to be equivalent to the prox regularity of c at x which is a condition on normal vectors that is commonly fulfilled in variational analysis and has the advantage of being verifiable by calculation additional characterizations are provided in terms of dc being locally of class c 1 or such that dc 2 is convex around x for some 0 prox regularity of c at x corresponds further to the normal cone mapping nc having a hypomonotone truncation around x and leads to a formula for pc by way of nc the local theory also yields new insights on the global level of the clarke stern wolenski results and on a property of sets introduced by shapiro as well as on the concept of sets with positive reach considered by federer in the finite dimensional setting

spatio temporal analysis of irregular vocal fold oscillations biphonation due to desynchronization of spatial modes this report is on direct observation and modal analysis of irregular spatio temporal vibration patterns of vocal fold pathologies in vivo the observed oscillation patterns are described quantitatively with multiline kymograms spectral analysis and spatio temporal plots the complex spatio temporal vibration patterns are decomposed by empirical orthogonal functions into independent vibratory modes it is shown quantitatively that biphonation can be induced either by left right asymmetry or by desynchronized anterior posterior vibratory modes and the term ap anterior posterior biphonation is introduced the presented phonation examples show that for normal phonation the first two modes sufficiently explain the glottal dynamics the spatio temporal oscillation pattern associated with biphonation due to left right asymmetry can be explained by the first three modes higher order modes are required to describe the pattern for biphonation induced by anterior posterior vibrations spatial irregularity is

interpretation of biomechanical simulations of normal and chaotic vocal fold oscillations with empirical eigenfunctions empirical orthogonal eigenfunctions are extracted from biomechanical simulations of normal and chaotic vocal fold oscillations for normal phonation two dominant empirical eigenfunctions capture the vibration patterns of the folds and exhibit a 1 1 entrainment the eigenfunctions show some correspondence to theoretical low order normal modes of a simplified three dimensional elastic continuum and to the normal modes of a linearized two mass model the eigenfunctions also facilitate a physical interpretation of energy transfer mechanisms in vocal fold dynamics subharmonic regimes and chaotic oscillations are observed during simulations of a lax cover in which case at least three empirical eigenfunctions are necessary to capture the resulting vocal fold oscillations these chaotic oscillations might be understood in terms of a desynchronization of a few of the low order modes and may be related to mechanisms of creaky voice or vocal fry furthermore some of the empirical eigenfunctions captured during complex oscillations correspond to higher order normal modes described in earlier theoretical work the empirical eigenfunctions may also be useful in the design of lower order models valid over the range for which the empirical eigenfunctions remain more or less constant and may help facilitate bifurcation analyses of the biomechanical simulation

a robust and efficient estimator for the tail index of inverse pareto distribution abstract based on the probability integral transform statistic finkelstein et al 2006 have proposed a robust estimator for the shape parameter of pareto distribution in this paper based on the same method a robust and efficient estimator for the shape parameter of the inverse pareto distribution is developed assuming that the threshold parameter is known to study the robustness properties of this new estimator we derive the asymptotic variance breakdown point and gross error sensitivity however since the inverse pareto distribution is literally an inverse of the pareto distribution some derivations and proofs for the probability integral transform statistic estimator presented in this paper are found closely related to those provided by finkelstein et al 2006 the performance of this new estimator and the maximum likelihood estimator is assessed through a simulation study for the application an inverse pareto distribution is fitted to the lower tail data of malaysian household incomes for the year of 2014 involving the proposed estimator in order to allow for the presence of outliers based on the inverse pareto model the parametric lorenz curve is fitted and the gini coefficient is estimated to measure the income inequality of poor households in malaysia

sweeping process with regular and nonregular sets abstract differential inclusions involving the normal cone to a moving set are investigated a special attention is paid to the sweeping process associated with sets for which no regularity assumption is required