scaling behavior of stochastic minimization algorithms in a perfect funnel landscape we determined scaling laws for the numerical effort to find the optimal configurations of a simple model potential energy surface pes with a perfect funnel structure that reflects key characteristics of the protein interactions generalized monte carlo methods mcm stun avoid an enumerative search of the pes and thus provide a natural resolution of the levinthal paradox we find that the computational effort grows with approximately the eighth power of the system size for mcm and stun while a genetic algorithm was found to scale exponentially the scaling behaviour of a derived lattice model is also rationalized

vibration of an axially moving string with geometric non linearity and translating acceleration the vibration of an axially moving string is studied when the string has geometric non linearity and translating acceleration based upon the von karman strain theory the equations of motion are derived considering the longitudinal and transverse deflections the equation for the longitudinal vibration is linear and uncoupled while the equation for the transverse vibration is non linear and coupled between the longitudinal and transverse deflections these equations are discretized by the galerkin method after they are transformed into the variational equations i e the weak forms so that the admissible and comparison functions can be used for the bases of the longitudinal and transverse deflections respectively with the discretized equations the natural frequencies the time histories of the deflections and the distributions of the deflection and stress are investigated in addition comparisons between the results of linear and non linear theories are provided

generalized treatment effects for clinical trials practice in the analysis of clinical trials with continuously measured endpoints is to focus on the difference or percentage change in mean or median response however treatments may have effects on the distribution of responses other than on the average response we sought an approach to such generalized treatment effects that i targets a parameter that is easily understood by our clinical colleagues and ii employs confidence intervals as the basis for inference we consider one such approach based on work in reliability theory namely setting pr y x as the target parameter and compare this approach to an earlier one due to o brien the two approaches have similar properties when they both seek to reject the null hypothesis of no effect due to different variances but differ when the larger variance corresponds to the larger mean in that case our approach views that the larger variance attenuates the effect of the larger mean out suggested approach applies easily to positive control clinical equivalence trials copyright 2000 john wiley sons ltd

a general solution procedure for the forced vibrations of a continuous system with cubic nonlinearities primary resonance case abstract nonlinear vibrations of a general model of continuous system is considered the model consists of arbitrary linear and cubic operators the equation of motion is solved by the method of multiple scales a perturbation method the primary resonances of external excitation is analysed the amplitude and phase modulation equations are presented approximate analytical solution is derived steady state solutions and their stability are discussed finally the solution algorithm is applied to two different engineering problems one of the application is the transverse vibration of an axially moving euler bernoulli beam and the other is a viscoelastic beam

efficient perturbation analysis of elastic network models application to acetylcholinesterase of t californica elastic network models in their different flavors have become useful models for the dynamics and functions of biomolecular systems such as proteins and their complexes perturbation to the interactions occur due to randomized and fixated changes in molecular evolution or designed modifications of the protein structures in bioengineering these perturbations are modifications in the topology and the strength of the interactions modeled by the elastic network models we discuss how a naive approach to compute properties for a large number of perturbed structures and interactions by repeated diagonalization can be replaced with an identity found in linear algebra we argue about the computational complexity and discuss the advantages of the protocol we apply the proposed algorithm to the acetylcholinesterase a well known enzyme in neurobiology and show how one can gain insight into the breathing dynamics of a structural funnel necessary for the function of the protein the computational speed up was a 60 fold increase in this example

the generalised autocovariance function the generalised autocovariance function is defined for a stationary stochastic process as the inverse fourier transform of the power transformation of the spectral density function depending on the value of the transformation parameter this function nests the inverse and the traditional autocovariance functions a frequency domain non parametric estimator based on the power transformation of the pooled periodogram is considered and its asymptotic distribution is derived the results are employed to construct classes of tests of the white noise hypothesis for clustering and discrimination of stochastic processes and to introduce a novel feature matching estimator of the spectrum

one sided approximate prediction intervals for at least p of m observations from a gamma population at each of r locations we develop simultaneous approximate statistical prediction limits for a gamma distributed random variable specifically we develop an upper prediction limit upl for p of m future samples at each of r locations based on a previous sample of n measurements a typical example is the environmental monitoring problem in which the distribution of an analyte of concern is typically non gaussian simultaneous determinations are required for multiple locations e g ground water monitoring wells and in the event of an initial exceedance of the prediction limit one or more verification samples are obtained to confirm evidence of an impact on the environment for example consider a ground water monitoring program with r wells and the requirement that at least p 1 of the m 2 samples in each of the r wells be below the upl we provide derivation of simultaneous approximate gamma upls illustration of the relevance of the gamma distribution to environmental data a limited simulation study of type i and i

testing reliability in a stress strength model when x and y are normally distributed we consider the stress strength problem in which a unit of strength x is subjected to environmental stress y an important problem in stress strength reliability concerns testing hypotheses about the reliability parameter r p x yl in this article we consider situations in which x and y are independent and have normal distributions or can be transformed to normality we do not require the two population variances to be equal our approach leads to test statistics which are exact p values that are represented as one dimensional integrals on the basis of the p value one can also construct approximate confidence intervals for the parameter of interest we also present an extension of the testing procedure to the case in which both strength and stress depend on covariates for comparative purposes the bayesian solution to the problem is also presented we use data from a rocket motor experiment to illustrate the procedure

on resonances and the applicability of galerkin s truncation method for an axially moving string with time varying velocity abstract in this paper an initial boundary value problem for a linear homogeneous equation describing an axially moving string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity with a small fluctuation amplitude the two timescales perturbation method and the laplace transform method have been employed to the equation of motion in search of infinite mode approximate solutions all resonance cases are investigated in detail it will be shown that galerkin s truncation method cannot be applied to this problem in all cases to obtain approximations valid on long timescales

updating the inverse of a matrix the sherman morrison woodbury formulas relate the inverse of a matrix after a small rank perturbation to the inverse of the original matrix the history of these fomulas is presented and various applications to statistics networks structural analysis asymptotic analysis optimization and partial differential equations are discussed the sherman morrison woodbury formulas express the inverse of a matrix after a small rank perturbation in terms of the inverse of the original matrix this paper surveys the history of these formulas and we examine some applications where these formulas are helpful

dynamic responses of axially moving viscoelastic beam under a randomly disordered periodic excitation abstract we investigate dynamic responses of axially moving viscoelastic beam subject to a randomly disordered periodic excitation the method of multiple scales is used to derive the analytical expression of first order uniform expansion of the solution based on the largest lyapunov exponent the almost sure stability of the trivial steady state solution is examined meanwhile we obtain the first order and the second order steady state moments for the non trivial steady state solutions specially we discuss the first mode theoretically and numerically results show that under the same conditions of the parameters as the intensity of the random excitation increases non trivial steady state solution fluctuation will become strenuous which will result in the non trivial steady state solution lose stability and the trivial steady state solution can be a possible in the case of parametric principal resonance the stochastic jump is observed for the first mode which indicates that the stationary joint probability density concentrates at the non trivial solution branch when the random excitation is small but with the increase of intensity of the random excitation the probability of the trivial steady state solution will become larger this phenomenon of stochastic jump can be defined as a stochastic bifurcation

transverse vibrations of elastically connected double string complex system part i free vibrations this paper analyzes the forced transverse vibrations of an elastically connected double string complex continuous system the general solutions of forced vibrations of strings subjected to arbitrarily distributed continuous loads are found by using the method of expansion in a series of the mode shape functions different cases of exciting loadings are analyzed the action of stationary harmonic loads and moving concentrated forces is considered vibrations caused by the harmonic exciting forces are discussed and conditions of resonance and dynamic vibration absorption are formulated thus the string type dynamic absorber can be used to suppress the excessive vibrations of corresponding string systems the dynamic string type damper is a new concept of a continuous dynamic vibration absorber cdva it is shown that a corresponding two degree of freedom discrete system is an analogue of an elastically connected double string complex system theoretical analysis is illustrated by a numerical example

infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations abstract the transverse vibrations of simply supported axially moving euler bernoulli beams are investigated the beam has a time varying axial velocity with viscous damping traveling beam eigenfunctions with infinite number of modes are considered approximate analytical solutions are sought using the method of multiple scales a perturbation technique a detailed analysis of the resonances in which upto four modes of vibration involved are performed stability analysis is treated for each type of resonance approximate stability borders are given for the resonances involving only two modes for higher number of modes involved in a resonance sample numerical examples are presented for stabilities

measuring the effectiveness of diagnostic markers in the presence of measurement error through the use of roc curves the area under the receiver operating characteristic curve is frequently used to assess the effectiveness of diagnostic markers in distinguishing between diseased and healthy individuals these markers are generally subject to measurement error in this paper confidence intervals for the area under the curve are developed which take measurement error into account these intervals depend on the availability of replicated observations for the subject both equal and unequal numbers of replicates per subject are considered the practice of averaging over replicates and then ignoring measurement error is examined and found wanting

one sided intervals for at least p of m observations from a normal population on each of r future occasions in environmental monitoring one must often use background data obtained before an installation begins operation to produce prediction intervals for future sets of m observations to be taken on each of r future occasions spanning the anticipated lifetime of the installation a future observation falling outside of its interval will be taken as evidence of a change in the process being monitored one would like to control the overall risk of false detection of change while maintaining an adequate sensitivity to real changes toward this end the procedure of fertig and mann 1977 is extended to produce simultaneous prediction intervals for at least p of m observations to be obtained on each of r future occasions tables with superior choices of p for selected m r and background sample size are provided these choices of p provide the best power given the other parameters where power is defined in terms of the chance of quick detection of a future shift in the process being monitored

refined models of elastic beams undergoing large in plane motions theory and experiment abstract accurate mechanical models of elastic beams undergoing large in plane motions are discussed theoretically and experimentally employing the geometrically exact theory of rods with appropriate kinematic assumptions and asymptotic arguments two approximate models are obtained a relaxed model and its constrained version that describe extensional and bending motions and neglect shear deformations these models are shown to be suitable to predict via an asymptotic approach closed form nonlinear motions of beams with general boundary conditions and in particular with boundary conditions that longitudinally constrain the motions on the other hand for axially unrestrained or weakly restrained beams an inextensible and unshearable model is presented that describes bending motions only the perturbations about the reference configuration up to third order are consistently derived for all beam models closed form solutions of the responses to primary resonance excitations are obtained via an asymptotic treatment of the governing equations of motion for two different beam configurations namely hinged hinged axially restrained and simply supported axially unrestrained beams in particular considering the present theory and the existing theories variations of the frequency response curves with the beam slenderness or the relative boundary mass are investigated for the lowest modes the fidelity of the proposed nonlinear models is ascertained comparing the theoretically obtained frequency response curves of the first mode with those experimentally obtained

three to one internal resonances in a general cubic non linear continuous system a general continuous system with an arbitrary cubic non linearity is considered the non linearity is expressed in terms of an arbitrary cubic operator three to one internal resonance case is considered a general approximate solution is presented for the system amplitude and phase modulation equations are derived steady state solutions and their stability are discussed in the general sense the sufficiency condition for such resonances to occur is derived finally the algorithm is applied to a beam resting on a non linear elastic foundation

a general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear time dependent internal boundary conditions abstract the subject of this paper is the development of a general solution procedure for the vibrations primary resonance and nonlinear natural frequency of systems with cubic nonlinearities subjected to nonlinear and time dependent internal boundary conditions this is a commonly occurring situation in the vibration analysis of continuous systems with intermediate elements the equations of motion form a set of nonlinear partial differential equations with nonlinear time dependent and coupled internal boundary conditions the method of multiple timescales an approximate analytical method is applied directly to each partial differential equation of motion as well as coupled boundary conditions i e on each sub domain and the corresponding internal boundary conditions for a continuous system with intermediate elements which ultimately leads to approximate analytical expressions for the frequency response relation and nonlinear natural frequencies of the system these closed form solutions provide direct insight into the relationship between the system parameters and vibration characteristics of the system moreover the suggested solution procedure is applied to a sample problem which is discussed in detail

direct treatment and discretizations of non linear spatially continuous systems abstract approximate analytical methods for the study of non linear vibrations of spatially continuous systems with general quadratic and cubic non linearities are discussed the cases of an external primary resonance of a non internally resonant mode and of a sub harmonically excited two to one internal resonance are investigated it is shown in a general fashion that application of the method of multiple scales to the original partial differential equations and boundary conditions produces the same approximate dynamics as those obtained by applying the reduction method to the full basis galerkin discretized system using the complete set of eigenfunctions of the associated linear system or to convenient low order rectified galerkin models as a corollary it is shown that due to the effects of the quadratic non linearities all of the modes from the relevant eigenspectrum in principle contribute to the non linear motions hence classical low order galerkin models may be inadequate to describe quantitatively and qualitatively the dynamics of the original continuous system although the direct asymptotic and rectified galerkin procedures seem to be more appealing from a computational standpoint the full basis galerkin discretization procedure furnishes a remarkably interesting spectral representation of the non linear motions

a general solution procedure for the forced vibrations of a system with cubic nonlinearities three to one internal resonances with external excitation a general vibrational model of a continuous system with arbitrary linear and cubic operators is considered approximate analytical solutions are found using the method of multiple scales the primary resonances of the external excitation and three to one internal resonances between two arbitrary natural frequencies are treated the amplitude and phase modulation equations are derived the steady state solutions and their stability are discussed the solution algorithm is applied to two specific problems 1 axially moving euler bernoulli beam and 2 axially moving viscoelastic beam

estimation of field reliability based on aggregate lifetime data because of the exponential distribution assumption many reliability databases recorded data in an aggregate way instead of individual failure times each aggregate data point is a summation of a series of collective failures representing the cumulative operating time of one component position from system commencement to the last component replacement the data format is different from traditional lifetime data and the statistical inference is challenging we first model the individual component lifetime by a gamma distribution confidence intervals for the gamma shape parameter can be constructed using a scaled 2 approximation to a modified ratio of the geometric mean to the arithmetic mean while confidence intervals for the gamma rate and mean parameters as well as quantiles are obtained using the generalized pivotal quantity method we then fit the data using the inverse gaussian ig distribution a useful lifetime model for failures caused by degradation procedures for point estimation and inte

energy landscape paving as a perfect optimization approach under detrended fluctuation analysis abstract global optimization go is one of the key numerical tools in computational physics among the go algorithms the ones originating in statistical physics are particularly powerful recently an adaptive scheme was developed to increase the efficiency of one of these algorithms stochastic tunneling this scheme is based on the time series of minima tested and the respective detrended fluctuation analysis dfa we here present a study on another go methodology energy landscape paving which in itself is adaptive and show that its performance is optimal under the dfa analysis we give arguments to explain this fact

principal parametric resonances of a general continuous system with cubic nonlinearities abstract a generalized vibrational model of cubic nonlinear continuous system with arbitrary parametric excitation is considered the method of multiple scales a perturbation method is used to find an approximate analytical solution the primary parametric resonance of the parametric excitation is considered the amplitude and phase modulation equations are derived steady state solutions and their stability are discussed the solution algorithm is applied to the problem of nonlinear vibrations of viscoelastic pipes conveying fluids natural frequencies of viscoelastic pipes are found frequency response curves and bifurcation points are drawn stable and unstable regions of trivial and nontrivial solutions are obtained

principal parametric resonance of axially accelerating viscoelastic strings with an integral constitutive law the steady state transverse responses and the stability of an axially accelerating viscoelastic string are investigated the governing equation is derived from the eulerian equation of motion of a continuum which leads to the mote model for transverse motion the kirchhoff model is derived from the mote model by replacing the tension with the averaged tension over the string the method of multiple scales is applied to the two models in the case of principal parametric resonance closed form expressions of the amplitudes and the existence conditions of steady state periodical responses are presented the lyapunov linearized stability theory is employed to demonstrate that the first second non trivial steady state response is always stable unstable numerical calculations show that the two models are qualitatively the same but quantitatively different numerical results are also presented to highlight the effects of the mean axial speed the axial speed fluctuation amplitude and the viscoelastic parameters

testing parameters of a gamma distribution for small samples the gamma distribution is relevant to numerous areas of application in the physical environmental and biological sciences the focus of this paper is on testing the shape scale and mean of the gamma distribution testing the shape parameter of the gamma distribution is relevant to failure time modeling where it can be used to determine if the failure rate is constant increasing or decreasing testing the scale parameter is also relevant to problems in survival analysis where when the shape parameter 1 the reciprocal of the scale parameter measures the hazard function finally testing the mean of the gamma distribution allows us to determine if the average concentration of an environmental contaminant is higher lower or equivalent to a health based standard in this paper we first derive new small sample based tests and then via simulation we study the type i error rate and statistical power of these tests results of these simulation studies reveal that in terms of maintaining type i error

inference on the gamma distribution this study develops inferential procedures for a gamma distribution based on the cornish fisher expansion and pivoting the cumulative distribution function an approximate confidence interval for

asymptotic approach for non linear periodical vibrations of continuous structures abstract an asymptotic approach for determining periodic solutions of non linear vibration problems of continuous structures such as rods beams plates etc is proposed starting with the well known perturbation technique the independent displacement and frequency is expanded in a power series of a natural small parameter it leads to infinite systems of interconnected non linear algebraic equations governing the relationships between modes amplitudes and frequencies a non trivial asymptotic technique based on the introduction of an artificial small parameter is used to solve the equations an advantage of the procedure is the possibility to take into account a number of vibration modes as examples free longitudinal vibrations of a rod and lateral vibrations of a beam under cubically non linear restoring force are considered resonance interactions between different modes are investigated and asymptotic formulae for corresponding backbone curves are derived

adaptive extremal optimization by detrended fluctuation analysis global optimization is one of the key challenges in computational physics as several problems e g protein structure prediction the low energy landscape of atomic clusters detection of community structures in networks or model parameter fitting can be formulated as global optimization problems extremal optimization eo has become in recent years one particular successful approach to the global optimization problem as with almost all other global optimization approaches eo is driven by an internal dynamics that depends crucially on one or more parameters recently the existence of an optimal scheme for this internal parameter of eo was proven so as to maximize the performance of the algorithm however this proof was not constructive that is one cannot use it to deduce the optimal parameter itself a priori in this study we analyze the dynamics of eo for a test problem spin glasses based on the results we propose an online measure of the performance of eo and a way to use this insight to reformulate the eo algorithm in order to construct optimal values of the internal parameter online without any input by the user this approach will ultimately allow us to make eo parameter free and thus its application in general global optimization problems much more efficient

statistical inference for pr y x the normal case this article examines statistical inference for pr y x where x and y are independent normal variates with unknown means and variances the case of unequal variances is stressed x can be interpreted as the strength of a component subjected to a stress y and pr y x is the component s reliability two approximate methods for obtaining confidence intervals and an approximate bayesian probability interval are obtained the actual coverage probabilities of these intervals are examined by simulation

dynamic responses of the in plane and out of plane vibrations for an axially moving membrane the dynamic responses of both the in plane and out of plane vibrations are investigated for an axially moving membrane using the extended hamilton principle equations of motion are derived for the moving membrane with no slip boundary conditions at rollers the equations of motion are discretized by using the galerkin method and then the generalized a time integration method is applied to compute the dynamic responses of the membrane based on the computed results the responses are compared between the in plane and out of plane vibrations in addition the effects of translating velocity acceleration critical speeds and velocity profiles on the dynamic behaviours for displacements and stresses are investigated and discussed r 2006 elsevier ltd all rights reserved

stability analysis of an axially accelerating string the dynamic response of an axially accelerating string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity approximate analytical solutions are sought using two different approaches in the first approach the equations are discretized first and then the method of multiple scales is applied to the resulting equations in the second approach the method of multiple scales is applied directly to the partial differential system principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for a band saw and a threadline problem

a comparison of different versions of the method of multiple scales for partial differential equations abstract applications of the methods of multiple scales a perturbation method to partial differential systems arising in non linear vibrations of continuous systems are considered two different versions of the method of multiple scales are applied to two general non linear models in one of the models the small parameter multiplies an arbitrary non linear cubic operator whereas in the other model arbitrary quadratic and cubic non linearities exist the linear parts of both models are represented by arbitrary operators general solutions are found by applying different versions of the method of multiple scales results of the first version reconstitution method and the second version proposed by rahman and burton 8 are compared for both models from the comparisons of both methods it is found that the second version yields better results applications of the general models to specific problems are also presented a final recommendation is to use the second version of the method of multiple scales combined with the direct perturbation method in finding steady state solutions of partial differential equations

normal based methods for a gamma distribution prediction and tolerance intervals and stress strength reliability in this article we propose inferential procedures for a gamma distribution using the wilson hilferty wh normal approximation specifically using the result that the cube root of a gamma random variable is approximately normally distributed we propose normal based approaches for a gamma distribution for a constructing prediction limits one sided tolerance limits and tolerance intervals b for obtaining upper prediction limits for at least l of m observations from a gamma distribution at each of r locations and c assessing the reliability of a stress strength model involving two independent gamma random variables for each problem a normal based approximate procedure is outlined and its applicability and validity for a gamma distribution are studied using monte carlo simulation our investigation shows that the approximate procedures are very satisfactory for all of these problems for each problem considered the results are illustrated using practical examples our overall conclusion is tha