a class of nonholonomic kinematic constraints in elasticity we propose a first example of a simple classical field theory with nonholonomic constraints our model is a straightforward modification of a cosserat rod based on a mechanical analogy we argue that the constraint forces should be modelled in a special way and we show how such a procedure can be naturally implemented in the framework of geometric field theory finally we derive the equations of motion and we propose a geometric integration scheme for the dynamics of a simplified model

prediction error and its estimation for subset selected models strategies are compared for development of a linear regression model and the subsequent assessment of its predictive ability simulations were performed as a designed experiment over a range of data structures approaches using a forward selection of variables resulted in slightly smaller prediction errors and less biased estimators of predictive accuracy than all possible subsets selection but often did not improve on the full model random and balanced data splitting resulted in increased prediction errors and estimators with large mean squared error to maximize predictive accuracy while retaining a reliable estimate of that accuracy it is recommended that the entire sample usually he used for model development and assessment

euler lagrange equations for variational problems on space curves we derive the euler lagrange equations for a large class of variational problems on curves our result generalizes a recent result obtained in the literature moreover it is simple and self contained it directly yields euler lagrange equations in the form of equilibrium equations for the internal force and moment

variable structure model reference adaptive control using only input and output measurements abstract a variable structure model reference adaptive controller vs mrac using only the input and output measurements of the plant is proposed stability and transient properties are analysed and discussed remarkable transient behaviour is revealed in particular model following can be perfectly achieved in a finite time the effect of plant input disturbance is investigated and the performance of the vs controller is also shown to be qualitatively superior to that obtained with conventional integral adaptation algorithms a link between the vs mrac and the conventional mrac is suggested simulations are presented to highlight the theoretical results

large sample bayesian inference on the parameters of the proportional hazard models this paper considers large sample bayesian analysis of the proportional hazards model when interest is in inference on the parameters and estimation of the log relative risk for specified covariate vectors rather than on prediction of the survival function we use a normal prior distribution for the parameters and make inferences based on the derived posterior distribution the suggested approach is much simpler than alternative bayesian analyses previously suggested for the proportional hazards models using simulated data we compare estimates obtained from the bayesian analysis with those obtained from the full proportional hazards model and the reduced model after backwards elimination we show that under a wider range of assumptions the bayesian analysis provides reduced estimation errors and improved rejection of noise variables finally we illustrate the methodology using data from a large study of prognostic markers in breast cancer

when should epidemiologic regressions use random coefficients summary regression models with random coefficients arise naturally in both frequentist and bayesian approaches to estimation problems they are becoming widely available in standard computer packages under the headings of generalized linear mixed models hierarchical models and multilevel models i here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed effects models now prevalent in epidemiology the argument invokes an antiparsimony principle attributed to l j savage which is that models should be rich enough to reflect the complexity of the relations under study it also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything often used to justify parsimony regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable selection algorithms and their attendant distortion of uncertainty assessments these points are illustrated with an analysis of data on diet nutrition and breast cancer

towards a classification of euler kirchhoff filaments euler kirchhoff filaments are solutions of the static kirchhoff equations for elastic rods with circular cross sections these equations are known to be formally equivalent to the euler equations for spinning tops this equivalence is used to provide a classification of the different shapes a filament can assume explicit formulas for the different possible configurations and specific results for interesting particular cases are given in particular conditions for which the filament has points of self intersection self tangency vanishing curvature or when it is closed or localized in space are provided the average properties of generic filaments are also studied they are shown to be equivalent to helical filaments on long length scales

hamilton equations for elasticae in the euclidean 3 space abstract the variational problem on spatial curves defined by the integral of the squared curvature whose solutions are the elasticae or nonlinear splines is analyzed from the hamiltonian point of view using a procedure developed by munoz masqueand pozo coronado j munoz masque l m pozo coronado j phys a 31 1998 6225 6242 the symmetry of the problem under rigid motions is then used to reduce the euler lagrange equations to a first order dynamical system

effective recursive algorithm for judging the positive definiteness of matrices of high dimension this paper presents a new efficient recursive algorithm for judging the positive definiteness of a matrix with this algorithm both a simpler computation process and a decreased memory requirement can be obtained

balancing torques in membrane mediated interactions exact results and numerical illustrations torques on interfaces can be described by a divergence free tensor which is fully encoded in the geometry this tensor consists of two terms one originating in the couple of the stress the other capturing an intrinsic contribution due to curvature in analogy to the description of forces in terms of a stress tensor the torque on a particle can be expressed as a line integral along a contour surrounding the particle interactions between particles mediated by a fluid membrane are studied within this framework in particular torque balance places a strong constraint on the shape of the membrane symmetric two particle configurations admit simple analytical expressions which are valid in the fully nonlinear regime in particular the problem may be solved exactly in the case of two membrane bound parallel cylinders this apparently simple system provides some flavor of the remarkably subtle nonlinear behavior associated with membrane mediated interactions

an isogeometric implicit g1 mixed finite element for kirchhoff space rods abstract in the paper we present a multi patch isogeometric mixed element with implicit geometric continuity at the ends for the analysis of non polar kirchhoff space rods rotations are introduced at the ends of the element analogously to the hermitian interpolation performing a change of basis for the configuration space a mixed method in which the internal forces are interpolated by means of an l 2 projection leading to a b formulation is used to cope with the membrane flexural locking that affects the solution the efficiency of the method in avoiding locking and instabilities is investigated the formulation adopted has the advantage with respect to other formulations that a non full global stiffness matrix is obtained this approach appears very appealing for efficient analyses of general assemblies of 3d non polar elements

the performance of random coefficient regression in accounting for residual confounding greenland 2000 biometrics 56 915 921 describes the use of random coefficient regression to adjust for residual confounding in a particular setting we examine this setting further giving theoretical and empirical results concerning the frequentist and bayesian performance of random coefficient regression particularly we compare estimators based on this adjustment for residual confounding to estimators based on the assumption of no residual confounding this devolves to comparing an estimator from a nonidentified but more realistic model to an estimator from a less realistic but identified model the approach described by gustafson 2005 statistical science 20 111 140 is used to quantify the performance of a bayesian estimator arising from a nonidentified model from both theoretical calculations and simulations we find support for the idea that superior performance can be obtained by replacing unrealistic identifying constraints with priors that allow modest departures from those constraints in terms of point estimator bias this superiority arises when the extent of residual confounding is substantial but the advantage is much broader in terms of interval estimation the benefit from modeling residual confounding is maintained when the prior distributions employed only roughly correspond to reality for the standard identifying constraints are equivalent to priors that typically correspond much worse

laplace pressure as a surface stress in fluid vesicles consider a surface enclosing a fixed volume described by a free energy depending only on the local geometry for example the canham helfrich energy quadratic in the mean curvature describes a fluid membrane the stress at any point on the surface is determined completely by geometry in equilibrium its divergence is proportional to the laplace pressure normal to the surface maintaining the constraint on the volume it is shown that this source itself can be expressed as the divergence of a position dependent surface stress as a consequence the equilibrium can be described in terms of a conserved effective surface stress various non trivial geometrical consequences of this identification are explored in a cylindrical geometry the cross section can be viewed as a closed planar euler elastic curve with respect to an appropriate centre the effective stress itself vanishes this provides a remarkably simple relationship between the curvature and the position along the loop in two or higher dimensions it is shown that the only geometry consistent with the vanishing of the effective stress is spherical it is argued that the appropriate generalization of the loop result will involve null stresses

discrete time lagrangian mechanics on lie groups with an application to the lagrange top we develop the theory of discrete time lagrangian mechanics on lie groups originated in the work of veselov and moser and the theory of lagrangian reduction in the discrete time setting the results thus obtained are applied to the investigation of an integrable time discretization of a famous integrable system of classical mechanics the lagrange top we recall the derivation of the euler poinsot equations of motion both in the frame moving with the body and in the rest frame the latter ones being less widely known we find a discrete time lagrange function turning into the known continuous time lagrangian in the continuous limit and elaborate both descriptions of the resulting discrete time system namely in the body frame and in the rest frame this system naturally inherits poisson properties of the continuous time system the integrals of motion being deformed the discrete time lax representations are also found kirchhoff s kinetic analogy between elastic curves and motions of the lagrange top is also generalised to the discrete context

nonlinear isogeometric spatial bernoulli beam abstract a new element formulation of a geometrically nonlinear spatial curved beam assuming bernoulli theory including torsion without warping is proposed the element formulation is derived directly from the 3d continuum by means of nonlinear kinematics thus accounting for large displacements the geometric description of the proposed element is adapted from the spatial rod of greco and cuomo 2013 and extended to a nonlinear element formulation the proposed formulation can handle arbitrary orientations of the cross section along the beam in this publication nurbs are used as basis functions for discretization since they can easily provide the required c 1 continuity between elements the presented element formulation has four degrees of freedom three for displacements and one for the rotation around the center line in order to prove the accuracy of the developed spatial bernoulli beam several numerical examples are presented and compared to analytic solutions and other element formulations

local geometric invariants of integrable evolution equations the integrable hierarchy of commuting vector fields for the localized induction equation of 3d hydrodynamics and its associated recursion operator are used to generate families of integrable evolution equations which preserve local geometric invariants of the evolving curve or swept out surface

eulerian formulation of constrained elastica the formulation of the constrained elastica problem proposed in this paper is predicated on two key concepts first the deformed elastica is described by means of the distance from the conduit axis second the problem is formulated in terms of the eulerian curvilinear coordinate of the conduit rather than the natural curvilinear coordinate of the elastica this approach is further implemented within a segmentation algorithm which transforms the global constrained elastica problem into a sequence of analogous auxiliary problems that result from dividing the conduit and the elastica into segments limited by contacts each auxiliary segment entails solving a segment of elastica subject to isoperimetric constraints corresponding to the assumed positions of the segment ends along the conduit this new formulation resolves in one stroke a series of issues that afflict the classical lagrangian approach i the contact detection is reduced to checking whether a threshold on the distance function is violated ii the isoperimetric conditions are transformed into regular boundary conditions instead of being treated as external integral constraints iii the method yields a well conditioned set of equations that does not degenerate with decreasing flexural rigidity of the elastica and or decreasing clearance between the conduit and the elastica

finite volume approach for the instationary cosserat rod model describing the spinning of viscous jets the spinning of slender viscous jets can be asymptotically described by one dimensional models that consist of systems of partial and ordinary differential equations whereas well established string models only possess solutions for certain choices of parameters and configurations the more sophisticated rod model is not limited by restrictions it can be considered as an regularized string model but containing the slenderness ratio in the equations complicates its numerical treatment we develop numerical schemes for fixed or enlarging time dependent domains using a finite volume approach in space with mixed central up and down winded differences and stiffly accurate radau methods for the time integration for the first time results of instationary simulations for a fixed or growing jet in a rotational spinning process are presented for arbitrary parameter ranges

an implicit multi patch b spline interpolation for kirchhoff love space rod abstract the paper presents a novel formulation for the isogeometric analysis of assemblies of kirchhoff love space rod elements introducing a multi patch implicit g 1 formulation so that an automatic non singular stiffness operator is obtained without the need of adding continuity conditions the goal is achieved using a polar decomposition of the deformation of the first and last segments of the control polygon that allows to introduce directly the end rotations as degrees of freedom both parametric and geometric continuity can be obtained in this way we use bezier and b spline interpolations and we show that they are able to attain very good accuracy for developing a 3d exact curve element with geometric torsion pre twisted rod in the paper the performance of the multi patch elements is examined comparing the rates of convergence of the l 2 error norm for the multi patch and single patch formulations it is shown that the rate of convergence remains the same although in certain cases the accuracy is lower for the multi patch solutions

stability of nonlinearly elastic rods this paper describes previously unknown stabilities and instabilities of planar equilibrium configurations of a nonlinearly elastic rod that is buckled under the action of a dead load the governing equations are derived from variational principles including ones of isoperimetric type properties of stability are accordingly determined by study of the second variation stabilities to deformations both in the plane and out of the plane are considered among the newly discovered properties are secondary bifurcation from the first buckled mode marked differences between stability to two dimensional and to three dimensional variations and the stabilizing influence of resistance to twist in the isoperimetric examples the analysis makes crucial use of a novel device to account for the dependence of the second variation on constraints

analytical expression of elastic rods at equilibrium under 3d strong anchoring boundary conditions abstract a general purpose method is presented and implemented to express analytically one stationary configuration of an ideal 3d elastic rod when the end to end relative position and orientation are imposed the mechanical equilibrium of such a rod is described by ordinary differential equations and parametrized by six scalar quantities when one end of the rod is anchored the analytical integration of these equations lead to one unique solution for given values of these six parameters when the second end is also anchored six additional nonlinear equations must be resolved to obtain parameter values that fit the targeted boundary conditions we find one solution of these equations with a zero finding algorithm by taking initial guesses from a grid of potential candidates we exhibit the symmetries of the problem which reduces drastically the size of this grid and shortens the time of selection of an initial guess the six variables used in the search algorithm forces and moments at one end of the rod are particularly adapted due to their unbounded definition domain more than 850 000 tests are performed in a large region of configurational space and in 99 9 of cases the targeted boundary conditions are reached with short computation time and a precision better than 10 5 we propose extensions of the method to obtain many solutions instead of only one using numerical continuation or starting from different initial guesses

lagrangian aspects of the kirchhoff elastic rod the relation between euler s planar elastic curves and vortex filaments evolving by the localized induction equation lie of hydrodynamics was discovered by hasimoto in 1971 basic facts about an integrable case of kirchhoff elastic rods are described here which amplify the connection between the variational problem for rods and the soliton equation lie in particular it is shown that the centerline of the kirchhoff rod is an equilibrium for a linear combination of the first three conserved hamiltonians in the lie hierarchy

output feedback model reference sliding mode control of uncertain multivariable systems this note considers the robust output tracking problem using a model reference sliding mode controller for linear multivariable systems of relative degree one it is shown that the closed loop system is globally exponentially stable and the performance is insensitive to bounded input disturbances and parameter uncertainties the strategy is based on output feedback unit vector control to generate sliding mode the only required a priori information about the plant high frequency gain matrix k sub p is the knowledge of a matrix s sub p such that k sub p s sub p is hurwitz which relaxes the positive definiteness requirement usually needed by other methods

hamiltonians for curves we examine the equilibrium conditions of a curve in space when a local energy penalty is associated with its extrinsic geometrical state characterized by its curvature and torsion to do this we tailor the theory of deformations to the frenet serret frame of the curve the euler lagrange equations describing equilibrium are obtained noether s theorem is exploited to identify the constants of integration of these equations as the casimirs of the euclidean group in three dimensions while this system appears not to be integrable in general it is in various limits of interest let the energy density be given as some function of the curvature and torsion f i ff is a linear function of either of its arguments but otherwise arbitrary we claim that the first integral associated with rotational invariance permits the torsion to be expressed as the solution of an algebraic equatio ni n terms ofthe bending curvature the first integral associated with translational invariance can then be cast as a quadrature for or for

hamiltonian structures and stability for rigid bodies with flexible attachments the dynamics of a rigid body with flexible attachments is studied a general framework for problems of this type is established in the context of poisson manifolds and reduction a simple model for a rigid body with an attached linear extensible shear beam is worked out for illustration second the energy casimir method for proving nonlinear stability is recalled and specific stability criteria for our model example are worked out the poisson structure and stability results take into account vibrations of the string rotations of the rigid body their coupling at the point of attachment and centrifugal and coriolis forces

environmental bias and elastic curves on surfaces the behavior of an elastic curve bound to a surface will reflect the geometry of its environment this may occur in an obvious way the curve may deform freely along directions tangent to the surface but not along the surface normal however even if the energy itself is symmetric in the curve s geodesic and normal curvatures which control these modes very distinct roles are played by the two if the elastic curve binds preferentially on one side or is itself assembled on the surface not only would one expect the bending moduli associated with the two modes to differ binding along specific directions reflected in spontaneous values of these curvatures may be favored the shape equations describing the equilibrium states of a surface curve described by an elastic energy accommodating environmental factors will be identified by adapting the method of lagrange multipliers to the darboux frame associated with the curve the forces transmitted to the surface along the surface normal will be determined features associated with a number of different energies both of physical relevance and of mathematical interest are described the conservation laws associated with trajectories on surface geometries exhibiting continuous symmetries are also examined

b spline interpolation of kirchhoff love space rods the paper deals with the isogeometric analysis via b splines of space rods under kirchhoff love hypotheses the approach was used by gontier and vollmer 12 for developing a plane curve element within the framework of the timoshenko rod model but they adopted only one patch to represent entirely the geometry of the rod furthermore the authors developed their theory only for plane elements in this work we develop an isogeometric approach for the numerical analysis of the 3d kirchhoff love rod theory we use b splines and bezier interpolations and we show that they are able to attain very good accuracy for rod structures particularly for developing a 3d exact curve element with geometric torsion the paper presents an original parametrization of the geometric torsion that proves to be very effective the use of b splines allows to avoid discontinuities on the geometrical quantities and particularly on the normal fields so that even relatively low order interpolation functions are able to yield accurate results

a discrete geometric approach for simulating the dynamics of thin viscous threads we present a numerical model for the dynamics of thin viscous threads based on a discrete lagrangian formulation of the smooth equations the model makes use of a condensed set of coordinates called the centerline spin representation the kinematic constraints linking the centerline s tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations based on a description of twist inspired from discrete differential geometry and from variational principles we build a full fledged discrete viscous thread model which includes in particular a discrete representation of the internal viscous stress consistency of the discrete model with the classical smooth equations for thin threads is established formally our numerical method is validated against reference solutions for steady coiling the method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way including the combined effects of inertia stretching bending twisting large rotations and surface tension

second stage least squares versus penalized quasi likelihood for fitting hierarchical models in epidemiologic analyses hierarchical regression analysis holds much promise for epidemiologic analysis but has as yet seen limited application because of lack of easily used software and the relatively lengthy run times of preferred fitting methods such as true maximum likelihood and bayesian approaches this paper compares three relatively simple choices for estimation of the regression coefficients maximum likelihood first stage combined with a weighted least squares second stage mlls joint iteratively reweighted least squares fitting of first and second stage jils and empirically penalized quasi likelihood epql these choices can be combined with various methods for estimating the second stage variance the two contrasted here are based on first and second stage residuals jils and epql yielded indistinguishable results and had small sample performance superior to mlls in larger samples there was little practical difference among the methods use of first stage residuals to estimate the prior variance required considerably more computation than use of second stage residuals but produced no discernible improvement in regression coefficient estimates all three methods performed well for estimation of first stage parameters but were less satisfactory for estimation of second stage parameters

variable structure model reference adaptive control vs mrac using only input and output measurements the general case a globally asymptotically stable vs mrac for the general case of plants with arbitrary relative degree is presented it is shown that the vs approach leads to general adaptive controllers with outstanding performance the controllers use only i o measurements and are free of differentiators the results indicate that several of the usual drawbacks of conventional mracs e g unsatisfactory transient behavior lack of robustness difficulties in designing controllers for time varying or nonlinear plants can be circumvented

on the geometric flow of kirchhoff elastic rods recently rod theory has been applied to the mathematical modeling of bacterial fibers and biopolymers e g dna to study their mechanical properties and shapes e g supercoiling in static rod theory an elastic rod in equilibrium is the critical point of an elastic energy this induces a natural question of how to find elasticae in this paper we focus on how to find the critical points by means of gradient flows we relate a geometric function of curves to the isotropic kirchhoff elastic energy of rods so that the generalized elastic curves are the centerlines of elastic rods in equilibrium thus the variational problem for rods is formulated in curve geometry this problem turns out to be a generalization of curve straightening flows which induce nonlinear fourth order evolution equations we establish the long time existence of length preserving gradient flow for the geometric energy furthermore by studying the asymptotic behavior we show that the limit curves are the centerlines of the ki

the intricate global structure of buckled states of compressible columns singularity theory and global multiparameter bifurcation theory are combined to show that nonbifurcating buckled states of compressible nonlinearly elastic columns lie on branches having detailed qualitative properties these properties distinguish the branches globally together with a delicate asymptotic analysis they are used to show that the global disposition of solution branches both bifurcating and not is strikingly different from that for incompressible columns

multiple imputation of industry and occupation codes in census public use samples using bayesian logistic regression abstract we describe methods used to create a new census data base that can be used to study comparability of industry and occupation classification systems this project represents the most extensive application of multiple imputation to date and the modeling effort was considerable as well hundreds of logistic regressions were estimated one goal of this article is to summarize the strategies used in the project so that researchers can better understand how the new data bases were created another goal is to show how modifications of maximum likelihood methods were made for the modeling and imputation phases of the project to multiply impute 1980 census comparable codes for industries and occupations in two 1970 census public use samples logistic regression models were estimated with flattening constants for many of the regression models considered the data were too sparse to support conventional maximum likelihood analysis so some alternative had to be employed these methods solve existence and

on the dynamics of rods in the theory of kirchhoff and clebsch we discuss here the dynamical equations of a theory of elastic rods that is due to kmcm ioff 1 2 and cl bsc 3 4 this properly invariant theory is applicable to motions in which the strains relative to an undistorted configuration remain small although rotations may be large it is constructed to be a first order theory i e a theory that is complete to within an error of order two in an appropriate dimensionless measure of thickness curvature twist and extension in a first order theory of thin rods one can treat the rod as inextensible and we do so here at the outset thus at each time t the arc length parameter s for the axial curve t is employed as a material coordinate i e a parameter whose value at a material point is constant in time and not only the resultant of the shearing forces on a cross section but also the tension in the rod are reactive quantities not given by constitutive equations consider for a moment a rod that is naturally prismatic and dynamically symmetric i e a rod that in an undistorted stress free configuration is a cylinder whose directrix although not necessarily a circle bounds a figure with equal principal moments of inertia a motion of the rod is said to be planar and twist flee i e a motion of pure flexure if it is such that t lies at all times in a fixed plane which contains a principal axis of inertia of each cross section for such a motion we employ a fixed cartesian coordinate system on and for consistency with a discussion of more general motions to be given later in this paper we call the abscissa z and the ordinate x we may write fz s t fx s t for the z and x components of the resultant force f at time t on the cross section with arc length coordinate s the motion of the rod may be described by giving the z x coordinates of the points on t as functions of s and t with o s t the counterclockwise angle from the z axis to the tangent of t at s we have

eulerian formulation of elastic rods in numerous biological medical and engineering applications elastic rods are constrained to deform inside or around tube like surfaces to solve efficiently this class of problems the equations governing the deflection of elastic rods are reformulated within the eulerian framework of this generic tubular constraint defined as a perfectly stiff normal ringed surface this reformulation hinges on describing the rod deformed configuration by means of its relative position with respect to a reference curve defined as the axis or spine curve of the constraint and on restating the rod local equilibrium in terms of the curvilinear coordinate parametrizing this curve associated with a segmentation strategy which partitions the global problem into a sequence of rod segments either in continuous contact with the constraint or free of contact except for their extremities this re parametrization not only trivializes the detection of new contacts but also transforms these free boundary problems into classic two points boundary value problems and suppresses the isoperimetric constraints resulting from the imposition of the rod position at the extremities of each rod segment

a new perspective on priors for generalized linear models abstract this article deals with specifications of informative prior distributions for generalized linear models our emphasis is on specifying distributions for selected points on the regression surface the prior distribution on regression coefficients is induced from this specification we believe that it is inherently easier to think about conditional means of observables given the regression variables than it is to think about model dependent regression coefficients previous use of conditional means priors seems to be restricted to logistic regression with one predictor variable and to normal theory regression we expand on the idea of conditional means priors and extend these to arbitrary generalized linear models we also consider data augmentation priors where the prior is of the same form as the likelihood we show that data augmentation priors are special cases of conditional means priors with current monte carlo methodology such as importance sampling and gibbs sampling our priors result in

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

parameter invariant second order variational problems in one variable a projection is defined such that a second order lagrangian density factors through this projection modulo contact forms if and only if it is parameter invariant in this way a geometric interpretation of the parameter invariance conditions is obtained the above projection is then used to prove the strict factorization of the poincare cartan form attached to a parameter invariant variational problem thus leading us to state the hamilton cartan formalism the complete description of symmetries and regularity for such problems the case of the squared curvature lagrangian in the plane is analysed especially

extendability of kirchhoff elastic rods in complete riemannian manifolds the kirchhoff elastic rod is a classical mathematical model of equilibrium configurations of thin elastic rods and is defined to be a solution of the euler lagrange equations associated to the energy with the effect of bending and twisting we consider the initial value problem for the euler lagrange equations in a riemannian manifold in a previous paper the author proved the existence and uniqueness of global solutions of the initial value problem in the case where the ambient space is a space form in the present paper we extend this result to the case where the ambient space is a general complete riemannian manifold this implies that an arbitrary kirchhoff elastic rod of finite length in a complete riemannian manifold extends to that of infinite length

analysis and design of i o based variable structure adaptive control this paper presents an overview of a technique for the design of variable structure model reference adaptive control vs mrac systems using only input output data the main ideas underlying the design and the analysis as well as the main properties of the controller are described having as point of departure a well known parameter adaptive mrac scheme then asymptotic properties of the vs mrac system are established taking into account the effect of the averaging filters necessary to implement some equivalent control signals in particular global exponential stability of the associated error system with respect to a small residual set is demonstrated the effect of linear zones in the relay functions is assessed showing that they can alleviate the chattering phenomena this is related with the fact that the vs mrac has a high gain stability property a procedure for noise sensitivity reduction is also proposed simulations illustrate the very satisfactory performance of the vs mrac in adverse operating conditions

atomic to continuum passage for nanotubes a discrete saint venant principle and error estimates we consider general infinite nanotubes of atoms in mathbb r 3 where each atom interacts with all the others through a two body potential at the equilibrium the positions of the atoms satisfy a euler lagrange equation when there are no exterior forces and for a suitable geometry a particular family of nanotubes is the set of perfect nanotubes at the equilibrium when exterior forces are applied on the nanotube we compare the nanotube to nanotubes of the previous family in part i of the paper this quantitative comparison is formulated in our first main result as a discrete saint venant principle as a corollary we also give a liouville classification result our saint venant principle can be derived for a large class of potentials including the lennard jones potential when the perfect nanotubes at the equilibrium are stable the approach is designed to be applicable to nanotubes that can have general shapes like for instance carbon nanotubes or dna under the oversimplified assumption that all the atoms are identical in part ii of the paper we derive from our saint venant principle a macroscopic mechanical model for general nanotubes we prove that every solution is well approximated by the solution of a continuum model involving stretching and twisting but no bending we establish error estimates between the discrete and the continuous solution more precisely we give two error estimates one at the microscopic level and one at the macroscopic level

the influence of elasticity on analysis the classic heritage etude des domaines suivants le catenaire solutions doubles et le calcul variationnel l elastique fonctions elliptiques analyse qualitative solutions multiples geometrie differentielle des courbes gauches systemes en petites vibrations nombres propres et modes simples equations differentielles lineaires fonctions de bessel polynomes de laguerre transformees integrales oscillations resonantes equations aux derives partielles concept de solution discontinuites la definition moderne d une fonction base fonctionnelle singularites solutions generalisees plaques la courbure gaussienne theorie tridimensionnelle deformation des regions deformation et rotation locale tenseurs nombres et vecteurs propres decomposition polaire resolution spectrale isotropie et hemitropie groupes torsion d un cylindre solution principale d un systeme d equations differentielles et son etat d approximation d autres solutions

putting background information about relative risks into conjugate prior distributions in bayesian and empirical bayes analyses of epidemiologic data the most easily implemented prior specifications use a multivariate normal distribution for the log relative risks or a conjugate distribution for the discrete response vector this article describes problems in translating background information about relative risks into conjugate priors and a solution traditionally conjugate priors have been specified through flattening constants an approach that leads to conflicts with the true prior covariance structure for the log relative risks one can however derive a conjugate prior consistent with that structure by using a data augmentation approximation to the true log relative risk prior although a rescaling step is needed to ensure the accuracy of the approximation these points are illustrated with a logistic regression analysis of neonatal death risk

generalized conjugate priors for bayesian analysis of risk and survival regressions le choix pour les analyses bayesiennes portant sur les risques relatifs de distributions a priori conjuguees peut etre tres limitant du fait que la forme de cette distribution depend du parametre de valeur centrale cependant en introduisant separement ce parametre on generalise ces distributions a priori ce qui permet de modeliser une tres large palette d opinions a priori tout en conservant les proprietes de simplicite des calculs propres aux analyses conjuguees cet article illustre les resultats fournis par ces analyses avec des conjuguees generalisees a partir d exemples sur des enquetes cas x temoins dont le but etait d etudier le lien des amenagements en c bles electriques wire codes en zone residentielle et des champs magnetiques avec les cas de leucemie chez l enfant

invariant isogeometric formulations for three dimensional kirchhoff rods abstract in the isogeometric formulation for three dimensional kirchhoff rods the invariance is required such that rigid body modes associated with translations and infinitesimal rotations can be exactly represented by enforcing the invariance in the isogeometric formulation of the rod the equilibrium of forces and moments at fixed ends is preserved and the performance is improved considerably for elements of finite sizes we recognize that not all existing isogeometric formulations are invariant for general geometry of rods though an alternative formulation based on the frenet serret frame and rotation angle representation was shown to be invariant it does not work for rods with vanishing curvature while its accuracy is affected by the low continuity of the angle of twist used motivated by this two new invariant isogeometric formulations are developed through different interpolations for the angle of twist one uses the derivatives of the nurbs functions as the basis for the angle of twist interpolation and the other uses a mixed interpolation incorporating both the lagrange and nurbs functions several representative numerical examples were prepared to verify the accuracy and robustness of the two new formulations particularly for rods of variable curvatures simulated by elements of finite or large sizes the proposed formulations are demonstrated to outperform the two existing ones mentioned in predicting the displacements end reactions and stress resultants

numerical solution of a bending torsion model for elastic rods aiming at simulating elastic rods we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods after reviewing this model and discussing topological effects of periodic rods we prove convergence of the discretized functionals and stability of a corresponding discrete flow our experiments numerically confirm thresholds e g for michell s instability and indicate a complex energy landscape in particular in the presence of impermeability

area constrained planar elastica we determine the equilibria of a rigid loop in the plane subject to the constraints of fixed length and fixed enclosed area rigidity is characterized by an energy functional quadratic in the curvature of the loop we find that the area constraint gives rise to equilibria with remarkable geometrical properties not only can the euler lagrange equation be integrated to provide a quadrature for the curvature but in addition the embedding itself can be expressed as a local function of the curvature the configuration space is shown to be essentially one dimensional with surprisingly rich structure distinct branches of integer indexed equilibria exhibit self intersections and bifurcations a gallery of plots is provided to highlight these findings perturbations connecting equilibria are shown to satisfy a first order ode which is readily solved we also obtain analytical expressions for the energy as a function of the area in some limiting regimes

data augmentation priors for bayesian and semi bayes analyses of conditional logistic and proportional hazards regression data augmentation priors have a long history in bayesian data analysis formulae for such priors have been derived for generalized linear models but their accuracy depends on two approximation steps this note presents a method for using offsets as well as scaling factors to improve the accuracy of the approximations in logistic regression this method produces an exceptionally simple form of data augmentation that allows it to be used with any standard package for conditional logistic or proportional hazards regression to perform bayesian and semi bayes analyses of matched and survival data the method is illustrated with an analysis of a matched case control study of diet and breast cancer

design and stability analysis of an indirect variable structure model reference adaptive control this paper presents the stability and robustness analysis of an indirect adaptive control based variable structure algorithm for uncertain plants with relative degree one the indirect approach has been proposed as a way to get an easier design of the switching laws compared to the direct relationship between the plant transfer function parameters and the physical parameters of the system here a singular perturbation approach is used to establish the robustness of the controller in the presence of unmodelled dynamics and disturbances it is shown that for sufficiently small parasitics the system remains stable with respect to some small residual set

approximate bayesian inference in conditionally independent hierarchical models parametric empirical bayes models abstract we consider two stage models of the kind used in parametric empirical bayes peb methodology calling them conditionally independent hierarchical models we suppose that there are k units which may be experimental subjects cities study centers etcetera at the first stage the observation vectors yi for units i 1 k are independently distributed with densities p yi i or more generally p yi i at the second stage the unit specific parameter vectors i are iid with densities p i the peb approach proceeds by regarding the second stage distribution as a prior and noting that if were known inference about could be based on its posterior since is not known the simplest peb methods estimate the parameter by maximum likelihood or some variant and then treat as if it were known to be equal to this estimate although this procedure is sometimes satisfactory a well known defect is that it neglects the uncertainty due to the estimation of in this article w

nonlinear dynamical theory of the elastica the dynamical behaviour of a slender rod is analyzed here in terms of a generalization of euler s elastica theory the model includes a linear stress strain relation but nonlinear geometric terms properties of the rod may vary along its length and various boundary conditions are considered a rotational inertia term that is neglected in many theories is retained and is essential to the analysis by use of the equivalence of an energy and a sobolev norm and by reformulation of the equations as a semilinear system global existence of solutions is proved for any smooth initial data equilibrium solutions that are stable in the static sense of minimizing the potential energy are then proved to be stable in the dynamic sense due to liapounov

invariant submanifold flows given a lie group acting on a manifold our aim is to analyze the evolution of differential invariants under invariant submanifold flows the constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex applications to integrable soliton dynamics and to the evolution of differential invariant signatures used in equivalence problems and object recognition and symmetry detection in images are discussed

helices for mathematical modelling of proteins nucleic acids and polymers abstract helices occur in modelling a range of structures including ropes fibers polymers and biopolymers in a recent paper with thamwattana and hill the authors derived euler lagrange equations for modelling protein structure where the energy being minimised was assumed to depend only on the curvature and torsion of the protein backbone space curve and their first derivatives such a model is applicable to helices occurring in other scenarios and in this article the author considers more generally which energies will yield helices as solutions of their corresponding euler lagrange equations he finds in particular classes of energy for which all circular helices are solutions and an energy depending on curvature and its derivative which generates conical helices as solutions of the euler lagrange equations also included are some new results for energies depending only on curvature extending previous investigations by feoli et al a feoli v v nesterenko g scarpetta functionals linear in curvature and statistics of helical proteins nuclear phys b 705 2005 577 592

new approach to robust model reference adaptive control for a class of plants motivated by recent advances in designing robust adaptive controllers and in dealing with uncertain dynamical systems a new model reference adaptive control which is robust to a class of unmodelled dynamics and bounded output disturbances in the case of relative degree one is presented the implementation of the controllers includes a switching mechanism which plays a crucially important role in functions of stabilizing as well as tracking it is shown that global stability of the overall system is achieved under no assumption of persistency of excitation and tracking errors will converge to a residual set whose size can be directly related to the size of unmodelled dynamics and of output disturbances explicitly in the ideal case the residual set degenerates to a single null point and convergence can be achieved in finite time without any requirement of persistency of excitation

l 2 flow of elastic curves with clamped boundary conditions abstract in this paper we investigate the l 2 flow of elastic curves with clamped boundary conditions in n dimensional euclidean spaces the l 2 flow corresponds to a fourth order parabolic equation in the case of closed curves the long time existence of solutions of this evolution equation has been derived in the literature we extend this result to the case of open i e non closed curves with clamped boundary conditions

spatial chaos of 3 d elastica with the kirchhoff gyrostat analogy using melnikov integrals summary the kirchhoff kinetic analogy from which the similarity between the governing equations for the static spatial equilibrium of a 3 d elastica and those for the temporal dynamics of a rigid body is constituted is revisited the melnikov integrals for detecting chaos cannot be easily formed for an elastica we shall modify the previous procedure of using the melnikov integrals for detecting temporal chaos for a gyrostat to solve the spatial chaos problem of an elastica one way to find the disturbed hamiltonian equations of the equilibrium equations of the elastica are by means of deprit s variables using the melnikov integrals the spatially chaotic deformation patterns can be resulted from the homoclinic transversal intersections of the stable and unstable manifolds at a saddle point in the poincare map when the elastica is disturbed by constant stress resultants the melnikov integrals are integrated for detecting homoclinic intersections the equations governing the evolution of the stress couples and the stress resultants are numerically integrated using the fourth runge kutta algorithms to crosscheck the analytical results the phase portraits of the poincare sections are created on a number of hyper planes to demonstrate the chaotic patterns of the stationary spatial deformations along the centreline of the elastica under weightless conditions the bounded non periodic solutions to the equilibrium of the elastica clearly show the existence of spatially chaotic deformation patterns the findings in this paper are useful in many structures in which the elastica are important examples are the mathematical modelling of the dna super coiling submarine cables and the design of the tethered satellites copyright 2004 john wiley sons ltd

geometrical equilibrium of curves a showcase of helical numerical solutions in this work we plot loop configurations that minimize energy functionals depending on geometrical invariants of the loop itself in particular we consider a family of functionals including curvature and torsion terms both linear and quadratic such that their combinations produce geometrical invariants in 1 noether s theorem was advantageously used to identify the constants of integration of the euler lagrange equations describing the equilibrium of loops for this family of energy functionals those authors demonstrated the integrability of these functionals by means of quadratures in this work we follow that approach to realize numeric calculations and to show plots of numerical solutions of the relevant equations for equilibrium of loops as these were presented but not studied in 1 we then show as the main result of this work a representative catalogue of such solutions in euclidean three dimensional space

a semi bayes approach to the analysis of correlated multiple associations with an application to an occupational cancer mortality study thomas et al presented the application of empirical bayes methods to the problem of multiple inference in epidemiologic studies one limitation of their approach which they noted was the need to assume exchangeable log relative risk parameters and independent relative risk estimates numerical integration was also required here i generalize their approach to allow for non exchangeable parameters and non independent estimates the resulting method is bayesian in so far as some feature of the prior distribution are specified from prior information but is empirical bayes in so far as some explicit parameters in the prior distribution are estimated from the data estimation is based on approximations to the posterior distribution this allows one to implement the approach with standard software packages for matrix algebra the method is illustrated in an occupational mortality study of 84 exposure cancer associations

non holonomic lagrangian systems in jet manifolds a geometrical setting in terms of jet manifolds is developed for time dependent non holonomic lagrangian systems an almost product structure on the evolution space is constructed in such a way that the constrained dynamics is obtained by projection of the free dynamics a constrained poincare cartan 2 form is defined if the non holonomic system is singular a constraint algorithm is constructed special attention is devoted to caplygin systems and a reduction theorem is proved

the korteweg de vries hierarchy as dynamics of closed curves in the plane the korteweg de vries modified korteweg de vries and harry dym hierarchies of integrable systems are shown to be equivalent to a hierarchy of chiral shape dynamics of closed curves in the plane these purely local dynamics conserve an infinite number of global geometric properties of the curves such as perimeter and enclosed area several techniques used to study these integrable systems are shown to have simple differential geometric interpretations connections with incompressible inviscid fluid flow in two dimensions are suggested

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea