performance analysis for a changepoint problem nonlinear stochastic differential equations are used to model a version of the changepoint problem state estimates of the minimum mean square error type are used in likelihood ratio tests to detect the time of change system performance is evaluated by deriving theoretical expressions for the false alarm probability and a special case of the miss error probability the approach uses a fokker planck equation

on the exploitation of chaos to build reduced order models the present study focuses on the model reduction of non linear systems the proper orthogonal decomposition is exploited to compute eigenmodes from time series of displacement these eigenmodes called the proper orthogonal modes are optimal with respect to energy content and are used to build a low dimensional model of the non linear system for this purpose the proper orthogonal modes obtained from a chaotic orbit are considered indeed such an orbit is assumed to cover a portion of the phase space of higher dimension and hence of greater measure this higher dimensional data is further assumed to contain more information about the system dynamics than data of a lower dimensional periodic orbit in an example it is shown that the modes for this particular behaviour are more representative of the system dynamics than any other set of modes extracted from a non chaotic response this is applied to a buckled beam with two permanent magnets and the reduced order model is validated using both qualitative and quantitative comparisons

non linear oscillator models in bluff body aero elasticity abstract a critique of non linear oscillator models is offered and a systematic and self consistent procedure for constructing such a model is proposed based upon theoretical and experimental fluid mechanical information numerical studies are conducted for the proposed model as well as for the earlier one of skop and griffin a comparison with jones experimental results is also made

flow induced vibration of an euler bernoulli beam abstract flow induced vibration of a fixed fixed elastic cylinder with a large aspect ratio 58 is considered the structural vibration is modelled by the euler bernoulli beam theory and the normal mode method is used to analyze the structural response the flow field are resolved using a finite element method and the flow induced forces are thereby calculated altogether two different cases are examined one at resonance and another at off resonance results thus obtained are compared with experimental measurements and a discrete parameter model a two degree of freedom 2 d o f model analysis the comparison shows that while the 2 d o f model gives reasonable prediction of the mid span vibration displacements for the resonant and off resonant case the present method yields the span wise multi mode response of the cylinder similar to that observed experimentally based on these results a correction formula is derived to estimate the span wise vibration from the 2 d o f model result correlation results are also presented to show that fluid structure interactions mainly affect the phase relation between the fluid forces and the corresponding vibration of the cylinder such influences have different effects along the cylinder span

an adaptive proper orthogonal decomposition method for model order reduction of multi disc rotor system abstract the proper orthogonal decomposition pod method is a main and efficient tool for order reduction of high dimensional complex systems in many research fields however the robustness problem of this method is always unsolved although there are some modified pod methods which were proposed to solve this problem in this paper a new adaptive pod method called the interpolation grassmann manifold igm method is proposed to address the weakness of local property of the interpolation tangent space of grassmann manifold itgm method in a wider parametric region this method is demonstrated here by a nonlinear rotor system of 33 degrees of freedom dofs with a pair of liquid film bearings and a pedestal looseness fault the motion region of the rotor system is divided into two parts simple motion region and complex motion region the adaptive pod method is compared with the itgm method for the large and small spans of parameter in the two parametric regions to present the advantage of this method and disadvantage of the itgm method the comparisons of the responses are applied to verify the accuracy and robustness of the adaptive pod method as well as the computational efficiency is also analyzed as a result the new adaptive pod method has a strong robustness and high computational efficiency and accuracy in a wide scope of parameter

a characterization of the spatial poisson process and changing time watanabe proved that if x t is a point process such that x t t is a martingale then x t is a poisson process and this result was generalized by bremaud for doubly stochastic poisson processes here we define two parameter point processes and extend this property without needing the strong martingale condition using this characterization we study the problem of transforming a two parameter point process into a two parameter poisson process by means of a family of stopping lines as a time change nualart and sanz gave conditions in order to transform a square integrable strong martingale into a wiener process here we do the same for the poisson process by a similar method but under more general conditions

a multiplicative seasonal component in commodity derivative pricing abstract in this paper we focus on a seasonal jump diffusion model to price commodity derivatives we propose a novel approach to estimate the functions of the risk neutral processes directly from data in the market even when a closed form solution for the model is not known then this new approach is applied to price some natural gas derivative contracts traded at new york mercantile exchange nymex moreover we use nonparametric estimation techniques in order to avoid arbitrary restrictions on the model after applying this approach we find that a jump diffusion model allowing for seasonality outperforms a standard jump diffusion model to price natural gas futures furthermore we also show that there are considerable differences in the option prices and the risk premium when we consider seasonality or not these results have important implications for practitioners in the market

reputation in continuous time games we study reputation dynamics in continuous time games in which a large player e g government faces a population of small players e g households and the large player s actions are imperfectly observable the major part of our analysis examines the case in which public signals about the large player s actions are distorted by a brownian motion and the large player is either a normal type who plays strategically or a behavioral type who is committed to playing a stationary strategy we obtain a clean characterization of sequential equilibria using ordinary differential equations and identify general conditions for the sequential equilibrium to be unique and markovian in the small players posterior belief we find that a rich equilibrium dynamics arises when the small players assign positive prior probability to the behavioral type by contrast when it is common knowledge that the large player is the normal type every public equilibrium of the continuous time game is payoff equivalent to one in which a static nash equilibrium is played after every history finally we examine variations of the model with poisson signals and multiple behavioral types

decoding movement trajectories through a t maze using point process filters applied to place field data from rat hippocampal region ca1 firing activity from neural ensembles in rat hippocampus has been previously used to determine an animal s position in an open environment and separately to predict future behavioral decisions however a unified statistical procedure to combine information about position and behavior in environments with complex topological features from ensemble hippocampal activity has yet to be described here we present a two stage computational framework that uses point process filters to simultaneously estimate the animal s location and predict future behavior from ensemble neural spiking activity first in the encoding stage we linearized a two dimensional t maze and used spline based generalized linear models to characterize the place field structure of different neurons all of these neurons displayed highly specific position dependent firing which frequently had several peaks at multiple locations along the maze when the rat was at the stem of the t maze the firing activity of several of these neurons also varied significantly as a function of the direction it would turn at the decision point as detected by anova second in the decoding stage we developed a state space model for the animal s movement along a t maze and used point process filters to accurately reconstruct both the location of the animal and the probability of the next decision the filter yielded exact full posterior densities that were highly nongaussian and often multimodal our computational framework provides a reliable approach for characterizing and extracting information from ensembles of neurons with spatially specific context or task dependent firing activity

spatio temporal dimensionality in the overall complex dynamics of an experimental cable mass system an experimental model of an elastic cable mass hanging at in phase or out of phase vertically moving supports is considered system parameters are adjusted to produce two different conditions of multiple internal resonance nonregular dynamics are analyzed in various frequency ranges including meaningful external resonance conditions attention is devoted to characterization of system dimensionality in terms of both time and spatial complexity the aims of this paper are i to give a general overview of the richness and robustness of different quasiperiodic and homoclinic bifurcation scenarios to chaos in various regions of the control parameter space ii to characterize steady nonregular response through delay embedding technique for attractor reconstruction and proper orthogonal decomposition of spatio temporal flow and iii to identify spatial configuration variables experimental eigenfunctions contributing mostly to nonregular dynamics thus obtaining hints about possible reduced models for reproducing complex regimes system dimensionality will be evaluated both by relating the dimension of attractors to the dimension of the linear phase space and from the dominating proper orthogonal modes

smoothing point processes as a means to increase throughput unlike the leaky bucket scheme which regulates the input rate the filters we study in this paper reduce the variability of interarrival times subject to a maximum delay constraint for each customer these filters are called smoothing filters for point processes by considering the output processes of various queueing systems we show that an infinite server queue acts as a smoothing filter for a doubly stochastic poisson process and a single server queue with deterministic service times acts as a smoothing filter for a stationary and ergodic point process based on the second point we provide a smoothing algorithm that satisfies a maximum delay constraint the algorithm is shown to be robust and consistent we then consider two examples where these filters can be applied to increase throughput one is the single server loss system with exponential service times the other is the leaky bucket scheme with token buffer size 1 numerical examples and simulations are also given for comparing the tradeoff between delay and throughput our approach is based on the variability ordering and a cut criterion for the majorization ordering the criterion appears to be new and of independent interest

numerical solution of stochastic quantum master equations using stochastic interacting wave functions abstract we develop a new approach for solving stochastic quantum master equations with mixed initial states first we obtain that the solution of the jump diffusion stochastic master equation is represented by a mixture of pure states satisfying a system of stochastic differential equations of schrodinger type then we design three exponential schemes for these coupled stochastic schrodinger equations which are driven by brownian motions and jump processes hence we have constructed efficient numerical methods for the stochastic master equations based on quantum trajectories the good performance of the new numerical integrators is illustrated by simulations of two quantum measurement processes

flows in queueing networks a martingale approach this paper applies the filtering theory for point process observations to the analysis of flows in networks an abstract model for the study of markovian queueing systems is developed and used to derive the filtering equations satisfied by the conditional probability distribution of the state given the past of an observed set of flows these filtering equations are used to obtain a necessary and sufficient condition for that observation to be independent of the value of the state of the system at any time this approach also yields a probabilistic interpretation of a necessary condition for a given flow in a multi class jackson network to be poisson these results are combined to give a proof of the loop criterion for single class jackson network and to show that this criterion does not apply to multi class networks examples of loop free jackson networks are given for which some of the flows are not poisson

synchronization of coupled self excited elastic beams abstract the behavior of four coupled self excited elastic beams is numerically studied using the finite difference method self excitation is modeled by adding a van der pol damping term coupling based on shared boundary conditions at the roots of the beams is proposed and the influence of the coupling on the dynamics is analyzed time and space correlation coefficients are employed to measure the degree of synchronization among beams through the power spectral density multiple frequencies of the beam tip time series are determined unveiling the complex nature of the beam motions finally the robustness of the proposed behavior to changes in fluid structure interaction and the mass of the beams is determined

a stable fluid structure interaction solver for low density rigid bodies using the immersed boundary projection method dispersion of low density rigid particles with complex geometries is ubiquitous in both natural and industrial environments we show that while explicit methods for coupling the incompressible navier stokes equations and newton s equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios for more complex particles such as a body with a protrusion they become unstable we present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method similarly to previous work on this method the resulting matrix equation in the present approach is solved using a block lu decomposition each step of the block lu decomposition is modified to incorporate the rigid body dynamics we show that our method achieves second order accuracy in space and first order in time third order for practical settings only with a small additional computational cost to the original method our implicit coupling yields stable solution for density ratios as low as 10 4 we also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method

point processes and queues martingale dynamics i martingales 1 histories and stopping times 2 martingales 3 predictability 4 square integrable martingales references solutions to exercises chapter i ii point processes queues and intensities 1 counting processes and queues 2 watanabe s characterization 3 stochastic intensity general case 4 predictable intensities 5 representation of queues 6 random changes of time 7 cryptographic point processes references solutions to exercises chapter ii iii integral representation of point process martingales 1 the structure of internal histories 2 regenerative form of the intensity 3 the representation theorem 4 hilbert space theory of poissonian martingales 5 useful extensions references solutions to exercises chapter iii iv filtering 1 the theory of innovations 2 state estimates for queues and markov chains 3 continuous states and nontrivial prehistory references solutions to exercises chapter iv v flows in markovian networks of queues 1 single station the historical results and the filtering method 2 jackson s networks 3 burke s output theorem for networks 4 cascades and loops in jackson s networks 5 independence and poissonian flows in markov chains references solutions to exercises chapter v vi likelihood ratios 1 radon nikodym derivatives and tests of hypotheses 2 changes of intensities a la girsanov 3 filtering by the method of the probability of reference 4 applications 5 the capacity of a point process channel 6 detection formula187 references189 solutions to exercises chapter vi vii optimal control 1 modeling intensity controls 2 dynamic programming for intensity controls complete observation case 3 input regulation a case study in impulsive control 4 attraction controls 5 existence via likelihood ratio references solutions to exercises chapter vii viii marked point processes 1 counting measure and intensity kernels 2 martingale representation and filtering 3 radon nikodym derivatives 4 towards a general theory of intensity references solutions to exercises chapter viii a1 background in probability and stochastic processes 1 introduction 2 monotone class theorem 3 random variables 4 expectations 5 conditioning and independence 6 convergence 7 stochastic processes 8 markov processes references a2 stopping times and point process histories 1 stopping times 2 changes of time and meyer dellacherie s integration formula 3 point process histories references a3 wiener driven dynamical systems 1 ito s stochastic integral 2 square integrable brownian martingales 3 girsanov s theorem references a4 stieltjes lebesgue calculus 1 the stieltjes lebesgue integral 2 the product and exponential formulas references general bibliography

vortex induced vibrations of two side by side euler bernoulli beams abstract vortex induced vibration of two side by side elastic beams in a cross flow is numerically studied the two beams are identical and fixed at both ends in the numerical approach the euler bernoulli beam theory is used to model the beam vibration and the laminar navier stokes equations are solved to give the flow field the flow equations are resolved using a finite element method and the flow induced forces are calculated at every time step in order to correctly reflect the fluid beam interaction the beam response is calculated using the modal analysis method free vibrations of the two beams with three pitch ratios t d 1 13 1 7 and 3 0 where t is the gap between the centers of the two beams and d is the beam diameter are simulated at re 800 results obtained are compared with experimental measurements and other numerical results obtained assuming a two degree of freedom 2 d o f model the agreement is good in general correlation analysis is carried out showing that the phase relation is different for different t d the short time fourier transform stft method is used to carry out the spectral analysis along with the conventional auto regressive moving averaging arma method for comparison the stft analysis shows that the time evolution of fluid force and beam vibration for t d 1 13 and 3 0 are stationary for these t d ratios the stft results are consistent with the arma results but give a clearer picture of the higher order harmonics for t d 1 7 the time evolution is non stationary the stft analysis shows that there are three types of frequency spectrum for the fluid force with one two and three dominant frequencies respectively the spectra intermittently change in a random way during the evolution the arma results though consistent with previous experiments can only reveal a particular feature of the three different types of spectrum this suggests that the stft method is more appropriate to analyze the spectra of non stationary time series in the study of flow induced vibrations

an overview of modeling and experiments of vortex induced vibration of circular cylinders abstract this paper reviews the literature on the mathematical models used to investigate vortex induced vibration viv of circular cylinders wake oscillator models single degree of freedom force decomposition models and other approaches are discussed in detail brief overviews are also given of numerical methods used in solving the fully coupled fluid structure interaction problem and of key experimental studies highlighting the nature of viv

constructing constrained invariant sets in multiscale continuum systems we present a method that we name the constrained invariant manifold method a visualization tool to construct stable and unstable invariant sets of a map or flow where the invariant sets are constrained to lie on a slow invariant manifold the construction of stable and unstable sets constrained to an unstable slow manifold is exemplified in a singularly perturbed model arising from a structural mechanical system consisting of a pendulum coupled to a viscoelastic rod additionally we extend the step and stagger method d sweet h nusse and j yorke phys rev lett 86 2261 2001 to calculate a delta pseudoorbit on a chaotic saddle constrained to the slow manifold in order to be able to compute the lyapunov exponents of the saddle

a non linear fluid force model for vortex induced vibration of an elastic cylinder abstract even under the assumption of a sinusoidal lift and drag force at a single frequency for a stationary cylinder in a cross flow higher harmonics that represent non linearity in the fluid structure interaction process are present this fact is considered in the formulation of a non linear fluid force model for a freely vibrating cylinder in a cross flow the force model is developed based on an iterative process and the modal analysis approach the fluid force components in the model can be evaluated from measured vibration data with the help of the auto regressive moving averaging arma technique an example is used to illustrate that non linear higher order force components are present at resonance even for a case with relatively weak fluid structure interaction further analysis reveals that the fluid force components are dependent on structural damping and mass ratio the non linear fluid force model is further modified by taking these considerations into account and is used to predict the dynamic characteristics of a freely vibrating cylinder over a range of reynolds numbers mass and structural damping ratios on comparison with measurements obtained from four different experiments and predictions made by previous single degree of freedom model good agreement is found over a wide range of these parameters

integrating experiments into an energy based reduced order model for vortex induced vibrations of a cylinder mounted as an inverted pendulum abstract high resolution digital particle image velocimetry has been used to measure fluid energy transport terms necessary for developing a scientifically rigorous hamilton s principle approach to modelling fluid structure interactions the interaction being modelled is the vortex induced vibration of a low mass damping circular cylinder mounted like an inverted pendulum in a water tunnel data in this paper are specifically focussed on the case where the cylinder undergoes large amplitude modulated oscillations slightly below the cylinder s natural frequency this paper describes the experimental methodology used to acquire key modelling data i e kinetic energy transport and work by viscous forces across the boundaries of an integral control volume integration of these data into the coupled energy equation is also described the ability of this modelling approach to accurately capture complex phenomena such as beating is demonstrated

a martingale approach to point processes in the plane on donne une definition rigoureuse des processus ponctuels a deux parametres comme une distribution d une quantite denombrable de points aleatoires du plan on obtient une caracterisation avec des droites d arret et une relation avec la predictibilite

a method for interpolating on manifolds structural dynamics reduced order models a rigorous method for interpolating a set of parameterized linear structural dynamics reduced order models roms is presented by design this method does not operate on the underlying set of parameterized full order models hence it is amenable to an online real time implementation it is based on mapping appropriately the rom data onto a tangent space to the manifold of symmetric positive definite matrices interpolating the mapped data in this space and mapping back the result to the aforementioned manifold algorithms for computing the forward and backward mappings are offered for the case where the roms are derived from a general galerkin projection method and the case where they are constructed from modal reduction the proposed interpolation method is illustrated with applications ranging from the fast dynamic characterization of a parameterized structural model to the fast evaluation of its response to a given input in all cases good accuracy is demonstrated at real time processing speeds copyright 2009 john wiley sons ltd

signal processing with levy information levy processes which have stationary independent increments are ideal for modelling the various types of noise that can arise in communication channels if a levy process admits exponential moments then there exists a parametric family of measure changes called esscher transformations if the parameter is replaced with an independent random variable the true value of which represents a message then under the transformed measure the original levy process takes on the character of an information process in this paper we develop a theory of such levy information processes the underlying levy process which we call the fiducial process represents the noise type each such noise type is capable of carrying a message of a certain specification a number of examples are worked out in detail including information processes of the brownian poisson gamma variance gamma negative binomial inverse gaussian and normal inverse gaussian type although in general there is no additive decomposition of information into signal and noise one is led nevertheless for each noise type to a well defined scheme for signal detection and enhancement relevant to a variety of practical situations

exact simulation of point processes with stochastic intensities point processes with stochastic arrival intensities are ubiquitous in many areas including finance insurance reliability health care and queuing they can be simulated from a poisson process by time scaling with the cumulative intensity the paths of the cumulative intensity are often generated with a discretization method however discretization introduces bias into the simulation results the magnitude of the bias is difficult to quantify this paper develops a sampling method that eliminates the need to discretize the cumulative intensity the method is based on a projection argument and leads to unbiased simulation estimators it is exemplified for a point process whose intensity is a function of a jump diffusion process and the point process itself in this setting the method facilitates the exact sampling of both the point process and the driving jump diffusion process numerical experiments demonstrate the effectiveness of the method

characterizing bifurcations and classes of motion in the transition to chaos through 3d tori of a continuous experimental system in solid mechanics abstract the dynamics of a continuous experimental system exhibiting quasiperiodic transition to chaos has been investigated an elastic cable mass system hanging at in phase vertically moving supports is considered with vibrational parameters in the neighbourhood of external and internal resonance conditions adjusted to be able to introduce three torus dynamics measurements of the nonregular response are made in frequency ranges including primary resonance of the first symmetric in plane mode of the cable quantitative characterisation of regular and nonregular attractors and of the configuration variables involved in the motion is made by means of delay embedding technique and proper orthogonal decomposition of spatio temporal flow attention is devoted to analyse in depth the scenario of transition to chaos exhibited by the model steady quasiperiodic motions on three tori partial and full phase locking of the flow and chaotic attractors are observed in spite of the dynamics variedness the systematic characterisation of the response allows us to set the bifurcation behaviour of the experimental system in the framework of theoretic numeric transition to chaos through three dimensional tori

on the drawdowns and drawups in diffusion type models with running maxima and minima we obtain closed form expressions for the values of joint laplace transforms of the running maximum and minimum of a diffusion type process stopped at the first time at which the associated drawdown and drawup processes hit constant levels it is assumed that the coefficients of the diffusion type process are regular functions of the running values of the process itself its maximum and minimum as well as its maximum drawdown and maximum drawup processes the proof is based on the solution to the equivalent boundary value problems and application of the normal reflection conditions for the value functions at the edges of the state space of the resulting five dimensional markov process we show that the joint laplace transforms represent linear combinations of solutions to the systems of first order partial differential equations arising from the application of the normal reflection conditions

methods for the analysis of sampled cohort data in the cox proportional hazards model methods are provided for regression parameter and cumulative baseline hazard estimation in the cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law the key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes leading to estimation methods parallel to those for full cohort data these techniques are illustrated for a number of sampling designs including three novel designs counter matching with additional randomly sampled controls quota sampling of controls and nested case control sampling with number of controls dependent on the failure s exposure status general asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs

an anti pasta result for markovian systems pasta poisson arrivals see time averages is a term coined by r wolff in his well known 1982 paper in keeping with wolff s terminology we use the term anti pasta to refer to the following converse of pasta given that arrivals do indeed see time averages when must the arrival process necessarily be poisson we show that anti pasta is satisfied in a pure jump markov process provided that the arrival process corresponds to a subset of the markov process jumps

on galerkin approximations for the zakai equation with diffusive and point process observations this paper studies galerkin approximations applied to the zakai equation of stochastic filtering the basic idea of this approach is to project the infinite dimensional zakai equation onto some finite dimensional subspace generated by smooth basis functions this leads to a finite dimensional system of stochastic differential equations that can be solved numerically the contribution of the paper is twofold on the theoretical side existing convergence results are extended to filtering models with observations of point process or mixed type on the applied side various issues related to the numerical implementation of the method are considered in particular we propose working with a subspace that is constructed from a basis of hermite polynomials the paper closes with a numerical case study

hamilton s principle for external viscous fluid structure interaction abstract hamilton s principle is extended so as to be able to model external flow structure interaction this is accomplished by using reynold s transport theorem in this form hamilton s principle is hybrid in the sense that it has an analytical part as well as a part that depends on experimentally derived functions examples are presented the discussion on implications and extensions is extensive in this work a general theory is developed for the case where the configuration is not prescribed at the end times of the variational principle this leads to a single governing equation of motion this limitation can be removed by prescribing the end times as usually done this is outlined in the present paper and will be the subject of a future paper a detailed discussion is also presented of the experimental work performed in parallel with and in support of the theoretical developments as a true fluid structural model it is necessary to fully couple the dynamics this has been the foundation of our formulation

zero rate reliability of the exponential server timing channel we determine the reliability function of the exponential server timing channel estc in the limit as the data rate approaches zero the limit shows that at low rates the estc is strictly more reliable than the poisson channel without dark current answering a question arikan posed in these transactions the proof employs a distance metric over inputs to timing channels that parallels euclidean and hamming distance for conventional channels a consequence of the proof is that bounded distance decoding with distance measured according to this metric is exponentially optimum for the estc in the low rate regime we also prove the straight line bound for the channel and a bound on the reliability of timing channels with general service distributions in the limit as the data rate approaches zero

flow induced vibrations of a light circular cylinder at reynolds numbers 103to 104 abstract stabilized space time finite element methods are employed to investigate vortex induced vibrations of a light circular cylinder placed in a uniform flow at reynolds number in the range of 103 104 the governing equations for the fluid flow are the navier stokes equations for incompressible flows the cylinder is mounted on lightly damped flexible supports and allowed to vibrate both in the in line and cross flow directions under the action of aerodynamic forces results are presented for various values of the structural frequency of the oscillator including those that are super harmonics of the vortex shedding frequency for a stationary cylinder in certain cases the effect of the mass of the oscillator is also examined the motion of the cylinder alters the fluid flow significantly to investigate the long term dynamics of the non linear oscillator beyond the initial transient solution long time integration of the governing equations is carried out for efficient utilization of the available computational resources the non linear equation systems resulting from the finite element discretization of the flow equations are solved using the preconditioned generalized minimal residual gmres technique flows at lower reynolds numbers are associated with organized wakes while disorganized wakes are observed at higher reynolds numbers in certain cases competition is observed between various modes of vortex shedding the fluid structure interaction shows a significant dependence on the reynolds number in the range that has been investigated in this article in certain cases lock in while in some other cases soft lock in is observed the trajectory of the cylinder shows very interesting patterns including the well known lissajou figure of 8 several mechanisms of the non linear oscillator for self limiting its vibration amplitude are observed

renewal theory properties of ion channels this paper uses a type of data to attack the problem of deciding whether or not the channels in a membrane are operating independently and if so estimating the distribution of the sojourn periods in emitting and nonomitting states

reduced order modeling of fluid structure interaction and vortex induced vibration systems using an extension of jourdain s principle abstract a first principles variational approach is proposed for reduced order modeling of fluid structure interaction fsi systems specifically vortex induced vibration viv fsi has to be taken into account in the design and analysis of many engineering applications yet a comprehensive theoretical development where analytical equations are derived from first principles is nonexistent an approach where jourdain s principle is modified and extended for fsi is used to derive reduced order models from an extended variational formulation where assumptions are explicitly stated two viv models are considered an elastically supported inverted pendulum and a translating cylinder both immersed in a flow and allowed to move transversely to the flow direction their reduced order models are obtained in the form of i a single governing equation and ii two general coupled equations as well as the coupled lift oscillator model comparisons are made with three existing models based on our theoretical results and especially the reduced order model we conclude that the first principles development herein is a viable framework for the modeling of complex fluid structure interaction problems such as vortex induced oscillations

proper orthogonal decomposition and its applications part ii model reduction for mems dynamical analysis abstract proper orthogonal decomposition pod methods are popular tools for data analysis aimed at obtaining low dimensional approximate descriptions of a high dimensional process in many engineering fields the applications of pod methods to model reduction for microelectromechanical systems mems are reviewed in this paper in view of the fact that existing pod methods in the model reduction for dynamic simulation of mems dealt with only noise free data this paper proposes a neural network based method that combines robust principal component analysis pca neural network model with galerkin procedure for dynamic simulation and analysis of non linear mems with noisy data simulations are given to show the performance of the proposed method in comparison with the existing method compared with the standard pca neural network model the robust pca neural network model has a number of numerical advantages such as the stability and robustness to noise injected data and the faster convergence of iterations in the training stages than the existing neural network technique the macro model generated by using the eigenvectors extracted from the proposed method as basis functions shows its flexibility and efficiency in the representation and simulation of the original non linear partial differential equations

multidimensional residual analysis of point process models for earthquake occurrences residual analysis methods for examining the fit of multidimensional point process models are applied to point process models for the space time magnitude distribution of earthquake occurrences using in particular the multidimensional version of ogata s epidemic type aftershock sequence etas model and a 30 year catalog of 580 earthquakes occurring in bear valley california one method involves rescaled residuals obtained by transforming points along one coordinate to form a homogeneous poisson process inside a random irregular boundary another method involves thinning the point process according to the conditional intensity to form a homogeneous poisson process on the original untransformed space the thinned residuals suggest that the fit of the model may be significantly improved by using an anisotropic spatial distance function in the estimation of the spatially varying background rate using rescaled residuals it is shown that the temporal magnitude distribution of aftershock activity is not

a first principles derivation procedure for wake body models in vortex induced vibration proof of concept abstract a generalized variational equation based on the extended hamilton s principle is presented as the starting point for a procedure from which wake body models for the two dimensional vortex induced vibration of a cylinder can be derived the case of an elastically mounted cylinder with a transverse degree of freedom in a uniform flow is offered as a model problem through which this derivation procedure is illustrated a number of wake body models from the literature are shown to be recoverable from the more general model derived here the correspondence with these classical models is presented as evidence of the feasibility of incorporating this methodology into vortex induced vibration modeling unlike these comparison models however which are often assigned an ad hoc form any assumptions made in arriving at the derived wake body model are explicitly stated

a probabilistic look at networks of quasi reversible queues probabilistic arguments are given to explain some recent results on networks of queues those results are the product form the output theorems the distributions at the jumps and the poisson character of the flows the proposed approach replaces the usual calculations by arguments showing these properties to be consequences of the behavior of the nodes in isolation

trees under attack a ray knight representation of feller s branching diffusion with logistic growth we obtain a representation of feller s branching diffusion with logistic growth in terms of the local times of a reflected brownian motion h with a drift that is affine linear in the local time accumulated by h at its current level as in the classical ray knight representation the excursions of h are the exploration paths of the trees of descendants of the ancestors at time t 0 and the local time of h at height t measures the population size at time t we cope with the dependence in the reproduction by introducing a pecking order of individuals an individual explored at time s and living at time t h s is prone to be killed by any of its contemporaneans that have been explored so far the proof of our main result relies on approximating h with a sequence of harris paths h n which figure in a ray knight representation of the total mass of a branching particle system we obtain a suitable joint convergence of h n together with its local times and with the girsanov densities that introduce the dependence in the reproduction

pricing vulnerable power exchange options in an intensity based framework abstract in this article we study the valuation of a european vulnerable power exchange option in an intensity based framework we assume that the default by the counter party is the time of the first jump of a doubly stochastic poisson process whose intensity is modeled by a jump diffusion process the dynamics of the two assets are assumed to be driven by correlated jump diffusion processes all the three processes are assumed to be correlated in continuous part as well as in the jump part in the proposed framework employing the measure change technique we obtain the explicit formula for the price of the power exchange option with counter party risk furthermore sensitivity analysis is given to illustrate the effects of counterparty risk on the price of the option and effect of various parameters on the option prices

proper orthogonal decomposition and its applications part i theory abstract in view of the increasing popularity of the application of proper orthogonal decomposition pod methods in engineering fields and the loose description of connections among the pod methods the purpose of this paper is to give a summary of the pod methods and to show the connections among these methods firstly the derivation and the performance of the three pod methods karhunen loeve decomposition kld principal component analysis pca and singular value decomposition svd are summarized then the equivalence problem is discussed via a theoretical comparison among the three methods the equivalence of the matrices for processing the objective functions the optimal basis vectors the mean square errors and the asymptotic connections of the three methods are demonstrated and proved when the methods are used to handle the pod of discrete random vectors

on arrivals that see time averages we investigate when arrivals see time averages asta in a stochastic model i e when the stationary distribution of an embedded sequence obtained by observing a continuous time stochastic process just prior to the points arrivals of an associated point process coincides with the stationary distribution of the observed process we also characterize the relation between the two distributions when asta does not hold we introduce a lack of bias assumption lba which stipulates that at any time the conditional intensity of the point process given the present state of the observed process be independent of the state of the observed process we show that lba without the poisson assumption is necessary and sufficient for asta in a stationary process framework consequently lba covers known examples of non poisson asta such as certain flows in open jackson queueing networks as well as the familiar poisson case pasta we also establish results to cover the case in which the process is observed just after the points e g when departures see time averages finally we obtain a new proof of the arrival theorem for product form queueing networks

asymptotic control for a class of piecewise deterministic markov processes associated to temperate viruses we aim at characterizing the asymptotic behavior of value functions in the control of piecewise deterministic markov processes pdmp of switch type under nonexpansive assumptions for a particular class of processes inspired by temperate viruses we show that uniform limits of discounted problems as the discount decreases to zero and time averaged problems as the time horizon increases to infinity exist and coincide the arguments allow the limit value to depend on initial configuration of the system and do not require dissipative properties on the dynamics the approach strongly relies on viscosity techniques linear programming arguments and coupling via random measures associated to pdmp as an intermediate step in our approach we present the approximation of discounted value functions when using piecewise constant in time open loop policies

noise induced unstable dimension variability and transition to chaos in random dynamical systems results are reported concerning the transition to chaos in random dynamical systems in particular situations are considered where a periodic attractor coexists with a nonattracting chaotic saddle which can be expected in any periodic window of a nonlinear dynamical system under noise the asymptotic attractor of the system can become chaotic as characterized by the appearance of a positive lyapunov exponent generic features of the transition include the following 1 the noisy chaotic attractor is necessarily nonhyperbolic as there are periodic orbits embedded in it with distinct numbers of unstable directions unstable dimension variability and this nonhyperbolicity develops as soon as the attractor becomes chaotic 2 for systems described by differential equations the unstable dimension variability destroys the neutral direction of the flow in the sense that there is no longer a zero lyapunov exponent after the noisy attractor becomes chaotic and 3 the largest lyapunov exponent becomes positive from zero in a continuous manner and its scaling with the variation of the noise amplitude is algebraic formulas for the scaling exponent are derived in all dimensions numerical support using both low and high dimensional systems is provided

a nonparametric dynamic additive regression model for longitudinal data in this work we study additive dynamic regression models for longitudinal data these models provide a flexible and nonparametric method for investigating the time dynamics of longitudinal data the methodology is aimed at data where measurements are recorded at random time points we model the conditional mean of responses given the full internal history and possibly time varying covariates we derive the asymptotic distribution for a new nonparametric least squares estimator of the cumulative time varying regression functions based on the asymptotic results confidence bands may be computed and inference about time varying coefficients may be drawn we propose two estimators of the cumulative regression function one estimator that involves smoothing and one that does not the latter however has twice the variance as the smoothing based estimator goodness of fit of the model is considered using martingale residuals finally we also discuss how partly conditional mean models in which the mean of the response is regressed onto selected time varying covariates may be analysed in the same framework we apply the methods to longitudinal data on height development for cystic fibrosis patients

detection of stochastic processes this paper reviews two streams of development from the 1940 s to the present in signal detection theory the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance this treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous time stochastic processes the mathematics and intuition behind such developments as the matched filter the rake receiver the estimator correlator maximum likelihood sequence detectors multiuser detectors sequential probability ratio tests and cumulative sum quickest detectors are described

martingale dynamics and optimal routing in a network in this paper we consider a dynamic routing problem in a store and forward computer communication network which consists of l parallel channels connected between the source and the destination we prove that if messages arrive at the network in accordance with a poisson process and all nodes have an exponential service rate then the routing strategy that minimizes the total expected time in transmitting all messages that arrive before t 0 is to route the arriving message to the channel along which the sum of all queue sizes is minimum techniques of martingale and dynamic programming are used in obtaining the result

vortex shedding analysis by finite elements abstract despite the rapid progress in numerical fluid dynamics vortex shedding simulation is still a complicated process requiring its representation by empirical models the applicability of these models is often restricted by their inherent non linearity to simple beams the complexities of most structural systems demand an improved generalization of the suggested models and a more representative method of analysis in this paper the finite element method in conjunction with scanlan s vortex shedding empirical model used extensively for long span bridges is employed to formulate a plane frame element based on simple assumptions conforming with the attributes of flow induced vibrations the proposed approach is extended further to encompass a space frame element the developed elements are then used to analyze elementary structures subjected to vortex shedding instability the vortex shedding oscillatory response is determined by assembling and solving the constituent nonlinear equations of motion using a direct integration scheme and an iterative process the results verify the validity of the proposed finite element procedure which should prove to be a flexible means of vortex shedding analysis for more complex structure types

option pricing with a general marked point process this paper examines the impact of a random number of price changes on the options valuation the model introduces the structure of the general marked point processes mpp this kind of model allows us to take account of more general distributions of interarrival times than usual jump diffusion models in particular stock price variations can be correlated with the times of transactions thus the investors can decide to trade according to the history of market values and the sizes of price variations can also depend on the past times of transactions by using the special decomposition of predictable processes with respect to a marked point process the determination of all risk neutral probabilities is detailed derivative prices are calculated in this context with different basic examples

resonance and symmetry breaking for the pendulum abstract periodic solutions of the differential equation for periodic forcing of a lightly damped pendulum are obtained on the alternative hypotheses that i the contributions of second and higher harmonics to the average lagrangian are negligible or ii the solution is close to that for free oscillations the resonance curves amplitude or root mean energy vs driving frequency and stability boundaries for symmetric swinging oscillations and their asymmetric descendents following symmetry breaking are determined for 1 and o where is the ratio of actual to critical damping and is the ratio of the maximum external moment to the maximum gravitational moment resonance as defined by synchronism between the external moment and the damping moment is found to be impossible and the conventional resonance curve separates into two branches if 3 28 o 3 which condition is necessary for normal symmetry breaking a numerical fourier series determination of the resonance curve and bifurcation points for 1 8 and 1 2 is presented in an appendix by p j bryant

dynamics of large scale coupled structural mechanical systems a singular perturbation proper orthogonal decomposition approach we have combined the theories of geometric singular perturbation and proper orthogonal decomposition to study systematically the dynamics of coupled systems in mechanics involving coupling between continuous structures and nonlinear oscillators here we analyze a prototypical structural mechanical system consisting of a planar nonlinear pendulum coupled to a flexible rod made of linear viscoelastic material we cast the equations of motion in a singularly perturbed set of oscillators and compute analytic approximations to an attractive global invariant manifold in phase space of the coupled system the invariant manifold two dimensional for the unforced system and three dimensional for the forced system carries a continuum of slow motions for a sufficiently stiff rod a proper orthogonal decomposition of any long time motion extracts a single structure for the spatial coherence of the dynamics which is a realization of the slow invariant manifold as the flexibility of the rod increases the energy of

karhunen loeve modes of a truss transient response reconstruction and experimental verification karhunen loeve k l or proper orthogonal decomposition modes are used to discretize the dynamics of a four bay linear truss this is achieved by defining global k l modal amplitudes and employing the orthogonality relations between k l modes that are inherent in the k l decomposition it is found that the k l based low order models can capture satisfactory the transient dynamics of the truss even when only a limited number of them is used for the order reduction a comparison between the exact and low order dynamics in the frequency domain reveals that the low order models capture the leading resonances of the truss a series of experiments with a practical three bay truss is then performed to validate the theoretical k l decomposition a comparison between theory and experiment indicates agreement between the predicted and realized dominant k l mode shapes but less so in the higher order modes the reasons for this discrepancy between theory and experiment are discussed and possible applications of the k l based order reduction to passive and active control of practical large scale flexible systems are outlined

estimation of continuous time markov processes sampled at random time intervals we introduce a family of generalized method of moments estimators of the parameters of a continuous time markov process observed at random time intervals the results include strong consistency asymptotic normality and a characterization of standard errors sampling is at an arrival intensity that is allowed to depend on the underlying markov process and on the parameter vector to be estimated we focus on financial applications including tick based sampling allowing for jump diffusions regime switching diffusions and reflected diffusions

relative efficiency of the log rank test within a multiplicative intensity model summary for large sample clinical trials with independent individuals randomly allocated to two treatment groups in which survival times follow a log linear multiplicative intensity model with treatment group as one covariate this paper calculates the asymptotic relative efficiency of the log rank test for treatment effect as compared with the optimal score test the method is to exhibit the failure hazard intensity not of proportional hazards form obtained by ignoring all covariates other than treatment group the efficiency formulae are illustrated in two examples and estimation from data of the loss of efficiency is illustrated for two clinical trial datasets

jump diffusion processes in random environments abstract in this paper we investigate jump diffusion processes in random environments which are given as the weak solutions of sdes we formulate conditions ensuring existence and uniqueness in law of solutions we investigate the markov property to prove uniqueness we solve a general martingale problem for cadlag processes this result is of independent interest application of our results to generalized exponential levy model are present in the last section

specification diagnostics for duration models a martingale approach abstract this paper develops specification diagnostics for discrete time duration models which are based on the martingale theory of stochastic processes the methods can be applied to parametric grouped data duration models with time varying covariates right censoring and which account for unobserved heterogeneity a residual process is defined such that under the correct model specification the process is approximately a martingale difference sequence chi square tests based on these residuals are derived results from monte carlo simulations are presented

dimensional implications of dynamical data on manifolds to empirical kl analysis abstract we explore the approximation of attracting manifolds of complex systems using dimension reducing methods complex systems having high dimensional dynamics typically are initially analyzed by exploring techniques to reduce the dimension linear techniques such as galerkin projection methods and nonlinear techniques such as center manifold reduction are just some of the examples used to approximate the manifolds on which the attractors lie in general if the manifold is not highly curved then both linear and nonlinear methods approximate the surface well however if the manifold curvature changes significantly with respect to parametric variations then linear techniques may fail to give an accurate model of the manifold this may not be a surprise in itself but it is a fact so often overlooked or misunderstood when utilizing the popular kl method that we offer this explicit study of the effects and consequences here we show that certain dimensions defined by linear methods are highly sensitive when modeled in situations where the attracting manifolds have large parametric curvature specifically we show how manifold curvature mediates the dimension when using a linear basis set as a model we punctuate our results with the definition of what we call a curvature induced parameter d c i both finite and infinite dimensional models are used to illustrate the theory