solution of 3d inverse scattering problems by combined inverse equivalent current and finite element methods an approach combining boundary integral and finite element methods is introduced for the solution of three dimensional inverse electromagnetic medium scattering problems based on the equivalence principle unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts a linear radiation problem and a nonlinear cavity problem the first problem is formulated by a boundary integral equation the computational burden of which is reduced by employing the multilevel fast multipole method mlfmm reconstructed cauchy data on the surface allows the utilization of the lorentz reciprocity and the poynting s theorems exploiting these theorems the noise level and an initial guess are estimated for the cavity problem moreover it is possible to determine whether the material is lossy or not in the second problem the estimated surface currents form inhomogeneous boundary conditions of the cavity problem the cavity problem is formulated by the finite element technique and solved iteratively by the gauss newton method to reconstruct the properties of the object regularization for both the first and the second problems is achieved by a krylov subspace method the proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained

an cal o n level set method for eikonal equations a propagating interface can develop corners and discontinuities as it advances level set algorithms have been extensively applied for the problems in which the solution has advancing fronts one of the most popular level set algorithms is the so called fast marching method fmm which requires total cal o n log 2n operations where n is the number of grid points the article is concerned with the development of an cal o n level set algorithm called the group marching method gmm the new method is based on the narrow band approach as in the fmm however it is incorporating a correction by iteration strategy to advance a group of grid points at a time rather than sorting the solution in the narrow band to march forward a single grid point after selecting a group of grid points appropriately the gmm advances the group in two iterations for the cost of slightly larger than one iteration numerical results are presented to show the efficiency of the method applied to the eikonal equation in two and three dimensions

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

a review of statistical data association for motion correspondence motion correspondence is a fundamental problem in computer vision and many other disciplines this article describes statistical data association techniques originally developed in the context of target tracking and surveillance and now beginning to be used in dynamic motion analysis by the computer vision community the mahalanobis distance measure is first introduced before discussing the limitations of nearest neighbor algorithms then the track splitting joint likelihood multiple hypothesis algorithms are described each method solving an increasingly more complicated optimization real time constraints may prohibit the application of these optimal methods the suboptimal joint probabilistic data association algorithm is therefore described the advantages limitations and relationships between the approaches are discussed

piecewise smoothed value picking regularization applied to 2 d tm and te inverse scattering the stepwise relaxed value picking srvp regularization technique proposed earlier for the iterative reconstruction of piecewise quasi homogeneous objects is a non spatial technique whereby the reconstruction unknowns are clustered around a limited number of a priori unknown reference values artifacts have been observed in some 2 d and 3d complex permittivity reconstructions this paper therefore combines the non spatial srvp technique with a spatial smoothing technique whereby the reference values provided by the former in each iteration are employed by the latter to define separate smoothing regions this way edges are preserved since the spatial smoothing constraints in the cost function are active within but not across the region boundaries this combined technique denoted as stepwise relaxed piecewise smoothed value picking srpsvp regularization is formulated for the 2 5d microwave inverse scattering problem and is illustrated with reconstructions from the institut fresnel 2 d scattering database

solutions to hybrid inclusions via set and graphical convergence with stability theory applications motivated by questions in stability theory for hybrid dynamical systems we establish some fundamental properties of the set of solutions to such systems using the notion of a hybrid time domain and general results on set and graphical convergence we establish under weak regularity and local boundedness assumptions that the set of solutions is sequentially compact and upper semicontinuous with respect to initial conditions and system perturbations the general facts are then used to establish several results for the behavior of hybrid systems that have asymptotically stable compact sets these results parallel what is already known for differential inclusions and difference inclusions for example the basin of attraction for a compact attractor is relatively open the attractivity is uniform from compact subsets of the basin of attraction and asymptotic stability is robust with respect to small perturbations

tracking multiple particles in fluorescence time lapse microscopy images via probabilistic data association tracking subcellular structures as well as viral structures displayed as particles in fluorescence microscopy images yields quantitative information on the underlying dynamical processes we have developed an approach for tracking multiple fluorescent particles based on probabilistic data association the approach combines a localization scheme that uses a bottom up strategy based on the spot enhancing filter as well as a top down strategy based on an ellipsoidal sampling scheme that uses the gaussian probability distributions computed by a kalman filter the localization scheme yields multiple measurements that are incorporated into the kalman filter via a combined innovation where the association probabilities are interpreted as weights calculated using an image likelihood to track objects in close proximity we compute the support of each image position relative to the neighboring objects of a tracked object and use this support to recalculate the weights to cope with multiple motion models we integrated the interacting multiple model algorithm the approach has been successfully applied to synthetic 2 d and 3 d images as well as to real 2 d and 3 d microscopy images and the performance has been quantified in addition the approach was successfully applied to the 2 d and 3 d image data of the recent particle tracking challenge at the ieee international symposium on biomedical imaging isbi 2012

an inexact newton based approach to microwave imaging within the contrast source formulation in this paper an approach to microwave imaging based on an inexact newton method within the contrast source formulation of the inverse scattering problem is considered in this framework the iteratively linearized equations of the inverse problem are solved by means of the regularizing truncated landweber algorithm this approach allows an effective and robust tool to inspect dielectric objects as it is shown by the reported numerical results moreover thanks to the structure of the involved integral equations within the contrast source formulation computer memory saving can be obtained with respect to the electric field integral equation framework finally the proposed method is validated against experimental data kindly provided by the institute fresnel marseille france

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

hybrid systems with memory existence and well posedness of generalized solutions hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena while systems of this type are frequently encountered in many physical and engineering systems particularly in control applications various issues centered around the robustness of hybrid delay systems have not been adequately dealt with in this paper we establish some basic results on a framework that allows us to study hybrid systems with memory through generalized concepts of solutions in particular we develop the basic existence of generalized solutions using regularity conditions on the hybrid data which are formulated in a phase space of hybrid trajectories equipped with the graphical convergence topology in contrast with the uniform convergence topology that has often been used adopting the graphical convergence topology allows us to establish well posedness of hybrid systems with memory we then show that as a consequence of well posedness preasymptotic stability of well posed hybrid systems wit

full wave three dimensional microwave imaging with a regularized gauss newton method theory and experiment a reconstruction algorithm is detailed for three dimensional full vectorial microwave imaging based on newton type optimization the goal is to reconstruct the three dimensional complex permittivity of a scatterer in a homogeneous background from a number of time harmonic scattered field measurements the algorithm combines a modified gauss newton optimization method with a computationally efficient forward solver based on the fast fourier transform method and the marching on in source position extrapolation procedure a regularized cost function is proposed by applying a multiplicative additive regularization to the least squares datafit this approach mitigates the effect of measurement noise on the reconstruction and effectively deals with the non linearity of the optimization problem it is furthermore shown that the modified gauss newton method converges much faster than the broyden fletcher goldfarb shanno quasi newton method promising quantitative reconstructions from both simulated and experimental data are presented the latter data are bi static polarimetric free space measurements provided by institut fresnel marseille france

a compressed implicit jacobian scheme for 3d electromagnetic data inversion we developed a compressed implicit jacobian scheme for the regularized gauss newton inversion algorithm for reconstructing 3d conductivity distributions from electromagnetic data in this algorithm the jacobian matrix whose storage usually requires a large amount of memory is decomposed in terms of electric fields excited by sources located and oriented identically to the physical sources and receivers as a result the memory usage for the jacobian matrix reduces from o nfnsnrnp to o nf ns nr np where nf is the number of frequencies ns is the number of sources nr is the number of receivers and np is the number of conductivity cells to be inverted when solving the gauss newton linear system of equations using iterative solvers the multiplication of the jacobian matrix with a vector is converted to matrix vector operations between the matrices of the electric fields and the vector in order to mitigate the additional computational overhead of this scheme these fields are further compressed us

an efficient implementation of reid s multiple hypothesis tracking algorithm and its evaluation for the purpose of visual tracking an efficient implementation of reid s multiple hypothesis tracking mht algorithm is presented in which the k best hypotheses are determined in polynomial time using an algorithm due to murly 1968 the mht algorithm is then applied to several motion sequences the mht capabilities of track initiation termination and continuation are demonstrated together with the latter s capability to provide low level support of temporary occlusion of tracks between 50 and 150 corner features are simultaneously tracked in the image plane over a sequence of up to 51 frames each corner is tracked using a simple linear kalman filter and any data association uncertainty is resolved by the mht kalman filter parameter estimation is discussed and experimental results show that the algorithm is robust to errors in the motion model an investigation of the performance of the algorithm as a function of look ahead tree depth indicates that high accuracy can be obtained for tree depths as shallow as three experimental results suggest that a real time mht solution to the motion correspondence problem is possible for certain classes of scenes

variants of bicgstab for matrices with complex spectrum recently van der vorst siam j sci statist comput 13 1992 pp 631 644 proposed for solving nonsymmetric linear systems az b a biconjugate gradient bicg based krylov space method called bicgstab that like the biconjugate gradient squared bicgs method of sonneveld does not require matrix vector multiplications with the transposed matrix a t and that has typically a much smoother convergence behavior than bicg and bicgs its nth residual polynomial is the product of the one of bicg i e the nth lanczos polynomial with a polynomial of the same degree with real zeros therefore nonreal eigenvalues of a are not approximated well by the second polynomial factor here the author presents for real nonsymmetric matrices a method bicgstab2 in which the second factor may have complex conjugate zeros moreover versions suitable for complex matrices are given for both methods

application of the multiplicative regularized gauss newton algorithm for three dimensional microwave imaging we apply the so called multiplicative regularized gauss newton inversion algorithm for solving three dimensional electromagnetic microwave inverse problems this inversion algorithm automatically adjusts the regularization parameter and when combined with the total variation type regularization function it can provide inversion results with excellent edge preserving characteristics in addition in order to deal with an extensive memory requirement for the gauss newton method we employ an implicit jacobian calculation scheme by using this scheme we do not have to explicitly store the jacobian matrix hence we are able to significantly reduce the memory requirement of the gauss newton method albeit at an additional computational overhead furthermore in order to be able to handle a large scale computational problem both the forward and the inversion algorithms are parallelized using the mpi library where we obtain a nearly linear speedup factor we demonstrate efficiency and robustness of this algorithm by inverting synthetic data fresnel experimental data and biomedical experimental data

razumikhin type theorems for hybrid system with memory in this paper we address the stability problem of hybrid systems with memory which are newly developed to model hybrid dynamic systems affected by delays for such systems stability criteria are developed based on razumikhin type conditions which are usually applied in the delay systems we prove that the hybrid system with memory is uniformly globally pre asymptotically stable by small gain theorem besides a relaxed razumikhin type stability criterion is also proposed which does not require strict decrease of the lyapunov razumikhin function during jumps several examples are given to illustrate the effectiveness and generality of the proposed results

fast marching methods fast marching methods are numerical schemes for computing solutions to the nonlinear eikonal equation and related static hamilton jacobi equations based on entropy satisfying upwind schemes and fast sorting techniques they yield consistent accurate and highly efficient algorithms they are optimal in the sense that the computational complexity of the algorithms is o n log n where n is the total number of points in the domain the schemes are of use in a variety of applications including problems in shape offsetting computing distances from complex curves and surfaces shape from shading photolithographic development computing first arrivals in seismic travel times construction of shortest geodesics on surfaces optimal path planning around obstacles and visibility and reflection calculations in this paper we review the development of these techniques including the theoretical and numerical underpinnings provide details of the computational schemes including higher order versions and demonstrate the techniques in a collection of different areas

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

uniform asymptotic stability of impulsive delay differential equations abstract in this paper criteria on uniform asymptotic stability are established for impulsive delay differential equations using lyapunov functions and razumikhin techniques it is shown that impulses do contribute to yield stability properties even when the underlying system does not enjoy any stability behavior some examples are also discussed to illustrate the theorems

stability and l2 gain analysis for switched delay systems a delay dependent method in this paper we study stability and l 2 gain for a class of switched systems with time varying delays sufficient conditions for exponential stability and weighted l 2 gain are developed for a class of switching signals with average dwell time these conditions are delay dependent and are given in the form of linear matrix inequalities lmis as a special case of such switching signals we can obtain exponential stability and normal l 2 gain under arbitrary switching signals the state decay estimate is explicitly given two examples illustrate the effectiveness and applicability of the proposed method

generalized lyapunov approach for functional differential inclusions abstract this paper is concerned with the generalized lyapunov approach for functional differential inclusions fdi at first we prove a class of generalized halanay s inequalities then by applying the generalization of halanay s inequalities we investigate the uniformly ultimate boundedness and uniformly asymptotic stability of fdi

iterative forward and inverse algorithms based on domain integral equations for three dimensional electric and magnetic objects an iterative approach to full vector three dimensional inverse scattering problems where the unknown objects can have conductivity permittivity and permeability different from the known background medium is discussed since this problem involves a large number of unknowns it has to be solved effectively and efficiently so that the results can be obtained in timely manner the forward modeling is based on a domain integral equation approach formulated in terms of the electric and magnetic contrast sources normalized with the characteristic impedance of the background medium our numerical tests indicate that this formulation is prerequisite in order to arrive at a forward solution within an acceptable number of iterations and hence it is also of significant importance in the optimization process of the inverse problem the inverse scattering problem is attacked using the multiplicative regularized contrast source inversion method as known in the literature the complexity of this inverse method is approximately equal to the complexity of two equivalent forward algorithms of the conjugate gradient type furthermore this inverse method has been armed with a weighted l2 norm regularizer which has been included as a multiplicative constraint some representative numerical testings will be presented to illustrate the ability of the our numerical algorithms

lyapunov razumikhin method for impulsive functional differential equations and applications to the population dynamics the present paper deals with the investigation of the stability of the zero solution of impulsive functional differential equations by means of piecewise continuous functions coupled with the razumikhin technique sufficient conditions for stability uniform stability and asymptotic stability of the zero solution of such equations are found

integral input to state stability for hybrid delayed systems with unstable continuous dynamics this paper considers integral input to state stability iiss for a class of hybrid time delay systems discrete dynamics includes impulsive and switching signals and continuous dynamics is not necessarily stable based on multiple lyapunov krasovskii functionals a dwell time bound is explicitly given to guarantee iiss of the hybrid delayed system compared with existing results on related problems the obtained stability criteria can be applied to a larger class of hybrid delayed systems moreover the obtained dwell time bound is less conservative than existing ones at last an example related to networked control systems ncss is provided to illustrate the effectiveness of the proposed result

lyapunov based sufficient conditions for stability of hybrid systems with memory hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena in this note we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions these generalized solutions motivated by studying robustness and well posedness of such systems are defined on hybrid time domains and parameterized by both continuous and discrete time we establish lyapunov based sufficient conditions for asymptotic stability using both lyapunov razumikhin functions and lyapunov krasovskii functionals examples are provided to illustrate these conditions

spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumor a reconstruction algorithm to simultaneously estimate the shape and location of three dimensional breast cancer tumor is presented and its utility is analyzed the approach is based on a spherical harmonic decomposition to capture the shape of the tumor we combine a gradient descent optimization method with a direct electromagnetic solver to determine the coefficients in the harmonic expansion as well as the coordinates of the center of the tumor the results demonstrate the potential advantage of collecting data using a multiple view tomographic type strategy we show how the order of the harmonic expansion must be increased to capture increasingly irregularly shaped tumors and explore the resulting increase in the central processing unit cpu time required by the algorithm our approach shows accurate reconstruction of the tumor image regardless of the source polarization this work demonstrates the promise of the algorithm when used on data corrupted with gaussian noise and when perfect knowledge of the tumor electrical properties is not available

nonlinear microwave imaging for breast cancer screening using gauss newton s method and the cgls inversion algorithm breast cancer screening using microwave imaging is emerging as a new promising technique as a supplement to x ray mammography to create tomographic images from microwave measurements it is necessary to solve a nonlinear inversion problem for which an algorithm based on the iterative gauss newton method has been developed at dartmouth college this algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the tikhonov algorithm in this paper a new algorithm for determining the iteration update values in the gauss newton algorithm is presented which is based on the conjugate gradient least squares cgls algorithm the iterative cgls algorithm is capable of solving the update problem by operating on just the jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations the new algorithm is compared to the gauss newton algorithm with tikhonov regularization and is shown to reconstruct images of similar quality using fewer iterations

brief paper razumikhin type stability theorems for discrete delay systems in this paper by employing the razumikhin technique and lyapunov functions razumikhin type theorems that guarantee the uniform stability uniformly asymptotic stability and uniformly exponential stability for the general discrete delay systems are established respectively moreover razumikhin type uniformly exponential stability theorem gives the estimation of the convergence speed as theoretic application the razumikhin type uniformly exponential stability result is further studied and used to show some well known stability results for some kinds of discrete delay systems finally examples are also worked through to illustrate our results

resolving motion correspondence for densely moving points studies the motion correspondence problem for which a diversity of qualitative and statistical solutions exist we concentrate on qualitative modeling especially in situations where assignment conflicts arise either because multiple features compete for one detected point or because multiple detected points fit a single feature point we leave out the possibility of point track initiation and termination because that principally conflicts with allowing for temporary point occlusion we introduce individual combined and global motion models and fit existing qualitative solutions in this framework additionally we present a tracking algorithm that satisfies these possibly constrained models in a greedy matching sense including an effective way to handle detection errors and occlusion the performance evaluation shows that the proposed algorithm outperforms existing greedy matching algorithms finally we describe an extension to the tracker that enables automatic initialization of the point tracks several experiments show that the extended algorithm is efficient hardly sensitive to its few parameters and qualitatively better than other algorithms including the presumed optimal statistical multiple hypothesis tracker

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

a lyapunov proof of an improved maximum allowable transfer interval for networked control systems simple lyapunov proofs are given for an improved relative to previous results that have appeared in the literature bound on the maximum allowable transfer interval to guarantee global asymptotic or exponential stability in networked control systems and also for semiglobal practical asymptotic stability with respect to the length of the maximum allowable transfer interval

exponential stability for impulsive delay differential equations by razumikhin method abstract in this paper we study exponential stability for impulsive delay differential equation of the form x t f t x t t t k x t i k t x t t t k k n by employing the razumikhin technique and lyapunov functions several exponential stability criteria are established some examples are also discussed to illustrate our results

finding trajectories of feature points in a monocular image sequence identifying the same physical point in more than one image the correspondence problem is vital in motion analysis most research for establishing correspondence uses only two frames of a sequence to solve this problem by using a sequence of frames it is possible to exploit the fact that due to inertia the motion of an object cannot change instantaneously by using smoothness of motion it is possible to solve the correspondence problem for arbitrary motion of several nonrigid objects in a scene we formulate the correspondence problem as an optimization problem and propose an iterative algorithm to find trajectories of points in a monocular image sequence a modified form of this algorithm is useful in case of occlusion also we demonstrate the efficacy of this approach considering synthetic laboratory and real scenes

lyapunov conditions for input to state stability of hybrid systems with memory this paper studies input to state stability for hybrid systems with memory which models hybrid dynamics affected by time delays using both lyapunov razumikhin functions and lyapunov krasovskii functionals lyapunov based sufficient conditions are established for input to state stability in addition further extensions and relaxations are proposed for special cases such as the stable flow jump cases and the cases that lyapunov functions do not decrease strictly during flow jumps finally two examples are used to illustrate the developed results

stabilization of nonlinear systems with time varying input and state delays by approximate predictor in this paper the stabilization problem of nonlinear systems with time varying input and state delays is considered by an approximate predictor due to the introduction of state delays the nonlinear dynamic without state delays is used to predict the plant state and a new error term is introduced into the approximation error between the prediction value and the future state of the plant by lyapunov krasovskii functional and small gain argument the stability of the whole closed loop system is guaranteed provided that the sampling period the predictor accuracy and the upper bound of state delays satisfy an inequality constraint the effectiveness of the proposed results is illustrated by a numerical example

2 5d forward and inverse modeling for interpreting low frequency electromagnetic measurements we present 2 5d fast and rigorous forward and inversion algorithms for deep electromagnetic em applications that include crosswell and controlled source em measurements the forward algorithm is based on a finite difference approach in which a multifrontal lu decomposition algorithm simulates multisource experiments at nearly the cost of simulating one single source experiment for each frequency of operation when the size of the linear system of equations is large the use of this noniterative solver is impractical hence we use the optimal grid technique to limit the number of unknowns in the forward problem the inversion algorithm employs a regularized gauss newton minimization approach with a multiplicative cost function by using this multiplicative cost function we do not need a priori data to determine the so called regularization parameter in the optimization process making the algorithm fully automated the algorithm is equipped with two regularization cost functions that allow us to reconstruct either a smooth or a sharp conductivity image to increase the robustness of the algorithm we also constrain the minimization and use a line search approach to guarantee the reduction of the cost function after each iteration to demonstrate the pros and cons of the algorithm we present synthetic and field data inversion results for crosswell and controlled source em measurements

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

connections between razumikhin type theorems and the iss nonlinear small gain theorem a razumikhin type theorem that guarantees input to state stability for functional differential equations with disturbances is established using the nonlinear small gain theorem the result is used to show that input to state stabilizability for nonlinear finite dimensional control systems is robust in an appropriate sense to small time delays at the input also relaxed razumikhin type conditions guaranteeing global asymptotic stability for differential difference equations are given

single quantum dot tracking based on perceptual grouping using minimal paths in a spatiotemporal volume semiconductor quantum dots qds are new fluorescent probes with great promise for ultrasensitive biological imaging when detected at the single molecule level qd tagged molecules can be observed and tracked in the membrane of live cells over unprecedented durations the motion of these individual molecules recorded in sequences of fluorescence images can reveal aspects of the dynamics of cellular processes that remain hidden in conventional ensemble imaging due to qd complex optical properties such as fluorescence intermittency the quantitative analysis of these sequences is however challenging and requires advanced algorithms we present here a novel approach which instead of a frame by frame analysis is based on perceptual grouping in a spatiotemporal volume by applying a detection process based on an image fluorescence model we first obtain an unstructured set of points individual molecular trajectories are then considered as minimal paths in a riemannian metric derived from the fluorescence image stack these paths are computed with a variant of the fast marching method and few parameters are required we demonstrate the ability of our algorithm to track intermittent objects both in sequences of synthetic data and in experimental measurements obtained with individual qd tagged receptors in the membrane of live neurons while developed for tracking qds this method can however be used with any fluorescent probes

hybrid systems with delayed jumps asymptotic stability via robustness and lyapunov conditions hybrid systems subject to delayed jumps form a class of dynamical systems with broad applications this article develops sufficient conditions for robust asymptotic stability of hybrid systems in the presence of delayed jumps more precisely given a delay free hybrid system we introduce a higher order delayed system parametrized by the length of delays we show that when the delay parameter is set to zero the higher order model captures the solutions of the delay free system under mild conditions it is shown that when the delay free system has an asymptotically stable compact set for small enough delays solutions of the delayed system converge to a neighborhood of a set of interest related to the aforementioned compact set then lyapunov functions for the delay free system are used to develop sufficient conditions for asymptotic stability in the presence of delays unlike prior work in the literature the results pertaining to these notions of stability hold for systems possessing zeno solutions with time varying delays importantly the required conditions are expressed in finite dimensional space and depend primarily on the data of the delay free system the practical stability result is validated numerically through the hybrid system model of a controlled boost converter circuit with state triggered switches and zeno solutions the higher order model and the derived lyapunov conditions are utilized to obtain quantitative bounds on maximum allowable delays for switched systems and sampled data control