unknown time varying input delay compensation for uncertain nonlinear systems abstract a tracking controller is developed for a class of uncertain nonlinear systems subject to unknown time varying input delay and additive disturbances a novel filtered error signal is designed using the past states in a finite integral over a constant estimated delay interval the maximum tolerable error between unknown time varying delay and a constant estimate of the delay is determined to establish uniformly ultimately bounded convergence of the tracking error to the origin the controller development is based on an approach which uses lyapunov krasovskii functionals to analyze the effects of unknown sufficiently slowly time varying input delays a stability analysis is provided to prove ultimate boundedness of the tracking error signals numerical simulation results illustrate the performance of the developed robust controller

achieving minimum length scale in topology optimization using nodal design variables and projection functions a methodology for imposing a minimum length scale on structural members in discretized topology optimization problems is described nodal variables are implemented as the design variables and are projected onto element space to determine the element volume fractions that traditionally define topology the projection is made via mesh independent functions that are based upon the minimum length scale a simple linear projection scheme and a non linear scheme using a regularized heaviside step function to achieve nearly 0 1 solutions are examined the new approach is demonstrated on the minimum compliance problem and the popular simp method is used to penalize the stiffness of intermediate volume fraction elements solutions are shown to meet user defined length scale criterion without additional constraints penalty functions or sensitivity filters no instances of mesh dependence or checkerboard patterns have been observed copyright 2004 john wiley sons ltd

positive forms and stability of linear time delay systems we consider the problem of constructing lyapunov functions for linear differential equations with delays for such systems it is known that exponential stability implies the existence of a positive lyapunov function which is quadratic on the space of continuous functions we give an explicit parameterization of a sequence of finite dimensional subsets of the cone of positive lyapunov functions using positive semidefinite matrices this allows stability analysis of linear time delay systems to be formulated as a semidefinite program

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

a relaxed quadratic function negative determination lemma and its application to time delay systems abstract the quadratic function with respect to the time varying delay has often been introduced for the analysis of systems with time varying delays to determine the negative definiteness of such function this paper develops a parameter adjustable based lemma which contains the lemma popularly used in literature as a special case and has potential to reduce the conservatism without requiring extra decision variables a stability criterion for a linear time delay system is established by using the proposed lemma whose advantage is demonstrated via a numerical example and the criterion is finally applied to analyze the stability of load frequency control scheme for a single area power system

dti segmentation using an information theoretic tensor dissimilarity measure in recent years diffusion tensor imaging dti has become a popular in vivo diagnostic imaging technique in radiological sciences in order for this imaging technique to be more effective proper image analysis techniques suited for analyzing these high dimensional data need to be developed in this paper we present a novel definition of tensor distance grounded in concepts from information theory and incorporate it in the segmentation of dti in a dti the symmetric positive definite spd diffusion tensor at each voxel can be interpreted as the covariance matrix of a local gaussian distribution thus a natural measure of dissimilarity between spd tensors would be the kullback leibler kl divergence or its relative we propose the square root of the j divergence symmetrized kl between two gaussian distributions corresponding to the diffusion tensors being compared and this leads to a novel closed form expression for the distance as well as the mean value of a dti unlike the traditional frobenius norm based tensor distance our distance is affine invariant a desirable property in segmentation and many other applications we then incorporate this new tensor distance in a region based active contour model for dti segmentation synthetic and real data experiments are shown to depict the performance of the proposed model

variation of constants for hybrid systems of functional differential equations the objective is to derive a variation of constants formula for systems of functional differential equations or delay differential equations coupled with functional equations or difference equations the difficulties arise because of the constraints imposed by the functional equations

structural optimization under uncertain loads and nodal locations this paper presents algorithms for solving structural topology optimization problems with uncertainty in the magnitude and location of the applied loads and with small uncertainty in the location of the structural nodes the second type of uncertainty would typically arise from fabrication errors where the tolerances for the node locations are small in relation to the length scale of the structural elements we first review the discrete form of the uncertain loads problem which has been previously solved using a weighted average of multiple load patterns with minor modifications we extend this solution to include loads described by continuous joint probability density functions we then proceed to the main contribution of this paper structural optimization under uncertainty in the nodal locations this optimization problem is computationally difficult because it involves variations of the inverse of the structural stiffness matrix it is shown however that for small uncertainties the problem can be recast into a simpler but equivalent structural optimization problem with equivalent uncertain loads by expressing these equivalent loads in terms of continuous random variables we are able to make use of the extended form of the uncertain loads problem presented in the first part of this paper the optimization algorithms are developed in the context of minimum compliance maximum stiffness design simple examples are presented the results demonstrate that load and nodal uncertainties can have dramatic impact on optimal design for structures containing thin substructures under axial loads it is shown that these uncertainties a are of first order significance influencing the linear elastic response quantities and b can affect designs by avoiding unrealistically optimistic and potentially unstable structures the additional computational cost associated with the uncertainties scales linearly with the number of uncertainties and is insignificant compared to the cost associated with solving the deterministic structural optimization problem

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

image segmentation by variational methods mumford and shah functional and the discrete approximations in this paper we discuss the links between mumford and shah s variational problem for signal and image segmentation based on an energy functional of a continuous grey level function and the numerical algorithms proposed to solve it these numerical approaches are based on a discrete functional we recall that in one dimension this discrete functional is asymptotically equivalent to the continuous functional this can be summarized in a gamma convergence result we show that the same result holds in dimension two provided that the continuous energy is adapted to the anisotropy of the discrete approaches we display a few experimental results in dimensions one and two

structural topology optimization based on non local shepard interpolation of density field abstract this paper presents a non local density interpolation strategy for topology optimization based on nodal design variables in this method design variable points can be positioned at any locations in the design domain and may not necessarily coincide with elemental nodes by using the shepard family of interpolants the density value of any given computational point is interpolated by design variable values within a certain circular influence domain of the point the employed interpolation scheme has an explicit form and satisfies non negative and range restricted properties required by a physically significant density interpolation since the discretizations of the density field and the displacement field are implemented on two independent sets of points the method is well suited for a topology optimization problem with a design domain containing higher order elements or non quadrilateral elements moreover it has the ability to yield mesh independent solutions if the radius of the influence domain is reasonably specified numerical examples demonstrate the validity of the proposed formulation and numerical techniques it is also confirmed that the method can successfully avoid checkerboard patterns as well as islanding phenomenon

non commutative discretize then optimize algorithms for elliptic pde constrained optimal control problems abstract in this paper we analyze the convergence of several optimize then discretize and discretize then optimize algorithms based on either a second order or a fourth order finite difference discretization for solving elliptic pde constrained optimal control problems to ensure the convergence of a discretize then optimize algorithm one well accepted criterion is to design the discretization scheme such that the resulting discretize then optimize algorithm commutes with the corresponding optimize then discretize algorithm in other words both algorithms should give rise to exactly the same discrete optimality system however such a restrictive criterion is not trivial to fulfill by investigating a distributed control problem governed by an elliptic equation we first show that enforcing such a stringent condition of commutative property is only sufficient but not necessary for achieving the desired convergence we then introduce some suitable h 1 semi norm penalty regularization terms to recover the lost convergence due to the inconsistency caused by the loss of commutativity numerical experiments are carried out to verify our theoretical analysis and also validate the effectiveness of our proposed regularization techniques

new finite sum inequalities with applications to stability of discrete time delay systems this paper is concerned with the problem of stability analysis of discrete time delay systems new finite sum inequalities which encompass the ones based on abel lemma or wirtinger type inequality are first proposed the potential capability of the newly derived inequalities is then demonstrated by establishing less conservative stability conditions for some classes of linear discrete time systems with delay the derived stability criteria are theoretically and numerically proved to be less conservative than existing results

topology optimization with implicit functions and regularization summary topology optimization is formulated in terms of the nodal variables that control an implicit function description of the shape the implicit function is constrained by upper and lower bounds so that only a band of nodal variables needs to be considered in each step of the optimization the weak form of the equilibrium equation is expressed as a heaviside function of the implicit function the heaviside function is regularized to permit the evaluation of sensitivities we show that the method is a dual of the bendshe kikuchi method the method is applied both to problems of optimizing single material and

improved constraint aggregation methods abstract many constraints in design optimization problems take the form of bounds on a physical quantity over a domain these infinite dimensional constraints are often addressed through aggregation methods that approximate the bound in a differentiable manner however the most common constraint aggregation methods exhibit mesh dependence as the mesh spacing decreases the aggregation function diverges in addition there are no established methods to assess the impact of constraint aggregation on the optimized design to address these deficiencies we propose a new class of constraint aggregation method that we call induced aggregates we examine the properties of these aggregation methods describe their numerical implementation and test their numerical accuracy on a pressure loaded circular cylinder test case furthermore we propose a post optimality estimation technique to assess the impact of the constraint aggregation method on the design we use this method to examine the optimized mass obtained from two stress constrained mass minimization problems a variable thickness sheet problem and a wingbox design problem

topology design optimization of geometrically non linear structures using meshfree method a topology optimization method using meshfree methods is developed for geometrically non linearly structures a density approach is used to optimally distribute the bulk material densities in a continuum design domain the reproducing kernel rk shape function is employed to discretize both displacement and bulk density fields thus the points can be located at any part of the design domain and be easily included in or excluded from the response analysis the well known convergence difficulty which normally occurs in the sub domain of low bulk density can be avoided by excluding the sub domain the numerical instability of bulk density solution due to the rank deficiency of system matrix is effectively prevented by properly selecting the number of independent design variables through numerous numerical examples we confirm that the developed method works very well even in the large deformation problems the sub domain exclusion scheme is found to be greatly beneficial in terms of computational costs compared with the results without the scheme

optimizing the layout of discrete objects in structures and materials a projection based topology optimization approach abstract this paper uses topology optimization to optimize the layout of discrete objects such as fixed shape void stiffening or functional inclusions in structures and periodic materials the methodology follows a material distribution approach and the heaviside projection method hpm is manipulated to ensure that the designed objects are discrete of fixed size length scale and shape and satisfy minimum spacing requirements these restrictions are achieved implicitly through projection without additional constraints or heuristics the methodology is built in the spirit of free form topology optimization and thus discrete objects are shown to appear vanish or translate across the design domain during the design evolution the technique is demonstrated on problems governed by mechanical stiffness including the design of structures and material microstructures whose elastic stiffness is to be enhanced by optimizing the location of stiff circular inclusions

multiresolution representation of data a general framework in this paper we present a general framework for a multiresolution representation of data which is obtained by the discretization of mappings this framework which can be viewed as a generalization of the theory of wavelets includes discretization corresponding to unstructured grids in several space dimensions and thus is general enough to enable us to embed most numerical problems in a multiresolution setting furthermore this framework allows for nonlinear data dependent multiresolution representation schemes and thus enables us to design adaptive data compression algorithms in this paper we also study the stability of linear schemes for a multiresolution representation and derive sufficient conditions for existence of a multiresolution basis

curve evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification we first address the problem of simultaneous image segmentation and smoothing by approaching the mumford shah 1989 paradigm from a curve evolution perspective in particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours each gradient step involves solving an optimal estimation problem for the data within each region connecting curve evolution and the mumford shah functional with the theory of boundary value stochastic processes the resulting active contour model offers a tractable implementation of the original mumford shah model i e without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner various implementations of this algorithm are introduced to increase its speed of convergence we also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions next by generalizing the data fidelity term of the original mumford shah functional to incorporate a spatially varying penalty we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing this more general model leads us to a novel pde based approach for simultaneous image magnification segmentation and smoothing thereby extending the traditional applications of the mumford shah functional which only considers simultaneous segmentation and smoothing

a mumford shah level set approach for the inversion and segmentation of x ray tomography data a level set based approach for the determination of a piecewise constant density function from data of its radon transform is presented simultaneously a segmentation of the reconstructed density is obtained the segmenting contour and the corresponding density are found as minimizers of a mumford shah like functional over the set of admissible contours and for a fixed contour over the space of piecewise constant densities which may be discontinuous across the contour shape sensitivity analysis is used to find a descent direction for the cost functional which leads to an update formula for the contour in the level set framework the descent direction can be chosen with respect to different metrics the use of an l 2 type and an h 1 type metric is proposed and the corresponding steepest descent flow equations are derived a heuristic approach for the insertion of additional components of the density is presented the method is tested for several data sets including synthetic as well as real world data it is shown that the method works especially well for large data noise 10 noise the choice of the h 1 metric for the determination of the descent direction is found to have positive effect on the number of level set steps necessary for finding the optimal contours and densities

piecewise linear approximation of vector valued images and curves via second order variational model variational models are known to work well for addressing image restoration regularization problems however most of the methods proposed in the literature are defined for scalar inputs and are used on multiband images such as rgb or multispectral imagery by the composition of a simple band wise processing this involves suboptimal results and may introduce artifacts only in a few cases variational models are extended to the case of vector valued inputs however the known implementations are restricted to the first order models while the second order models are never considered thus typical problems of the first order models such as the staircasing effect cannot be overtaken this paper considers a second order functional model to function approximation with free discontinuities given by blake zisserman bz and proposes an efficient minimization algorithm in the case of vector valued inputs in the bz model the hessian of the solution is penalized outside a set of finite length therefore the solution is forced to be piecewise linear moreover the model allows the formation of free discontinuities and free gradient discontinuities the proposed algorithm is applied to difficult color image restoration regularization problems and to piecewise linear approximation of curves in space

a finite element analysis of optimal variable thickness sheets a quasi mixed finite element fe method for maximum stiffness of variable thickness sheets is analyzed the displacement is approximated with nine node lagrange quadrilateral elements and the thickness is approximated as elementwise constant one is guaranteed that the fe displacement solutions will converge in hh but in an example it is shown that in general one cannot expect any subsequence of the fe thickness solutions to converge in any l p omega norm however under a regularity and biaxiality assumption on the optimal stress field uniqueness of the optimal thickness function as well as convergence in l p omega 1 leq p infty of fe thickness solutions are proven

optimal detection of changepoints with a linear computational cost in this article we consider the problem of detecting multiple changepoints in large datasets our focus is on applications where the number of changepoints will increase as we collect more data for example in genetics as we analyze larger regions of the genome or in finance as we observe time series over longer periods we consider the common approach of detecting changepoints through minimizing a cost function over possible numbers and locations of changepoints this includes several established procedures for detecting changing points such as penalized likelihood and minimum description length we introduce a new method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost which under mild conditions is linear in the number of observations this compares favorably with existing methods for the same problem whose computational cost can be quadratic or even cubic in simulation studies we show that our new method can

topology design of structures subjected to periodic loading although a lot of attention in the topology optimization literature has focused on the optimization of eigenfrequencies in free vibration problems relatively little work has been done on the optimization of structures subjected to periodic loading in this paper we propose two measures one global and the other local for the minimization of vibrations of structures subjected to periodic loading the global measure which we term as the dynamic compliance reduces the vibrations in an overall sense and thus has important implications from the viewpoint of reducing the noise radiated from a structure while the local measure reduces the vibrations at a user defined point both measures bring about a reduction in the vibration level by moving the natural frequencies which contribute most significantly to the measures away from the driving frequencies although as expected in different ways quite surprisingly the structure of the dynamic compliance optimization problem turns out to be very similar to the structure of the static compliance optimization problem the availability of analytical sensitivities results in an efficient algorithm for both measures we show the effectiveness of the measures by presenting some numerical examples

exponential stability of coupled linear delay time varying differential difference equations coupled linear delay time varying differential difference equations are considered explicit criteria for exponential stability of such equations are presented the obtained results are used to derive sufficient conditions for exponential stability in linear time varying differential equations of neutral type and in singular linear delay time varying differential equations some illustrative examples are given

displacement minimization of thermoelastic structures by evolutionary thickness design structural optimization aims at finding an appropriate material distribution to achieve the best structural performance in this paper the evolutionary structural optimization method is further developed to deal with thermoelastic optimization where structural material is progressively redistributed so as to minimize the displacement under thermal and mechanical loading to evaluate the effects of material removal or addition on the displacement of thermoelastic structures a sensitivity number is proposed on the basis of the thickness variation of an element the method proves to be very simple in its mathematical operations and suitable for computer implementation the numerical examples are compared against those by the homogenization method to verify and validate this method of solving thermoelastic optimizations in addition the effect of various temperature distributions on the final optimum structures is investigated in detail

complex hill s equation and the complex periodic korteweg de vries equations on etudie la classe spectrale des operateurs differentiels l d 2 dx 2 q avec un potentiel q de periode un on traite des potentiels complexes et des operateurs auto adjoints

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

topology design with optimized self adaptive materials significant performance improvements can be obtained if the topology of an elastic structure is allowed to vary in shape optimization problems we study the optimal shape design of a two dimensional elastic continuum for minimum compliance subject to a constraint on the total volume of material the macroscopic version of this problem is not well posed if no restrictions are placed on the structure topology relaxation of the optimization problem via quasiconvexification or homogenization methods is required the effect of relaxation is to introduce a perforated microstructure that must be optimized simultaneously with the macroscopic distribution of material

structural topology and shape optimization using a level set method with distance suppression scheme abstract in level set methods for structural topology and shape optimization the level set function gradients at the design interface need to be controlled in order to ensure stability of the optimization process one popular way to do this is to enforce the level set function to be a signed distance function by periodically using initialization schemes which is commonly known as re initialization however such re initialization schemes are time consuming as additional partial differential equations need to be solved in every iteration step furthermore the use of re initialization brings some undesirable problems for example it may move the zero level set away from the expected position this paper presents a level set method with distance suppression scheme for structural topology and shape optimization an energy functional is introduced into the level set equation to maintain the level set function to close to a signed distance function near the structural boundaries meanwhile forcing the level set function to be a constant at locations far away from the structural boundaries as a result the present method not only can avoid the need for re initialization but also can simplify the setting of the initial level set function the validity of the proposed method is tested on the mean compliance minimization problem and the compliant mechanisms synthesis problem different aspects of the proposed method are demonstrated on a number of benchmarks from the literature of structural optimization

topology optimization of continuum structures with local stress constraints we introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria we first consider relevant stress criteria for porous composite materials initially by studying the stress states of the so called rank 2 layered materials then on the basis of the theoretical study of the rank 2 microstructures we propose an empirical model that extends the power penalized stiffness model also called simp for solid isotropic microstructure with penalization for inter mediate densities in a second part solution aspects of topology problems are considered to deal with the so called singularity phenomenon of stress constraints in topology design an constraint relaxation of the stress constraints is used we describe the mathematical programming approach that is used to solve the numerical optimization problems and show results for a number of example applications 1998 john wiley sons ltd

filters in topology optimization based on helmholtz type differential equations the aim of this paper is to apply a helmholtz type partial differential equation as an alternative to standard density filtering in topology optimization problems previously this approach has been successfully applied as a sensitivity filter the usual filtering techniques in topology optimization require information about the neighbor cells which is difficult to obtain for fine meshes or complex domains and geometries the complexity of the problem increases further in parallel computing when the design domain is decomposed into multiple non overlapping partitions obtaining information from the neighbor subdomains is an expensive operation the proposed filter technique requires only mesh information necessary for the finite element discretization of the problem the main idea is to define the filtered variable implicitly as a solution of a helmholtz type differential equation with homogeneous neumann boundary conditions the properties of the filter are demonstrated for various 2d and 3d topology optimization problems in linear elasticity solved on serial and parallel computers copyright 2010 john wiley sons ltd

material cloud method for topology optimization material cloud method mcm a new approach for topology optimization is presented in mcm an optimal structure can be obtained by manipulating the sizes and positions of material clouds which are material patches with finite sizes and constant material densities the optimal distributions of material clouds can be obtained by mcm using fixed background finite element meshes in the numerical analysis procedure only active elements where more than one material cloud is contained are treated optimal material distribution can be element wise extracted from the distribution of material clouds with mcm an expansion reduction procedure of design domain can be naturally realized through movements of material clouds so that a true optimal solution can be found without any significant increase of computational costs it is also shown that a clear material distribution with narrow region of intermediate density can be obtained with relatively fast convergence several numerical examples are shown some of the results are compared with those of the traditional density distribution method ddm copyright 2005 john wiley sons ltd

topology optimization of viscoelastic structures using a time dependent adjoint method abstract we present a mathematical framework for producing optimal designs of structures that exhibit viscoelastic creep deformation using a linear viscoelastic finite element model we implement a corresponding time dependent adjoint sensitivity formulation the resulting formula is then incorporated into a computational topology optimization framework in order to achieve optimal topologies based on the expected lifespan or operating cycle of the structure designs are optimized for minimum mass subject to a constraint on the maximum local deflection we validate the method using several two dimensional numerical examples that include design dependent gravitational loading self weight and time dependent applied loads creep plots are used to quantify the impact of the viscoelastic optimization method the results show that the design of the optimal structure is highly dependent on the load duration and the complete load history this result supports the design premise that it is necessary to account for the full viscoelastic response of the structure when designing for optimal long term performance

reducing the complexity of the sum of squares test for stability of delayed linear systems this technical note considers the problem of reducing the computational complexity associated with the sum of squares approach to stability analysis of time delay systems specifically this technical note considers systems with a large state space but where delays affect only certain parts of the system this yields a coefficient matrix of the delayed state with low rank a common scenario in practice the technical note uses the general framework of coupled differential difference equations with delays in feedback channels this framework includes systems of both the neutral and retarded type the approach is based on recent results which introduced a new lyapunov krasovskii structure which was shown to be necessary and sufficient for stability of this class of systems this technical note shows how exploiting the structure of the new functional can yield dramatic improvements in computational complexity numerical examples are given to illustrate this improvement

a new scheme for imposing a minimum length scale in topology optimization a new scheme for imposing a minimum length scale in topology optimization is presented it guarantees the existence of an optimal design for a large class of topology optimization problems of practical interest it is formulated as one constraint that is computationally cheap and for which sensitivities are also cheap to compute the constraint value is ideally zero but it can be relaxed to a positive value the effect of the method is illustrated in topology optimization for minimum compliance and design of compliant mechanisms notably the method produces compliant mechanisms with distributed flexibility something that has previously been difficult to obtain using topology optimization for the design of compliant mechanisms the term mole method is suggested for the method copyright 2003 john wiley sons ltd

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

bounds for decoupled design and analysis discretizations in topology optimization summary topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution this paper discusses the relation between the number of design variables per element and the order of the elements used for analysis we derive that beyond a maximum number of design variables certain sets of material distributions cannot be discriminated based on the corresponding analysis results this makes the design description inefficient and the solution of the optimization problem non unique to prevent this we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non uniqueness copyright 2016 the authors international journal for numerical methods in engineering published by john wiley sons ltd

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

level set evolution with locally linear classification for image segmentation this paper presents a novel local region based level set model for image segmentation in each local region we define a locally weighted least squares energy to fit a linear classifier with level set representation these local energy functions are then integrated over the whole image domain to develop a global segmentation model the objective function in this model is thereafter minimized via level set evolution in this process the parameters related to the locally linear classifier are iteratively estimated by introducing the locally linear functions to separate background and foreground in local regions our model not only achieves accurate segmentation results but also is robust to initialization extensive experiments are reported to demonstrate that our method holds higher segmentation accuracy and more initialization robustness compared with the classical region based and local region based methods

stability of finite element models for distributed parameter optimization and topology design abstract we address a problem of numerical instability that is often encountered in finite element solutions of distributed parameter optimization and variable topology shape design problems we show that the cause of this problem is numerical rather than physical in nature we consider a two field distributed parameter optimization problem involving a design field and a response field and show that the optimization problem corresponds to a mixed variational problem an improper selection of the discrete function spaces for these two fields leads to grid scale anomalies in the numerical solutions to optimization problems similar to those that are sometimes encountered in mixed formulations of the stokes problem we present a theoretical framework to explain the cause of these anomalies and present stability conditions for discrete models the general theoretical framework is specialized to analyze the stability of specific optimization problems and stability results for various mixed finite element models are presented we propose patch tests that are useful in identifying unstable elements

exponential stability of time delay systems via new weighted integral inequalities in this paper new weighted integral inequalities wiis are first derived based on jensen s integral inequalities in single and double forms it is theoretically shown that the newly derived inequalities in this paper encompass both the jensen inequality and its most recent improvement based on wirtinger s integral inequality the potential capability of wiis is demonstrated through applications to exponential stability analysis of some classes of time delay systems in the framework of linear matrix inequalities lmis the effectiveness and least conservativeness of the derived stability conditions using wiis are shown by various numerical examples

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

on joint design of intentionally introduced delay and controller gain for stabilization of second order oscillatory systems this paper focuses on stabilization of second order oscillatory systems using both feedback control and intentionally introduced time delay the argument principle is employed as a key technique to divide the parameter space of time delay and controller gain into several regions every admissible value in these regions moves the poles of the closed loop system towards the left of the complex plane such that stability improvement is achieved the concept of potent asymptotic stability is first introduced referring to the property that all the poles of the closed loop system are stable and lie on the left of open loop system poles in the complex plane analytical characterizations on parameter pairs of time delay and controller gain that result in potent asymptotic stability are established all the poles and corresponding root locus with respect to gain are examined numerical examples and simulations are given to illustrate the usefulness and merits of the theoretical results

a robust dual algorithm for topology design of structures in discrete variables dual optimization algorithms for the topology optimization of continuum structures in discrete variables are gaining popularity in recent times since in topology design problems the number of constraints is small in comparison to the number of design variables good topologies can be obtained for the minimum compliance design problem when the perimeter constraint is imposed in addition to the volume constraint however when the perimeter constraint is relaxed the dual algorithm tends to give bad results even with the use of higher order finite element models as we demonstrate in this work since a priori one does not know what a good value of the perimeter to be specified is it is essential to have an algorithm which generates good topologies even in the absence of the perimeter constraint we show how the dual algorithm can be made more robust so that it yields good designs consistently in the absence of the perimeter constraint in particular we show that the problem of checkerboarding which is frequently observed with the use of lower order finite elements is eliminated

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

estimating stable delay intervals with a discretized lyapunov krasovskii functional formulation abstract in general a system with time delay may have multiple stable delay intervals especially a stable delay interval does not always contain zero asymptotically accurate stability conditions such as discretized lyapunov krasovskii functional dlf method and sum of square sos method are especially effective for such systems in this article a dlf based method is proposed to estimate the maximal stable delay interval accurately without using bisection when one point in this interval is given the method is formulated as a generalized eigenvalue problem gevp of linear matrix inequalities lmis and an accurate estimate may be reached by iteration either in a finite number of steps or asymptotically the coupled differential difference equation formulation is used to illustrate the method however the idea can be easily adapted to the traditional differential difference equation setting

technical communique α dissipativity analysis of singular time delay systems in this paper the problem of delay dependent a dissipativity analysis is investigated for continuous time singular systems with time delay using the delay partitioning technique sufficient conditions are established in terms of linear matrix inequalities lmis which guarantees a singular system to be admissible and strictly q s r email protected in addition to delay dependence the obtained results are also dependent on the parameter a moreover the results of h performance analysis and passivity analysis are unified from the dissipative analysis results the results developed in this paper are less conservative than existing ones in the literature which are illustrated by several examples

solutions to shape and topology eigenvalue optimization problems using a homogenization method a solution strategy to find the shape and topology of structures that maximize a natural frequency is presented the methodology is based on a homogenization method and the representation of the shape of the structure as a material property the problem is formulated as a reinforcement problem in which a given structure is reinforced using a prescribed amount of material two dimensional plane elasticity problems are considered examples are presented for illustration

approximation of functional depending on jumps by elliptic functional via t convergence we show how it is possible to approximate the mumford shah see 29 image segmentation functional by elliptic functionals defined on sobolev spaces the heuristic idea is to consider functionals h u z with z ranging between 0 and 1 and related to the set k the minimizing zh are near to 1 in a neighborhood of the set k and far from the neighborhood they are very small the neighborhood shrinks as h for a similar approach to the problem compare kulkarni see 25 the approximation of h to takes place in a variational sense the de giorgi f convergence

a further refinement of discretized lyapunov functional method for the stability of time delay systems the discretized lyapunov functional method for the stability problem of time delay systems is further refined using a combination of integral inequality and variable elimination technique as a result the computational requirement is further reduced for the same discretization mesh for systems without uncertainty the convergence to the analytical solution is greatly accelerated for uncertain systems the new method is much less conservative numerical examples are presented to illustrate the effectiveness of the method

iterative potts and blake zisserman minimization for the recovery of functions with discontinuities from indirect measurements signals with discontinuities appear in many problems in the applied sciences ranging from mechanics electrical engineering to biology and medicine the concrete data acquired are typically discrete indirect and noisy measurements of some quantities describing the signal under consideration the task is to restore the signal and in particular the discontinuities in this respect classical methods perform rather poor whereas non convex non smooth variational methods seem to be the correct choice examples are methods based on mumford shah and piecewise constant mumford shah functionals and discretized versions which are known as blake zisserman and potts functionals owing to their non convexity minimization of such functionals is challenging in this paper we propose a new iterative minimization strategy for blake zisserman as well as potts functionals and a related jump sparsity problem dealing with indirect noisy measurements we provide a convergence analysis and underpin our findings with numerical experiments

smoothing for signals with discontinuities using higher order mumford shah models minimizing the mumford shah functional is frequently used for smoothing signals or time series with discontinuities a significant limitation of the standard mumford shah model is that linear trends and in general polynomial trends in the data are not well preserved this can be improved by building on splines of higher order which leads to higher order mumford shah models in this work we study these models in the univariate situation we discuss important differences to the first order mumford shah model and we obtain uniqueness results for their solutions as a main contribution we derive fast minimization algorithms for mumford shah models of arbitrary orders we show that the worst case complexity of all proposed schemes is quadratic in the length of the signal remarkably they thus achieve the worst case complexity of the fastest solver for the piecewise constant mumford shah model which is the simplest model of the class further we obtain stability results for the proposed algorithms we complement these results with a numerical study our reference implementation processes signals with more than 10 000 elements in less than 1 s

the stability chart for the linearized cushing equation with a discrete delay and with gamma distributed delays in a proper setting the problem of the title amounts to the determination of all pairs d t for which the function z z 1 exp zt d and the functions fn z z 1 1 ztn n d n n d t 0 have all their zeros in re z 0 of the complex z plane correct versions of results and proofs found in papers of k l cooke and j m grossman j math anal appl 86 1982 592 627 and s p blythe r m nisbeth w s c gurney and n macdonald j math anal appl 109 1985 388 396 are given the argumentation in the proofs of the present paper differs from that of the studies mentioned in contrast to blythe et al the stability behaviours of both models are seen as similar stability charts and stability conditions for some other classes of systems are also given in addition to the gamma distribution for the lags other distributions which are similar in shape but differ greatly in their stability behaviour are also considered

the l 1 potts functional for robust jump sparse reconstruction we investigate the nonsmooth and nonconvex l 1 potts functional in discrete and continuous time we show gamma convergence of discrete l 1 potts functionals toward their continuous counterpart and obtain a convergence statement for the corresponding minimizers as the discretization gets finer for the discrete l 1 potts problem we introduce an o n 2 time and o n space algorithm to compute an exact minimizer we apply l 1 potts minimization to the problem of recovering piecewise constant signals from noisy measurements f it turns out that the l 1 potts functional has a quite interesting blind deconvolution property in fact we show that mildly blurred jump sparse signals are reconstructed by minimizing the l 1 potts functional furthermore for strongly blurred signals and a known blurring operator we derive an iterative reconstruction algorithm

an engineer s approach to optimal material distribution and shape finding abstract the fundamental aim of shape optimization involves the optimal distribution of mass in space observing global and local design constraints the practical realization in applied mechanics can be performed by introducing a foam like material with variable density as discussed by bendsoe and kikuchi this paper uses for the evaluation of material properties a simple energy approach the application is extended to three dimensional domains multiple loading cases are also considered further the approach is implemented in a preoptimizer for optimal shape finding

interpolation and approximation of piecewise smooth functions this paper provides approximation orders for a class of nonlinear interpolation procedures for uniformly sampled univariate data the interpolation is based on essentially nonoscillatory eno and subcell resolution sr reconstruction techniques these nonlinear techniques aim at reducing significantly the approximation error for functions with isolated singularities and are therefore attractive for applications such as shock computations or image compression we prove that in the presence of isolated singularities the approximation order provided by the interpolation procedure is improved by a factor of h relative to the linear methods where h is the sampling rate moreover for h below a critical value we recover the optimal approximation order as for uniformly smooth functions

composite material design of two dimensional structures using the homogenization design method summary composite materials of two dimensional structures are designed using the homogenization design method the composite material is made of two or three dierent material phases designing the composite material consists of nding a distribution of material phases that minimizes the mean compliance of the macrostructure subject to volume fraction constraints of the constituent phases within a unit cell of periodic microstructures at the start of the computational solution the material distribution of the microstructure is represented as a pure mixture of the constituent phases as the iteration procedure unfolds the component phases separate themselves out to form distinctive interfaces the eective material properties of the articially mixed materials are dened by the interpolation of the constituents the optimization problem is solved using the sequential linear programming method both the macrostructure and the microstructures are analysed using the nite element method in each iteration step several examples of optimal topology design of composite material are presented to demonstrate the validity of the present numerical algorithm copyright 2001 john wiley sons ltd