multi constrained matroidal knapsack problems we consider multi constrained knapsack problems where the sets of elements to be selected are subject to combinatorial constraints of matroidal nature for this important class of np hard combinatorial optimization problems we prove that lagrangean relaxation techniques not only provide good bounds to the value of the optimum but also yield approximate solutions which are asymptotically optimal under mild probabilistic assumptions

a g space theory and a weakened weak w2 form for a unified formulation of compatible and incompatible methods part ii applications to solid mechanics problems in part i of this paper we have established the g space theory and fundamentals for w 2 formulation part ii focuses on the applications of the g space theory to formulate w 2 models for solid mechanics problems we first define a bilinear form prove some of the important properties and prove that the w 2 formulation will be spatially stable and convergent to exact solutions we then present examples of some of the possible w 2 models including the sfem ns fem es fem ns pim es pim and cs pim we show the major properties of these models 1 they are variationally consistent in a conventional sense if the solution is sought in a proper h space compatible cases 2 they pass the standard patch test when the solution is sought in a proper g space with discontinuous functions incompatible cases 3 the stiffness of the discretized model is reduced compared with the finite element method fem model and possibly to the exact model allowing us to obtain upper bound solutions with respect to both the fem and the exact solutions and 4 the w 2 models are less sensitive to the quality of the mesh and triangular meshes can be used without any accuracy problems these properties and theories have been confirmed numerically via examples solved using a number of w 2 models including compatible and incompatible cases we shall see that the g space theory and the w 2 forms can formulate a variety of stable and convergent numerical methods with the fem as one special case

probabilistic analysis of the multidimensional knapsack problem we analyse the multi constraint zero one knapsack problem under the assumption that all coefficients are drawn from a uniform 0 1 distribution and there are m 01 constraints as the number of variables grows we show that results on the single constraint problem can be extended to this situation chiefly we generalise a result of lueker on the duality gap and a result of goldberg marchetti spaccamela on exact solvability in the latter case our methods differ markedly from those for the single constraint result

a mass redistributed finite element method mr fem for acoustic problems using triangular mesh the accuracy of numerical results using standard finite element method fem in acoustic problems will deteriorate with increasing frequency due to the dispersion error such dispersion error depends on the balance between the stiffness and mass of discretization equation systems this paper reports an improved finite element method fem for solving acoustic problems by re distributing the mass in the mass matrix to tune the balance aiming to minimize the dispersion errors this is done by shifting the integration point locations when computing the entries of the mass matrix while ensuring the mass conservation the new method is verified through the detailed numerical error analysis and a strategy is also proposed for the best mass redistribution in terms of minimizing dispersion error the relative dispersion error of present mass redistributed finite element method mr fem is found to be much smaller than the fem solution in both theoretical prediction and numerical examination the present mr fem works well by using the linear triangular elements that can be generated automatically which enables automation in computation and saving computational cost in mesh generation numerical examples demonstrate the advantages of mr fem in comparison with the standard fem using the same triangular meshes and quadrilateral meshes

topology recognition with advice in topology recognition each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph with all ports correctly marked this task is usually unfeasible without any a priori information such information can be provided to nodes as advice an oracle knowing the network can give a possibly different string of bits to each node and all nodes must reconstruct the network using this advice after a given number of rounds of communication during each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations the time of completing topology recognition is the number of rounds it takes and the size of advice is the maximum length of a string given to nodes we investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes we provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time in the class of all graphs of size n and diameter d n for any constant 1 in most cases our bounds are asymptotically tight

a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

on extensions of the deterministic online model for bipartite matching and max sat abstract the surprising results of karp vazirani and vazirani 39 and respectively buchbinder et al 18 are examples where rather simple randomization provides provably better approximations than the corresponding deterministic counterparts for online bipartite matching and respectively unconstrained non monotone submodular we show that seemingly strong extensions of the deterministic online computation model can at best match the performance of naive randomization more specifically for bipartite matching we show that in the priority model allowing very general ways to order the input stream we cannot improve upon the trivial 1 2 approximation achieved by any greedy maximal matching algorithm and likewise cannot improve upon this approximation by any l o g n log log n number of online algorithms running in parallel the latter result yields an improved log log n log log log n lower bound for the number of advice bits needed to beat the simple deterministic greedy algorithm for max sat we adapt the recent de randomization approach of buchbinder and feldman 16 applied to the buchbinder et al 17 algorithm for max sat to obtain a deterministic 3 4 approximation algorithm using width 2n parallelism in order to improve upon this approximation we show that exponential width parallelism of online algorithms is necessary in a model that is more general than what is needed for the width 2n algorithm we relate our results to previous work concerning the priority branching tree pbt model of alekhnovich et al 2

a novel alpha finite element method αfem for exact solution to mechanics problems using triangular and tetrahedral elements abstract the paper presents an alpha finite element method fem for computing nearly exact solution in energy norm for mechanics problems using meshes that can be generated automatically for arbitrarily complicated domains three node triangular fem t3 and four node tetrahedral fem t4 elements with a scale factor are formulated for two dimensional 2d and three dimensional 3d problems respectively the essential idea of the method is the use of a scale factor 0 1 to obtain a combined model of the standard fully compatible model of the fem and a quasi equilibrium model of the node based smoothed fem n sfem this novel combination of the fem and n sfem makes the best use of the upper bound property of the n sfem and the lower bound property of the standard fem using meshes with the same aspect ratio a unified approach has been proposed to obtain a nearly exact solution in strain energy for linear problems the proposed elements are also applied to improve the accuracy of the solution of nonlinear problems of large deformation numerical results for 2d using fem t3 and 3d using fem t4 problems confirm that the present method gives the much more accurate solution comparing to both the standard fem and the n sfem with the same number of degrees of freedom and similar computational efforts for both linear and nonlinear problems

one sided cross validation abstract a new method of selecting the smoothing parameters of nonparametric regression estimators is introduced the method termed one sided cross validation oscv has the objectivity of cross validation and statistical properties comparable to those of a plug in rule the new method may be viewed as an application of the prequential model selection method of dawid as such our results identify a situation in which the prequential method is a more efficient model selector than cross validation an example simulations and theoretical results demonstrate the utility of oscv when used with local linear and kernel estimators

randomized algorithms for metrical task systems abstract borodin et al 1992 introduce a general model for online systems in 3 called task systems and show a deterministic algorithm which achieves a competitive ratio of 2n 1 for any metrical task system with n states we present a randomized algorithm which achieves a competitive ratio of e e 1 n 1 e 1 1 5820n 0 5820 for this same problem for the uniform metric space borodin et al present an algorithm which achieves a competitive ratio of 2hn and they show a lower bound of hn for any randomized algorithm we improve their upper bound for the uniform metric space by showing a randomized algorithm which is hn o log n competitive

meshfree and finite element nodal integration methods nodal integration can be applied to the galerkin weak form to yield a particle type method where stress and material history are located exclusively at the nodes and can be employed when using meshless or finite element shape functions this particle feature of nodal integration is desirable for large deformation settings because it avoids the remapping or advection of the state variables required in other methods to a lesser degree nodal integration can be desirable because it relies on fewer stress point evaluations than most other methods in this work aspects regarding stability consistency efficiency and explicit time integration are explored within the context of nodal integration both small and large deformation numerical examples are provided copyright 2007 john wiley sons ltd

the online knapsack problem advice and randomization we study the advice complexity and the random bit complexity of the online knapsack problem given a knapsack of unit capacity and n items that arrive in successive time steps an online algorithm has to decide for every item whether it gets packed into the knapsack or not the goal is to maximize the value of the items in the knapsack without exceeding its capacity in the model of advice complexity of online problems one asks how many bits of advice about the unknown parts of the input are both necessary and sufficient to achieve a specific competitive ratio it is well known that even the unweighted online knapsack problem does not admit any competitive deterministic online algorithm for this problem we show that a single bit of advice helps a deterministic online algorithm to become 2 competitive but that w logn advice bits are necessary to further improve the deterministic competitive ratio this is the first time that such a phase transition for the number of advice bits has been observed for any problem additionally we show that surprisingly instead of an advice bit a single random bit allows for a competitive ratio of 2 and any further amount of randomness does not improve this moreover we prove that in a resource augmentation model i e when allowing the online algorithm to overpack the knapsack by some small amount a constant number of advice bits suffices to achieve a near optimal competitive ratio we also study the weighted version of the problem proving that with o logn bits of advice we can get arbitrarily close to an optimal solution and using asymptotically fewer bits we are not competitive furthermore we show that an arbitrary number of random bits does not permit a constant competitive ratio

miscellanea kernel type density estimation on the unit interval we consider kernel type methods for the estimation of a density on 0 1 which eschew explicit boundary correction we propose using kernels that are symmetric in their two arguments these kernels are conditional densities of bivariate copulas we give asymptotic theory for the version of the new estimator using gaussian copula kernels and report on simulation comparisons of it with the beta kernel density estimator of chen 1 we also provide automatic bandwidth selection in the form of rule of thumb bandwidths for both estimators as well as its competitive integrated squared error performance advantages of the new approach include its greater range of possible values at 0 and 1 the fact that it is a bona fide density and that the individual kernels and resulting estimator are comprehensible in terms of a single simple picture

approximate distance oracles let g v e be an undirected weighted graph with vvv n and vev m let k 1 be an integer we show that g v e can be preprocessed in o kmn1 k expected time constructing a data structure of size o kn1p1 k such that any subsequent distance query can be answered approximately in o k time the approximate distance returned is of stretch at most 2k 1 that is the quotient obtained by dividing the estimated distance by the actual distance lies between 1 and 2k 1 a 1963 girth conjecture of erdos implies that n1p1 k space is needed in the worst case for any real stretch strictly smaller than 2kp1 the space requirement of our algorithm is therefore essentially optimal the most impressive feature of our data structure is its constant query time hence the name oracle previously data structures that used only o n1p1 k space had a query time of n1 k our algorithms are extremely simple and easy to implement efficiently they also provide faster constructions of sparse spanners of weighted graphs and improved tree covers and distance labelings of weighted or unweighted graphs

on the advice complexity of the online l 2 1 coloring problem on paths and cycles in an l 2 1 coloring of a graph the vertices are colored with colors from an ordered set such that neighboring vertices get colors that have distance at least 2 and vertices at distance 2 in the graph get different colors we consider the problem of finding an l 2 1 coloring using a minimum range of colors in an online setting where the vertices arrive in consecutive time steps together with information about their neighbors and vertices at distance 2 among the previously revealed vertices for this we restrict our attention to paths and cycles offline paths can easily be colored within the range 0 4 of colors we prove that considering deterministic algorithms in an online setting the range 0 6 is necessary and sufficient while a simple greedy strategy needs range 0 7 advice complexity is a recently developed framework to measure the complexity of online problems the idea is to measure how many bits of advice about the yet unknown parts of the input an online algorithm needs to compute a solution of a certain quality we show a sharp threshold on the advice complexity of the online l 2 1 coloring problem on paths and cycles while achieving color range 0 6 does not need any advice improving over this requires a number of advice bits that is linear in the size of the input thus the l 2 1 coloring problem is the first known example of an online problem for which sublinear advice does not help we further use our advice complexity results to prove that no randomized online algorithm can achieve a better expected competitive ratio than 5 4 1 for any 0

analysis and implementation of a new constant acceleration subcycling algorithm an algorithm for explicit integration of structural dynamics problems with multiple time steps is proposed that averages accelerations to obtain subcycle states at a nodal interface between regions integrated with different time steps with integer time step ratios the resulting subcycle updates at the interface sum to give the same effect as a central difference update over a major cycle the algorithm is shown to have good accuracy and stability properties in linear elastic analysis similar to those of constant velocity subcycling algorithms the implementation of a generalised form of the algorithm with non integer time step ratios is presented c 1997 by john wiley sons ltd

2d knapsack packing squares in this paper we study a two dimensional knapsack problem packing squares as many as possible into a unit square our results are the following i we propose an algorithm called ihs increasing height shelf and prove that the packing is optimal if in an optimal packing there are at most 5 squares and this upper bound is sharp ii if all the squares have side length at most 1k we propose a simple and fast algorithm with an approximation ratio k 2 3k 2k 2 in time o nlogn iii we give an eptas for the problem where the previous result in jansen and solis oba 2008 16 is a ptas not an eptas however our approach does not work on the previous model of jansen and solis oba 2008 16 where each square has an arbitrary weight

online removable knapsack with limited cuts in this paper we study online maximization and minimization knapsack problems with limited cuts in which 1 items are given one by one over time i e after a decision is made on the current item the next one is given 2 items are allowed to be cut at most k 1 times and 3 items are allowed to be removed from the knapsack we obtain the following three results i for the maximization knapsack problem we propose a k 1 k competitive online algorithm and show that it is the best possible i e no online algorithm can have a competitive ratio less than k 1 k ii for the minimization knapsack problem we show that no online algorithm can have a constant competitive ratio iii we extend the result in i to the resource augmentation model where an online algorithm is allowed to use a knapsack of capacity m 1 while the optimal algorithm uses a unit capacity knapsack

smooth optimum kernel estimators near endpoints summary kernel estimators for smooth curves like density spectral density or regression functions require modifications when estimating near endpoints of the support both for practical and asymptotic reasons the construction of such boundary kernels as solutions of a variational problem is addressed and representations in orthogonal polynomials are given including explicit solutions for the most important cases based on explicit formulae for certain functionals of the kernels it is shown that local bandwidth variation might be indicated near boundaries various bandwidth variation schemes are discussed and

on metric ramsey type phenomena the main question studied in this article may be viewed as a nonlinear analogue of dvoretzky s theorem in banach space theory or as part of ramsey theory in combinatorics given a finite metric space on n points we seek its subspace of largest cardinality which can be embedded with a given distortion in hilbert space we provide nearly tight upper and lower bounds on the cardinality of this subspace in terms of n and the desired distortion our main theorem states that for any 0 every n point metric space contains a subset of size at least n1 which is embeddable in hilbert space with o log 1 distortion the bound on the distortion is tight up to the log 1 factor we further include a comprehensive study of various other aspects of this problem

on the k server conjecture we prove that the work function algorithm for the k server problem has a competitive ratio at most 2 k 1 manasse et al 1988 conjectured that the competitive ratio for the k server problem is exactly k it is trivially at least k previously the best known upper bound was exponential in k our proof involves three crucial ingredients a quasiconvexity property of work functions a duality lemma that uses quasiconvexity to characterize the configuration that achieve maximum increase of the work function and a potential function that exploits the duality lemma

local multiplicative bias correction for asymmetric kernel density estimators abstract we consider semiparametric asymmetric kernel density estimators when the unknown density has support on 0 we provide a unifying framework which relies on a local multiplicative bias correction and contains asymmetric kernel versions of several semiparametric density estimators considered previously in the literature this framework allows us to use popular parametric models in a nonparametric fashion and yields estimators which are robust to misspecification we further develop a specification test to determine if a density belongs to a particular parametric family the proposed estimators outperform rival non and semiparametric estimators in finite samples and are easy to implement we provide applications to loss data from a large swiss health insurer and brazilian income data

theoretical aspects of the smoothed finite element method sfem this paper examines the theoretical bases for the smoothed finite element method sfem which was formulated by incorporating cell wise strain smoothing operation into standard compatible finite element method fem the weak form of sfem can be derived from the hu washizu three field variational principle for elastic problems it is proved that 1d linear element and 2d linear triangle element in sfem are identical to their counterparts in fem while 2d bilinear quadrilateral elements in sfem are different from that of fem when the number of smoothing cells scs of the elements equals 1 the sfem solution is proved to be variationally consistent and has the same properties with those of fem using reduced integration when sc approaches infinity the sfem solution will approach the solution of the standard displacement compatible fem model when sc is a finite number larger than 1 the sfem solutions are not variationally consistent but energy consistent and will change monotonously from the solution of sfem sc 1 to that of sfem sc it is suggested that there exists an optimal number of sc such that the sfem solution is closest to the exact solution the properties of sfem are confirmed by numerical examples copyright 2006 john wiley sons ltd

bivariate frequency analysis of floods using a diffusion based kernel density estimator recent focus of flood frequency analysis ffa studies has been on development of methods to model joint distributions of variables such as peak flow volume and duration that characterize a flood event as comprehensive knowledge of flood event is often necessary in hydrological applications diffusion process based adaptive kernel d kernel is suggested in this paper for this purpose it is data driven flexible and unlike most kernel density estimators always yields a bona fide probability density function it overcomes shortcomings associated with the use of conventional kernel density estimators in ffa such as boundary leakage problem and normal reference rule the potential of the d kernel is demonstrated by application to synthetic samples of various sizes drawn from known unimodal and bimodal populations and five typical peak flow records from different parts of the world it is shown to be effective when compared to conventional gaussian kernel and the best of seven commonly used copulas gumbel hougaard frank clayton joe normal plackett and student s t in estimating joint distribution of peak flow characteristics and extrapolating beyond historical maxima selection of optimum number of bins is found to be critical in modeling with d kernel

hazard rate estimation under random censoring with varying kernels and bandwidths we discuss the estimation of hazard rates under random censoring with the kernel method two practically relevant problems that occur when applying unmodified kernel estimators are boundary effects near the endpoints of the support of the hazard rate and a substantial increase in the variance from left to right over the range of abscissae where the hazard rate is estimated a new class of boundary kernels is proposed for the first problem explicit formulas for these kernels are developed and it is shown that this boundary correction works well in practice a data adaptive varying bandwidth selection procedure is proposed for the second problem this procedure generally will lead to increasing bandwidths near the left endpoint and toward the right endpoint and will lead to smaller integrated mean squared error of the hazard rate estimator as compared to a fixed bandwidth method a practically feasible method incorporating the new boundary kernels and local bandwidth choices is implemented and illustrated with survival data from a leukemia study

a stabilized nodally integrated tetrahedral a stabilized nodally integrated linear tetrahedral is formulated and analysed it is well known that linear tetrahedral elements perform poorly in problems with plasticity nearly incompressible materials and acute bending for a variety of reasons low order tetrahedral elements are preferable to quadratic tetrahedral elements particularly for nonlinear problems but the severe locking problems of tetrahedrals have forced analysts to employ hexahedral formulations for most nonlinear problems on the other hand automatic mesh generation is often not feasible for building many 3d hexahedral meshes a stabilized nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity nearly incompressible materials and acute bending the formulation is analytically and numerically shown to be stable and optimally convergent for the compressible case provided sufficient smoothness of the exact solution u c2 h1 3 future work may extend the formulation to the incompressible regime and relax the regularity requirements nonetheless the results demonstrate that the method is not susceptible to locking and performs quite well in several standard linear and nonlinear benchmarks published in 2006 by john wiley sons ltd

online removable knapsack problem under convex function abstract in this paper we address an online knapsack problem under a convex size profit function we first give a greedy online algorithm with a competitive ratio 2 then we propose an improved online algorithm with a competitive ratio 5 3 we also prove that when the convex function has a specific property our improved online algorithm is 1 5 2 competitive which is optimal finally we prove that the lower bound of this problem is 1 5 2

online knapsack problem under concave functions in this paper we address an online knapsack problem under concave function f x i e an item with size x has its profit f x we first obtain a simple lower bound max q frac f 0 f 1 where q approx 1 618 then show that this bound is not tight and give an improved lower bound finally we find the online algorithm for linear function 8 can be employed to the concave case and prove its competitive ratio is frac f 0 f 1 q then we give a refined online algorithm with a competitive ratio frac f 0 f 1 1 and we also give optimal algorithms for some piecewise linear functions

modified integration rules for reducing dispersion error in finite element methods abstract this paper describes a simple but effective technique for reducing dispersion errors in finite element solutions of time harmonic wave propagation problems the method involves a simple shift of the integration points to locations away from conventional gauss or gauss lobatto integration points for bilinear rectangular elements such a shift results in fourth order accuracy with respect to dispersion error error in wavelength as opposed to the second order accuracy resulting from conventional integration numerical experiments involving distorted meshes indicate that the method has superior performance in comparison with other dispersion reducing finite elements

linear smoothed polygonal and polyhedral finite elements the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method in this work we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes the main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain this new strain is then used in the computation of the stiffness matrix the convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations the accuracy is also improved and all the methods tested pass the patch test to machine precision

an edge based smoothed finite element method es fem for static free and forced vibration analyses of solids abstract this paper presents an edge based smoothed finite element method es fem to significantly improve the accuracy of the finite element method fem without much changing to the standard fem settings the es fem can use different shape of elements but prefers triangular elements that can be much easily generated automatically for complicated domains in the es fem the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the edges of the triangles intensive numerical results demonstrated that the es fem possesses the following excellent properties 1 the es fem model possesses a close to exact stiffness it is much softer than the overly stiff fem and much stiffer than the overly soft ns fem model 2 the results are often found superconvergence and ultra accurate much more accurate than the linear triangular elements of fem and even more accurate than those of the fem using quadrilateral elements with the same sets of nodes 3 there are no spurious non zeros energy modes found and hence the method is also temporally stable and works well for vibration analysis and 4 the implementation of the method is straightforward and no penalty parameter is used and the computational efficiency is better than the fem using the same sets of nodes in addition a novel domain based selective scheme is proposed leading to a combined es ns fem model that is immune from volumetric locking and hence works very well for nearly incompressible materials these properties of the es fem are confirmed using examples of static free and forced vibration analyses of solids

an improved transformation based kernel estimator of densities on the unit interval the kernel density estimator kde suffers boundary biases when applied to densities on bounded supports which are assumed to be the unit interval transformations mapping the unit interval to the real line can be used to remove boundary biases however this approach may induce erratic tail behaviors when the estimated density of transformed data is transformed back to its original scale we propose a modified transformation based kde that employs a tapered and tilted back transformation we derive the theoretical properties of the new estimator and show that it asymptotically dominates the naive transformation based estimator while maintains its simplicity we then propose three automatic methods of smoothing parameter selection our monte carlo simulations demonstrate the good finite sample performance of the proposed estimator especially for densities with poles near the boundaries an example with real data is provided

online minimization knapsack problem in this paper we address the online minimization knapsack problem i e the items are given one by one over time and the goal is to minimize the total cost of items that covers a knapsack we study the removable model where it is allowed to remove old items from the knapsack in order to accept a new item we obtain the following results i we propose a 8 competitive deterministic and memoryless algorithm for the problem which contrasts with the result for the online maximization knapsack problem that no online algorithm has a bounded competitive ratio 14 ii we propose a 2e competitive randomized algorithm for the problem iii we derive a lower bound of 2 for deterministic algorithms for the problem iv we propose a 1 618 competitive deterministic algorithm for the case in which each item has size equal to its cost and show that this is best possible

inferring stochastic dynamics from functional data in most current data modelling for time dynamic systems one works with a prespecified differential equation and attempts to estimate its parameters in contrast we demonstrate that in the case of functional data the equation itself can be inferred assuming only that the dynamics are described by a first order nonlinear differential equation with a random component we obtain data adaptive dynamic equations from the observed data via a simple smoothing based procedure we prove consistency and introduce diagnostics to ascertain the fraction of variance that is explained by the deterministic part of the equation this approach is shown to yield useful insights into the time dynamic nature of human growth copyright 2012 oxford university press

kernels for nonparametric curve estimation summary the choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error imse the present proof of the optimality of the latter kernels is restricted up to order k 5 these kernels are also of interest for the nonparametric estimation of probability densities and spectral densities a finite sample study indicates that higher order kernels asymptotically improving the rate of convergence may become attractive for realistic finite sample size suitably modified kernels are considered for estimating at the extremities of the data in a way which allows to retain the order of the bias found for interior points

randomized algorithms for online knapsack problems in this paper we study online knapsack problems the input is a sequence of items e 1 e 2 e n each of which has a size and a value given the ith item e i we either put e i into the knapsack or reject it in the removable setting when e i is put into the knapsack some items in the knapsack are removed with no cost if the sum of the size of e i and the total size in the current knapsack exceeds the capacity of the knapsack our goal is to maximize the profit i e the sum of the values of items in the last knapsack we present a simple randomized 2 competitive algorithm for the unweighted non removable case and show that it is the best possible where knapsack problem is called unweighted if the value of each item is equal to its size for the removable case we propose a randomized 2 competitive algorithm despite there is no constant competitive deterministic algorithm we also provide a lower bound 1 1 e 1 368 for the competitive ratio for the unweighted removable case we propose a 10 7 competitive algorithm and provide a lower bound 1 25 for the competitive ratio

the accommodating function a generalization of the competitive ratio a new measure the accommodating function for the quality of on line algorithms is presented the accommodating function which is a generalization of both the competitive ratio and the competitive ratio on accommodating sequences measures the quality of an on line algorithm as a function of the resources that would be sufficient for an optimal off line algorithm to fully grant all requests more precisely if we have some amount of resources n the function value at alpha is the usual ratio still on some fixed amount of resources n except that input sequences are restricted to those where the optimal off line algorithm will not obtain a better result by having more than the amount alpha n of resources the accommodating functions for three specific on line problems are investigated a variant of bin packing in which the goal is to maximize the number of items put in n bins the seat reservation problem and the problem of optimizing total flow time when preemption is allowed we also show that when trying to distinguish between two algorithms the decision as to which one performs better cannot necessarily be made from the competitive ratio or the competitive ratio on accommodating sequences alone for the variant of bin packing considered we show that worst fit has a strictly better competitive ratio than first fit while first fit has a strictly better competitive ratio on accommodating sequences than worst fit

multi time step integration using nodal partitioning an algorithm is presented which integrates different groups of nodes of a finite element mesh with different time steps and different integrators since the nodal groups are updated independently no unsymmetric systems need be solved stability is demonstrated by showing that an energy norm of the solution decreases after every update if the time step is less than a given critical value the element eigenvalue inequality theorem is used to give the critical time step in terms of element eigenvalues

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

a faster and accurate explicit algorithm for quasi harmonic dynamic problems summary it is known that the explicit time integration is conditionally stable the very small time step leads to increase of computational time dramatically in this paper a mass redistributed method is formulated in different numerical schemes to simulate transient quasi harmonic problems the essential idea of the mass redistributed method is to shift the integration points away from the gauss locations in the computation of mass matrix for achieving a much larger stable time increment in the explicit method for the first time it is found that the stability of explicit method in transient quasi harmonic problems is proportional to the softened effect of discretized model with mass redistributed method with adjustment of integration points in the mass matrix the stability of transient models is improved significantly numerical experiments including 1d 2d and 3d problems with regular and irregular mesh have demonstrated the superior performance of the proposed mass redistributed method with the combination of smoothed finite element method in terms of accuracy as well as stability copyright 2016 john wiley sons ltd

online multi coloring with advice we consider the problem of online graph multi coloring with advice multi coloring is often used to model frequency allocation in cellular networks we give several nearly tight upper and lower bounds for the most standard topologies of cellular networks paths and hexagonal graphs for the path negative results trivially carry over to bipartite graphs and our positive results are also valid for bipartite graphs for hexagonal graphs negative results trivially carry over to 3 colorable graphs and most of our positive results do as well the advice given represents information that is likely to be available studying for instance the data from earlier similar periods of time

better algorithms for unfair metrical task systems and applications unfair metrical task systems are a generalization of online metrical task systems in this paper we introduce new techniques to combine algorithms for unfair metrical task systems and apply these techniques to obtain improved randomized online algorithms for metrical task systems on arbitrary metric spaces

improved analysis of the online set cover problem with advice abstract we study the advice complexity of an online version of the set cover problem the goal is to quantify the information that online algorithms for this problem need to be supplied with to compute high quality solutions and to overcome the drawback of not knowing future requests this concept was successfully applied to many prominent online problems in the past while trying to capture the essence of what makes an online problem hard the online set cover problem was introduced by alon et al 2009 2 for a ground set of size n and a set family of m subsets of the ground set we obtain bounds in both n and m we show that a linear number with respect to both n and m of advice bits is both sufficient and necessary to perform optimally furthermore we prove that o n log c c bits are sufficient to design a c competitive online algorithm and this bound is tight up to a factor of o log c we further give upper and lower bounds for achieving c competitiveness with respect to m finally we analyze the advice complexity of the problem with respect to some natural parameters i e measurable properties of the inputs

adaptive bandwidth choice for kernel regression abstract a data based procedure is introduced for local bandwidth selection for kernel estimation of a regression function at a point the estimated bandwidth is shown to be consistent and asymptotically normal as an estimator of the asymptotic optimal value for minimum mean square estimation simulation studies indicate satisfactory behavior of the new bandwidth estimator in finite samples the findings are improvements over a global bandwidth estimator the same methodology works for local linear regression and extends easily to weighted local polynomial fits

predictive inference for integrated volatility numerous volatility based derivative products have been engineered in recent years this has led to interest in constructing conditional predictive densities and confidence intervals for integrated volatility in this article we propose nonparametric estimators of the aforementioned quantities based on model free volatility estimators we establish consistency and asymptotic normality for the feasible estimators and study their finite sample properties through a monte carlo experiment finally using data from the new york stock exchange we provide an empirical application to volatility directional predictability

a new family of explicit time integration methods for linear and non linear structural dynamics a new family of explicit single step time integration methods with controllable high frequency dissipation is presented for linear and non linear structural dynamic analyses the proposed methods are second order accurate and completely explicit with a diagonal mass matrix even when the damping matrix is not diagonal in the linear structural dynamics or the internal force vector is a function of velocities in the non linear structural dynamics stability and accuracy of the new explicit methods are analysed for the linear undamped damped cases furthermore the new methods are compared with other explicit methods

online knapsack of unknown capacity how to optimize energy consumption in smartphones abstract we propose a new variant of the standard online knapsack problem where the only information missing to the provided instances is the capacity b of the knapsack we refer to this problem as the online knapsack of unknown capacity kuc problem any algorithm solving the kuc problem must provide a strategy for filling online the knapsack until its capacity is revealed when the knapsack capacity is revealed no other item can be inserted and also the last inserted item is discarded if it does not completely fit in the knapsack apart for the interest in a new version of the fundamental knapsack problem the motivations that lead to define this new variant come from energy consumption constraints in smartphones communications we provide lower and upper bounds to the problem for various cases in general we design an optimal algorithm admitting a 1 2 competitive ratio when all items admit uniform ratio of profit over size our algorithm provides a 49 86 569 competitive ratio that leaves some gap with the provided bound of 1 618 the inverse of the golden number we then conduct experimental analysis for the competitive ratio guaranteed algorithms compared to the optimum and to various heuristics

a multi time step integration algorithm for structural dynamics based on the modified trapezoidal rule an explicit multi time step subcycling integration method is proposed for solving semi discretized structural dynamics problems based on nodal partition theory this method is derived from the modified trapezoidal rule method mtm to achieve numerical stability virtually fixed physical quantities displacement and velocity are assumed for the non updated nodal groups the energy method is used to analyze the stability of the new algorithm and the critical time step for each nodal group is determined in terms of the maximum frequency of the elements in the associated subdomain some example problems are evaluated to numerically examine the accuracy and stability of the algorithm

online computation with advice we consider a model for online computation in which the online algorithm receives together with each request some information regarding the future referred to as advice the advice is a function defined by the online algorithm of the whole request sequence the advice provided to the online algorithm may allow an improvement in its performance compared to the classical model of complete lack of information regarding the future we are interested in the impact of such advice on the competitive ratio and in particular in the relation between the size b of the advice measured in terms of bits of information per request and the improved competitive ratio since b 0 corresponds to the classical online model and b log a where a is the algorithm s action space corresponds to the optimal offline one our model spans a spectrum of settings ranging from classical online algorithms to offline ones in this paper we propose the above model and illustrate its applicability by considering two of the most extensively studied online problems namely metrical task systems mts and the k server problem for mts we establish tight up to constant factors upper and lower bounds on the competitive ratio of deterministic and randomized online algorithms with advice for any choice of 1 b q logn where n is the number of states in the system we prove that any randomized online algorithm for mts has competitive ratio w log n b and we present a deterministic online algorithm for mts with competitive ratio o log n b for the k server problem we construct a deterministic online algorithm for general metric spaces with competitive ratio k o 1 b for any choice of q 1 b logk

upper bound solution to elasticity problems a unique property of the linearly conforming point interpolation method lc pim it is well known that the displacement based fully compatible finite element method fem provides a lower bound in energy norm for the exact solution to elasticity problems it is however much more difficult to bound the solution from above for general problems in elasticity and it has been a dream of many decades to find a systematical way to obtain such an upper bound this paper presents a very important and unique property of the linearly conforming point interpolation method lc pim it provides a general means to obtain an upper bound solution in energy norm for elasticity problems this paper conducts first a thorough theoretical study on the lc pim we derive its weak form based on variational principles study a number of properties of the lc pim and prove that lc pim is variationally consistent and that it produces upper bound solutions we then demonstrate these properties through intensive numerical studies with many examples of 1d 2d and 3d problems using the lc pim together with the fem we now have a systematical way to numerically obtain both upper and lower bounds of the exact solution to elasticity problems as shown in these example problems copyright 2007 john wiley sons ltd

predictive density estimators for daily volatility based on the use of realized measures abstract the main objective of this paper is to propose a feasible model free estimator of the predictive density of integrated volatility in this sense we extend recent papers by andersen et al andersen t g bollerslev t diebold f x labys p 2003 modelling and forecasting realized volatility econometrica 71 579 626 and by andersen et al andersen t g bollerslev t meddahi n 2004 analytic evaluation of volatility forecasts international economic review 45 1079 1110 andersen t g bollerslev t meddahi n 2005 correcting the errors volatility forecast evaluation using high frequency data and realized volatilities econometrica 73 279 296 who address the issue of pointwise prediction of volatility via arma models based on the use of realized volatility our approach is to use a realized volatility measure to construct a non parametric kernel estimator of the predictive density of daily volatility we show that by choosing an appropriate realized measure one can achieve consistent estimation even in the presence of jumps and microstructure noise in prices more precisely we establish that four well known realized measures i e realized volatility bipower variation and two measures robust to microstructure noise satisfy the conditions required for the uniform consistency of our estimator furthermore we outline an alternative simulation based approach to predictive density construction finally we carry out a simulation experiment in order to assess the accuracy of our estimators and provide an empirical illustration that underscores the importance of using microstructure robust measures when using high frequency data

evaluating utility measurement from recurrent marker processes in the presence of competing terminal events abstractin follow up studies utility marker measurements are usually collected upon the occurrence of recurrent events until a terminal event such as death takes place in this article we define the recurrent marker process to characterize utility accumulation over time for example with medical cost and repeated hospitalizations being treated as marker and recurrent events respectively the recurrent marker process is the trajectory of cumulative cost which stops to increase after death in many applications competing risks arise as subjects are at risk of more than one mutually exclusive terminal event such as death from different causes and modeling the recurrent marker process for each failure type is often of interest however censoring creates challenges in the methodological development because for censored subjects both failure type and recurrent marker process after censoring are unobserved to circumvent this problem we propose a nonparametric framework for the recurrent marker proce

change points in nonparametric regression analysis an otherwise smooth regression model are proposed the assumptions needed are much weaker than those made in parametric models the proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change points of slope and of higher order curvature the proposed estimators are based on a comparison of left and right one sided kernel smoothers weak convergence of a stochastic process in local differences to a gaussian process is established for properly scaled versions of estimators of the location of a change point the continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change point estimators these rates are typically faster than n 1 2 rates of global lp convergence of curve estimates with appropriate kernel modifications adapting to estimated change points are derived as a consequence it is shown that these rates of convergence are the same as if the location of the change point was known the methods are illustrated by means of the well known data on the annual flow volume of the nile river between 1871 and 1970 1 introduction nonparametric regression methods are usually applied in order to obtain a smooth fit of a regression curve without having to specify a parametric class of regression functions sometimes a generally smooth curve might contain an isolated discontinuity or change point in the curve or in a possibly higher order derivative and in many cases interest focuses on the occurrence of such change points in parametric approaches to the regression change point problem simple linear regressions before and after a possible change point are assumed and then the possibility of a discontinuity in the form of a jump or of a jump in the first derivative or equivalently a slope change is incorporated into the model see for instance hinkley 1969 and brown durbin and evans 1975 the analysis of change points which describe sudden localized changes typically occurring in economics medicine and the physical sciences has recently found increasing interest general smoothness assumptions allowing for a large class of regression functions to be considered seem to be more appropriate in a variety of applied problems than parametric modelling an

a test for model specification of diffusion processes we propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process the empirical likelihood is used to formulate a statistic for each kernel smoothing bandwidth which is effectively a studentized l2 distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process to reduce the sensitivity of the test on smoothing bandwidth choice the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths to better capture the finite sample distribution of the test statistic and data dependence the critical value of the test is obtained by a parametric bootstrap procedure properties of the test are evaluated asymptotically and numerically by simulation and by a real data example

nonparametric instrumental regression the focus of this paper is the nonparametric estimation of an instrumental regression function f defined by conditional moment restrictions that stem from a structural econometric model e y f z w 0 and involve endogenous variables y and z and instruments w the function f is the solution of an ill posed inverse problem and we propose an estimation procedure based on tikhonov regularization the paper analyzes identification and overidentification of this model and presents asymptotic properties of the estimated nonparametric instrumental regression function

quantile treatment effects in the regression discontinuity design abstract we introduce a nonparametric estimator for local quantile treatment effects in the regression discontinuity rd design the procedure uses local distribution regression to estimate the marginal distributions of the potential outcomes we illustrate the procedure through monte carlo simulations and an application on the distributional effects of a universal pre k program in oklahoma we find that participation in a pre k program significantly raises the lower end and the middle of the distribution of test scores

stochastic on line knapsack problems different classes of on line algorithms are developed and analyzed for the solution of 0 1 and relaxed stochastic knapsack problems in which both profit and size coefficients are random variables in particular a linear time on line algorithm is proposed for which the expected difference between the optimum and the approximate solution value iso log3 2n an 1 lower bound on the expected difference between the optimum and the solution found by any on line algorithm is also shown to hold

root n bandwidth selectors for kernel estimation of density derivatives abstract based on a random sample of size n from an unknown density f on the real line the problem of adaptively selecting the bandwidth in kernel estimation of f k is investigated where f k denotes the kth derivative of f the estimates of density derivatives can be used to evaluate modes and inflection points of f and can be applied to the estimation of scores in certain additive models and to the empirical verification of the law of demand in econometrics for all k the information bounds for bandwidth selectors are given and two types of adaptive bandwidth selectors are proposed a careful analysis of the kernel estimate of the integrated squared bias isb term contained in a generalization of smoothed cross validation indicates that the sync kernel is the proper choice for estimating isb and consequently leads to the first type of selector the second type of selector is based on the plug in method which involves expanding isb up to suitable order and estimating integrated squared den

on a semiparametric variance function model and a test for heteroscedasticity we propose a general semiparametric variance function model in a fixed design regression setting in this model the regression function is assumed to be smooth and is modelled nonparametrically whereas the relation between the variance and the mean regression function is assumed to follow a generalized linear model almost all variance function models that were considered in the literature emerge as special cases least squares type estimates for the parameters of this model and the simultaneous estimation of the unknown regression and variance functions by means of nonparametric kernel estimates are combined to infer the parametric and nonparametric components of the proposed model the asymptotic distribution of the parameter estimates is derived and is shown to follow usual parametric rates in spite of the presence of the nonparametric component in the model this result is applied to obtain a data based test for heteroscedasticity under minimal assumptions on the shape of the regression function

an improved estimator of the density function at the boundary abstract we propose a new method of boundary correction for kernel density estimation the technique is a kind of generalized reflection method involving reflecting a transformation of the data the transformation depends on a pilot estimate of the logarithmic derivative of the density at the boundary in simulations the new method is seen to clearly outperform an earlier generalized reflection idea it also has overall advantages over boundary kernel methods and a nonnegative adaptation thereof although the latter are competitive in some situations we also present the theory underlying the new methodology

multivariate boundary kernels and a continuous least squares principle summary whereas there are many references on univariate boundary kernels the construction of boundary kernels for multivariate density and curve estimation has not been investigated in detail the use of multivariate boundary kernels ensures global consistency of multivariate kernel estimates as measured by the integrated mean squared error or sup norm deviation for functions with compact support we develop a class of boundary kernels which work for any support regardless of the complexity of its boundary our construction yields a boundary kernel for each point in the boundary region where the function is to be estimated these boundary kernels provide a natural continuation of non negative kernels used in the interior onto the boundary they are obtained as solutions of the same kernel generating variational problem which also produces the kernel function used in the interior as its solution we discuss the numerical implementation of the proposed boundary kernels and their relationship to locally weighted least squares along the way we establish a continuous least squares principle and a continuous analogue of the gauss markov theorem

an optimal on line algorithm for metrical task system in practice almost all dynamic systems require decisions to be made on line without full knowledge of their future impact on the system a general model for the processing of sequences of tasks is introduced and a general on line decision algorithm is developed it is shown that for an important class of special cases this algorithm is optimal among all on line algorithms specifically a task system s d for processing sequences of tasks consists of a set s of states and a cost matrix d where d i j is the cost of changing from state i to state j we assume that d satisfies the triangle inequality and all diagonal entries are 0 the cost of processing a given task depends on the state of the system a schedule for a sequence t 1 t 2 t k of tasks is a sequence s 1 s 2 s k of states where s i is the state in which t i is processed the cost of a schedule is the sum of all task processing costs and the state transition costs incurred an on line scheduling algorithm is one that chooses s i only knowing t 1 t 2 t i such an algorithm is w competitive if on any input task sequence its cost is within an additive constant of w times the optimal offline schedule cost the competitive ratio w s d is the infimum w for which there is a w competitive on line scheduling algorithm for s d it is shown that w s d 2 s 1 for every task system in which d is symmetric and w s d o s 2 for every task system finally randomized on line scheduling algorithms are introduced it is shown that for the uniform task system in which d i j 1 for all i j the expected competitive ratio w s d o log s

upper and lower bounds for natural frequencies a property of the smoothed finite element methods node based smoothed finite element method ns fem using triangular type of elements has been found capable to produce upper bound solutions to the exact solutions for force driving static solid mechanics problems due to its monotonic soft behavior this paper aims to formulate an ns fem for lower bounds of the natural frequencies for free vibration problems to make the ns fem temporally stable an fem is devised by combining the compatible and smoothed strain fields in a partition of unity fashion controlled by 0 1 so that both the properties of stiff fem and the monotonically soft ns fem models can be properly combined for a desired purpose for temporally stabilizing ns fem is chosen small so that it acts like a regularization parameter making the ns fem stable but still with sufficient softness ensuring lower bounds for natural frequency solution our numerical studies demonstrate that 1 using a proper the spurious non zero energy modes can be removed and the ns fem becomes temporally stable 2 the stabilized ns fem becomes a general approach for solids to obtain lower bounds to the exact natural frequencies over the whole spectrum 3 fem can even be tuned for obtaining nearly exact natural frequencies

stabilized conforming nodal integration in the natural element method a stabilized conforming nodal integration scheme is implemented in the natural neighbour method in conjunction with non sibsonian interpolation in this approach both the shape functions and the integration scheme are defined through use of first order voronoi diagrams the method illustrates improved performance and significant advantages over previous natural neighbour formulations the method also shows substantial promise for problems with large deformations and for the computation of higher order gradients copyright 2004 john wiley sons ltd

instrumental variable methods for recovering continuous linear functionals abstract this paper develops methods for estimating continuous linear functionals in nonparametric instrumental variable problems examples of such functionals include consumer surplus and weighted average derivatives the estimation procedure is robust to a setting where the underlying model is not identified but the linear functional is in order to attain such robustness it is necessary to employ a partially identified nuisance parameter we address this problem by consistently estimating a unique element of the identified set for nuisance parameters which we then use to construct a n asymptotically normal estimator for the desired linear functional

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation

explicit multi time step integration for first and second order finite element semidiscretizations abstract explicit multi time step subcycling integration algorithms based on nodal partitions for both first and second order systems are presented the algorithm is identical to an earlier algorithm of the senior author but some simplifications have been made in the actual algorithm which make it easier to implement in general purpose programs consistency convergence and stability analyses of this algorithm for first order systems are given interpolations on the interfaces between different time step domains are studied a general conjecture on the stability criterion for second order systems with subcycling and nodal partitions is also proposed and some unsolved theoretical difficulties are posed