on reliable stabilization via rectangular dilated lmis and dissipativity based certifications in this short note we consider the problem of reliable stabilization for multi channel systems where our main objective is to maintain the robust stability of the perturbed closed loop system when there is a single controller failure in any of the control channels specifically we present a less conservative result than results in the literature in terms of a set of dilated lmis for the reliable state feedback stabilization of the nominal system while a dissipativity based certification is used to extend the stability condition when there is an additive model perturbation in the system finally a numerical example is presented to illustrate the applicability of the proposed technique

modified adaptive algorithms it is well known that the adaptive algorithm is simple and easy to program but the results are not fully competitive with other nonlinear methods such as free knot spline approximation we modify the algorithm to take full advantages of nonlinear approximation the new algorithms have the same approximation order as other nonlinear methods which is proved by characterizing their approximation spaces one of our algorithms is implemented on the computer with numerical results illustrated by figures and tables

euler s elastica and curvature based inpainting image inpainting is a special image restoration problem for which image prior models play a crucial role euler s elastica was first introduced to computer vision by mumford algebraic geometry and its applications springer verlag new york 1994 pp 491 506 as a curve prior model by functionalizing the elastica energy masnou and morel proceedings of the 5th ieee international conference image processing 3 1998 pp 259 263 proposed an elastica based variational inpainting model the current paper is intended to contribute to the development of its mathematical foundation and the study of its properties and connections to the earlier works of bertalmio sapiro caselles and ballester siggraph 2000 acm press new york 2000 and chan and shen j visual comm image rep 12 2001 pp 436 449 a computational scheme based on numerical pdes is presented which allows the automatic handling of topologically complex inpainting domains

sparse geometric image representations with bandelets this paper introduces a new class of bases called bandelet bases which decompose the image along multiscale vectors that are elongated in the direction of a geometric flow this geometric flow indicates directions in which the image gray levels have regular variations the image decomposition in a bandelet basis is implemented with a fast subband filtering algorithm bandelet bases lead to optimal approximation rates for geometrically regular images for image compression and noise removal applications the geometric flow is optimized with fast algorithms so that the resulting bandelet basis produces minimum distortion comparisons are made with wavelet image compression and noise removal algorithms

density estimation by wavelet thresholding density estimation is a commonly used test case for nonparametric estimation methods we explore the asymptotic properties of estimators based on thresholding of empirical wavelet coefficients minimax rates of convergence are studied over a large range of besov function classes b pq and for a range of global l p error measures 1 p p some form of nonlinearity is essential since the minimax linear estimators are suboptimal by polynomial powers of n a second approach using an approximation of a gaussian white noise model in a mallows metric is used to attain exactly optimal rates of convergence for quadratic error p 2

upper bounds on coarsening rates we consider two standard models of surface energy driven coarsening a constant mobility cahn hilliard equation whose large time behavior corresponds to mullins sekerka dynamics and a degenerate mobility cahn hilliard equation whose large time behavior corresponds to motion by surface diffusion arguments based on scaling suggest that the typical length scale should behave as in the first case and in the second we prove a weak one sided version of this assertion showing roughly speaking that no solution can coarsen faster than the expected rate our result constrains the behavior in a time averaged sense rather than pointwise in time and it constrains not the physical length scale but rather the perimeter per unit volume the argument is simple and robust combining the basic dissipation relations with an interpolation inequality and an ode argument

conditional independence in propositional logic independence the study of what is relevant to a given problem of reasoning is an important ai topic in this paper we investigate several notions of conditional independence in propositional logic darwiche and pearl s conditional independence and some more restricted forms of it many characterizations and properties of these independence relations are provided we show them related to many other notions of independence pointed out so far in the literature mainly formula variable independence irrelevance and novelty under various forms separability interactivity we identify the computational complexity of conditional independence and of all these related independence relations

axiomatisation of functional dependencies in incomplete relations abstract incomplete relations are relations which contain null values whose meaning is value is at present unknown such relations give rise to two types of functional dependency fd the first type called the strong fd sfd is satisfied in an incomplete relation if for all possible worlds of this relation the fd is satisfied in the standard way the second type called the weak fd wfd is satisfied in an incomplete relation if there exists a possible world of this relation in which the fd is satisfied in the standard way we exhibit a sound and complete axiom system for both strong and weak fds which takes into account the interaction between sfds and wfds an interesting feature of the combined axiom system is that it is not k ary for any natural number k 0 we show that the combined implication problem for sfds and wfds can be solved in time polynomial in the size of the input set of fds finally we show that armstrong relations exist for sfds and wfds

the total variation flow in rn the purpose of this chapter is to prove existence and uniqueness of the minimizing total variation flow in n frac partial u partial t div left frac du left du right right in left 0 infty right times mathbb r n 3 1 coupled with the initial condition u 0 x u 0 x text x in mathbb r n 3 2 when u0 l loc 1 l n

wavelet frame accelerated reduced support vector machines in this paper a novel method for reducing the runtime complexity of a support vector machine classifier is presented the new training algorithm is fast and simple this is achieved by an over complete wavelet transform that finds the optimal approximation of the support vectors the presented derivation shows that the wavelet theory provides an upper bound on the distance between the decision function of the support vector machine and our classifier the obtained classifier is fast since a haar wavelet approximation of the support vectors is used enabling efficient integral image based kernel evaluations this provides a set of cascaded classifiers of increasing complexity for an early rejection of vectors easy to discriminate this excellent runtime performance is achieved by using a hierarchical evaluation over the number of incorporated and additional over the approximation accuracy of the reduced set vectors here this algorithm is applied to the problem of face detection but it can also be used for other image based classifications the algorithm presented provides a 530 fold speedup over the support vector machine enabling face detection at more than 25 fps on a standard pc

a constrained risk inequality with applications to nonparametric functional estimation a general constrained minimum risk inequality is derived given two densities f and f 0 we find a lower bound for the risk at the point given an upper bound for the risk at the point 0 the inequality sheds new light on superefficient estimators in the normal location problem and also on an adaptive estimation problem arising in nonparametric functional estimation

analysis of the lack of compactness in the critical sobolev embeddings let un be a bounded sequence inhs p rd 0 s d p we show that un has a subsequence u n such that eachu ncan be expressed as a finite sum plus a remainder of translations dilations of functions mand such that the remainder has arbitrary small norm inlq 1 q 1 p s d this generalizes a result obtained by patrick gerard for the casep 2

tractable reasoning via approximation abstract problems in logic are well known to be hard to solve in the worst case two different strategies for dealing with this aspect are known from the literature language restriction and theory approximation in this paper we are concerned with the second strategy our main goal is to define a semantically well founded logic for approximate reasoning which is justifiable from the intuitive point of view and to provide fast algorithms for dealing with it even when using expressive languages we also want our logic to be useful to perform approximate reasoning in different contexts we define a method for the approximation of decision reasoning problems based on multivalued logics our work expands and generalizes in several directions ideas presented by other researchers the major features of our technique are 1 approximate answers give semantically clear information about the problem at hand 2 approximate answers are easier to compute than answers to the original problem 3 approximate answers can be improved and eventually they converge to the right answer 4 both sound approximations and complete ones are described the method we propose is flexible enough to be applied to a wide range of reasoning problems in our research we considered approximation of several decidable problems with different worstcase complexity involving both propositional and first order languages in particular we defined approximation techniques for propositional logic fragments of first order logic concept description languages and modal logic in our research we also addressed the issue of representing the knowledge of a reasoner with limited resources and how to use such a knowledge for approximate reasoning purposes

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

reliable state feedback control of t s fuzzy systems with sensor faults this paper is concerned with reliable state feedback control synthesis for takagi and sugeno t s fuzzy systems with sensor multiplicative faults by considering the influence of sensor faults on both the system states and premise variables of fuzzy controllers a class of new convex reliable stabilization conditions are proposed for t s fuzzy systems using the properties of fuzzy product inference engines furthermore the obtained result is extended to the h infty reliable control case the resulting controllers are reliable in that they provide guaranteed asymptotic stability and h infty performance when all sensors are operational as well as when some sensor experiences failures different from the proposed approach the influence of sensor faults on premise variables is not considered in the existing results then it might not guarantee the stability and control performance for t s fuzzy systems with premise variables dependent on the system states a numerical example is given to illustrate the effectiveness of the proposed method

a logical notion of conditional independence properties and applications abstract we propose a notion of conditional independence with respect to prepositional logic and study some of its key properties we present several equivalent formulations of the proposed notion each oriented towards a specific application of logical reasoning such as abduction and diagnosis we suggest a framework for utilizing logical independence computationally by structuring a propositional logic database around a directed acyclic graph this structuring explicates many of the independences satisfied by the underlying database based on these structural independences we develop an algorithm for a class of structured databases that is not necessarily horn the algorithm is linear in the size of a database structure and can be used for deciding entailment computing abductions and diagnoses the presented results are motivated by similar results in the literature on probabilistic and constraint based reasoning

reliable decentralized stabilization of linear systems reliable stabilization of linear time invariant multi input multi output plants is considered using a two channel decentralized controller configuration necessary and sufficient conditions are obtained for existence of reliable controllers that maintain stability under the possible failure of either one of the two controllers all decentralized controllers that achieve reliable stabilization are characterized

on the equivalence of soft wavelet shrinkage total variation diffusion total variation regularization and sides soft wavelet shrinkage total variation tv diffusion tv regularization and a dynamical system called sides are four useful techniques for discontinuity preserving denoising of signals and images in this paper we investigate under which circumstances these methods are equivalent in the one dimensional case first we prove that haar wavelet shrinkage on a single scale is equivalent to a single step of space discrete tv diffusion or regularization of two pixel pairs in the translationally invariant case we show that applying cycle spinning to haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of tv diffusion we prove that space discrete tv diffusion and tv regularization are identical and that they are also equivalent to the sides system when a specific force function is chosen afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the laplacian pyramid of the signal we analyze possibilities to avoid gibbs like artifacts for multiscale haar wavelet shrinkage by scaling the thresholds finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and pde variational approaches these methods are based on iterated shift invariant wavelet shrinkage at multiple scales with scaled thresholds

nonlinear wavelet image processing variational problems compression and noise removal through wavelet shrinkage this paper examines the relationship between wavelet based image processing algorithms and variational problems algorithms are derived as exact or approximate minimizers of variational problems in particular we show that wavelet shrinkage can be considered the exact minimizer of the following problem given an image f defined on a square i minimize over all g in the besov space b11 l1 i the functional f g l2 i 2 g b11 l1 i we use the theory of nonlinear wavelet image compression in l2 i to derive accurate error bounds for noise removal through wavelet shrinkage applied to images corrupted with i i d mean zero gaussian noise a new signal to noise ratio snr which we claim more accurately reflects the visual perception of noise in images arises in this derivation we present extensive computations that support the hypothesis that near optimal shrinkage parameters can be derived if one knows or can estimate only two parameters about an image f the largest for which f bq lq i 1 q 2 1 2 and the norm f bq lq i both theoretical and experimental results indicate that our choice of shrinkage parameters yields uniformly better results than donoho and johnstone s visushrink procedure an example suggests however that donoho and johnstone s 1994 1995 1996 sureshrink method which uses a different shrinkage parameter for each dyadic level achieves a lower error than our procedure

design of reliable decentralized controllers a unified continuous discrete formulation abstract we present observer based controller designs for decentralized systems that are reliable to sets of control channel outages the designs guarantee stability and a h norm bound on the closed loop system despite complete sensor or actuator outages for any subset of a preselected set of control channels the results are presented in a unified discrete continuous setting we show how the continuous time and discrete time results can be generated from the unified formulation and present an algorithm for solving the discrete time design equations by making use of the delta operator formulation

approximation dans les espaces metriques et theorie de l estimation we investigate the relations between the speed of estimation and the metric structure of the parameter space especially in the case when its metric dimension is infinite given some distance d on generally hellinger distance in the case of n i i d variables we consider the minimax risk for n observations r n q mathop inf sup limits t n theta in theta text ie theta d q theta t n t n being any estimate of we shall look for functions r such that for positive constants c 1 q and c 2 q c 1 r q n r n q c2 r q n r n is the speed of estimation and we shall show under fairly general conditions including i i d variables and regular cases of markov chains and stationnary gaussian processes that r n is determined up to multiplicative constants by the metric structure of we shall also give a construction for some sort of universal estimates the risk of which is bounded by c 2 r q n in all cases where the preceding theory applies

the grenader estimator a nonasymptotic approach on examine certaines proprietes non asymtotiques de l estimateur de grenander d une densite decroissante f cet estimation est defini comme la pente du plus petit majorant concave de la fonction de repartition empirique on montre que son risque mesure avec perte l 1 est borne par une certaine fonctionnelle qui depend de f et du nombre d observations n le comportement asymptotique de la fonctionnelle quand n tend vers l infini est en accord avec les performances asymptotiques connues de l estimation de grenander

flexible parsimonious smoothing and additive modeling a simple method is presented for fitting regression models that are nonlinear in the explanatory variables despite its simplicity or perhaps because of it the method has some powerful characteristics that cause it to be competitive with and often superior to more sophisticated techniques especially for small data sets in the presence of high noise

accelerating l1 l2 deblurring using wavelet expansions of operators abstract image deblurring is a fundamental problem in imaging usually solved with computationally intensive optimization procedures the goal of this paper is to provide new efficient strategies to reduce computing times for simple deblurring models regularized using orthogonal wavelet transforms we show that the minimization can be significantly accelerated by leveraging the fact that images and blur operators are compressible in the same orthogonal wavelet basis the proposed methodology consists of three ingredients i a sparse approximation of the blur operator in wavelet bases ii a diagonal preconditioner and iii an implementation on massively parallel architectures combining the three ingredients leads to acceleration factors ranging from 4 to 250 on a typical workstation for instance a 1024 1024 image can be deblurred in 0 15 s

iterative regularization and nonlinear inverse scale space applied to wavelet based denoising in this paper we generalize the iterative regularization method and the inverse scale space method recently developed for total variation tv based image restoration to wavelet based image restoration this continues our earlier joint work with others where we applied these techniques to variational based image restoration obtaining significant improvement over the rudin osher fatemi tv based restoration here we apply these techniques to soft shrinkage and obtain the somewhat surprising result that a the iterative procedure applied to soft shrinkage gives firm shrinkage and converges to hard shrinkage and b that these procedures enhance the noise removal capability both theoretically in the sense of generalized bregman distance and for some examples experimentally in terms of the signal to noise ratio leaving less signal in the residual

np hardness of some linear control design problems we show that some basic linear control design problems are np hard implying that unless p np they cannot be solved by polynomial time algorithms the problems that we consider include simultaneous stabilization by output feedback stabilization by state or output feedback in the presence of bounds on the elements of the gain matrix and decentralized control these results are obtained by first showing that checking the existence of a stable matrix in an interval family of matrices is np hard

filtered wavelet thresholding methods when working with nonlinear filtering algorithms for image denoising problems there are two crucial aspects namely the choice of the thresholding parameter and the use of a proper filter function both greatly influence the quality of the resulting denoised image in this paper we propose two new filters which are a piecewise quadratic and an exponential function of respectively arid we show how they can be successfully used instead of the classical donoho and johnstone s soft thresholding filter we exploit the increased regularity and flexibility of the new filters to improve the quality of the final results moreover we prove that our filtered approximation is a near minimizer of the functional which has to be minimized to solve the denoising problem we also show that the quadratic filter due to its shape yields good results if we choose as the donoho and johnstone universal threshold while the exponential one is more suitable if we use the recently proposed h curve criterion encouraging results in extensive numerical experiments on several test images confirm the effectiveness of our proposal

gagliardo nirenberg inequalities on manifolds abstract we prove gagliardo nirenberg inequalities on some classes of manifolds lie groups and graphs

statistical estimation and optimal recovery new formulas are given for the minimax linear risk in estimating a linear functional of an unknown object from indirect data contaminated with random gaussian noise the formulas cover a variety of loss functions and do not require the symmetry of the convex a priori class it is shown that affine minimax rules are within a few percent of minimax even among nonlinear rules for a variety of loss functions it is also shown that difficulty of estimation is measured by the modulus of continuity of the functional to be estimated the method of proof exposes a correspondence between minimax affine estimates in the statistical estimation problem and optimal algorithms in the theory of optimal recovery

interpolation of besov spaces we investigate besov spaces and their connection with dyadic spline approximation in lp q 0 p oo our main results are the determination of the interpolation spaces between a pair of besov spaces an atomic decomposition for functions in a besov space the characterization of the class of functions which have certain prescribed degree of approximation by dyadic splines

frontiers for propositional reasoning about fragments of probabilistic conditional independence and hierarchical database decompositions abstract conditional independence provides an essential framework to deal with knowledge and uncertainty in artificial intelligence and is fundamental in probability and multivariate statistics its associated implication problem is paramount for building bayesian networks unfortunately the problem does not enjoy an axiomatization by a finite set of horn rules and is already conp complete to decide for some fragments of conditional independencies saturated conditional independencies form an important fragment whose implication problem is decidable in almost linear time we establish an axiomatization by a finite set of horn rules for the fragment of generalized saturated conditional independencies these state the conditional independence between finitely many sets of random variables the special case of two sets captures geiger and pearl s finite axiomatization for saturated conditional independencies even for this special case our completeness proof is new the proof argument utilizes special probability models where two events have probability one half special probability models allow us to establish an equivalence between the implication of generalized saturated conditional independencies and that of formulae in a boolean propositional fragment this duality is then extended to a trinity including the implication problem of delobel s full first order hierarchical database decompositions already for the independence between two sets of random variables the dualities cannot be extended to cover conditional independencies in general or first order hierarchical decompositions

robust dissipativity of interval uncertain linear systems in this paper we are concerned with the problem of robust dissipativity of linear systems with parameters affected by box uncertainty our major goal is to evaluate the largest uncertainty level for which all perturbed instances share a common dissipativity certificate while it is np hard to compute this quantity exactly we demonstrate that under favorable circumstances one can build an o 1 tight lower bound of this intractable quantity by solving an explicit semidefinite program of the size polynomial in the size of the system we consider a number of applications including the robust versions of the problems of extracting nearly optimal available storage providing nearly optimal required supply lyapunov stability analysis and linear quadratic control

robust solutions of uncertain quadratic and conic quadratic problems we consider a conic quadratic and in particular a quadratically constrained optimization problem with uncertain data known only to reside in some uncertainty set cal u the robust counterpart of such a problem leads usually to an np hard semidefinite problem this is the case for example when cal u is given as the intersection of ellipsoids or as an n dimensional box for these cases we build a single explicit semidefinite program which approximates the np hard robust counterpart and we derive an estimate on the quality of the approximation which is essentially independent of the dimensions of the underlying conic quadratic problem

nonlinear approximation and the space bv r2 given a function 2 0 q 0 l 2 and a real number t 0 let u f t infg bv g 11 ll vgig where the infimum is taken over all functions g g bv of bounded variation on this and related extremal problems arise in several areas of mathematics such as interpolation of operators and statistical estimation as well as in digital image processing techniques for finding minimizers g for u f t based on variational calculus and nonlinear partial differential equations have been put forward by several authors dms ro ms cl the main disadvantage of these approaches is that they are numerically intensive on the other hand it is well known that more elementary methods based on wavelet shrinkage solve related extremal problems for example the above problem with bv replaced by the besov space b l i see e g cdll however since bv has no simple description in terms of wavelet coefficients it is not clear that minimizers for u f t can be realized in this way we shall show in this paper that simple methods based on haar thresholding provide near minimizers for u f t our analysis of this extremal problem brings forward many interesting relations between haar decompositions and the space bv 1 introduction nonlinear approximation has recently played an impor tant role in several problems of image processing including compression noise removal and feature extraction we have in mind techniques such as wavelet compression djl wavelet shrinkage or thresholding djkp1 wavelet packets cw and greedy algorithms mz dt there has also been an impressive contribution of techniques based on variational calculus and nonlinear partial dif ferential equations see e g dms ro ms cl especially to the problems of noise removal and image segmentation the common point between these two approaches is their ability to adapt to the composite nature of images edge tex tures and smooth regions should be treated adaptively a requirement which is certainly not fulfilled by the classical linear filtering techniques

minimax risk over hyperrectangles and implications consider estimating the mean of a standard gaussian shift when that mean is known to lie in an orthosymmetric quadratically convex set in l 2 such sets include ellipsoids hyperrectangles and l p bodies with p 2 the minimax risk among linear estimates is within 25 of the minimax risk among all estimates the minimax risk among truncated series estimates is within a factor 4 44 of the minimax risk this implies that the difficulty of estimation a statistical quantity is measured fairly precisely by the n widths a geometric quantity if the set is not quadratically convex as in the case of l p bodies with p 2 things change appreciably minimax linear estimators may be out performed arbitrarily by nonlinear estimates the ordinary kolmogorov n widths still determine the difficulty of linear estimation but the difficulty of nonlinear estimation is tied to the inner bernstein n widths which can be far smaller essential use is made of a new heuristic that the difficulty of the hardest rectangular subproblem is equal to the difficulty of the full problem

sobolev type inequalities for dunkl operators abstract in this paper we study the sobolev inequality in the dunkl setting using two new approaches which provide a simpler elementary proof of the classical case p 2 as well as an extension to the coefficient p 1 that was previously unknown we also find estimates of the sharp constants for the sobolev inequality for dunkl gradient related inequalities and some improvements are also considered nash inequality besov space embeddings

an equivalence between relational database dependencies and a fragment of propositional logic it is known that there is an eqmvalence between functional dependencies m a relatmonal database and a certain fragment of proposmonal logic thins eqmvalence is extended to include both functional and multivalued dependencmes thus for each dependency there is a corresponding statement m proposmonal logic it ms then shown that a dependency funcuonal or multivalued is a consequence of a set of dependencies ff and only ff the corresponding proposiuonal statement s a consequence of the corresponding set of proposmonal statements examples are given to show that these techniques are valuable mn provmdmg much shorter proofs of theorems about dependencies than have been obtained by more tradmonal means it is shown that this eqmvalence cannot be extended to include either join dependencies or embedded multmvalued dependencies

synthesis of strictly positive real ℋ2 controllers using dilated lmis abstractthis paper considers strictly positive real spr controller design via direct minimisation of an upper bound on the closed loop h2 norm to realise a tractable design problem an observer

nonlinear and nonseparable bidimensional multiscale representation based on cell average representation the aim of this paper is to construct a new nonlinear and nonseparable multiscale representation of piecewise continuous bidimensional functions this representation is based on the definition of a linear projection and a nonlinear prediction operator which locally adapts to the function to be represented this adaptivity of the prediction operator proves to be very interesting for image encoding in that it enables a considerable reduction in the number of significant coefficients compared with other representations applications of this new nonlinear multiscale representation to image compression and super resolution conclude this paper

brief paper reliable stabilization using a multi controller configuration given a plant p we consider the problem of designing a pair of controllers c 1 and c 2 such that their sum stabilizes p and in addition each of them also stabilizes p should the other one fail this is referred to as the reliable stabilization problem it is shown that every strongly stabilizable plant can be reliably stabilized moreover one of the two controllers can be specified arbitrarily subject only to the constraint that it should be stable the stabilization technique is extended to reliable regulation

operator splittings bregman methods and frame shrinkage in image processing we examine the underlying structure of popular algorithms for variational methods used in image processing we focus here on operator splittings and bregman methods based on a unified approach via fixed point iterations and averaged operators in particular the recently proposed alternating split bregman method can be interpreted from different points of view as a bregman as an augmented lagrangian and as a douglas rachford splitting algorithm which is a classical operator splitting method we also study similarities between this method and the forward backward splitting method when applied to two frequently used models for image denoising which employ a besov norm and a total variation regularization term respectively in the first setting we show that for a discretization based on parseval frames the gradient descent reprojection and the alternating split bregman algorithm are equivalent and turn out to be a frame shrinkage method for the total variation regularizer we also present a numerical comparison with multistep methods

functional dependencies and constraints on null values in database relations database relations with incomplete information are considered the no information interpretation of null values is adopted due to its characteristics of generality and naturalness coherently with the framework and its motivation two meaningful classes of integrity constraints are studied a functional dependencies which have been widely investigated in the classical relational theory and b constraints on null values which control the presence of nulls in the relations specifically three types of constraints on null values are taken into account nullfree subschemes existence constraints disjunctive existence constraints and the interaction of each of them with functional dependencies is studied in each of the three cases the inference problem is solved the complexity of the algorithms for its solution analyzed and the existence of a complete axiomatization discussed

greedy wavelet projections are bounded on bv let bv bv ir d be the space of functions of bounded variation on ir d with d 2 let be a wavelet system of compactly supported functions normalized in bv i e bv ir d 1 each f bv has a unique wavelet

on the undecidability of implications between embedded multivalued database dependencies the implication and finite implication problems for embedded multivalued database dependencies are both shown to be algorithmically undecidable the proof is by an interpretation of semigroup word problems via systems of permuting equivalence relations into database dependencies in contrast it is shown that for each fixed premise h one has a decision procedure for implications h f

wavelet shrinkage asymptopia much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects curves densities spectral densities images from noisy data a now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems unfortunately the results have rarely moved into practice for a variety of reasons among them being similarity to known methods computational intractability and lack of spatial adaptivity we discuss a method for curve estimation based on n noisy data translate the empirical wavelet coefficients towards the origin by an amount 2 log n n the proposal differs from those in current use is computationally practical and is spatially adaptive it thus avoids several of the previous objections further the method is nearly minimax both for a wide variety of loss functions pointwise error global error measured in l p norms pointwise and global error in estimation of derivatives and for a wide range of smoothness classes including standard holder and sobolev classes and bounded variation this is a much broader near optimality than anything previously proposed we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves finally the theory underlying the method is interesting as it exploits a correspondence between statistical questions and questions of optimal recovery and information based complexity

on the conditional independence implication problem a lattice theoretic approach abstract conditional independence is a crucial notion in the development of probabilistic systems which are successfully employed in areas such as computer vision computational biology and natural language processing we introduce a lattice theoretic framework that permits the study of the conditional independence ci implication problem relative to the class of discrete probability measures semi lattices are associated with ci statements and a finite sound and complete inference system relative to semi lattice inclusions is presented this system is shown to be 1 sound and complete for inferring general from saturated ci statements and 2 complete for inferring general from general ci statements we also show that the general probabilistic ci implication problem can be reduced to that for elementary ci statements the completeness of the inference system together with its lattice theoretic characterization yields a criterion we can use to falsify instances of the probabilistic ci implication problem as well as several heuristics that approximate this falsification criterion in polynomial time we also propose a validation criterion based on representing constraints and sets of constraints as sparse 0 1 vectors which encode their semi lattices the validation algorithm works by finding solutions to a linear programming problem involving these vectors and matrices we provide experimental results for this algorithm and show that it is more efficient than related approaches

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

axioms and algorithms for inferences involving probabilistic independence abstract this paper offers an axiomatic characterization of the probabilistic relation x is independent of y written x y where x and y are two disjoint sets of variables four axioms for x y are presented and shown to be complete based on these axioms a polynomial membership algorithm is developed to decide whether any given independence statement x y logically follows from a set of such statements i e whether x y holds in every probability distribution that satisfies the complexity of the algorithm is o k2 n where is the number of given statements n is the number of variables in x y and k is the number of variables in x y

stability radius for structured perturbations and the algebraic riccati equation abstract in this paper we generalize the notion of stability radius introduced in 1 to allow for structured perturbations we then relate the stability radius to the existence of hermitian solutions of an algebraic riccati equation and give some applications of this result

asymptotic minimax risk for sup norm loss solution via optimal recovery we study the problem of estimating an unknown function on the unit interval or itsk th derivative with supremum norm loss when the function is observed in gaussian white noise and the unknown function is known only to obey lipschitz smoothness k 0 we discuss an optimization problem associated with the theory ofoptimal recovery although optimal recovery is concerned with deterministic noise chosen by a clever opponent the solution of this problem furnishes the kernel of the minimax linear estimate for gaussian white noise moreover this minimax linear estimator is asymptotically minimax among all estimates we sketch also applications to higher dimensions and to indirect measurement e g deconvolution problems

unit interpolation in h bounds of norm and degree of interpolants abstract this paper studies the problem of unit interpolation in h specifically bounds of the norm and degree of interpolants are obtained using the nevanlinna pick interpolation theory also simpler bounds are given using the poincare metric these results indicate that strong stabilization and simultaneous stabilization need a cautious approach if the system is ill conditioned in fact it is demonstrated that the degree of stable compensator is not bounded for the class of plants with fixed degree also an example shows that there is a class of plants for which the sensitivity can be made small only if unstable compensators are used

a tikhonov based projection iteration for nonlinear ill posed problems with sparsity constraints in this paper we consider nonlinear inverse problems where the solution is assumed to have a sparse expansion with respect to a preassigned basis or frame we develop a scheme which allows to minimize a tikhonov functional where the usual quadratic regularization term is replaced by a one homogeneous typically weighted l p penalty on the coefficients or isometrically transformed coefficients of such expansions for p 2 the regularized solution will have a sparser expansion with respect to the basis or frame under consideration the computation of the regularized solution amounts in our setting to a landweber fixed point iteration with a projection applied in each fixed point iteration step the performance of the resulting numerical scheme is demonstrated by solving the nonlinear inverse single photon emission computerized tomography spect problem