a finite axiomatization of conditional independence and inclusion dependencies we present a complete finite axiomatization of the unrestricted implication problem for inclusion and conditional independence atoms in the context of dependence logic for databases this result implies a finite axiomatization of the unrestricted implication problem for inclusion functional and embedded multivalued dependencies in the unirelational case we also indicate the generality of our approach by showing the analogous result for inclusion and embedded join dependencies

variational bayesian sparse kernel based blind image deconvolution with student s t priors in this paper we present a new bayesian model for the blind image deconvolution bid problem the main novelty of this model is the use of a sparse kernel based model for the point spread function psf that allows estimation of both psf shape and support in the herein proposed approach a robust model of the bid errors and an image prior that preserves edges of the reconstructed image are also used sparseness robustness and preservation of edges are achieved by using priors that are based on the student s t probability density function pdf this pdf in addition to having heavy tails is closely related to the gaussian and thus yields tractable inference algorithms the approximate variational inference methodology is used to solve the corresponding bayesian model numerical experiments are presented that compare this bid methodology to previous ones using both simulated and real data

the implication problem for functional and inclusion dependencies is undecidable the implication problem for a class of dependencies is the following given a finite set of dependencies determine if they logically imply another dependency we show that the implication problem is undecidable for the class of functional and inclusion dependencies this holds true even if the inclusion dependencies are restricted to be binary it may be noted that the implication problem is known to be decidable for functional and unary inclusion dependencies and also for inclusion dependencies without functional dependencies

multi observation blind deconvolution with an adaptive sparse prior this paper describes a robust algorithm for estimating a single latent sharp image given multiple blurry and or noisy observations the underlying multi image blind deconvolution problem is solved by linking all of the observations together via a bayesian inspired penalty function which couples the unknown latent image along with a separate blur kernel and noise variance associated with each observation all of which are estimated jointly from the data this coupled penalty function enjoys a number of desirable properties including a mechanism whereby the relative concavity or sparsity is adapted as a function of the intrinsic quality of each corrupted observation in this way higher quality observations may automatically contribute more to the final estimate than heavily degraded ones while troublesome local minima can largely be avoided the resulting algorithm which requires no essential tuning parameters can recover a sharp image from a set of observations containing potentially both blurry and noisy examples without knowing a priori the degradation type of each observation experimental results on both synthetic and real world test images clearly demonstrate the efficacy of the proposed method

on acyclic database decompositions given a universal relation scheme presented as a set of attributes and a set of dependencies it may be advantageous to decompose it into a collection of schemes each with its own sets of attributes and dependencies that has some desired properties a basic requirement for such a decomposition to be useful is that the corresponding decomposition map on universal relations be injective a central problem in database theory is to find the reconstruction map i e the inverse map of an injective decomposition map it is proved here that when the decomposition viewed as a hypergraph is acyclic and the given dependencies are full implicational dependencies then the reconstruction map is the natural join based on this it is shown that there is a polynomial time algorithm to test for injectiveness of decompositions

polynomial time implication problems for unary inclusion dependencies unary inclusion dependencies are database constraints expressing subset relationships the decidability of implication for these dependencies together with embedded implicational dependencies such as functional dependencies are investigated as shown by casanova et al the unrestricted and finite implication problems are different for the class of functional and unary inclusion dependencies also for this class and for any fixed k finite implication has no k ary complete axiomatization for both of these problems complete axiomatizations and polynomial time decision procedures are provided linear time for unrestricted implication and cubic time for finite implication it follows that functional and unary inclusion dependencies form a semantically natural class of first order sentences with equality which although not finitely controllable is efficiently solvable and docile generalizing from these results it is shown that the interaction between functionaland inclusion dependencies characterizes 1 unrestricted implication of unary inclusion and all embedded implicational dependencies 2 finite implication of unary inclusion and all full implicational dependencies 3 finite implication of unary inclusion and all embedded tuple generating dependencies as a direct consequence of this analysis most of the applications of dependency implication are extended within polynomial time to database design problems involving unary inclusion dependencies such examples are tests for lossless joins and tests for complementarity of projective views finally if one additionally requires that

the bayesian lasso the lasso estimate for linear regression parameters can be interpreted as a bayesian posterior mode estimate when the regression parameters have independent laplace i e double exponential priors gibbs sampling from this posterior is possible using an expanded hierarchy with conjugate normal priors for the regression parameters and independent exponential priors on their variances a connection with the inverse gaussian distribution provides tractable full conditional distributions the bayesian lasso provides interval estimates bayesian credible intervals that can guide variable selection moreover the structure of the hierarchical model provides both bayesian and likelihood methods for selecting the lasso parameter slight modifications lead to bayesian versions of other lasso related estimation methods including bridge regression and a robust variant

formal systems for tuple and equality generating dependencies we develop several formal systems for tuple and equality generating dependencies there are three kinds of systems based upon substitution tuple elimination and transitivity we specialize our systems to several subclasses total dependencies template dependencies and binary dependencies we also show that finding a formal system for embedded multivalued dependencies is equivalent to solving the implication problem for that class

richardson lucy deblurring for scenes under a projective motion path this paper addresses how to model and correct image blur that arises when a camera undergoes ego motion while observing a distant scene in particular we discuss how the blurred image can be modeled as an integration of the clear scene under a sequence of planar projective transformations i e homographies that describe the camera s path this projective motion path blur model is more effective at modeling the spatially varying motion blur exhibited by ego motion than conventional methods based on space invariant blur kernels to correct the blurred image we describe how to modify the richardson lucy rl algorithm to incorporate this new blur model in addition we show that our projective motion rl algorithm can incorporate state of the art regularization priors to improve the deblurred results the projective motion path blur model along with the modified rl algorithm is detailed together with experimental results demonstrating its overall effectiveness statistical analysis on the algorithm s convergence properties and robustness to noise is also provided

linearized pipe flow to reynolds number 10 7 a fourier chebyshev petro galerkin spectral method is described for high accuracy computation of linearized dynamics for flow in an infinite circular pipe our code is unusual in being based on solenoidal velocity variables and in being written in matlab systematic studies are presented of the dependence of eigenvalues transient growth factors and other quantities on the axial and azimuthal wave numbers and the reynolds number r for r ranging from 102 to the idealized physically unrealizable value 107 implications for transition to turbulence are considered in the light of recent theoretical results of s j chapman

revisiting bayesian blind deconvolution blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation because this problem is fundamentally ill posed strong priors on both the sharp image and blur kernel are required to regularize the solution space while this naturally leads to a standard map estimation framework performance is compromised by unknown trade off parameter settings optimization heuristics and convergence issues stemming from non convexity and or poor prior selections to mitigate some of these problems a number of authors have recently proposed substituting a variational bayesian vb strategy that marginalizes over the high dimensional image space leading to better estimates of the blur kernel however the underlying cost function now involves both integrals with no closed form solution and complex function valued arguments thus losing the transparency of map beyond standard bayesian inspired intuitions it thus remains unclear by exactly what mechanism these methods are able to operate rendering understanding improvements and extensions more difficult to elucidate these issues we demonstrate that the vb methodology can be recast as an unconventional map problem with a very particular penalty prior that conjoins the image blur kernel and noise level in a principled way this unique penalty has a number of useful characteristics pertaining to relative concavity local minima avoidance normalization and scale invariance that allow us to rigorously explain the success of vb including its existing implementational heuristics and approximations it also provides strict criteria for learning the noise level and choosing the optimal image prior that perhaps counter intuitively need not reflect the statistics of natural scenes in so doing we challenge the prevailing notion of why vb is successful for blind deconvolution while providing a transparent platform for introducing enhancements and extensions moreover the underlying insights carry over to a wide variety of other bilinear models common in the machine learning literature such as independent component analysis dictionary learning sparse coding and non negative matrix factorization

understanding blind deconvolution algorithms blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown recent algorithms have afforded dramatic progress yet many aspects of the problem remain challenging and hard to understand the goal of this paper is to analyze and evaluate recent blind deconvolution algorithms both theoretically and experimentally we explain the previously reported failure of the naive map approach by demonstrating that it mostly favors no blur explanations we show that using reasonable image priors a naive simulations map estimation of both latent image and blur kernel is guaranteed to fail even with infinitely large images sampled from the prior on the other hand we show that since the kernel size is often smaller than the image size a map estimation of the kernel alone is well constrained and is guaranteed to succeed to recover the true blur the plethora of recent deconvolution techniques makes an experimental evaluation on ground truth data important as a first step toward this experimental evaluation we have collected blur data with ground truth and compared recent algorithms under equal settings additionally our data demonstrate that the shift invariant blur assumption made by most algorithms is often violated

framelet based blind motion deblurring from a single image how to recover a clear image from a single motion blurred image has long been a challenging open problem in digital imaging in this paper we focus on how to recover a motion blurred image due to camera shake a regularization based approach is proposed to remove motion blurring from the image by regularizing the sparsity of both the original image and the motion blur kernel under tight wavelet frame systems furthermore an adapted version of the split bregman method is proposed to efficiently solve the resulting minimization problem the experiments on both synthesized images and real images show that our algorithm can effectively remove complex motion blurring from natural images without requiring any prior information of the motion blur kernel

on a general class of data dependencies in the relational model and its implication problems abstract the present paper deals with an important problem of the relational database theory with analysis of dependencies in the first part of the paper it is shown that a sufficiently large class of dependencies hypothesis conclusion type of dependencies can be expressed as first order sentences in the second part of the paper we deal with implication problems for egd ttgd tgd types of dependencies of relational databases wich are generalizations of dependencies introduced by beeri vardi 2 for these implication problems we give a generalized version of the proof procedure called chase we introduce exchangeability generating dependencies xgd and analyze the structure of relational database classes satisfying a system of xgds ex

hypernormal form theory foundations and algorithms abstract hypernormal forms unique normal forms simplest normal forms are investigated both from the standpoint of foundational theory and algorithms suitable for use with computer algebra the baider theory of the campbell hausdorff group is refined by a study of its subgroups to determine the smallest substages into which the hypernormalization process can be divided this leads to a linear algebra algorithm to compute the generators needed for each substage with the least amount of work a concrete interpretation of jan sanders spectral sequence for hypernormal forms is presented examples are given and a proof is given for a little known theorem of belitskii expressing the hypernormal form space in the inner product style as the kernel of a higher order differential operator

on rules with existential variables walking the decidability line we consider positive rules in which the conclusion may contain existentially quantified variables which makes reasoning tasks such as conjunctive query answering or entailment undecidable these rules called email protected rules have the same logical form as tuple generating dependencies in databases and as conceptual graph rules the aim of this paper is to provide a clearer picture of the frontier between decidability and non decidability of reasoning with these rules previous known decidable classes were based on forward chaining on the one hand we extend these classes on the other hand we introduce decidable classes based on backward chaining a side result is the definition of a backward mechanism that takes the complex structure of email protected rule conclusions into account we classify all known decidable classes by inclusion then we study the question of whether the union of two decidable classes remains decidable and show that the answer is negative except for one class and a still open case this highlights the interest of studying interactions between rules we give a constructive definition of dependencies between rules and widen the landscape of decidable classes with conditions on rule dependencies and a mixed forward backward chaining mechanism finally we integrate rules with equality and negative constraints to our framework

updates of relational views the problem of translating updates of database views is studied view updates are disambi guated by requiring that a specified view complement i e a second view that contains all the information omitted from the given view remain constant during the translation some of the computational problems related to the apphcafion of this general methodology in the context of relational databases are studied projective views of databases that consist of a single relation and satisfy funcuonal dependencies are emphasized after characterizing complementary views the authors show that finding a minimum complement of a given view is np complete the problem of translating the insertion of a tuple into a view is then studied in detail and the results are extended to the cases of deletion and replacement of a tuple finally the explicit functional dependencies a new kind of dependency that intuitively states that some part of the database information can be computed from the rest are defined and studied

regularized motion blur kernel estimation with adaptive sparse image prior learning this paper proposes a regularized negative log marginal likelihood minimization method for motion blur kernel estimation which is the core problem of blind motion deblurring in contrast to existing approaches the proposed method treats the blur kernel as a deterministic parameter in a directed graphical model wherein the sharp image is sparsely modeled by using a three layer hierarchical bayesian prior and the inverse noise variance is supposed distributed to the gamma hyper prior by borrowing the ideas of mean filed approximation and iteratively reweighted least squares the posterior distributions of the sharp image the inverse noise variance and the hyper parameters involved in the image prior as well as the deterministic model parameters including the motion blur kernel and those involved in the hyper priors are all estimated automatically for each blind motion deblurring problem it is worthy to note that the new approach relies on a strict minimization objective function and learns a more adaptive sparse image prior while with considerably less implementation heuristics compared with existing motion blur kernel estimation approaches experimental results on both benchmark and real world motion blurred images demonstrate that the proposed method has achieved state of the art or even better performance than the current blind motion deblurring approaches in terms of the image deblurring quality the results also show that the proposed approach is robust to the size of the motion blur kernel to a great extent a new motion blur kernel estimation method is proposed for blind image deblurring the new method is formulated in a unified and rigorous optimization perspective sparse image priors are learned adaptively for each blind deblurring problem the noise variance is automatically estimated unlike state of the art vb methods the method achieves better performance in terms of deblurring effectiveness

null inclusion dependencies in relational databases abstract functional dependencies fds and inclusion dependencies inds are the most fundamental integrity constraints that arise in practice in relational databases we introduce null inclusion dependencies ninds to cater for the situation when a database is incomplete and contains null values we show that the implication problem for ninds is the same as that for inds we then present a sound and complete axiom system for null functional dependencies nfds and ninds and prove that the implication problem for nfds and ninds is decidable and exptime complete by contrast when no nulls are allowed this implication problem is undecidable this undecidability result has motivated several researchers to restrict their attention to fds and noncircular inds in which case the implication problem was shown to be exptime complete our results imply that when considering nulls in relational database design we need not assume that ninds are noncircular

guaranteeing no interaction between functional dependencies and tree like inclusion dependencies functional dependencies fds and inclusion dependencies inds are the most fundamental integrity constraints that arise in practice in relational databases a given set of fds does not interact with a given set of inds if logical implication of any fd can be determined solely by the given set of fds and logical implication of any ind can be determined solely by the given set of inds the set of tree like inds constitutes a useful subclass of inds whose implication problem is polynomial time decidable we exhibit a necessary and sufficient condition for a set of fds and tree like inds not to interact this condition can be tested in polynomial time

on the decidability and axiomatization of query finiteness in deductive databases a database query is finite if its result consists of a finite sets tuples for queries formulated as sets of pure horn rules the problem of determining finiteness is in general undecidable in this paper we consider superfiniteness a stronger kind of finiteness which applies to horn queries whose function symbols are replaced by the abstraction of infinite relations with finiteness constraints abbr fc s we show that superfiniteness is not only decidable but also axiomatizable and the axiomatization yields an effective decision procedure although there are finite queries that are not superfinite we demonstrate that superfinite queries represent an interesting and nontrivial subclass within the class of all finite queries the we turn to the issue of inference of finiteness constraints an important practical problem that is instrumental in deciding if a query is evaluable by a bottom up algorithm although it is not known whether fc entailment is decidable for sets of function free horn rules we show that super entailment a stronger form of entailment is decidable we also show how a decision procedure for super entailment can be used to enhance tests for query finiteness

a proof procedure for data dependencies definition d une classe de dependances dependances generant l equalite et les triples et generalisation du processus de poursuite pour traiter ces dependances on montre quelques cas pour lesquels il y a une procedure de decision redondance de l egalite pour decider de l implication des dependances generant les triples et presque redondance pour decider de l implication des dependances generant l egalite

fields of experts we develop a framework for learning generic expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks the approach provides a practical method for learning high order markov random field mrf models with potential functions that extend over large pixel neighborhoods these clique potentials are modeled using the product of experts framework that uses non linear functions of many linear filter responses in contrast to previous mrf approaches all parameters including the linear filters themselves are learned from training data we demonstrate the capabilities of this field of experts model with two example applications image denoising and image inpainting which are implemented using a simple approximate inference scheme while the model is trained on a generic image database and is not tuned toward a specific application we obtain results that compete with specialized techniques

majorization minimization algorithms for wavelet based image restoration standard formulations of image signal deconvolution under wavelet based priors regularizers lead to very high dimensional optimization problems involving the following difficulties the non gaussian heavy tailed wavelet priors lead to objective functions which are nonquadratic usually nondifferentiable and sometimes even nonconvex the presence of the convolution operator destroys the separability which underlies the simplicity of wavelet based denoising this paper presents a unified view of several recently proposed algorithms for handling this class of optimization problems placing them in a common majorization minimization mm framework one of the classes of algorithms considered when using quadratic bounds on nondifferentiable log priors shares the infamous singularity issue si of iteratively re weighted least squares irls algorithms the possibility of having to handle infinite weights which may cause both numerical and convergence issues in this paper we prove several new results which strongly support the claim that the si does not compromise the usefulness of this class of algorithms exploiting the unified mm perspective we introduce a new algorithm resulting from using bounds for nonconvex regularizers the experiments confirm the superior performance of this method when compared to the one based on quadratic majorization finally an experimental comparison of the several algorithms reveals their relative merits for different standard types of scenarios

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

the implication problem for functional and inclusion dependencies there are two implication problems for functional dependencies and inclusion dependencies general implication and finite implication given a set of dependencies the problems are to determine whether holds in all databases satisfying or all finite databases satisfying contrary to the possibility suggested in casanova fagin and papadimitriou proceedings 1st acm conf on principles of database system pp 171 176 1982 there is a natural complete axiom system for general implication however a simple observation shows that both implication problems are recursively unsolvable it follows that there is no recursively enumerable set of axioms for finite implication

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

fold pitchfork bifurcation for maps with z 2 symmetry in pipe flow this study aims to provide a better understanding of recently identified transition scenarios exhibited by traveling wave solutions in pipe flow this particular family of solutions are invariant under certain reflectional symmetry transformations and they emerge from saddle node bifurcations within a two dimensional parameter space characterized by the length of the pipe and the reynolds number the present work precisely provides a detailed analysis of a codimension two saddle node bifurcation arising in discrete dynamical systems maps with z2 symmetry normal form standard techniques are applied in order to obtain the reduced map up to cubic order all possible bifurcation scenarios exhibited by this normal form are analyzed in detail finally a qualitative comparison of these scenarios with the ones observed in the aforementioned hydrodynamic problem is provided

a simple global characterization for normal forms of singular vector fields we derive a new global characterization of the normal forms of amplitude equations describing the dynamics of competing order parameters in degenerate bifurcation problems using an appropriate scalar product in the space of homogeneous vector polynomials we show that the resonant terms commute with the group generated by the adjoint of the original critical linear operator this leads to a very efficient constructive method to compute both the nonlinear coefficients and the unfolding of the normal form explicit examples and results obtained when there are additional symmetries are also presented