anti collusion fingerprinting for multimedia digital fingerprinting is a technique for identifying users who use multimedia content for unintended purposes such as redistribution these fingerprints are typically embedded into the content using watermarking techniques that are designed to be robust to a variety of attacks a cost effective attack against such digital fingerprints is collusion where several differently marked copies of the same content are combined to disrupt the underlying fingerprints we investigate the problem of designing fingerprints that can withstand collusion and allow for the identification of colluders we begin by introducing the collusion problem for additive embedding we then study the effect that averaging collusion has on orthogonal modulation we introduce a tree structured detection algorithm for identifying the fingerprints associated with k colluders that requires o klog n k correlations for a group of n users we next develop a fingerprinting scheme based on code modulation that does not require as many basis signals as orthogonal modulation we propose a new class of codes called anti collusion codes accs which have the property that the composition of any subset of k or fewer codevectors is unique using this property we can therefore identify groups of k or fewer colluders we present a construction of binary valued acc under the logical and operation that uses the theory of combinatorial designs and is suitable for both the on off keying and antipodal form of binary code modulation in order to accommodate n users our code construction requires only o spl radic n orthogonal signals for a given number of colluders we introduce three different detection strategies that can be used with our acc for identifying a suspect set of colluders we demonstrate the performance of our acc for fingerprinting multimedia and identifying colluders through experiments using gaussian signals and real images

upper bounds on separating codes the combinatorial concept of separating systems has numerous applications such as automata theory digital fingerprinting group testing and hashing in this correspondence we derive upper bounds on the size of codes with various separating properties

dct domain watermarking techniques for still images detector performance analysis and a new structure a spread spectrum like discrete cosine transform dct domain watermarking technique for copyright protection of still digital images is analyzed the dct is applied in blocks of 8 spl times 8 pixels as in the jpeg algorithm the watermark can encode information to track illegal misuses for flexibility purposes the original image is not necessary during the ownership verification process so it must be modeled by noise two tests are involved in the ownership verification stage watermark decoding in which the message carried by the watermark is extracted and watermark detection which decides whether a given image contains a watermark generated with a certain key we apply generalized gaussian distributions to statistically model the dct coefficients of the original image and show how the resulting detector structures lead to considerable improvements in performance with respect to the correlation receiver which has been widely considered in the literature and makes use of the gaussian noise assumption as a result of our work analytical expressions for performance measures such as the probability of errors in watermark decoding and the probabilities of false alarms and of detection in watermark detection are derived and contrasted with experimental results

asymptotic bounds on frameproof codes we study the asymptotic behavior of frameproof codes some lower bounds are derived from the theory of error correcting codes in particular the lower bound obtained directly by applying algebraic geometry codes is improved by employing the jacobian group structure of algebraic curves

effective watermarking scheme in the encrypted domain for buyer seller watermarking protocol in most watermarking schemes for copyright protection a seller usually embeds a watermark in multimedia content to identify a buyer when an unauthorized copy is found by the seller the traitor s identity can be traced by the embedded watermark however it incurs both repudiation issue and framing issue to solve these problems some buyer seller watermarking protocols have been proposed based on watermarking scheme in the encrypted domain in this paper an enhanced watermarking scheme is presented compared with solanki et al s scheme the enhanced scheme increases effective watermarking capacity avoids additional overhead and overcomes an inherent flaw that watermarking capacity depends on the probability distribution of input watermark sequence based on the security requirements of buyer seller watermarking protocols a new watermarking scheme in the encrypted domain with flexible watermarking capacity is proposed it improves the robustness of watermark sequence against image compressions and enables image tampering detection watermark extraction is blind which employs the same threshold criterion and secret keys as watermark embedding experimental results demonstrate that the enhanced watermarking scheme eliminates the drawbacks of solanki et al s scheme and that the proposed watermarking scheme in the encrypted domain outperforms kuribayashi and tanaka s scheme

stochastic modeling of the transform domain varepsilon rm lms algorithm this paper presents a statistical analysis of the transform domain least mean square tdlms algorithm resulting in a more accurate model than those discussed in the current open literature the motivation to analyze such an algorithm comes from the fact that the tdlms presents a higher convergence speed for correlated input signals as compared with other adaptive algorithms possessing a similar computational complexity such a fact makes it a highly competitive alternative to some applications approximate analytical models for the first and second moments of the filter weight vector are obtained the tdlms algorithm has an orthonormal transformation stage accomplishing a decomposition of the input signal into distinct frequency bands in which the interband samples are practically uncorrelated on the other hand the intraband samples are correlated the larger the number of bands the higher their correlation the model is then derived taking into account such a correlation requiring that a high order hyperelliptic integral be computed in addition to the proposed model an approximate procedure for computing high order hyperelliptic integrals is presented a regularization parameter is also considered in the model expressions permitting to assess its impact on the adaptive algorithm behavior an upper bound for the step size control parameter is also obtained through simulation results the accuracy of the proposed model is assessed

improved constructions of frameproof codes frameproof codes are used to preserve the security in the context of coalition when fingerprinting digital data let mc l q be the largest cardinality of a q ary c frameproof code of length l and rc l limq mc l q q l c it has been determined by blackburn that rc l 1 when l 1 mod c rc l 2 when c 2 and l is even and r3 5 5 3 in this paper we give a recursive construction for c frameproof codes of length l with respect to the alphabet size q as applications of this construction we establish the existence results for q ary c frameproof codes of length c 2 and size c 2 c q 1 2 1 for all odd q when c 2 and for all q 4 when c 3 furthermore we show that rc c 2 c 2 c meeting the upper bound given by blackburn for all integers c such that c 1 is a prime power

the existence of current vortex sheets in ideal compressible magnetohydrodynamics we prove the local in time existence of solutions with a surface of current vortex sheet tangential discontinuity of the equations of ideal compressible magnetohydrodynamics in three space dimensions provided that a stability condition is satisfied at each point of the initial discontinuity this paper is a natural completion of our previous analysis trakhinin in arch ration mech anal 177 331 366 2005 where a sufficient condition for the weak stability of planar current vortex sheets was found and a basic a priori estimate was proved for the linearized variable coefficients problem for nonplanar discontinuities the original nonlinear problem is a free boundary hyperbolic problem since the free boundary is characteristic the functional setting is provided by the anisotropic weighted sobolev spaces h m the fact that the kreiss lopatinski condition is satisfied only in a weak sense yields losses of derivatives in a priori estimates therefore we prove our existence theorem by a suitable nash moser type iteration scheme

new results on frame proof codes and traceability schemes we derive lower bounds on the maximum number of codewords in a class of frame proof codes and traceability schemes and give constructions for both with more codewords than the best known

applications of list decoding to tracing traitors we apply results from algebraic coding theory to solve problems in cryptography by using recent results on list decoding of error correcting codes to efficiently find traitors who collude to create pirates we produce schemes for which the traceability ta traitor tracing algorithm is very fast we compare the ta and identifiable parent property ipp traitor tracing algorithms and give evidence that when using an algebraic structure the ability to trace traitors with the ipp algorithm implies the ability to trace with the ta algorithm we also demonstrate that list decoding techniques can be used to find all possible pirate coalitions finally we raise some related open questions about linear codes and suggest uses for other decoding techniques in the presence of additional information about traitor behavior

maximum likelihood parameter estimation of superimposed signals by dynamic programming the problem of fitting a model composed of a number of superimposed signals to noisy data using the maximum likelihood criterion is considered it is shown using the cramer rao bound for the estimation accuracy that in many instances useful models for the composite signal can be restricted without loss of generality to component signals that directly interact only with one or two of their closest neighbors in parameter space it is shown that for such models the global extremum of the criterion can be found efficiently by dynamic programming the computation requirements are linear in the number of signals rather than exponential as in the case of exhaustive search the technique applies for arbitrary sampling of the signals the dynamic programming method is easily adapted to determining the number of signals as well as is demonstrated using the minimum description length principle computer simulation results are given for several examples

existence and stability of compressible current vortex sheets in three dimensional magnetohydrodynamics compressible vortex sheets are fundamental waves along with shocks and rarefaction waves in entropy solutions to multidimensional hyperbolic systems of conservation laws understanding the behavior of compressible vortex sheets is an important step towards our full understanding of fluid motions and the behavior of entropy solutions for the euler equations in two dimensional gas dynamics the classical linearized stability analysis on compressible vortex sheets predicts stability when the mach number m sqrt 2 and instability when m sqrt 2 for the euler equations in three dimensions every compressible vortex sheet is violently unstable and this instability is the analogue of the kelvin helmholtz instability for incompressible fluids the purpose of this paper is to understand whether compressible vortex sheets in three dimensions which are unstable in the regime of pure gas dynamics become stable under the magnetic effect in three dimensional magnetohydrodynamics mhd one of the main features is that the stability problem is equivalent to a free boundary problem whose free boundary is a characteristic surface which is more delicate than noncharacteristic free boundary problems another feature is that the linearized problem for current vortex sheets in mhd does not meet the uniform kreiss lopatinskii condition these features cause additional analytical difficulties and especially prevent a direct use of the standard picard iteration to the nonlinear problem in this paper we develop a nonlinear approach to deal with these difficulties in three dimensional mhd we first carefully formulate the linearized problem for the current vortex sheets to show rigorously that the magnetic effect makes the problem weakly stable and establish energy estimates especially high order energy estimates in terms of the nonhomogeneous terms and variable coefficients then we exploit these results to develop a suitable iteration scheme of the nash moser hormander type to deal with the loss of the order of derivative in the nonlinear level and establish its convergence which leads to the existence and stability of compressible current vortex sheets locally in time in three dimensional mhd

wavelet transform domain adaptive fir filtering this paper presents and studies two new wavelet transform domain least mean square lms algorithms the algorithms exploit the special sparse structure of the wavelet transform of wide classes of correlation matrices and their cholesky factors in order to compute a whitening transformation of the input data in the wavelet domain and minimize computational complexity the procedures differ in the exact estimates they use and in the way they identify the data dependent whitening transformation the first approach explicitly computes a sparse estimate of the wavelet domain correlation matrix of the input process it then computes the cholesky factor of that matrix and uses its inverse to whiten the input the complexity of this first approach is o n log sup 2 n in contrast the second approach computes a sparse estimate of the cholesky factor of the wavelet domain correlation matrix of the input process directly this second approach has a computational complexity of o n log n floating point operations however it requires a more complex bookkeeping procedure both algorithms have a convergence rate that is faster than that of time domain lms and discrete fourier transform dft or discrete cosine transform dct based lms procedures the paper compares the two procedures and analyzes their mean and mean square performance

tardos fingerprinting is better than we thought tardos has proposed a randomized fingerprinting code that is provably secure against collusion attacks we revisit his scheme and show that it has significantly better performance than suggested in the original paper first we introduce variables in place of tardos hard coded constants and we allow for an independent choice of the desired false positive fp and false negative fn error rates following through tardos proofs with these modifications we show that the code length can be reduced by more than a factor of two in typical content distribution applications where high fn rates can be tolerated second we study the statistical properties of the code under some reasonable assumptions the accusation sums can be regarded as gaussian distributed stochastic variables in this approximation the desired error rates are achieved by a code length twice shorter than in the first approach overall typical fp and fn error rates may be achieved with a code length approximately five times shorter than in the original construction

new lower bounds for secure codes and related hash families a hypergraph theoretical approach various kinds of secure codes and their related hash families are broadly studied combinatorial structures for protecting copyrighted materials the codewords in such a structure can be regarded as a subset of q n the set of all q ary vectors of given length n satisfying some constraints we use a hypergraph model to characterize the combinatorial structure by applying a result of duke et al on the lower bound of the independence number of hypergraphs we provide a new approach to evaluate the lower bounds for several kinds of secure codes and related hash families in particular the general method is illustrated via the examples of existence results on some perfect hash families frameproof codes and separable codes

convergence and performance analysis of the normalized lms algorithm with uncorrelated gaussian data it is demonstrated that the normalized least mean square nlms algorithm can be viewed as a modification of the widely used lms algorithm the nlms is shown to have an important advantage over the lms which is that its convergence is independent of environmental changes in addition the authors present a comprehensive study of the first and second order behavior in the nlms algorithm they show that the nlms algorithm exhibits significant improvement over the lms algorithm in convergence rate while its steady state performance is considerably worse

robust parent identifying codes and combinatorial arrays an n word y y1 yn over a finite alphabet of cardinality q is called a descendant of a set of t words x1 xt if every coordinate yi i 1 n is contained in the set x1i xti a code c x1 xm is said to have the t ipp property if for any n word y that is a descendant of at most t parents belonging to the code it is possible to identify at least one of them from earlier works it is known that t ipp codes of positive rate exist if and only if t q 1 we introduce a robust version of ipp codes which allows error free identification of parents in the presence of a certain number of mutations i e coordinates in y that can break away from the descent rule taking arbitrary values from the alphabet or becoming completely unreadable we show existence of robust t ipp codes for all t q 1 and some positive proportion of such coordinates we uncover a relation between the hash distance of codes and the ipp property and use it to find the exact proportion of mutant coordinates that permits identification of pirates with zero probability of error in the case of size 2 coalitions

linear stability of compressible vortex sheets in two dimensional elastodynamics abstract the linear stability of rectilinear compressible vortex sheets is studied for two dimensional isentropic elastic flows this problem has a free boundary and the boundary is characteristic a necessary and sufficient condition is obtained for the linear stability of the rectilinear vortex sheets more precisely it is shown that besides the stable supersonic zone the elasticity exerts an additional stable subsonic zone we also find that there is a class of states in the interior of subsonic zone where the stability of such states is weaker than the stability of other states in the sense that there is an extra loss of tangential derivatives with respect to the source terms this is a new feature that the euler flow does not possess one of the difficulties for the elastic flow is that the non differentiable points of the eigenvalues may coincide with the roots of the lopatinskii determinant as a result the kreiss symmetrization cannot be applied directly instead we perform an upper triangularization of the system to separate only the outgoing modes at all points in the frequency space so that an exact estimate of the outgoing modes can be obtained moreover all the outgoing modes are shown to be zero due to the l 2 regularity of solutions the estimates for the incoming modes can be derived directly from the lopatinskii determinant this new approach avoids the lengthy computation and estimates for the outgoing modes when kreiss symmetrization is applied this method can also be applied to the euler flow and mhd flow

performance of transform domain lms adaptive digital filters in this paper we analyze the performance particularly the convergence behavior of the transform domain least mean square lms adaptive digital filter adf using the discrete fourier transform and discrete orthogonal transforms such as discrete cosine and sine transforms we first obtain the optimum wiener solution and the minimum mean squared error mse in the transform domain it is shown that the two minimum mse s in the time and transform domains are identical independently of the transforms used we then study the convergence conditions and the steady state excess mse s of the transform domain lms trlms algorithms both for the cases of having a constant and a time varying convergence factors when a constant convergence factor is used the convergence behaviors of the lms and trlms adf s appear to be almost identical provided that each has an appropriate value of the convergence factor depending on the transform used also based on the concept of a self orthogonalizing algorithm in the transform domain it is shown that the convergence speed of the trlms adf can be improved significantly for the same excess mse as that of the lms adf in addition we compare the computational complexities of the lms and trlms adf s finally we investigate by computer simulation the effects of system parameter values and different transforms on the convergence behavior of the trlms adf

transform domain lms algorithm the concept of transform domain adaptive filtering is introduced in certain applications filtering in the transform domain results in great improvements in convergence rate over the conventional time domain adaptive filtering the relationship between several existing frequency domain adaptive filtering algorithms is established applications of the discrete fourier transform dft and the discrete cosine transform dct domain adaptive filtering algorithms in the areas of speech processing and adaptive line enhancers are discussed

separable codes multimedia fingerprinting is an effective technique to trace the sources of pirate copies of copyrighted multimedia information separable codes can be used to construct fingerprints resistant to the averaging collusion attack on multimedia contents in this paper we investigate separable codes from a combinatorial point of view we first derive several upper bounds on the sizes of separable codes and then turn our attention to the constructions of optimal separable codes with short length two infinite families of optimal separable codes of length 2 are constructed from projective planes and all optimal separable codes of length 3 are explicitly constructed by means of difference matrices these optimal separable codes with short length can be used to construct good separable codes with long length by a known composition construction

stability of multidimensional thermoelastic contact discontinuities we study the system of nonisentropic thermoelasticity describing the motion of thermoelastic nonconductors of heat in two and three spatial dimensions where the frame indifferent constitutive relation generalizes that for compressible neo hookean materials thermoelastic contact discontinuities are characteristic discontinuities for which the velocity is continuous across the discontinuity interface mathematically this renders a nonlinear multidimensional hyperbolic problem with a characteristic free boundary we identify a stability condition on the piecewise constant background states and establish the linear stability of thermoelastic contact discontinuities in the sense that the variable coefficient linearized problem satisfies a priori tame estimates in the usual sobolev spaces under small perturbations our tame estimates for the linearized problem do not break down when the strength of thermoelastic contact discontinuities tends to zero the missing normal derivatives are recovered from the estimates of several quantities relating to physical involutions in the estimate of tangential derivatives there is a significant new difficulty namely the presence of characteristic variables in the boundary conditions to overcome this difficulty we explore an intrinsic cancellation effect which reduces the boundary terms to an instant integral then we can absorb the instant integral into the instant tangential energy by means of the interpolation argument and an explicit estimate for the traces on the hyperplane

stochastic model for the mean weight evolution of the iaf pnlms algorithm this correspondence studies the adaptive weight evolution of the individual activation factor proportionate normalized least mean square iaf pnlms algorithm for such the modeling methodology used considers that the gain matrix is time varying and the input signal is not restricted to be white a model is obtained that predicts the algorithm mean weight behavior for both transient and steady state phases through simulation results the accuracy of the proposed model is verified in addition the approach developed here is general and can be applied to other pnlms type algorithms

linear stability of compressible vortex sheets in 2d elastodynamics variable coefficients the linear stability with variable coefficients of the vortex sheets for the two dimensional compressible elastic flows is studied as in our earlier work chen et al in adv math 311 18 60 2017b on the linear stability with constant coefficients the problem has a free boundary which is characteristic and also the kreiss lopatinskii condition is not uniformly satisfied in addition the roots of the lopatinskii determinant of the para linearized system may coincide with the poles of the system such a new collapsing phenomenon causes serious difficulties when applying the bicharacteristic extension method of coulombel siam j math anal 34 1 142 172 2002 ann inst h poincare anal non lineaire 21 4 401 443 2004 and coulombel and secchi indiana univ math j 53 4 941 1012 2004 motivated by our method introduced in the constant coefficient case adv math 311 18 60 2017b we perform an upper triangularization to the para linearized system to separate the outgoing mode into a closed form where the outgoing mode only appears at the leading order this procedure results in a gain of regularity for the outgoing mode which allows us to overcome the loss of regularity of the characteristic components at the poles and hence to close all the energy estimates we find that analogous to the constant coefficient case elasticity generates notable stabilization effects and there are additional stable subsonic regions compared with the isentropic euler flows moreover since our method does not rely on the construction of the characterisic curves it can also be applied to other fluid models such as the non isentropic euler equations and the mhd equations

the use of the modified escalator algorithm to improve the performance of transform domain lms adaptive filters this paper describes a new algorithm that improves the convergence performance of the transform domain least mean square trlms algorithm the algorithm exploits the sparse structure of the correlation matrix of the transformed input process to derive a data dependent gram schmidt orthogonalization type transform of the process we show its faster convergence compared with the time domain least mean square lms algorithm and the dct or the dwt based trlms algorithm the gram schmidt orthogonalization is realized using a modified adaptive escalator algorithm the modification significantly reduces the computational complexity of the adaptive escalator algorithm and determines the computational complexity of the proposed algorithm

transform domain adaptive filters an analytical approach transform domain adaptive filters refer to lms filters whose inputs are preprocessed with a unitary data independent transformation followed by a power normalization stage the transformation is typically chosen to be the discrete fourier transform dft although other transformations such as the cosine transform dct the hartley transform dht or the walsh hadamard transform have also been proposed in the literature the resulting algorithms are generally called dft lms dct lms etc this preprocessing improves the eigenvalue distribution of the input autocorrelation matrix of the lms filter and as a consequence ameliorates its convergence speed in this paper we start with a brief intuitive explanation of transform domain algorithms we then analyze the effects of the preprocessing performed in dft lms and dct lms for first order markov inputs in particular we show that for markov 1 inputs of correlation parameter spl rho spl isin 0 1 the eigenvalue spread after dft and power normalization tends to 1 spl rho l 1 spl rho as the size of the filter gets large whereas after dct and power normalization it reduces to 1 spl rho for comparison the eigenvalue spread before transformation is asymptotically equal to 1 spl rho sup 2 1 spl rho sup 2 the analytical method used in the paper provides additional insight into how the algorithms work and is expected to extend to other input signal classes and other transformations

maximum likelihood localization of multiple sources by alternating projection an algorithm referred to as apm for computing the maximum likelihood estimator of the locations of simple sources in passive sensor arrays is presented the algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot the algorithm is iterative the maximum of the likelihood function is computed by successive approximations the convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios the key to this global convergence is the initialization scheme

fixed point error analysis of the normalized ladder algorithm an attempt is made to analyze the fixed point error performance of the normalized ladder algorithm for autoregressive system identification assuming rounding arithmetic a preliminary simulation study of this algorithm has shown that the bias in the estimated reflection coefficients is much more predominant than the variance of the error in the estimate the study therefore is directed to find a model for predicting the bias in the estimated reflection coefficients the analysis shows that the roundoff errors associated with the square root operations in one of the algorithm equations are mainly responsible for the bias in the estimated reflection coefficients these errors arise because of the normalization procedure that makes the quantities under the square root operations very close to one two main results are presented in the paper 1 a simplified theoretical expression for predicting the average bias in the estimated reflection coefficients at any stage is derived 2 a recursive relation for the average error arising from the finite precision arithmetic in the squared residuals is derived this relation illustrates how the errors made in one stage affect the errors in the succeeding stages simulations are performed to check the theoretical models the experimental results agree very closely with the theoretical predictions

upper bounds for constant weight codes let a n d w denote the maximum possible number of codewords in an n d w constant weight binary code we improve upon the best known upper bounds on a n d w in numerous instances for n spl les 24 and d spl les 12 which is the parameter range of existing tables most improvements occur for d 8 10 where we reduce the upper bounds in more than half of the unresolved cases we also extend the existing tables up to n spl les 28 and d spl les 14 to obtain these results we develop new techniques and introduce new classes of codes we derive a number of general bounds on a n d w by means of mapping constant weight codes into euclidean space this approach produces among other results a bound on a n d w that is tighter than the johnson bound a similar improvement over the best known bounds for doubly constant weight codes studied by johnson and levenshtein is obtained in the same way furthermore we introduce the concept of doubly bounded weight codes which may be thought of as a generalization of the doubly constant weight codes subsequently a class of euclidean space codes called zonal codes is introduced and a bound on the size of such codes is established this is used to derive bounds for doubly bounded weight codes which are in turn used to derive bounds on a n d w we also develop a universal method to establish constraints that augment the delsarte inequalities for constant weight codes used in the linear programming bound in addition we present a detailed survey of known upper bounds for constant weight codes and sharpen these bounds in several cases all these bounds along with all known dependencies among them are then combined in a coherent framework that is amenable to analysis by computer this improves the bounds on a n d w even further for a large number of instances of n d and w

global solutions for incompressible viscoelastic fluids we prove the existence of both local and global smooth solutions to the cauchy problem in the whole space and the periodic problem in the n dimensional torus for the incompressible viscoelastic system of oldroyd b type in the case of near equilibrium initial data the results hold in both two and three dimensional spaces the results and methods presented in this paper are also valid for a wide range of elastic complex fluids such as magnetohydrodynamics liquid crystals and mixture problems

analysis of the normalized lms algorithm with gaussian inputs the lms adaptive filter algorithm requires a priori knowledge of the input power level to select the algorithm gain parameter for stability and convergence since the input power level is usually one of the statistical unknowns it is normally estimated from the data prior to beginning the adaptation process it is then assumed that the estimate is perfect in any subsequent analysis of the lms algorithm behavior in this paper the effects of the power level estimate are incorporated in a data dependent that appears explicitly within the algorithm the transient mean and second moment behavior of the modified lms nlms algorithm are evaluated taking into account the explicit statistical dependence of upon the input data the mean behavior of the algorithm is shown to converge to the wiener weight a constant coefficient matrix difference equation is derived for the weight fluctuations about the wiener weight the equation is solved for a white data covariance matrix and for the adaptive line enhancer with a single frequency input in steady state for small expressions for the misadjustment error are also presented it is shown for the white data covariance matrix case that the averaging of about ten data samples causes negligible degradation as compared to the lms algorithm in the ale application the steady state weight fluctuations are shown to be mode dependent being largest at the frequency of the input

probabilistic existence results for parent identifying schemes parent identifying schemes provide a way to identify causes from effects for some information systems such as digital fingerprinting and group testing in this paper we consider the combinatorial structures for parent identifying schemes first we establish an equivalent relationship between the parent identifying schemes and forbidden configurations based on this relationship we derive the probabilistic existence lower bounds for two related combinatorial structures that is t parent identifying set systems t ipps and t multimedia parent identifying codes t mippc which are used in broadcast encryption and multimedia fingerprinting respectively the probabilistic lower bound for the maximum size of a t ipps has the asymptotically optimal order of magnitude in many cases and that for t mippc provides the asymptotically optimal code rate when t 2 and the best known asymptotic code rate when t ge 3 furthermore we analyze the structure of 2 ipps and prove some bounds for certain cases

combinatorial properties of frameproof and traceability codes in order to protect copyrighted material codes may be embedded in the content or codes may be associated with the keys used to recover the content codes can offer protection by providing some form of traceability ta for pirated data several researchers have studied different notions of ta and related concepts in previous years strong versions of ta allow at least one member of a coalition that constructs a pirate decoder to be traced weaker versions of this concept ensure that no coalition can frame a disjoint user or group of users all these concepts can be formulated as codes having certain combinatorial properties we study the relationships between the various notions and we discuss equivalent formulations using structures such as perfect hash families we use methods from combinatorics and coding theory to provide bounds necessary conditions and constructions sufficient conditions for the objects of interest

convergence analysis of lms filters with uncorrelated gaussian data statistical analysis of the least mean squares lms adaptive algorithm with uncorrelated gaussian data is presented exact analytical expressions for the steady state mean square error mse and the performance degradation due to weight vector misadjustment are derived necessary and sufficient conditions for the convergence of the algorithm to the optimal wiener solution within a finite variance are derived it is found that the adaptive coefficient which controls the rate of convergence of the algorithm must be restricted to an interval significantly smaller than the domain commonly stated in the literature the outcome of this paper therefore places fundamental limitations on the mse performance and rate of convergence of the lms adaptive scheme

some improved bounds for secure frameproof codes and related separating hash families we present some improved bounds on necessary conditions for separating hash families of type w w and type w w 1 in particular these bounds apply to secure frame proof codes which are equivalent to separating hash families of type w w we also consider existence results for separating hash families of type w w2 that can be obtained from the probabilistic method the asymptotic behavior of these bounds is analyzed

nonadaptive group testing with random set of defectives in a group testing scheme a series of tests are designed to identify a small number t of defective items that are present among a large number n of items each test takes a group of items as input and produces a binary output indicating whether any defective item is present in the group in a non adaptive scheme the tests have to be designed in one shot in this setting designing a testing scheme is equivalent to the construction of a disjunct matrix an m times n binary matrix where the union of supports of any t columns does not contain the support of any other column in principle one wants to have such a matrix with a minimum possible number m of rows in this paper we consider the scenario where defective items are random and follow simple probability distributions in particular we consider the cases where 1 each item can be defective independently with probability frac t n and 2 each t set of items can be defective with uniform probability in both the cases our aim is to design a testing matrix that successfully identifies the set of defectives with high probability both of these models have been studied in the literature before and it is known that theta t log n tests are necessary as well as sufficient via random coding in both the cases our main focus is explicit deterministic construction of the test matrices amenable to above scenarios one of the most popular ways of constructing test matrices relies on constant weight error correcting codes and their minimum distance in particular it is known that codes result in test matrices with o t 2 log n rows that identify any t defectives we go beyond the minimum distance analysis and connect the average distance of a constant weight code to the parameters of the resulting test matrix indeed we show how distance a pairwise property of the columns of the matrix translates to a t 1 wise property of the columns with our relaxed requirements we show that using explicit constant weight codes e g based on algebraic geometry codes we may achieve a number of tests equal to o t log 2 n log t for both the first and second cases while only away by a factor of log n log t from the optimal number of tests this is the best set of parameters that one can obtain from a deterministic construction and our main contribution lies in relating the group testing properties to the average and minimum distances of constant weight codes

global well posedness for compressible viscoelastic fluids near equilibrium in this paper we prove local well posedness for compressible viscoelastic fluids of the oldroyd model under the assumption that the initial density is bounded away from zero and global well posedness near equilibrium the proof of global well posedness relies on some intrinsic properties of viscoelastic fluids and on a uniform estimate for a linearized hyperbolic parabolic system with convection terms

crc handbook of combinatorial designs balanced incomplete block designs and t designs2 v k l designs of small orderbibds with small block sizet designs t 3steiner systemssymmetric designsresolvable and near resolvable designslatin squares mols and orthogonal arrayslatin squaresmutually orthogonal latin squares mols incomplete molsorthogonal arrays of index more than oneorthogonal arrays of strength more than twopairwise balanced designspbds and gdds the basicspbds recursive constructionspbd closurepairwise balanced designs as linear spacespbds and gdds of higher indexpbds frames and resolvabilityother combinatorial designsassociation schemesbalanced part ternary designsbalanced tournament designsbhaskar rao designscomplete mappings and sequencings of finite groupsconfigurationscostas arrayscoveringscycle systemsdifference familiesdifference matricesdifference sets abeliandifference sets nonabeliandifference triangle setsdirected designsd optimal matricesembedding partial quasigroupsequidistant permutation arraysfactorial designsfrequency squaresgeneralized quadranglesgraph decompositions and designsgraphical designshadamard matrices and designshall triple systemshowell designsmaximal sets of molsmendelsohn designsthe oberwolfach problemordered designs and perpendicular arraysorthogonal designsorthogonal main effect planspackingspartial geometriespartially balanced incomplete block designsquasigroupsquasi symmetric designs r l designsroom squaresself orthogonal latin squares sols sols with a symmetric orthogonal mate solssom sequences with zero autocorrelationskolem sequencesspherical t designsstarterstrades and defining sets t m s netstuscan squarest wise balanced designsuniformly resolvable designsvector space designsweighing matrices and conference matriceswhist tournamentsyouden designs generalizedyouden squaresapplicationscodescomputer science selected applicationsapplications of designs to cryptographyderandomizationoptimality and efficiency comparing block designsgroup testingscheduling a tournamentwinning the lotteryrelated mathematics and computational methodsfinite groups and designsnumber theory and finite fieldsgraphs and multigraphsfactorizations of graphsstrongly regular graphstwo graphsclassical geometriesprojective planes nondesarguesiancomputational methods in design theoryindex

a least squares algorithm for multipath time delay estimation we consider the problem of estimating the arrival times of overlapping ocean acoustic signals from a noisy received waveform that consists of attenuated and delayed replicas of a known transient signal we assume that the transmitted signal and the number of paths in the multipath environment are known and develop an algorithm that gives least squares ls estimates of the amplitude and time delay of each path direct computation of the ls estimates would involve minimization of a highly oscillatory error function by allowing the amplitudes to be complex valued a much smoother error function that is easier to minimize using gradient based techniques is obtained using this property and the knowledge derived from the data of the spacing between adjacent minima in the actual ls error function an efficient algorithm is devised the algorithm is a function of a data dependent parameter and we give rules for choosing this parameter the algorithm is demonstrated on a broad band signal using simulated data the proposed method is shown to achieve the cramer rao lower bound over a wide range of snr s comparisons are made with alternating projection ap and estimate maximize em algorithms

on the fingerprinting capacity under the marking assumption we address the maximum attainable rate of fingerprinting codes under the marking assumption studying lower and upper bounds on the value of the rate for various sizes of the attacker coalition lower bounds are obtained by considering typical coalitions which represents a new idea in the area of fingerprinting and enables us to improve the previously known lower bounds for coalitions of size two and three for upper bounds the fingerprinting problem is modeled as a communications problem it is shown that the maximum code rate is bounded above by the capacity of a certain class of channels which are similar to the multiple access channel mac converse coding theorems proved in the paper provide new upper bounds on fingerprinting capacity it is proved that capacity for fingerprinting against coalitions of size two and three over the binary alphabet satisfies and respectively for coalitions of an arbitrary fixed size we derive an upper bound on fingerprinting capacity in the binary case finally for general alphabets we establish upper bounds on the fingerprinting capacity involving only single letter mutual information quantities

well posedness of characteristic symmetric hyperbolic systems we consider the initial boundary value problem for quasi linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity we show the well posedness in hadamard s sense i e existence uniqueness and continuous dependence of solutions on the data of regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary

comments on new results on frame proof codes and traceability schemes the paper new results on frame proof codes and traceability schemes claims to give results for two code classes frame proof codes and traceability schemes in the form of lower bounds on the maximum code size and explicit code constructions we will here briefly review the four claims of noting that the proofs and constructions presented in fail and that the claims also contradict previously published upper bounds

new bounds for frameproof codes frameproof codes are used to fingerprint digital data they can prevent copyrighted materials from unauthorized use in this paper we study upper and lower bounds for w frameproof codes of length n over an alphabet of size q the upper bound is based on a combinatorial approach and the lower bound is based on a probabilistic construction both bounds can improve one of the previous results when q is small compared with w say cq leq w for some constant c leq q furthermore we pay special attention to binary frameproof codes we show a binary w frameproof code of length n cannot have more than n codewords if n

global existence for the multi dimensional compressible viscoelastic flows abstract the global solutions in critical spaces to the multi dimensional compressible viscoelastic flows are considered the global existence of the cauchy problem with initial data close to an equilibrium state is established in besov spaces using uniform estimates for a hyperbolic parabolic linear system with convection terms we prove the global existence in the besov space which is invariant with respect to the scaling of the associated equations several important estimates are achieved including a smoothing effect on the velocity and the l 1 decay of the density and deformation gradient

well posedness of the linearized problem for mhd contact discontinuities abstract we study the free boundary problem for contact discontinuities in ideal compressible magnetohydrodynamics mhd they are characteristic discontinuities with no flow across the discontinuity for which the pressure the magnetic field and the velocity are continuous whereas the density and the entropy may have a jump under the rayleigh taylor sign condition p n 0 on the jump of the normal derivative of the pressure satisfied at each point of the unperturbed contact discontinuity we prove the well posedness in sobolev spaces of the linearized problem for 2d planar mhd flows

on competitive group testing in many fault detection problems the goal is to identify defective items from a set of items with a minimum number of tests each test is on a subset of items which tells whether the subset contains a defective item or not the concept of competitive algorithm has been developed to relate the properties of the group testing algorithms that assume that the number of defective items d is known to those without any a priori knowledge on d a new concept of strongly competitive algorithm is defined that relates different characteristics of these two classes of algorithms and present an interesting relationship between the two concepts competitive and strongly competitive a strongly competitive algorithm is also presented

modifications of competitive group testing many fault detection problems fall into the following model there is a set of n items some of which are defective the goal is to identify the defective items by using the minimum number of tests each test is on a subset of items and tells whether the subset contains a defective item or not let m alpha d n m alpha d n denote the maximum number of tests for an algorithm alpha to identify d defectives from a set of n items provided that d the number of defective items is known unknown before the testing let m d n min alpha m alpha d n an algorithm alpha is called a it competitive algorithm if there exist constants c and a such that for all n d 0 m alpha d n leq cm d n a this paper confirms a recent conjecture that there exists a bisecting algorithm a such that m a d n leq 2m d n 1 also an algorithm b such that m b d n leq 1 65m d n 10 is presented

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

mean weight behavior of the filtered x lms algorithm a new stochastic analysis is presented for the filtered x lms fxlms algorithm the analysis does not use independence theory an analytical model is derived for the mean behavior of the adaptive weights the model is valid for white or colored reference inputs and accurately predicts the mean weight behavior even for large step sizes the constrained wiener solution is determined as a function of the input statistics and the impulse responses of the adaptation loop filters effects of secondary path estimation error are studied monte carlo simulations demonstrate the accuracy of the theoretical model

well posedness of the free boundary problem in compressible elastodynamics abstract we study the free boundary problem for the flow of a compressible isentropic inviscid elastic fluid at the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary and the pressure vanishes outside the flow domain we prove the local in time existence of a unique smooth solution of the free boundary problem provided that among three columns of the deformation gradient there are two which are non collinear vectors at each point of the initial free boundary if this non collinearity condition fails the local in time existence is proved under the classical rayleigh taylor sign condition satisfied at the first moment by constructing an hadamard type ill posedness example for the frozen coefficients linearized problem we show that the simultaneous failure of the non collinearity condition and the rayleigh taylor sign condition leads to rayleigh taylor instability

relative entropy for hyperbolic parabolic systems and application to the constitutive theory of thermoviscoelasticity we extend the relative entropy identity to the class of hyperbolic parabolic systems whose hyperbolic part is symmetrizable the resulting identity in the general theory is useful for providing stability of viscous solutions and yields a convergence result in the zero viscosity limit to smooth solutions in an l p framework it also provides a weak strong uniqueness theorem for measure valued solutions of the hyperbolic problem in the second part the relative entropy identity is developed for the systems of gas dynamics for viscous and heat conducting gases and for the system of thermoviscoelasticity both including viscosity and heat conduction effects the dissipation mechanisms and the concentration measures play different roles when applying the method to the general class of hyperbolic parabolic systems and to the specific examples and their ramifications are highlighted

on the convergence behavior of the lms and the normalized lms algorithms it is shown that the normalized least mean square nlms algorithm is a potentially faster converging algorithm compared to the lms algorithm where the design of the adaptive filter is based on the usually quite limited knowledge of its input signal statistics a very simple model for the input signal vectors that greatly simplifies analysis of the convergence behavior of the lms and nlms algorithms is proposed using this model answers can be obtained to questions for which no answers are currently available using other perhaps more realistic models examples are given to illustrate that even quantitatively the answers obtained can be good approximations it is emphasized that the convergence of the nlms algorithm can be speeded up significantly by employing a time varying step size the optimal step size sequence can be specified a priori for the case of a white input signal with arbitrary distribution

combinatorial properties for traceability codes using error correcting codes in this correspondence the combinatorial properties of traceability codes constructed from error correcting codes are studied necessary and sufficient conditions for traceability codes constructed from maximum distance separable mds codes are provided the known sufficient conditions for a traceability code are proven to be also necessary for linear mds codes

optimal probabilistic fingerprint codes we construct binary codes for fingerprinting digital documents our codes for n users that are e secure against c pirates have length o c2log n e this improves the codes proposed by boneh and shaw l1998r whose length is approximately the square of this length the improvement carries over to works using the boneh shaw code as a primitive for example to the dynamic traitor tracing scheme of tassa l2005r by proving matching lower bounds we establish that the length of our codes is best within a constant factor for reasonable error probabilities this lower bound generalizes the bound found independently by peikert et al l2003r that applies to a limited class of codes our results also imply that randomized fingerprint codes over a binary alphabet are as powerful as over an arbitrary alphabet and the equal strength of two distinct models for fingerprinting