isometric dilations for infinite sequences of noncommuting operators this paper develops a dilation theory for t n l an infinite sequence of noncommuting operators on a hilbert space when the matrix t1 t2 is a contraction a wold decomposition for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for tn i are obtained some theorems on the geometric structure of the space of the minimal isometric dilation and some consequences are given this results are used to extend the sz nagy foia lifting theorem to this noncommutative setting this paper is a continuation of 5 and develops a dilation theory for an infinite sequence tn n of noncommuting operators on a hilbert space when en 1 tn tn i i is the identity on s many of the results and techniques in dilation theory for one operator 8 and also for two operators 3 4 are extended to this setting first we extend wold decomposition 8 4 to the case of an infinite sequence vn i of isometries with orthogonal final spaces in 2 we obtain a minimal isometric dilation for tn 1 by extending the schaffer construction in 6 4 using these results we give some theorems on the geometric structure of the space of the minimal isometric dilation finally we give some sufficient conditions on a sequence t7 n to be simultaneously quasi similar to a sequence rn n i of isometries on a hilbert space x with en rnrn n ix in 3 we use the above mentioned theorems to obtain the sz nagy foia5 lifting theorem 7 8 1 4 in our setting in a subsequent paper we will use the results of this paper for studying the characteristic function associated to a sequence tn lo 1 with ez 1 t t i throughout this paper a stands for the set 1 2 k k e n or the set n 1 2 received by the editors september 1 1987 1980 mathematics subject classification 1985 revision primary 47a20 secondary 47a45

quantum error correction on infinite dimensional hilbert spaces we present a generalization of quantum error correction to infinite dimensional hilbert spaces we find that under relatively mild conditions much of the structure known from systems in finite dimensional hilbert spaces carries straightforwardly over to infinite dimensions we also find that at least in principle there exist qualitatively new classes of quantum error correcting codes that have no finite dimensional counterparts we begin with a shift of focus from states to algebras of observables standard subspace codes and subsystem codes are seen as the special case of algebras of observables given by finite dimensional von neumann factors of type i the new classes of codes that arise in infinite dimensions are shown to be characterized by von neumann algebras of types ii and iii for which we give in principle physical examples

invariant character recognition with zernike and orthogonal fourier mellin moments abstract in this paper we consider the use of orthogonal moments for invariant classification of alphanumeric characters of different size in addition to the zernike and pseudo zernike moments zms and pzms which have been previously proposed for invariant character recognition a new method of combining orthogonal fourier mellin moments ofmms with centroid bounding circle scaling is introduced which is shown to be useful in characterizing images with large variability through extensive experimentation using zms and ofmms as features different scaling methodologies and classifiers it is shown that ofmms give the best overall performance in terms of both image reconstruction and classification accuracy

image quality assessment by discrete orthogonal moments this paper proposes a novel full reference quality assessment qa metric that automatically assesses the quality of an image in the discrete orthogonal moments domain this metric is constructed by representing the spatial information of an image using low order moments the computation up to fourth order moments is performed on each individual 8x8 non overlapping block for both the test and reference images then the computed moments of both the test and reference images are combined in order to determine the moment correlation index of each block in each order the number of moment correlation indices used in this study is nine next the mean of each moment correlation index is computed and thereafter the single quality interpretation of the test image with respect to its reference is determined by taking the mean value of the computed means of all the moment correlation indices the proposed objective metrics based on two discrete orthogonal moments tchebichef and krawtchouk moments are developed and their performances are evaluated by comparing them with subjective ratings on several publicly available databases the proposed discrete orthogonal moments based metric performs competitively well with the state of the art models in terms of quality prediction while outperforms them in terms of computational speed

noncommutative poisson boundaries of unital quantum operations in this paper poisson boundaries of unital quantum operations also called markov operators are investigated in the case of unital quantum channels compact operators belonging to poisson boundaries are characterized using the characterization of amenable groups by the injectivity of their von neumann algebras we will answer negatively some conjectures appearing in the work of arias et al fixed points of quantum operations j math phys 43 5872 2002 about injectivity of the commuting algebra of the kraus operators of unital quantum operations and their injective envelopes

fixed points of commutative luders operations this paper verifies a conjecture posed in a pair of papers on the fixed point sets for a class of quantum operations specifically it is proved that if a quantum operation has mutually commuting operation elements that are effects forming a resolution of the identity then the fixed point set of the quantum operation is exactly the commutant of the operation elements

approximate p values for local sequence alignments assume that two sequences from a finite alphabet are optimally aligned according to a scoring system that rewards similarities according to a general scoring scheme and penalizes gaps insertions and deletions under the assumption that the letters in each sequence are independent and identically distributed and the two sequences are also independent approximate p values are obtained for the optimal local alignment when either i there are at most a fixed number of gaps or ii the gap initiation cost is sufficiently large in the latter case the approximation can be written in the same form as the well known case of ungapped alignments

classification of invariant image representations using a neural network a neural network nn based approach for classification of images represented by translation scale and rotation invariant features is presented the utilized network is a multilayer perceptron mlp classifier with one hidden layer back propagation learning is used for its training two types of features are used moment invariants derived from geometrical moments of the image and features based on zernlike moments which are the mapping of the image onto a set of complex orthogonal polynomials the performance of the mlp is compared to the bayes nearest neighbor and minimum mean distance statistical classifiers through extensive experimentation with noiseless as well as noisy binary images of all english characters 26 classes the following conclusions are reached 1 the mlp outperforms the other three classifiers especially when noise is present 2 the nearest neighbor classifier performs about the same as the nn for the noiseless case 3 the nn can do well even with a very small number of training samples 4 the nn has a good degree of fault tolerance and 5 the zernlike moment based features possess strong class separability power and are more powerful than moment invariants

an extreme value theory for long head runs for an infinite sequence of independent coin tosses withp heads p 0 1 the longest run of consecutive heads in the firstn tosses is a natural object of study we show that the probabilistic behavior of the length of the longest pure head run is closely approximated by that of the greatest integer function of the maximum ofn 1 p i i d exponential random variables these results are extended to the case of the longest head run interrupted byk tails the mean length of this run is shown to be log n klog n k 1 log 1 p log k k 1 2 r1 n o 1 where log log1 p 0 577 is the euler mascheroni constant ln 1 p andr1 n is small the variance is 2 6 2 1 12 r2 n o 1 wherer2 n is again small upper and lower class results for these run lengths are also obtained and extensions discussed

fixed points of quantum operations quantum operations frequently occur in quantum measurement theory quantum probability quantum computation and quantum information theory if an operator a is invariant under a quantum operation we call a a fixed point physically the fixed points are the operators that are not disturbed by the action of our main purpose is to answer the following question if a is a fixed point is a compatible with the operation elements of we shall show in general that the answer is no and we shall give some sufficient conditions under which the answer is yes our results will follow from some general theorems concerning completely positive maps and injectivity of operator systems and von neumann algebras

recognitive aspects of moment invariants moment invariants are evaluated as a feature space for pattern recognition in terms of discrimination power and noise tolerance the notion of complex moments is introduced as a simple and straightforward way to derive moment invariants through this relation properties of complex moments are used to characterize moment invariants aspects of information loss suppression and redundancy encountered in moment invariants are investigated and significant results are derived the behavior of moment invariants in the presence of additive noise is also described

fast computation of geometric moments using a symmetric kernel this paper presents a novel set of geometric moments with symmetric kernel sgm obtained using an appropriate transformation of image coordinates by using this image transformation the computational complexity of geometric moments gm is reduced significantly through the embedded symmetry and separability properties in addition it minimizes the numerical instability problem that occurs in high order gm computation the novelty of the method proposed in this paper lies in the transformation of gm kernel from interval 0 to interval 1 1 the transformed gm monomials are symmetry at the origin of principal cartesian coordinate axes and hence possess symmetrical property the computational complexity of sgm is reduced significantly from order o n 4 using the original form of computation to order o n 3 for the proposed symmetry separable approach experimental results show that the percentage of reduction in computation time of the proposed sgm over the original gm is very significant at about 75 0 and 50 0 for square and non square images respectively furthermore the invariant properties of translation scaling and rotation in hu s moment invariants are maintained the advantages of applying sgm over gm in zernike moments computation in terms of efficient representation and computation have been shown through experimental results

image analysis by tchebichef moments this paper introduces a new set of orthogonal moment functions based on the discrete tchebichef polynomials the tchebichef moments can be effectively used as pattern features in the analysis of two dimensional images the implementation of the moments proposed in this paper does not involve any numerical approximation since the basis set is orthogonal in the discrete domain of the image coordinate space this property makes tchebichef moments superior to the conventional orthogonal moments such as legendre moments and zernike moments in terms of preserving the analytical properties needed to ensure information redundancy in a moment set the paper also details the various computational aspects of tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction

image analysis by krawtchouk moments a new set of orthogonal moments based on the discrete classical krawtchouk polynomials is introduced the krawtchouk polynomials are scaled to ensure numerical stability thus creating a set of weighted krawtchouk polynomials the set of proposed krawtchouk moments is then derived from the weighted krawtchouk polynomials the orthogonality of the proposed moments ensures minimal information redundancy no numerical approximation is involved in deriving the moments since the weighted krawtchouk polynomials are discrete these properties make the krawtchouk moments well suited as pattern features in the analysis of two dimensional images it is shown that the krawtchouk moments can be employed to extract local features of an image unlike other orthogonal moments which generally capture the global features the computational aspects of the moments using the recursive and symmetry properties are discussed the theoretical framework is validated by an experiment on image reconstruction using krawtchouk moments and the results are compared to that of zernike pseudo zernike legendre and tchebyscheff moments krawtchouk moment invariants are constructed using a linear combination of geometric moment invariants an object recognition experiment shows krawtchouk moment invariants perform significantly better than hu s moment invariants in both noise free and noisy conditions

fixed points of dual quantum operations abstract let a be a normal completely positive map on b h with kraus operators a i i 1 denote m the subset of normal completely positive maps by m a i 1 a i a i i i 1 a i a i i and a is normal in this note the relations between the fixed points of a and a are investigated we obtain that b k h a b b b k h a b b where k h is the set of all compact operators on h and a is the dual of a m in addition we show that the map a a is a bijection on m

a new fast algorithm for moment computation abstract a new fast algorithm for the computation of discrete image moments is presented the procedure is based on a discrete analogon of green s theorem and is much faster than the method introduced earlier by zakaria et al the new scheme produces exact results unlike methods based on the continuous green s theorem

the range of generalized quantum operations abstract a completely positive map is called a generalized quantum operation if tr a tr a for all positive operators a in this note we mainly characterize the sets of b is a generalized quantum operation b is a generalized quantum operation and b and are generalized quantum operations where is a dual of and b is a self adjoint operator in particular the third set is relevant to uhlmann s theorem in quantum information

longest runs in a sequence of m dependent random variables let x i i 1 be a sequence of random 0 s and 1 s we define the lengthr n of the longest head run as follows r n max left k leqq n mathop max limits 0 leqq i leqq n k 1 x i 1 cdots x i k 1 1 right the limit law for the distribution ofr n asn was found in 1943 the rate of convergence in that limit theorem remained unknown until recently even for bernoulli independent trials supposing that x i i 1 is a stationary sequence ofm dependent r v s we given an estimate on the rate of convergence in that limit theorem this estimate provides the unimprovable raten 1 lnn for the independent case a result of lim inf type is obtained too

geometric invariance in image watermarking surviving geometric attacks in image watermarking is considered to be of great importance in this paper the watermark is used in an authentication context two solutions are being proposed for such a problem both geometric and invariant moments are used in the proposed techniques an invariant watermark is designed and tested against attacks performed by stirmark using the invariant moments on the other hand an image normalization technique is also proposed which creates a normalized environment for watermark embedding and detection the proposed algorithms have the advantage of being robust computationally efficient and no overhead needs to be transmitted to the decoder side the proposed techniques have proven to be highly robust to all geometric manipulations filtering compression and slight cropping which are performed as part of stirmark attacks as well as noise addition both gaussian and salt pepper

the erdos renyi strong law for pattern matching with a given proportion of mismatches 1 informal introduction the erdos bnyi law erdijs and r6nyi 1970 l for coin tossing is a strong law for the behavior of the length of long success rich runs for the length r of the longest run of pure heads in n tosses the result is that with probability l lin rjlog n 1 where p flheads 0 a more general result is quoted as formula 1 in section 2 for rz the longest head rich run in which the fraction of heads is at least a p note that r ri in many practical situations such as manufacturing or roulette observations are taken sequentially and each can be classified as success or failure for these cases it is possible to use the erdijs wnyi law to test the hypothesis that the success probability is p from another point of view the erdijs bnyi law can be used to recognize patterns of unusually long runs of succe88e8 or failures our interest is in the recognition of unusually long patterns or words common to two random sequences the patterns are unknown prior to an examination of the sequences the motivation for this work is the comparison of dna sequences which can be modeled as sequences of i i d or markov distributed letters evolution operates to conserve although imperfectly patterns important to biological function it is a task of biology to discover these patterns and their function in earlier work we generalized the erdiie bnyi law for pure head runs a 1 to exact matching patterns between two sequences in this paper we extend those results to include matchings of quality a between p and 1 the examples below illustrate the natural analogs of rz studied in this paper two words form a quality a matching if they have the same length and the

on the efficient computation of 2 d image moments using the discrete radon transform abstract in this paper a fast algorithm for the computation of two dimensional image moments is proposed in our approach a new discrete radon transform drt is used for the major part of the algorithm the new drt preserves an important property of the continuous radon transform that the regular or geometric moments can be directly obtained from the projection data with this property the computation of two dimensional 2 d image moments can be decomposed to become a number of one dimensional 1 d ones hence it reduces greatly the computational complexity the new drt algorithm can be applied with a recursive approach such that the number of multiplication required is further reduced however the number of addition will then be increased it suits to the situation where the effort for realizing multiplication is much greater than addition comparisons of the present approaches with some known methods show that the proposed algorithms significantly reduce the complexity and computation time

a note on the run length function for intermittent maps abstract we study the run length function for intermittent maps in particular we show that the longest consecutive zero digits resp one digits having a time window of polynomial resp logarithmic length our proof is relatively elementary in the sense that it only relies on the classical borel cantelli lemma and the polynomial decay of intermittent maps our results are compensational to the erd s renyi law obtained by denker and nicol in 8

fixed points of normal completely positive maps on b h abstract given a sequence of bounded operators a j on a hilbert space h with j 1 a j a j 1 j 1 a j a j we study the map defined on b h by x j 1 a j x a j and its restriction to the hilbert schmidt class c 2 h in the case when the sum j 1 a j a j is norm convergent we show in particular that the operator 1 is not invertible if and only if the c algebra a generated by a j j 1 has an amenable trace this is used to show that may have fixed points in b h which are not in the commutant a of a even in the case when the weak closure of a is injective however if a is abelian then all fixed points of are in a even if the operators a j are not positive

on the shortest distance between orbits and the longest common substring problem abstract in this paper we study the behaviour of the shortest distance between orbits and show that under some rapidly mixing conditions the decay of the shortest distance depends on the correlation dimension for irrational rotations we prove a different behaviour depending on the irrational exponent of the angle of the rotation for random processes this problem corresponds to the longest common substring problem we extend the result of 6 on sequence matching to mixing processes with exponential decay

fast algorithm for the computation of moment invariants abstract moment invariants have been used as feature descriptors in a variety of object recognition applications when assuming a continuous image function moments calculated using a double integral formulation are invariant to variations in translation rotation and size of the object however due to the recursive nature of the calculations and the limited speed of microprocessors the moments were not computable in real time in this paper we present fast invariant moment computations using the delta method as a means of scene representation this method computes moments of contiguous images by using the contribution of each line rather than individual pixel

critical phenomena for sequence matching with scoring consider two independent sequences x 1 x n and y 1 y n suppose that x 1 x n are i i d x and y 1 y n are i i d y where x and y are distributions on finite alphabets x and y respectively a score f x x y r is assigned to each pair x i y j and the maximal nonaligned segment score is m n max 0 i j n 0 l 1 f x i l y j l our result is that m n log n x y a s with determined by a tractable variational formula moreover the pair empirical measure of x i l y j l during the segment where m n is achieved converges to a probability measure which is accessible by the same formula these results generalize to x i y j taking values in any polish space to intrasequence scores under shifts to long quality segments and to more than two sequences

characterizations of fixed points of quantum operations let a be a general quantum operation an operator b is said to be a fixed point of a if a b b in this note we shall show conditions under which b a fixed point a implies that b is compatible with the operation element of a in particular we offer an extension of the generalized luders theorem

normality and fixed points associated to commutative row contractions abstract let a a k k 1 n n is a positive integer or be a commutative row contraction on a complex hilbert space h and a the normal completely positive map associated with a we give some characterizations for a to be a normal sequence in the case that a is unital we show a is normal if either a is contained in a finite von neumann algebra or the set k h of all compact operators or k 1 n a k a k i moreover the fixed point set b h a of a is considered when a j i is convergent to a projection in strong operator topology

3 d moment forms their construction and application to object identification and positioning the 3 d moment method is applied to object identification and positioning a general theory of deriving 3 d moments invariants is proposed the notion of complex moments is introduced complex moments are defined as linear combinations of moments with complex coefficients and are collected into multiplets such that each multiplet transforms irreducibly under 3 d rotations the application of the 3 d moment method to motion estimation is also discussed using group theoretic techniques various invariant scalars are extracted from compounds of complex moments via clebsch gordon expansion twelve moment invariants consisting of the second order and third order moments are explicitly derived based on a perturbation formula it is shown that the second order moment invariants can be used to predict whether the estimation using noisy data is reliable or not the new derivation of vector forms also facilities the calculation of motion estimation in a tensor approach vectors consisting of the third order moments can be derived in a similar manner

maximal length of common words among random letter sequences on considere des suites de lettres aleatoires basees sur un alphabet fini genere par des processus stationnaires uniformement melangeants on etudie les proprietes des distributions asymptotiques de la longueur du plus grand mot commun

fast computation of exact zernike moments using cascaded digital filters zernike moments have been extensively used and have received much research attention in a number of fields object recognition image reconstruction image segmentation edge detection and biomedical imaging however computation of these moments is time consuming thus we present a fast computation technique to calculate exact zernike moments by using cascaded digital filters the novelty of the method proposed in this paper lies in the computation of exact geometric moments directly from digital filter outputs without the need to first compute geometric moments the mathematical relationship between digital filter outputs and exact geometric moments is derived and then they are used in the formulation of exact zernike moments a comparison of the speed of performance of the proposed algorithm with other state of the art alternatives shows that the proposed algorithm betters current computation time and uses less memory

universal collective rotation channels and quantum error correction we present and investigate a new class of quantum channels what we call universal collective rotation channels that includes the class of collective rotation channels as a special case the fixed point set and noise commutant coincide for a channel in this class computing the precise structure of this c algebra is a core problem in a particular noiseless subsystem method of quantum error correction we prove that there is an abundance of noiseless subsystems for every channel in this class and that the young tableaux combinatorial machine may be used to explicitly compute these subsystems

efficient computation of local geometric moments local moments have attracted attention as local features in applications such as edge detection and texture segmentation the main reason for this is that they are inherently integral based features so that their use reduces the effect of uncorrelated noise the computation of local moments when viewed as a neighborhood operation can be interpreted as a convolution of the image with a set of masks nevertheless moments computed inside overlapping windows are not independent and convolution does not take this fact into account by introducing a matrix formulation and the concept of accumulation moments this paper presents an algorithm which is computationally much more efficient than convolving and yet as simple

fixed points for luders operations and commutators let b h be the algebra of all bounded linear operators on a complex hilbert space h and let tj j 1 b h be a sequence of operators such that j 1tj tj 1h in the weak operator topology let us define t b h b h by setting t y j 1t jytj for y b h we show that if x b h is an operator such that all the commutators xtj tjx as well as x itself are fixed points for t then xtj tjx 0 for all j 1 in the case when tj j 1 consists of commuting normal operators this shows that every fixed point for t commutes with all tj for j 1

optimal data compression algorithm abstract a practical source coding scheme based on approximate string matching is proposed it is an approximate fixed length string matching data compression combined with a block coder based on the empirical distribution a lemma on approximate string matching which is an extension of the kac lemma is proved it is shown based on the lemma that the deterministic algorithm converts the stationary and ergodic source u into an output process v and under the assumption that v is a stationary process after the scheme has run for an infinite time the optimal compression ratio r d is achieved this reduces the problem of the universal lossy coder to the proof of stationarity of the output process v in the proposed algorithm the main advantages of the proposed method are the asymptotic sequential behavior of the encoder and the simplicity of the decoder

an extreme value theory for sequence matching on considere des suites finies x 1 x 2 x m et y 1 y 2 y m ou les lettres x i et y i sont choisies i i d sur un alphabet denombrable avec p p x 1 y 1 0 1 on etudie la distribution de la plus longue sequence contigue de couples entre les x et les y avec au plus k mauvais couplages

approximations for distributions of scan statistics abstract certain statistical applications deal with the extremal distributions of the number of points in a moving interval or window of fixed length this article gives an approximation that is highly accurate for several of these distributions applications include the maximum cluster of points on a line or circle multiple coverage by subintervals or subarcs of fixed size the length of the longest success run in bernoulli trials and the generalized birthday problem

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

a new computation of geometric moments abstract geometric moments gms have been successfully used in pattern recognition and object orientation determination however their computation is too expensive which limits the application of gms in this paper a new method is proposed to calculate geometric moments firstly the pixel based calculation of gms is converted into the line segment based calculation then a new approach is proposed to calculate the line segment integrals after line segment integrals are calculated hatamian s filter method is introduced to calculate gms which further simplifies the moment calculation finally this method is compared with the known results which show that our method can calculate any complicated object moments and also efficiently reduces both addition and multiplication complexity

toeplitz operators associated to commuting row contractions let h be a complex hilbert space and let tn n 1 be a sequence of commuting bounded operators on h such that n 1tntn ih let f t denote the space of all operators x in b h for which n 1tnxtn x and suppose that f t 0 we will show that there exists a triple k un n 1 where k is a hilbert space k h is a bounded operator and un n 1 b k is a sequence of commuting normal operators with n 1unun ik such that tn un for n 1 and for which the mapping y y is a complete isometry from the commutant of un n 1 onto the space f t moreover we show that the inverse of this mapping can be extended to a homomorphism c ih f t un n 1 from the unital c algebra generated by f t onto the commutant of un n 1 we also show that there exists a homomorphism c ih tn n 1 c ik un n 1 such that tn un for n 1 in the particular case when tn n 1 has only a finite number of non zero components it turns out that un n 1 is unitarily equivalent to the spherical unitary part of the standard commuting dilation of tn n 1

a suboptimal lossy data compression based on approximate pattern matching a practical suboptimal variable source coding algorithm for lossy data compression is presented this scheme is based on approximate string matching and it naturally extends the lossless lempel ziv 1977 data compression scheme among others we consider the typical length of an approximately repeated pattern within the first n positions of a stationary mixing sequence where d percent of mismatches is allowed we prove that there exists a constant r sub 0 d such that the length of such an approximately repeated pattern converges in probability to 1 r sub 0 d log n pr but it almost surely oscillates between 1 r sub spl infin d log n and 2 r sub 1 d log n where r sub spl infin d r sub 0 d r sub 1 d 2 are some constants these constants are natural generalizations of renyi entropies to the lossy environment more importantly we show that the compression ratio of a lossy data compression scheme based on such an approximate pattern matching is asymptotically equal to r sub 0 d we also establish the asymptotic behavior of the so called approximate waiting time n sub l which is defined as the time until a pattern of length c repeats approximately for the first time we prove that log n sub l l spl rarr r sub 0 d pr as l spl rarr spl infin in general r sub 0 d r d where r d is the rate distortion function thus for stationary mixing sequences we settle in the negative the problem investigated by steinberg and gutman by showing that a lossy extension of the wyner ziv 1989 scheme cannot be optimal

a comparison of scores of two protein structures with foldings let x i i 1 y i i 1 u u i i 1 and v v i i 1 be four i i d sequences of random variables suppose u and v are uniformly distributed on 0 1 3 for each realization of u j 1 j n x i p 1 p n is constructed as a certain permutation of x p 1 p n for any 1 i n also y j p 1 p n 1 j n are constructed the same way based on y j and v j for a score function f we show that formula math has an asymptotic extreme distribution with the same parameters as in the one dimensional case this model is constructed for a comparison of scores of protein structures with foldings

fast and exact computation of cartesian geometric moments using discrete green s theorem abstract green s theorem evaluates a double integral over a planar object by a simple integration along the boundary of the object it can be used in fast computation of cartesian geometric moments of two dimensional binary objects since the object shape is totally determined by the boundary li and shen pattern recognition 24 807 813 1991 used an approximation of green s theorem to deal with discrete objects this method is fast but not accurate in this paper we present a discrete version of green s theorem which evaluates a double sum over a two dimensional discrete object by a simple summation along the discrete boundary of the object by using the discrete green s theorem we propose a new algorithm for fast computation of the geometric moments the new algorithm is faster than the previous methods and gives exactly the same results as if a double sum were used the importance of the exact computation is discussed by examining the accuracy of hu s moment invariants and some other moment based shape features which are frequently used in various shape description and pattern recognition tasks a fast method for computing moments of regions in gray level images using the discrete green s theorem is also presented we show that the moments of this type are useful in structural texture analysis

a novel approach to the fast computation of zernike moments this paper presents a novel approach to the fast computation of zernike moments from a digital image most existing fast methods for computing zernike moments have focused on the reduction of the computational complexity of the zernike 1 d radial polynomials by introducing their recurrence relations instead in our proposed method we focus on the reduction of the complexity of the computation of the 2 d zernike basis functions as zernike basis functions have specific symmetry or anti symmetry about the x axis the y axis the origin and the straight line y x we can generate the zernike basis functions by only computing one of their octants as a result the proposed method makes the computation time eight times faster than existing methods the proposed method is applicable to the computation of an individual zernike moment as well as a set of zernike moments in addition when computing a series of zernike moments the proposed method can be used with one of the existing fast methods for computing zernike radial polynomials this paper also presents an accurate form of zernike moments for a discrete image function in the experiments results show the accuracy of the form for computing discrete zernike moments and confirm that the proposed method for the fast computation of zernike moments is much more efficient than existing fast methods in most cases

an efficient method for the computation of legendre moments legendre moments are continuous moments hence when applied to discrete space images numerical approximation is involved and error occurs this paper proposes a method to compute the exact values of the moments by mathematically integrating the legendre polynomials over the corresponding intervals of the image pixels experimental results show that the values obtained match those calculated theoretically and the image reconstructed from these moments have lower error than that of the conventional methods for the same order although the same set of exact legendre moments can be obtained indirectly from the set of geometric moments the computation time taken is much longer than the proposed method

critical phenomena in sequence matching we give a generalization of the result of erdos and renyi on the length r n of the longest head run in the first n tosses of a coin consider two independent sequences x 1 x 2 cdots x m and y 1y 2 cdots y n suppose that x 1 x 2 cdots are i i d mu and y 1 y 2 cdots are i i d nu where mu and nu are possibly different distributions on a common finite alphabet s let p equiv p x 1 y 1 in 0 1 the length of the longest matching consecutive subsequence is m m n equiv max k x i r y j r for r 1 to k for some 0 leq i leq m k 0 leq j leq n k for m and n rightarrow infty with log m log mn rightarrow lambda in 0 1 our result is that there is a constant k equiv k mu nu lambda in 0 1 rbrack such that p lim m m n log 1 p mn k 1 the proof uses large deviation methods the constant k is determined from a variational formula involving the kullback liebler distance or relative entropy a simple necessary and sufficient condition for k 1 is given for the case m n lambda 1 2 and mu nu k 1 the set of mu nu lambda for which k 1 has nonempty interior the boundary of this set is the location of a phase transition the results generalize to more than two sequences and to markov chains a strong law of large numbers is given for the proportion of letters within the longest matching word the limiting proportion exhibits critical behavior similar to that of k

efficient computation of radial moment functions using symmetrical property the applications of radial moment functions such as orthogonal zernike and pseudo zernike moments in real world have been limited by the computational complexity of their radial polynomials the common approaches used in reducing the computational complexity include the application of recurrence relations between successive radial polynomials and coefficients in this paper a novel approach is proposed to further reduce the computation complexity of zernike and pseudo zernike polynomials based on the symmetrical property of radial polynomials by using this symmetrical property the real valued radial polynomials computation is reduced to about one eighth of the full set polynomials while the computation of the exponential angle values is reduced by half this technique can be integrated with existing fast computation methods to further improve the computation speed besides significant reduction in computation complexity it also provides vast reduction in memory storage