a right normed basis for free lie algebras and lyndon shirshov words abstract in this article we construct a basis of a free lie algebra that consists of right normed words i e the words that have the following form a i 1 a i 2 a i t 1 a i t where a i p are free generators of the lie algebra

properties of the error linear complexity spectrum this paper studies the error linear complexity spectrum of binary sequences with period 2n a precise categorization of those sequences having two distinct critical points in their spectra as well as an enumeration of these sequences is given an upper bound on the maximum number of distinct critical points that the spectrum of a sequence can have is proved and a construction which yields a lower bound on this number is given in the process simpler proofs of some known results on the linear complexity and k error linear complexity of sequences with period 2n are provided

new approaches to plactic monoid via grobner shirshov bases abstract we give two explicit quadratic presentations of the plactic monoid in row and column generators correspondingly then we give direct independent proofs that these presentations are grobner shirshov bases of the plactic algebra in deg lex orderings of generators from composition diamond lemma for associative algebras it follows that the set of young tableaux is the knuth normal form for plactic monoid 30 see also ch 5 in 32

a note on binary arrays with a certain window property corresp for some rs 2 mn there exist periodic r times s binary arrays such that all m times n binary matrices will appear in it as two dimensional versions of de bruijn sequences these kinds of arrays have possible applications in cryptography and the design of mask configurations for spectrometers

3d structure recovery and unwarping of surfaces applicable to planes the deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry lengths and areas are conserved and vanishing gaussian curvature we show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape we show that these partial differential equations can be reduced to the hopf equation that arises in non linear wave propagation and deformations of the paper can be interpreted in terms of the characteristics of this equation a new exact integration of these equations is developed that relates the 3 d structure of the applicable surface to an image the solution is tested by comparison with particular exact solutions we present results for both the forward and the inverse 3d structure recovery problem

sequence folding lattice tiling and multidimensional coding folding a sequence b into a multidimensional box is a well known method which is used as a multidimensional coding technique the operation of folding is generalized in a way that the sequence b can be folded into various shapes and not just a box the novel definition of folding is based on a lattice tiling for the given shape s and a direction in the d dimensional integer grid necessary and sufficient conditions that a lattice tiling for s combined with a direction define a folding of a sequence into s are derived the immediate and most impressive applications are some new lower bounds on the number of dots in two dimensional synchronization patterns asymptotically optimal such patterns were known only for rectangular shapes we show asymptotically optimal such patterns for a large family of hexagons this is also generalized for multidimensional synchronization patterns the best known patterns in terms of dots for circles and other polygons are also given the technique and its application for two dimensional synchronization patterns raises some interesting problems in discrete geometry we will also discuss these problems it is also shown how folding can be used to construct multidimensional error correcting codes finally by using the new definition of folding new types of multidimensional pseudo random arrays with various shapes are generated

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

dense mirroring surface recovery from 1d homographies and sparse correspondences in this work we recover the 3d shape of mirrors sunglasses and stainless steel implements a computer monitor displays several images of parallel stripes each image at a different angle reflections of these stripes in a mirroring surface are captured by the camera for every image point the direction of the displayed stripes and their reflections in the image are related by a 1d homography matrix computed with a robust version of the statistically accurate heteroscedastic approach by focusing on a sparse set of image points for which monitor image correspondence is computed the depth and the local shape may be estimated from these homographies the depth estimation relies on statistically correct minimization and provides accurate reliable results even for the image points where the depth estimation process is inherently unstable we are able to characterize this instability and develop an algorithm to detect and correct it after correcting the instability dense surface recovery of mirroring objects is performed using constrained interpolation which does not simply interpolate the surface depth values but also uses the locally computed 1d homographies to solve for the depth the correspondence and the local surface shape the method was implemented and the shape of several objects was densely recovered at submillimeter accuracy

surface reconstruction using deformable models with interior and boundary constraints the authors introduce a technique for 3d surface reconstruction using elastic deformable models the model used is an imaginary elastic grid which is made of membranous thin plate type material the elastic grid can bent twisted compressed and stretched into any desired 3d shape which is specified by the shape constraints derived automatically from images of a real 3d object shape reconstruction is guided by a set of imaginary springs that enforce the consistency in the position orientation and or curvature measurements of the elastic grid and the desired shape the dynamics of a surface reconstruction process is regulated by hamilton s principle or the principle of the least action furthermore a 1d deformable template that borders the elastic grid may be used this companion boundary template is attracted repelled by image forces to conform with the silhouette of the imaged object implementation results using simple analytic shapes and images of real objects are presented

computing the error linear complexity spectrum of a binary sequence of period 2 sup n binary sequences with high linear complexity are of interest in cryptography the linear complexity should remain high even when a small number of changes are made to the sequence the error linear complexity spectrum of a sequence reveals how the linear complexity of the sequence varies as an increasing number of the bits of the sequence are changed we present an algorithm which computes the error linear complexity for binary sequences of period spl lscr 2 sup n using o spl lscr log spl lscr sup 2 bit operations the algorithm generalizes both the games chan 1983 and stamp martin 1993 algorithms which compute the linear complexity and the k error linear complexity of a binary sequence of period spl lscr 2 sup n respectively we also discuss an application of an extension of our algorithm to decoding a class of linear subcodes of reed muller codes

pbw bases of coideal subalgebras and a freeness theorem let h be a character hopf algebra every right coideal subalgebra u that contains the coradical has a pbw basis which can be extended up to a pbw basis of h if additionally u is a bosonization of an invariant with respect to the left adjoint action subalgebra then h is a free left and right u module with a free pbw basis over u these results remain valid if h is a braided hopf algebra generated by a categorically ordered subset of primitive elements if the ground field is algebraically closed the results are still true provided that h is a pointed hopf algebra with commutative coradical and is generated over the coradical by a direct sum of finite dimensional yetter drinfeld submodules of skew primitive elements

mds array codes for correcting a single criss cross error we present a family of maximum distance separable mds array codes of size p 1 spl times p 1 p a prime number and minimum criss cross distance 3 i e the code is capable of correcting any row or column in error without a priori knowledge of what type of error occurred the complexity of the encoding and decoding algorithms is lower than that of known codes with the same error correcting power since our algorithms are based on exclusive or operations over lines of different slopes as opposed to algebraic operations over a finite field we also provide efficient encoding and decoding algorithms for errors and erasures

maximum rank array codes and their application to crisscross error correction a mu n n k array code c over a field f is a k dimensional linear space of n n matrices over f such that every nonzero matrix in c has rank or mu it is first shown that the dimension of such array codes must satisfy the singleton like bound k

simple and robust binary self location patterns a simple method to generate a 2 d binary grid pattern which allows for absolute and accurate self location in a finite planar region is proposed the pattern encodes position information in a local way so that reading a small number of its black or white pixels at any place provides sufficient data from which the location can be decoded both efficiently and robustly

a three level checkerboard pattern tcp projection method for curved surface measurement abstract this paper describes a new pattern projection method by which the 3d range and shape of a curved surface can be measured simply rapidly and precisely a three level checkerboard pattern tcp is projected onto a curved surface and the projection pattern on the surface is observed by a well defined camera the spatial feature codes of the tcp are used to match an observed pattern image to the slide mask pattern this method provides high spatial resolution and makes it possible to take highly accurate measurements of stable and moving object surfaces a new approach for rapid and precise calibration of the slide projector is also presented in our experiments using real objects about 0 8 m from the camera the surface measurement error was 0 5 1 mm in s d and 2 mm maximum which corresponds to a relative accuracy of about 0 2 this result coincides well with the theoretical prediction from image digitizing errors the semi automatic procedure for surface measurement together with camera and projector calibrations can be completed within 40 s which includes cpu time of about 5 s in vax11 780 1 mips

bounds for the size of radar arrays etablissement de bornes ameliorees superieure et inferieure pour la taille des tableaux radars formes de matrices rectangulaires a elements 0 et 1

on the existence of optimum cyclic burst correcting codes it is shown that for each integer b geq 1 infinitely many optimum cyclic b burst correcting codes exist i e codes whose length n redundancy r and burst correcting capability b satisfy n 2 r b 1 1 some optimum codes for b 3 4 and 5 are also studied in detail

constructions for perfect maps and pseudorandom arrays a construction of perfect maps i e periodic r v binary arrays in which each n m binary matrix appears exactly once is given a similar construction leads to arrays in which only the zero n m matrix does not appear and to a construction in which only a few n m binary matrices do not appear a generalization to the nonbinary case is given the constructions involve an interesting problem in shift register theory the solution is given for almost all the case of this problem

interleaving schemes for multidimensional cluster errors we present two dimensional and three dimensional interleaving techniques for correcting two and three dimensional bursts or clusters of errors where a cluster of errors is characterized by its area or volume correction of multidimensional error clusters is required in holographic storage an emerging application of considerable importance our main contribution is the construction of efficient two dimensional and three dimensional interleaving schemes the proposed schemes are based on t interleaved arrays of integers defined by the property that every connected component of area or volume t consists of distinct integers in the two dimensional case our constructions are optimal they have the lowest possible interleaving degree that is the resulting t interleaved arrays contain the smallest possible number of distinct integers hence minimizing the number of codewords required in an interleaving scheme in general we observe that the interleaving problem can be interpreted as a graph coloring problem and introduce the useful special class of lattice interleavers we employ a result of minkowski dating back to 1904 to establish both upper and lower bounds on the interleaving degree of lattice interleavers in three dimensions for the case t spl equiv 0 mod 6 the upper and lower bounds coincide and the minkowski lattice directly yields an optimal lattice interleaver for t spl ne 0 mod 6 we construct efficient lattice interleavers using approximations of the minkowski lattice

two dimensional synchronization patterns for minimum ambiguity a number of closely related combinatorial problems corresponding to specific assumptions about the type of time frequency sequence which may be appropriate in a particular application are formulated in terms of square or rectangular arrays of dots with appropriate constraints on the two dimensional correlation function the current state of knowledge concerning each of these problems is summarized it is hoped that more general constructions may be found leading to larger families of solutions as well as better computational algorithms for finding individual solutions which may lie outside of the general families

a survey of full length nonlinear shift register cycle algorithms shift registers have been used to generate sequences of 0 s and 1 s for over thirty years a wide variety of applications has been made of these sequences principally communications have made use of the sequences generated one particular class of shift register sequences for which applications exist is the full length nonlinear shift register sequences these sequences are periodic and of length 2 n and all 2 n different binary n tuples appear exactly one time in a periodic portion of the sequence in this paper we discuss various algorithms which have been suggested for generating these sequences

incremental model building of polyhedral objects using structured light abstract a vision method using active sensing to construct the complete geometric model of a polyhedral object is presented the model is constructed incrementally from multiple views each view produces a partial object model three different methods are described for integrating all the partial models into a final complete model theorems regarding the sufficient number of views required and how these views can be set up during the reconstruction process are also given from theoretical analysis and experimental results our method is shown to produce an accurate object geometric model not just an approximate model furthermore it does not rely on a precise object to image space transformation moreover the method is fast and robust since the basic geometric entity it derives is a face instead of a point

representation and shape matching of 3 d objects a three dimensional scene analysis system for the shape matching of real world 3 d objects is presented various issues related to representation and modeling of 3 d objects are addressed a new method for the approximation of 3 d objects by a set of planar faces is discussed the major advantage of this method is that it is applicable to a complete object and not restricted to single range view which was the limitation of the previous work in 3 d scene analysis the method is a sequential region growing algorithm it is not applied to range images but rather to a set of 3 d points the 3 d model of an object is obtained by combining the object points from a sequence of range data images corresponding to various views of the object applying the necessary transformations and then approximating the surface by polygons a stochastic labeling technique is used to do the shape matching of 3 d objects the technique matches the faces of an unknown view against the faces of the model it explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification it is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels the objective here is to match the individual views of the object taken from any vantage point details of the algorithm are presented and the results are shown on several unknown views of a complicated automobile casting

a single shot structured light means by encoding both color and geometrical features color encoded structured light is an important means for single shot 3d reconstruction in this article we present a pseudorandom array based structured light method the proposed pattern is composed with four colors and one geometric shape is inlaid to the color elements to extend the coding element from four to eight as a result a relatively small coding window with the size of 2 2 can be obtained grid point between each two adjacent pattern elements is defined as the pattern feature and an improved feature detector is proposed for the robust and accurate grid point localization the grid points are divided into two types and represented by a topological structure the decoding procedure is performed in two steps the shape decoding and color decoding finally the epipolar constraint and neighboring constraint are introduced to improve the decoding reliability accuracy and robustness of the proposed method are evaluated in the experiments some real objects including human face are reconstructed to demonstrate the 3d reconstruction quality of the proposed structured light method compared with conventional color sl pattern a novel color geometrical pattern was proposed the pattern consists of four colors and one embedded geometrical feature with a coding capacity of 65 63 a relative small unique window size of 2 2 was obtained the decoding procedure was implemented as color decoding and geometrical decoding a robust and accurate pattern feature detection algorithm was also presented

determining surface orientation by projecting a stripe pattern a method is presented for determining the surface orientations of an object by projecting a stripe pattern on to it assuming orthographical projection as a camera model and parallel light projection of the stripe pattern the method obtains a 2 1 2 d representation of objects by estimating surface normals from the slopes and intervals of the stripes in the image the 2 1 2 d image is further divided into planar or singly curved surfaces by examining the distribution of the surface normals in gradient space a simple application to finding a planar surface and determining its orientation and shape is shown the error in surface orientation is discussed

error analysis of 3d shape construction from structured lighting abstract in this paper we present a detailed model and analysis of several error sources and thier effects on measuring three dimensional 3d surface properties using the structured lighting technique the analysis is based on a general system configuration and identifies three types of error surces system modeling error image processing error and experimental error absolute and relative error bounds in obtaining 3d surface orientation and curvature measurements using structured lighting are derived in terms of the system parameters and likely error sources in addition to the quantization error other likely error sources in system modeling and experimental setup are also considered even though our analysis is on structured lighting the results are readily applicable to other triangulation based techniques such as stereopsis finally our analysis focuses on error in inferring surface orientation and principal surface curvature such analyses to our knowledge have never been attempted before

characterizing three dimensional surface structures from visual images a new technique for computing intrinsic surface properties is presented intrinsic surface properties are those properties of a surface that are not affected by the choice of the coordinate system the position of the viewer relative to the surface and the particular parametric representation used to describe the imaged surface since intrinsic properties are characteristics of a surface they are ideal for the purposes of representation and recognition the intrinsic properties of interest are the principal curvatures the gaussian curvatures and the lines of curvature it is proposed that a structured light sensing configuration where a grid pattern is projected to encode the imaged surfaces for analysis be adopted at each stripe junction the curvatures of the projected stripes on the imaged surface are computed and related to those of the normal sections that share the same tangential directional as the projected curves the principal curvatures and their directions at the stripe junction under consideration are then recovered using euler s theorem results obtained using both synthetic and real images are presented

algorithms for the generation of full length shift register sequences two algorithms are presented for the generation of full length shift register cycles also referred to as de bruijn sequences the first algorithm generates 2 k cdot g n k full cycles of length 2 n using 3n k cdot g n k bits of storage where k is a free parameter in the range 1 leq k leq 2 n 4 2 and g n k is of the order of n 2 log k the second algorithm generates about 2 n 2 4 full cycles of length 2 n using about n 2 2 bits of storage in both algorithms the time required to produce the next bit from the last n bits is close to n a possible application to the construction of stream ciphers is indicated

construction of de bruijn sequences of minimal complexity it is well known that the linear complexity of a de bruijn sequence s of length 2 n is bounded below by 2 n 1 n for n geq 3 it is shown that this lower bound is attainable for all n

linear complexity of de bruijn sequences old and new results the linear complexity of a de bruijn sequence is the degree of the shortest linear recursion which generates the sequence it is well known that the complexity of a binary de bruijn sequence of length 2 sup n is bounded below by 2 sup n 1 n and above by 2 sup n 1 for n spl ges 3 we briefly survey the known knowledge in this area some new results are also presented in particular it is shown that for each interval of length 2 sup log n 1 in the above range there exist binary de bruijn sequences of length 2 sup n with linear complexity in the interval

on optimum time hopping patterns time hopping patterns can be constructed from simple difference sets by studying such constructions it has been proven that whenever n 2 n 1 or n 1 is a prime power then time hopping patterns that have n terms can be constructed and are of length less than n sup 2 by computation it is shown that such patterns can have length less than n sup 2 n sup 1 44 for all n

error correction of multidimensional bursts we present several methods and constructions to generate binary codes for correction of a multidimensional cluster error whose shape can be a box error a lee sphere error or an error with an arbitrary shape our codes have very low redundancy close to optimal and a large range of parameters of arrays and clusters our main results are summarized as follows 1 a construction of two dimensional codes capable to correct a rectangular error with considerably more flexible parameters from previously known constructions this construction is easily generalized for d dimensions 2 a novel method based on d colorings of the d dimensional space for constructing d dimensional codes correcting a d dimensional cluster error of various shapes 3 a transformation of the d dimensional space into another d dimensional space in a way that a d dimensional lee sphere is transformed into a shape located in a d dimensional box of a relatively small size 4 applying the coloring method to correct more efficiently a two dimensional error whose shape is a lee sphere 5 a construction of d dimensional codes capable to correct a d dimensional cluster error of size b in which the number of erroneous positions is relatively small compared to b 6 we present a code which corrects a d dimensional arbitrary cluster error with relatively small redundancy

computation of surface orientation and structure of objects using grid coding in this correspondence algorithms are introduced to infer surface orientation and structure of visible object surfaces using grid coding we adopt the active lighting technique to spatially encode the scene for analysis the observed objects which can have surfaces of arbitrary shape are assumed to rest on a plane base plane in a scene which is encoded with light cast through a grid plane two orthogonal grid patterns are used where each pattern is obtained with a set of equally spaced stripes marked on a glass pane the scene is observed through a camera and the object surface orientation is determined using the projected patterns on the object surface if the surfaces under consideration obey certain smoothness constraints a dense orientation map can be obtained through proper interpolation the surface structure can then be recovered given this dense orientation map both planar and curved surfaces can be handled in a uniform manner the algorithms we propose yield reasonably accurate results and are relatively tolerant to noise especially when compared to shape from shading techniques in contrast to other grid coding techniques reported which match the grid junctions for depth reconstruction under the stereopsis principle our techniques use the direction of the projected stripes to infer local surface orientation and do not require any correspondence relationship between either the grid lines or the grid junctions to be specified the algorithm has the ability to register images and can therefore be embedded in a system which integrates knowledge from multiple views

integer sets with distinct sums and differences and carrier frequency assignments for nonlinear repeaters the problem of assigning n carrier frequencies so as to avoid certain types third and fifth order of intermodulation interference is discussed for the third order case close upper and lower bounds on the optimal solution are established and close to optimal solutions are given for n previously suboptimal solutions were known only for n leq 23 for the fifth order case it is shown that some existing results can be applied to this problem and suboptimal solutions obtained by this construction are given for n leq 17 no solutions were known previously

surface orientation from a projected grid two simple methods are given for obtaining the surface shape using a projected grid after the camera is calibrated to the 3 d workspace the only input date needed for the computation of surface normals are grid intersect points in a single 2 d image the first method performs nonlinear computations based on the distortion of the lengths of the grid edges and does not require a full calibration matrix the second method requires that a full parallel projection model of the imaging is available which enables it to compute 3 d normals using simple linear computations the linear method performed better overall in the experiments but both methods produced normals within 4 8 degrees of known 3 d directions these methods appear to be superior to methods based on shape from shading because the results are comparable yet the equipment setup is simpler and the processing is not very sensitive to object reflectance

green s functions sum rules and matrix elements for susy partners it is now well known that the solutions in the schrodinger equations for two potentials which are supersymmetric partners are linked by intertwining relations involving first order differential operators in this paper we explore the consequence of this linkage for the green s functions corresponding to susy partners and the relation between the sums over the inverses of the eigenvalues for the two potentials we also establish some relations between the matrix elements of certain operators evaluated between the eigenstates of two partner potentials we show that there can be circumstances where some matrix elements vanish as a consequence of the presence of supersymmetry

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

aperiodic and semi periodic perfect maps paterson see ibid vol 40 p 743 1993 has shown that the trivial necessary conditions are sufficient for the existence of a binary perfect map these periodic structures can be transformed very simply into corresponding aperiodic and semi periodic perfect maps however aperiodic and semi periodic perfect maps can exist for parameter sets for which the corresponding periodic perfect maps cannot in this paper it is shown by construction that binary aperiodic and semi periodic perfect maps exist for all possible parameter sets

a state of the art in structured light patterns for surface profilometry shape reconstruction using coded structured light is considered one of the most reliable techniques to recover object surfaces having a calibrated projector camera pair a light pattern is projected onto the scene and imaged by the camera correspondences between projected and recovered patterns are found and used to extract 3d surface information this paper presents an up to date review and a new classification of the existing techniques some of these techniques have been implemented and compared obtaining both qualitative and quantitative results the advantages and drawbacks of the different patterns and their potentials are discussed

universal bound on the performance of lattice codes we present a lower bound on the probability of symbol error for maximum likelihood decoding of lattices and lattice codes on a gaussian channel the bound is tight for error probabilities and signal to noise ratios of practical interest as opposed to most existing bounds that become tight asymptotically for high signal to noise ratios the bound is also universal it provides a limit on the highest possible coding gain that may be achieved at specific symbol error probabilities using any lattice or lattice code in n dimensions in particular it is shown that the effective coding gains of the densest known lattices are much lower than their nominal coding gains the asymptotic as n spl rarr spl infin behavior of the new bound is shown to coincide with the shannon 1948 limit for gaussian channels

a trace formula for dirac green s functions related by darboux transformations we construct green s functions and a trace formula for pairs of stationary dirac equations under sturm liouville boundary conditions where the equations are related to each other by a darboux transformation our findings generalize former results pozdeeva e 2008 j phys a math theor at press

filtrations and distortion in infinite dimensional algebras abstract a tame filtration of an algebra is defined by the growth of its terms which has to be majorated by an exponential function a particular case is the degree filtration used in the definition of the growth of finitely generated algebras the notion of tame filtration is useful in the study of possible distortion of degrees of elements when one algebra is embedded as a subalgebra in another a geometric analogue is the distortion of the riemannian metric of a lie subgroup when compared to the metric induced from the ambient lie group the distortion of a subalgebra in an algebra also reflects the degree of complexity of the membership problem for the elements of this algebra in this subalgebra one of our goals here is to investigate mostly in the case of associative or lie algebras if a tame filtration of an algebra can be induced from the degree filtration of a larger algebra

quickest sequence phase detection a phase detection sequence is a length n cyclic sequence such that the location of any length k contiguous subsequence can be determined from a noisy observation of that subsequence in this paper we derive bounds on the minimal possible k in the limit of n to infty and describe some sequence constructions we further consider multiple phase detection sequences where the location of any length k contiguous subsequence of each sequence can be determined simultaneously from a noisy mixture of those subsequences we study the optimal trade offs between the lengths of the sequences and describe some sequence constructions we compare these phase detection problems to their natural channel coding counterparts and show a strict separation between the fundamental limits in the multiple sequence case both adversarial and probabilistic noise models are addressed

a family of efficient burst correcting array codes a family of binary burst correcting array codes that are defined as follows is discussed consider an n sub 1 nn sub 2 array with n sub 1 4u nu 2 and n sub 2 6u 2 nu 5 u or 1 nu or 0 nu not 1 where each row and column has even parity the bits are read diagonally starting from the upper left corner the columns are viewed cyclically i e the array is a cylinder if one diagonal has been read out one proceeds with the second diagonal preceding it it is proven that the codes of this type can correct any burst of length up to n sub 1 the burst correcting efficiency of this family tends to 4 5 as u to infinity as a comparison the burst correcting efficiency of other families of array codes tends to 2 3 the same is true for fire codes a simple decoding algorithm for the codes is also presented

structured light using pseudorandom codes we solve the correspondence problem in active stereo vision using a novel pseudorandom coded structured light sl this coding scheme performs well in the presence of occlusion in settings where color coding is feasible 3d information can be obtained using a single image

golomb rectangles as folded rulers a correspondence between two dimensional golomb rectangles and one dimensional golomb rulers is given results are translated from rulers to rectangles the extension of these results to an arbitrary number of dimensions is given a new bound is developed on the number of ones in a golomb array of any dimension some new optimum golomb squares rectangles and higher dimensional arrays are given

a method for constructing decodable de bruijn sequences we present two related methods of construction for de bruijn 1946 sequences both based on interleaving smaller de bruijn sequences sequences obtained using these construction methods have the advantage that they can be decoded very efficiently i e the position within the sequence of any particular window can be found very simply sequences with simple decoding algorithms are of considerable practical importance in position location applications

a class of burst error correcting array codes corresp the usual k 2 1 times k 1 1 array code in which the last row and the last column contain redundant bits can correct any single error however if the bits are read diagonally instead of horizontally the code can correct bursts of errors it is shown that the k 2 1 times k 1 1 array code with diagonal readout can correct any burst of length up to k 1 if and only if k 2 geq 2 k 1 1

numerical shape from shading and occluding boundaries an iterative method for computing shape from shading using occluding boundary information is proposed some applications of this method are shown we employ the stereographic plane to express the orientations of surface patches rather than the more commonly used gradient space use of the stereographic plane makes it possible to incorporate occluding boundary information but forces us to employ a smoothness constraint different from the one previously proposed the new constraint follows directly from a particular definition of surface smoothness we solve the set of equations arising from the smoothness constraints and the image irradiance equation iteratively using occluding boundary information to supply boundary conditions good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution numerical experiments show that the method is effective and robust finally we analyze scanning electron microscope sem pictures using this method other applications are also proposed

a fast algorithm for determining the complexity of a binary sequence with period 2 n corresp the complexity of a periodic sequence s is defined to be the least number of stages in a linear feedback shift register that generates s

the visual interpretation of surface contours this article examines the computational problems underlying the 3 d interpretation of surface contours a surface contour is the image of a curve across a physical surface such as the edge of a shadow cast across a surface a gloss contour wrinkle seam or pigmentation marking surface contours by and large are not as restricted as occluding contours and therefore pose a more difficult interpretation problem nonetheless we are adept at perceiving a definite 3 d surface from even simple line drawings e g graphical depictions of continuous functions of two variables the solution of a specific surface shape comes by assuming that the physical curves are particularly restricted in their geometric relationship to the underlying surface these geometric restrictions are examined

limiting efficiencies of burst correcting array codes the author evaluates the limiting efficiencies e s of burst correcting array codes a n sub 1 n sub 2 s for all negative readouts s as n sub 2 tends to infinity and n sub 1 is properly chosen to maximize the efficiency specializing the result to the products of the first i primes donated by s sub i 1 or 4 5 and e 1 or 2 3 this result reveals the existence of burst correcting array codes with efficiencies arbitrarily close to 1 and with rates also arbitrarily close to 1

lyndon shirshov basis and anti commutative algebras abstract chen fox lyndon 1958 10 and shirshov 1958 29 introduced non associative lyndon shirshov words and proved that they form a linear basis of a free lie algebra independently in this paper we give another approach to definition of lyndon shirshov basis i e we find an anti commutative grobner shirshov basis s of a free lie algebra such that irr s is the set of all non associative lyndon shirshov words where irr s is the set of all monomials of n x a basis of the free anti commutative algebra on x not containing maximal monomials of polynomials from s following from shirshov s anti commutative grobner shirshov bases theory shirshov 1962 32 the set irr s is a linear basis of a free lie algebra

perfect maps given positive integers r s u and spl upsi an r s u spl upsi perfect map pm is defined to be a periodic r spl times s binary array in which every u spl times spl upsi binary array appears exactly once as a periodic subarray perfect maps are the natural extension of the de bruijn sequences to two dimensions in the paper the existence question for perfect maps is settled by giving constructions for perfect maps for all parameter sets subject to certain simple necessary conditions extensive use is made of previously known constructions by finding new conditions which guarantee their repeated application these conditions are expressed as bounds on the linear complexities of the periodic sequences formed from the rows and columns of perfect maps

detection of rotationally symmetric shape orientations by fold invariant shape specific points abstract two new types of shape specific points called fold invariant centroid fic and fold invariant radius weighted mean firwm are introduced for detecting the orientations of rotationally symmetric shapes a given rotationally symmetric shape is first transformed into a new fold invariant shape the centroid and the radius weighted mean of the new shape are then transformed back to obtain the proposed fic and firwm respectively fic and firwm points are proved to be invariant to translation rotation and scaling and so can be used for matching rotationally symmetric shapes using the proposed fold invariant shape specific points to detect the orientations of rotationally symmetric shapes is easier to implement than that of using the fold principal axes some illustrative examples and a method to avoid the case where the proposed fold invariant shape specific points are too close to the centroid are also given

two dimensional patterns with distinct differences constructions bounds and maximal anticodes a two dimensional 2 d grid with dots is called a configuration with distinct differences if any two lines which connect two dots are distinct either in their length or in their slope these configurations are known to have many applications such as radar sonar physical alignment and time position synchronization rather than restricting dots to lie in a square or rectangle as previously studied we restrict the maximum distance between dots of the configuration the motivation for this is a new application of such configurations to key distribution in wireless sensor networks we consider configurations in the hexagonal grid as well as in the traditional square grid with distances measured both in the euclidean metric and in the manhattan or hexagonal metrics we note that these configurations are confined inside maximal anticodes in the corresponding grid we classify maximal anticodes for each diameter in each grid we present upper bounds on the number of dots in a pattern with distinct differences contained in these maximal anticodes our bounds settle in the negative a question of golomb and taylor on the existence of honeycomb arrays of arbitrarily large size we present constructions and lower bounds on the number of dots in configurations with distinct differences contained in various 2 d shapes such as anticodes by considering periodic configurations with distinct differences in the square grid

symmetric pseudo random matrices we consider the problem of generating symmetric pseudo random sign 1 matrices based on the similarity of their spectra to wigner s semicircular law using binary m sequences golomb sequences of lengths n 2 m 1 we give a simple explicit construction of circulant n times n sign matrices and show that their spectra converge to the semicircular law when n grows the kolmogorov complexity of the proposed matrices equals to that of golomb sequences and is at most 2 mathrm log 2 n bits

susy transformation of the green function and a trace formula an integral relation is established between the green functions corresponding to two hamiltonians which are supersymmetric susy partners and in general may possess both discrete and continuous spectra it is shown that when the continuous spectrum is present the trace of the difference of the green functions for susy partners is a finite quantity which may or may not be equal to zero despite the divergence of the traces of each green function our findings are illustrated by using the free particle example considered both on the whole real line and on a half line

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

golomb rectangles there are a number of communications problems involving two dimensional arrays with constrained correlation functions golomb s two classes of radar arrays and sonar arrays are examined improved bounds optimal cases and computational procedures are reported

pseudo wigner matrices we consider the problem of generating pseudo random matrices based on the similarity of their spectra to wigner s semicircular law we introduce the notion of an r independent pseudo wigner matrix ensemble and prove the closeness of the spectra of its matrices to the semicircular density in the kolmogorov distance we give an explicit construction of a family of n times n pseudo wigner ensembles using dual bch codes and show that the kolmogorov complexity of the obtained matrices is of the order of mathrm log n bits for a fixed designed kolmogorov distance precision we compare our construction with the quasi random graphs introduced by chung et al and demonstrate that the pseudo wigner matrices pass stronger randomness tests than the adjacency matrices of these graphs lifted by the mapping 0 rightarrow 1 and 1 rightarrow 1 do finally we provide numerical simulations verifying our theoretical results

an algebraic approach to shape from image problems abstract this paper presents a new method for recovering three dimensional shapes of polyhedral objects from their single view images the problem of recovery is formulated in a constrained optimization problem in which the constraints reflect the assumption that the scene is composed of polyhedral objects and the objective function to be minimized is a weighted sum of quadric errors of surface information such as shading and texture for practical purpose it is decomposed into the two more tractable problems a linear programming problem and an unconstrained optimization problem in the present method the global constraints placed by the polyhedron assumption are represented in terms of linear algebra whereas similar constraints have usually been represented in terms of a gradient space moreover superstrictness of the constraints can be circumvented by a new concept position free incidence structure for this reason the present method has several advantages it can recover the polyhedral shape even if image data are incorrect due to vertex position errors it can deal with perspective projection as well as orthographic projection the number of variables in the optimization problem is very small three or a little greater than three and any kinds of surface information can be incorporated in a unifying manner