golay complementary sequence sets with large zero correlation zones zero correlation zone zcz sequence sets and golay complementary sets gcss have different correlation properties and hence have different engineering applications a number of constructions of zcz sequence sets and gcss have been proposed respectively in the literature in addition some zcz sequence sets can be constructed from mutually orthogonal gcss in this paper the relationship between gcss and zcz sets is discovered further we propose a new type of sequence sets which are zcz sequence sets and also gcss they are called the golay zcz sequence sets in this paper therefore they have low peak to average power ratios when employed in ofdm systems due to the good autocorrelation properties of gcss besides the golay zcz sets possess zero autocorrelations and cross correlations within their zcz and hence have the potential application to synchronization furthermore a construction of golay zcz sequence family with flexible set sizes various sequence lengths and large zcz widths is proposed in this paper

generalized chirp like polyphase sequences with optimum correlation properties a new general class of polyphase sequences with ideal periodic autocorrelation function is presented the new class of sequences is based on the application of zadoff chu polyphase sequences of length n sm sup 2 where s and m are any positive integers it is shown that the generalized chirp like sequences of odd length have the optimum crosscorrelation function under certain conditions finally recently proposed generalized p4 codes are derived as a special case of the generalized chirp like sequence

sticky hidden markov modeling of comparative genomic hybridization we develop a sticky hidden markov model hmm with a dirichlet distribution dd prior motivated by the problem of analyzing comparative genomic hybridization cgh data as formulated the sticky dd hmm prior is employed to infer the number of states in an hmm while also imposing state persistence the form of the proposed hierarchical model allows efficient variational bayesian vb inference of interest for large scale cgh problems we compare alternative formulations of the sticky hmm while also examining the relative efficacy of vb and markov chain monte carlo mcmc inference to validate the formulation example results are presented for an illustrative synthesized data set and our main application cgh for which we consider data for breast cancer for the latter we also make comparisons and partially validate the cgh analysis through factor analysis of associated but distinct gene expression data

a new class of sequences with zero or low correlation zone based on interleaving technique by interleaving one length n perfect sequence or ideal sequence according to elaborate phases a new method of construction of zero correlation zone zcz and low correlation zone lcz sequence sets is presented the resultant sequence sets are optimal or almost optimal with respect to tang fan and matsufuji bound furthermore the new method provides flexible choice for the zcz and lcz lengths

propagation of probabilities means and variances in mixed graphical association models abstract a scheme is presented for modeling and local computation of exact probabilities means and variances for mixed qualitative and quantitative variables the models assume that the conditional distribution of the quantitative variables given the qualitative is multivariate gaussian the computational architecture is set up by forming a tree of belief universes and the calculations are then performed by local message passing between universes the asymmetry between the quantitative and qualitative variables sets some additional limitations for the specification and propagation structure approximate methods when these are not appropriately fulfilled are sketched it has earlier been shown how to exploit the local structure in the specification of a discrete probability model for fast and efficient computation thereby paving the way for exploiting probability based models as parts of realistic systems for planning and decision support the purpose of this article is to extend this computational s

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

complete mutually orthogonal golay complementary sets from reed muller codes recently golay complementary sets were shown to exist in the subsets of second order cosets of a q ary generalization of the first order reed muller rm code we show that mutually orthogonal golay complementary sets can also be directly constructed from second order cosets of a q ary generalization of the first order rm code this identification can be used to construct zero correlation zone zcz sequences directly and it also enables the construction of zcz sequences with special subsets

new constructions of zero correlation zone sequences in this paper we propose three classes of systematic approaches for constructing zero correlation zone zcz sequence families in most cases these approaches are capable of generating sequence families that achieve the upper bounds on the family size and the zcz width for a given sequence period our approaches can produce various binary and polyphase zcz families with desired parameters and alphabet size they also provide additional tradeoffs amongst the above four system parameters and are less constrained by the alphabet size furthermore the constructed families have nested like property that can be either decomposed or combined to constitute smaller or larger zcz sequence sets we make detailed comparisons with related works and present some extended properties for each approach we provide examples to numerically illustrate the proposed construction procedure

a new systematic construction of zero correlation zone sequences based on interleaved perfect sequences in the literature many constructions of zero correlation zone zcz sequences have been reported while most of them are suboptimal with respect to the known upper bound some constructed by matsufuji et al and torii et al respectively are almost optimal or even optimal in this paper we propose a systematic construction of almost optimal zcz sequence sets which generalizes the aforementioned constructions so that more flexible relationships between the set size and the sequence length are allowed in particular the obtained almost optimal zcz sequence sets of size m and length mn are new for 1 gcd m n min m n in addition their alphabets can be binary or nonbinary since our construction is only based on interleaving perfect sequences according to a certain orthogonal matrix

a monte carlo investigation of the planar lebwohl lasher lattice model abstract a monte carlo computer simulation of a planar version of the lebwohl lasher model is presented the model consists of a set of interaction centres forming a simple square lattice the pair potential is nearest neighbours attractive and varies as a second legendre polynomial of the relative orientation between the two particles five lattice sizes 5 5 10 10 20 20 60 60 and 80 80 of this two dimensional system have been simulated with monte carlo and periodic boundary conditions a study of the orientational pair correlation function indicates a power law decay in the ordered phase and an exponential decay above the pseudo transition temperature our results are consistent with the absence of a true phase transition but also indicate a low temperature phase with long short range order comparisons are made with one existing simulation and with the mean field theory results

a study on smoothing for particle filtered 3d human body tracking stochastic models have become the dominant means of approaching the problem of articulated 3d human body tracking where approximate inference is employed to tractably estimate the high dimensional 30d posture space of these approximate inference techniques particle filtering is the most commonly used approach however filtering only takes into account past observations almost no body tracking research employs smoothing to improve the filtered inference estimate despite the fact that smoothing considers both past and future evidence and so should be more accurate in an effort to objectively determine the worth of existing smoothing algorithms when applied to human body tracking this paper investigates three approximate smoothed inference techniques particle filtered backwards smoothing variational approximation and gibbs sampling results are quantitatively evaluated on both the humaneva dataset as well as a scene containing occluding clutter surprisingly it is found that existing smoothing techniques are unable to provide much improvement on the filtered estimate and possible reasons as to why are explored and discussed

optimal odd length binary z complementary pairs a pair of sequences is called a golay complementary pair gcp if their aperiodic auto correlation sums are zero for all out of phase time shifts existing known binary gcps only have even lengths in the form of 21026 where are non negative integers to fill the gap left by the odd lengths we investigate the optimal oddlength binary pairs which display the closest correlation property to that of gcps our criteria of closeness is that each pair has the maximum possible zero correlation zone zcz width and minimum possible out of zone aperiodic auto correlation sums such optimal pairs are called optimal odd length binary z complementary pairs ob zcp in this paper we show that each optimal ob zcp has maximum zcz width of n 1 2 and minimum out of zone aperiodic sum magnitude of 2 where n denotes the sequence length odd systematic constructions of such optimal op zcps are proposed by insertion and deletion of certain binary gcps which settle the 2011 li fan tang tu open problem positively the proposed optimal ob zcps may serve as a replacement for gcps in many engineering applications where odd sequence lengths are preferred in addition they give rise to a new family of base two almost difference families adf which are useful in studying partially balanced incomplete block design bibd index terms aperiodic correlation almost difference set ads almost difference families adf golay complementary pair gcp zero correlation zone zcz z complementary pair zcp

simplified ranging systems using discrete wavelet decomposition we employ the concepts and tools of the discrete wavelet transform dwt to encapsulate a body of previous research on efficiently analyzable phase coded waveforms for use in ranging applications this dwt perspective enables the direct synthesis of half rate implementations which are suitable for high speed applications we introduce and study a set of sequences based on a classical welti construction which are both dwt decomposable and exhibit a zero autocorrelation zone property under cyclic extension we propose a general extension technique which extends the zero correlation width while retaining the same simple receiver filter and show that this technique is appropriate for many of the sequences in our construction finally we propose a transmit waveform construction which allows a further reduction of two in the receiver hardware complexity we discuss the resulting tradeoffs between receiver complexity and transmit power

phase diagram of onsager crosses onsager crosses are hard nonconvex bodies formed by rigidly connecting three elongated rods equally thick but not necessarily equally long to form perpendicular crosses we study the phase behavior of systems of such particles focusing on their ability to form spatially homogeneous orientationally ordered phases with a symmetry lower than that of the standard uniaxial nematic we treat these systems in the onsager second virial coefficient approximation we apply bifurcation analysis to build up a global picture of the phase diagram which is then refined using approximate numerical calculations finally we generalize the gaussian approximation for the nematic orientational distribution function to deal with the more ordered phases encountered here and compare with the results from the previous techniques to see whether it is feasible to reliably predict the phase diagrams from a computationally cheaper technique

finding optimal bayesian network given a super structure classical approaches used to learn bayesian network structure from data have disadvantages in terms of complexity and lower accuracy of their results however a recent empirical study has shown that a hybrid algorithm improves sensitively accuracy and speed it learns a skeleton with an independency test it approach and constrains on the directed acyclic graphs dag considered during the search and score phase subsequently we theorize the structural constraint by introducing the concept of super structure s which is an undirected graph that restricts the search to networks whose skeleton is a subgraph of s we develop a super structure constrained optimal search cos its time complexity is upper bounded by o m n where m 2 depends on the maximal degree m of s empirically complexity depends on the average degree m and sparse structures allow larger graphs to be calculated our algorithm is faster than an optimal search by several orders and even finds more accurate results when given a sound super structure practically s can be approximated by it approaches significance level of the tests controls its sparseness enabling to control the trade off between speed and accuracy for incomplete super structures a greedily post processed version cos still enables to significantly outperform other heuristic searches

binary and quadriphase sequences with optimal autocorrelation properties a survey time discrete signals with good autocorrelation properties are used in various applications in communications engineering from an implementation point of view usually sequences with a small phase alphabet and a maximal energy efficiency i e a uniform envelope are most favorable for this reason known methods as well as several new construction techniques of binary and quadriphase sequences with optimal or best known autocorrelation properties are discussed in this correspondence in many cases the achievable correlation properties can be improved significantly if a single zero element per sequence is accepted these almost binary and almost quadriphase sequences are considered as well the optimality criteria used include the maximum absolute sidelobe and the merit factor of the periodic and the odd periodic autocorrelation function respectively for sequence lengths of up to 44 in the binary case and up to 32 in the quadriphase case the best known parameters obtained by computer search are compared with the constructed results

bat chirps with good properties zak space construction of perfect polyphase sequences previously a discretization of the linear fm chirp of length n kl 2 l and kl isin z was given and the conditions for its minimal zak space support were derived chirps satisfying these conditions are known as finite chirps in this work subsets of finite chirps of length n l 2 l a prime are examined the investigation leads to a new zak space construction of general polyphase sequence sets of size l 1 with optimal auto and cross correlation properties known as perfect sequence sets it is shown that perfect sequence sets are closely related to sets of finite chirps and in particular include the sets of zadoff chu sequences which are identical with subsets of finite chirps and the sets of generalized frank sequences which are identical with sets of modulations of finite chirps as special cases the entire collection of perfect sequence sets is then given by a partition of the set of perfect auto correlation sequences obtained by right coset decomposition of the group of all permutations with respect to a certain cyclic group the construction suggests several further generalizations that can be obtained by operating exclusively on subgroups of the permutation group

texture analysis with variational hidden markov trees a variational bayes formulation of the hidden markov tree hmt model is proposed for texture analysis utilizing a multilevel wavelet decomposition of imagery the variational method yields an approximation to the full posterior of the hmt parameters texture classification is based on the posterior predictive distribution or marginalized evidence with example results presented

statistical mechanics of hard ellipsoids i overlap algorithm and the contact function abstract a contact function for two arbitrary ellipsoids is derived the numerical value of the contact function is less than 1 if they overlap and greater than 1 if they do not this extends previous work by vieillard baron who derived an overlap criterion for spheroids without use of a contact function the equivalence of the two criteria has been checked by extensive numerical test with spheroids it is shown that the use of the contact function greatly facilitates the calculation of the pressure in monte carlo simulations

variational message passing bayesian inference is now widely established as one of the principal foundations for machine learning in practice exact inference is rarely possible and so a variety of approximation techniques have been developed one of the most widely used being a deterministic framework called variational inference in this paper we introduce variational message passing vmp a general purpose algorithm for applying variational inference to bayesian networks like belief propagation vmp proceeds by sending messages between nodes in the network and updating posterior beliefs using local operations at each node each such update increases a lower bound on the log evidence unless already at a local maximum in contrast to belief propagation vmp can be applied to a very general class of conjugate exponential models because it uses a factorised variational approximation furthermore by introducing additional variational parameters vmp can be applied to models containing non conjugate distributions the vmp framework also allows the lower bound to be evaluated and this can be used both for model comparison and for detection of convergence variational message passing has been implemented in the form of a general purpose inference engine called vibes variational inference for bayesian networks which allows models to be specified graphically and then solved variationally without recourse to coding

adaptive iterative detectors for phase uncertain channels via variational bounding the problem of iterative detection decoding of data symbols transmitted over an additive white gaussian noise awgn channel in the presence of phase uncertainty is addressed in this paper by modelling the phase uncertainty either as an unknown deterministic variable process or random variable process with a known a priori probability density function a number of non bayesian and bayesian detection algorithms with various amount of suboptimality have been proposed in the literature to solve the problem in this paper a new set of suboptimal iterative detection algorithms is obtained by utilizing the variational bounding technique especially applying the generic variational bayesian vb framework efficient iterative joint estimation and detection decoding schemes are derived for the constant phase model as well as for the dynamic phase model in addition the relation of the vb based approach to the optimal noncoherent receiver as well as to the classical approach via the expectation maximization em algorithm is provided performance of the proposed detectors in the presence of a strong dynamic phase noise is compared to the performance of the existing detectors furthermore an incremental scheduling of the vb or em algorithm is shown to reduce the overall complexity of the receiver

a new framework for constructing mutually orthogonal complementary sets and zcz sequences in this correspondence new characterizations for the construction of zero correlation zone zcz sequences from mutually orthogonal golay complementary sets mogcs is presented it is shown that the recursive construction of mogcs is inherent in these characterizations previously known constructions of zcz sequences and mogcs are shown to be special cases of this characterization the notion of mutually orthogonal zcz sequence sets is also introduced

renormalisation group study of a lattice model of the isotropic nematic transition the isotropic nematic transition is studied using the lebwohl lasher lattice model of liquid crystal behaviour the details of the transition are investigated using the migdal kadanoff potential moving version of the real space renormalisation group the method gives good results when applied to the closely related heisenberg model of ferromagnetism a second order transition is predicted in disagreement with mean field and some computer simulation results

first order transitions for n vector models in two and more dimensions rigorous proof we prove that various so n invariant n vector models with interactions which have a deep and narrow enough minimum have a first order transition in the temperature the result holds in dimensions two or more and is independent of the nature of the low temperature phase

new designs for signal sets with low cross correlation balance property and large linear span gf p case new designs for families of sequences over gf p with low cross correlation balance property and large linear span are presented the key idea of the new designs is to use short p ary sequences of period spl upsi with the two level autocorrelation function together with the interleaved structure to construct a set of long sequences with the desired properties the resulting sequences are interleaved sequences of period spl upsi sup 2 there are spl upsi cyclically shift distinct sequences in each family the maximal correlation value is 2 spl upsi 3 which is optimal with respect to the welch bound each sequence in the family is balanced and has large linear span in particular for binary case cross out of phase autocorrelation values belong to the set 1 spl upsi spl upsi 2 2 spl upsi 3 2 spl upsi 1 any sequence where the short sequences are quadratic residue sequences achieves the maximal linear span it is shown that some families of these sequences can be implemented efficiently in both hardware and software

new bounds and optimal binary signature sets part ii aperiodic total squared correlation we derive new bounds on the aperiodic total squared correlation atsc of binary antipodal signature sets for any number of signatures k and any signature length l we then present optimal designs that achieve the new bounds for several k l cases as interesting arguably side results we show that individual maximal merit factor sequences for example barker sequences are single user atsc optimal while neither the familiar gold nor the kasami set designs are atsc optimal in general the atsc optimal signature set designs provided in this work are in this sense better suited for asynchronous and or multipath code division multiplexing applications

first order phase transition in the two and three dimensional rpn 1 and cpn 1 models in the large n limit solving the lattice rpn 1 and cpn 1 models in the large n limit the authors show that they undergo a first order phase transition for dimensions greater than or equal to two in the latter case although there is no long range order they argue that at least in the rpn 1 model the transition corresponds to a condensation of defects

a new class of zero correlation zone sequences in this correspondence two new methods for constructing sets of zero correlation zone zcz sequences are proposed these methods are based on perfect sequences and unitary matrices compared with previous methods the proposed methods can generate sets of nonbinary zcz sequences having a longer zero correlation zone the sequences obtained by these methods are suitable for approximately synchronized code division multiple access as cdma systems

on certain sets of polyphase sequences with sparse and highly structured zak and fourier transforms this paper describes a km2 m k q m km z zak space construction of zero correlation zone polyphase sequence sets of sequence length km3 and set size km with all zero cross correlation the construction includes the sets with an m 1 point and t2m 1 point zero autocorrelation zone where t2 is an arbitrary nontrivial factor of m all sequences in these sets have sparse highly structured semipolyphase finite zak transforms with constant nonzero magnitude at m points and zero magnitude at selectable km3 m points and sparse semipolyphase km3 point discrete fourier transforms with constant nonzero magnitude at m2 points and zero magnitude at selectable km3 m2 points

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

construction of orthogonal and nearly orthogonal designs for computer experiments this paper presents new infinite families of orthogonal designs for computer experiments in cases where orthogonal designs cannot exist we construct alternative nearly orthogonal designs our designs can accommodate many factors and a large set of levels no iterative computer search is required to build up the desired orthogonal designs we develop and use new infinite classes of periodic golay pairs

approximate riemannian conjugate gradient learning for fixed form variational bayes variational bayesian vb methods are typically only applied to models in the conjugate exponential family using the variational bayesian expectation maximisation vb em algorithm or one of its variants in this paper we present an efficient algorithm for applying vb to more general models the method is based on specifying the functional form of the approximation such as multivariate gaussian the parameters of the approximation are optimised using a conjugate gradient algorithm that utilises the riemannian geometry of the space of the approximations this leads to a very efficient algorithm for suitably structured approximations it is shown empirically that the proposed method is comparable or superior in efficiency to the vb em in a case where both are applicable we also apply the algorithm to learning a nonlinear state space model and a nonlinear factor analysis model for which the vb em is not applicable for these models the proposed algorithm outperforms alternative gradient based methods by a significant margin

absence of the kosterlitz thouless fixed points in the migdal kadanoff recursion formulas it is shown that the migdal approximate renormalization recursion formulas always bring the initial state into the high temperature region for the u 1 invariant models at the critical dimensions this means that the migdal recursion formulas fail to exhibit the kosterlitz thouless transitions this is also the case for the recursion formulas of kadanoff type the method developed here is extended to non abelian systems by some additional tricks

polyphase codes for uplink ofdm cdma systems we propose a ofdm cdma system that employs polyphase codes to support variable spreading factors a systematic approach for constructing the polyphase code sequences of variable spreading factors is developed polyphase codes exhibit better auto and cross correlation properties than hadamard codes when employed in ofdm cdma systems polyphase codes result in certain structured multiple access interference mai caused by multipath analytical and numerical results show that ofdm cdma systems employing polyphase codes have better papr performance than those using hadamard codes the ber performance of the ofdm cdma system using polyphase codes is evaluated by numerical results and compared to that of the ofdm cdma system using hadamard codes with and without clipping

on learning conditional random fields for stereo until recently the lack of ground truth data has hindered the application of discriminative structured prediction techniques to the stereo problem in this paper we use ground truth data sets that we have recently constructed to explore different model structures and parameter learning techniques to estimate parameters in markov random fields mrfs via maximum likelihood one usually needs to perform approximate probabilistic inference conditional random fields crfs are discriminative versions of traditional mrfs we explore a number of novel crf model structures including a crf for stereo matching with an explicit occlusion model crfs require expensive inference steps for each iteration of optimization and inference is particularly slow when there are many discrete states we explore belief propagation variational message passing and graph cuts as inference methods during learning and compare with learning via pseudolikelihood to accelerate approximate inference we have developed a new method called sparse variational message passing which can reduce inference time by an order of magnitude with negligible loss in quality learning using sparse variational message passing improves upon previous approaches using graph cuts and allows efficient learning over large data sets when energy functions violate the constraints imposed by graph cuts

convolutional spreading cdma and comparison with the ds cdma with rake receiver for synchronous downlink direct sequence code division multiple access ds cdma we introduce a cyclic prefix cp based convolutional spreading cdma cs cdma cp scheme employing zero correlation zone zcz codes which gives a class of multiuser interference mui free cdma schemes including suehiro s cdma and block spreading bs cdma as special cases we show that cs cdma cp employing appropriately selected binary and ternary zcz codes have good user capacity peak to average power ratio papr and transmission power loss compared with previously proposed bs cdma schemes by simulation we show the effect of papr to its bit error rate ber performance when nonlinear amplifiers are used and also compare its ber performance with the conventional ds cdma scheme employing a rake receiver

optimum sets of interference free sequences with zero autocorrelation zones a general construction of a particular class of zero correlation zone sequences is proposed the general construction produces the sets of so called interference free zero autocorrelation zone if zaz sequences where any two sequences from a set have all zero periodic cross correlation while each sequence has periodic autocorrelation equal to zero in multiple zones of non zero delays the length d of each such zaz has the maximum possible value d t 1 for given sequence length n tm and for the given number of sequences in the set m m as an important special case of the general construction we present the construction of generalized chirp like if zaz sequences that allow particularly simple implementation of the corresponding banks of matched filters

modulatable orthogonal sequences and their application to ssma systems a set of n 1 orthogonal sequences of period n sup 2 is proposed where n is a natural number each orthogonal sequence proposed can be modulated by n complex numbers of absolute value 1 so the modulated sequence is also orthogonal when n is an odd prime number the absolute value of the cross correlation function between any two of the n 1 orthogonal sequences is constant and satisfies the mathematical lower bound this property of the cross correlation function is not changed when each of the two orthogonal sequences is modulated by n complex numbers of absolute value 1 two spread spectrum multiple access ssma systems using these sequences are proposed one system is an asynchronous ssma system using the proposed sequences unmodulated the cochannel interference peak between any two channels in this system realizes the mathematical lower bound for an asynchronous ssma system using a set of orthogonal sequences the other system is a synchronous ssma system without cochannel interference which uses the modulated form of the proposed sequences

bent function sequences in this paper we construct a new family of nonlinear binary signal sets which achieve welch s lower bound on simultaneous cross correlation and autocorrelation magnitudes given a parameter n with n 0 pmod 4 the period of the sequences is 2 n 1 the number of sequences in the set is 2 n 2 and the cross auto correlation function has three values with magnitudes leq 2 n 2 1 the equivalent linear span of the codes is bound above by sum i 1 n 4 left stackrel n i right these new signal sets have the same size and correlation properties as the small set of kasami codes but they have important advantages for use in spread spectrum multiple access communications systems first the sequences are balances which represents only a slight advantage second the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly hopped from sequence to sequence for code division multiple access operation most importantly the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it this high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing

two dimensional perfect binary arrays with 64 elements perfect binary arrays can exist for numbers of elements that are even square numbers two dimensional 2 d perfect binary arrays are 4 16 36 and 144 elements are known perfect binary arrays with 64 elements can be constructed for three or more dimensions here two dimensional binary arrays with 64 elements are examined the results of computer search for symmetric binary arrays with 64 elements are presented in the form of two 2 d perfect binary arrays with sizes 8 8 and 4 16 applications of these perfect binary arrays are in 2 d synchronization time frequency coding and coding loudspeaker fields

a construction of multiple optimal zcz sequence sets with good cross correlation zero correlation zone zcz sequences are a class of spreading sequences having ideal auto correlation and cross correlation in a zone around the origin they have been extensively studied in recent years due to their important applications in quasi synchronous code division multiple access systems in this paper a construction of zcz sequence sets is proposed based on perfect nonlinear functions it generates multiple zcz sequence sets with the properties 1 each sequence is perfect in the sense that its out of phase auto correlation is always zero 2 each zcz sequence set is optimal with respect to the tang fan matsufuji bound in which all the sequences are pairwise cyclically distinct and 3 the maximum inter set cross correlation of multiple sequence sets achieves the well known sarwate bound

weighted zak transforms and the dual tiling condition abstract for t 0 and a periodic complex valued sequence c we introduce the weighted zak transform z c t and study its properties as our main result we give characterizations for mapping properties and unitarity of z c t l 2 r l 2 s where functions in the image are understood as restrictions to a set s r 2 in particular we show that for almost every choice of l periodic sequences c the mapping properties of z c t l 2 r l 2 s simplify to statements on the geometry of s they involve a dual tiling condition on s with respect to the lattices t z z and l t z l z where 1 l t

new sets of zero or low correlation zone sequences via interleaving techniques sequence families with zero or low correlation zone can be used in the quasi synchronous code division multiple access qs cdma communication systems interleaving techniques are very useful for sequence design in this paper we present a general construction of sequence families with zero or low correlation zone using interleaving techniques and complex hadamard matrices the component sequences are perfect or ideal two level in two cases we construct the shift sequences 1 p l 2 p is even and l p 2 mod p which results in sequence families with zero or low correlation zone of parameters np mp l p where n is the period of component sequences m is the number of inequivalent shift sequences and 0 or 1 the conditions are derived under which the new construction is optimal some examples are also given to specify the new construction

prime phase sequences with periodic correlation properties better than binary sequences for the case where p is an odd prime n or 2 is an integer and omega is a complex primitive pth root of unity a construction is presented for a family of p sup n p phase sequences symbols of the form omega sup i where each sequence has length p sup n 1 and where the maximum nontrivial correlation value c sub max does not exceed 1 square root p sup n a complete distribution of correlation values is provided as a special case of this construction a previous construction due to sidelnikov 1971 is obtained the family of sequences is asymptotically optimum with respect to its correlation properties and in comparison with many previous nonbinary designs the present design has the additional advantage of not requiring an alphabet of size larger than three the new sequences are suitable for achieving code division multiple access and are easily implemented using shift registers they wee discovered through an application of deligne s bound 1974 on exponential sums of the weil type in several variables the sequences are also shown to have strong identification with certain bent functions

fractional convolution and correlation via operator methods and an application to detection of linear fm signals using operator theory methods together with our previously introduced unitary fractional operator we derive explicit definitions of fractional convolution and correlation operations in a systematic and comprehensive manner via operator manipulations we also provide alternative formulations of those fractional operations that suggest efficient algorithms for discrete implementation through simulation examples we demonstrate how well the proposed efficient method approximates the continuous formulation of fractional autocorrelation it is also shown that the proposed fractional autocorrelation corresponds to radial slices of the ambiguity function af we also suggest an application of the fast fractional autocorrelation for detection and parameter estimation of linear fm signals

bond moving transformations for continuous spin systems we consider two and three dimensional lattices with on each lattice a d dimensional classical spin vector we restrict ourselves to nearest neighbour interactions which only depend on the angle between the spin vectors for these systems the bond moving approximation of migdal and kadanoff is used to derive renormalisation group equations which do not violate the symmetry of the lattice without further approximations these equations are then solved numerically in addition to the specific heat we also calculate critical temperatures critical exponents and phase diagrams for ferromagnets liquid crystals and other related systems for the simple cubic lattice we find a rich phase diagram which among others indicates the existence of an anti nematic phase in liquid crystals

periodic complementary binary sequences existence conditions and recursive construction procedures for sets of periodic complementary binary sequences are given relationships to sets of aperiodic complementary binary sequences and to perfect binary arrays whose two dimensional periodic autocorrelation function is a delta function are noted the connections of periodic complementary binary sequences and difference families are given sets of periodic complementary binary sequences which result from computer search are presented a diagram showing what is currently known about the existence of periodic complementary binary sequences with p

sequence of discrete spin models approximating the classical heisenberg ferromagnet systematic investigation of a recent proposal of rapaport 1985 to describe the heisenberg model with discrete spin models is presented in two and three dimensions it is argued that in three dimensions a 12 state discretisation already accounts satisfactorily for the critical properties the corresponding anisotropy operators being irrelevant

first order transitions for some generalized xy models in this letter we demonstrate the occurrence of first order transitions in temperature for some recently introduced generalized xy models and also point out the connection between them and annealed site diluted lattice gas continuous spin models

constructions of permutation arrays a permutation array pa of length n and minimum distance d is a set of permutations of n elements such that any two permutations coincide in at most n d positions some constructions of pas are given

partial period correlations of zadoff chu sequences and their relatives partial period correlations of sequences are an important performance measure of communication systems employing them but are known to be notoriously difficult to analyze in this paper we present a systematic approach to partial period correlations as a generalization of the paterson lothian approach for a pair of sequences not necessarily distinct we introduce the linear phase shifting sequences of one of them and analyze their full period correlations called the induced correlations with the other one by exploiting the induced correlations we obtain the partial period correlation properties of the given pair we then investigate zadoff chu sequences and give some theoretical results on their partial period autocorrelations including closed form expressions and the first and second moments we also derive an upper bound on the magnitudes of the partial period cross correlations of zadoff chu sequences finally we explore generalized chirp like discrete fourier transform sequences and show that their partial period cross correlations have the same magnitudes as the partial period autocorrelations of the employed zadoff chu sequence up to permutation

sequence design to minimize the weighted integrated and peak sidelobe levels sequences with low aperiodic autocorrelation sidelobes are well known to have extensive applications in active sensing and communication systems in this paper we first consider the problem of minimizing the weighted integrated sidelobe level wisl which can be used to design sequences with impulse like autocorrelation and a zero or low correlation zone two algorithms based on the general majorization minimization method are developed to tackle the wisl minimization problem with guaranteed convergence to a stationary point the proposed methods are then extended to optimize the ell p norm of the autocorrelation sidelobes which leads to a way to minimize the peak sidelobe level psl criterion all the proposed algorithms can be implemented via the fast fourier transform fft and thus are computationally efficient an acceleration scheme is considered to further accelerate the algorithms numerical experiments show that the proposed algorithms can efficiently generate sequences with virtually zero autocorrelation sidelobes in a specified lag interval and can also produce very long sequences with much smaller psl compared with some well known analytical sequences

analysis of the migdal transformation for models with planar spins on a two dimensional lattice by numerical and analytical investigations we show that the bond moving transformation of migdal for planar spins on a two dimensional lattice possesses a very rich structure we find an infinite hierarchy of one three and higher dimensional fixed spaces in addition to phase transitions of the kosterlitz thouless type we find ising like transitions for which the critical exponents are the same as those of the q state potts model in the migdal approximation these critical exponents are constant within each fixed space the phase diagram is constructed for two specially chosen potentials

correlation and set size bounds of complementary sequences with low correlation zone the correlation lower bounds as well as the set size upper bounds of low correlation zone complementary sequences are presented in this paper they can be treated as an extension of tang fan matsufuji bounds in and which considered only the conventional non complementary low correlation zone sequence sets

characterization of zak space support of a discrete chirp general conditions are derived for an n kl2 point discrete chirp with chirp rate a and carrier frequency b to have minimal support on the ltimeskl zak transform lattice earlier it has been shown that when the normalized chirp parameters amacr ak amacr ak 2 and 2bmacr 2bk are integers the last two of the same parity then the discrete chirp is supported at kl points here this condition is relaxed by allowing amacr to be a rational number i e amacr n d n disin z n d 1 and requiring only that amacr and bmacrl be integers of arbitrary parity it is shown that the support of the zak space chirp satisfying the new condition then increases to dkl points the results provide foundations for future constructions of sophisticated radar and communications signal processing algorithms examples of direct applications of the zak space conditions in chirp parameter estimation chirp detection and chirp de noising are included

generalized chirp like sequences with zero correlation zone in this paper a new construction of optimum sets of zero correlation zone zcz sequences derived from generalized chirp like gcl sequences is presented a special case with reduced alphabet size is also described in a set of gcl zcz sequences the length of the zero correlation zone d has the maximum possible value d t 1 for a given sequence length n tm and for a given number of sequences in the set m m many values of n can be decomposed into multiple products of two positive integers thus allowing for flexible tradeoff between the length of the zcz and the number of sequences in the set as the set of gcl zcz sequences is obtained by modulating a common carrier sequence with a set of orthogonal modulating sequences there is a possibility for efficient implementation of the corresponding bank of matched filters

topological transitions in two dimensional lattice models of liquid crystals the phase diagram of hard core nematogenic models in three dimensional space can be studied by means of onsager s theory and on the other hand the critical properties of continuous interaction potentials can be investigated using the molecular field approach pioneered by maier and saupe comparison between these treatments shows a certain formal similarity reflecting their common variational root on this basis hard core potential models can be mapped onto continuous ones via their excluded volume some years ago this line of reasoning had been applied to hard spherocylinders hence the continuous potential g ensuremath tau a b sqrt 1 ensuremath ensuremath tau 2 bg0 had been used to define a mesogenic model on a three dimensional lattice s romano int j mod phys b 9 85 1995 in the formula ensuremath tau denotes the scalar product between the two unit vectors defining particle orientations here we went on by addressing the same interaction potential on a two dimensional lattice our analysis based on extensive monte carlo simulations found evidence of a topological transition and the critical behavior in its vicinity was studied in detail results obtained for the present model were compared with those already obtained in the literature for interaction potentials defined by legendre polynomials of second and fourth orders in the scalar product ensuremath tau

on aperiodic and periodic complementary binary sequences we give direct and recursive constructions for aperiodic and periodic complementary sequences using these constructions many missing entries in the table of bomer and antweiler 1990 can be filled

infinite hidden markov models for unusual event detection in video we address the problem of unusual event detection in a video sequence invariant subspace analysis isa is used to extract features from the video and the time evolving properties of these features are modeled via an infinite hidden markov model ihmm which is trained using ldquonormalrdquo ldquotypicalrdquo video the ihmm retains a full posterior density function on all model parameters including the number of underlying hmm states anomalies unusual events are detected subsequently if a low likelihood is observed when associated sequential features are submitted to the trained ihmm a hierarchical dirichlet process framework is employed in the formulation of the ihmm the evaluation of posterior distributions for the ihmm is achieved in two ways via markov chain monte carlo and using a variational bayes formulation comparisons are made to modeling based on conventional maximum likelihood based hmms as well as to dirichlet process based gaussian mixture models

extended high temperature series for the classical heisenberg model in three dimensions extended series expansions are derived for the high temperature susceptibility of the classical heisenberg model on three dimensional lattices series coefficients are presented to twelfth order for the simple cubic sc and face centred cubic fcc lattices and to eleventh order for the body centred cubic bcc lattice the results are in agreement with earlier calculations apart from a small discrepancy at the tenth order on the fcc lattice extrapolation studies on the extended series are used to obtain revised estimates for the critical points kc and the susceptibility exponent gamma on the fcc lattice the authors also investigate the possibility of a confluent non analytic correction to the dominant singularity while the coefficients are consistent with the presence of such a correction term with an exponent delta 1 of 0 55 as predicted by renormalisation group rg calculations the amplitude of the correction term appears to be very small compared with that of the first analytic correction term

phase transition in a nematic n vector model the large n limit the free energy of the rpn 1 model is rigorously computed in the n infinity limit the system shows a first order transition with latent heat in two and three dimensions the first correction in 1 n is also computed comparison of the results with numerical ones show that whereas in three dimensions the large n limit correctly reproduces the behaviour of the system for n or 3 it does not in two dimensions for some observables

computing the ambiguity surface the computation of the discrete ambiguity function is considered two straightforward methods are developed depending upon whether we write the discrete ambiguity as a filter or as a discrete fourier transform a modification of the transform method produces an approximation to the discrete ambiguity function but has increased computational efficiency this method is based on a recent work 1 in most major applications we need to compute limited portions of the dft description of the discrete ambiguity function to do so we first pass a long sequence of data through a decimated fir filter and then use the fft algorithm on the results the remez algorithm is employed to control the resulting aliasing errors in the final section approximation theory is applied directly to the problem of computing the discrete ambiguity function the algorithm required to carry out the necessary computations turns out to be the same as on the prevoius approximation method based on a decimating fir filter

watermarking in the space spatial frequency domain using two dimensional radon wigner distribution a two dimensional 2 d signal with a variable spatial frequency is proposed as a watermark in the spatial domain this watermark is characterized by a linear frequency change it can be efficiently detected by using 2 d space spatial frequency distributions the projections of the 2 d wigner distribution the 2 d radon wigner distribution are used in order to emphasize the watermark detection process the watermark robustness with respect to some very important image processing attacks such as for example the translation rotation cropping jpeg compression and filtering is demonstrated and tested by using stirmark 3 1

linear frequency modulated signal detection using radon ambiguity transform a novel time frequency technique for linear frequency modulated lfm signal detection is proposed the design of the proposed detectors is based on the radon transform of the modulus square or the envelope amplitude of the ambiguity function af of the signal a practical assumption is made that the chirp rate is the only parameter of interest since the af of lfm signals will pass through the origin of the ambiguity plane the line integral of the radon transform is performed over all lines passing through the origin of the ambiguity plane the proposed detectors yield maxima over chirp rates of the lfm signals this reduces the two dimensional 2 d problem of the conventional wigner ville distribution wvd based detection or the radon wigner transform rwt based detector to a one dimensional 1 d problem and consequently reduces the computation load and keeps the feature of built in filtering related issues such as the finite length effect the resolution and the effect of noise are studied the result is a tool for lfm detection as well as the time varying filtering and adaptive kernel design for multicomponent lfm signals

n shift cross orthogonal sequences n shift cross orthogonal sequences and a complete complementary code derived from them are defined and discussed a general method for generating this code is also discussed a synchronous multiple user spread spectrum multiple system is proposed that uses n shift cross orthogonal sequences

quadratic optimization with similarity constraint for unimodular sequence synthesis this paper considers unimodular sequence synthesis under similarity constraint for both the continuous and discrete phase cases a computationally efficient iterative algorithm for the continuous phase case ia cpc is proposed to sequentially optimize the quadratic objective function the quadratic optimization problem is turned into multiple one dimensional optimization problems with closed form solutions for the discrete phase case we present an iterative block optimization algorithm specifically we partition the design variables into k blocks and then we sequentially optimize each block via exhaustive search while fixing the remaining k 1 blocks finally we evaluate the computational costs and performance gains of the proposed algorithms in comparison with power method like and semidefinite relaxation related techniques

constructions of binary array set with zero correlation zone based on the perfect binary array and the orthogonal matrix a new method of constructing zero correlation zone binary array set is proposed yielding binary array sets with member sizes almost achieve the theoretical upper bound a recursive construction of zero correlation zone binary array set is also proposed and the obtained array sets have even larger sizes as well as additional good correlation properties

learning module networks methods for learning bayesian networks can discover dependency structure between observed variables although these methods are useful in many applications they run into computational and statistical problems in domains that involve a large number of variables in this paper we consider a solution that is applicable when many variables have similar behavior we introduce a new class of models module networks that explicitly partition the variables into modules so that the variables in each module share the same parents in the network and the same conditional probability distribution we define the semantics of module networks and describe an algorithm that learns the modules composition and their dependency structure from data evaluation on real data in the domains of gene expression and the stock market shows that module networks generalize better than bayesian networks and that the learned module network structure reveals regularities that are obscured in learned bayesian networks

binary odd periodic complementary sequences a pair of binary sequences is called complementary if the sum of their aperiodic autocorrelation functions is zero except for zero shift such sequences are known for relatively few lengths this correspondence therefore introduces pairs of binary odd periodic complementary sequences which can be constructed using q ary m sequences for many more lengths

new sequences design from weil representation with low two dimensional correlation in both time and phase shifts a new elementary expression of the construction first proposed by gurevich hadani and sochen is given which avoids the explicit use of the weil representation the sequences in this signal set are given by both multiplicative character and additive character of finite field fp such a signal set consists of p2 p 2 time shift distinct sequences the magnitude of the two dimensional autocorrelation function i e the ambiguity function in both time and phase of each sequence is upper bounded by 2 p at any shift not equal to 0 0 furthermore the magnitude of their fourier transform spectrum is less than or equal to 2 for a subset consisting of p p 2 phase shift distinct sequences in this signal set the magnitude of the ambiguity function of any pair is upper bounded by 4 p a proof is given through finding a new expression of the sequences in the finite harmonic oscillator system an open problem for directly establishing these assertions without involving the weil representation is addressed

computational design of sequences with good correlation properties in this paper we introduce a computational framework based on an iterative twisted approximation itrox and a set of associated algorithms for various sequence design problems the proposed computational framework can be used to obtain sequences or complementary sets of sequences possessing good periodic or aperiodic correlation properties and in an extended form to construct zero or low correlation zone sequences furthermore as constrained e g finite alphabets are of interest in many applications we introduce a modified version of our general framework that can be useful in these cases several applications of itrox are studied and numerical examples focusing on the construction of real valued and binary sequences are provided to illustrate the performance of itrox for each application

compact modeling of data using independent variable group analysis in this paper we introduce a modeling approach called independent variable group analysis ivga which can be used for finding an efficient structural representation for a given data set the basic idea is to determine such a grouping for the variables of the data set that mutually dependent variables are grouped together whereas mutually independent or weakly dependent variables end up in separate groups computation of an ivga model requires a combinatorial algorithm for grouping of the variables and a modeling algorithm for the groups in order to be able to compare different groupings a cost function which reflects the quality of a grouping is also required such a cost function can be derived for example using the variational bayesian approach which is employed in our study this approach is also shown to be approximately equivalent to minimizing the mutual information between the groups the modeling task is computationally demanding we describe an efficient heuristic grouping algorithm for the variables and derive a computationally light nonlinear mixture model for modeling of the dependencies within the groups finally we carry out a set of experiments which indicate that ivga may turn out to be beneficial in many different applications

system identification using chirp signals and time variant filters in the joint time frequency domain we propose a novel method to identify an unknown linear time invariant lti system in low signal to noise ratio snr environment the method is based on transmitting chirp signals for the transmitter and using linear time variant filters in the joint time frequency tf domain for the receiver to reduce noise before identification due to the tf localization property of chirp signals a large amount of additive white noise can be reduced and therefore the snr before identification can be significantly increased this however cannot be achieved in the conventional methods where pseudo random signals are used and therefore noise reduction techniques do not apply our simulation results indicate that the method proposed outperforms the conventional methods significantly in a low snr environment this paper provides a good application of time frequency analysis and synthesis

unsupervised learning of parsimonious mixtures on large spaces with integrated feature and component selection estimating the number of components the order in a mixture model is often addressed using criteria such as the bayesian information criterion bic and minimum message length however when the feature space is very large use of these criteria may grossly underestimate the order here it is suggested that this failure is not mainly attributable to the criterion e g bic but rather to the lack of structure in standard mixtures these models trade off data fitness and model complexity only by varying the order the authors of the present paper propose mixtures with a richer set of tradeoffs the proposed model allows each component its own informative feature subset with all other features explained by a common model shared by all components parameter sharing greatly reduces complexity at a given order since the space of these parsimonious modeling solutions is vast this space is searched in an efficient manner integrating the component and feature selection within the generalized expectation maximization gem learning for the mixture parameters the quality of the proposed unsupervised solutions is evaluated using both classification error and test set data likelihood on text data the proposed multinomial version learned without labeled examples without knowing the true number of topics and without feature preprocessing compares quite favorably with both alternative unsupervised methods and with a supervised naive bayes classifier a gaussian version compares favorably with a recent method introducing feature saliency in mixtures