data record size requirements for adaptive space time ds cdma signal detection we investigate the data record size requirements of sample matrix inversion based minimum variance distortionless response and maximum signal to interference plus noise ratio adaptive algorithms to meet a given performance objective in joint space time signal detection problems for direct sequence code division multiple access systems we derive closed form expressions that provide the data record size that is necessary to achieve a given performance confidence level in a neighborhood of the optimal performance point as well as expressions that identify the performance level that can be reached for a given data record size this is done by using close approximations of the involved probability density functions the practical significance of the derived expressions lies in the fact that the expressions are functions of the number of antenna elements the number of multipaths and the system spreading gain only while they depend neither on the ideal input covariance matrix which is not known in most realistic applications nor on the exact ideal performance value

random walks on graphs electric networks and fractals this paper is devoted to the problem of the nearest neighbour random walk on infinite graphs we investigate the rw x n started from a fixed vertex x0 x v of the graph g v e and the expected value of the first exit time t n from the n ball b n in g it will be shown that if g is sufficiently regular then d underset raise0 3em hbox smash scriptscriptstyle geqslant d omega d r underset raise0 3em hbox smash scriptscriptstyle geqslant 2 and d r d 2 d omega where d r is the rw dimension d is the fractal dimension and d is the exponent of the growth of the resistance of b n though the method of the paper was developed for the case when x0 x is a fixed vertex of the graph we hope that the result can be generalized

the 1 vertex transfer matrix and accurate estimation of channel capacity the notion of a 1 vertex transfer matrix for multidimensional codes is introduced it is shown that the capacity of such codes or the topological entropy can be expressed as the limit of the logarithm of spectral radii of 1 vertex transfer matrices storage and computations using the 1 vertex transfer matrix are much smaller than storage and computations needed for the standard transfer matrix the method is applied to estimate the first 15 digits of the entropy of the 2 d 0 1 run length limited channel a large scale computation of eigenvalues for the 0 1 run length limited channel in 2 d and 3 d have been carried out this was done in order to be able to compare the computational cost of the new method with the standard transfer matrix and have rigorous bounds to compare the estimates with this in turn leads to improvements on the best previous lower and upper bounds for these channels

a notion of effectiveness for subshifts on finitely generated groups abstract we generalize the classical definition of effectively closed subshift to finitely generated groups we study classical stability properties of this class and then extend this notion by allowing the usage of an oracle to the word problem of a group this new class of subshifts forms a conjugacy class that contains all sofic subshifts motivated by the question of whether there exists a group where the class of sofic subshifts coincides with that of effective subshifts we show that the inclusion is strict for several groups including recursively presented groups with undecidable word problem amenable groups and groups with more than two ends we also provide an extended model of turing machine which uses the group itself as a tape and characterizes our extended notion of effectiveness as applications of these machines we prove that the origin constrained domino problem is undecidable for any group of the form g z subject to a technical condition on g and we present a simulation theorem which is valid in any finitely generated group

block pickard models for two dimensional constraints in pickard random fields prf the probabilities of finite configurations and the entropy of the field can be calculated explicitly but only very simple structures can be incorporated into such a field given two markov chains describing a boundary an algorithm is presented which determines whether a prf consistent with the distribution on the boundary and a 2 d constraint exists iterative scaling is used as part of the algorithm which also determines the conditional probabilities yielding the maximum entropy for the given boundary description if a solution exists a prf is defined for the domino tiling constraint represented by a quaternary alphabet prf models are also presented for higher order constraints including the no isolated bits n i b constraint and a minimum distance 3 constraint by defining super symbols on blocks of binary symbols

finite state automata representing two dimensional subshifts a new type of two dimensional automaton has been defined to recognize a class of two dimensional shifts of finite type having the property that every admissible block found within the related local picture language can be extended to a point of the subshift here it is shown that this automaton accurately represents the image of the represented two dimensional shift of finite type under a block code it is then shown that these automata can be used to check for a certain type of two dimensional transitivity in the factor language of the corresponding shift space and how this relates to periodicity in the two dimensional case the paper closes with a notion of follower sets that are used to reduce the size of the automata representing two dimensional sofic shifts

statistics of adaptive nulling and use of the generalized eigenrelation ger for modeling inhomogeneities in adaptive processing this paper examines the integrity of the generalized eigenrelation ger which is an approach to assessing performance in an adaptive processing context involving covariance estimation when the adaptive processors are subject to undernulled interference the ger is a mathematical relation which if satisfied often facilitates closed form analysis of adaptive processors employing estimated covariances subject to inhomogeneities the goal of this paper is to determine what impact this constraint has on the integrity of the adaptive nulling process in order to examine the impact of the ger constraint on adaptive nulling we establish fundamental statistical convergence properties of an adaptive null for the sample covariance based scb minimum variance distortionless response mvdr beamformer novel exact expressions relating the mean and variance of an adaptive null of a homogeneously trained beamformer to the mean and variance of a nonhomogeneous trained beamformer are derived in addition it is shown that the reed et al 1974 result for required sample support can be highly inaccurate under nonhomogeneous conditions indeed the required sample support can at times depend directly on the power of the undernulled interference

growth type invariants for ℤ d subshifts of finite type and arithmetical classes of real numbers we discuss some numerical invariants of multidimensional shifts of finite type sfts which are associated with the growth rates of the number of admissible finite configurations extending an unpublished example of tsirelson a strange two dimensional symbolic system 1992 we show that growth complexities of the form exp n o 1 are possible for non integer s in terminology of de carvalho port math 54 1 19 40 1997 such subshifts have entropy dimension the class of possible s are identified in terms of arithmetical classes of real numbers of weihrauch and zheng math log q 47 1 51 65 2001

performance analysis of the minimum variance beamformer we present an analysis of the signal to interference plus noise ratio sinr at the output of the minimum variance beamformer the analysis is based on the assumption that the signals and noise are gaussian and that the number of samples is large compared to the array size and it yields an explicit expression for the sinr in terms of the different parameters affecting the performance including signal to noise ratio snr interference to noise ratio inr signal to interference ratio sir angular separation between the desired signal and the interference array size and shape correlation between the desired signal and the interference and finite sample size

limit eigenvalues of nonnegative matrices abstract in this paper we give a simple closed formula for a certain limit eigenvalue of a nonnegative matrix we bound the spectral radius of a nonnegative matrix in terms of this limit eigenvalue

entropy bounds for constrained two dimensional random fields the maximum entropy and thereby the capacity of two dimensional 2 d fields given by certain constraints on configurations is considered upper and lower bounds are derived a new class of 2 d processes yielding good lower bounds is introduced asymptotically the process achieves capacity for constraints with limited long range effects the processes are general and may also be applied to e g data compression of digital images results are given for the binary hard square model which is a 2 d run length limited model and some other 2 d models with simple constraints

pdf s confidence regions and relevant statistics for a class of sample covariance based array processors we add to the many results on sample covariance matrix scm dependent array processors by i weakening the traditional assumption of gaussian data and ii providing for a class of array processors additional performance measures that are of value in practice the data matrix is assumed drawn from a class of multivariate elliptically contoured mec distributions the performance measures include the exact probability density functions pdfs confidence regions and moments of the weight vector matrix beam response and beamformer output of certain scm based scb array processors the array processors considered include the scb i maximum likelihood ml signal vector estimator ii linearly constrained minimum variance beamformer lcmv iii minimum variance distortionless response beamformer mvdr and iv generalized sidelobe canceller gsc implementation of the lcmv beamformer it is shown that the exact joint pdfs for the weight vectors matrices of the aforementioned scb array processors are a linear transformation from a complex multivariate extension of the standardized t distribution the scb beam responses are generalized t distributed and the pdfs of the scb beamformer outputs are given by kummer s function all but the beamformer outputs are shown to be completely invariant statistics over the class of mecs considered

mahler measure and entropy for commuting automorphisms of compact groups we compute the joint entropy ofd commuting automorphisms of a compact metrizable group letr d u 1 1 d 1 1 be the ring of laurent polynomials ind commuting variables andm be anr d module then the dual groupx m ofm is compact and multiplication onm by each of thed variables corresponds to an action m of d by automorphisms ofx m every action of d by automorphisms of a compact abelian group arises this way iff r d our main formula shows that the topological entropy of alpha r d left langle f right rangle is given by h left alpha r d left langle f right rangle right log m left f right int limits 0 1 ldots int limits 0 1 log left f left e 2 pi it 1 ldots e 2 pi it d right right dt 1 ldots dt d where m f is the mahler measure off this reduces to the classical result for toral automorphisms via jensen s formula while the entropy of a single automorphism of a compact group is always the logarithm of an algebraic integer this no longer seems to hold for joint entropy of commuting automorphisms since values such as 7 3 4 2 occur if p is a non principal prime ideal we show h left alpha r d p right 0 using an analogue of the yuzvinskii thomas addition formula we computeh m for arbitraryr d modulesm and then the joint entropy for an action of d on a not necessarily abelian compact group using a result of boyd we characterize those m which have completely positive entropy in terms of the prime ideals associated tom and show this condition implies that m is mixing of all orders we also establish an analogue of berg s theorem proving that if m has finite entropy then haar measure is the unique measure of maximal entropy if and only if m has completely positive entropy finally we show that for expansive actions the growth rate of the number of periodic points equals the topological entropy

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

automorphisms of some banach algebras of analytic functions abstract in this paper we factorize an arbitrary automorphism of the algebra considered by peters in j peters j functional anal 59 1984 498 534 and its weak version and use it to identify an isomorphism invariant which is the quotient group of the full automorphism group over the maximal ideal fixing automorphisms subgroup

dimension theory of graphs and networks starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the planck scale one of the many problems one has to face in this enterprise is to find the discrete protoforms of the building blocks of continuum physics and mathematics a core concept is the notion of dimension in the following we develop such a notion for irregular structures such as large graphs and networks and derive a number of its properties among other things we show its stability under a wide class of perturbations which is important if one has dimensional phase transitions in mind furthermore we systematically construct graphs with almost arbitrary fractal dimension which may be of some use in the context of dimensional renormalization or statistical mechanics on irregular sets

on the capacity of two dimensional run length constrained channels two dimensional binary patterns that satisfy one dimensional d k run length constraints both horizontally and vertically are considered for a given d and k the capacity c sub d k is defined as c sub d k lim sub m n spl rarr spl infin log sub 2 n sub m n sup d k mn where n sub m n sup d k denotes the number of m spl times n rectangular patterns that satisfy the two dimensional d k run length constraint bounds on c sub d k are given and it is proven for every d spl ges 1 and every k d that c sub d k 0 if and only if k d 1 encoding algorithms are also discussed

pre expansivity in cellular automata we introduce the property of pre expansivity for cellular automata ca it is the property of being expansive on asymptotic pairs of configurations i e configurations that differ in only finitely many positions pre expansivity therefore lies between expansivity and pre injectivity two important notions of ca theory we show that there exist one dimensional positively pre expansive cas which are not positively expansive and they can be chosen reversible while positive expansivity is impossible for reversible cas we show however that no bi dimensional ca which is linear over an abelian group can be pre expansive we also consider the finer notion of k expansivity expansivity over pairs of configurations with exactly k differences and show examples of linear ca in dimension 2 and on the free group that are k expansive depending on the value of k whereas no positively expansive ca exists in this setting

an iterative algorithm for the computation of the mvdr filter statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter or constraint vector and generates a sequence of filters that converges to the minimum variance distortionless response mvdr solution for any positive definite input autocorrelation matrix computationally the algorithm is a simple noninvasive recursive procedure that avoids any form of explicit autocorrelation matrix inversion decomposition or diagonalization theoretical analysis reveals basic properties of the algorithm and establishes formal convergence when the input autocorrelation matrix is replaced by a conventional sample average positive definite estimate the algorithm effectively generates a sequence of mvdr filter estimators the bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample matrix inversion smi estimator in fact formal convergence of the estimator sequence to the smi estimate is established however for short data records it is the early nonasymptotic elements of the generated sequence of estimators that offer favorable bias covariance balance and are seen to outperform in mean square estimation error constraint lms rls type orthogonal multistage decomposition as well as plain and diagonally loaded smi estimates an illustrative interference suppression example is followed throughout this presentation

semicrossed products generated by two commuting automorphisms abstract in this paper we study the semicrossed product of a finite dimensional c algebra for two types of z 2 actions and identify them with matrix algebras of analytic functions in two variables we look at the connections with semicrossed by z actions

entropy dimension of shift spaces on monoids we consider the entropy dimension of g shifts of finite type for the case where g is a non abelian monoid entropy dimension tells us whether a shift space has zero topological entropy suppose the cayley graph cg of g has a finite representation that is cgg g g is a finite set up to graph isomorphism and relations among generators of g are determined by a matrix a we reveal an association between the characteristic polynomial of a and the finite representation of the cayley graph after introducing an algorithm for the computation of the entropy dimension the set of entropy dimensions is related to a collection of matrices in which the sum of each row of every matrix is bounded by the number of leaves of the graph furthermore the algorithm extends to g having finitely many free followers

positive expansiveness versus network dimension in symbolic dynamical systems a symbolic dynamical system is a continuous transformation f x x of closed subset x a v where a is a finite set and v is countable examples include subshifts odometers cellular automata and automaton networks the function f induces a directed graph network structure on v whose geometry reveals information about the dynamical system x f the dimensiondim v is an exponent describing the growth rate of balls in this network as a function of their radius we show that if x has positive entropy and dim v 1 and the system a v x f satisfies minimal symmetry and mixing conditions then x f cannot be positively expansive this generalizes a well known result of shereshevsky about multidimensional cellular automata we also construct a counterexample to a version of this result without the symmetry condition finally we show that network dimension is invariant under topological conjugacies which are holder continuous

blind adaptive constrained constant modulus reduced rank interference suppression algorithms based on interpolation and switched decimation this work proposes a blind adaptive reduced rank scheme and constrained constant modulus ccm adaptive algorithms for interference suppression in wireless communications systems the proposed scheme and algorithms are based on a two stage processing framework that consists of a transformation matrix that performs dimensionality reduction followed by a reduced rank estimator the complex structure of the transformation matrix of existing methods motivates the development of a blind adaptive reduced rank constrained barc scheme along with a low complexity reduced rank decomposition the proposed barc scheme and a reduced rank decomposition based on the concept of joint interpolation switched decimation and reduced rank estimation subject to a set of constraints are then detailed the proposed set of constraints ensures that the multipath components of the channel are combined prior to dimensionality reduction we develop low complexity joint interpolation and decimation techniques stochastic gradient and recursive least squares reduced rank estimation algorithms a model order selection algorithm for adjusting the length of the estimators is devised along with techniques for determining the required number of switching branches to attain a predefined performance an analysis of the convergence properties and issues of the proposed optimization and algorithms is carried out and the key features of the optimization problem are discussed we consider the application of the proposed algorithms to interference suppression in ds cdma systems the results show that the proposed algorithms outperform the best known reduced rank schemes while requiring lower complexity

recursive short data record estimation of av and mmse mvdr linear filters for ds cdma antenna array systems the presence of the desired signal during estimation of the minimum mean square error mmse minimum variance distortionless response mvdr and auxiliary vector av filters under limited data support leads to significant signal to interference plus noise ratio sinr performance degradation we quantify this observation in the context of direct sequence code division multiple access ds cdma communications by deriving close approximations for the mean square filter estimation error the probability density function of the output sinr and the probability density function of the symbol error rate ser of the sample matrix inversion smi receiver evaluated using both a desired signal present and desired signal absent input covariance matrix to avoid such performance degradation we propose a ds cdma receiver that utilizes a simple pilot assisted algorithm that estimates and then subtracts the desired signal component from the received signal prior to filter estimation then to accommodate decision directed operation we develop two recursive algorithms for the on line estimation of the av and mmse mvdr filter and we study their convergence properties finally simulation studies illustrate the ser performance of the overall receiver structures

on the entropy of zd subshifts of finite type abstract in this paper we study the combinatorial the topological and the periodic entropies of z d subshifts of finite type we show that the combinatorical and the topological entropies are equal we give sufficient conditions for the periodic entropy to be equal to the topological entropy

weak crossed products and a generalisation of a result of sarason abstract in this paper the weak semicrossed products of finite dimensional w algebras by z are identified with algebras of matrices of functions of h t and then they are classified up to algebraic isomorphism in the second part of the paper the weak operator density of matrices of polynomials in the unit ball of our main algebra is shown moreover a generalisation of a result due to d sarason trans amer math soc 127 1967 179 203 about the closure of h t c t in l t is obtained

on the dynamics and recursive properties of multidimensional symbolic systems we study the sub dynamics of multidimensional shifts of finite type and sofic shifts and the action of cellular automata on their limit sets such a subaction is always an effective dynamical system i e it is isomorphic to a subshift over the cantor set the complement of which can be written as the union of a recursive sequence of basic sets our main result is that to varying degrees this recursive theoretic condition is also sufficient we show that the class of expansive subactions of multidimensional sofic shifts is the same as the class of expansive effective systems and that a general effective system can be realized modulo a small extension as the subaction of a shift of finite type or as the action of a cellular automaton on its limit set after removing a dynamically trivial set as applications we characterize in terms of their computational properties the numbers which can occur as the entropy of cellular automata and construct sfts and cas with various interesting properties

convex programming upper bounds on the capacity of 2 d constraints the capacity of 1 d constraints is given by the entropy of a corresponding stationary maxentropic markov chain namely the entropy is maximized over a set of probability distributions which is defined by some linear equalities and inequalities in this paper certain aspects of this characterization are extended to 2 d constraints the result is a method for calculating an upper bound on the capacity of 2 d constraints the key steps are as follows the maxentropic stationary probability distribution on square configurations is considered set of linear equalities and inequalities is derived from this stationarity the result is then a convex program which can be easily solved numerically our method improves upon previous upper bounds for the capacity of the 2 d no isolated bits constraint as well as certain 2 d rll constraints

bounds on the capacity of constrained two dimensional codes bounds on the capacity of constrained two dimensional 2 d codes are presented the bounds of calkin and wilf see siam j discr math vol 11 no 1 p 54 60 1998 apply to first order symmetric constraints the bounds are generalized in a weaker form to higher order and nonsymmetric constraints results are given for constraints specified by run length limits or a minimum distance between pixels of a given value

c algebras associated with hilbert c quad modules of c textile dynamical systems abstract a c textile dynamical system a consists of a unital c algebra a two families of endomorphisms and a a of a and certain commutation relations among them it yields a two dimensional subshift and a multistructure hilbert c bimodule which we call a hilbert c quad module we introduce a c algebra from the hilbert c quad module as a two dimensional analogue of pimsner s construction of c algebras from hilbert c bimodules we study the c algebras defined by the hilbert c quad modules and prove that they have universal properties subject to certain operator relations we also present examples arising from commuting matrices

spectra of graphs and fractal dimensions i in this paper we consider the nearest neighbour random walk on infinite graphs we discuss the connection between the two smallest eigenvalues of the laplacian of the graph and the diffusion speed of the rw

entropy of bit stuffing induced measures for two dimensional checkerboard constraints a modified bit stuffing scheme for two dimensional 2 d checkerboard constraints is introduced the entropy of the scheme is determined based on a probability measure defined by the modified bit stuffing entropy results of the scheme are given for 2 d constraints on a binary alphabet the constraints considered are 2 d rll d infin for d 2 3 and 4 as well as for the constraint with a minimum 1 norm distance of 3 between 1s for these results the entropy is within 1 2 of an upper bound on the capacity for the constraint as a variation of the scheme periodic merging arrays are also considered

on the period two property of the majority operator in infinite graphs a self mapping m x x of a nonempty set x has the period two property p2p if m2x x holds for every af periodic point x e x let x be the set of all 0 1 labelings x v 0 1 of the set of vertices f of a locally finite connected graph g for x e x let mx x label v e v by the majority bit that x applies to its neighbors retaining v s x label in case of a tie we show that m has the p2p if there is a finite bound on the degrees in g and log b 0 where b is the number of v 6 v at a distance at most n from a fixed vertex vq v

an alternate derivation of the distribution of the conditioned signal to noise ratio a result in multiple regression analysis is used to derive the probability distribution of the conditioned signal to noise ratio

data record based criteria for the selection of an auxiliary vector estimator of the mmse mvdr filter when the auxiliary vector av filter generation algorithm utilizes sample average estimated input data statistics it provides a sequence of estimates of the ideal minimum mean square error or minimum variance distortionless response filter for the given signal processing receiver design application evidently early nonasymptotic elements of the sequence offer favorable bias variance balance characteristics and outperform in mean square filter estimation error the unbiased sample matrix inversion smi estimator as well as the constraint least mean square recursive least squares multistage nested wiener filter and diagonally loaded smi filter estimators selecting the most successful in some appropriate sense av filter estimator in the sequence for a given data record is a critical problem that has not been addressed so far we deal exactly with this problem and we propose two data driven selection criteria the first criterion minimizes the cross validated sample average variance of the av filter output and can be applied to general filter estimation problems the second criterion maximizes the estimated j divergence of the av filter output conditional distributions and is tailored to binary phase shift keying type detection problems

decidability of irreducible tree shifts of finite type we reveal an algorithm for determining the complete prefix code irreducibility cpc irreducibility of dyadic trees labeled by a finite alphabet by introducing an extended directed graph representation of tree shift of finite type tsft we show that the cpc irreducibility of tsfts is related to the connectivity of its graph representation which is a similar result to one dimensional shifts of finite type

computing the hausdorff dimension of subshifts using matrices abstract on a subshift of finite type sft we introduce a pseudometric d given by a nonnegative matrix b satisfying the cycle condition we show that the hausdorff dimension of this sft with respect to d is given by the mauldin williams formula if the ratio of the logarithms of any two nonzero entries of b is rational we show that this hausdorff dimension can be expressed essentially in terms of the logarithm of the spectral radius of a certain digraph we apply our results to the hausdorff dimension of the limit set of finitely generated free groups of isometrics of infinite trees to each finitely generated subgroup g of a given finitely generated free group f we attach an invariant p g which gives the rate of growth of all words g of length l at most with respect to a fixed set of minimal generators of f we show that p g is the spectral radius of a digraph g induced by g then h g f p g p h moreover p g p h g h

representation and poly time approximation for pressure of mathbb z 2 lattice models in the non uniqueness region we develop a new pressure representation theorem for nearest neighbour gibbs interactions and apply this to obtain the existence of efficient algorithms for approximating the pressure in the 2 dimensional ferromagnetic potts multi type widom rowlinson and hard core models for potts model our results apply to every inverse temperature but the critical for widom rowlinson and hard core models they apply to certain subsets of both the subcritical and supercritical regions the main novelty of our work is in the latter

design and analysis of supervised and decision directed estimators of the mmse lcmv filter in data limited environments we consider sample matrix inversion smi type estimates of the minimum mean square error mmse and the linearly constrained minimum variance lcmv linear filters obtained from data records of limited size we quantify theoretically the detrimental effect of the desired signal energy level on the mean square ms filter estimation error and the normalized output signal to interference plus noise ratio sinr by deriving a new exact analytical expression and a lower bound respectively for cases where accumulation of pure disturbance observations is not possible we show theoretically how certain intuitive pilot assisted and decision directed adaptive filter implementations that utilize desired signal present data observations perform close to their desired signal absent counterparts simulation studies illustrate our theoretical developments in the context of spread spectrum communications over multipath fading channels under perfect and nonperfect synchronization

c algebras and fell bundles associated to a textile system abstract the notion of textile system was introduced by m nasu in order to analyze endomorphisms and automorphisms of topological markov shifts a textile system is given by two finite directed graphs g and h and two morphisms p q g h with some extra properties it turns out that a textile system determines a first quadrant two dimensional shift of finite type via a collection of wang tiles and conversely any such shift is conjugate to a textile shift in the case the morphisms p and q have the path lifting property we prove that they induce groupoid morphisms g h between the corresponding etale groupoids of g and h we define two families a m n and a m n of c algebras associated to a textile shift and compute them in specific cases these are graph algebras associated to some one dimensional shifts of finite type constructed from the textile shift under extra hypotheses we also define two families of fell bundles which encode the complexity of these two dimensional shifts we consider several classes of examples of textile shifts including the full shift the golden mean shift and shifts associated to rank two graphs

a characterization of the entropies of multidimensional shifts of finite type we show that the values of entropies of multidimensional shifts of finite type sfts are characterized by a certain computation theoretic property a real number h 0 is the entropy of such an sft if and only if it is right recursively enumerable i e there is a computable sequence of rational numbers converging to h from above the same characterization holds for the entropies of sofic shifts on the other hand the entropy of strongly irreducible sfts is computable

adaptive convergence of linearly constrained beamformers based on the sample covariance matrix a statistical analysis of the adaptive convergence behavior of linearly constrained beamformers is given assuming the sample covariance estimator is used to estimate the covariance matrix the sensor data are assumed to be gaussian distributed and independent from data vector to data vector the output power and mean squared error in the absence of the desired signal are shown to be multiples of chi squared random variables the presence of the desired signal results in an excess mean squared error that is beta distributed and depends only on the signal power number of data vectors and number of adaptive degrees of freedom the expected value of the excess mean squared error resulting from the signal presence is directly proportional to the signal power and number of adaptive degrees of freedom but is inversely proportional to the number of data vectors

derivations for a class of matrix function algebras abstract we study a class of matrix function algebras here denoted t c n we introduce a notion of point derivations and classify the point derivations for certain finite dimensional representations of t c n we use point derivations and information about n n matrices to show that every t c n valued derivation on t c n is inner

mixing properties of tree shifts the uncertainty of multidimensional shift spaces draws attracted attention of researchers for example the emptiness problem is undecidable there exist aperiodic shifts of finite type there is a nonempty shift of finite type exhibiting nonextensible local patterns this paper investigates symbolic dynamics on cayley trees and gives affirmative answers to the above questions in tree shifts beyond that with introducing block gluing tree shift a sufficient condition of exhibiting positive topological entropy is revealed