on the haar measure of the quantumsu n group we prove that the haar state associated to the compact matrix quantum groupsu n is faithful for 1 1 0 and anyn 2

optimal shadowing and noise reduction abstract the shadowing problem is that of finding a deterministic orbit as close as possible to a given noisy orbit we present an optimal solution to this problem in the sense of least mean squares which also provides an effective and convenient numerical method for noise reduction for data generated by a dynamical system given a noisy orbit y and a dynamical system we derive a set of nonlinear equations whose solution x is the deterministic orbit with the smallest possible euclidean distance to y we present a numerical method for solving these equations the quality of the solution depends on the initial noise level when is known exactly the noise can be reduced to machine precision over long trajectory segments with higher noise levels there are regions where the algorithm has difficulty but significant overall noise reductions are still achieved if must be learned from the data the noise reduction is limited by the accuracy of the learning algorithm and the number of available data points but large reductions are still possible in some cases

on consistent nonparametric order determination and chaos summary we give a brief introduction to deterministic chaos and a link between chaotic deterministic models and stochastic time series models we argue that it is often natural to determine the embedding dimension in a noisy environment first in any systematic study of chaos setting the stochastic models within the framework of non linear autoregression we introduce the notion of a generalized partial autocorrelation and an order we approach the estimation of the embedding dimension via order determination of an unknown non linear autoregression by cross validation and give justification by proving its consistency under global boundedness as a by product we provide a theoretical justification of the final prediction error approach of auestad and tj0stheim some illustrations based on the henon map and several real data sets are given the bias of the residual sum of squares as essentially a noise variance estimator is quantified

amenable groups and stabilizers of measures on the boundary of a hadamard manifold let x be a symmetric space of noncompact type or more generally a hadamard manifold i e a complete simply connected riemannian manifold of nonpositive sectional curvature we consider a finite positive borel measure on the ideal boundary x see sect 2 for the definitions let g be the isometry group of x and g the subgroup which stabilizes the measure in the case of a symmetric space we obtain the following result

on the stability of static poisson networks under random access we investigate the stable packet arrival rate region of a discrete time slotted random access network where the sources are distributed as a poisson point process each of the sources in the network has a destination at a given distance and a buffer of infinite capacity the network is assumed to be random but static i e the sources and the destinations are placed randomly and remain static during all the time slots we employ tools from queueing theory as well as point process theory to study the stability of this system using the concept of dominance the problem is an instance of the interacting queues problem further complicated by the poisson spatial distribution we obtain sufficient conditions and necessary conditions for stability numerical results show that the gap between the sufficient conditions and the necessary conditions is small when the access probability the density of transmitters or the sinr threshold is small the results also reveal that a slight change of the arrival rate may greatly affect the fraction of unstable queues in the network

a dynamic regularized radial basis function network for nonlinear nonstationary time series prediction in this paper constructive approximation theorems are given which show that under certain conditions the standard nadaraya watson 1964 regression estimate nwre can be considered a specially regularized form of radial basis function networks rbfns from this and another related result we deduce that regularized rbfns are m s consistent like the nwre for the one step ahead prediction of markovian nonstationary nonlinear autoregressive time series generated by an i i d noise processes additionally choosing the regularization parameter to be asymptotically optimal gives regularized rbfns the advantage of asymptotically realizing minimum m s prediction error two update algorithms one with augmented networks infinite memory and the other with fixed size networks finite memory are then proposed to deal with nonstationarity induced by time varying regression functions for the latter algorithm tests on several phonetically balanced male and female speech samples show an average 2 2 db improvement in the predicted signal noise error ratio over corresponding adaptive linear predictors using the exponentially weighted rls algorithm further rls filtering of the predictions from an ensemble of three such rbfns combined with the usual autoregressive inputs increases the improvement to 4 2 db on average over the linear predictors

free products of compact quantum groups we construct and study compact quantum groups from free products ofc algebras in this connection we discover two mysterious classes of natural compact quantum groups a u m anda o m thea u m s respectivelya o m s are non isomorphic to each other for differentm s and are not obtainable by the ordinary quantization method we also clarify some basic concepts in the theory of compact quantum groups

detecting nonlinear dynamics in spatio temporal systems examples from ecological models mathematical models of marine populations exhibit chaotic dynamics however we hypothesize that in moving water eulerian sampling of spatially heterogeneous populations may obscure any deterministic signal beyond the resolving capabilities of presently available nonlinear signal processing techniques to examine this hypothesis we created two spatio temporal models of population dynamics to caricature actual ocean sampling limitations we sampled the model output in two ways random walks to simulate eulerian sampling and spatial averages to simulate population measurements from finite volumes results indicate that the ability to identify underlying nonlinear dynamics quickly degrades as the step size of a random walk sampling increases on the other hand the analysis techniques used are more robust in the face of spatial averaging

van kampen s embedding obstruction for discrete groups we give a lower bound to the dimension of a contractible mani fold on which a given group can act properly discontinuously in particular we show that the n fold product of nonabelian free groups cannot act prop erly discontinuously on r 2n 1

compact quantum ergodic systems we develop theory of multiplicity maps for compact quantum groups as an application we obtain a complete classification of right coideal c algebras of c suq 2 for q 1 1 0 they are labeled with dynkin diagrams but classification results for positive and negative cases of q are different many of the coideals are quantum spheres or quotient spaces by quantum subgroups but we do have other ones in our classification list

tannaka krein duality for compact matrix pseudogroups twisted su n groups the notion of concrete monoidalw category is introduced and investigated a generalization of the tannaka krein duality theorem is proved it leads to new examples of compact matrix pseudogroups among them we have twistedsu n groups denoted bys u n it is shown that the representation theory fors u n is similar to that ofsu n irreducible representations are labeled by young diagrams and formulae for dimensions and multiplicity are the same as in the classical case

frasa feedback retransmission approximation for the stability region of finite user slotted aloha feedback retransmission approximation for slotted aloha frasa is proposed to study the stability region of finite user slotted aloha under the collision channel with frasa the stability region is derived in closed form for any number of users in the system the result derived from frasa is shown to be identical to the analytical result of finite user slotted aloha when there are two users it is shown that the stability region obtained from frasa is a good approximation to the stability region of finite user slotted aloha the convex hull bound which is convex piecewise linear and outer bounds the stability region of frasa is provided p convexity an essential property that the stability region of frasa should have to ensure the convex hull bound is close to the boundary is characterized from these it is derived that the stability region of frasa can never be convex when there are more than two users a separate convex and piecewise linear inner bound on the stability region of frasa the supporting hyperplane bound is also given

how far are automatically chosen regression smoothing parameters from their optimum abstract we address the problem of smoothing parameter selection for nonparametric curve estimators in the specific context of kernel regression estimation call the optimal bandwidth the minimizer of the average squared error we consider several automatically selected bandwidths that approximate the optimum how far are the automatically selected bandwidths from the optimum the answer is studied theoretically and through simulations the theoretical results include a central limit theorem that quantifies the convergence rate and gives the differences asymptotic distribution the convergence rate turns out to be excruciatingly slow this is not too disappointing because this rate is of the same order as the convergence rate of the difference between the minimizers of the average squared error and the mean average squared error in some simulations by john rice the selectors considered here performed quite differently from each other we anticipated that these differences would be reflected in differ

the number of packets transmitted by collision detect random access schemes on considere le cas ou la seule information que la station possede sur les autres stations ou sur l utilisation du canal est l historique de ses propres essais de transmission

analysis of backoff protocols for mulitiple accesschannels in this paper we analyze the stochastic behavior of backoff protocols for multiple access channels such as the ethernet in particular we prove that binary exponential backoff is unstable if the arrival rate of new messages at each station is lam n for any lam 1 over 2 and the number of stations n is sufficiently large for small n we prove that lam geq lam 0 1 over 4n 2 implies instability where lam 0 approx 567 more importantly we also prove that any superlinear polynomial backoff protocol e g quadratic backoff is stable for any set of arrival rates that sum to less than one and any number of stations the results significantly extend the previous work in the area and provide the first examples of acknowledgment based protocols known to be stable for a nonnegligible overall arrival rate distributed over an arbitrarily large number of stations the results also disprove a popular assumption that exponential backoff is the best choice among acknowledgment based protocols for systems with large overall arrival rates finally we prove that any linear or sublinear backoff protocol is unstable if the arrival rate at each station is lambda over n for any fixed lambda and sufficiently large n

the asymptotic distribution of nonparametric estimates of the lyapunov exponent for stochastic time series this paper derives the asymptotic distribution of a smoothing based estimator of the lyapunov exponent for a stochastic time series under two general scenarios in the first case we are able to establish root t consistency and asymptotic normality while in the second case which is more relevant for chaotic processes we are only able to establish asymptotic normality at a slower rate of convergence we provide consistent confidence intervals for both cases we apply our procedures to simulated data

asymptotic stability region of slotted aloha we analyze the stability of standard buffered slotted aloha systems specifically we consider a set of n users each equipped with an infinite buffer packets arrive into user i s buffer according to some stationary ergodic markovian process of intensity lambda i at the beginning of each slot if user i has packets in its buffer it attempts to transmit a packet with fixed probability p i over a shared resource channel the transmission is successful only when no other user attempts to use the channel the stability of such systems has been open since their very first analysis in 1979 by tsybakov and mikhailov in this paper we propose an approximate stability condition that is provably exact when the number of users n grows large we provide theoretical evidence and numerical experiments to explain why the proposed approximate stability condition is extremely accurate even for systems with a restricted number of users even two or three

embeddings in finitely presented groups which preserve the center abstract v n remeslennikov proposed in 1976 the following problem is any countable abelian group a subgroup of the center of some finitely presented group we prove that every finitely generated recursively presented group g is embeddable in a finitely presented group k such that the center of g coincide with that of k we prove also that there exists a finitely presented group h with soluble word problem such that every countable abelian group is embeddable in the center of h this gives a strong positive answer to the question raised by v n remeslennikov

on u statistics and v mise statistics for weakly dependent processes some probabilistic limit theorems for hoeffding s u statistic 13 and v mises functional are established when the underlying processes are not necessarily independent we consider absolutely regular processes 24 and processes x n n 1 which are uniformly mixing 14 as well as their time reversal x n n 1 called uniformly mixing in both directions of time many authors have weakened the hypothesis of independence in statistical limit theorems and considered m dependent markov or weakly dependent processes in particular for u statistics under weak dependence sen 22 has considered mixing processes and derived a central limit theorem and a law of the iterated logarithm while yoshihara 26 proved central limit theorems and a s results in the absolutely regular and uniformly mixing case here we extend these results considerably and prove central limit theorems and their rate of convergence in the prohorov metric and a berry esseen type theorem functional central limit theorems and a s approximation by a brownian motion extensions to multisample versions and other extensions are briefly discussed

convexity of the nonachievable rate region for the collision channel without feedback it is shown that the set of nonachievable rates for the collision channel without feedback is convex as had been conjectured by massey

nonparametric identification of nonlinear time series selecting significant lags abstract in this article we suggest a nonparametric procedure for selecting significant lags in the model description of a general nonlinear stationary time series the procedure can be applied to both the conditional mean and the conditional variance and is valid for heteroscedastic series the procedure is illustrated by simulations and sunspot data lynx data and blowfly data are analyzed it is indicated that projectors can be used in conjunction with the procedure for selecting significant lags to check the adequacy of an additive time series model

stability conditions for multidimensional queueing systems with computer applications a fundamental question arising in the analysis of queueing systems is whether a system is stable or unstable for systems modeled by infinite markov chains we may study the ergodicity and nonergodicity of the chains foster showed that sufficient conditions for ergodicity are linked with the average drift however complications arise when multidimensional markov chains are analyzed we present three methods that provide sufficient conditions for ergodicity and nonergodicity of a multidimensional markov chain these methods are next applied to two multidimensional queueing systems buffered contention packet broadcast systems and coupled processor systems

an extension of path coupling and its application to the glauber dynamics for graph colorings a new method for analyzing the mixing time of markov chains is described this method is an extension of path coupling and involves analyzing the coupling over multiple steps the expected behavior of the coupling at a certain stopping time is used to bound the expected behavior of the coupling after a fixed number of steps the new method is applied to analyze the mixing time of the glauber dynamics for graph colorings we show that the glauber dynamics has o n log n mixing time for triangle free delta regular graphs if k colors are used where k geq 2 eta delta for some small positive constant eta this is the first proof of an optimal upper bound for the mixing time of the glauber dynamics for some values of k in the range k leq 2 delta

stability of multiple access network control schemes with carrier sensing and exponential backoff abstract a new approach to determine the stability of multiple access network control schemes is presented a busy network the precise meaning of the term busy will be presented in the text is modelled as a switched single server hybrid dynamical system whose switching laws are stochastic and are based on typical multiple access network control protocols such as aloha and ethernet the techniques are used to compute the critical ratio of traffic production per network node to total available bandwidth that ensures that data packets will not accumulate unboundedly in waiting queues at each node this is a measure of stability of the network and is an emergent global property determined by decentralized autonomous behavior of each node the behavior of each individual node is regarded as microscopic and the collective behavior of the network as a whole are emergent consequences of such microscopic laws the results follow from the stationary distribution property of ergodic markov chains

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

simple compact quantum groups i the notion of simple compact quantum group is introduced as non trivial noncommutative and noncocommutative examples the following families of compact quantum groups are shown to be simple a the universal quantum groups bu q for q gl n c satisfying qq in n 2 b the quantum automorphism groups aaut b of finite dimensional c algebras b endowed with the canonical trace when dim b 4 including the quantum permutation groups aaut xn on n points n 4 c the standard deformations kq of simple compact lie groups k and their twists kqu as well as rieffel s deformation kj

a consistent characteristic function based test for conditional independence abstract y is conditionally independent of z given x if pr f y x z f y x 1 for all y on its support where f denotes the conditional density of y given x z or x this paper proposes a nonparametric test of conditional independence based on the notion that two conditional distributions are equal if and only if the corresponding conditional characteristic functions are equal we extend the test of su and white 2005 a hellinger metric nonparametric test for conditional independence discussion paper department of economics ucsd in two directions 1 our test is less sensitive to the choice of bandwidth sequences 2 our test has power against deviations on the full support of the density of x y z we establish asymptotic normality for our test statistic under weak data dependence conditions simulation results suggest that the test is well behaved in finite samples applications to stock market data indicate that our test can reveal some interesting nonlinear dependence that a traditional linear granger causality test fails to detect

application of a least absolute shrinkage and selection operator to aeroelastic flight test data identification of non linear systems involves estimating unknown parameters and model regressor selection selection of a subset of candidate terms that best describes the observed output model selection is an important step in black box modelling of any observed process this procedure is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design in this study a least absolute shrinkage and selection operator lasso technique is investigated for computing efficient model descriptions of non linear aeroelastic systems the lasso minimises the residual sum of squares by the addition of an l1 penalty term on the parameter vector of the traditional l2 minimisation problem its use for model selection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and the

quantum symmetry groups of finite spaces we determine the quantum automorphism groups of finite spaces these are compact matrix quantum groups in the sense of woronowicz

analysis of a multiaccess control scheme we consider a multiaccess channel under the infinite source model and ternary feedback we consider a recently proposed scheme for the decentralized control of transmissions through the channel and we prove that it is stable as long as the rate of generation of new packets is smaller than e 1

properties of an aloha like stability region a well known inner bound on the stability region of the finite user slotted aloha protocol is the set of all arrival rates for which there exists some choice of the contention probabilities such that the associated worst case service rate for each user exceeds the user s arrival rate denoted lambda although testing membership in lambda of a given arrival rate can be posed as a convex program it is nonetheless of interest to understand the properties of this set in this paper we develop new results of this nature including 1 an equivalence between membership in lambda and the existence of a positive root of a given polynomial 2 a method to construct a vector of contention probabilities to stabilize any stabilizable arrival rate vector 3 the volume of lambda 4 explicit polyhedral spherical and ellipsoid inner and outer bounds on lambda and 5 characterization of the generalized convexity properties of a natural excess rate function associated with lambda including the convexity of the set of contention probabilities that stabilize a given arrival rate vector

connected components of compact matrix quantum groups and finiteness conditions abstract we introduce the notion of identity component of a compact quantum group and that of total disconnectedness as a drawback of the generalized burnside problem we note that totally disconnected compact matrix quantum groups may fail to be profinite we consider the problem of constructing the identity component by introducing canonical approximating transfinite sequences of subgroups these sequences have lengths 1 in the classical case but can be countably infinite for duals of discrete groups we give examples of free product quantum groups where the identity component is not normal and the associated sequence has length 1 we give necessary and sufficient conditions for normality of the identity component in the sense of wang and finiteness or profiniteness of the quantum component group among them we introduce an ascending chain condition on the representation ring called lie property which characterizes lie groups in the classical case and reduces to group noetherianity of the discrete group dual in the cocommutative case it is weaker than ring noetherianity but ensures existence of a generating representation the lie property and ring noetherianity are inherited by quotient quantum groups we show that a u f is not of lie type we discuss an example arising from the compact real form of u q sl 2 for q 0

the dimension of chaotic attractors dimension is perhaps the most basic property of an attractor in this paper we discuss a variety of different definitions of dimension compute their values for a typical example and review previous work on the dimension of chaotic attractors the relevant definitions of dimension are of two general types those that depend only on metric properties and those that depend on the frequency with which a typical trajectory visits different regions of the attractor both our example and the previous work that we review support the conclusion that all of the frequency dependent dimensions take on the same value which we call the dimension of the natural measure and all of the metric dimensions take on a common value which we call the fractal dimension furthermore the dimension of the natural measure is typically equal to the lyapunov dimension which is defined in terms of lyapunov numbers and thus is usually far easier to calculate than any other definition because it is computable and more physically relevant we feel that the dimension of the natural measure is more important than the fractal dimension

memory universal prediction of stationary random processes we consider the problem of one step ahead prediction of a real valued stationary strongly mixing random process xi sub i spl infin sup spl infin the best mean square predictor of x sub 0 is its conditional mean given the entire infinite past x sub i sub i spl infin sup 1 given a sequence of observations x sub 1 x sub 2 x sub n we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasing dimension for example neural networks and legendre polynomials the proposed estimators select both the model memory and the model dimension in a data driven fashion by minimizing certain complexity regularized least squares criteria when the underlying predictor function has a finite memory we establish that the proposed estimators are memory universal the proposed estimators which do not know the true memory deliver the same statistical performance rates of integrated mean squared error as that delivered by estimators that know the true memory furthermore when the underlying predictor function does not have a finite memory we establish that the estimator based on legendre polynomials is consistent

a locally compact quantum group analogue of the normalizer of su 1 1 in sl 2 c s l woronowicz proved in 1991 that quantum su 1 1 does not exist as a locally compact quantum group results by l i korogodsky in 1994 and more recently by woronowicz gave strong indications that the normalizer of su 1 1 in sl 2 is a much better quantization candidate than su 1 1 itself in this paper we show that this is indeed the case by constructing a new example of a unimodular locally compact quantum group depending on a parameter 0 q 1 that is a deformation of after defining the underlying von neumann algebra of we use a certain class of q hypergeometric functions and their orthogonality relations to construct the comultiplication the coassociativity of this comultiplication is the hardest result to establish we define the haar weight and obtain simple formulas for the antipode and its polar decomposition as a final result we produce the underlying c algebra of the proofs of all these results depend on various properties of q hypergeometric 1 1 functions

equivalent notions of normal quantum subgroups compact quantum groups with properties f and fd and other applications abstract the notion of normal quantum subgroup introduced in algebraic context by parshall and wang when applied to compact quantum groups is shown to be equivalent to the notion of normal quantum subgroup introduced by the author as applications a quantum analog of the third fundamental isomorphism theorem for groups is obtained which is used along with the equivalence theorem to obtain results on structure of quantum groups with property f and quantum groups with property fd other results on normal quantum subgroups for tensor products free products and crossed products are also proved

identification of nonlinear time series first order characterization and order determination summary we study the possibility of identifying nonlinear time series using nonparametric estimates of the conditional mean and conditional variance it is shown that most nonlinear models satisfy the assumptions needed to apply nonparametric asymptotic theory sampling variations of the conditional quantities are studied by simulation and explained by asymptotic arguments for a number of first order nonlinear autoregressive processes the conditional mean and variance can be used for identification purposes but one must be aware of bias and misspecification effects we also propose a criterion for determining the order of a general nonlinear model the criterion is justified in parts by heuristics but encouraging results are obtained from a limited set of simulation experiments several

4 dimensional locally cat 0 manifolds with no riemannian smoothings we construct examples of 4 dimensional manifolds m supporting a locally cat 0 metric whose universal covers q m satisfy hruska s isolated flats condition and contain 2 dimensional flats f with the property that 1f s s s s 1 q m are nontrivial knots as a consequence we obtain that the group 1 m cannot be isomorphic to the fundamental group of any compact riemannian manifold of nonpositive sectional curvature in particular if k is any compact locally cat 0 manifold then m k is a locally cat 0 manifold which does not support any riemannian metric of nonpositive sectional curvature

the stability region of the finite user slotted aloha protocol a version of the discrete time slotted aloha protocol operating with finitely many buffered terminals is considered the stability region is defined to be the set of vectors of arrival rates lambda lambda sub 1 lambda sub m for which there exists a vector of transmission probabilities such that the system is stable it is assumed that arrivals are independent from slot to slot and the following model for the arrival distribution in a slot is assumed the total number of arrivals in any slots is geometrically distributed with the probability that such an arrival is at node i being lambda sub i times sigma sub k lambda sub k sup 1 independent of the others with this arrival model it is proven that the closure of the stability region of the protocol is the same as the closure of the shannon capacity region of the collision channel without feedback as determined by j l massey and p mathys 1985 at present it is not clear if this result depends on the choice of arrival distribution the basic probabilistic observation is that the stationary distribution and certain conditional distributions derived from it have positive correlations for bounded increasing functions

at infinity of finite dimensional cat 0 spaces we show that any filtering family of closed convex subsets of a finite dimensional cat 0 space x has a non empty intersection in the visual bordification x over bar x boolean or partial derivative x using this fact several results known for proper cat 0 spaces may be extended to finite dimensional spaces including the existence of canonical fixed points at infinity for parabolic isometries algebraic and geometric restrictions on amenable group actions and geometric superrigidity for non elementary actions of irreducible uniform lattices in products of locally compact groups

symmetries of quantum spaces subgroups and quotient spaces of quantum su 2 and so 3 groups we prove that each action of a compact matrix quantum group on a compact quantum space can be decomposed into irreducible representations of the group we give the formula for the corresponding multiplicities in the case of the quotient quantum spaces we describe the subgroups and the quotient spaces of quantumsu 2 andso 3 groups

on the stability of finite queue slotted aloha protocol we revisit the stability analysis of the well known slotted aloha protocol with a finite number of queues under standard modeling assumptions we derive a sufficient condition for the stability by applying a positive recurrence criterion due to rosberg jap vol 17 no 3 1980 our sufficiency condition for stability is linear in arrival rates and does not require knowledge of the stationary joint statistics of queue lengths as has been the case in previous results we also derive some sufficient conditions for instability of the protocol we believe that the technique reported here could be useful in analyzing other stability problems in countable space markovian settings

the double of a hyperbolic manifold and non positively curved exotic pl structures we give examples of non compact finite volume real hyperbolic manifolds of dimension greater than five such that their doubles admit at least three non equivalent smoothable pl structures two of which admit a riemannian metric of non positive curvature while the third does not we also prove that the doubles of non compact finite volume real hyperbolic manifolds of dimension greater than four are differentiably rigid

liberation of orthogonal lie groups abstract we show that under suitable assumptions we have a one to one correspondence between classical groups and free quantum groups in the compact orthogonal case we classify the groups under correspondence with the result that there are exactly 6 of them o n s n h n b n s n b n we investigate the representation theory aspects of the correspondence with the result that for o n s n h n b n this is compatible with the bercovici pata bijection finally we discuss some more general classification problems in the compact orthogonal case notably with the construction of a new quantum group

filtered monte carlo by a filtered monte carlo estimator we mean one whose constituent parts summands or integral increments are conditioned on an increasing family of fields unbiased estimators of this type are suggested by compensator identities replacing a point process integrator with its intensity gives rise to one class of examples exploiting levy s formula gives rise to another we establish variance inequalities complementing compensator identities among estimators that are stieltjes stochastic integrals we show that filtering reduces variance if the integrand and the increments of the integrator have conditional positive correlation we also provide more primitive hypotheses that ensure this condition making use of stochastic monotonicity properties our most detailed conditions apply in a markov setting where monotone up down and convex generators play a central role we give examples as an application of our results we compare certain estimators that do and do not exploit the property that poisson arr

random walk or chaos a formal test on the lyapunov exponent abstract a formal test on the lyapunov exponent is developed to distinguish a random walk model from a chaotic system which is based on the nadaraya watson kernel estimator of the lyapunov exponent the asymptotic null distribution of our test statistic is free of nuisance parameter and simply given by the range of standard brownian motion on the unit interval the test is consistent against the chaotic alternatives a simulation study shows that the test performs reasonably well in finite samples we apply our test to some of the standard macro and financial time series finding no significant empirical evidence of chaos

regularized local linear prediction of chaotic time series abstract local linear prediction based on the ordinary least squares ols approach is one of several methods that have been applied to prediction of chaotic time series apart from potential linearization errors a drawback of this approach is the high variance of the predictions under certain conditions here a different set of so called linear regularization techniques originally derived to solve ill posed regression problems are compared to ols for chaotic time series corrupted by additive measurement noise these methods reduce the variance compared to ols but introduce more bias a main tool of analysis is the singular value decomposition svd and a key to successful regularization is to damp the higher order svd components several of the methods achieve improved prediction compared to ols for synthetic noise corrupted data from well known chaotic systems similar results were found for real world data from the r r intervals of ecg signals good results are also obtained for real sunspot data compared to published predictions using nonlinear techniques

percentage points of likelihood ratio tests for threshold autoregression summary likelihood ratio tests for threshold autoregression have been considered by chan and chan and tong however except for the simplest case percentage points of the asymptotic null distribution of the test statistic have not been tabulated the purpose of this paper is to tabulate the approximate upper percentage points for the general case this is done via the poisson clumping heuristic developed by aldous monte carlo experiments show that the approximation is quite good as an illustration the test is then applied to two data sets

nonparametric identification of nonlinear time series projections abstract we study the possibility of identifying general linear and nonlinear time series models using nonparametric methods the kernel estimators of the conditional mean and variance are used as a basis and the properties of these quantities as model indicators are briefly discussed some drawbacks are pointed out and motivated by these we introduce projections as tools of identification the projections are especially useful for additive modeling expressions for the asymptotic bias and variance are obtained the projection of the conditional variance is suggested as a tool for identifying heteroscedastic time series the results are illustrated by simulations for both the estimators of the projections and the estimators of the conditional mean and variance

a duality theorem for ergodic actions of compact quantum groups on c algebras the spectral functor of an ergodic action of a compact quantum group g on a unital c algebra is quasitensor in the sense that the tensor product of two spectral subspaces is isometrically contained in the spectral subspace of the tensor product representation and the inclusion maps satisfy natural properties we show that any quasitensor functor from rep g to the category of hilbert spaces is the spectral functor of an ergodic action of g on a unital c algebra

kazhdan quotients of golod shafarevich groups the main goal of this paper is to prove that every golod shafarevich group has an infinite quotient with kazhdan s property t in particular this gives an affirmative answer to the well known question about non amenability of golod shafarevich groups

closed quantum subgroups of locally compact quantum groups abstract we investigate the fundamental concept of a closed quantum subgroup of a locally compact quantum group two definitions one due to s vaes and one due to s l woronowicz are analyzed and relations between them discussed among many reformulations we prove that the former definition can be phrased in terms of quasi equivalence of representations of quantum groups while the latter can be related to an old definition of podle from the theory of compact quantum groups the cases of classical groups duals of classical groups compact and discrete quantum groups are singled out and equivalence of the two definitions is proved in the relevant context a deep relationship with the quantum group generalization of the herz restriction theorem from classical harmonic analysis is also established in particular in the course of our analysis we give a new proof of the herz restriction theorem

reconstructions and predictions of nonlinear dynamical systems a hierarchical bayesian approach an attempt is made to reconstruct model nonlinear dynamical systems from scalar time series data via a hierarchical bayesian framework reconstruction is performed by fitting given training data with a parameterized family of functions without overfitting the reconstructed model dynamical systems are compared with respect to approximated model marginal likelihood which is a natural bayesian information criterion the best model is selected with respect to this criterion and is utilized to make predictions the results are applied to two problems i chaotic time series prediction and ii building air conditioning load prediction the former is a very good class of problems for checking the abilities of prediction algorithms for at least two reasons first since no linear dynamical systems can admit chaotic behavior an algorithm must capture the nonlinearities behind the time series second chaotic dynamical systems are sensitive to initial conditions more precisely the error grows exponentially with respect to time so that crispness of capturing nonlinearities is also important experimental results appear to indicate that the proposed scheme can capture difficult nonlinearities behind the chaotic time series data the latter class of problems air conditioning load prediction is motivated by a great amount of demand for reducing co sub 2 emissions associated with electric power generation the authors won a prediction competition using the proposed algorithm therefore it appears to be reasonably sound

network control by bayesian broadcast a transmission control strategy is described for slotted aloha type broadcast channels with ternary feedback at each time slot each station estimates the probability that n stations are ready to transmit a packet for each n using bayes rule and the observed history of collisions successful transmissions and holes empty slots a station transmits a packet in a probabilistic manner based on these estimates this strategy is called bayesian broadcast an elegant and very practical strategy pseudo bayesian broadcast is then derived by approximating the probability estimates with a poisson distribution with mean nu and further simplifying each station keeps a copy of nu transmits a packet with probability 1 nu and then updates nu in two steps for collisions increment nu by e 2 l 1 39221 cdots for successes and holes decrement nu by 1 set nu to max nu hat lambda 1 where hat lambda is an estimate of the arrival rate lambda of new packets into the system simulation results are presented showing that pseudo bayesian broadcast performs well in practice and methods that can be used to prove that certain versions of pseudo bayesian broadcast are stable for lambda are discussed

miscellanea a note on tests for nonlinearity in a vector time series a multivariate extension of the univariate nonlinearity test of tsay 1986 is presented simulation results show that the multivariate test is more powerful than its univariate counterpart especially for series having nonlinear structure involving several components of the vector process and weakly or moderately cross correlated process error terms for illustration the test is applied to a set of seasonally adjusted quarterly capital expenditures and appropriations in u s manufacturing and a vector nonlinear model for the data is constructed

a bound on the capacity of backoff and acknowledgment based protocols we study contention resolution protocols for multiple access channels we show that every backoff protocol is transient if the arrival rate lambda is at least 0 42 and that the capacity of every backoff protocol is at most 0 42 thus we show that backoff protocols have provably smaller capacity than full sensing protocols finally we show that the corresponding results with the larger arrival bound of 0 531 also hold for every acknowledgment based protocol

ergodic actions of universal quantum groups on operator algebras we construct ergodic actions of compact quantum groups on c algebras and von neumann algebras and exhibit phenomena of such actions that are of different nature from ergodic actions of compact groups

proper actions of lattices on contractible manifolds every lattice in a connected semi simple lie group g acts properly discontinuously by isometries on the contractible manifold g k k a maximal compact subgroup of g we prove that if acts on a contractible manifold w and if either 1 the action is properly discontinuous or 2 w is equipped with a complete riemannian metric the action is by isometries and with unbounded orbits g is simple with finite center and rank 1 then dimw dimg k

semiparametric non linear time series model selection summary semiparametric time series regression is often used without checking its suitability resulting in an unnecessarily complicated model in practice one may encounter computational difficulties caused by the curse of dimensionality the paper suggests that to provide more precise predictions we need to choose the most significant regressors for both the parametric and the nonparametric time series components we develop a novel cross validation based model selection procedure for the simultaneous choice of both the parametric and the nonparametric time series components and we establish some asymptotic properties of the model selection procedure proposed in addition we demonstrate how to implement it by using both simulated and real examples our empirical studies show that the procedure works well

an open collar theorem for 4 manifolds let m 4 be an open 4 manifold with boundary conditions are given under which m 4 is homeomorphic to m 0 1 applications include a 4 dimensional weak h cobordism theorem and a classification of weakly flat embeddings of 2 spheres in s 4 specific examples of n 2 spheres embedded in s n including n 4 are also discussed

a new approach to fuzzy modeling of nonlinear dynamic systems with noise relevance vector learning mechanism this paper presents a new fuzzy inference system for modeling of nonlinear dynamic systems based on input and output data with measurement noise the proposed fuzzy system has a number of fuzzy rules and parameter values of membership functions which are automatically generated using the extended relevance vector machine rvm the rvm has a probabilistic bayesian learning framework and has good generalization capability the rvm consists of the sum of product of weight and kernel function which projects input space into high dimensional feature space the structure of proposed fuzzy system is same as that of the takagi sugeno fuzzy model however in the proposed method the number of fuzzy rules can be reduced under the process of optimizing a marginal likelihood by adjusting parameter values of kernel functions using the gradient ascent method after a fuzzy system is determined coefficients in consequent part are found by the least square method examples illustrate effectiveness of the proposed new fuzzy inference system