finite word length effects of pipelined recursive digital filters scattered look ahead sla pipelining is a new iir filter structure that can achieve very high throughput regardless of multiplier latency however the numerical properties of sla have been largely unexplored the authors analyze the finite word length fwl performance of sla filters under fixed point arithmetic to support this analysis two new state variable descriptions svd are introduced first a state variable based description especially suited for analysis of certain sla structures called the sectioned k and w description skwd is defined by sectioning the noise contributions of the nonrecursive nodes second a noncanonic state variable description ncsvd is introduced which explicitly includes the pipelined delay variables in the state space roundoff noise ron and statistical coefficient quantization noise scqn are derived under an independent pseudonoise source model scqn is shown to be interpretable as ron under the single length accumulation model which enables the unification of ron and scqn analysis analytic closed form solutions for first and second order direct form df sla filters are derived and compared to results from sla minimum roundoff noise mron structures the sla structures are all found to have generally good numerical properties except that the df sla structure performs poorly in certain regions near the unit circle however the df sla structure actually performs better than the mron form over much of the unit disk at a far smaller implementation cost

floating point arithmetic and digital filters the roundoff noise properties of floating point digital filters are examined to make the analysis tractable a high level model to deal with the errors in the inner product operation is developed this model establishes a broad connection between coefficient sensitivity and roundoff noise along with the model an efficient procedure to keep track of the addition scheme used in the inner product and to compute the statistics of the errors is introduced a systematic procedure based on the model is then developed to derive general expressions for the roundoff noise of fir direct form iir and state space filters the expressions in the context of state space filters are explored in some detail optimality issues are considered and it is shown that when double precision accumulation is used the optimal filters are similar in nature to those derived in the context of fixed point arithmetic with the essential difference that they also do depend on the spectrum of the input signal optimality with respect to addition schemes and second order filters are also examined in some detail

a unified approach to the optimal synthesis of fixed point state space digital filters this paper proposes two expressions of the output error variance due to coefficient quantization of fixed point state space digital filters in the time domain one is the deterministic approach which gives precisely the output error variance of state space digital filters the other is the statistical approach where the errors of coefficient quantization are assumed to be independent random variables the statistical approach gives a simple and easy way to analyze the output error variance due to coefficient quantization of state space digital filters the statistical coefficient sensitivity introduced by the statistical approach is shown to be equivalent to the round off noise power gain thus state space digital filters which are optimal with respect to both coefficient sensitivity and roundoff noise can be synthesized by the method of minimization of the roundoff noise such optimal state space digital filters which could be of any order are proved to be free of autonomous overflow limit cycles a numerical example is given to illustrate the effectiveness of the analysis of the output error variance due to coefficient quantization and the synthesis method proposed here

a systematic approach to synthesis of limit cycle free digital filters a systematic approach to synthesis of limit cycle free digital filters under constant input conditions is proposed structures of limit cycle free digital filters under constant input conditions are easily led from structures of limit cycle free digital filters under zero input conditions there exist various realizations which can suppress limit cycles for constant input signals

asymptotic and exponential stability of nonlinear two dimensional continuous discrete roesser models abstract sufficient conditions guaranteeing lyapunov stability asymptotic stability and exponential stability of nonlinear two dimensional continuous discrete systems are proposed special attention is paid to neutrally stable systems such as some two dimensional system descriptions of vehicle platoons which may be stable or asymptotically stable but never exponentially stable our conditions for lyapunov stability and asymptotic stability only require the corresponding two dimensional lyapunov function to have a negative semidefinite divergence they are thus suitable for the analysis of non exponential versions of 2d stability examples are given to illustrate the results

diffusion limited aggregation a paradigm of disorderly cluster growth the purpose of this talk is to present a brief overview of our group s recent research into dynamic mechanisms of disorderly growth an exciting new branch of condensed matter physics in which the methods and concepts of modern statistical mechanics are proving to be useful our strategy has been to focus on attempting to understand a single model system diffusion limited aggregation dla this philosophy was the guiding principle for years of research in phase transitions and critical phenomena for example by focusing on the ising model steady progress was made over a period of six decades and eventually led to understanding a wide range of critical point phenomena since even systems for which the ising model was not appropriate turned out to be described by variants of the ising model such as the xy and heisenberg models so also we are optimistic that whatever we may learn in trying to understand dla will lead to generic information helpful in understanding general aspects of dynamic mechanisms underlying disorderly growth

the split algebras and noncompact hopf maps we develop a noncompact version of the hopf maps based on the split algebras the split algebras consist of three species split complex numbers split quaternions and split octonions they correspond to three noncompact hopf maps that represent topological maps between hyperboloids in different dimensions with hyperboloid bundle we realize such noncompact hopf maps in two ways one is to utilize the split imaginary unit and the other is to utilize the ordinary imaginary unit topological structures of the hyperboloid bundles are explored and the canonical connections are naturally regarded as noncompact gauge field of monopoles

division algebras pseudo orthogonal groups and spinors the groups so nu 1 so nu so nu 1 so nu 1 1 and so nu 2 2 nu 1 2 4 8 and their spin representations are described in terms of the division algebras r c h and o

stability analysis of 2 d digital filters with saturation arithmetic an lmi approach an improved lmi based criterion for the nonexistence of overflow oscillations in two dimensional 2 d digital filters described by the roesser model employing saturation arithmetic is presented the criterion makes use of the structural properties as prevailing in the system under consideration of the saturation nonlinearities in a greater detail than the usual sector restriction 0 1

self similarity of harmonic measure on dla abstract the right hand side of the curve of the harmonic measure on dla is undefined this does not necessarily imply that the harmonic measure and the dla geometry are not self similar we show for off lattice dla that the right hand tail satisfies a different rescaling rule this cauchy rescaling is compatible with self similarity the analysis is done on off off lattice dla in which both the brownian motion and the laplace equation are off lattice the cluster sizes range between 32 and 50 000 atoms the square lattice used to numerically estimate the laplacian potential introduces a lower cutoff on the spatial resolution of this potential we find a dependence of the right tail of the distribution of holders on this ultraviolet cutoff whereas the shape of the tail does depend on this ultraviolet lattice cutoff the applicability of the collapse rules do not

multifractal fluctuations in the dynamics of disordered systems we review recent developments in the study of the multifractal properties of dynamical processes in disordered systems in particular we discuss the multifractality of the growth probabilities of dla clusters and of the probability density for random walks on random fractals the results for multifractality in dla are based mainly on numerical studies while the results for random walks on random fractals are based on analytical results we find that although a phase transition in the multifractal spectrum occurs for d 2 dla there seems to be no phase transition for d 3 dla this might be explained by the topological differences between d 2 and d 3 dla clusters for the probability density of random walks on random fractals it is found that multifractality occurs for a finite range of moments q qmin q qmax the approach can be applied to other dynamical processes such as fractons or tracer concentration in stratified media

on the absence of limit cycles in a class of state space digital filters which contains minimum noise realizations this paper presents a theorem for the absence of limit cycles in a class of state space digital filters such a class contains minimum noise realizations of any order as a special case that is it is proved that the transition matrix a of minimum noise realizations of any order satisfies i a t a geq 0 and thus the realizations are free of limit cycles

new anomalous multiplicative multifractals left sided ƒ α and the modelling of dla abstract a sharp distinction is drawn between general multiplicative multifractals as originally introduced by the author and the more familiar but more restricted class defined by frisch and parisi and by halsey et al all the general multiplicative multifractals are exactly renormalizable by design however this is important and perhaps suprising it is shown that the scaling relations that serve to define the restricted class fail to extend to certain multiplicative multifractals as a result in addition to the familiar restricted class the general multifractals are shown to allow for a wide variety of anomalous behaviors several of which are described we believe that suitable examples of these anomalies are of the most important concrete applications to fully developed turbulence and to diffusion limited aggregates dla this paper concerns several new classes of multifractals we have recently proposed as tools to model the anomalies of dla they are left sided that is characterized by max with max d 0 related multifractals characterized by max 0 and even by max and min 0 are encountered along the way

stability of linear discrete dynamics employing state saturation arithmetic this note is concerned with the stability of discrete time dynamical systems employing saturation arithmetic in the state space a matrix measure is introduced so that it can administer the proximity evaluation of a matrix to the set of diagonal matrices and the measure is utilized for making an additional condition to the lyapunov stein matrix inequality the solvability of the modified matrix inequality ensures not only the stability but also the absence of overflow oscillation under the state saturation arithmetic and this approach has the advantage of being free from auxiliary parameters as an application the obtained result is applied to the stability analysis of two dimensional dynamics numerical examples are given to illustrate the results

on hankel singular values and reflected zeros of linear dynamical systems this note discusses a relationship between the hankel singular values and reflected zeros of linear systems our main result proves that the hankel singular values of a linear continuous time system increase decrease pointwise when one or more zeros of the transfer function are reflected with respect to the imaginary axis that is move from the left right half to the right left half of the complex plane we also derive a similar result for linear discrete time systems

spatially self organized resilient networks by a distributed cooperative mechanism abstract the robustness of connectivity and the efficiency of paths are incompatible in many real networks we propose a self organization mechanism for incrementally generating onion like networks with positive degree degree correlations whose robustness is nearly optimal as a spatial extension of the generation model based on cooperative copying and adding shortcut we show that the growing networks become more robust and efficient through enhancing the onion like topological structure on a space the reasonable constraint for locating nodes on the perimeter in typical surface growth as a self propagation does not affect these properties of the tolerance and the path length moreover the robustness can be recovered in the random growth damaged by insistent sequential attacks even without any remedial measures

dirac operators on the fuzzy ads2 with the spins 12 and 1 it is shown here how the pseudo chirality and dirac operators with the spins 12 and 1 on the commutative and fuzzy ads2 should be constructed the finite dimensional and nonunitary representations of su 1 1 carrying the spin degrees of freedom 12 and 1 are used for the dirac fields on commutative and fuzzy ads2 in the fuzzy case an explicit description of pseudo generalization of the ginsparg wilson algebra is used to construct projective modules the projector couplings left angular momentum and spin on the fuzzy ads2 are used to produce minimum total angular momenta they are realized by the first two and three representations of the total angular momentum for the spins 12 and 1 respectively the pseudo projectors the pseudo chirality and dirac operators with the spins 12 and 1 on the fuzzy ads2 tend to their corresponding operators in the commutative limit

an embedding technique for the solution of coupled riccati equations a new method of solving analytically coupled riccati equations by means of embedding them into a matrix riccati equation is proposed this process imposes certain conditions onto the coefficients of the original equations whenever it is impossible to match these requirements the calculation of less demanding invariants is discussed the algebraic structure of these is simple enough to be practically used for lowering the system s dimension in general the newly soluble equations do not possess the painleve property

two dimensional digital filters without overflow oscillations and instability due to finite word length new criteria for the absence of finite word length effects such as overflow oscillations and instability in two dimensional digital filters are presented the criteria are formulated using the state space representations and are based on results concerning the 2d lyapunov equation several examples illustrate the theoretical results

novel dynamical scaling in kinetic growth phenomena abstract a novel dynamical scaling characterized by infinitely many growth exponents is presented this new behavior is manifested in the time dependent pair correlation function and therefore is amenable to direct experimental observation an exact analytical solution on the time dependent ginzburg landau model is obtained in the large n limit for a quench at zero temperature which exhibits such multiscaling behavior this new form of behavior reflects a morphological pattern in the growing domains and is expected in other growth phenomena as indicated by preliminary analysis on dla clusters a connection between multiscaling and multifractality is discussed

comments on stability and absence of overflow oscillations for 2 d discrete time systems in their article xiao and hill see ibid vol 44 p 2108 10 1996 show via an example that the conditions of the theorem 3 in an earlier paper by tzafestas et al 1992 may not guarantee stability of 2 d linear systems the authors incorrectly conclude that the bibo unstable 2 d linear system may have a stable finite wordlength implementation using saturation arithmetic the authors comment that this incorrect conclusion is due to an erroneous result in the earlier paper by tzafestas et al

behaviour of the harmonic measure at the bottom of fjords diffusion limited aggregates are among many important fractal shapes that involve deep indentations usually called fjords to estimate the harmonic measure at the bottom of a fjord seems a prohibitive task but the authors find that a new mathematical equality due to beurling carleson and jones makes it easy they find that the harmonic measure at the bottom of a fjord as a function of its euclidean depth can exhibit a wide range of behaviours they introduce an infinite family of model fjords for which the equality takes a very simple form in this family the decay of the harmonic measure at their bottoms can be for example power law semi exponential stretched exponential and exponentially stretched exponential they show that self affinity or randomness can lead to faster than power law decays of the minimal growth probability on boundaries

robust extended kalman filtering linearization errors inherent in the specification of an extended kalman filter ekf can severely degrade its performance this correspondence presents a new approach to the robust design of a discrete time ekf by application of the robust linear design methods based on the h sub spl infin norm minimization criterion the results of simulations are presented to demonstrate an advantage for signal demodulation and nonlinear equalization applications

plane dla is not self similar is it a fractal that becomes increasingly compact as it grows abstract using two new methods of geometric analysis this paper establishes that dla clusters are definitely not self similar compared to small clusters the morphology of large clusters of sizes up to 30 million particles can be characterized both visually and quantitatively as being far more compact or less lancunar qualitatively the number of arms increases during growth the evidence does not exclude that the cluster remains fractal and that its fractal dimension remains constant however new pitfalls in the estimation of d are revealed the gradual change in the morphology of dla opens the possibility that there is continuity between the standard morphology observed for small to medium computer generated dla clusters and the compact morphology observed in many actual physical phenomena

a hopf bundle over a quantum four sphere from the symplectic group we construct a quantum version of the su 2 hopf bundle s7 s4 the quantum sphere s7q arises from the symplectic group spq 2 and a quantum 4 sphere s4q is obtained via a suitable self adjoint idempotent p whose entries generate the algebra a s4q of polynomial functions over it this projection determines a deformation of an anti instanton bundle over the classical sphere s4 we compute the fundamental k homology class of s4q and pair it with the class of p in the k theory getting the value 1 for the topological charge there is a right coaction of suq 2 on s7q such that the algebra a s7q is a non trivial quantum principal bundle over a s4q with structure quantum group a suq 2

reply to comment on parseval relationship of nonuniform samples of one and two dimensional signals the author presents a reply to the paper by zhu and leung ieee trans signal processing vol 42 no 3 p 2183 1994 which commented on the paper by marvasti and liu ieee trans acoust speech signal processing vol 38 no 6 p 1061 3 1990 the present author discusses a typographical error in the paper by marvasti and liu it is concluded that the theorem proofs are still correct and the conclusion still valid

generation of a time series having a specified power spectrum with minimum roundoff noise the problem of determining a shaping filter which minimized the output roundoff noise variance is discussed it is shown that in the family of shaping filters of an identical mcmillan degree having an identical power spectrum the shaping filter of minimum phase attains a minimum output roundoff noise variance in either the case of optimal word lengths or the case of equal word lengths it is shown out by examples that this is not valid in the family of shaping filters having an identical power spectrum and different mcmillan degrees

criteria for the absence of limit cycles in two dimensional discrete systems sufficient conditions for the nonexistence of zero input limit cycles in two dimensional systems which contain a finite number of memoryless nonlinearities are presented two different conditions are given the first one is based on the frequency domain representation of the linear part of the discrete system and it is shown to be more general than the one already presented in 1 the second condition is formulated using the state space representation and is based on the properties of quasidominant matrices and on partial results on the 2 d lyapunov equation

stability and absence of overflow oscillations for 2 d discrete time systems it is shown that a 2 d linear time invariant discrete time system could be bounded input bounded output bibo unstable even if the 2 d system which is implemented by finite word length is free of overflow oscillations with zero input according to a previous criterion for the absence of overflow oscillations in 2 d discrete time systems an improved criterion is presented to ensure both stability properties

multifractality of the harmonic measure on fractal aggregates and extended self similarity abstract we show that dla follows a surprising new scaling rule it expresses that the screened region in which the harmonic measure is tiny increases more than proportionately as the cluster grows this scaling rule also gives indirect evidence that the harmonic measure of lattice dla follows a hyperbolic probability distribution of exponent equal to 1 this distribution predicts that sample moments behave erratically hence explains why the common restricted multifractal formalism fails to apply to dla

stability analysis of 2 d state space digital filters using lyapunov function a caution a previously proposed lyapunov based approach for the stability analysis of two dimensional 2 d state space digital filters is reviewed it is shown that the approach as it is may lead to an erroneous conclusion

stability and overflow oscillations in 2 d state space digital filters an important theorem relating to the lyapunov stability of two dimensional discrete systems is proven using this theorem it is shown that for any 2 d digital filter satisfying shanks criterion there exists a realization that cannot support overflow oscillations in the process of proving the theorem some interesting results on the multi dimensional bilinear transformation are developed one of these results yields a simple test that can be used to check the stability of a 2 d discrete transfer function that has been obtained from the bilinear transform of a 2 d continuous transfer function with a 2 d hurwitzian denominator polynomial a technique is given for determining whether a normal realization exists for a given 2 d discrete system also a theorem is presented that allows the determination of the norm of the minimum norm realization of a given transfer function a noniterative technique for obtaining a low norm realization and an iterative technique for obtaining a minimum norm realization are developed