distance spectra and upper bounds on error probability for trellis codes the problem of estimating error probability for trellis codes is considered the set of all squared euclidean distances between code sequences is presented as a countable set this representation is used for calculating the generating functions for upper bounding error probability and bit error probability for trellis codes satisfying some symmetry conditions the generating functions of squared euclidean distances distance spectra are obtained by inversion of a matrix of order 2 sup spl nu it is shown that the generating functions are defined in terms of one formal variable for qam and uniform am and in terms of q 4 formal variables for q ary psk q 2 sup m where m spl ges 2 is an integer for small spl nu the generating functions may be found in closed form for larger spl nu a numerical technique for obtaining some initial terms of the power series expansion is proposed this algorithm is based on the recurrent matrix equations and the chinese remainder theorem

self similarity of quasilattices in two dimensions ii the non bravais type n gonal quasilattice for pt i see ibid vol 22 p 193 1989 presents a systematic method of dividing an n gonal lattice into identical sublattices which are also n gonal lattices a non bravais type n gonal quasilattice in two dimensions is constructed with the projection method by assigning windows with different shapes sizes and or orientations to the sublattices the symmetries and the orientations of the windows are determined by the relative point symmetries of the sublattices to the n gonal lattice and windows assigned to equivalent sublattices differ from one another only in their orientations the sublattices are transformed among themselves by a volume conserving linear transformation induced by a complex pv unit in the n cyclotomic field a necessary and sufficient condition for a pv unit to be a complex self similarity ratio of a non bravais type quasilattice is presented it is shown that every non bravais type n gonal quasilattice has a self similarity characterised by pv unit

solution of kramers problem abstract the escape of a brownian particle across a potential barrier was introduced by kramers he derived expressions for the escape or transition rate in the limits of large and small damping several expressions that are supposed to be valid for the whole damping regime were put forward some years ago it seemed that the solution of matkowsky schuss and tier settled the bridging issue in this article however it will be argued why the mean first passage time approach followed by matkowsky et al is not suited to formulate kramers problem an alternative treatment is given based on the kramers equation which is solved separately in two regions of phase space corresponding to well and barrier the escape rate follows from the matching conditions of both solutions the new expressions resembles the one of matkowsky et al but is simpler and clarifies the connection with unimolecular chemical reactions

eigenvalues and eigenfunctions of the fokker planck equation for the extremely underdamped brownian motion in a double well potential the eigenvalues and eigenfunctions of the fokker planck equation describing the extremely underdamped brownian motion in a symmetric double well potential are investigated by transforming the fokker planck equation to energy and position coordinates and by performing a suitable averaging over the position coordinate a differential equation depending only on energy is derived for finite temperatures this equation is solved by numerical integration whereas in the weak noise limit an analytic result for the lowest nonzero eigenvalue is obtained furthermore by using a boundary layer theory near the critical trajectory the correction term to the zero friction limit result is found

epidemic models and percolation the authors argue that local epidemic models with immunisation are in the same universality class as percolation cluster growth models and show that the static exponents are equal to all orders in the epsilon expansion they calculate the dynamic exponent nu t 1 1 28 epsilon o epsilon 2 and relate this to other exponents involving the chemical distance

universal groups for point sets and tilings abstract we study the universal groups of inverse semigroups associated with point sets and with tilings we focus our attention on two classes of examples the first class consists of point sets which are obtained by a cut and projection scheme so called model sets here we introduce another inverse semigroup which is given in terms of the defining data of the projection scheme and related to the model set by the empire congruence the second class is given by one dimensional tilings

error probability for maximum likelihood sequence estimation of trellis coded modulation on isi channels a method is presented for upper bounding the error probability of trellis coded modulation on multipath fading isi channels that uses one directional stack algorithm the method provides a tighter upper bound than transfer function bounding techniques and is useful for large state systems because the transfer function is not required the stack algorithm exploits the symmetry properties of the trellis code to reduce computing time

quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability two 2d quasiperiodic tilings with generalized tenfold symmetry are derived from the lattice a4r the reciprocal of the root lattice a4 both tilings are built from four tiles triangles in one case rhombi and hexagons in the other after a brief description of the tilings and their structures the authors introduce the equivalence concept of mutual local derivability they present its key properties and its application to several tenfold tilings and discuss some implications on a future classification of tilings in position space

field theoretic formulation of an epidemic process with immunisation the author describes a model of the spread of an epidemic on a lattice in which sites may be infected by their neighbours after which they recover and are subsequently immune it corresponds to a modification of the directed percolation problem and also to a growth model of clusters the model is analysed using a continuum field theory both within a self consistent approximation and using an epsilon expansion below six transverse dimensions

a fourth order algorithm for solving the multi dimensional kramers equation in langevin form we propose a new fourth order numerical method for solving the multi dimensional kramers equation in standard and overdamped regimes the algorithm is developed for modelling the trajectories of airborne particles propagating through porous media such as three dimensional fibre networks it disentangles the deterministic and stochastic parts of the solution so that standard fourth order numerical methods can be used to calculate the deterministic component the stochastic correction to the solution is obtained using a perturbative expansion of the stochastic force in the overdamped regime our method avoids the need for extremely small time steps required by conventional methods we compare the convergence rate of our algorithm to that of other methods by solving the one dimensional duffing equation the proposed algorithm is finally used to evaluate the performance of various filters made from fibres of two different sizes

theory of self similarity of periodic approximants to a quasilattice it is shown that self similarity of a quasilattice has a profound effect on the periodic approximants to the quasilattice the periodic approximants are grouped into series so that i each series is generated from its prototype by a successive application of the deflation and rescaling ii the space group is common among the members of the series and iii the unit cell of the approximant is scaled up by tau with the series number where tau is the scale of self similarity of the relevant quasilattice these results are exemplified with application to the case of the octagonal quasilattice

special points of 2 1 reducible quasilattices in three dimensions presents a complete classification of special points of five dimensional 5d bravais lattices which yield with the cut and projection method 2 1 reducible quasilattices in 3d the quasilattices are periodic along the c axis but quasiperiodic only along the plane perpendicular to it there exist five bravais classes of 5d lattices associated with the 2 1 reducible quasilattices namely primitive octagonal decagonal and dodecagonal lattices the centred octagonal lattice and the pentagonal lattice the author also discusses the special points of the reciprocal lattices of these 5d lattices

special lines of quasilattices i the case of irreducible quasilattices in two and three dimensions a general theory for special lines in quasilattices is developed using the theory the author classifies completely the special lines of the three bravais classes of icosahedral quasilattices in three dimensions and another three of n gonal quasilattices in two dimensions where n 8 10 and 12 he establishes compatibility relationships between the classes of special lines and those of special points for each of the six bravais classes of quasilattices

renormalisation of random walks with memory the renormalisation of field theoretic models of the true self avoiding random walk is analysed for short range interactions the field theory is shown to be renormalisable only in a special case which corresponds to the problem of a random walk in a random environment and non renormalisable otherwise the long range version of the field theory is shown to be renormalisable in a larger region of the parameter space in the case which corresponds to the original long range true self avoiding random walk the renormalisation group analysis is carried out to two loop order anomalous dimensions of various composite operators are calculated and the crossover between scaling regimes described by short range and long range models is discussed

the exact distribution of the oscillation period in the underdamped one dimensional sinai model we consider the newtonian dynamics of a massive particle in a one dimensional random potential which is a brownian motion in space this is the zero temperature nondamped sinai model as there is no dissipation the particle oscillates between two turning points where its kinetic energy becomes zero the period of oscillation is a random variable fluctuating from sample to sample of the random potential we compute the probability distribution of this period exactly and show that it has a power law tail for large period p t t 5 3 and an essential singularity p t exp 1 t as t 0 our exact results are confirmed by numerical simulations and also via a simple scaling argument

scd patterns have singular diffraction among the many families of nonperiodic tilings known so far scd tilings are still a bit mysterious here we determine the diffraction spectra of point sets derived from scd tilings and show that they have no absolutely continuous part that they have a uniformly discrete pure point part on the axis re3 and that they are otherwise supported on a set of concentric cylinder surfaces around this axis for scd tilings with additional properties more detailed results are given

theory of self similarity of periodic approximants to a quasilattice ii the case of the dodecagonal quasilattice for pt i see ibid vol 24 p 4873 87 1991 the space groups of the periodic approximants pas to the dodecagonal quasilattice in two dimensions are investigated the bravais lattices of the pas are tetragonal p4mm rectangular pmm hexagonal p6mm and rhombic cmm the author presents several series of pas each of which is derived from a prototype pa by a successive application of the deflation and rescaling dar and the space group is common among the members each series is composed of two subseries the consecutive members in each subseries are related by the proper dar and the two subseries are related to each other by the improper dar

a classification of special points of quasilattices in two dimensions a complete classification of the special points of octagonal decagonal and dodecagonal quasilattices in two dimensions 2d is presented they are obtained by projecting the special points of the starting n gonal lattice n 8 10 or 12 in 4d onto a 2d subspace a set of equivalent special points of a quasilattice are located on the centres of a single kind of tile in the quasiperiodic tiling associated with the quasilattice the point symmetry of the special points is identical to that of the tiles they form a quasilattice with the same point symmetry as that of the original quasilattice the new quasilattice is of a bravais type or non bravais type according to whether the point symmetry group of the special points is identical to the full point symmetry group of the quasilattice or its true subgroup respectively

projection of the danzer tiling we derive the icosahedrally symmetric octahedral tiling of danzer 1991 denoted by t d locally from the tiling t 2f of kramer et al 1989 obtained by icosahedral projection from the root lattice d6 moreover we determine all windows such that the tiling t d can be obtained by projection from the 6d root lattice d6 we reconstruct all vertex configurations of the tiling t d using the tools of the projection method

trellis coding with asymmetric modulations traditionally symmetric signal constellations i e those with uniformly spaced signal points have been used for both uncoded and coded systems although symmetric signal constellations are optimum with no coding the same is not necessarily true for coded systems this paper shows that by designing the signal constellations to be asymmetric one can in many instances obtain a performance gain over the traditional symmetric constellations combined with trellis coding in particular we consider the joint design of n n 1 trellis codes and asymmetric 2 n 1 point signal constellations which has no bandwidth expansion relative to an uncoded 2n point symmetric signal set the asymptotic performance gains due to coding and asymmetry are evaluated in terms of the minimum free euclidean distance d free of the trellis a comparison of the maximum value of this performance measure to the minimum distance d min of the uncoded system is an indication of the maxiamm reduction in required e b n 0 that can be achieved for arbitrarily small system bit error rates bit error probability analysis is carried out for general cases a few examples are given to show the performance gain due to the asymmetry of the signal set it is to be emphasized that the introduction of asymmetry into the signal set does not affect the bandwidth or power requirements of the system hence the abovementioned improvements in performance come at little or no cost asymmetric signal sets in coded systems first appear in the work of divsalar and yuen 1 2 here we expand upon these results by considering various types of asymmetric signal sets combined with the optimum in the sense of maximum d free trellis code having 2 4 8 and 16 states the numerical results obtained will clearly demonstrate the tradeoff between the additional savings in required e b n 0 and the additional complexity more trellis states needed to achieve it

error probability for digital transmission over nonlinear channels with application to tcm the computation of upper and lower bounds to error probability in digital transmission over nonlinear channels with a finite memory is considered by using orthogonal volterra series the authors derive a canonical representation for discrete nonlinear systems based on a linear convolutional code and a memoryless mapper this representation shows that finite memory discrete nonlinear systems can be analyzed in much the same way as tcm trellis coded modulation schemes in particular tcm over nonlinear channels can be analyzed a technique is derived that expresses an upper bound to error probability based on the computation of the transfer of a state diagram with n branches and whose branch labels are matrices rather than scalars some examples of its application are given in particular error bounds are derived for nonlinear tcm schemes and for tcm schemes operating on nonlinear channels

a classification of special points of icosahedral quasilattices investigates special points of icosahedral quasilattices in three dimensions 3d they are given as the projections onto the real space of the special points of icosahedral lattices which are periodic lattices in 6d there exist three bravais classes of 6d icosahedral lattices and the author present a complete classification of their special points

quasiperiodic icosahedral tilings from the six dimensional bcc lattice the cell geometry of the six dimensional bcc lattice is investigated via klotz construction two different classes of icosahedrally projected quasiperiodic tilings are defined for both cases we determine the acceptance domains of tiles and give a detailed description of the geometry of all tiles

on the area under a continuous time brownian motion till its first passage time the area swept out under a one dimensional brownian motion till its first passage time is analysed using a fokker planck technique we obtain an exact expression for the area distribution for the zero drift case and provide various asymptotic results for the nonzero drift case emphasizing the critical nature of the behaviour in the limit of vanishing drift the results offer important insights into the asymptotic behaviour of a number of discrete models we also provide a succinct derivation for the distribution of the maximum displacement observed during a first passage

crossover between field theories with short range and long range exchange or correlations the relation between scalar field theories with short range and long range exchange or correlations is studied it is shown to all orders in perturbation theory that the critical exponents of fields and composite operators are continuous functions of the parameters alpha xi characterising the decay rate of the long range exchange correlations with power like falloff 1 rd 2 2 alpha 1 rd 2 xi the scaling law d 2 xi v 2 where v is the correlation length exponent as well as the harris criteria 1970 are shown to be exact to all orders in perturbation theory a discrepancy between two widely used approaches to the crossover problem is pointed out

two dimensional dodecagonal quasilattices two dimensional quasiperiodic lattices with 12 fold rotational symmetry are constructed by projecting a four dimensional hyperhexagonal lattice onto a two dimensional subspace the projection method in the present case is greatly simplified by representing the four dimensional lattice as a complex two dimensional lattice by choosing windows with different forms one obtains several quasiperiodic tilings which have a self similarity one of the tilings is quite similar to the pattern of the dodecagonal quasicrystal of a nicr alloy

renormalisation of the true self avoiding walk it is shown that the renormalisation of the true self avoiding walk of amit et al 1982 is its upper critical dimensionality two involves at least two possibly three coupling constants fixed points to first order in epsilon 2 d are identified and the asymptotic behaviour at d 2 is discussed

use of hamiltonian mechanics in systems driven by colored noise the evaluation of the path integral representation for stochastic processes in the weak noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics we show that even when the noise is colored these may be put into a hamiltonian form which leads to better insights and improved numerical treatments we concentrate on solving hamilton s equations over an infinite time interval in order to determine the leading order contribution to the mean escape time for a bistable potential the paths may be oscillatory and inherently unstable in which case one must use a multiple shooting numerical technique over a truncated time period in order to calculate the infinite time optimal paths to a given accuracy we look at two systems in some detail the underdamped langevin equation driven by external exponentially correlated noise and the overdamped langevin equation driven by external quasi monochromatic noise we deduce that caustics focusing and bifurcation of the optimal path are general features of all but the simplest stochastic processes

renormalisation of the long range true self avoiding walk the authors show that the true self avoiding walk with long range interactions leads to a renormalisable field theory they compute the characteristic exponent of the gyration radius up to first order in the difference between the upper critical dimension and space dimensionality and compare it with the estimates based on flory like arguments

atomistic octagonal random tiling model a random tiling model with octagonal symmetry is presented the tiles are the square and various hexagons when each vertex of the tiling is decorated by a disc a valid disc packing is formed which is an octagonal disc packing of maximum density under certain constraints a simple inflation rule is given that produces one member of the random tiling ensemble the space group of this tiling is non symmorphic the projection description of this tiling involves a fractal acceptance domain with fourfold symmetry for the even nodes of a four dimensional cubic lattice and the same acceptance domain rotated by pi 4 in perpendicular space for the odd nodes other tilings can be generated by an inflation rule with constrained randomness additional members of the random tiling ensemble can be created from inflation generated tilings by a set of update moves that rearrange the positions of the discs along closed loops an update move does not always conserve the number of each kind of tile

efficient computation of trellis code generating functions for trellis codes generating function techniques provide the distance spectrum and a union bound on bit error rate the computation of the generating function of a trellis code may be separated into two stages the first stage reduces the number of states as much as possible using low complexity approaches the second stage produces the generating function from the reduced state diagram through some form of matrix inversion which has a relatively high complexity in this paper we improve on the amount of state reduction possible during the low complexity first stage we also show that for a trellis code that is a linear convolutional code followed by a signal mapper the number of states may always be reduced from n sup 2 to n sup 2 n 2 1 using low complexity techniques finally we analytically compare the complexity of various matrix inversion techniques and verify through simulation that the two stage approach we propose has the lowest complexity in an example the new technique produced the union bound in about half the time required by the best algorithm already in the literature

reduced state representations for trellis codes using constellation symmetry this paper presents a symmetry based technique for trellis code state diagram reduction that has more general applicability than the quasi regularity technique of rouanne et al and zehavi et al for trellis codes using standard constellations and labelings for a 2 sup spl nu x state trellis code the new technique reduces the 2 sup 2 spl nu x state diagram to 2 sup spl nu x spl nu q state diagram where 0 spl les spl nu sub q spl les spl nu sub x the particular value of spl nu sub q depends on the constellation labeling and the convolutional encoder for standard rate k k 1 set partitioned trellis codes spl nu sub q 0 and the overall number of states is the same with the new technique as with quasi regularity for codes that are not quasi regular and thus not amenable to the quasi regularity technique the new technique often provides some improvement when spl nu sub q spl nu sub x for 8 phase shift keying trellis codes the new technique always yields spl nu sub q 0

a new description of trellis codes a trellis code is a sliding window method of encoding a binary data stream as a sequence of real or complex numbers that are input to a noisy transmission channel ungerboeck has constructed simple trellis codes that provide the same noise immunity as is given by increasing the power of uncoded transmission by factors ranging from two to four his method is to specify an underlying convolutional code and a rule mapping by set partitioning that maps the output of this code onto a fixed signal constallation a new description of a trellis code is given that combines these two steps into one the new description is analytic rather than graphical many practical codes can be described very simply and strict bounds on performance can be obtained a method for differential encoding trellis codes is presented that was suggested by the authors representation

an n gonal quasilattice in two dimensions as a dual lattice to a multiple periodic grid an n gonal quasilattice in two dimensions is constructed for the case of n 6m m or 2 as a dual to an m tuple periodic grid gm g0 union rg0 union union rm 1g0 where g0 is a periodic grid with hexagonal point symmetry and r the rotation operation of the plane by angle 2 pi n the author investigates the case where g0 is a honeycomb triangular kagome or diced grid the resulting quasilattice is not of bravais type unless g0 is the honeycomb grid it is shown also that the same quasilattice is obtained with the projection method from the 2m dimensional lattice l l0 l0 l0 where l0 is a triangular honeycomb diced or kagome lattice being dual to g0 in the projection method the 2m dimensional euclidean space is divided into cells with a 2m dimensional grid g which is dual to l it is shown that gm is identical to a two dimensional section of g

inertial effects on the escape rate of a particle driven by colored noise an instanton approach a recent calculation in the weak noise limit of the rate of escape of a particle over a one dimensional potential barrier is extended by including an inertial term in the langevin equation specifically we consider a system described by the langevin equation m ddot x dot x v prime x xi where is a gaussian colored noise with mean zero and correlator t t d exp t t a pathintegral formulation is augmented by a steepest descent calculation valid in the weak noise d 0 limit this yields an escape rate exp s d where the action s is the minimum over paths characterizing escape over the barrier of a generalized onsager machlup functional the extremal path being an instanton of the theory the extremal actions is calculated analytically for smallm and for general potentials and numerical results fors are displayed for various ranges ofm and for the typical case of the quartic potentialv x x2 2 x4 4

a classification of two dimensional quasiperiodic tilings obtained with the grid method two dimensional quasiperiodic tilings qpt obtained from n grids are classified into local isomorphism li classes by using the invariants of the grids the number of the invariants is given by n phi n if n is odd or n phi 2n if n is even where phi is euler s function in number theory all the qpt obtained from n grids with n 2k k or 2 belong to a single li class whose point symmetry is d2n when n is not a power of 2 the qpt are classified into several li classes of the li classes two have the highest point symmetry d2n one of the two classes is associated with n grids in which all the invariants vanish and the other with n grids in which all of them take 1 2 in the case of an odd n there is also one continuous series of qpt with point symmetry dn the author also presents a general formula of the tile statistics of the quasiperiodic tilings obtained with the grid method

superquasicrystals self similar ordered structures with non crystallographic point symmetries we present a systematic method of constructing limit quasiperiodic structures with non crystallographic point symmetries such structures are different aperiodic ordered structures from quasicrystals and we call them superquasicrystals they are sections of higher dimensional limit periodic structures constructed on super bravais lattices we enumerate important super bravais lattices superquasicrystals with strong self similarities form an important subclass the simplest example is a two dimensional octagonal superquasicrystal

combined coding and modulation theory and applications the theoretical aspects of the encoding process are investigated resulting in a precise definition of linear codes together with theorems that clarify how they can be obtained a particular subset of linear codes called superlinear codes for which the performance analysis is highly simplified is identified the most relevant performance measures for the analysis of this class of codes are discussed the minimum euclidean distance and the event and bit error probabilities are found analytically using the uniform error property when applicable or variations on it this yields accurate upper and lower bounds to the error rate at the price of reasonable computational complexity the theory is then applied to the search for good codes and to their performance evaluation the cases of 16 and 32 psk codes which are good candidates for use in digital satellite transmission are considered several new results in terms of error event and bit error probabilities are presented showing considerable gains in terms of snr with respect to the uncoded case

random walk in a two dimensional self affine random potential properties of the anomalous diffusion phase at small external force we study the dynamical response to an external force f for a particle performing a random walk in a two dimensional quenched random potential of hurst exponent h 1 2 we present numerical results on the statistics of first passage times that satisfy closed backward master equations we find that there exists a zero velocity phase in a finite region of the external force 0lfl f c where the dynamics follows the anomalous diffusion law x t ensuremath sim ensuremath xi f t ensuremath mu f the anomalous exponent 0l ensuremath mu f l1 and the correlation length ensuremath xi f vary continuously with f in the limit of vanishing force f ensuremath rightarrow 0 we measure the following power laws the anomalous exponent vanishes as ensuremath mu f ensuremath propto f a with a ensuremath simeq 0 6 instead of a 1 in dimension d 1 and the correlation length diverges as ensuremath xi f ensuremath propto f ensuremath ensuremath nu with ensuremath nu ensuremath simeq 1 29 instead of ensuremath nu 2 in dimension d 1 our main conclusion is thus that the dynamics renormalizes onto an effective directed trap model where the traps are characterized by a typical length ensuremath xi f along the direction of the force and by a typical barrier 1 ensuremath mu f the fact that these traps are smaller in linear size and in depth than in dimension d 1 means that the particle uses the transverse direction to find lower barriers

on the performance evaluation of trellis codes generating function techniques for analyzing the error event and the bit error probabilities for trellis codes are considered the conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states cannot be applied directly to arbitrary trellis codes and instead a state diagram where the number of states is equal to the square of the number of trellis states must be used it is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states em is equal to the number of trellis states the class of codes considered includes trellis codes of rate r n 1 n based upon set partitioning whenever the first partition breaks the signal constellation into two subsets which have the same configuration matrix i e the same ordered set of mutual distances the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convolutional code with the same number of trellis states bounds on the performance of some interesting codes are given based upon this method

an efficient algorithm to compute the euclidean distance spectrum of a general intersymbol interference channel and its applications we present an efficient algorithm to compute the distance spectrum of a general finite intersymbol interference isi channel whose complexity is lower than those of existing methods closed form expressions are derived for both input output euclidean distance enumerators and asymptotic distance spectrum shapes for 2 tap and 3 tap isi channels coded and or precoded isi channels are also discussed

self similarity of quasilattices in two dimensions iii inflation by a non unit pv number for pt ii see ibid vol 22 205 1989 it is shown that every n gonal quasilattice in two dimensions has self similarity with a complex self similarity ratio which is equal to a non unit pv number in the n cyclotomic field in this self similarity the original quasilattice can be inflated to a number of different quasilattices which are locally isomorphous to each other the number is equal to the algebraic norm of the relevant pv number in the n cyclotomic field several examples are presented for the cases of octagonal decagonal and dodecagonal quasilattices the difference between the present self similarity and that associated with a pv unit is clarified

tiling spaces are inverse limits let m be an arbitrary riemannian homogeneous space and let be a space of tilings of m with finite local complexity relative to some symmetry group and closed in the natural topology then is the inverse limit of a sequence of compact finite dimensional branched manifolds the branched manifolds are finite unions of cells constructed from the tiles themselves and the group this result extends previous results of anderson and putnam of ormes radin and sadun of bellissard benedetti and gambaudo and of gahler in particular the construction in this paper is a natural generalization of gahler s

uniform distance and error probability properties of tcm schemes the class of uniform trellis coded modulation tcm techniques is defined and simple explicit conditions for uniformity are derived uniformity is shown to depend on the metric properties of the two subconstellations resulting from the first step in set partitioning as well as on the assignment of binary labels to channel symbols the uniform distance property and uniform error property which are both derived from uniformity but are not equivalent are discussed the derived concepts are extended to encompass transmission over a not necessarily gaussian memoryless channel in which the metric used for detection may not be maximum likelihood an appropriate distance measure is defined that generalizes the euclidean distance it is proved that uniformity of a tcm scheme can also be defined under this new distance the results obtained are shown to hold for channels with phase offset or independent amplitude only fading examples are included to illustrate the applicability of the results

generalised 2d penrose tilings structural properties usual penrose tilings are defined by a set of five phases gamma j which add up to an integer the authors study the general case where the phases add up to any number and show that these generalised tilings can be obtained with four tiles two thick rhombi and two thin rhombi with different colourings of the edges the consideration of generalised tilings is relevant for the study of phase distortions local structural transitions and therefore various defects of the usual things

behaviour of a newtonian particle in a random environment abstract we consider the behaviour of a newtonian particle in a quenched random environment within the perturbation theory the diffusion coefficient of the particle for dimensionality d 1 is obtained as d 5 0 m 2 d d 1 0 1 d 2 with 0 m being respectively the velocity and the mass 0 is the strength of the disorder describes the shape of the disorder correlator

self similarity of quasilattices in two dimensions i the n gonal quasilattice the self similarity of a two dimensional quasilattice with an n gonal point symmetry has been investigated for even n n or 8 it is shown that for any n an n gonal quasilattice has a self similarity characterised by a complex number tau on inflation the quasilattice is scaled by mod tau mod and subsequently rotated by arg tau tau is a pv unit of the n cyclotomic field q zeta zeta exp 2 pi i n tau satisfies i tau and tau 1 are both algebraic integers in q zeta ii mod tau mod 1 and iii mod tau mod 1 for any conjugate tau but tau the complex conjugate of tau in q zeta pv units are calculated for every n gonal quasilattice whose multiplicity m phi n 2 with phi being the eulerian function is less than 5 m 2 for n 8 10 12 m 3 for n 14 18 and m 4 for n 16 20 24 30 it is found that a quasilattice has two or more independent scales of self similarity if its multiplicity is larger than 2

diffusion in a one dimensional random medium and hyperbolic brownian motion classical diffusion in a random medium involves an exponential functional of brownian motion this functional also appears in the study of brownian diffusion on a riemann surface of constant negative curvature we analyse in detail this relationship and study various distributions using stochastic calculus and functional integration

diffraction pattern calculations for a certain class of n fold quasilattices using the cut and project method we obtain seven and nine fold quasiperiodic lattices for such quasilattices the structure factors are calculated analytically through integration in higher dimensional spaces the obtained formulae are compared with the direct numerical calculations of fourier transforms

a classification of the space groups of approximant lattices to a decagonal quasilattice a periodic approximant to a two dimensional 2d decagonal quasilattice is obtained by the projection method from a 4d periodic lattice l which is a commensurate deformation of the 4d decagonal lattice the bravais lattice of the approximant is given by the restriction of l onto the physical space while its space group by the symmetry of the phase vector with respect to the 2d lattice ls which is the projection of l onto the internal space there exist 12 space groups of the rectangular approximants pmm pmg pgm pgg pm1 p1m pg1 p1g cmm gamma cmm y cm1 and c1m which are derived from the special points or special lines of ls

inelastic collapse of a ball bouncing on a randomly vibrating platform a theoretical study is undertaken of the dynamics of a ball which is bouncing inelastically on a randomly vibrating platform of interest are the distributions of the number of flights n f and the total time ensuremath tau c until the ball has effectively collapsed i e coalesced with the platform in the strictly elastic case both distributions have power law tails characterized by exponents that are universal i e independent of the detail of the platform noise distribution however in the inelastic case both distributions have exponential tails p n f ensuremath sim mathrm exp ensuremath ensuremath theta 1 n f and p ensuremath tau c ensuremath sim mathrm exp ensuremath ensuremath theta 2 ensuremath tau c the decay exponents ensuremath theta 1 and ensuremath theta 2 depend continuously on the coefficient of restitution and are nonuniversal however as one approaches the elastic limit they vanish in a manner which turns out to be universal an explicit expression for ensuremath theta 1 is provided for a particular case of the platform noise distribution

a self similar dodecagonal quasiperiodic tiling of the plane in terms of squares regular hexagons and thin rhombi the author presents a dodecagonal quasiperiodic tiling of the plane in terms of three kinds of tiles a square a regular hexagon and a thin rhombus whose acute inner angles are 30 degrees the dodecagonal tiling is self similar with respect to a dilatation by 2 square root 3 it is associated with a dodecagonal quasiperiodic lattice which is obtained by a projection from a hyperhoneycomb lattice in four dimensions the hyperhoneycomb lattice is a non bravais lattice composed of four bravais sublattices and the author must assign windows with different orientations to different sublattices the author discusses in detail the relationships of the present method of obtaining a dodecagonal tiling to other methods

a simple derivation of quasi crystalline spectra a quasi crystalline solid is an aperiodic array of atoms which gives rise to bragg like diffraction peaks using the projection method for generating such structures the authors provide a simple derivation of this paradoxical behaviour

achievable rates for nonlinear volterra channels random coding theorems and achievable rates for nonlinear additive noise channels are presented modeling the channel s nonlinear behavior as a causal stationary volterra system upper bounds on the average error probability are obtained for maximum likelihood and weakly typical set decoding the proposed bounds are deduced by treating correct decoding regions as subspaces of high concentration measure and deploying exponential martingale inequalities due to the union bound effect and the i i d assumption imposed on the codewords components the deduced exponents constitute only lower bounds on the true random coding exponents of nonlinear channels cubic and fourth order nonlinearities are used as examples to illustrate the relation of the random coding exponents and achievable rates with respect to the channel s parameters

self similar quasilattices with windows having fractal boundaries the point inflation rule is presented as a powerful scheme to produce a self similar quasilattice with a non crystallographic point symmetry alternatively the conjugate point inflation rule which is a set map acting on the internal space has the unique fixed point which is a compact set w and the quasilattice ql is obtained with the projection method by taking w as the window the fixed point w is the attractor of the set map if w is topologically a disc a ball for a three dimensional case its boundary is usually fractal we investigate conditions for the boundary of the window to be a von koch curve a practical method of constructing windows and the relevant qls is presented a lot of windows with fractal boundaries are determined on the basis of this method we introduce isomerism which has priority of rank to the mutual local derivability as a classification scheme for self similar qls it is argued that the pir and isomerism can be the key points of classification of self similar qls

on the performance evaluation of isi channels the performance of finite intersymbol interference isi channels in the presence of additive white gaussian noise is evaluated by interpreting the isi channel as a trellis code closed form results are obtained for isi channels with one and two symbols of interference an efficient algorithm is also introduced to evaluate the minimum free euclidean distance of any isi channel

matching rules and growth rules for pentagonal quasicrystal tilings preuve de l existence de ces regles pour un ensemble infini de pavages pentagonaux 2d autres que le pavage de peurose

renormalisability and renormalisation of the true self avoiding random walks renormalisation of the recently proposed field theoretic model for the true self avoiding random walk is analysed apart from a special case which corresponds to the problem of a random walk in a random environment the model is shown to be non renormalisable in the case of short range interactions contrary to earlier conjectures the long range version of this field theoretic model is shown to be renormalisable in certain regions of the parameter space and renormalisation group analysis of the model is carried out to two loop order in the region corresponding to the true self avoiding random walk with long range repulsion in a different region of the parameter space the anomalous dimension of the diffusion coefficient is determined exactly in perturbation theory

conjugacies for tiling dynamical systems we consider tiling dynamical systems and topological conjugacies between them we prove that the criterion of being of finite type is invariant under topological conjugacy for substitution tiling systems under rather general conditions including the penrose and pinwheel systems we show that substitutions are invertible and that conjugacies are generalized sliding block codes

wiener path integral based response determination of nonlinear systems subject to non white non gaussian and non stationary stochastic excitation abstract the recently developed wiener path integral wpi technique for determining the joint response probability density function of nonlinear systems subject to gaussian white noise excitation is generalized herein to account for non white non gaussian and non stationary excitation processes specifically modeling the excitation process as the output of a filter equation with gaussian white noise as its input it is possible to define an augmented response vector process to be considered in the wpi solution technique a significant advantage relates to the fact that the technique is still applicable even for arbitrary excitation power spectrum forms in such cases it is shown that the use of a filter approximation facilitates the implementation of the wpi technique in a straightforward manner without compromising its accuracy necessarily further in addition to dynamical systems subject to stochastic excitation the technique can also account for a special class of engineering mechanics problems where the media properties are modeled as stochastic fields several numerical examples pertaining to both single and multi degree of freedom systems are considered including a marine structural system exposed to flow induced non white excitation as well as a bending beam with a non gaussian and non homogeneous young s modulus comparisons with monte carlo simulation data demonstrate the accuracy of the technique

critical behaviour of non equilibrium q state systems we present two classes of non equilibrium models with critical behaviour each model is characterized by an integer q 1 and is defined on configurations of q valued spins on regular lattices the definitions of the models are very similar to the updating rules in wolff s algorithm for the potts model but both classes break detailed balance except for q 2 and q infinity in the first case both models reduce to the ising model while one of them reduces to percolation more precisely to the general epidemic process for q infinity locations of the critical point and critical exponents are estimated in two dimensions

fractally shaped acceptance domains of quasiperiodic square triangle tilings with dedecagonal symmetry abstract we generate a quasiperiodic dodecagonally symmetric tiling of the plane by squares and equilateral triangles embedded in a higher dimensional periodic structure starting from a 4d lattice frequently used for the embedding of dodecagonal structures we iteratively construct an acceptance domain ad for a quasiperiodic point set which proves to be the vertex set of a square triangle tiling it turns out that our procedure leads to fractally bounded ads but leaves enough freedom to generate several different local isomorphism classes

dualisation of voronoi domains and klotz construction a general method for the generation of proper space fillings the authors present a general method for the generation of proper space fillings of euclidean spaces with convex polytopes by projection from higher dimensional spaces as a special case quasiperiodic tilings are obtained by the projection of periodic structures the concept is general enough for the treatment of defects in quasiperiodic tilings by placing defects in high dimensional translation lattices

canonical substitutions tilings of ammann beenker type we present a large class of parallelogram tilings that have two important features in common with the ammann beenker tiling they can be constructed by canonical projection from z4 r4 to a plane and they admit substitution rules