a series test of the scaling limit of self avoiding walks it is widely believed that the scaling limit of self avoiding walks saws at the critical temperature is conformally invariant and consequently describable by schramm loewner evolution with parameter 8 3 we consider saws in a rectangle which originate at its centre and end at the boundary we assume that the boundary density transforms covariantly in a way that depends precisely on as conjectured by lawler schramm and werner 2004 fractal geometry and applications a jubilee of benoit mandelbrot part 2 pp 339 64 it has previously been shown by guttmann and kennedy 2013 j eng math at press that in the limit of an infinitely large rectangle the ratio of the fraction of saws hitting the side of the rectangle to the fraction that hit the end of the rectangle can be calculated by considering rectangles of fixed aspect ratio 2 and also rectangles of aspect ratio 10 we calculate this ratio exactly for larger and larger rectangles by extrapolating this data to infinite rectangle size and invoking the above conjectures we obtain the estimate 2 666 64 0 000 07 for rectangles of aspect ratio 2 and 2 666 75 0 000 15 for rectangles of aspect ratio 10 we also provide numerical evidence supporting the conjectured distribution of saws striking the boundary at various points in the case of rectangles with aspect ratio 2

asymptotically optimal blind fractionally spaced channel estimation and performance analysis when the received data are fractionally sampled the magnitude and phase of most linear time invariant fir communications channels can be estimated from second order output only statistics we present a general cyclic correlation matching algorithm for known order fir blind channel identification that has closed form expressions for calculating the asymptotic variance of the channel estimates we show that for a particular choice of weights the weighted matching estimator yields at least for large samples the minimum variance channel estimator among all unbiased estimators based on second order statistics furthermore the matching approach unlike existing methods provides a useful estimate even when the channel is not uniquely identifiable from second order statistics

nonasymptotic pseudo state estimation for a class of fractional order linear systems this paper aims at designing a nonasymptotic and robust pseudo state estimator for a class of fractional order linear systems which can be transformed into the brunovsky s observable canonical form of pseudo state space representation with unknown initial conditions first this form is expressed by a fractional order linear differential equation involving the initial values of the fractional sequential derivatives of the output based on which the modulating functions method is applied then the former initial values and the fractional derivatives of the output are exactly given by algebraic integral formulae using a recursive way which are used to nonasymptotically estimate the pseudo state of the system in noisy environment second the pseudo state estimator is studied in discrete noisy case which contains the numerical error due to a used numerical integration method and the noise error contribution due to a class of stochastic processes then the noise error contribution is analyzed where an error bound useful for the selection of design parameter is provided finally numerical examples illustrate the efficiency of the proposed pseudo state estimator where some comparisons with the fractional order luenberger like observer and a new fractional order mathcal h infty like observer are given

self avoiding polygons on the square l and manhattan lattices transfer matrix techniques are used to extend the self avoiding polygon generating function on the square lattice to terms in x46 corresponding to 46 step polygons these techniques are then extended to apply to directed square lattices such as the l and manhattan lattice and the self avoiding polygon generating function to x48 is found for these lattices series analysis confirms that the specific heat exponent alpha 1 2 for the self avoiding walk problem and gives the following estimates for the connective constants mu sq 2 638155 or 0 000025 mu l 1 5657 or 0 0019 and mu man 1 7328 or 0 0005 some evidence for a correction to scaling exponent delta approximately 0 84 is found from square lattice series

direct blind mmse channel equalization based on second order statistics a family of new mmse blind channel equalization algorithms based on second order statistics are proposed instead of estimating the channel impulse response we directly estimate the cross correlation function needed in wiener hopf filters we develop several different schemes to estimate the cross correlation vector with which different wiener filters are derived according to minimum mean square error mmse unlike many known sub space methods these equalization algorithms do not rely on signal and noise subspace separation and are consequently more robust to channel order estimation errors their implementation requires no adjustment for either single or multiple user systems they can effectively equalize single input multiple output simo systems and can reduce the multiple input multiple output mimo systems into a memoryless signal mixing system for source separation the implementations of these algorithms on simo system are given and simulation examples are provided to demonstrate their superior performance over some existing algorithms

polygons on the honeycomb lattice the authors enumerated the number of self avoiding polygons on the honeycomb lattice to 82 steps analysis of the resulting series gives for the connective constant mu 1 8477594 or 6 10 6 in agreement with nienhuis value 1984 of mu 2 2 12 1 84775906 the critical exponent alpha 0 4999 or 10 4 unbiased or alpha 0 49998 or 2 10 0 5 biased a non physical singularity on the negative real axis is accurately located and some curious results concerning the confluent singularity are obtained

fractionally spaced equalization using cma robustness to channel noise and lack of disparity in the noise free case the fractionally spaced equalization using constant modulus fse cm criterion has been studied previously its minima were shown to achieve perfect equalization when zero forcing zf conditions are satisfied and to be able to still achieve fair equalization when there is lack of disparity however to our best knowledge the effect of additive channel noise on the fse cm cost function minima has not been studied in this paper we show that the noisy fse cm cost function is subject to a smoothing effect with respect to the noise free cost function the result of which is a tradeoff between achieving zero forcing and noise enhancement furthermore we give an analytical closed form expression for the loss of performance due to the noise in terms of input output mean square error mse under the zf conditions the fse cm mse is shown to be mostly due to output noise enhancement and not to residual intersymbol interference isi when there is lack of disparity an irreducible amount of isi appears independently of the algorithm it is the lower equalizability bound for given channel conditions and equalizer length the so called minimum mse mmse the mmse lower bound is the sum of the mmse and of additional mse mostly due to noise enhancement finally we compare the fse cm mse to this lower bound

transforming fixed length self avoiding walks into radial sle8 3 we conjecture a relationship between the scaling limit of the fixed length ensemble of self avoiding walks in the upper half plane and radial sle8 3 in this half plane from 0 to i the relationship is that if we take a curve from the fixed length scaling limit of the saw weight it by a suitable power of the distance to the endpoint of the curve and apply the conformal map of the half plane that takes the endpoint to i then we get the same probability measure on curves as radial sle8 3 in addition to a non rigorous derivation of this conjecture we support it with monte carlo simulations of the saw using the conjectured relationship between the saw and radial sle8 3 our simulations give estimates for both the interior and boundary scaling exponents the values we obtain are within a few hundredths of a percent of the conjectured values

on subspace methods for blind identification of single input multiple output fir systems blind identification of single input multiple output simo fir systems based on second order statistics has attracted a great deal of research effort we focus on subspace estimation procedures which exploit the structure of the range space of certain matrix valued statistics constructed by arranging in a prescribed order the covariance coefficients of the observations general subspace identifiability results are obtained based on properties of minimal polynomial bases of rational subspaces several subspace estimation procedures are then derived these estimators are all based on a weighted least square solution of an overdetermined system of linear equations an asymptotic statistical analysis of these estimators is carried out to evaluate the potential of these methods and the impact of the weighting

identification of linear stochastic systems via second and fourth order cumulant matching the identification problem for time invariant single input single output linear stochastic systems driven by non gaussian white noise is considered the system is not restricted to be minimum phase and it is allowed to contain all pass components a least squares criterion that involves matching the second and the fourth order cumulant functions of the noisy observations is proposed knowledge of the probability distribution of the driving noise is not required an order determination criterion that is a modification of the akaike information criterion is also proposed strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are presented to illustrate the method

blind equalization using a tricepstrum based algorithm an adaptive blind equalization method is introduced for nonminimum phase communication channels the method estimates the inverse channel impulse response by using the complex cepstrum of the fourth order cumulants tricepstrum of the synchronously sampled received signal as such the proposed adaptive method depends only on the statistics of the received sequence and is capable of reconstructing separately both the minimum and maximum phase response of the channel it is demonstrated by means of extensive simulations that the proposed tricepstrum based equalization scheme performs well and outperforms other existing blind equalizers at the expense of higher computational complexity

blind and semi blind fir multichannel estimation global identifiability conditions two channel estimation methods are often opposed training sequence methods that use the information induced by known symbols and blind methods that use the information contained in the received signal and possibly hypotheses on the input symbol statistics but without integrating the information from known symbols if present semi blind methods combine both training sequence and blind information and are more powerful than the two methods separately we investigate the identifiability conditions for blind and semi blind finite impulse response fir multichannel estimation in terms of channel characteristics received data length and input symbol excitation modes as well as number of known symbols for semi blind estimation two models corresponding to two different cases of a priori knowledge on the input symbols are studied the deterministic model in which the unknown symbols are considered as unknown deterministic quantities and the gaussian model in which they are considered as gaussian random variables this last model includes the methods using the second order statistics of the received data semi blind methods appear superior to blind and training sequence methods and allow the estimation of any channel with only few known symbols furthermore the gaussian model appears more robust than the deterministic one as it leads to less demanding identifiability conditions

the extension of self avoiding random walk series in two dimensions the authors have extended the enumeration of square lattice and triangular lattice self avoiding walks and their end to end distance by two terms they have also calculated 17 terms in the series for the resistance of saws with bridges on the square lattice analysis of the new data allows the connective constants to be more accurately estimated and affirms the values gamma 43 32 and v 3 4 and 1 gamma for the exponent of the resistance series

self avoiding walks in two to five dimensions exact enumerations and series study the method of concatenation the addition of precomputed shorter chains to the ends of a centrally generated longer chain has permitted the extension of the exact series for cn the number of distinct configurations for self avoiding walks of length n the authors report on the leading exponent y and xc the reciprocal of the connectivity constant for the 2d honeycomb lattice 42 terms 1 3437 0 541 1968 the 2d square lattice 30 terms 1 3436 0 379 0520 the 3d simple cubic lattice 23 terms 1 161 932 0 213 4987 the 4d hypercubic 18 terms y approximately 1 0 147 60 and the 5d hypercubic lattice 13 terms y or 1 025 0 113 05 in addition they have also evaluated the leading correction terms honeycomb delta approximately 1 square delta approximately 0 85 simple cubic delta approximately 1 0 and the 4d hypercubic logarithmic correction with delta approximately 0 25

determination of the exponent for saws on the two dimensional manhattan lattice we present a high statistics monte carlo determination of the exponent for self avoiding walks on a manhattan lattice in two dimensions a conservative estimate is in agreement with the universal value on regular lattices but in conflict with predictions from conformal field theory and with a recent estimate from exact enumerations we find strong corrections to scaling that seem to indicate the presence of a non analytic exponent if we assume we find where the error is purely statistical

an improved pseudo state estimator for a class of commensurate fractional order linear systems based on fractional order modulating functions abstract in this paper a non asymptotic pseudo state estimator for a class of commensurate fractional order linear systems is designed in noisy environment different from existing modulating functions methods the proposed method is based on the system model with fractional sequential derivatives by introducing fractional order modulating functions by applying the fractional order integration by parts formula and thanks to the properties of the fractional order modulating functions a set of fractional derivatives and fractional order initial values of the output are analogously obtained by algebraic integral formulas then an explicit formula of the pseudo state is accomplished by using the fractional sequential derivatives of the output computed based on the previous results this formula does not contain any source of errors in continuous noise free case and can be used to non asymptotically estimate the pseudo state in discrete noisy case the construction of the fractional order modulating functions is also shown which is independent of the time finally simulations and comparison results demonstrate the efficiency and robustness of the proposed method

asymptotically optimal estimation of ma and arma parameters of non gaussian processes from high order moments a description is given of an asymptotically minimum variance algorithm for estimating the ma moving average and arma autoregressive moving average parameters of non gaussian processes from sample high order moments the algorithm uses the statistical properties covariances and cross covariances of the sample moments explicitly a simpler alternative algorithm that requires only linear operations is also presented the latter algorithm is asymptotically minimum variance in the class of weighted least squares algorithms

on channel identification based on second order cyclic spectra gardener 1991 presented an interesting use of cyclostationarity for channel identification in pam data communication systems the present paper presents new results that address the identification of linear rational channels with higher than minimum bandwidth based on the use of second order cyclic statistics unlike the approach taken by gardener the present authors show that channel identification is achievable for a class of linear channels without the need for a pilot tone or training periods moreover channel identification based on cyclic statistics does not preclude gaussian or near gaussian inputs

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

an extension of the two dimensional self avoiding walk series on the square lattice the authors have adapted the dimerization algorithm for enumerating self avoiding walks to exploit the parallelism of the connection machine system by this approach they have extended the series for the number of self avoiding walks on the 2d square lattice by five terms these data may permit more accurate estimates of critical properties

a parallel algorithm for the enumeration of self avoiding polygons on the square lattice we have developed a parallel algorithm that allows us to enumerate the number of self avoiding polygons on the square lattice to perimeter length 110 we have also extended the series for the first 10 area weighted moments and the radius of gyration to 100 analysis of the resulting series yields very accurate estimates of the connective constant 2 638 158 530 31 3 biased and the critical exponent 0 500 000 1 2 unbiased in addition we obtain very accurate estimates for the leading amplitudes confirming to a high degree of accuracy various predictions for universal amplitude combinations

non asymptotic fractional order differentiator for a class of fractional order linear systems this paper aims at designing a non asymptotic fractional order differentiator for a class of fractional order linear systems to estimate the riemannliouville fractional derivatives of the output in discrete noisy environment the adopted method is a recent algebraic method originally introduced by fliess and sira ramirez firstly the fractional derivative of the output of an arbitrary order is exactly given by a new algebraic formula in continuous noise free case without knowing the initial conditions of the considered system secondly a digital fractional order differentiator is introduced in discrete noisy cases which can provide robust estimations in finite time then some error analysis is given where an error bound useful for the selection of the design parameter is provided finally numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator

self avoiding rings on the triangular lattice the finite lattice method of series expansion is used to extend the enumeration of self avoiding polygons on the triangular lattice through to rings of 35 steps the authors also give the enumeration of these triangular polygons grouped by perimeter and area of up to 21 unit triangles for perimeters up to 24 steps

arma bispectrum approach to nonminimum phase system identification an identification procedure is proposed for a nongaussian white noise driven linear time invariant nonminimum phase fir finite impulse response system the method is based on parametric modeling of the third moments of the output sequence and uses causal and anticausal autoregressive moving average arma models the magnitude and phase response of the system are expressed in terms of the ar parameters of the arma models in particular the ar part of the causal arma model captures the minimum phase component of the system and the ar part of the anticausal arma captures the maximum phase component both sets of parameters are obtained by solving overdetermined linear systems of equations a model order selection criterion based on third order moments is proposed the arma bispectrum approach is compared to more conventional approaches for magnitude and phase reconstruction it is demonstrated that the proposed identification procedure exhibits improved modeling performance the method does not require knowledge of the non gaussian noise distribution

a new transfer matrix algorithm for exact enumerations self avoiding polygons on the square lattice we present a new and more efficient implementation of transfer matrix methods for exact enumerations of lattice objects the new method is illustrated by an application to the enumeration of self avoiding polygons on the square lattice a detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm the new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110

self avoiding walks crossing a square we study a restricted class of self avoiding walks saws which start at the origin 0 0 end at l l and are entirely contained in the square 0 l 0 l on the square lattice z 2 the number of distinct walks is known to grow as l 2 o l 2 we estimate 1 744 550 0 000 005 as well as obtaining strict upper and lower bounds 1 628 1 it grows as l 2 h ere is the growth constant of unconstrained saws in z 2 f orx 1 we provide numerical evidence but no proof that the average walk length grows as l 4 3 another problem we study is that of saws as described above that pass through the central vertex of the square we estimate the proportion of such walks as a fraction of the total and find it to be just below 80 of the total number of saws we also consider hamiltonian walks under the same restriction they are known to grow as l 2 o l2

parameter and differentiation order estimation in fractional models this paper deals with continuous time system identification using fractional differentiation models an adapted version of the simplified refined instrumental variable method is first proposed to estimate the parameters of the fractional model when all the differentiation orders are assumed known then an optimization approach based on the use of the developed instrumental variable estimator is presented two variants of the algorithm are proposed either all differentiation orders are set as integral multiples of a commensurate order which is estimated or all differentiation orders are estimated the former variant allows to reduce the number of parameters and can be used as a good initial hit for the latter variant the performances of the proposed approaches are evaluated by monte carlo simulation analysis finally the proposed identification algorithms are used to identify thermal diffusion in an experimental setup

innovative fractional derivative estimation of the pseudo state for a class of fractional order linear systems in this paper a non asymptotic and robust method is proposed to estimate the fractional integral and derivative of the pseudo state for a class of fractional order linear systems in noisy environment with unknown initial conditions to the best of our knowledge no method has been developed for such estimation firstly the estimation problem is transformed into estimating the fractional integral and derivative of the output and a set of fractional derivative initial values then algebraic integral formulas are exactly derived for the sought estimators by applying different modulating functions with specified properties in particular a design parameter is introduced in the formulas of fractional derivative initial values which can improve the robustness by choosing appropriate values secondly it is shown how to construct the required modulating functions in an efficient way where another design parameter is involved moreover some error analysis is given to choose the design parameters finally numerical simulations are provided to demonstrate the efficiency and the robustness to noises of the proposed method

algebraic techniques for enumerating self avoiding walks on the square lattice the authors describe a new algebraic technique for enumerating self avoiding walks on the rectangular lattice the computational complexity of enumerating walks of n steps is of order 3n 4 times a polynomial in n and so the approach is greatly superior to direct counting techniques they have enumerated walks of up to 39 steps as a consequence they are able to accurately estimate the critical point critical exponent and critical amplitude

blind channel identification via stochastic approximation constant step size algorithms this work is devoted to the study of a class of recursive algorithms for blind channel identification using weak convergence methods the convergence of the algorithm is obtained and the rate of convergence is ascertained the technique discussed can also be used in the analysis of rates of convergence for decreasing step size algorithms

fractional order differentiation by integration and error analysis in noisy environment the integer order differentiation by integration method based on the jacobi orthogonal polynomials for noisy signals was originally introduced by mboup join and fliess we propose to extend this method from the integer order to the fractional order to estimate the fractional order derivatives of noisy signals firstly two fractional order differentiators are deduced from the jacobi orthogonal polynomial filter using the riemann liouville and the caputo fractional order derivative definitions respectively exact and simple formulae for these differentiators are given by integral expressions hence they can be used for both continuous time and discrete time models in on line or off line applications secondly some error bounds are provided for the corresponding estimation errors these bounds allow to study the design parameters influence the noise error contribution due to a large class of stochastic processes is studied in discrete case the latter shows that the differentiator based on the caputo fractional order derivative can cope with a class of noises whose mean value and variance functions are polynomial time varying thanks to the design parameters analysis the proposed fractional order differentiators are significantly improved by admitting a time delay thirdly in order to reduce the calculation time for on line applications a recursive algorithm is proposed finally the proposed differentiator based on the riemann liouville fractional order derivative is used to estimate the state of a fractional order system and numerical simulations illustrate the accuracy and the robustness with respect to corrupting noises

nonuniform star polymers in two dimensions we present simulation results for nonuniform 2d star polymers using a recursive implementation of the enrichment method we show that the choice of parameters in this method is not trivial and that a good choice can lead to extremely efficient code we find that the exponents gamma f governing the increase of the f star partition function with n are compatible with the prediction gamma funiform f 1 by duplantier 1986

lower bound on the connective constant for square lattice self avoiding walks by enumerating irreducible bridges exactly up to 40 steps and by obtaining a lower bound to the number of bridges with less than 125 steps a lower bound for the connective constant for square lattice self avoiding walks of 2 62 is obtained

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

blind equalization using least squares lattice prediction second order statistics of the received signal can be used to equalize a communication channel without knowledge of the transmitted sequence blind zero forcing zf and minimum mean square error mmse equalization can be achieved with linear prediction error filtering the equivalence with the equalizers derived by giannakis and halford see ibid vol 45 p 2277 92 1997 is shown and adaptive predictors that result in a lattice filtering structure are applied the required channel coefficient vector is obtained with adaptive eigen pair tracking either forward or backward prediction errors can be used the performance of the blind equalizer is examined by simulations the mmse of the optimum fse is approached and the algorithm exhibits robustness to channels with common subchannel zeros

fractional order sliding mode based extremum seeking control of a class of nonlinear systems this paper develops a fractional order sliding mode based extremum seeking controller fo sm esc for the optimization of nonlinear systems the proposed fo sm esc involving an fo derivative function 0 d t q sgn e 0 q 1 is shown to achieve faster tracking and higher control accuracy than the integer order io sm esc the tradeoff between control performance and parameters selection is analyzed and visualized the comparison between the fo io sm esc is given to reveal the potential advantages of the fo controller over the io controller simulation and experimental results show that the fo sm esc can have a faster convergence speed and a smaller neighborhood around the optimal operational point

the fixed irreducible bridge ensemble for self avoiding walks we define a new ensemble for self avoiding walks in the upper half plane the fixed irredicible bridge ensemble by considering self avoiding walks in the upper half plane up to their n th bridge height y n and scaling the walk by 1 y n to obtain a curve in the unit strip and then taking n rightarrow infty we then conjecture a relationship between this ensemble to sle 8 3 in the unit strip from 0 to a fixed point along the upper boundary of the strip integrated over the conjectured exit density of self avoiding walk spanning a strip in the scaling limit we conjecture that there exists a positive constant sigma such that n sigma y n converges in distribution to that of a stable random variable as n rightarrow infty then the conjectured relationship between the fixed irreducible bridge scaling limit and sle 8 3 can be described as follows if one takes a saw considered up to y n and scales by 1 y n and then weights the walk by y n to an appropriate power then in the limit n rightarrow infty one should obtain a curve from the scaling limit of the self avoiding walk spanning the unit strip in addition to a heuristic derivation we provide numerical evidence to support the conjecture and give estimates for the boundary scaling exponent

square lattice self avoiding walks and biased differential approximants the model of self avoiding lattice walks and the asymptotic analysis of power series have been two of the major research themes of tony guttmann in this paper we bring the two together and perform a new analysis of the generating functions for the number of square lattice self avoiding walks and some of their metric properties such as the mean square end to end distance the critical point x c for self avoiding walks is known to a high degree of accuracy and we utilise this knowledge to undertake a new numerical analysis of the series using biased differential approximants the new method is major advance in asymptotic power series analysis in that it allows us to bias differential approximants to have a singularity of order q at x c when biasing at x c with the analysis yields a very accurate estimate for the critical exponent thus confirming the conjectured exact value to eight significant digits and removing a long standing minor discrepancy between exact and numerical results the analysis of the mean square end to end distance yields thus confirming the exact value to seven significant digits

the size and number of rings on the square lattice the authors have calculated the number of self avoiding polygons on the square lattice to 56 steps and the caliper size to 54 steps analysis of the generating function permits estimates of the connective constant mu 2 638 1585 or 10 6 and the critical exponents alpha 0 500 06 or 0 000 06 and v 0 753 or 0 007 the singularity structure of the polygon generating function is found to be consistent with a correction to the scaling exponent delta 1 5 as predicted by nienhuis 1982 1984 the confluent part however maps into the additive analytic term due to the value of the exponent alpha

on the area of square lattice polygons we consider the generating function of self avoiding square lattice polygons grouped by both area and perimeter the generating function for polygons of arean is found to diverge atx c 0 251834 with an exponent of zero the mean perimeter of polygons with arean is found to be proportional ton while the mean area of polygons with perimetern is found to be proportional ton 1 5

the self avoiding walk spanning a strip we review the existence of the infinite length self avoiding walk in the half plane and its relationship to bridges we prove that this probability measure is also given by the limit as c of the probability measure on all finite length walks with the probability of proportional to where is the number of steps in c is the reciprocal of the connective constant the self avoiding walk in a strip z 0 operatorname im z y is defined by considering all self avoiding walks in the strip which start at the origin and end somewhere on the top boundary with probability proportional to beta c omega we prove that this probability measure may be obtained by conditioning the saw in the half plane to have a bridge at height y this observation is the basis for simulations to test conjectures on the distribution of the endpoint of the saw in a strip and the relationship between the distribution of this strip saw and sle8 3

performance bounds for multistep prediction based blind equalization blind equalization attempts to remove the interference caused by a communication channel without using any known training sequences blind equalizers may be implemented with linear prediction error filters pefs for many practical channel types a suitable delay at the output of the equalizer allows for achieving a small estimation error the delay cannot be controlled with one step predictors consequently multistep pef based algorithms have been suggested as a solution to the problem the derivation of the existing algorithms is based on the assumption of a noiseless channel which results in zero forcing equalization we consider the effects of additive noise at the output of the multistep pef analytical error bounds for two pef based blind equalizers in the presence of noise are derived the obtained results are verified with simulations the effect of energy concentration in the channel impulse response on the error bound is also addressed