large deviations hypotheses testing and source coding for finite markov chains let x n n geq 1 be a finite markov chain with transition probability matrix of strictly positive entries a large deviation theorem is proved for the empirical transition count matrix and is used to get asymptotically optimal critical regions for testing simple hypotheses about the transition matrix as a corollary the error exponent in the source coding theorem for x n is obtained these results generalize the corresponding results for the independent and identically distributed case

fine asymptotics for universal one to one compression of parametric sources universal source coding at short blocklengths is considered for an i i d exponential family of distributions the type size code has previously been shown to be optimal up to the third order rate for universal compression of all memoryless sources over finite alphabets the type size code assigns sequences ordered based on their type class sizes to binary strings ordered lexicographically to generalize this type class approach for parametric sources a natural scheme is to define two sequences to be in the same type class if and only if they are equiprobable under any model in the parametric class this natural approach however is shown to be suboptimal a variation of the type size code is introduced where type classes are defined based on neighborhoods of minimal sufficient statistics the asymptotics of the overflow rate of this variation are derived and a converse result establishes its optimality up to the third order term

information geometry on hierarchy of probability distributions an exponential family or mixture family of probability distributions has a natural hierarchical structure this paper gives an orthogonal decomposition of such a system based on information geometry a typical example is the decomposition of stochastic dependency among a number of random variables in general they have a complex structure of dependencies pairwise dependency is easily represented by correlation but it is more difficult to measure effects of pure triplewise or higher order interactions dependencies among these variables stochastic dependency is decomposed quantitatively into an orthogonal sum of pairwise triplewise and further higher order dependencies this gives a new invariant decomposition of joint entropy this problem is important for extracting intrinsic interactions in firing patterns of an ensemble of neurons and for estimating its functional connections the orthogonal decomposition is given in a wide class of hierarchical structures including both exponential and mixture families as an example we decompose the dependency in a higher order markov chain into a sum of those in various lower order markov chains

a new proof for decell s finite algorithm for generalized inverses a new proof for decell s finite algorithm for determining the moore penrose generalized inverse of a rectangular matrix is given in this proof we develop additional properties of the algorithm and point out how it can be used for further development of the algebraic properties of the moore penrose generalized inverse

definition of percolation thresholds on self affine surfaces we study the percolation transition on a two dimensional substrate with long range self affine correlations we find that the position of the percolation threshold on a correlated lattice is no longer unique and depends on the spanning rule employed numerical results are provided for spanning across the lattice in specified horizontal or vertical either or both directions

maximum entropy principles for disordered spins we transform nonstationary independent random fields with exponential radon nikodym factors and study the asymptotics of the transformed processes as applications we deduce conditional limit theorems for such random fields and we study a curie weiss type mean field model of a quenched mixed magnetic crystal this model has quenched site disorder and frustration but non random coupling constants we find a continuous phase transition with critical exponents equal to those of the classical curie weiss theory

asymptotics of likelihood ratio derivative estimators in simulations of highly reliable markovian systems we discuss the estimation of derivatives of a performance measure using the likelihood ratio method in simulations of highly reliable markovian systems we compare the difficulties of estimating the performance measure and of estimating its partial derivatives with respect to component failure rates as the component failure rates tend to 0 and the component repair rates remain fixed we first consider the case when the quantities are estimated using naive simulation i e when no variance reduction technique is used in particular we prove that in the limit some of the partial derivatives can be estimated as accurately as the performance measure itself this result is of particular interest in light of the somewhat pessimistic empirical results others have obtained when applying the likelihood ratio method to other types of systems however the result only holds for certain partial derivatives of the performance measure when using naive simulation more specifically we can estimate a certain partial

percolation through self affine surfaces we study the percolation transition in a long range correlated system a self affine surface for all relevant physical cases i e positive roughness exponents it is found that the onset of percolation is governed by the largest wavelength of the height distribution and thus self averaging breaks down self averaging is recovered for negative roughness exponents i e power law decay of the height pair correlation function and in this case the critical exponents that characterize the transition are explicitly dependent on the roughness exponent above a threshold value below this threshold the spatial correlations are no longer relevant the problem is analytically investigated for a hierarchical network and by means of numerical simulations in two dimensions finally we discuss the application of those properties to mercury porosimetry in cracks

the method of types information theory the method of types is one of the key technical tools in shannon theory and this tool is valuable also in other fields in this paper some key applications are presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method and a wide selection of further applications are surveyed these range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems while the method of types is suitable primarily for discrete memoryless models its extensions to certain models with memory are also discussed

large deviations for the empirical measure of a markov chain with an application to the multivariate empirical measure on demontre les proprietes de grandes deviations uniformes pour la mesure empirique et la mesure empirique multivariable d une chaine de markov qui prend ses valeurs dans un espace metrique separable complet

an oblique projection iterative method to compute drazin inverse and group inverse in this paper an oblique projection iterative method is presented to compute matrix equation axa a of a square matrix a with ind a 1 by this iterative method when taken the initial matrix x 0 a the group inverse a g can be obtained in absence of the roundoff errors if we use this iterative method to the matrix equation a kxa k a k a group inverse a k g of matrix a k is got then we use the formulae a d a k 1 a k g the drazin inverse a d can be obtained

maximum entropy and conditional probability it is well known that maximum entropy distributions subject to appropriate moment constraints arise in physics and mathematics in an attempt to find a physical reason for the appearance of maximum entropy distributions the following theorem is offered the conditional distribution of x l given the empirical observation 1 n sum n i l h x i alpha where x 1 x 2 cdots are independent identically distributed random variables with common density g converges to f lambda x e lambda t h x g x suitably normalized where lambda is chosen to satisfy int f lambda x h x dx alpha thus the conditional distribution of a given random variable x is the normalized product of the maximum entropy distribution and the initial distribution this distribution is the maximum entropy distribution when g is uniform the proof of this and related results relies heavily on the work of zabell and lanford

dependency of percolation critical exponents on the exponent of power law size distribution abstract the standard percolation theory uses objects of the same size moreover it has long been observed that the percolation properties of the systems with a finite distribution of sizes are controlled by an effective size and consequently the universality of the percolation theory is still valid in this study the effect of power law size distribution on the critical exponents of the percolation theory of the two dimensional models is investigated two different object shapes i e stick shaped and square are considered these two shapes are the representative of the fractures in fracture reservoirs and the sandbodies in clastic reservoirs the finite size scaling arguments are used for the connectivity to determine the dependency of the critical exponents on the power law exponent in particular the deviations of percolation exponents from their universal values as well as the connectivity behavior of such systems are investigated numerically as a result this extends the applicability of the conventional percolation approach to study the connectivity of systems with a very broad size distribution

new bounds and constructions for granular media coding improved lower and upper bounds on the size and the rate of grain correcting codes are presented the lower bound is gilbert varshamov like combined with a construction by gabrys et al and it improves on the previously best known lower bounds on the asymptotic rate of lceil tau n rceil grain correcting codes of length n on the interval 0 0 0668 one of the two newly presented upper bounds improves on the best known upper bounds on the asymptotic rate of lceil tau n rceil grain correcting codes of length n on the interval tau in 0 1 8 and meets the lower bound of 1 2 for tau geq 1 8 moreover in a nonasymptotic regime both upper bounds improve on the previously best known results on the largest size of t grain correcting codes of length n for certain values of n and t constructions of 1 grain correcting codes based on a partitioning technique are presented for lengths up to 18 finally a lower bound of 1 2 log 2 n on the minimum redundancy of infty grain detecting codes of length n is presented

complete equivalence of the gibbs ensembles for one dimensional markov systems we show the equivalence of the gibbs ensembles at the level of measures for one dimensional markov systems with arbitrary boundary conditions that is the limit of the microcanonical gibbs ensemble is a gibbs measure with an interaction depending on the microcanonical constraint in fact the usual microcanonical condition is replaced by the sharper constraint that all type frequencies of neighboring spins including the boundary spins are fixed when conditioning on a set of different frequencies of neighboring spins compatible with physical quantities like energy density we get the usual microcanonical ensemble we show that the limit is a gibbs measure for a nearest neighbor potential depending on the pair measure which maximizes the entropy on the given set of pair measures for this we show the large deviation property of the pair empirical measure for arbitrary boundary conditions we establish analogous results for finite range potentials

fast universal coding with context models a universal code using context models is constructed which is optimal in the strong sense that the mean per symbol code length approaches asymptotically the entropy of any data generating tree machine at the fastest possible rate the number of coding operations required is o n log log n for a string of length n which is much less than in the earlier codes using context models this is made possible by two new results the first is a theorem stating that the updates required for universality need be done only once for each batch the length of which grows at nearly exponential rate in the number of batches the second is a fast implementation of the tree building part in algorithm context

invasion percolation in fractal fractures abstract invasion percolation ip with trapping was studied on two dimensional substrates with a correlated distribution of invasion thresholds the substrates represented the void spaces of variable aperture fracture models that were formed by 2 1 dimensional self affine rough surfaces and their replicas displaced relative to each other void spaces generated in this manner were self affine on length scales less than the horizontal displacement rd and uncorrelated on larger length scales the geometry of the ip clusters reflected the void space geometry with different scaling behavior on length scales below and beyond rd

a bayesian approach for classification of markov sources a bayesian approach for classification of markov sources whose parameters are not explicitly known is developed and studied a universal classifier is derived and shown to achieve within a constant factor the minimum error probability in a bayesian sense the proposed classifier is based on sequential estimation of the parameters of the sources and it is closely related to earlier proposed universal tests under the neyman pearson criterion

variable length state splitting with applications to average runlength constrained arc codes a new class of constrained systems average runlength constraints arcs is defined by requiring that the sum of n consecutive run lengths be bounded above by a linear function of n in particular the running average runlength of every sequence in the system is bounded above by a constant a general result is given on the capacity of arc systems the state splitting algorithm is then improved for variable length graphs this is then applied to obtain high fixed rate codes from the free binary source to arc systems as an example a rate 1 2 d k

refinements of the gibbs conditioning principle refinements of sanov s large deviations theorem lead via csiszar s information theoretic identity to refinements of the gibbs conditioning principle which are valid for blocks whose length increase with the length of the conditioning sequence sharp bounds on the growth of the block length with the length of the conditioning sequence are derived

on the connectivity of three dimensional fault networks natural fault networks involve a very broad range of fault lengths modeled in general by a power law length distribution n l al such a scaling law does not allow to define any a priori pertinent scale of observation for hydraulic field experiments in fractured media to investigate the relative effects of faults depending on their length we undertake in the spirit of percolation theory a theoretical and numerical study of the connectivity of three dimensional fault networks following power law length distributions we first establish the correct analytical expression of a percolation parameter p which describes the connectivity of the system the parameter p is found to be dependent on the third moment of the length distribution for fault planes it allows us to identify different regimes of connectivity depending on a the exponent of the fault length distribution the geometrical properties of the infinite cluster which partly control transport properties are also established at the percolation threshold for natural fault networks our theoretical analysis suggests that faults larger than a critical length scale may form a well connected network while smaller faults may be not connected on average this result which implies an increase of the connectivity with scale is consistent with scaling effects observed on permeability measurements

deinterleaving finite memory processes via penalized maximum likelihood we study the problem of deinterleaving a set of finite memory markov processes over disjoint finite alphabets which have been randomly interleaved by a finite memory switch the deinterleaver has access to a sample of the resulting interleaved process but no knowledge of the number or structure of the component markov processes or of the switch we study conditions for uniqueness of the interleaved representation of a process showing that certain switch configurations as well as memoryless component processes can cause ambiguities in the representation we show that a deinterleaving scheme based on minimizing a penalized maximum likelihood cost function is strongly consistent in the sense of reconstructing almost surely as the observed sequence length tends to infinity a set of component and switch markov processes compatible with the original interleaved process furthermore under certain conditions on the structure of the switch including the special case of a memoryless switch we show that the scheme recovers all possible interleaved representations of the original process experimental results are presented demonstrating that the proposed scheme performs well in practice even for relatively short input samples

on the converse theorem in statistical hypothesis testing for markov chains hypothesis testing for two markov chains is considered under the constraint that the error probability of the first kind is less than or equal to exp rn the error probability of the second kind is minimized the geodesic that connects the two markov chains is defined by analyzing the geodesic the power exponents are calculated and then represented in terms of kullback leibler divergence

minimum cross entropy estimation with inaccurate side information given a prior estimate of a probability q and a constraint spl sigma p sub i x sub i a one well known way of estimating p is to minimize the cross entropy i p q subject to the constraint a modification to this method is proposed for use when the value a is only approximately known the modification is based on the penalty function method in constrained optimization it has an interpretation in differential geometry methods in statistics and it sometimes gives a maximum likelihood estimate

arma models prewhitening and minimum cross entropy the problem of spectral estimation on the basis of observations from a finite stretch of a stationary time series is considered in connection with knowledge of a prior estimate of the spectral density a reasonable posterior spectral density estimate would be the density that is closest to the prior according to some measure of divergence while at the same time being compatible with the data the cross entropy has often been proposed to serve as such a measure of divergence a correction of the original minimum cross entropy spectral analysis mcesa method of j e shore see ieee trans acoust speech signal process vol 29 p 230 7 1981 to traditional prewhitening techniques and to autoregressive moving average arma models is pointed out and a fast approximate solution of the minimum cross entropy problem is proposed the solution is in a standard multiplicative form that is the posterior is equal to the prior multiplied by a correction factor

a finite algorithm for the drazin inverse of a polynomial matrix based on greville s finite algorithm for drazin inverse of a constant matrix we propose a finite numerical algorithm for the drazin inverse of polynomial matrices we also present a new proof for decell s finite algorithm through greville s finite algorithm

entropy at a weight per symbol and embeddings of markov chains in 11 krieger gave a remarkable embedding result for shifts of finite type he proved that two simple necessary conditions strict inequality of the topological entropies of the shifts and the existence of an embedding for their periodic points are in fact sufficient for markov chains when the appropriate definitions of embedding and subsystem were supplied in 10 analogous necessary conditions strict inequality of functions and the existence of a weight preserving embedding for periodic points became apparent however an example in 10 also revealed these conditions to not be sufficient in this paper we bring to bear on embeddings of markov chains the ideas we introduced in 16 in fact we work in the closely related setting of triples z a a a f where 2 a aa is a shift of finite type and f is a function assigning weights to the edges of the graph associated with sa aa the func t ionf takes values in ir or more generally in n q for some qen the weight of a periodic orbit which corresponds to a cycle in the graph is then the sum of the weights of the edges lying on the cycle division by the length of the cycle gives the weight per symbol in 16 we continued the rational linear span of the set wps i of weights per symbol is a finite dimensional vector space vs the convex hull of wps i in v i is a polytope wpsi called the weight per symbol polytope consideration of the faces of wps i gives subsystems of r a aa f which are ordered according to the ordering of the faces the resulting nesting of subsystems is the scaffold of a o a f an embedding of a triple i a a a f in another 2 b ab g is a continuous shift commuting injection q 2 a 12 which preserves weights of periodic orbits the two necessary conditions mentioned above imply w p s i c w when the boundary c wpsi meets wpsg that is when a face f of wps i meets a face g of wpsg any embedding must carry the subsystem corresponding to f into that corresponding to g and this gives rise to further necessary conditons a discussion of these complications and a description of the example of 10 in these terms will be given in sect 7 before that the main embedding

an information theoretic spectral density an information theoretic spectrum which minimizes the kullback leibler 1951 information number subject to the first p 1 autocovariance terms is proposed the kl spectrum includes the maximum entropy spectrum and the arma autoregressive moving average spectrum as special cases a method is proposed for modifying a spectral estimate on the basis of the results for the kl spectrum so that the revised spectral estimate is more loyal to the given observations than the primary estimate

expectations for nonreversible markov chains bounds are given for an irreducible markov chain on the probability that the time average of a functional on the state space exceeds its stationary expectation without assuming reversibility the bounds are in terms of the singular values of the discrete generator

a new extension of leverrier s algorithm abstract an algorithm for computing the inverse of a matrix polynomial s n j s n 1a 1 sa n 1 a n is given where j is a singular matrix this algorithm is a new extension of leverrier s algorithm for computing the inverse of a matrix polynomial s n i s n 1 a 1 sa n 1 a n where i denotes the unit matrix

limit representations of generalized inverses and related methods we generalize the iterative method for implementation of the limit representation of the moore penrose inverse lim a email protected a a 1a introduced by zukovski and lipcer z vicisl mat i mat fiz 12 1972 843 15 1975 489 more precisely we define an iterative process for implementing the general limit formula lim a 0 ai r s 1r in a certain case the presented method gives an iterative process which implements the known limit representation of the drazin inverse introduced by meyer siam j appl math 26 1974 469 also the known limit representation of the generalized inverse a t s 2 is a special case of the general limit formula in the case of a full rank matrix a we define a limit representation and an iterative method for computation of the left or right inverses of a also we introduce two alternative limit representations for the set of 2 and 1 2 inverses and develop the corresponding iterative processes moreover we propose a finite algorithm for computation of the generalized inverses contained in the limit formula lim a 0 ai r s 1r using the method developed by ji appl math comput 61 1994 151

sequential prediction and ranking in universal context modeling and data compression most state of the art lossless image compression schemes use prediction followed by some form of context modeling this might seem redundant at first as the contextual information used for prediction is also available for building the compression model and a universal coder will eventually learn the predictive patterns of the data in this correspondence we provide a format justification to the combination of these two modeling tools by showing that a combined scheme may result in faster convergence rate to the source entropy this is achieved via a reduction in the model cost of universal coding in deriving the main result we develop the concept of sequential ranking which can be seen as a generalization of sequential prediction and we study its combinatorial and probabilistic properties

hydraulic properties of two dimensional random fracture networks following a power law length distribution 1 effective connectivity natural fracture networks involve a very broad range of fractures of variable lengths and apertures modeled in general by a power law length distribution and a lognormal aperture distribution the objective of this two part paper is to characterize the permeability variations as well as the relevant flow structure of two dimensional isotropic models of fracture networks as determined by the fracture length and aperture distributions and by the other parameters of the model such as density and scale in this paper we study the sole influence of the fracture length distribution on permeability by assigning the same aperture to all fractures in the following paper de dreuzy et al this issue we study the more general case of networks in which fractures have both length and aperture distributions theoretical and numerical studies show that the hydraulic properties of power law length fracture networks can be classified into three types of simplified model if a power law length distribution n l l a is used in the network design the classical percolation model based on a population of small fractures is applicable for a power law exponent a higher than 3 for a lower than 2 on the contrary the applicable model is the one made up of the largest fractures of the network between these two limits i e for a in the range 2 3 neither of the previous simplified models can be applied so that a simplified two scale structure is proposed for this latter model the crossover scale is the classical correlation length defined in the percolation theory above which networks can be homogenized and below which networks have a multipath multisegment structure moreover the determination of the effective fracture length range within which fractures significantly contribute to flow corroborates the relevance of the previous models and clarifies their geometrical characteristics finally whatever the exponent a the sole significant scale effect is a decrease of the equivalent permeability for networks below or at percolation threshold

a finite algorithm for computing the weighted moore penrose inverse a mn this paper presents a finite algorithm for computing the weighted moore penrose inverse of a rectangular matrix this algorithm may be viewed as an extension of decell s algorithm

maxentropic markov chains corresp the markov chain that has maximum entropy for given first and second moments is determined the solution provides a discrete analog to the continuous gauss markov process

type classes of context trees it is well known that a tree model does not always admit a finite state machine fsm representation with the same minimal number of parameters therefore known characterizations of type classes for fsms do not apply in general to tree models in this paper the type class of a sequence with respect to a given context tree is studied an exact formula is derived for the size of the class extending whittle s formula for type classes with respect to fsms the derivation is more intricate than in the fsm case since some basic properties of fsm types do not hold in general for tree types the derivation also yields an efficient enumeration of the tree type class a formula for the number of type classes with respect to is also derived the formula is asymptotically tight up to a multiplicative constant and also extends the corresponding result for fsms the asymptotic behavior of the number of type classes and of the size of a class is expressed in terms of the so called minimal canonical extension of t a tree that is generally larger than but smaller than its fsm closure

an alternative limit expression of drazin inverse and its application abstract we present an alternative limit expression of drazin inverse of a square matrix and a new proof for a finite algorithm for determining the drazin inverse is given using our new limit expression

conditional limit theorems under markov conditioning let x 1 x 2 cdots be independent identically distributed random variables taking values in a finite set x and consider the conditional joint distribution of the first m elements of the sample x 1 cdots x n on the condition that x 1 x 1 and the sliding block sample average of a function h cdot cdot defined on x 2 exceeds a threshold alpha eh x 1 x 2 for m fixed and n rightarrow infty this conditional joint distribution is shown to converge m the m step joint distribution of a markov chain started in x 1 which is closest to x l x 2 cdots in kullback leibler information divergence among all markov chains whose two dimensional stationary distribution p cdot cdot satisfies sum p x y h x y geq alpha provided some distribution p on x 2 having equal marginals does satisfy this constraint with strict inequality similar conditional limit theorems are obtained when x 1 x 2 cdots is an arbitrary finite order markov chain and more general conditioning is allowed

interpolation algorithm for computing drazin inverse of polynomial matrices in this paper we introduce an interpolation method for computing the drazin inverse of a given polynomial matrix this method is an extension of the known method from a schuster p hippe inversion of polynomial matrices by interpolation ieee trans automat control 37 3 1992 363 365 applicable to usual matrix inverse also we improve our interpolation method using a more effective estimation of degrees of polynomial matrices generated in leverrier faddeev method algorithms are implemented and tested in the symbolic package mathematica

a finite algorithm for generalized inverses of polynomial and rational matrices there are proposed two types of finite algorithms for symbolic computation of outer inverses of a given polynomial or rational matrix based on the extension of the leverrier faddeev algorithm the implementation of the algorithm corresponding to rational matrices is developed in the symbolic package mathematica

flooding transition in the topography of toppling surfaces of stochastic and rotational sandpile models a continuous phase transition occurs in the topography of toppling surfaces of stochastic and rotational sandpile models when they are flooded with liquid say water the toppling surfaces are extracted from the sandpile avalanches that appear due to sudden burst of toppling activity in the steady state of these sandpile models though a wide distribution of critical flooding heights exists a critical point is defined by merging the flooding thresholds of all the toppling surfaces the criticality of the transition is characterized by power law distributionofislandareainthecriticalregime afinitesizescalingtheoryisdevelopedandverifiedbycalculating several new critical exponents the flooding transition is found to be an interesting phase transition and does not belong to the percolation universality class the universality class of this transition is found to depend on the degree of self affinity of the toppling surfaces characterized by the hurst exponent h and the fractal dimension df of critical spanning islands the toppling surfaces of different stochastic sandpile models are found to have a single hurst exponent whereas those of different rotational sandpile models have another hurst exponent as a consequence the universality class of different sandpile models remains preserved within the same symmetry of the models

the error exponent for the noiseless encoding of finite ergodic markov sources a new approach to the classical fixed length noiseless source coding problem is proposed for the case of finite ergodic markov sources this approach is based on simple counting arguments the central notion of markov type a set containing all the source sequences having the same transition counts from letter to letter is introduced and the cardinality of such a set is evaluated via graph theoretical tools the error exponent is shown to be a weighted average of informational divergences and the universal character of the result is stressed as a corollary the classical source coding theorem determining the achievable rates is rederived

universal delay estimation for discrete channels the use of information theory concepts for universal estimation of delay for classes of discrete channels is discussed the problem is presented as one of hypothesis testing although the channel statistics are not known for large enough signal duration the exponent of the average error probability is equal to that associated with the optimal maximum likelihood ml decision procedure which utilizes full knowledge of the channel parameters two categories of problems are discussed the single channel problem where the random transmitted signal is known to the receiver and the two sensor problem where the random signal is unknown

further remarks on the cayley hamilton theorem and leverrier s method for the matrix pencil se a some results for matrix pencils are extended to the singular case se a a singular leverrier s relation cayley hamilton theorem and newton s formula are given a finite series expansion for se a 1 is given in terms of the generalized tschirnhausen polynomials

a universal finite memory source an irreducible parameterization for a finite memory source is constructed in the form of a tree machine a universal information source for the set of finite memory sources is constructed by a predictive modification of an earlier studied algorithm context it is shown that this universal source incorporates any minimal data generating tree machine in an asymptotically optimal manner in the following sense the negative logarithm of the probability it assigns to any long typical sequence generated by any tree machine approaches that assigned by the tree machine at the best possible rate

critical properties of island perimeters in the flooding transition of stochastic and rotational sandpile models critical properties of external perimeters of islands that appear at the flooding transition in the toppling surfaces defined by the toppling number si of each sand column of stochastic and rotational sandpile models are studied a set of new critical exponents are estimated by extensive numerical simulation and finite size scaling analysis the values of the critical exponents are found different for these sandpile models several scaling relations among the critical exponents and the hurst exponent describing the self affinity of the toppling surfaces are established and verified the critical exponents obtained here are also found connected to the exponents describing the avalanche size distribution

bond percolation of polymers we study bond percolation of n non interacting gaussian polymers of l segments on a 2d square lattice of size l with reflecting boundaries through simulations we find the fraction of configurations displaying no connected cluster which span from one edge to the opposite edge from this fraction we define a critical segment density lc l and the associated critical fraction of occupied bonds plc l so that they can be identified as the percolation threshold in the l limit whereas plc l is found to decrease monotonically with l for a wide range of polymer lengths lc l is non monotonic we give physical arguments for this intriguing behaviour in terms of the competing effects of multiple bond occupancies and polymerization