the critical behavior of dimer dimer surface reaction models monte carlo and finite size scaling investigation two models based upon the well known mechanism for the oxidation of hydrogen on transition metal surfaces which may also apply to generic dimerdimer surface reaction processes of the type 1 2 a2 b2 b2a are proposed and studied on the square lattice of sidel l 600 by means of monte carlo simulations and finite size analysis both models exhibit irreversible kinetic phase transitions ipt from a reactive state with sustained production of b2a molecules to off equilibrium surface poisoned states with the reactants i e without production the location of the critical points at which the ipts take place in thel limit is determined by means of a finite size scaling analysis also it is shown that at criticality some relevant quantities such as the rate of b2a production and the coverage with the reactants exhibit simple power law behavior which allow us to determine the corresponding critical exponents

the resistive susceptibility of a three dimensional random diode insulator network the resistive susceptibility chi r p of harris and fisch is expanded graphically for the directed simple cubic bond problem as a power series in the diode density p up to p11 standard pade analysis shows that chi r p diverges with the exponent gamma r 2 70 or 0 04 and using a scaling relation the exponent t for the conductivity of the infinite cluster is estimated to be t 1 29 or 0 02

low density series expansions for directed percolation i a new efficient algorithm with applications to the square lattice a new algorithm for the derivation of low density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems numerical evidence shows that the computational complexity grows exponentially but with a growth factor which is much smaller than the growth factor of the previous best algorithm for bond site percolation on the directed square lattice the series has been extended to order 171 158 analysis of the series yields sharper estimates of the critical points and exponents

critical behaviour of a surface reaction model with infinitely many absorbing states in a recent letter yaldram et al 1993 studied the critical behaviour of a simple lattice gas model of the co no catalytic reaction the model exhibits a second order non equilibrium phase transition from an active state into one out of infinitely many absorbing states estimates for the critical exponent beta suggested that the model belongs to a new universality class the results reported in this article contradict this notion as estimates for various critical exponents show that the model belongs to the universality class of directed percolation

nonnegative matrix factorization for spectral data analysis data analysis is pervasive throughout business engineering and science very often the data to be analyzed is nonnegative and it is often preferable to take this constraint into account in the analysis process here we are concerned with the application of analyzing data obtained using astronomical spectrometers which provide spectral data which is inherently nonnegative the identification and classification of space objects that cannot be imaged in the normal way with telescopes is an important but difficult problem for tracking thousands of objects including satellites rocket bodies debris and asteroids in orbit around the earth in this paper we develop an effective nonnegative matrix factorization algorithm with novel smoothness constraints for unmixing spectral reflectance data for space object identification and classification purposes promising numerical results are presented using laboratory and simulated datasets

directed percolation with a wall or edge we examine the effects of introducing a wall or edge into a directed percolation process scaling ansatze are presented for the density and survival probability of a cluster in these geometries and we make the connection to surface critical phenomena and field theory the results of previous numerical work for a wall can thus be interpreted in terms of surface exponents satisfying scaling relations generalizing those for ordinary directed percolation new exponents for edge directed percolation are also introduced they are calculated in mean field theory and measured numerically in 2c 1 dimensions

series expansions of the percolation probability for directed square and honeycomb lattices we have derived long series expansions of the percolation probability for site and bond percolation on directed square and honeycomb lattices for the square bond problem we have extended the series from 41 terms to 54 for the square site problem from 16 terms to 37 and for the honeycomb bond problem from 13 terms to 36 analysis of the series clearly shows that the critical exponent beta is the same for all the problems confirming expectations of universality for the critical probability and exponent we find in the square bond case qc 0 3552994 or 0 0000010 beta 0 27643 or 0 00010 in the square site case qc 0 294515 or 0 000005 beta 0 2763 or 0 0003 and in the honeycomb bond case qc 0 177143 or 0 000002 beta 0 2763 or 0 0002 in addition we have obtained accurate estimates for the critical amplitudes in all cases we find that the leading correction to scaling term is analytic i e the confluent exponent delta 1

an extension of wollenberg s redundancy analysis an extension of wollenberg s redundancy analysis is proposed to derivey variates corresponding to the optimalx variates these variates are maximally correlated with the givenx variates and depending upon the standardization chosen they also have certain properties of orthogonality

alternative gradient algorithms for computing the nearest correlation matrix the correlation matrix has a wide range of applications in finance and risk management however due to the constraints of practical operations the correlation matrix cannot satisfy the positive semidefinite property in most cases in this paper an elementwisely alternative gradient algorithm and a columnwisely alternative gradient algorithm are presented to compute the nearest correlation matrix that satisfies the semidefinite property for a given set of constraints the convergence properties and the implementation of these two algorithms are discussed numerical experiments show that the proposed methods are efficient furthermore the columnwisely alternative gradient algorithm outperforms other algorithms in terms of the number of iterations and the objective value of the cost function

one dimensional generalized branching annihilating random walker process with stochastic generation of offsprings abstract we introduce a branching annihilating random walker process with two species particles a and b which diffuse creating new particles and annihilating instantaneously a b 0 when they meet each kind of particle branches stochastically having offsprings of the same or different type the model is defined and studied by means of epidemic simulations in a one dimensional discrete lattice the phase diagram of the model exhibits two states the vacuum and the active one separated by a critical line along that line the system undergoes irreversible second order phase transitions monte carlo results show that the transitions belong to the same universality class as directed percolation in the limiting case when the generation of offsprings is forbidden the model is mapped into the standard diffusion limited reaction a b 0 which asymptotically evolves towards the vacuum state the transition between the stationary regime and such vacuum states is also studied

redundancy analysis for qualitative variables redundancy analysis also called principal components analysis of instrumental variables is a technique for two sets of variables one set being dependent of the other its aim is maximization of the explained variance of the dependent variables by a linear combination of the explanatory variables the technique is generalized to qualitative variables it then gives implicitly a simultaneous optimal scaling of the dependent qualitative variables examples are taken from the dutch life situation survey 1977 using satisfaction with life and happiness as dependent variables the analysis leads to one well being scale defined by the explanatory variables marital status schooling income and activity

block triangular and skew hermitian splitting methods for positive definite linear systems by further generalizing the concept of hermitian or normal and skew hermitian splitting for a non hermitian and positive definite matrix we introduce a new splitting called positive definite and skew hermitian splitting pss and then establish a class of pss methods similar to the hermitian or normal and skew hermitian splitting hss or nss method for iteratively solving the positive definite systems of linear equations theoretical analysis shows that the pss method converges unconditionally to the exact solution of the linear system with the upper bound of its convergence factor dependent only on the spectrum of the positive definite splitting matrix and independent of the spectrum of the skew hermitian splitting matrix as well as the eigenvectors of all matrices involved when we specialize the pss to block triangular or triangular and skew hermitian splitting btss or tss the pss method naturally leads to a btss or tss iteration method which may be more practical and efficient than the hss and nss iteration methods applications of the btss method to the linear systems of block two by two structures are discussed in detail numerical experiments further show the effectiveness of our new methods

image processing using newton based algorithm of nonnegative matrix factorization in this paper we propose a newton based algorithm for nonnegative matrix factorization in image processing we employ the new algorithm to three real world databases extensive numerical results show the feasibility and validity of the proposed algorithm

dynamic critical exponents of discontinuous kinetic phase transitions in surface reaction models abstract dynamical critical exponents of three surface reaction models a monomer monomer process and two variants of the dimer dimer process which exhibit discontinuous kinetics phase transitions kpts are evaluated the obtained exponents differ from those characteristic of continuous kpts and suggest that the three models belongs to distinct universality classes

phase structure of systems with infinite numbers of absorbing states critical properties of systems exhibiting phase transitions into phases with infinite numbers of absorbing states are studied we analyze a non markovian langevin equation recently proposed to describe the critical behavior of such systems and also introduce and study a non markovian discrete model which is argued to present the same critical features on the basis of mean field analysis monte carlo simulations and theoretical arguments we conclude that the phenomenology of the non markovian models closely parallels that of systems with many absorbing states in one and two dimensions the bulk or static critical properties of these systems fall in the directed percolation dp universality class by contrast the critical properties associated with the spread of an initially localized seed exhibit a more complex behavior depending on parameter values they can both in one and two dimensions fall either in the dynamical percolation or dp universality class or else exhibit apparently nonuniversal exponents in contrast to previous results however the nonuniversal exponents in 2d are found to satisfy a scaling law which implies that a particular linear combination of them is universal and assumes dp values these results demonstrate the efficacy of the non markovian approach for understanding systems with many absorbing states which are difficult to analyze in their original microscopic formulation

critical and oscillatory behavior of a system of smart preys and predators it is shown that a system of smart preys and predators exhibits irreversible phase transitions between a regime of prey predator coexistence and an state where predator extinction is observed within the coexistence regime the system exhibits a transition between a regime where the densities of species remain constant and another with self sustained oscillations respectively this transition is located by means of a combined treatment involving finite size scaling and fourier transforms furthermore it is shown that the transition can be rationalized in terms of the standard percolation theory the existence of an oscillatory regime in the thermodynamic limit which is in contrast to previous findings of boccara et al phys rev e 50 4531 1994 may be due to subtle differences between the studied models

on the optimality of the simultaneous redundancy transformations the objective of this paper is to introduce and motivate additional properties and interpretations for the redundancy variables it is shown that these variables can be derived by application of certain invariance arguments and without reference to the index of redundancy in addition an optimality property for the variables is presented which is important whenever one restricts attention in a study to a subset of the redundancy variables this optimality property pertains to the subset rather than to the individual variables

alternative gradient algorithms with applications to nonnegative matrix factorizations three nonnegative matrix factorization nmf algorithms are discussed and employed to three real world applications based on the alternative gradient algorithm with the iteration steps being determined columnwisely without projection and columnwisely and elementwisely with projections three algorithms are developed respectively also the computational costs and the convergence properties of the new algorithms are given the numerical examples show the advantage of our algorithms over the multiplicative update algorithm proposed by lee and seung 11

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

a new type of kinetic critical phenomenon the authors study a new critical phenomenon in an non thermal one dimensional lattice model it is characterised by the transition from stability to instability of kinks between ordered states below the critical point the kinks are stable and move by annihilating random walks above the critical point they are unstable against creation of kink antikink pairs the spontaneous production of pairs is assumed to be absent at the critical point p pcr the density of kinks decreases like n approximately talpha with alpha 0 27 or 0 08 above the critical point the density of kinks in the stationary state is approximately p pcr beta with beta 0 06 or 0 2 possible extensions to two or more dimensions and possible applications are discussed

monte carlo simulation of 3d self avoiding walks presents simulation results for 3d self avoiding walks of moderate length n or 2000 using a recently introduced recursive sampling method it is shown that this method is indeed maximally efficient for determining the connectivity constant mu combining the data with previous results from exact enumerations and from simulations of very long walks using the pivot algorithm the author obtains very precise estimates of mu and of the critical exponents gamma and nu he also points out significant deviations from uniformity in a very popular random number generator which was considered safe until now

newton s method for large bound constrained optimization problems we analyze a trust region version of newton s method for bound constrained problems our approach relies on the geometry of the feasible set not on the particular representation in terms of constraints the convergence theory holds for linearly constrained problems and yields global and superlinear convergence without assuming either strict complementarity or linear independence of the active constraints we also show that the convergence theory leads to an efficient implementation for large bound constrained problems

competing two species directed percolation the authors study an extension of conventional directed percolation dp with two species a and b using mean field and monte carlo methods the densities of the two species in the steady state exhibit phase transitions which are due both to simple percolation and to competition between the species in 1 1 dimensions as well as a simple dp transition there is a line of first order transitions between pure a and pure b phases the phase diagram in a 2 1 dimensions agrees qualitatively with that obtained from mean field calculations with second order transitions between pure and mixed phases preliminary studies suggest that the critical exponents are in the same universality class as one species dp

on two dimensional directed percolation extended series expansions for the mean size and the first and second moments of the pair connectedness for both bond and site percolation on the directed square and triangular lattices have been obtained analysis based on differential approximants allows the critical percolation probabilities and exponents to be estimated and as a result the critical exponents are conjectured to be gamma 41 18 nu perpendicular to 79 72 and nu sub 26 15 scaling then gives beta 199 720 alpha 299 360 and delta 1839 199

the dimer trimer model for heterogeneous catalysis a new universality class the authors study a new model for heterogeneous catalysis in which dimers a2 and trimers b3 are chemisorbed onto a triangular lattice nearest adsorbed a and b neighbours react and desorb leaving behind two empty sites they observe a phase diagram similar to that of the monomer dimer model of ziff gulari and barshad 1986 with a stationary reactive phase in between a dimer poisoned and a trimer poisoned phase there is a first order transition from the reactive phase to the dimer poisoned phase and a second order transition to the trimer poisoned phase however the second order transition is in a different universality class from reggeon field theory in contrast to all previously studied models for catalysis the difference stems from the infinite number of absorbing states in the trimer poisoned phase special to their model

testing the significance of the successive components in redundancy analysis in this paper we study the interrelationships between two sets of data measured on the same subjects via redundancy analysis we consider redundancy analysis from an inferential point of view under the hypothesis of multinormality tests of significance are obtained for each successive redundancy component so that only the significant factors are retained for prediction purposes an example illustrates the method

self affine fractal clusters conceptual questions and numerical results for directed percolation in this paper we address the question of the existence of a well defined non trivial fractal dimensiond of self affine clusters in spite of the obvious relevance of such clusters to a wide range of phenomena this problem is still open since thedifferent published predictions ford have not been tested yet an interesting aspect of the problem is that a nontrivial global dimension for clusters is in contrast with the trivial global dimension of self affine functions as a much studied example of self affine structures we investigate the infinite directed percolation cluster at the threshold we measuredd ind 2 dimensions by the box counting method using a correction to scaling analysis we obtainedd 1 765 10 this result does not agree with any of the proposed relations but it favorsd 1 1 where and are the correlation length exponents and is a fisher exponent in the cluster scaling

critical exponents for a dimer dimer irreversible surface reaction abstract a dimer dimer reaction model of the type a2 b2 2ab is investigated by means of computer simulations the desorption of b2 dimer with probability p is studied here we investigate the critical behaviour the critical exponents of our model do not fall into the reggeon field theory or directed percolation universality class the universality class of the reaction changes with changes in p

conditions under which canonical correlation and redundancy maximization produce identical results summary redundancy analysis was proposed as an alternative to canonical correlation van den wollenberg 1977 the following paper examines the conditions under which canonical correlation and redundancy analysis produce identical solutions it is shown that identical results are possible when all nonzero eigenvalues of the correlation matrix of the criterion variables are equal as a special case when there is only one canonical root or when all criterion variables are uncorrelated canonical correlation and redundancy analysis produce identical results

the three species monomer monomer model in the reaction controlled limit we study the one dimensional three species monomer monomer reaction model in the reaction controlled limit using mean field theory and dynamic monte carlo simulations the phase diagram consists of a reactive steady state bordered by three equivalent adsorbing phases where the surface is saturated with one monomer species the transitions from the reactive phase are all continuous while the transitions between adsorbing phases are first order bicritical points occur where the reactive phase simultaneously meets two adsorbing phases the transitions from the reactive to an adsorbing phase show directed percolation critical behaviour while the universal behaviour at the bicritical points is in the even branching annihilating random walk class the results are contrasted and compared with previous results for the adsorption controlled limit of the same model

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

nonuniversal critical spreading in two dimensions continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations spreading from a localized source is characterized by nonuniversal critical exponents which vary continuously with the density ensuremath varphi in the surrounding region the exponent ensuremath delta changes by more than an order of magnitude and ensuremath eta changes sign the location of the critical point also depends on ensuremath varphi which has important implications for scaling as expected on the basis of universality the static critical behavior belongs to the directed percolation class textcopyright 1996 the american physical society

tricritical directed percolation we consider a modification of the contact process incorporating higher order reaction terms the original contact process exhibits a non equilibrium phase transition belonging to the universality class of directed percolation the incorporated higher order reaction terms lead to a non trivial phase diagram in particular a line of continuous phase transitions is separated by a tricritical point from a line of discontinuous phase transitions the corresponding tricritical scaling behavior is analyzed in detail i e we determine the critical exponents various universal scaling functions as well as universal amplitude combinations

critical behaviour of the irreversible phase transitions of a dimer monomer process on fractal media the dynamic critical behaviour of a dimer monomer surface reaction process the zgb model of the type 1 2 a2 b to ab is studied on two different fractals namely a sierpinski carpet and percolating clusters which have almost the same fractal dimension df equivalent to 1 89 in both surfaces the model exhibits two continuous irreversible phase transitions for the sierpinski carpet the values of the critical exponents interpolate between those of directed percolation in 1 1 and 1 2 dimensions results corresponding to percolating clusters are not conclusive enough to assign the universality class of the model

directed percolation in 2 1 dimensions the author presents results of monte carlo simulations for directed percolation in 2 1 dimensions very close to the percolation threshold his values for pc for bond and site percolation on the bcc and simple cubic lattices are more precise than previous estimates by one to two orders of magnitude the improvement on the critical exponents describing the behaviour at pc is less impressive but they are also substantially more precise than previous ones

directed percolation series expansion for some three dimensional lattices low density series expansions have been obtained for the directed cubic lattice bond problem and the directed cubic and body centred cubic lattice site problems estimates of the critical probabilities and critical exponents gamma gamma 0 nu nu perpendicular to for these problems are obtained the exponent values are found to be consistent with the universality of directed percolation and reggeon field theory and the hyperscaling relation beta d nu perpendicular to nu gamma 2

self organized formulation of standard percolation phenomena abstract we consider standard percolation processes such as epidemic processes with or without immunization we show that their dynamics can be formulated so that they mimic self organized critical phenomena the wetting probability p needs not to be fine tuned to its critical value p c in order to arrive at criticality but it rather emerges as a singularity in some time dependent distribution on the one hand this casts doubts on the significance of self organized as opposed to ordinary criticality on the other hand it suggests very efficient algorithms where percolation problems are studied at several values of p in a single run as an example we apply such an algorithm to directed percolation in 2 1 dimensions where it allows a very precise determination of critical behavior

are damage spreading transitions generically in the universality class of directed percolation we present numerical evidence for the fact that the damage spreading transition in the domany kinzel automaton found by martinset al is in the same universality class as directed percolation we conjecture that also other damage spreading transitions should be in this universality class unless they coincide with other transitions as in the ising model with glauber dynamics and provided the probability for a locally damaged state to become healed is not zero

a new class of critical exponents in a dimer monomer catalytic surface reaction the critical behaviour of a dimer monomer bc a to 1 2c2 ab irreversible catalytic surface reaction is investigated by means of monte carlo simulation technique on a hexagonal lattice each site having six nearest neighbours the reaction exhibits a steady reactive state between two critical concentrations ya1 and ya2 of a the critical exponents associated with various order parameters i e coverages at the second order phase transition ya1 have been obtained these exponents do not fall in the universality class of reggeon field theory as is the case of 1 2b2 a to ab the usual dimer monomer reaction

projected gradient methods for nonnegative matrix factorization nonnegative matrix factorization nmf can be formulated as a minimization problem with bound constraints although bound constrained optimization has been studied extensively in both theory and practice so far no study has formally applied its techniques to nmf in this letter we propose two projected gradient methods for nmf both of which exhibit strong optimization properties we discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach a simple matlab code is also provided