adsorbing and collapsing directed animals a model of a self interacting directed animal which also interacts with a solid wall is studied as a model of a directed branched polymer which can undergo both a collapse and an adsorption transition the directed animal is confined to a 45 wedge and it interacts with one of the walls of this wedge the existence of a thermodynamic limit in this model shown and the presence of an adsorption transition is demonstrated by using constructive techniques by comparing this model to a process of directed percolation we show that there is also a collapse or transition in this model we examine directed percolation in a wedge to show that there is a collapse phase present for arbitrary large values of the adsorption activity the generating function of adsorbing directed animals in a half space is found next from which we find the tricritical exponents associated with the adsorption transition a full solution for a collapsing directed animal seems intractible so instead we examine the collapse transition of a model of column convex directed animals with a contact activity next

exact results for 2d directed animals on a strip of finite width proves a conjecture giving the exact number of directed animals of s sites with any root on a strip of finite width of a square lattice the authors also rederive more simply some previous results concerning the connective constant and particular eigenvectors of the transfer matrix

optimal structuring elements for the morphological pattern restoration of binary images in this paper we derive the optimal structuring elements of morphological filters in image restoration the expected pattern transformation of random sets is presented an estimation theory framework for random sets is subsequently proposed this framework is based on the least mean difference lmd estimator the lmd estimator is defined to minimize the cardinality of the expected pattern transformation of the set difference of the parameter and the estimate several important results for the determination of the lmd estimator are derived the lmd structuring elements of morphological filters in image restoration are finally derived

an α 1 2 singularity in the vicinity of a disorder variety and its random walk interpretation the authors exhibit a new solution of the anisotropic triangular ising model it is based on diagrammatics well suited to the study of the vicinity of the so called disorder varieties a systematic expansion in this vicinity reveals an unexpected alpha 1 2 singularity this hidden singularity is in turn interpreted as the genuine critical behaviour of a related random walk process

open loop and closed loop attitude dynamics and controls of miniature spacecraft using pseudowheels this paper presents open loop and closed loop attitude control strategies of miniature spacecraft using pseudowheels which are composed of multiple bimorphs and are mounted on the three principal axes of the spacecraft due to the conservation of angular momentum the vibrations of the bimorph excited by applied voltages can rotate the spacecraft by applying a sequence of rotations along the three axes the attitude of the spacecraft can be changed the modeling of the spacecraft pseudowheel system includes the inverse piezoelectric effect and the gravity gradient torques since one cannot guarantee that a solution will be found for every rotation sequence this paper proposes an approach to solve this problem in addition the voltages applied to the bimorphs are reduced to meet the specifications of the voltage amplifiers furthermore a closed loop attitude control strategy is presented to reduce the applied voltages and to compensate the attitude error caused by the gravity gradient torques

the random generation of directed animals abstract in this paper we propose an algorithm to randomly generate a directed animal directed animals are well known combinatorial objects and have been widely used for modelling the physical phenomenon of percolation the algorithm consists of three steps and we prove that each of them is performed in linear time finally we report the results of our experiments made by means of appropriate computer programs in order to give empirical evidence that our algorithm really works

map estimation of finite gray scale digital images corrupted by supremum infimum noise finite gray scale digital images are modeled as realizations of discrete random functions drf and then the estimation of realizations of drf corrupted by a supremum infimum noise model is considered it is proved that morphological operators such as openings closings supremum of openings and infimum of closings are optimal maximum a posteriori map estimators under an appropriate and minimal set of assumptions relating to the structural and statistical constraints on image drf and noise drf these results are obtained for independent identically distributed i i d noise for single and multiframe observation scenarios next the assumption of i i d noise is relaxed and the map optimality and strong consistency of morphological filters for filtering image drf degraded by morphologically smooth noise i e colored noise is proved simulations on actual image data are carried out in support of the validity of theoretical results presented

directed animals on two dimensional lattices previously directed animals on square and triangular lattices have been enumerated by area and have been found to have simple generating functions whilst the hexagonal lattice generating function has not been obtained directed animals on several new lattices are enumerated one class of which is solved exactly directed animals by bonds with and without loops are also enumerated in each case an asymptotic growth like n 1 2 mu n is observed and precise estimates for mu are given

morphological representation of order statistics filters we propose a comprehensive theory for the morphological bounds on order statistics filters and their repeated iterations conditions are derived for morphological openings and closings to serve as bounds lower and upper respectively on order statistics filters and their repeated iterations under various assumptions morphological open closings and close openings are also shown to serve as tighter bounds lower and upper respectively on iterations of order statistics filters simulations of the application of the results presented to image restoration are finally provided

automatic average case analysis of algorithms abstract many probabilistic properties of elementary discrete combinatorial structures of interest for the average case analysis of algorithms prove to be decidable this paper presents a general framework in which such decision procedures can be developed it is based on a combination of generating function techniques for counting and complex analysis techniques for asymptotic estimations we expose here the theory of exact analysis in terms of generating functions for four different domains the iterative recursive and unlabelled labelled data type domains we then present some major components of the associated asymptotic theory and exhibit a class of naturally arising functions that can be automatically analyzed a fair fragment of this theory is also incorporated into a system called lambda upsilon omega in this way using computer algebra one can produce automatically non trivial average case analyses of algorithms operating over a variety of decomposable combinatorial structures at a fundamental level this paper is part of a global attempt at understanding why so many elementary combinatorial problems tend to have elementary asymptotic solutions in several cases it proves possible to relate entire classes of elementary combinatorial problems whose structure is well defined with classes of elementary special functions and classes of asymptotic forms relative to counting probabilities or average case complexity

random generation of trees and other combinatorial objects abstract in this paper we present a general method for the random generation of some classes of combinatorial objects our basic idea is to translate eco method enumerating combinatorial objects from a method for the enumeration of combinatorial objects into a random generation method the algorithms we illustrate are based on the concepts of succession rule and generating tree the former is a law that predicts the combinatorial object class growth according to a given parameter the generating tree related to a given succession rule is a particular labelled plane tree that represents the rule in an extensive way each node of a generating tree can also be seen as a particular combinatorial object and so a random path in the generating tree coincides with the random generation of that combinatorial object the generation is uniform if we take the probability of each branch to be selected into account when the path is generated we also give the formulae evaluating complexity finally we take the class of m ary trees into consideration in order to illustrate our general method in this case the average time complexity of the generating algorithm can be estimated as o mn

application of directed lattice animal theory to river networks it is shown that the theory of directed lattice animals is a good candidate for determining the exponents which describe river networks

spatially variant morphological restoration and skeleton representation the theory of spatially variant sv mathematical morphology is used to extend and analyze two important image processing applications morphological image restoration and skeleton representation of binary images for morphological image restoration we propose the sv alternating sequential filters and sv median filters we establish the relation of sv median filters to the basic sv morphological operators i e sv erosions and sv dilations for skeleton representation we present a general framework for the sv morphological skeleton representation of binary images we study the properties of the sv morphological skeleton representation and derive conditions for its invertibility we also develop an algorithm for the implementation of the sv morphological skeleton representation of binary images the latter algorithm is based on the optimal construction of the sv structuring element mapping designed to minimize the cardinality of the sv morphological skeleton representation experimental results show the dramatic improvement in the performance of the sv morphological restoration and sv morphological skeleton representation algorithms in comparison to their translation invariant counterparts

analytic models and ambiguity of context free languages we establish that several classical context free languages are inherently ambiguous by proving that their counting generating functions when considered as analytic functions exhibit some characteristic form of transcendental behaviour to that purpose we survey some general results on elementary analytic properties and enumerative uses of algebraic functions in relation to formal languages in particular the paper contains a general density theorem for unambiguous context free languages

animals and skew trees resume les animaux diriges sont mis en bijection avec une famille d arbres asymetriques les arbres guingois cette bijection conduit a un codage simple des animaux et permet leur enumeration elle correspond aussi a une representation des animaux comme empilements de dominos

pattern spectrum and multiscale shape representation the results of a study on multiscale shape description smoothing and representation are reported multiscale nonlinear smoothing filters are first developed using morphological opening and closings g matheron 1975 used openings and closings to obtain probabilistic size distributions of euclidean space sets continuous binary images these distributions are used to develop a concept of pattern spectrum a shape size descriptor a pattern spectrum is introduced for continuous graytone images and arbitrary multilevel signals as well as for discrete images by developing a discrete size family of patterns large jumps in the pattern spectrum at a certain scale indicate the existence of major protruding or intruding substructures of the signal at the scale an entropy like shape size complexity measure is also developed based on the pattern spectrum for shape representation a reduced morphological skeleton transform is introduced for discrete binary and graytone images this transform is a sequence of skeleton components sparse images which represent the original shape at various scales it is shown that the partially reconstructed images from the inverse transform on subsequences of skeleton components are the openings of the image at a scale determined by the number of eliminated components in addition two way correspondences are established among the degree of shape smoothing via multiscale openings or closings the pattern spectrum zero values and the elimination or nonexistence of skeleton components at certain scales

enumeration of directed site animals on two dimensional lattices studies the problem of directed site animals on the square triangular and hexagonal lattices closed form expressions are proposed for a s the number of animals of size s on the square and triangular lattices these expressions have been checked for s or 33 and s or 10 for the square and triangular lattices respectively by explicit enumeration they imply that a s varies as lambda 2 s 0 for large s where lambda 3 for the square lattice and lambda 4 for the triangular and theta 1 2 for both for the hexagonal lattice a s is found for s or 48 the results are consistent with lambda 2 0252 or 0 0005 and theta 1 2

some exact results for moments of 2d directed animals using computer enumerations and the algebraic approximant method of series analysis several new exact results have been found for moments of width perimeter and loops for directed animals on the square and triangular lattices a proof using q series is given for exact solutions for widths on both the square and triangular lattices

directed percolation a finite size renormalisation group approach the finite size renormalisation group technique introduced by nightingale 1976 is applied to the directed percolation problem the decay of correlations is anisotropic in this model and finite size scaling is extended to treat such anisotropy precise estimates for critical exponents and percolation probabilities are obtained for site bond and site bond percolation on the square lattice with bonds directed along the positive axes both free boundary conditions for which the results converge linearly with 1 n as n to infinity and helical boundary conditions for which unexpectedly the results converge linearly with 1 n3 are considered

a representation theory for morphological image and signal processing a unifying theory for many concepts and operations encountered in or related to morphological image and signal analysis is presented the unification requires a set theoretic methodology where signals are modeled as sets systems signal transformations are viewed as set mappings and translational invariant systems are uniquely characterized by special collections of input signals this approach leads to a general representation theory in which any translation invariant increasing upper semicontinuous system can be presented exactly as a minimal nonlinear superposition of morphological erosions or dilations the theory is used to analyze some special cases of image signal analysis systems such as morphological filters median and order statistic filters linear filters and shape recognition transforms although the developed theory is algebraic its prototype operations are well suited for shape analysis hence the results also apply to systems that extract information about the geometrical structure of signals

uniform random generation of strings in a context free language let s be the set of all strings of length n generated by a given context free grammar a uniform random generator is one which produces strings from s with equal probability in generating these strings care must be taken in choosing the disjuncts that form the right hand side of a grammar rule so that the produced string will have the specified length uniform random generators have applications in studying the complexity of parsers in estimating the average efficiency of theorem provers for the propositional calculus in establishing a measure of ambiguity of a grammar etc two methods are presented for generating uniform random strings in an unambiguous context free language the first method will generate a random string of length n in linear time but must use a precomputed table of size o n r 1 where r is the number of nonterminals in the grammar used to specify the language the second method precomputes part of the table and calculates the other entries as they are called for it requi

further results on map optimality and strong consistency of certain classes of morphological filters morphological openings and closings can be viewed as consistent map estimators of smooth random binary image signals immersed in i i d clutter or suffering from i i d random dropouts we revisit this viewpoint under much more general assumptions and show that quite surprisingly the above interpretation is still valid

simulating size constrained galton watson trees we discuss various methods for generating random galton watson trees conditional on their sizes being equal to n a linear expected time algorithm is proposed

conjectures for the first perimeter moment of directed animals using computer enumerations and a rational approximant method of series analysis we conjecture an expression for the first perimeter moment of directed animals on the square lattice which are confined in a strip of a given width with open boundary conditions when the width tends to infinity the conjecture leads to an algebraic series for the first perimeter moment of directed animals on one half of the square lattice similar to conway s earlier conjecture for the whole square lattice

flory theory for directed lattice animals and directed percolation the free energies of directed lattice animals in good and theta solvents and the free energy of directed percolation are found by the use of a simple flory type approximation which accounts for the inherent anisotropy of these systems from these free energies the authors obtain the upper critical dimension below which mean field theory breaks down they also calculate closed form dimension dependent expressions for the parallel and perpendicular correlation length exponents which characterise the asymptotic cluster shapes these exponents are in excellent agreement with existing numerical data

probabilistic analysis of some un directed animals using weak convergence theorems we analyze stochastic properties of some parameters of directed or undirected animals for directed column convex animals with fixed large area we obtain asymptotic distributions for the number of columns the internal path length the trajectories and the right width for general directed animals we derive asymptotic densities of the lower width and of some decomposition parameter the limiting processes are given by gaussian stochastic processes based on brownian motion or stochastic integrals on such

uniform random generation of decomposable structures using floating point arithmetic the em recursive method formalized by nijenhuis and wilf cite niwi78 and systematized by flajolet van cutsem and zimmermann cite flziva94 is extended here to floating point arithmetic the resulting adz method enables one to generate decomposable data structures both labelled or unlabelled uniformly at random in expected o n 1 epsilon time and space after a preprocessing phase of o n 2 epsilon time which reduces to o n 1 epsilon for context free grammars

a new dichotomic algorithm for the uniform random generation of words in regular languages we present a new algorithm for generating uniformly at random words of any regular language l when using floating point arithmetics its bit complexity is o qlg 2n in space and o qnlg 2n in time where n stands for the length of the word and q stands for the number of states of a finite deterministic automaton of l we implemented the algorithm and compared its behavior to the state of the art algorithms on a set of large automata from the vlts benchmark suite both theoretical and experimental results show that our algorithm offers an excellent compromise in terms of space and time requirements compared to the known best alternatives in particular it is the only method that can generate long paths in large automata

a quasi polynomial time algorithm for sampling words from a context free language abstract a quasi polynomial time algorithm is presented for sampling almost uniformly at random from then slice of the languagel g generated by an arbitrary context free grammarg then slice of a languagelover an alphabet is the subsetl nof words of length exactlyn the time complexity of the algorithm ise 2 n g o log n where the parameterebounds the variation of the output distribution from uniform and g is a natural measure of the size of grammarg the algorithm applies to a class of language sampling problems that includes slices of context free languages as a proper subclass for the restricted case of homogeneous languages expressed by regular expressions without kleene star a truly polynomial time algorithm is presented

2d directed compact site animals on a lattice of finite width the authors present a transfer matrix method for calculating the properties of directed compact site animals in two dimensions the non degeneracy of the largest eigenvalue of a truncated 50 50 matrix implies that the critical exponent theta o they also predict that the exponents vperpendicular to 1 2 and v sub 1

exact results for the generating function of directed column convex animals on the square lattice the mathematical properties of the generating function s x for the number sn of directed column convex lattice animals on a square lattice with a given directed site perimeter n are investigated in particular it is shown that s x can be expressed exactly in terms of algebraic hypergeometric functions a detailed investigation of the asymptotic behaviour of sn as n to infinity is carried out by applying the darboux method to the hypergeometric formula for s x it is also demonstrated that sn satisfies a four term recurrence relation finally it is noted that the techniques used to analyse the lattice animal generating function s x can be applied to any other generating function which satisfies a cubic algebraic equation

a fast thresholded linear convolution representation of morphological operations in this correspondence we present a fast thresholded linear convolution representation of morphological operations the thresholded linear convolution representation of dilation and erosion is first proposed a comparison of the efficiency of the direct implementation of morphological operations and the thresholded linear convolution representation of morphological operations is subsequently conducted mathematical morphology has emerged as a powerful new tool for image processing

bifurcation and nonlinear dynamic analysis of united gas lubricated bearing system this paper studies the bifurcation and nonlinear behaviors of a united gas lubricated bearing ugb system by a hybrid numerical method combining the differential transformation method and the finite difference method the analytical results reveal a complex dynamic behavior comprising periodic sub harmonic quasi periodic and chaotic responses of the rotor center furthermore the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass and bearing number are increased the current analytical results are found to be in good agreement with those of other numerical methods therefore the proposed method provides an effective means of gaining insights into the nonlinear dynamics of ugb systems

map signal estimation in noisy sequences of morphologically smooth images sidiropoulos et al 1994 demonstrated that morphological openings and closings can be viewed as maximum a posteriori map estimators of morphologically smooth signals in signal independent i i d noise the present authors extend these results to the m fold independent observation case and show that the aforementioned estimators are strongly consistent we also demonstrate the validity of a thresholding conjecture sidiropoulos et al 1994 by simulation and use it to evaluate estimator performance taken together these results can help determine the least upper bound m on m which guarantees virtually error free reconstruction of morphologically smooth images

morphological filters part ii their relations to median order statistic and stack filters this paper extends the theory of median order statistic os and stack filters by using mathematical morphology to analyze them and by relating them to those morphological erosions dilations openings closings and open closings that commute with thresholding the max min representation of os filters is introduced by showing that any median or other os filter is equal to a maximum of erosions moving local minima and also to a minimum of dilations moving local maxima thus os filters can be computed by a closed formula that involves a max min on prespecified sets of numbers and no sorting stack filters are established as the class of filters that are composed exactly of a finite number of max min operations the kernels of median os and stack filters are collections of input signals that uniquely represent these filters due to their translation invariance the max min functional definitions of these nonlinear iliters is shown to be equivalent to a maximum of erosions by minimal with respect to a signal ordering kernel elements and also to a minimum of dilations by minimal kernel elements of dual filters the representation of stack filters based on their minimal kernel elements is proven to be equivalent to their representation based on irreducible sum of products expressions of boolean functions it is also shown that median filtering and its iterations of any signal by convex 1 d windows is bounded below by openings and above by closings a signal is a root fixed point of the median iff it is a root of both an opening and a closing the open closing and clos opening yield median roots in one pass suppress impulse noise similarly to the median can discriminate between positive and negative noise impulses and are computationally less complex than the median some similar results are obtained for 2 d median filtering

uniform random generation of words of rational languages the problem of generating uniformly at random words of a given language has been the subject of extensive study in the last few years an important part of that work is devoted to the generation of words of context free languages see e g 6 8 9 12 for a given integer n 0 the words of length n 0 of any unambiguous context free language can be generated uniformly at random by using algorithms derived from the general method which was introduced by wilf 14 15 and systematized by flajolet et al 7 clearly this can be applied to the set of rational languages which constitute an important special case of context free languages most authors use the uniform measure of complexity see 1 in order to compute the complexity of the algorithms of generation this measure is based on the following hypotheses any simple arithmetic operation addition multiplication has time cost 0 1 and a constant amount of memory space is taken by any number thus we know that words of any rational language can be generated by using an algorithm which with respect to the uniform measure of complexity runs in linear time in terms of the length of the words and constant space 9 this measure is realistic only if there is a reasonable bound on the numbers involved in the operations however the classical random generation algorithms involve operations on numbers which grow exponentially in terms of the length of the words to be generated moreover the programs which make use of these algorithms are generally used to generate very large words for example for the purpose of studying the asymptotic behavior of some parameters therefore the uniform measure does not reflect the real behavior of such programs it turns out that the logarithmic measure of complexity is much more realistic one assumes that the space taken by a number k is o log k and that any simple arithmetic operation can be done in time o log k it is with respect to this measure that we will evaluate the performance of algorithms in this paper our goal is to design efficient algorithms in terms of logarithmic complexity to generate uniformly at random words from certain classes of rational languages we consider rational languages defined by their minimal finite deterministic automata when computing complexity neither the size of the automaton nor the cardinality of the alphabet are taken in account in section 2 we present some background on rational languages and their generating series we describe briefly the classical method for generating words of such languages and we study its logarithmic complexity we show that it is at best quadratic for most languages this is due mainly to computations on numbers which grow exponentially with the length of the words to be generated in order to improve significantly the efficiency of the algorithms we must avoid handling of large numbers or at least decrease substantially the frequency of computations on such numbers another alternative briefly discussed in 7 and 12 is to compute with floating point numbers instead of integers in this case the logarithmic complexity is time linear however using floating point numbers leads inevitably to approximations which prevent the exact uniformity of the generation in sections 3 and 4 we show that in some cases we can avoid computations on large numbers entirely or almost entirely while keeping the exact uniformity of the generation we determine two classes of rational languages for which this is the case section 3 concerns languages whose associated generating series have a unique singularity we present a simple version of the classical algorithm which totally avoids handling of large numbers the logarithmic complexity of the method is o n log n in time and o log n in memory space section 4 focuses on languages whose associated generating series have the following property there exists a unique singularity of minimum modulus and this singularity is simple for such languages we give a probabilistic version of the classical algorithm which generates words randomly while avoiding most computations on large numbers this method needs a preprocessing stage which can be done in polynomial time and linear space in terms of the length n of the words following preprocessing any word of length n can be generated in average linear time and space

a calculus for the random generation of labelled combinatorial structures a systematic approach to the random generation of labelled combinatorial objects is presented it applies to structures that are decomposable i e formally specifiable by grammars involving set sequence and cycle constructions a general strategy is developed for solving the random generation problem with two closely related types of methods for structures of size n the boustrophedonic algorithms exhibit a worst case behaviour of the form o n log n the sequential algorithms have worst case o n2 while offering good potential for optimizations in the average case the complexity model is in terms of arithmetic operations and both methods appeal to precomputed numerical table of linear size that can be computed in time o n2 a companion calculus permits systematically to compute the average case cost of the sequential generation algorithm associated to a given specification using optimizations dictated by the cost calculus several random generation algorithms of the sequential type are developed most of them have expected complexity 1 2n log n and are thus only slightly superlinear the approach is exemplified by the random generation of a number of classical combinatorial structures including cayley trees hierarchies the cycle decomposition of permutations binary trees functional graphs surjections and set partitions

bifurcation and chaos analysis of the porous squeeze film damper mounted gear bearing system porous squeeze film damper psfd has been widely used in the industry and the advantages are very abundant this study presents a systematic analysis of the dynamic behavior of a gear bearing system with psfd under nonlinear suspension nonlinear oil film force and nonlinear gear meshing force effect it can be found that the system exhibits very rich forms of nt periodic and chaotic vibrations the bifurcation diagrams also reveal that greater values of permeability may not only improve non periodic motions effectively but also suppress dynamic amplitudes of the system therefore we may conclude that psfd can improve dynamic stability of gear bearing systems the results presented in this study provide some useful insights into the design and development of a gear bearing system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes

optimal morphological pattern restoration from noisy binary images a theoretical analysis of morphological filters for the optimal restoration of noisy binary images is presented the problem is formulated in a general form and an optimal solution is obtained by using fundamental tools from mathematical morphology and decision theory consideration is given to the set difference distance function as a measure of comparison between images this function is used to introduce the mean difference function as a quantitative measure of the degree of geometrical and topological distortion introduced by morphological filtering it is proved that the class of alternating sequential filters is a set of parametric smoothing morphological filters that best preserve the crucial structure of input images in the least mean difference sense

enumeration of directed animals on an infinite family of lattices we prove algebraic equations satisfied by the area generating function for directed animals on an infinite family of regular non planar two dimensional graphs

application of the differential transformation method to bifurcation and chaotic analysis of an afm probe tip the afm atomic force microscope has become a popular and useful instrument for measuring intermolecular forces with atomic resolution that can be applied in electronics biological analysis and studying materials semiconductors etc this paper conducts a systematic investigation into the bifurcation and chaotic behavior of the probe tip of an afm using the differential transformation dt method the validity of the analytical method is confirmed by comparing the dt solutions for the displacement and velocity of the probe tip at various values of the vibrational amplitude with those obtained using the runge kutta rk method the behavior of the probe tip is then characterized utilizing bifurcation diagrams phase portraits power spectra poincare maps and maximum lyapunov exponent plots the results indicate that the probe tip behavior is significantly dependent on the magnitude of the vibrational amplitude specifically the tip motion changes first from subharmonic to chaotic motion then from chaotic to multi periodic motion and finally from multi periodic motion to subharmonic motion with windows of chaotic behavior as the non dimensional vibrational amplitude is increased from 1 0 to 5 0

the pair connectedness for directed percolation on the honeycomb and diamond lattices the pair connectedness for directed site percolation on the honeycomb and diamond lattices is related to that of the square and simple cubic lattices respectively in the case of bond percolation the same correspondence leads to site bond percolation on the latter pair of lattices