some model theory of polish structures we introduce a notion of polish structure and in doing so provide a setting which allows the application of ideas and techniques from model theory descriptive set theory topology and the theory of profinite groups we define a topological notion of independence in polish structures and prove that it has some nice properties using this notion we prove counterparts of some basic results from geometric stability theory in the context of small polish structures then we prove some structural theorems about compact groups regarded as polish structures each small nm stable compact g group is solvable by finite each small compact g group of finite n m rank is nilpotent by finite examples of small polish structures and groups are also given

amenability definable groups and automorphism groups abstract we prove several theorems relating amenability of groups in various categories discrete definable topological automor phism group to model theoretic invariants quotients by connected components lascar galois group g compactness among the main tools which is possibly of independent interest is the adaptation and generalization of theorem 12 of 27 to other settings including amenable topological groups whose topology is generated by a family of subgroups on the side of definable groups we prove that if g is definable in a model m and g is definably amenable then the connected components g m 00 and g m 000 coincide answering positively a question from 22 we also prove some natural counterparts for topological groups using our generalizations of 27 by finding a dictionary relating quotients by connected components and galois groups of categorical theories we conclude that if m is countable and categorical and aut m is amenable as a topological group then t th m is g compact i e the lascar galois group gal l t is compact hausdorff equivalently the natural epimorphism from gal l t to gal k p t is an isomorphism we also take the opportunity to further develop the model theoretic approach to topological dynamics obtaining for example some new invariants for topological groups as well as allowing a uniform approach to the theorems above and the various categories

reversibility of general 1d linear cellular automata over the binary field z 2 under null boundary conditions the reversibility of cellular automata ca has long been studied but there are still many problems untouched this paper tackles the reversibility problem of the general case concerning 1d ca under null boundary conditions defined by linear rules over the binary field z 2 although transition matrix has been widely used for some special linear ca lca rules it has severe limitations its complexity depends on the number of cells and determining its reversibility becomes another unsolved tough problem for general rules by constructing deterministic finite automata dfa of the de bruijn graph presentation of ca we conclude the reversibility problem of all 1d linear rules over z 2 under null boundary conditions it turns out that any 1d lca except for some unilateral rules over z 2 under null boundary conditions can be reversible once having a proper number of cells and dfa provides an efficient way to find those numbers moreover the complexity of the dfa solution is independent of the number of cells in addition the relative low complexity of dfa can be further significantly reduced by using only a small part of it

unstable dimension variability a source of nonhyperbolicity in chaotic systems the hyperbolicity or nonhyperbolicity of a chaotic set has profound implications for the dynamics on the set a familiar mechanism causing nonhyperbolicity is the tangency of the stable and unstable manifolds at points on the chaotic set here we investigate a different mechanism that can lead to nonhyperbolicity in typical invertible respectively noninvertible maps of dimension 3 respectively 2 and higher in particular we investigate a situation first considered by abraham and smale in 1970 for different purposes in which the dimension of the unstable and stable tangent spaces are not constant over the chaotic set we call this unstable dimension variability a simple two dimensional map that displays behavior typical of this phenomenon is presented and analyzed

projective fraisse limits and the pseudo arc the aim of the present work is to develop a dualization of the fraisse limit construction from model theory and to indicate its surprising connections with the pseudo arc as corollaries of general results on the dual fraisse limits we obtain mioduszewski s theorem on surjective universality of the pseudo arc among chainable continua and a theorem on projective homogeneity of the pseudo arc which generalizes a result of lewis and smith on density of homeomorphisms of the pseudo arc among surjective continuous maps from the pseudo arc to itself we also get a new characterization of the pseudo arc via the projective homogeneity property

rotational chaos and strange attractors on the 2 torus we construct a 2 torus homeomorphism h homotopic to the identity with an attracting r h bing s pseudocircle c such that the rotation set of h c is not a unique vector the only known examples of such an attractor were birkhoff s attractors arising for dissipative maps with a twist our construction relies heavily on the barge martin method for constructing attractors as inverse limits of graphs

locally finite profinite rings abstract we investigate the structure of locally finite profinite rings we classify jacobson semisimple locally finite profinite rings as products of complete matrix rings of bounded cardinality over finite fields and we prove that the jacobson radical of any locally finite profinite ring is nil of finite nilexponent our results apply to the context of small compact g rings where we also obtain a description of possible actions of g on the underlying ring

stable extensions of homeomorphisms on the pseudo arc we prove the following theorem if p is a proper subcontinuum of the pseudoarc p h is a homeomorphism from p onto itself and 0 is an open set in p that contains p then there is a homeomorphism h from p onto itself such that h p h and h x x for x 0 a pseudoarc can be characterized as a chainable hereditarily indecomposable continuum although the main result here extends a result of w lewis lw and answers in the affirmative a question he asked in that same paper stable homeomorphisms of the pseudoarc this paper was motivated by a conversation the author had with professor marcy barge who works in the area of topological dynamics professor barge is interested in knowing what sort of self homeomorphisms the pseudoarc admits and in particular what sort of homeomorphisms it admits with the property that some of the points of the space have periodic orbits that pseudoarcs admit many such homeomorphisms will follow from a much earlier result of g lehner lg and the result here it will also follow by combining the theorem proven here g lehner s theorem and a theorem in kj that any continuum with the property that all its proper nondegenerate subcontinua are pseudoarcs admits many such homeomorphisms examples of continua with this property include pseudocircles b pseudosolenoids f some examples due to t ingram i and h cook c as well as the pseudoarc itself we will prove the following theorem theorem if p is a proper nondegenerate subcontinuum of the pseudoarc p p c o an open set in p and h is a homeomorphism from p onto itself then h can be extended to a homeomorphism h of p onto itself such that h x x for x o a continuum is indecomposable if no proper subcontinuum of it has interior and it is hereditarily indecomposable if each subcontinuum is indecomposable a chain is a collection of sets c co cy cn such that ci f c3 0 if and only if i j 1 a continuum is chainable if it has open chain covers of arbitrarily small mesh as mentioned previously the pseudoarc p is a hereditarily indecomposable chainable continuum kb this continuum also has the fixed point property h received by the editors june 9 1987 this research was presented at the annual spring topology conference march 1 1987 university of alabama at birmingham this conference was supported by the nsf 1980 mathematics subject classification 1985 revision primary 54f20 54f50

a dual bound algorithm for very fast and exact template matching recently proposed fast template matching techniques employ rejection schemes derived from lower bounds on the match measure this paper generalizes that idea and shows that in addition to lower bounds upper bounds on the match measure can be used to accelerate the search an algorithm is proposed that utilizes both lower and upper bounds to detect the k best matches in an image the performance of this dual bound algorithm is guaranteed it always detects the k best matches theoretical analysis and experimental results show that its runtime compares favorably with previously proposed real time exact template matching schemes

improving dynamic programming to solve image registration a new method of dynamic programming dp is presented a picture is paired with a reference map in order to arrive at picture registration an ordered sequence of primitive patterns is formed from the map an attempt is made to locate a similar sequence from the picture using classical picture processing methods this yields a distorted and unordered sequence marked by noise dp is then used to search for a common match to the two sequences both the initial and final registration states are however unknown moreover the continuity of the path is frequently interrupted due to shortcomings in detection or perhaps occlusions thus classical dp algorithms appear to give only poor results under practical conditions when well adapted to treat signals issued from a first order markovian process they can be used as this method shows to treat kth order processes the concept of the virtual state kept in memory suspends broken paths until they can be reconnected thus bridging the existing gaps between the different parts of the path the proposed algorithm has been applied to satellite images with their contours sectioned by clouds the result leads to the guarantee of very good registration in spite of image contours badly hampered by noise and or clouds

exploiting transitivity of correlation for fast template matching elimination algorithms are often used in template matching to provide a significant speed up by skipping portions of the computation while guaranteeing the same best match location as exhaustive search in this work we develop elimination algorithms for correlation based match measures by exploiting the transitivity of correlation we show that transitive bounds can result in a high computational speed up if strong autocorrelation is present in the dataset generally strong intrareference local autocorrelation is found in natural images strong inter reference autocorrelation is found if objects are to be tracked across consecutive video frames and strong intertemplate autocorrelation is found if consecutive video frames are to be matched with a reference image for each of these cases the transitive bounds can be adapted to result in an efficient elimination algorithm the proposed elimination algorithms are exact that is they guarantee to yield the same peak location as exhaustive search over the entire solution space while the speed up obtained is data dependent we show empirical results of up to an order of magnitude faster computation as compared to the currently used efficient algorithms on a variety of datasets

correlation coefficient based fast template matching through partial elimination partial computation elimination techniques are often used for fast template matching at a particular search location computations are prematurely terminated as soon as it is found that this location cannot compete with an already known best match location due to the nonmonotonic growth pattern of the correlation based similarity measures partial computation elimination techniques have been traditionally considered inapplicable to speed up these measures in this paper we show that partial elimination techniques may be applied to a correlation coefficient by using a monotonic formulation and we propose basic mode and extended mode partial correlation elimination algorithms for fast template matching the basic mode algorithm is more efficient on small template sizes whereas the extended mode is faster on medium and larger templates we also propose a strategy to decide which algorithm to use for a given data set to achieve a high speedup elimination algorithms require an initial guess of the peak correlation value we propose two initialization schemes including a coarse to fine scheme for larger templates and a two stage technique for small and medium sized templates our proposed algorithms are exact i e having exhaustive equivalent accuracy and are compared with the existing fast techniques using real image data sets on a wide variety of template sizes while the actual speedups are data dependent in most cases our proposed algorithms have been found to be significantly faster than the other algorithms

fluctuation driven computing on number conserving cellular automata a number conserving cellular automaton ncca is a cellular automaton in which the states of cells are denoted by integers and the sum of all of the numbers in a configuration is conserved throughout its evolution nccas have been widely used to model physical systems that are ruled by conservation laws of mass or energy imai et al 13 showed that the local transition function of ncca can be effectively translated into the sum of a binary flow function over pairs of neighboring cells in this paper we explore the computability of nccas in which the pairwise number flows are performed at fully asynchronous timings despite the randomness that is associated with asynchronous transitions useful computation still can be accomplished efficiently in the cellular automata through the active exploitation of fluctuations 18 specifically certain numbers may flow randomly fluctuating between forward and backward directions in the cellular space as if they were subject to brownian motion because random fluctuations promise a powerful resource for searching through a computational state space the brownian like flow of the numbers allows for efficient embedding of logic circuits into our novel asynchronous ncca

emergence of universal global behavior from reversible local transitions in asynchronous systems reversible computing usually focuses on how to establish a valid equivalence between the global reversibility and local reversibility in computational systems hitherto the equivalence has been precisely developed in cellular automata combinational circuits and quantum computers but it implicitly assumes that the underlying systems are synchronously timed alternative systems include the delay insensitive di circuits and asynchronous cellular automata acas where the local operations of each component cell may be executed independently at random times despite the randomness associated with asynchronous timings equivalence between the global and local reversibility can be simply achieved in both di circuits morita 2001 and acas lee et al 2003 provided that their local operations transitions are thoroughly serialized the complete exclusion of concurrency in local behavior however will profoundly depress the parallel processing efficiency of di circuits as well as the intrinsic massive parallelism of acas this paper aims at exploring what kind of complex global behavior may arise from the concurrent operations that are invertible at local level to this end we show that di circuits composed of reversible elements can actually exhibit universal input and output behavior with the universality emerging from the concurrency in reversible local operations likewise by further embedding all circuits into the cellular space the emergence of universal global transitions from reversible local transitions can be exactly identified in an aca which due to the bijectivity of its local function has significantly lower complexity as compared to other models

on the size of the inverse neighborhoods for one dimensional reversible cellular automata in this paper we investigate the possible neighborhood size of the inverse automaton of some types of one dimensional reversible cellular automata considering only the case when the local function is a size two map we give a quadratic upper bound for the neighborhood size of the inverse automaton we show that this bound can be lowered in some particular cases and give an algorithm for computing these better bounds

matching of tomographic slices for interpolation an automatic method that can transform a sequence of tomographic image slices into an isotropic volume data set is described in this method correspondence is established between points in consecutive slices and then this correspondence is used to estimate data between the slices by linear interpolation the method takes advantage of the fact that consecutive slices have small geometric differences and carries out the search in predicted small neighborhoods only points with high gradient magnitudes are used in the search process to increase the reliability of the correspondences mismatches that occur are detected and corrected using the continuity constraint in the correspondences experimental results showing the matching and interpolation of magnetic resonance slices and computed tomography slices are presented

pseudocircles in dynamical systems we construct an example of a coo map on a 3 manifold which has an invariant set with an uncountable number of components each of which is a pseudocircle furthermore any map which is sufficiently close in the c1metric to the constructed map has a similar set

correcting the geometry and color of digital images a unified method for correcting the geometry and color of digital images is presented the method uses a color chart with a prearranged array of known color patches using the true geometry and color of the chart and geometry and color of the image of the chart transformation functions that describe the geometry and color characteristics of the camera are determined the transformation functions are then used to correct the geometry and color of obtained images experimental results of the proposed method on images acquired under different scene illuminations and camera settings are presented and evaluated

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

a comparative study of transformation functions for nonrigid image registration transformation functions play a major role in nonrigid image registration in this paper the characteristics of thin plate spline tps multiquadric mq piecewise linear pl and weighted mean wm transformations are explored and their performances in nonrigid image registration are compared tps and mq are found to be most suitable when the set of control point correspondences is not large fewer than a thousand and variation in spacing between the control points is not large when spacing between the control points varies greatly pl is found to produce a more accurate registration than tps and mq when a very large set of control points is given and the control points contain positional inaccuracies wm is preferred over tps mq and pl because it uses an averaging process that smoothes the noise and does not require the solution of a very large system of equations use of transformation functions in the detection of incorrect correspondences is also discussed

rotational chaos in dissipative systems abstract an investigation is made into chaotic attractors arising from a quasiperiodic transition to chaos using a quantity called the rotation interval the rotation interval describes the short term rotation rates available to the attractor we present algorithms to calculate it given an appropriate map differential equation or time series we find that the rotation interval has a very robust parameter dependence its endpoints are almost always phase locked our numerical ideas are based on the theory of dissipative twist maps which is reviewed this theory is also used to prove a theorem about the non existence of certain strange attractors in nearly conservative systems finally an investigation is made into the relationship between the rotation interval and topological entropy and the breakup of invariant circles

clustering in the one dimensional three color cyclic cellular automaton cyclic cellular automaton the author has previously shown that this process fluctuates meaning that each lattice site changes color infinitely often so that there is no final state for the system the focus of the current work is on the clustering properties of this system this paper demonstrates that the one dimensional three color cyclic cellular automaton clusters and the mean cluster size as a function of time t is asymptotic to ct1 2 where c is an explicitly calculable constant the method of proof also allows us to compute asymptotic estimates of the mean interparticle distance for a one dimensional system of particles which undergo deterministic motion and which annihilate upon collision no clustering results are known about the four color process but evidence is presented to suggest that the mean cluster size of such systems grows at a rate different from t1 2

quadtree structured linear prediction models for image sequence processing a summary is presented of a study on two dimensional linear prediction models for image sequence processing and its application to change detection and scene coding the study focused on two dimensional joint process modeling of interframe relationships the derivation of computationally efficient matching algorithms and the implementation of a block adaptive interframe predictor for use in interframe predictive coding and change detection in the approach presented the spatial nonstationarity is handled by an underlying quadtree segmentation structure a maximum likelihood criterion and a simpler minimum variance criterion are discussed as detection and segmentation rules the results of this research indicate that a constrained joint process model involving only a single gain parameter and a shift parameter is the best tradeoff between performance and computational complexity

realizing rotation numbers on annular continua an annular continuum is a compact connected set k which separates a closed annulus a into exactly two connected components one containing each boundary component the topology of such continua can be very intricate for instance non locally connected we adapt a result proved by handel in the case where k a showing that if k is an invariant annular continuum of a homeomorphism of a isotopic to the identity then the rotation set in k is closed moreover every element of the rotation set is realized by an ergodic measure supported in k and by a periodic orbit if the rotation number is rational and most elements are realized by a compact invariant set our second result shows that if the continuum k is minimal with the property of being annular what we call a circloid then every rational number between the extrema of the rotation set in k is realized by a periodic orbit in k as a consequence the rotation set is a closed interval and every number in this interval rational or not is realized by an orbit moreover by an ergodic measure in k this improves a previous result of barge and gillette

small profinite structures we propose a model theoretic framework for investigating profinite structures we prove that in many cases small profinite structures interpret infinite groups this corresponds to results of hrushovski and peterzil on interpreting groups in locally modular stable and o minimal structures

a transitive homeomorphism on the pseudoarc which is semiconjugate to the tent map a powerful theorem and construction of wayne lewis are used to build two homeomorphisms on the pseudoarc each of which is semiconjugate to the tent map on the unit interval the first homeomorphism is transitive thus answering a question of marcy barge as to whether such homeomorphisms exist the second homeomorphism admits wandering points also it is proven that any homeomorphism on the pseudoarc that is semiconjugate to the tent map and is irreducible with respect to the semiconjugacy must either be transitive or admit wandering points a continuum is a compact connected metric space a continuum x is indecomposable if every proper subcontinuum of x is nowhere dense in x and x is hereditarily indecomposable if each subcontinuum of x is indecomposable a continuum x is chainable if for each e 0 there is a chain c c0 cn of open sets of diameter less than e that covers x c is a chain means that ci n ej 0 iff ii ii 2 or in the hilbert cube are pseudoarcs here we will show that this continuum admits a transitive homeomorphism thus answering a question of marcy barge in addition this homeomorphism has the property that it is semiconjugate to the tent map on the unit interval for more information on pseudoarcs and indecomposable continua see bil bi4 l1 l2 k km kr and ot exotic continua have been making their appearance in dynamical systems ever since the early part of this century with the work of c caratheodory c received by the editors may 20 1988 and in revised form july 25 1989 presented at the 1988 spring topology conference university of florida gainesville florida 32611 1980 mathematics subject classification 1985 revision primary 54f20 secondary 54h20

a counterexample to wood s conjecture abstract we prove that if the one point compactification of a locally compact noncompact hausdorff space l is the topological space called pseudoarc then c 0 l c is almost transitive we also obtain two necessary conditions on a metrizable locally compact hausdorff space l for c 0 l being almost transitive

invertible behavior in elementary cellular automata with memory elementary cellular automata ecas have been studied for their ability to generate complex global behavior despite their simplicity one variation of ecas is obtained by adding memory to each cell in a neighborhood this process generates a provisional configuration in which the application of an evolution rule establishes the dynamics of the system this version is known as an eca with memory ecam most previous work on ecams analyzed the complex behavior taking chaotic ecas however the present paper investigates reversible ecams as obtained from reversible and permutative ecas these ecas have at least one ancestor for every configuration thus the correct permutation of states may specify the memory function to obtain reversible ecams for permutative ecas which are often irreversible we demonstrate that the use of a quiescent state and the correct manipulation of de bruijn blocks produce reversible ecams

template matching in rotated images a rotationally invariant template matching using normalized invariant moments is described it is shown that if normalized invariant moments in circular windows are used then template matching in rotated images becomes similar to template matching in translated images a speedup technique based on the idea of two stage template matching is also described in this technique the zeroth order moment is used in the first stage to determine the likely match positions and the second and third order moments are used in the second stage to determine the best match position among the likely ones

reversible cellular automata with memory two dimensional patterns from a single site seed standard cellular automata ca are ahistoric memoryless i e the new state of a cell depends on its neighborhood configuration only at the preceding time step historic memory of all past iterations can be incorporated into ca by featuring each cell by a weighted mean of all its past states in this paper a new kind of reversible ca which incorporates memory is introduced in a two dimensional scenario

moment preserving pattern matching abstract an accurate template matching algorithm of low computational complexity that facilitates low cost hardware design and vlsi implementation is highly desired by many image processing applications this paper describes a template matching method called moment preserving pattern matching mppm which reduces the computational complexity of template matching significantly and provides several advantages in hardware implementation the methodology is based on the concepts of pairing function and moment preserving quantization the experimental results show that it is computationally fast and accurate in locating the template if noise corruption is not too severe for obtaining a template matching algorithm of high accuracy and robustness against noise and low computational cost mppm is applied to a two stage matching scheme a statistical model for estimating the correlation threshold is also given

welch sets for random generation and representation of reversible one dimensional cellular automata abstract reversible one dimensional cellular automata are studied from the perspective of welch sets this paper presents an algorithm to generate random welch sets that define a reversible cellular automaton then properties of welch sets are used in order to establish two bipartite graphs describing the evolution rule of reversible cellular automata the first graph gives an alternative representation for the dynamics of these systems as block mappings and shifts the second graph offers a compact representation for the evolution rule of reversible cellular automata both graphs and their matrix representations are illustrated by the generation of random reversible cellular automata with 6 and 18 states

spiral aggregation map splam this paper describes a robust template matching algorithm undergoing rotation scaling translation rst variations via our proposed spiral aggregation map splam which is a novel image warping scheme it not only provides an efficient method for generating the desired projection profiles for matching it also enables us to determine the rotation angle and is invariant to scale changes compared to other model based methods the proposed spiral projection model spm provides the structural and statistical information about the template in a more general and easier to comprehend format the spm is a model based texture description scheme that enables the simultaneous representation for each value of projection profile the profile a set of parametric projection values functions by angular indexing is the aggregate from a group of spiral sampling pixels the experimental evaluation shows that the properties of the algorithm achieved very attractive results this paper describes a robust and fast template matching algorithm we introduced a novel image warping scheme called the spiral aggregation map splam this descriptor is capable of expressing the template with high order texture characteristics

relatively compact siegel disks with non locally connected boundaries we construct holomorphic maps f with a siegel disk whose boundary is not locally connected and is an indecomposable continuum yet compactly contained in the domain of definition of the map our examples are injective and defined on a subset of mathbb c

replication in one dimensional cellular automata abstract in a cellular automaton ca replication is the ability to indefinitely generate copies of a finite collection of patterns starting from finite seeds a transparent feature of additive ca replication mechanisms are less clear in the absence of additivity this paper investigates such dynamics through several examples for the 1 or 2 rule and its generalizations replication is inevitable and we investigate self organization properties in the perturbed exactly 1 rule we study frequency of replicators and the new phenomenon is called quasireplication the last ca is the extended 1 or 3 rule which allows for replication on different backgrounds we employ a mixture of rigorous and empirical techniques

multiple subclass pattern recognition a maximin correlation approach this paper addresses a correlation based nearest neighbor pattern recognition problem where each class is given as a collection of subclass templates the recognition is performed in two stages in the first stage the class is determined templates for this stage are created using the subclass templates assignment into subclasses occurs in the second stage this two stage approach may be used to accelerate template matching in particular the second stage may be omitted when only the class needs to be determined the authors present a method for optimal aggregation of subclass templates into class templates for each class the new template is optimal in that it maximizes the worst case i e minimum correlation with its subclass templates an algorithm which solves this maximin optimization problem is presented and its correctness is proved in addition test results are provided indicating that the algorithm s execution time is polynomial in the number of subclass templates the authors show tight bounds on the maximin correlation the bounds are functions only of the number of original subclass templates and the minimum element in their correlation matrix the algorithm is demonstrated on a multifont optical character recognition problem

a complete classification of homogeneous plane continua we show that the only compact and connected subsets i e continua x of the plane mathbb r 2 which contain more than one point and are homogeneous in the sense that the group of homeomorphisms of x acts transitively on x are up to homeomorphism the circle mathbb s 1 the pseudo arc and the circle of pseudo arcs these latter two spaces are fractal like objects which do not contain any arcs it follows that any compact and homogeneous space in the plane has the form x z where x is either a point or one of the three homogeneous continua above and z is either a finite set or the cantor set the main technical result in this paper is a new characterization of the pseudo arc following lelek we say that a continuum x has span zero provided for every continuum c and every pair of maps f g colon c to x such that f c subset g c there exists c 0 in c so that f c 0 g c 0 we show that a continuum is homeomorphic to the pseudo arc if and only if it is hereditarily indecomposable i e every subcontinuum is indecomposable and has span zero

orbits of the pseudocircle the following theorem is proved theorem the pseudocircle has uncountably many orbits under the action of its homeomorphism group each orbit is the union of uncountably many composants a pseudocircle is a circularly chainable hereditarily indecomposable separating plane continuum r h bing 1 constructed a pseudocircle in 1951 and asked two questions are any two pseudocircles homeomorphic is a pseudocircle homogeneous in 1968 l fearnley 6 proved that the answer to the first question is yes and fearnley 5 and j t rogers jr 14 independently proved that the answer to the second question is no since the advent of the effros theorem several elegant proofs of the nonhomogeneity of the pseudocircle have appeared 7 10 and 13 in 1968 after seeing the proof that the pseudocircle is not homogeneous f b jones asked the second author how many orbits the pseudocircle had under the action of its homeomorphism group but the matter was not pursued further recently however the question has arisen again and wayne lewis 3 has asked if the pseudocircle has uncountably many orbits the purpose of this paper is to prove the following theorem which gives an affirmative answer to this question theorem the pseudocircle has uncountably many orbits under the action of its homeomorphism group each of these orbits is the union of uncountably many composants an interesting sidelight of the proof is the construction of two homeomorphic sets one being an open set of the pseudocircle and the other being an open set of the pseudoarc during the proof we construct an uncountable abelian subgroup of the homeomorphism group of the pseudocircle the homeomorphism constructed by handel 8 might be an element of this group each orbit of the pseudocircle is a borel set 4 lewis has announced that no orbit can be a g6 in the course of our argument we prove this but we do not determine further restrictions on the type of the borel set for the orbit question what classes of borel sets occur as the orbits of the pseudocircle in particular are each two orbits of the same class received by the editors may 1 1984 and in revised form august 13 1985 1980 mathematics subject classification primary 54f20 54f50

small profinite groups and rings abstract a small profinite ring has an open nil ideal of finite nil exponent we also discuss various conjectures about small profinite rings and give examples illustrating them

a two stage cross correlation approach to template matching two stage template matching with sum of absolute differences as the similarity measure has been developed by vanderburg and rosenfeld 1 2 this correspondence shows the development of two stage template matching with cross correlation as the similarity measure the threshold value of the first stage is derived analytically and its validity is verified experimentally considerable speed up over the one stage process can be obtained by introducing only a small false dismissal probability

a closed formula for the inverse of a reversible cellular automaton with 2r 1 cyclic rule abstract reversibility of cellular automata ca has been an extensively studied problem from both a theoretical and a practical point of view it is known when a 2 r 1 cyclic cellular automaton with periodic boundary conditions p b c is reversible see siap et al 2013 but as far as we know no explicit expression is given for its inverse cellular automaton apart from the case r 1 see encinas and del rey 2007 in this paper we give a closed formula for the inverse rule of a reversible 2 r 1 cyclic cellular automaton with p b c over the finite field f 2 for any value of the neighbourhood radius r it turns out that the inverse of a reversible 2 r 1 cyclic ca with p b c is again a cyclic ca with p b c but with a different neighbourhood radius and this radius depends on certain numbers which need to be computed by a new algorithm we introduce finally we apply our results to the case r 1 which is the eca with wolfram rule number 150 to introduce an alternative and improved expression for the inverse transition dipolynomial formulated in encinas and del rey 2007 we also illustrate these results by giving explicit computations for the inverse transition dipolynomial of a reversible cellular automaton with penta cyclic rule

on the conjecture of wood and projective homogeneity abstract in 2005 kawamura and rambla independently constructed a metric counterexample to wood s conjecture from 1982 we exhibit a new nonmetric counterexample of a space l such that c 0 l c is almost transitive and show that it is distinct from a nonmetric space whose existence follows from the work of greim and rajagopalan in 1997 up to our knowledge this is only the third known counterexample to wood s conjecture we also show that contrary to what was expected if a one point compactification of a space x is r h bing s pseudo circle then c 0 x c is not almost transitive for a generic choice of points finally we point out close relation of these results on wood s conjecture to a work of irwin and solecki on projective fraisse limits and projective homogeneity of the pseudo arc and addressing their conjecture we show that the pseudo circle is not approximately projectively homogeneous

products of finite abelian groups as profinite groups abstract we investigate products of finite abelian groups of bounded exponent as profinite structures in the sense of newelski in such groups we describe orbits under the action of the standard structural group of automorphisms then we conclude that such groups are small m normal and m stable let x be a product of countably many finite abelian groups we also investigate the influence of modifications of the standard structural group of x on its smallness m normality and m stability

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

polyhedron recognition using three view analysis abstract using three view analysis this paper proposes a new approach for single polyhedron recognition both the 3d surface data and 2d image projection patterns are used to find the exact corresponding model of an unknown input object the recognition process first applies a hypothesis generation verification process to match the 3d partial object of the unknown input which is reconstructed by applying the three view matching strategy chiou et al proc ics 88 pp 1516 1521 1988 and the polyhedron reconstruction process hung et al pattern recognition 22 231 246 1989 against the data based models for selecting the possible corresponding models candidates it then backprojects each candidate onto the three image planes and matches the outer boundaries of the three backprojections by a simple method for judging the exact corresponding model measurement error is also analyzed theoretically to give a bound of the threshold value so that it can be automatically chosen in each decision making process the approach is implemented on a pc level vision system experimental results show that the system is feasible and reliable even in a noisy environment