measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

time discretization of an integro differential equation of parabolic type the stability and convergence properties of two time discretizations of an integro differential equation of parabolic type are studied the methods reduce to the backward euler and crank nicolson methods if the integral term is absent the integral term is approximated in each case by a quadrature rule with relatively high order truncation error so that a relatively large time step can be used for the quadrature in order to reduce the memory and computational requirements of the method

variable step size predictor corrector schemes for second kind volterra integral equations in this paper a family of implicit multistep methods for the solution of volterra integral equations is derived these methods together with an explicit euler predictor permit the use of a variable step size when solving integral equations means of controlling the error and stability by varying the step size and the order of the method are described extensive numerical results are presented

balancing survival and extinction in nonautonomous competitive lotka volterra systems abstract we generalise and unify some recent results about extinction in n th order nonautonomous competitive lotka volterra systems for each r n we show that if the coefficients are continuous bounded by strictly positive constants and satisfy certain inequalities then any solution with strictly positive initial values has the property that n r of its components vanish whilst the remaining r components asymptotically approach a canonical solution of an r dimensional restricted system in other words r of the species being modeled survive whilst the remaining n r are driven to extinction

w tsv weighted topological signature vector for lexicon reduction in handwritten arabic documents this paper proposes a holistic lexicon reduction method for ancient and modern handwritten arabic documents the word shape is represented by the weighted topological signature vector w tsv which encodes graph data into a low dimensional vector space three directed acyclic graph dag representations are proposed for arabic word shapes based on topological and geometrical features lexicon reduction is achieved by a nearest neighbors search in the w tsv space the proposed framework has been tested on the ifn enit and the ibn sina databases achieving respectively a degree of reduction of 83 5 and 92 9 for an accuracy of reduction of 90

recent progress in discrete population dynamics abstract the purpose of this lecture is to display recent results concerning the relation between discrete continuous and data based population models the lecture is organized as follows 1 we begin by motivating why discrete models are used under what circumstances and for what purposes 2 it is not obvious how discrete models should be derived and we show how discrete models are derived in our case 3 we continue by discussing the relation between continuous and discrete models and their dynamical analogies 4 we end up by discussing possible problems that appear as models fitted to data are used for making conclusions regarding its long term behavior

random catalytic reaction networks abstract we study networks that are a generalization of replicator or lotka volterra equations they model the dynamics of a population of object types whose binary interactions determine the specific type of interaction product such a system always reduces its dimension to a subset that contains production pathways for all of its members the network equation can be rewritten at a level of collectives in terms of two basic interaction patterns replicator sets and cyclic transformation pathways among sets although the system contains well known cases that exhibit very complicated dynamics the generic behavior of randomly generated systems is found numerically to be extremely robust convergence to a globally stable rest point it is easy to tailor networks that display replicator interactions where the replicators are entire self sustaining subsystems rather than structureless units a numerical scan of random systems highlights the special properties of elementary replicators they reduce the effective interconnectedness of the system resulting in enhanced competition and strong correlations between the concentrations

a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

diffusion wavelet embedding a multi resolution approach for graph embedding in vector space abstract in this article we propose a multiscale method of embedding a graph into a vector space using diffusion wavelets at each scale we extract a detail subspace and a corresponding lower scale approximation subspace to represent the graph representative features are then extracted at each scale to provide a scale space description of the graph the lower scale is constructed using a super node merging strategy based on nearest neighbor or maximum participation and the new adjacency matrix is generated using vertex identification this approach allows the comparison of graphs where the important structural differences may be present at varying scales additionally this method can improve the differentiating power of the embedded vectors and this property reduces the possibility of cospectrality typical in spectral methods substantially the experimental results show that augmenting the features of abstract levels to the graph features increases the graph classification accuracies in different datasets

adaptive discretization of fractional order viscoelasticity using sparse time history an efficient numerical method to integrate the constitutive response of fractional order viscoelasticity is developed the method can handle variable time steps to overcome the problem of the growing amount of data that has to be stored and used in each time step we introduce sparse quadrature we use an internal variable formulation of the viscoelastic equations where the internal variable is of stress type the rate equation that governs the evolution of the internal variable involves a fractional integral and can be identified as a volterra integral equation of the second kind with a weakly singular kernel for the numerical integration of the rate equation we adopt the finite element method in time in particular the discontinuous galerkin method with piecewise constant basis functions is used a priori and a posteriori error estimates are proved an adaptive strategy based on the a posteriori error estimate is developed finally the precision and effectiveness of the method are demonstrated by comparing the numerical solutions with analytical solutions

landscapes and molecular evolution abstract evolution of rna molecules in vitro is visualized as a hill climbing process on a fitness landscape that can be derived from molecular properties and functions the optimization process is shaped by a high degree of redundance in sequence to structure mappings there are many more sequences than structures and sequences folding into the same structure are almost randomly distributed in sequence space two consequences of this redundance are important for evolution shape space covering by small connected regions in sequence space and the existence of extended neutral networks both results together explain how nature can fast and efficiently find solutions to complex optimization problems by trial and error while the number of possible genotypes exceeds all imagination in the presence of neutral networks populations avoid being caught in evolutionary traps and eventually reach the global optimum through a composite dynamics of adaptive walks and random drift results derived from mathematical analysis are confronted with the results of computer simulation and available experimental data

adaptive collocation methods for volterra integral and integro differential equations in this paper the a posteriori error estimates of collocation methods are derived for volterra integral and integro differential equations with smooth and weakly singular kernels the derived error indicators are constructed in an iterative way and used to adaptively refine the meshes in the ports of large gradients this approach is much more efficient than the collocation methods on the fixed meshes numerical computations confirm the analysis via several examples

complex dynamics of a catalytic network having faulty replication into error species abstract we examine the dynamics of catalytic networks when error is introduced through faulty self replication into a mutant molecular species the model consists of n species that individually self replicate through noncatalytic and catalytic action and catalyze the replication of other species faulty replication produces error mutants which are assumed to be kinetically indistinguishable from one another this aggregate error species error tail undergoes noncatalyzed self replication but has no effect on the catalytic species a constant population criterion produces competition among all reactants the time evolution of the catalytic species can be expressed by a set of ordinary differential equations we provide a detailed parametric analysis of the dynamics in a computationally tractable reduced model kinetic constants k ji controlling the enzymatic reactions can be used as bifurcation parameters to generate a rich repertoire of periodic and complex chaotic dynamics except for changes in the parametric position of bifurcation points system dynamics is stable in response to changes in the quality of replication q where 1 q is the mutation rate and in the amplification constant a for the catalytic species at low values of q the system falls out of chaotic regimes and into a random replication state at which there are no catalytic species present there is a similar insensitivity to changes in the amplification factor for the error species a e except for a 0 at which the chaotic regimes remain stable throughout the full range of q we discuss the behavior of our model against one in which error is handled by means of mutual intermulation between the catalytic species complex behavior in this intermutation model is extremely sensitive to the mutation rate because the error tail is expressed only in terms of the catalytic species themselves rather than in variables representing the error species the error tail model may provide a useful method with which to examine models of error utilization in neuronal and other biological systems involving competitive interactions among their constituent parts

bifurcation phenomena near homoclinic systems a two parameter analysis the bifurcations of periodic orbits in a class of autonomous three variable nonlinear differential equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues i where 1 sil nikov s condition are studied in a two parameter space the perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period doubling bifurcations leading to periodic orbits which may be attractors if 1 2 the accumulation rate of the critical parameter values at the homoclinic system is exp 2 a global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity a countable set of these cusp bifurcations with scaling properties related to the eigenvalues i of the stationary state are shown to occur in infinitely contractive flows in the two parameter space the periodic orbit attractor domain exhibits a spiral structure globally around the set of homoclinic systems in which all the different periodic orbits are continuously connected

crises sudden changes in chaotic attractors and transient chaos abstract the occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated it is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor we call such collisions crises phenomena associated with crises include sudden changes in the size of chaotic attractors sudden appearances of chaotic attractors a possible route to chaos and sudden destructions of chaotic attractors and their basins this paper presents examples illustrating that crisis events are prevalent in many circumstances and systems and that just past a crisis certain characteristic statistical behavior whose type depends on the type of crisis occurs in particular the phenomenon of chaotic transients is investigated the examples discussed illustrate crises in progressively higher dimension and include the one dimensional quadratic map the two dimensional henon map systems of ordinary differential equations in three dimensions and a three dimensional map in the case of our study of the three dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four respectively based on the examples presented the following conjecture is proposed almost all sudden changes in the size of chaotic attractors and almost all sudden destruction or creations of chaotic attractors and their basins are due to crises

modal matching for correspondence and recognition modal matching is a new method for establishing correspondences and computing canonical descriptions the method is based on the idea of describing objects in terms of generalized symmetries as defined by each object s eigenmodes the resulting modal description is used for object recognition and categorization where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects in general modes provide a global to local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison in contrast to previous techniques which required correspondence to be computed with an initial or prototype shape modal matching utilizes a new type of finite element formulation that allows for an object s eigenmodes to be computed directly from available image information this improved formulation provides greater generality and accuracy and is applicable to data of any dimensionality correspondence results with 2d contour and point feature data are shown and recognition experiments with 2d images of hand tools and airplanes are described

entropy and distance of random graphs with application to structural pattern recognition the notion of a random graph is formally defined it deals with both the probabilistic and the structural aspects of relational data by interpreting an ensemble of attributed graphs as the outcomes of a random graph we can use its lower order distribution to characterize the ensemble to reflect the variability of a random graph shannon s entropy measure is used to synthesize an ensemble of attributed graphs into the distribution of a random graph or a set of distributions we propose a distance measure between random graphs based on the minimum change of entropy before and after their merging when the ensemble contains more than one class of pattern graphs the synthesis process yields distributions corresponding to various classes this process corresponds to unsupervised learning in pattern classification using the maximum likelihood rule and the probability computed for the pattern graph based on its matching with the random graph distributions of different classes we can classify the pattern graph to a class

robust point pattern matching based on spectral context finding correspondences between two related feature point sets is a basic task in computer vision and pattern recognition in this paper we present a novel method for point pattern matching via spectral graph analysis in particular we aim to render the spectral matching algorithm more robust for positional jitter and outlier a local structural descriptor namely the spectral context is proposed to describe the attribute domain of point sets which is fundamentally different from the previous methods furthermore the approximate distance order is defined and employed as the metric for geometric consistency of neighboring points in this work by combining these two novel ingredients we formulate feature point set matching as an optimization problem with one to one constraints the correspondences are then obtained by maximizing the given objective function via the technique of probabilistic relaxation comparative experiments conducted on both synthetic and real data demonstrate the effectiveness of the proposed method especially in the presence of positional jitter and outliers a novel spectral method is proposed for the problem of point pattern matching we propose a local structural descriptor via spectral graph analysis we define a metric of geometric consistency by using the quantity of order

on adaptive finite element methods for fredholm integral equations of the second kind a posteriors and a priori error estimates are derived for a finite element discretization of a fredholm integral equation of the second kind a reliable and efficient adaptive algorithm is then designed for a specific computational goal with applications to potential problems the reliability of the algorithm is guaranteed by the a posteriors error estimate and the efficiency follows from the a priori error estimate which shows that the a posteriors error bound is sharp

finite element methods for partial volterra integro differential equations on two dimensional unbounded spatial domains abstract the precise and effective way for solving a partial volterra integro differential equation on unbounded spatial domain is to derive artificial boundary conditions for some feasible and prescribed computational domain thus the unsolvable problem on unbounded domain is converted to the computational problem on bounded domain which is often called reduced problem a feasible numerical method will then be applied to solve the reduced problem with the artificial boundary conditions which often exhibit nonlocal properties in this paper the finite element method for the spatial space and the recently developed discontinuous galerkin time stepping method for the temporal space are considered to solve the reduced problem the convergence rate explicitly with those interesting parameters spatial grid size h temporal mesh size k the location of the artificial boundary d and the truncation number m is obtained this paper is the first theoretical analysis of the numerical methods for volterra integro differential equations on unbounded spatial domains

space and time bounds on indexing 3d models from 2d images model based visual recognition systems often match groups of image features to groups of model features to form initial hypotheses which are then verified in order to accelerate recognition considerably the model groups can be arranged in an index space hashed offline such that feasible matches are found by indexing into this space for the case of 2d images and 3d models consisting of point features bounds on the space required for indexing and on the speedup that such indexing can achieve are demonstrated it is proved that even in the absence of image error each model must be represented by a 2d surface in the index space this places an unexpected lower bound on the space required to implement indexing and proves that no quantity is invariant for all projections of a model into the image theoretical bounds on the speedup achieved by indexing in the presence of image error are also determined and an implementation of indexing for measuring this speedup empirically is presented it is found that indexing can produce only a minimal speedup on its own however when accompanied by a grouping operation indexing can provide significant speedups that grow exponentially with the number of features in the groups

a posteriori error estimates for space time finite element approximation of quasistatic hereditary linear viscoelasticity problems abstract we give a space time galerkin finite element discretisation of the quasistatic compressible linear viscoelasticity problem as described by an elliptic partial differential equation with a fading memory volterra integral the numerical scheme consists of a continuous galerkin approximation in space based on piecewise polynomials of degree p 0 cg p with a discontinuous galerkin piecewise constant dg 0 or linear dg 1 approximation in time a posteriori galerkin error estimates are derived by exploiting the galerkin framework and optimal stability estimates for a related dual backward problem the a posteriori error estimates are quite flexible strong lp energy norms of the errors are estimated using time derivatives of the residual terms when the data are smooth while weak energy norms are used when the data are non smooth in time we also give upper bounds on the dg 0 cg 1 a posteriori error estimates which indicate optimality however a complete analysis is not given

adaptive space time finite element solution for volterra equations arising in viscoelasticity problems abstract we give a short overview of our recent efforts towards constructing adaptive space time finite element solvers for some partial differential volterra equations arising in viscoelasticity theory

object recognition as many to many feature matching object recognition can be formulated as matching image features to model features when recognition is exemplar based feature correspondence is one to one however segmentation errors articulation scale difference and within class deformation can yield image and model features which don t match one to one but rather many to many adopting a graph based representation of a set of features we present a matching algorithm that establishes many to many correspondences between the nodes of two noisy vertex labeled weighted graphs our approach reduces the problem of many to many matching of weighted graphs to that of many to many matching of weighted point sets in a normed vector space this is accomplished by embedding the initial weighted graphs into a normed vector space with low distortion using a novel embedding technique based on a spherical encoding of graph structure many to many vector correspondences established by the earth mover s distance framework are mapped back into many to many correspondences between graph nodes empirical evaluation of the algorithm on an extensive set of recognition trials including a comparison with two competing graph matching approaches demonstrates both the robustness and efficacy of the overall approach

negative norm error control for second kind convolution volterra equations summary we consider a piecewise constant finite element approximation to the convolution volterra equation problem of the second kind find u such that u f phi u in a time interval 0 t an a posteriori estimate of the error measured in the w 1 p 0 t norm is developed and used to provide a time step selection criterion for an adaptive solution algorithm numerical examples are given for problems in which phi is of a form typical in viscoelasticity theory

deterministic continuation of stochastic metastable equilibria via lyapunov equations and ellipsoids numerical continuation methods for deterministic dynamical systems have been one of the most successful tools in applied dynamical systems theory continuation techniques have been employed in all branches of the natural sciences as well as in engineering to analyze ordinary partial and delay differential equations here we show that the deterministic continuation algorithm for equilibrium points can be extended to track information about metastable equilibrium points of stochastic differential equations we stress that we do not develop a new technical tool but that we combine results and methods from probability theory dynamical systems numerical analysis optimization and control theory into an algorithm that augments classical equilibrium continuation methods in particular we use ellipsoids defining regions of high concentration of sample paths it is shown that these ellipsoids and the distances between them can be efficiently calculated using iterative methods that take advantage of the numer

belyakov homoclinic bifurcations in a tritrophic food chain model complex dynamics of the most frequently used tritrophic food chain model are investigated in this paper first it is shown that the model admits a sequence of pairs of belyakov bifurcations codimension two homoclinic orbits to a critical node then fold and period doubling cycle bifurcation curves associated to each pair of belyakov points are computed and analyzed the overall bifurcation scenario explains why stable limit cycles and strange attractors with different geometries can coexist the analysis is conducted by combining numerical continuation techniques with theoretical arguments

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

numerical techniques for the treatment of quasistatic viscoelastic stress problems in linear isotropic solids abstract for quasistatic stress problems two alternative constitutive relationships expressing the stress in a linear isotropic viscoelastic solid body as a linear functional of the strain are available in conjunction with the equations of equilibrium these form the mathematical models for the stress problems these models are first discretized in the space domain using a finite element method and semi discrete error estimates are presented corresponding to each constitutive relationship through the use respectively of quadrature rules and finite difference replacements each semi discrete scheme is fully discretized into the time domain so that two practical algorithms suitable for the numerical stress analysis of linear viscoelastic solids are produced the semi discrete estimates are then also extended into the time domain to give spatially h 1 error estimates for each algorithm the numerical schemes are predicated on exact analytical solutions for a simple model problem and finally on design data for a real polymeric material

graph matching with a dual step em algorithm this paper describes a new approach to matching geometric structure in 2d point sets the novel feature is to unify the tasks of estimating transformation geometry and identifying point correspondence matches unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the em algorithm according to our em framework the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters these gating probabilities measure the consistency of the matched neighborhoods in the graphs the recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log likelihood function we evaluate the technique on two real world problems

analytical study of a triple hopf bifurcation in a tritrophic food chain model we provide an analytical proof of the existence of a stable periodic orbit contained in the region of coexistence of the three species of a tritrophic chain the method used consists in analyzing a triple hopf bifurcation for some values of the parameters three limit cycles born via this bifurcation one is contained in the plane where the top predator is absent another one is not contained in the domain of interest where all variables are positive the third one is contained where the three species coexist the techniques for proving these results have been introduced in previous articles by the second author and are based on the averaging theory of second order existence of this triple hopf bifurcation has been previously discovered numerically by kooij et al

on the appearance of multiple attractors in discrete food chains abstract klebanoff and hastings a klebanoff a hastings chaos in three species food chains journal of mathematical biology 32 1994 427 451 detected cases of multiple attractors in continuous food chains in this paper we discuss similar phenomena in the discrete food chains introduced by lindstrom t lindstrom on the dynamics of discrete food chains low and high frequency behavior and chaos journal of mathematical biology 45 2002 396 418 the results imply that the dynamical properties including species persistence may change due to disturbances that do not involve changes in the environmental parameters thus there are possibilities that species may be eradicated or start to oscillate at different frequencies without any changes in the environment since this is now shown to hold in both seasonal and non seasonal environments we expect that this is a rather general property of ecosystems

the second largest eigenvalue of a tree denote by 2 t the second largest eigenvalue of a tree t an easy algorithm is given to decide whether 2 t for a given number and a structure theorem for trees with 2 t is proved also it is shown that a tree t with n vertices has 2 t lsqb n 3 2rsqb12 this bound is best possible for odd n

low and high frequency oscillations in three dimensional food chain systems the dynamic behavior of a three trophic level food chain prey predator superpredator is analyzed in this paper prey is logistic while predator and superpredator have functional response of the holling type moreover the trophic levels are assumed to be characterized by increasing and quite diversified time responses using a singular perturbation approach explicit conditions for the persistence of the three populations are derived and the structure of the corresponding attractors is noted as well as the nature of transients the analysis shows that the system can have low frequency cycles due to the interactions between predator and superpredator nevertheless the interactions between prey and predator can give rise to high frequency oscillations which can arise during the transients toward the attractor or during the low frequency cycle this periodic burst of high frequency oscillations develops in particular when the two predators are fairly efficient these results note in a very concise w

discrete schemes for treating hereditary problems of viscoelasticity and applications abstract mathematical models for treating problems of linear viscoelasticity involving hereditary constitutive relations for compressible solids are presented and their discretisation using finite element methods in space together with quadrature rules in time to treat the hereditary integrals is described theoretical error estimates in appropriate sobolev space settings are given both as they arise as a result of using a gronwall inequality and also from employing a more sensitive comparison theorem which for the quasistatic problem and under physically reasonable assumptions on the relaxation function yields much sharper constants in the estimates the range of applicability of the mathematical models and hence the numerical schemes and error estimates are discussed in the context of various materials primarily polymeric materials and extensions of the techniques to the modelling of manufacturing processes such as thermoforming are presented

a new algorithm for error tolerant subgraph isomorphism detection we propose a new algorithm for error correcting subgraph isomorphism detection from a set of model graphs to an unknown input graph the algorithm is based on a compact representation of the model graphs this representation is derived from the set of model graphs in an off line preprocessing step the main advantage of the proposed representation is that common subgraphs of different model graphs are represented only once therefore at run time given an unknown input graph the computational effort of matching the common subgraphs for each model graph onto the input graph is done only once consequently the new algorithm is only sublinearly dependent on the number of model graphs furthermore the new algorithm can be combined with a future cost estimation method that greatly improves its run time performance

period doubling cascades in a predator prey model with a scavenger the dynamics of the classic planar two species lotka volterra predator prey model are well understood we introduce a scavenger species that scavenges the predator and is also a predator of the common prey for this model we analytically prove that all trajectories are bounded in forward time and numerically demonstrate persistent bounded paired cascades of period doubling orbits over a wide range of parameter values standard analytical and numerical techniques are used in the analysis of this model making it an ideal pedagogical tool we include exercises and an open ended project to promote mastery of these techniques

the dimension of chaotic attractors dimension is perhaps the most basic property of an attractor in this paper we discuss a variety of different definitions of dimension compute their values for a typical example and review previous work on the dimension of chaotic attractors the relevant definitions of dimension are of two general types those that depend only on metric properties and those that depend on the frequency with which a typical trajectory visits different regions of the attractor both our example and the previous work that we review support the conclusion that all of the frequency dependent dimensions take on the same value which we call the dimension of the natural measure and all of the metric dimensions take on a common value which we call the fractal dimension furthermore the dimension of the natural measure is typically equal to the lyapunov dimension which is defined in terms of lyapunov numbers and thus is usually far easier to calculate than any other definition because it is computable and more physically relevant we feel that the dimension of the natural measure is more important than the fractal dimension

record breaking optimization results using the ruin and recreate principle a new optimization principle is presented solutions of problems are partly but significantly ruined and rebuilt or recreated afterwards performing this type of change frequently one can obtain astounding results for classical optimization problems the new method is particularly suited for more complex optimization problems discontinuous ones problems with hard to find admissible solutions problems with complex objectives or many constraints the method is an all purpose heuristic numerical results are given for the traveling salesman problem for the vehicle routing problem with time windows and for network optimization numerical evidence for the quality of the proposed principle is given for most of the instances of a research library of problems the ruin and recreate r r implementation achieved the best published results for many instances better or much better solutions could be found

path similarity skeleton graph matching this paper proposes a novel graph matching algorithm and applies it to shape recognition based on object silhouettes the main idea is to match skeleton graphs by comparing the geodesic paths between skeleton endpoints in contrast to typical tree or graph matching methods we do not consider the topological graph structure our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures the proposed comparison of geodesic paths between endpoints of skeleton graphs yields correct matching results in such cases the skeletons are pruned by contour partitioning with discrete curve evolution which implies that the endpoints of skeleton branches correspond to visual parts of the objects the experimental results demonstrate that our method is able to produce correct results in the presence of articulations stretching and contour deformations

discontinuous galerkin method with a posteriori l_p 0 t_i error estimate for second kind volterra problems we consider a discontinuous galerkin finite element method applied in time to a model volterra equation of the second kind a residual based computable l p 0 t i galerkin error estimate is derived for 1 le p le infty this estimate does not explicitly contain the time step and therefore the time step control must be based on a heuristic criterion the estimate can then be used to demonstrate the integrity or otherwise of the finite element solution after performing some numerical experiments we conclude that this approach is at least competetive with classical discretizations since it is computationally simple to implement but has the added advantage of reliable error feedback

rich dynamics of a food chain model with hassell varley type functional responses abstract complex dynamics of a tritrophic food chain model with hassell varley functional responses is discussed in this paper dynamical behaviours such as boundedness stability and bifurcation of the model are studied the effect of discrete time delay on the model is investigated various solutions are found using computer simulations it is discussed how these ideas illuminate some of the observed properties of real populations in the field and explores practical implications

effects of supplying alternative food in a predator prey model with harvesting in this paper we propose a tritrophic predator prey model with harvesting where the top predator population is partially supported with alternative food we report the consequences of providing alternative food to the top predator in a top predator harvested model the extinction criterion for top predator population local stability of equilibrium points and persistence conditions are discussed theoretically pontryagins maximum principle is used to characterize the optimal control of harvesting we have derived the condition of hopf bifurcation by varying harvesting effort the bifurcation diagrams of the system with respect to harvesting effort in presence of alternative food are given our analysis show that alternative food can prevent top predator extinction risk at higher harvesting effort and plays a vital role for biological conservation of species

3 d shape recovery using distributed aspect matching an approach to the recovery of 3 d volumetric primitives from a single 2 d image is presented the approach first takes a set of 3 d volumetric modeling primitives and generates a hierarchical aspect representation based on the projected surfaces of the primitives conditional probabilities capture the ambiguity of mappings between levels of the hierarchy from a region segmentation of the input image the authors present a formulation of the recovery problem based on the grouping of the regions into aspects no domain independent heuristics are used only the probabilities inherent in the aspect hierarchy are exploited once the aspects are recovered the aspect hierarchy is used to infer a set of volumetric primitives and their connectivity as a front end to an object recognition system the approach provides the indexing power of complex 3 d object centered primitives while exploiting the convenience of 2 d viewer centered aspect matching aspects are used to represent a finite vocabulary of 3 d parts from which objects can be constructed

fuzzy multilevel graph embedding structural pattern recognition approaches offer the most expressive convenient powerful but computational expensive representations of underlying relational information to benefit from mature less expensive and efficient state of the art machine learning models of statistical pattern recognition they must be mapped to a low dimensional vector space our method of explicit graph embedding bridges the gap between structural and statistical pattern recognition we extract the topological structural and attribute information from a graph and encode numeric details by fuzzy histograms and symbolic details by crisp histograms the histograms are concatenated to achieve a simple and straightforward embedding of graph into a low dimensional numeric feature vector experimentation on standard public graph datasets shows that our method outperforms the state of the art methods of graph embedding for richly attributed graphs highlights we propose an explicit graph embedding method we perform multilevel analysis of graph to extract global topological structural and attribute information we use homogeneity of subgraphs in graph for extracting topological structural details we encode numeric information by fuzzy histograms and symbolic information by crisp histograms our method outperforms graph embedding methods for richly attributed graphs

invariant descriptors for 3d object recognition and pose invariant descriptors are shape descriptors that are unaffected by object pose by perspective projection or by the intrinsic parameters of the camera these descriptors can be constructed using the methods of invariant theory which are briefly surveyed a range of applications of invariant descriptors in 3d model based vision is demonstrated first a model based vision system that recognizes curved plane objects irrespective of their pose is demonstrated curves are not reduced to polyhedral approximations but are handled as objects in their own right models are generated directly from image data once objects have been recognized their pose can be computed invariant descriptors for 3d objects with plane faces are described all these ideas are demonstrated using images of real scenes the stability of a range of invariant descriptors to measurement error is treated in detail

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

multiscale symmetric part detection and grouping skeletonization algorithms typically decompose an object s silhouette into a set of symmetric parts offering a powerful representation for shape categorization however having access to an object s silhouette assumes correct figure ground segmentation leading to a disconnect with the mainstream categorization community which attempts to recognize objects from cluttered images in this paper we present a novel approach to recovering and grouping the symmetric parts of an object from a cluttered scene we begin by using a multiresolution superpixel segmentation to generate medial point hypotheses and use a learned affinity function to perceptually group nearby medial points likely to belong to the same medial branch in the next stage we learn higher granularity affinity functions to group the resulting medial branches likely to belong to the same object the resulting framework yields a skeletal approximation that is free of many of the instabilities that occur with traditional skeletons more importantly it does not require a closed contour enabling the application of skeleton based categorization systems to more realistic imagery

fourier analysis of multi frequency dynamical systems abstract the fourier spectrum of a multiply periodic system appears complex due to resonances at integer combinations of the fundamental frequencies we show how to reorder the peaks in the fourier spectrum to yield a simpler structure which reveals important aspects of the time series which are not clearly seen in the ordinary fourier transform as examples we study time series from circle and torus maps and from experimental data by gollub and benson

continuation techniques and interactive software for bifurcation analysis of odes and iterated maps physics abstract we present a numerical technique for the analysis of local bifurcations which is based on the continuation of structurally unstable invariant sets in a suitable phase parameter space the invariant sets involved in our study are equilibrium points and limit cycles of autonomous odes periodic solutions of time periodic nonautonomous odes fixed points and periodic orbits of iterated maps the more general concept of a continuation strategy is also discussed it allows the analysis of various singularities of generic systems and of their mutual relationships the approach is extended to codimension three singularities we introduce several bifurcation functions and show how to use them to construct well posed continuation problems the described continuation technique is supported by an interactive graphical program called locbif we discuss briefly the concepts of the locbif interface and give some examples of typical applications

stationary distribution and ergodicity of a stochastic food chain model with levy jumps abstract in this paper a three species stochastic food chain model with levy jumps is proposed and analyzed sharp sufficient criteria for the existence and uniqueness of an ergodic stationary distribution are established the effects of levy jumps on the existence of the stationary distribution are revealed in some cases the levy jumps could make the stationary distribution appear while in some cases the levy jumps could make the stationary distribution disappear some numerical simulations are introduced to illustrate the theoretical results

local and global behavior near homoclinic orbits we study the local behavior of systems near homoclinic orbits to stationary points of saddle focus type we explicitly describe how a periodic orbit approaches homoclinicity and with the help of numerical examples discuss how these results relate to global patterns of bifurcations

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

indexing hierarchical structures using graph spectra hierarchical image structures are abundant in computer vision and have been used to encode part structure scale spaces and a variety of multiresolution features in this paper we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic graph dag into a low dimensional vector space based on a novel spectral characterization of a dag this topological signature allows us to efficiently retrieve a promising set of candidates from a database of models using a simple nearest neighbor search we establish the insensitivity of the signature to minor perturbation of graph structure due to noise occlusion or node split merge to accommodate large scale occlusion the dag rooted at each nonleaf node of the query votes for model objects that share that part effectively accumulating local evidence in a model dag s topological subspaces we demonstrate the approach with a series of indexing experiments in the domain of view based 3d object recognition using shock graphs

applications and numerical analysis of partial differential volterra equations a brief survey this article contains a concise survey of the numerical analysis of volterra equations and leads up to some recent results on a posteriori error estimation for finite element approximations

dynamical consequences of adaptation of the growth rates in a system of three competing populations we investigate the nonlinear dynamics of a system of populations competing for the same limited resource for the case where each of the populations adapts its growth rate to the total number of individuals in all populations we consider regions of parameter space where chaotic motion of the shilnikov kind exists and present results for two characteristic values of the growth ratio adaptation factor r r 0 15 and 5 negative r can lead to vanishing of regions of chaotic motion and to a stabilization of a fixed point of the studied model system of differential equations positive r lead to changes of the shape of the bifurcation diagrams in comparison with the bifurcation diagrams for the case without adaptation for the case r 5 we observe transition to chaos by period doubling bifurcations windows of periodic motion between the regions of chaotic motion and a region of transient chaos after the last window of periodic motion the lyapunov dimension for the chaotic attractors is close to two and the lyapunov spectrum has a structure which allows a topological analysis of the attractors of the investigated system

matching hierarchical structures using association graphs it is well known that the problem of matching two relational structures can be posed as an equivalent problem of finding a maximal clique in a derived association graph however it is not clear how to apply this approach to computer vision problems where the graphs are hierarchically organized i e are trees since maximal cliques are not constrained to preserve the partial order we provide a solution to the problem of matching two trees by constructing the association graph using the graph theoretic concept of connectivity we prove that in the new formulation there is a one to one correspondence between maximal cliques and maximal subtree isomorphisms this allows us to cast the tree matching problem as an indefinite quadratic program using the motzkin straus theorem and we use replicator dynamical systems developed in theoretical biology to solve it such continuous solutions to discrete problems are attractive because they can motivate analog and biological implementations the framework is also extended to the matching of attributed trees by using weighted association graphs we illustrate the power of the approach by matching articulated and deformed shapes described by shock trees

a metric for comparing relational descriptions relational models are frequently used in high level computer vision finding a correspondence between a relational model and an image description is an important operation in the analysis of scenes in this paper the process of finding the correspondence is formalized by defining a general relational distance measure that computes a numeric distance between any two relational descriptions a model and an image description two models or two image descriptions the distance measure is proved to be a metric and is illustrated with examples of distance between object models a variant measure used in our past studies is shown not to be a metric

full characterization of a strange attractor chaotic dynamics in low dimensional replicator system abstract two chaotic attractors observed in lotka volterra equations of dimension n 3 are shown to represent two different cross sections of one and the same chaotic regime the strange attractor is studied in the equivalent four dimensional catalytic replicator network analytical expressions are derived for the lyapunov exponents of the flow in the centre of the chaotic regime the strange attractor was characterized by the lyapunov dimension dl 2 06 0 02 and the renyi fractal dimensions the set corresponding to the attractor represents a multifractal its singularity spectrum is computed one route in parameter space leading into the chaotic regime and crossing it was studied in detail it leads to a feigenbaum type cascade of bifurcations before the chaos is fully developed the dynamic system passes an internal crisis through a period two tangent bifurcation then a second sequence of period doubling bifurcations leading to another chaotic regime is observed which eventually ends in a crisis and then after a rather complicated periodic regime the attractor finally disappears trajectories in the intermediate periodic regime show transient chaotic bursts of intermittency type a series of one dimensional maps is derived from a properly chosen poincare cross section which illustrates structural changes in the attractor mutations are included in the catalytic replicator network and the changes in the dynamics observed are compared with the predictions of an approach based on perturbation theory the most striking result is the gradual disappearance of complex dynamics with increasing mutation rates the parameter space spanned by the mutation rate and selected parameters of the replication network is split in regions of complex periodic behaviour near the chaotic regime fractal boundaries of these regions are likely to occur but the data available do not allow definitive conclusions yet

structural matching in computer vision using probabilistic relaxation in this paper we develop the theory of probabilistic relaxation for matching features extracted from 2d images derive as limiting cases the various heuristic formulae used by researchers in matching problems and state the conditions under which they apply we successfully apply our theory to the problem of matching and recognizing aerial road network images based on road network models and to the problem of edge matching in a stereo pair for this purpose each line network is represented by an attributed relational graph where each node is a straight line segment characterized by certain attributes and related with every other node via a set of binary relations

numerical solution of linear quasistatic hereditary viscoelasticity problems we give a space time galerkin finite element discretization of the linear quasistatic compressible viscoelasticity problem as described by an elliptic partial differential equation with a volterra memory term the discretization consists of a continuous piecewise linear approximation in space with a discontinuous piecewise constant or linear approximation in time we derive an a priori maximum energy error estimate by exploiting galerkin orthogonality and the data stability of a related discrete backward problem illustrative numerical experiments are also included as also is a brief description of our first results on a posteriori error estimation this allows for adaptive control of the space mesh but not of the time step

effect of time delay on a food chain model this paper aims to study the effect of discrete time delay on a tritrophic food chain model with holling type ii functional responses dynamical behaviours such as boundedness stability persistence and bifurcation of the model are studied our analytical findings are illustrated through computer simulation biological implications of our analytical findings are addressed critically

focusr feature oriented correspondence using spectral regularization a method for precise surface matching existing methods for surface matching are limited by the tradeoff between precision and computational efficiency here we present an improved algorithm for dense vertex to vertex correspondence that uses direct matching of features defined on a surface and improves it by using spectral correspondence as a regularization this algorithm has the speed of both feature matching and spectral matching while exhibiting greatly improved precision distance errors of 1 4 percent the method focusr incorporates implicitly such additional features to calculate the correspondence and relies on the smoothness of the lowest frequency harmonics of a graph laplacian to spatially regularize the features in its simplest form focusr is an improved spectral correspondence method that nonrigidly deforms spectral embeddings we provide here a full realization of spectral correspondence where virtually any feature can be used as an additional information using weights on graph edges but also on graph nodes and as extra embedded coordinates as an example the full power of focusr is demonstrated in a real case scenario with the challenging task of brain surface matching across several individuals our results show that combining features and regularizing them in a spectral embedding greatly improves the matching precision to a submillimeter level while performing at much greater speed than existing methods

modeling and dynamical analysis of a triple delayed prey predator scavenger system with levy jumps abstract in this paper a hybrid triple delayed prey predator scavenger system with commercial harvesting and levy jumps is established where both maturation delay for prey population and gestation delays for predator and scavenger population are considered for deterministic system positivity and uniform permanence of solution are discussed local stability analysis of deterministic system around interior equilibrium is investigated due to variations of triple time delays for stochastic system without time delay sufficient conditions for stochastically ultimate boundedness and stochastic permanence are discussed for stochastic system with triple time delays existence and uniqueness of global positive solution are studied by constructing appropriate lyapunov functions asymptotic behavior of the hybrid stochastic system with triple time delays and levy jumps is discussed numerical simulations are supported to illustrate theoretical results

shapes shocks and deformations i the components of two dimensional shape and the reaction diffusion space we undertake to develop a general theory of two dimensional shape by elucidating several principles which any such theory should meet the principles are organized around two basic intuitions first if a boundary were changed only slightly then in general its shape would change only slightly this leads us to propose an operational theory of shape based on incremental contour deformations the second intuition is that not all contours are shapes but rather only those that can enclose physical material a theory of contour deformation is derived from these principles based on abstract conservation principles and hamilton jacobi theory these principles are based on the work of sethian 1985a c the osher sethian 1988 level set formulation the classical shock theory of lax 1971 1973 as well as curve evolution theory for a curve evolving as a function of the curvature and the relation to geometric smoothing of gage hamilton grayson 1986 1989 the result is a characterization of the computational elements of shape deformations parts bends and seeds which show where to place the components of a shape the theory unifies many of the diverse aspects of shapes and leads to a space of shapes the reaction diffusion space which places shapes within a neighborhood of similar ones such similarity relationships underlie descriptions suitable for recognition

region based hierarchical image matching this paper presents an approach to region based hierarchical image matching where given two images the goal is to identify the largest part in image 1 and its match in image 2 having the maximum similarity measure defined in terms of geometric and photometric properties of regions e g area boundary shape and color as well as region topology e g recursive embedding of regions to this end each image is represented by a tree of recursively embedded regions obtained by a multiscale segmentation algorithm this allows us to pose image matching as the tree matching problem to overcome imaging noise one to one many to one and many to many node correspondences are allowed the trees are first augmented with new nodes generated by merging adjacent sibling nodes which produces directed acyclic graphs dags then transitive closures of the dags are constructed and the tree matching problem reformulated as finding a bijection between the two transitive closures on dags while preserving the connectivity and ancestor descendant relationships of the original trees the proposed approach is validated on real images showing similar objects captured under different types of noise including differences in lighting conditions scales or viewpoints amidst limited occlusion and clutter

dynamics of molecular evolution abstract molecular evolution is visualized as a dynamical process described by nonlinear differential equations which are derived from the kinetics of polynucleotide replication first and higher order autocatalytic processes lead to different behavior in selection dynamics one consequence of this fundamental difference is of primary importance for the evolutionary process optimization of the mean rates of replication in the sense of darwin s theory of evolution is restricted to first order autocatalysis and to some special cases of second order autocatalytic processes dynamical systems which model these processes are fairly simple they can be represented by some kind of generalized gradient systems based on a potential function and they admit only saddle node bifurcations emergence of new properties like oscillatory patterns dissipative spatial structures and various forms of control and organization however is possible only in systems with complex dynamics which require at least second order autocatalysis error propagation through replication sets a limit to the genetic information content which can be transferred stably over many generations this limitation is casted into quantitative terms by the theory it leads to an error threshold which can be derived either from the differential equations of biochemical kinetics or from the theory of branching processes the latter derivation is certainly more adequate since it allows to account for stochastic phenomena which are fundamental to evolution biological evolution is a superposition of many hierarchically ordered processes which take place on different time scales we shall discuss three levels on which molecular evolution operates elementary step dynamics of replication kinetics selection dynamics leading to stationary mutant distributions called quasispecies and evolutionary adaptation

learning context sensitive shape similarity by graph transduction shape similarity and shape retrieval are very important topics in computer vision the recent progress in this domain has been mostly driven by designing smart shape descriptors for providing better similarity measure between pairs of shapes in this paper we provide a new perspective to this problem by considering the existing shapes as a group and study their similarity measures to the query shape in a graph structure our method is general and can be built on top of any existing shape similarity measure for a given similarity measure a new similarity is learned through graph transduction the new similarity is learned iteratively so that the neighbors of a given shape influence its final similarity to the query the basic idea here is related to pagerank ranking which forms a foundation of google web search the presented experimental results demonstrate that the proposed approach yields significant improvements over the state of art shape matching algorithms we obtained a retrieval rate of 91 61 percent on the mpeg 7 data set which is the highest ever reported in the literature moreover the learned similarity by the proposed method also achieves promising improvements on both shape classification and shape clustering

graph simplification and matching using commute times this paper exploits the properties of the commute time for the purposes of graph simplification and matching our starting point is the lazy random walk on the graph which is determined by the heat kernel of the graph and can be computed from the spectrum of the graph laplacian we characterise the random walk using the commute time between nodes and show how this quantity may be computed from the laplacian spectrum using the discrete green s function in this paper we explore two different but essentially dual simplified graph representations delivered by the commute time the first representation decomposes graphs into concentric layers to do this we augment the graph with an auxiliary node which acts as a heat source we use the pattern of commute times from this node to decompose the graph into a sequence of layers our second representation is based on the minimum spanning tree of the commute time matrix the spanning trees located using commute time prove to be stable to structural variations we match the graphs by applying a tree matching method to the spanning trees we experiment with the method on synthetic and real world image data where it proves to be effective

spectral embedding of graphs in this paper we explore how to embed symbolic relational graphs with unweighted edges in a pattern space we adopt a graph spectral approach we use the leading eigenvectors of the graph adjacency matrix to define eigenmodes of the adjacency matrix for each eigenmode we compute vectors of spectral properties these include the eigenmode perimeter eigenmode volume cheeger number inter mode adjacency matrices and intermode edge distance we embed these vectors in a pattern space using two contrasting approaches the first of these involves performing principal or independent components analysis on the covariance matrix for the spectral pattern vectors the second approach involves performing multidimensional scaling on the l2 norm for pairs of pattern vectors we illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2d images of 3d polyhedral objects two problems are investigated the first of these is the clustering of graphs representing distinct objects viewed from different directions the second is the identification of characteristic views of single objects these two studies reveal that both embedding methods result in well structured view spaces for graph data extracted from 2d views of 3d objects

fast monte carlo algorithms for matrices ii computing a low rank approximation to a matrix in many applications the data consist of or may be naturally formulated as an m times n matrix a it is often of interest to find a low rank approximation to a i e an approximation d to the matrix a of rank not greater than a specified rank k where k is much smaller than m and n methods such as the singular value decomposition svd may be used to find an approximation to a which is the best in a well defined sense these methods require memory and time which are superlinear in m and n for many applications in which the data sets are very large this is prohibitive two simple and intuitive algorithms are presented which when given an m times n matrix a compute a description of a low rank approximation d to a and which are qualitatively faster than the svd both algorithms have provable bounds for the error matrix a d for any matrix x let x f and x 2 denote its frobenius norm and its spectral norm respectively in the first algorithm c columns of a are randomly chosen if the m times c matrix c consists of those c columns of a after appropriate rescaling then it is shown that from c tc approximations to the top singular values and corresponding singular vectors may be computed from the computed singular vectors a description d of the matrix a may be computed such that mathrm rank d le k and such that left a d right xi 2 le min d mathrm rank d le k left a d right xi 2 poly k 1 c left a right 2 f holds with high probability for both xi 2 f this algorithm may be implemented without storing the matrix a in random access memory ram provided it can make two passes over the matrix stored in external memory and use o cm c 2 additional ram the second algorithm is similar except that it further approximates the matrix c by randomly sampling r rows of c to form a r times c matrix w thus it has additional error but it can be implemented in three passes over the matrix using only constant additional ram to achieve an additional error beyond the best rank k approximation that is at most epsilon a 2 f both algorithms take time which is polynomial in k 1 epsilon and log 1 delta where delta 0 is a failure probability the first takes time linear in mbox max m n and the second takes time independent of m and n our bounds improve previously published results with respect to the rank parameter k for both the frobenius and spectral norms in addition the proofs for the error bounds use a novel method that makes important use of matrix perturbation theory the probability distribution over columns of a and the rescaling are crucial features of the algorithms which must be chosen judiciously

unsupervised category modeling recognition and segmentation in images suppose a set of arbitrary unlabeled images contains frequent occurrences of 2d objects from an unknown category this paper is aimed at simultaneously solving the following related problems 1 unsupervised identification of photometric geometric and topological properties of multiscale regions comprising instances of the 2d category 2 learning a region based structural model of the category in terms of these properties and 3 detection recognition and segmentation of objects from the category in new images to this end each image is represented by a tree that captures a multiscale image segmentation the trees are matched to extract the maximally matching subtrees across the set which are taken as instances of the target category the extracted subtrees are then fused into a tree union that represents the canonical category model detection recognition and segmentation of objects from the learned category are achieved simultaneously by finding matches of the category model with the segmentation tree of a new image experimental validation on benchmark data sets demonstrates the robustness and high accuracy of the learned category models when only a few training examples are used for learning without any human supervision

3 d object recognition using bipartite matching embedded in discrete relaxation the authors show how large efficiencies can be achieved in model based 3 d vision by combining the notions of discrete relaxation and bipartite matching the computational approach presented is capable of pruning large segments of search space an indispensable step when the number of objects in the model library is large and when recognition of complex objects with a large number of surfaces is called for bipartite matching is used for quick wholesale rejection of inapplicable models and for the determination of compatibility of a scene surface with a potential model surface taking into account relational considerations the time complexity function associated with those aspects of the procedure that are implemented via bipartite matching is provided the algorithms do not take more than a couple of iterations even for objects with more than 30 surfaces

error estimates with sharp constants for a fading memory volterra problem in linear solid viscoelasticity the problem characterizing nonageing linear isothermal quasi static isotropic compressible solid viscoelasticity in the time interval 0 t is described this is essentially a volterra equation of the second kind arrived at by adding smooth fading memory to the elliptic linear elasticity equations we analyze the errors resulting from replacing the relaxation functions with practical approximations in a semidiscrete finite element approximation and in a fully discrete scheme derived by replacing the hereditary integral with the trapezoidal rule for numerical integration the error estimates are sharp in the sense that if certain bounds on the data are independent of t then so also are the constants involved in them this is a consequence of bypassing the usual gronwall lemmas with arguments that are more sensitive to the fading memory of the physical problem

reconstructing attractors from scalar time series a comparison of singular system and redundancy criteria abstract a delay vector phase space reconstruction in which the delay time satisfiesa minimum redundancy criterion is compared with a reconstruction obtained using a singular system approach minimum redundancy produces the better reconstruction the reconstructions are compared using a distortion functional d which measures how well the location of a point in the original phase space can be determined on the basis of its image under the reconstruction process the superiority of the redundancy analysis over the singular system analysis is found to arise from the former s foundation on the notion of general independence as opposed to the latter s foundation on the notion of linear independence

coined quantum walks lift the cospectrality of graphs and trees in this paper we explore how a spectral technique suggested by coined quantum walks can be used to distinguish between graphs that are cospectral with respect to standard matrix representations the algorithm runs in polynomial time and moreover can distinguish many graphs for which there is no subexponential time algorithm that is proven to be able to distinguish between them in the paper we give a description of the coined quantum walk from the field of quantum computing the evolution of the walk is governed by a unitary matrix we show how the spectrum of this matrix is related to the spectrum of the transition matrix of the classical random walk however despite this relationship the behaviour of the quantum walk is vastly different from the classical walk this leads us to define a new matrix based on the amplitudes of paths of the walk whose spectrum we use to characterise graphs we carry out three sets of experiments using this matrix representation firstly we test the ability of the spectrum to distinguish between sets of graphs that are cospectral with respect to standard matrix representation these include strongly regular graphs and incidence graphs of balanced incomplete block designs bibds secondly we test our method on all regular graphs on up to 14 vertices and all trees on up to 24 vertices this demonstrates that the problem of cospectrality is often encountered with conventional algorithms and tests the ability of our method to resolve this problem thirdly we use distances obtained from the spectra of s u 3 to cluster graphs derived from real world image data and these are qualitatively better than those obtained with the spectra of the adjacency matrix thus we provide a spectral representation of graphs that can be used in place of standard spectral representations far less prone to the problems of cospectrality