on tiling under tomographic constraints given a tiling of a 2d grid with several types of tiles we can count for every row and column how many tiles of each type it intersects these numbers are called the projections we are interested in the problem of reconstructing a tiling which has given projections some simple variants of this problem involving tiles that are 1 1 or 1 2 rectangles have been studied in the past and were proved to be either solvable in polynomial time or np complete in this note we make progress toward a comprehensive classification of various tiling reconstruction problems by proving np completeness results for several sets of tiles

epidemics and percolation in small world networks we study some simple models of disease transmission on small world networks in which either the probability of infection by a disease or the probability of its transmission is varied or both the resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network and we give exact solutions for the position of this threshold in a variety of cases we confirm our analytic results by numerical simulation

interactive shape preserving interpolation by curvature continuous rational cubic splines abstract a scheme is described for interactively modifying the shape of convexity preserving planar interpolating curves an initial curve is obtained by patching together rational cubic and straight line segments this scheme has in general geometric continuity of order 2 g2 continuity and preserves the local convexity of the data a method for interactively modifying such curves while maintaining their desirable properties is discussed in detail in particular attention is focused upon local changes to the curve while retaining g2 continuity and shape preserving properties this is achieved by interactive adjustment of the bezier control points followed by automatic adjustment of the values of weights and curvatures in a prescribed manner a number of examples are presented

correlation effects in a discrete quantum random walk we introduce memory dependent discrete time quantum random walk models by adding uncorrelated memory terms and also by modifying the hamiltonian of the walker to include couplings with memory keeping agents we next study numerically the correlation effects in these models we also propose a correlation exponent as a relevant and promising tool for investigation of correlation or memory hence non markovian effects our analysis can easily be applied to more realistic models in which different regimes may emerge because of competition between different underlying physical mechanisms

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

random walk on percolation under an external field random walk on percolation under an external field has been investigated by using statistical analysis and monte carlo simulation the mean square displacement r2 as a function of time t was obtained there exist some steps in the log r2 logt plot the defect in the percolation plays the part of the trap for the walker each step corresponds to a type of trap the height of the steps indicates the mean square displacement before the walker enters the trap and the width of the step expresses the trapping time spent in the trap the calculated height and width by the probability theory are in agreement with simulation results quite well

directed random walks in continuous space the investigation on diffusion with directed motion in a two dimensional continuous space is completed by using the model of the continuous directed random walks the average square end to end distance approximately t 2nu is calculated the results show that this type of walks belongs asymptotically to the same class nu 1 0 as the ballistic motions for short time we observe a crossover from purely random walks nu 0 5 to ballistic motions nu 1 0 the dependence of the crossover on the direction parameter theta is studied there exists a scaling relation of the form approximately tf t theta 2 the return probability p00 t is also investigated and the scaling form similar to is obtained

multiparticle random walks on a deformable medium multiparticle random walks on a deformable medium have been investigated in 2 1 dimensions the time evolution of the particle distribution is studied the results show that the randomly distributed particles in the beginning will be self organized into a cluster pattern in the intermediate stage and then return to the random distribution pattern in the late stage the dependence of the clustering degree on the stiffness parameter of medium ensuremath alpha stability parameter of systems ensuremath beta and average particle density ensuremath rho 0 is also investigated there exists an optimal clustering stability ensuremath beta p at which the system has the strongest clustering ability and corresponds to a maximum clustering coefficient ensuremath gamma p the dependence of the optimal clustering coefficient ensuremath gamma p on the stiffness ensuremath alpha and particle density ensuremath rho 0 is obtained and the landscape of the medium generated by particles is also investigated

a tiling system for the class of l convex polyominoes a polyomino is said to be l convex if any two of its cells can be connected by a path entirely contained in the polyomino and having at most one change of direction in this paper answering a problem posed by castiglione and vaglica 6 we prove that the class of l convex polyominoes is tiling recognizable to reach this goal first we express the l convexity constraint in terms of a set of independent properties then we show that each class of convex polyominoes having one of these properties is tiling recognizable

reconstructing convex polyominoes from horizontal and vertical projections in 1 we studied the problem of reconstructing a discrete set 5 from its horizontal and vertical projections we defined an algorithm that establishes the existence of a convex polyomino whose horizontal and vertical projections are equal to a pair of assigned vectors h v with h m and v n its computational cost is o n4m4 in this paper we introduce some operations for recontructing convex polyominoes by means of vectors h s and v s partial sums these operations allows us to define a new algorithm whose complexity is less than o n2m2

reconstruction of convex polyominoes with a blocking component several papers in the available literature tackled problems concerning convex polyominoes in discrete tomography an interesting subclass consists of l convex polyominoes since the related reconstruction problem can have only a unique solution on the other hand recent studies have modeled an approach to reconstruct objects even in the case that some of the projections are unavailable due to a particularly dense part of the scanned object that we refer to as a blocking component in this work we merge the two problems in order to obtain efficient reconstruction algorithms for convex and l convex polyominoes in case a blocking component is included

non uniform interpolatory subdivision surface abstract this paper presents an interpolatory subdivision scheme with non uniform parametrization for arbitrary polygon meshes with arbitrary manifold topology this is the first attempt to generalize the non uniform four point interpolatory curve subdivision to surface with extraordinary points the scheme is constructed from the inspiration of the relation between the non uniform four point interpolatory subdivision scheme and the non uniform b spline refinement rule numerical examples and comparisons with the uniform interpolatory subdivision schemes indicate that the quality of the limit surface can be improved by using non uniform parameter values for non uniform initial data

self attracting walk with nu 1 2 a model of a self attracting walk is proposed mean square displacement of a particle xi grows with time t as a power law xi 2 approximately t2 nu with the exponent nu 1 2 it is shown that nu 1 2d db where d is the fractal dimension of the cluster consisting of the visited sites and db is the fractal dimension of its boundary a compact cluster with fractal boundaries was obtained by a computer simulation for d 2 the derived value of nu is in a good agreement with that obtained by computer simulation

nurbs for curve and surface design from the publisher nurbs nonuniform rational b splines promises to be the future geometry standard for free form curves and surfaces this volume contains recent results and new nurbs techniques and developments the most important being curve surface from the cad cam industry the book has been carefully refereed researchers system programmers and graduate students in cagd cad cam and computer graphics will find this book uniquely suited to their field of work

memory controlled diffusion memory effects require for their incorporation into random walk models an extension of the conventional equations the linear fokker planck equation for the probability density p stackrel p vec r t is generalized by including nonlinear and nonlocal spatial temporal memory effects the realization of the memory kernel is restricted due the conservation of the basic quantity p a general criteria is given for the existence of stationary solutions in case the memory kernel depends on p polynomially transport may be prevented owing to the delay effects a finite amount of particles remains localized and the further transport is terminated for diffusion with nonlinear memory effects we find an exact solution in the long time limit although the mean square displacement exhibits diffusive behavior higher order cumulants offer differences to diffusion and they depend on the memory strength

on quasi consistent integration by nordsieck methods in this paper we study advantages of numerical integration by quasi consistent nordsieck formulas all quasi consistent numerical methods possess at least one important property for practical use which has not attracted attention yet i e the global error of a quasi consistent method has the same order as its local error this means that the usual local error control will produce a numerical solution for the prescribed accuracy requirement if the principal term of the local error dominates strongly over remaining terms in other words the global error control can be as cheap as the local error control in the methods under discussion here we apply the above mentioned idea to nordsieck adams moulton methods which are known to be quasi consistent moreover some nordsieck adams moulton methods are even super quasi consistent the latter property means that their propagation matrices annihilate two leading terms in the defect expansion of such methods in turn this can impose a strong relation between the local and global errors of the numerical solution and allow the global error to be controlled effectively by a local error control we also introduce implicitly extended nordsieck methods such that in some sense they form pairs of embedded formulas with their source nordsieck methods this facilitates the local error control in quasi consistent nordsieck schemes numerical examples presented in this paper confirm clearly the power of quasi consistent integration in practice

on parametrization of interpolating curves in parametric curve interpolation there is given a sequence of data points and corresponding parameter values nodes and we want to find a parametric curve that passes through data points at the associated parameter values we consider those interpolating curves that are described by the combination of control points and blending functions we study paths of control points and points of the interpolating curve obtained by the alteration of one node we show geometric properties of quadratic bezier interpolating curves with uniform and centripetal parameterizations finally we propose geometric methods for the interactive modification and specification of nodes for interpolating bezier curves

shape preserving interpolation by parametrically defined curves criteria are discussed for interpolation which preserves local convexity and local monotonicity particular schemes are then given for interpolation by parametric piecewise polynomials the interpolating curves can have any desired order of geometric continuity and they are convex in a region where the data are convex if the data arise from a function then the curve is also single valued and in this case the curve can also preserve local monotonicity if desired

random walk with memory enhancement and decay a model of random walk with memory enhancement and decay was presented on the basis of the characteristics of the biological intelligent walks in this model the movement of the walker is determined by the difference between the remaining information at the jumping out site and jumping in site the amount of the memory information s i t at a site i is enhanced with the increment of visiting times to that site and decays with time t by the rate e beta t where beta is the memory decay exponent when beta 0 there exists a transition from brownian motion bm to the compact growth of walking trajectory with the density of information energy u increasing but for beta 0 this transition does not appear and the walk with memory enhancement and decay can be considered as the bm of the mass center of the cluster composed of remembered sites in the late stage

conjugacy relationship between m convex and l convex functions in continuous variables by extracting combinatorial structures in well solved nonlinear combinatorial optimization problems murota 1996 1998 introduced the concepts of m convexity and l convexity to functions defined over the integer lattice recently murota shioura 2000 2001 extended these concepts to polyhedral convex functions and quadratic functions in continuous variables in this paper we consider a further extension to more general convex functions defined over the real space and provide a proof for the conjugacy relationship between general m convex and l convex functions

the best parameterization for parametric interpolation we consider the problem of interpolation of curves and surfaces using parametric functions in this problem the choice of parameters has a strong influence on the form of interpolants we formulate and prove the necessary and sufficient conditions of the parameterization that provides the best quality of interpolation

swelling collapse transition of self attracting walks we study the structural properties of self attracting walks in d dimensions using scaling arguments and monte carlo simulations we find evidence of a transition analogous to the theta transition of polymers above a critical attractive interaction u c the walk collapses and the exponents nu and k characterizing the scaling with time t of the mean square end to end distance approximately t 2nu and the average number of visited sites approximately t k are universal and given by nu 1 d 1 and k d d 1 below u c the walk swells and the exponents are as with no interaction i e nu 1 2 for all d k 1 2 for d 1 and k 1 for d 2 at u c the exponents are found to be in a different universality class