density of states and dynamic scaling on the vicsek snowflake fractal real space rescaling techniques have been employed to obtain recursion relations for the parameters characterising the dynamics of both the heisenberg ferromagnet and antiferromagnet on the infinite vicsek snowflake fractal the authors have calculated the associated dynamic exponents zf and za by linearising about the respective fixed points of the ferromagnetic antiferromagnetic recursion relations and find them to satisfy the relation za zf 2 in addition using a functional integral method both the ferromagnetic and antiferromagnetic density of states rho f omega and rho a omega have been calculated exactly and the resulting spectra were found to satisfy the scaling equation rho alpha omega approximately bz alpha df rho lambda alpha omega near their respective fixed points alpha a f df denoting the fractal dimension finally the amplitudes galpha omega appearing in the solution to the scaling equation rho alpha omega approximately galpha omega omega dfz alpha 1 for the density of states rho alpha omega were found to be periodic functions of ln omega with period ln lambda alpha where lambda alpha is the eigenvalue associated with ferromagnetic alpha f or antiferromagnetic alpha a fixed point

a branch and bound algorithm for determining locations of long term care facilities this paper focuses on the problem of determining locations for long term care facilities with the objective of balancing the numbers of patients assigned to the facilities we present a branch and bound algorithm by developing dominance properties a lower bounding scheme and a heuristic algorithm for obtaining an upper bound for the problem for evaluation of the suggested branch and bound algorithm computational experiments are performed on a number of test problems results of the experiments show that the suggested algorithm gives optimal solutions of problems of practical sizes in a reasonable amount of computation time

global structure and finite size effects in the f alpha of diffusion limited aggregates the multifractal spectrum f alpha characterizing the scaling properties of the growth probability on the boundary of radial diffusion limited aggregates is known to exhibit strong finite size effects we demonstrate that there exists a correlation between these finite size effects and those present in measurements of the angular width of the fjords which lie between the principal cluster arms we subsequently conclude that it is the evolution in the global structure of the clusters which is responsible for the slow convergence in f alpha and discuss how this global structure induces a phase transition in f alpha

a lagrangean heuristic for the maximal covering location problem abstract we develop a lagrangean heuristic for the maximal covering location problem upper bounds are given by a vertex addition and substitution heuristic and lower bounds are produced through a subgradient optimization algorithm the procedure was tested in networks of up to 150 vertices a duality gap was generally present at the end of the heuristic for the larger problems the test problems were run in an ibm 3090 600j super computer the maximum computing time was kept below three minutes of cpu

a regular model for cluster numbers and structure just below percolation threshold a two dimensional deterministic fractal model is proposed to imitate the geometric texture just below percolation threshold the model is constructed for bond percolation via a rule of bond occupation on the square lattice it show the typical percolation behaviour as a function of a parameter p p is the bond concentration the model describes the approach towards the threshold below criticality the critical bond concentration pc and the correlation length exponent nu are found the scaling property of the cluster size distribution is studied below the threshold the critical concentration and critical exponents are shown to agree with those derived from the regular model proposed for the geometric texture above the threshold the scaling relations for the critical exponents are shown to be satisfied

synchronization in coupled map lattices with small world delayed interactions abstract we study the synchronization of coupled map lattices with small world interactions and coupling delays in this paper a stability criterion for the synchronized state is derived numerical examples are presented to demonstrate the correctness of our theoretical result

the wilson hilferty transformation is locally saddlepoint interest in transform methods for normalising test statistics declined with the advent of computers more recently small sample asymptotic methods have been developed to approximate the distributions of complicated test statistics we propose a generalisation of a classical symmetrising transform to a similar range of statistics it is shown to behave comparably in a parametric neighbourhood to methods that exploit exponential tilting

exact methods for the knapsack problem and its generalizations abstract a unified approach and a summary of the most important results concerned with exact methods for solving the binary knapsack problem and its generalizations are given we stress the importance of dual methods for solving linear programming relaxations of the considered problems two ways of generalization of the knapsack problem are described if the special ordered sets are added then the multiple choice knapsack problem is obtained if the constraints have the nested structure then we get the nested knapsack problem also the multiple choice nested knapsack problem is discussed

graph operations and synchronization of complex networks the effects of graph operations on the synchronization of coupled dynamical systems are studied the operations range from addition or deletion of links to various ways of combining networks and generating larger networks from simpler ones methods from graph theory are used to calculate or estimate the eigenvalues of the laplacian operator which determine the synchronizability of continuous or discrete time dynamics evolving on the network results are applied to explain numerical observations on random scale free and small world networks an interesting feature is that when two networks are combined by adding links between them the synchronizability of the resulting network may worsen as the synchronizability of the individual networks is improved similarly adding links to a network may worsen its synchronizability although it decreases the average distance in the graph

renormalisation on sierpinski type fractals presents a family of deterministic fractals which generalise the d dimensional sierpinski gaskets and establishes their order of ramification and their fractal and spectral dimensions random walks on these fractals are renormalisable and lead to rational not necessarily polynomial mapping

simple estimation of synchronization threshold in ensembles of diffusively coupled chaotic systems in this paper we define a simple criterion of the synchronization threshold in the set of coupled chaotic systems flows or maps with diagonal diffusive coupling the condition of chaotic synchronization is determined only by two parameters of order i e the largest lyapunov exponent and the coupling coefficient our approach can be applied for both regular chaotic networks and arrays or lattices of chaotic oscillators with irregular arbitrarily assumed structure of coupling the main idea of the synchronization stability criterion is based on linear analysis of the ensembles of simplest dynamical systems numerical simulations confirm that such a linear approach approximates the synchronization threshold with high precision

scaling invariance in spectra of complex networks a diffusion factorial moment approach a new method called diffusion factorial moment is used to obtain scaling features embedded in the spectra of complex networks for an erdos renyi network with connecting probability p mathit er l1 n the scaling parameter is ensuremath delta 0 51 while for p mathit er ensuremath geqslant 1 n the scaling parameter deviates from it significantly for ws small world networks in the special region p r 0 05 0 2 typical scale invariance is found for growing random networks in the range of ensuremath theta 0 33 049 we have ensuremath delta 0 6 ifmmode pm else textpm fi 0 1 and the value of ensuremath delta oscillates around ensuremath delta 0 6 abruptly in the range of ensuremath theta 0 54 1 we have basically ensuremath delta g0 7 scale invariance is one of the common features of the three kinds of networks which can be employed as a global measurement of complex networks in a unified way

coupled maps on trees we study coupled maps on a cayley tree with local nearest neighbor interactions and with a variety of boundary conditions the homogeneous state where every lattice site has the same value and the node synchronized state where sites of a given generation have the same value are both shown to occur for particular values of the parameters and coupling constants we study the stability of these states and their domains of attraction since the number of sites that become synchronized is much higher compared to that on a regular lattice control is easier to achieve a general procedure is given to deduce the eigenvalue spectrum for these states perturbations of the synchronized state lead to different spatiotemporal structures we find that a mean field like treatment is valid on this effectively infinite dimensional lattice

the exact solution of the mean geodesic distance for vicsek fractals vicsek fractals are one of the most interesting classes of fractals and the study of their structural properties is important in this paper the exact formula for the mean geodesic distance of vicsek fractals is found the quantity is computed precisely through the recurrence relations derived from the self similar structure of the fractals considered the obtained exact solution exhibits that the mean geodesic distance approximately increases as a power law function of the number of nodes with the exponent equal to the reciprocal of the fractal dimension the closed form solution is confirmed by extensive numerical calculations

anomalous diffusion on regular and random models for diffusion limited aggregation families of regular fractal models for witten sander dla clusters in d dimensions are proposed resembling the computer generated aggregates the authors evaluate random walk dimensionalities exactly using resistance scaling ideas the applicability of the conflicting conjectures of alexander orbach 1982 ao dw 3df 2 and aharony stauffer 1984 as dw df 1 to dla is then examined one finds that the dendritic nature of the fractals presented ensures that as is satisfied exactly in all dimensions an rsrg fugacity transformation method is applied to the simplest of the regular fractals in d 2 the result for dw is compared with the exact resistance scaling result to obtain an estimate of the error introduced by the rsrg the rg method is then generalised to treat the random dla problem the resulting estimate for dw is in fortuitously good agreement with as the corresponding monte carlo data and the results above for the regular fractal models

on the augmented lagrangian dual for integer programming we consider the augmented lagrangian dual for integer programming and provide a primal characterization of the resulting bound as a corollary we obtain proof that the augmented lagrangian is a strong dual for integer programming we are able to show that the penalty parameter applied to the augmented lagrangian term may be placed at a fixed large value and still obtain strong duality for pure integer programs

spatial temporal rainfall simulation using generalized linear models 1 we consider the problem of simulating sequences of daily rainfall at a network of sites in such a way as to reproduce a variety of properties realistically over a range of spatial scales the properties of interest will vary between applications but typically will include some measures of extreme rainfall in addition to means variances proportions of wet days and autocorrelation structure our approach is to fit a generalized linear model glm to rain gauge data and with appropriate incorporation of intersite dependence structure to use the glm to generate simulated sequences we illustrate the methodology using a data set from southern england and show that the glm is able to reproduce many properties at spatial scales ranging from a single site to 2000 km2 the limit of the available data

directed recursion models for fractal growth fractals constructed by recursive processes are introduced to model growth phenomena these fractals are simultaneously directed and self similar in analogy with patterns growing under diffusion limited conditions the multifractal nature of the harmonic measure associated with laplacian interfaces is qualitatively interpreted using the models calculation of the largest singularity exponent allows one to make conclusions about the behaviour of diffusion limited aggregates

nonlocal coupling can prevent the collapse of spatiotemporal chaos spatiotemporal chaos on a regular ring network of excitable gray scott dynamical elements is transient we find that the addition of very few nonlocal network connections drastically changes the average lifetime of spatiotemporal chaos in the presence of a single shortcut local interface formation delays the collapse of spatiotemporal chaos this competes with a reduced average characteristic path length that advances the collapse process two added shortcuts can prevent the collapse of spatiotemporal chaos by causing an asymptotic local collapse

turbulence in small world networks the transition to turbulence via spatiotemporal intermittency is investigated in the context of coupled maps defined on small world networks the local dynamics is given by the chate manneville minimal map previously used in studies of spatiotemporal intermittency in ordered lattice the critical boundary separating laminar and turbulent regimes is calculated on the parameter space of the system given by the coupling strength and the rewiring probability of the network windows of relaminarization are present in some regions of the parameter space new features arise in small world networks for instance the character of the transition to turbulence changes from second order to a first order phase transition at some critical value of the rewiring probability a linear relation characterizing the change in the order of the phase transition is found the global quantity used as order parameter for the transition also exhibits nontrivial collective behavior for some values of the parameters these models may describe several processes occurring in nonuniform media where the degree of disorder can be continuously varied through a parameter

a comparison of lagrangean and surrogate relaxations for the maximal covering location problem abstract we compare heuristics based on lagrangean and surrogate relaxations of the maximal covering location problem mclp the lagrangean relaxation of mclp used in this paper has the integrality property and the surrogate relaxed problem we solve is the lp relaxation of the original 0 1 knapsack problem the heuristics were compared using 331 test problems available in the literature corresponding to networks ranging from 55 to 900 vertices the gaps obtained with both heuristics were very low and did not differ substantially among themselves for the several problem sets used in accordance with theoretical results reviewed in the paper when the initial set of multipliers was determined using a valid bound for mclp the computing times did not differ significantly between the lagrangean and surrogate heuristics

determining mean first passage time on a class of treelike regular fractals relatively general techniques for computing mean first passage time mfpt of random walks on networks with a specific property are very useful since a universal method for calculating mfpt on general graphs is not available because of their complexity and diversity in this paper we present techniques for explicitly determining the partial mean first passage time pmfpt i e the average of mfpts to a given target averaged over all possible starting positions and the entire mean first passage time emfpt which is the average of mfpts over all pairs of nodes on regular treelike fractals we describe the processes with a family of regular fractals with treelike structure the proposed fractals include the t fractal and the peano basin fractal as their special cases we provide a formula for mfpt between two directly connected nodes in general trees on the basis of which we derive an exact expression for pmfpt to the central node in the fractals moreover we give a technique for calculating emfpt which is based on the relationship between characteristic polynomials of the fractals at different generations and avoids the computation of eigenvalues of the characteristic polynomials making use of the proposed methods we obtain analytically the closed form solutions to pmfpt and emfpt on the fractals and show how they scale with the number of nodes in addition to exhibit the generality of our methods we also apply them to the vicsek fractals and the iterative scale free fractal tree and recover the results previously obtained

the theory of wavelet transform method on chaotic synchronization of coupled map lattices the wavelet transform method originated by wei et al phys rev lett 89 284103 4 2002 was proved juang and li j math phys 47 072704 16 2006 juang et al j math phys 47 122702 11 2006 shieh et al j math phys 47 082701 10 2006 to be an effective tool to reduce the order of coupling strength for coupled chaotic systems to acquire the synchrony regardless the size of oscillators in juang et al ieee trans circuits syst i regul pap 56 840 2009 such method was applied to coupled map lattices cmls it was demonstrated that by adjusting the wavelet constant of the method can greatly increase the applicable range of coupling strengths the parameters range of the individual oscillator and the number of nodes for local synchronization of cmls no analytical proof is given there in this paper the optimal or near optimal wavelet constant can be explicitly identified as a result the above described scenario can be rigorously verified

restricted likelihood ratio lack of fit tests using mixed spline models penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non linearity in the smooth function estimates this motivates the study of lack of fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values for this one sided testing problem a further complication is that the variance component belongs to the boundary of the parameter space under the null hypothesis conditions are obtained on the design of the regression spline models under which asymptotic distribution theory applies and finite sample approximations to the asymptotic distribution are provided test statistics are studied for simple as well as multiple regression models

noise reduced diffusion limited deposition to investigate the role of fluctuations in diffusion limited growth the authors apply the noise reduction algorithm to the problem of two dimensional deposition on a substrate consisting of a straight line the authors consider the scaling of the height and the width of trees growing on the square lattice for the sizes studied they find two length scales characterised by different exponents depending on the noise reduction parameter m using these exponents the effective fractal dimension deff of trees is calculated and for m 1 they obtain deff approximately 1 57 the density profile in the direction of growth and the scaling properties of the lateral correlation function are also determined

general saddlepoint approximations with applications to l statistics abstract saddlepoint approximations are extended to general statistics the technique is applied to derive approximations to the density of linear combinations of order statistics including trimmed means a comparison with exact results shows the accuracy of these approximations even in very small sample sizes

spectral properties and pattern selection in fractal growth networks a model for the generation of fractal growth networks in euclidean spaces of arbitrary dimension is presented these networks are considered as the spatial support of reaction diffusion and pattern formation processes the local dynamics at the nodes of a fractal growth network is given by a nonlinear map giving raise to a coupled map system the coupling is described by a matrix whose eigenvectors constitute a basis on which spatial patterns on fractal growth networks can be expressed by linear combination the spectrum of eigenvalues the coupling matrix exhibits a nonuniform distribution that is reflected in the presence of gaps or niches in the boundaries of stability of the synchronized states on the space of parameters of the system these gaps allow for the selection of specific spatial patterns by appropriately varying the parameters of the system

synchronization threshold in coupled logistic map lattices abstract we consider regular lattices of coupled chaotic maps whose local dynamics is ruled by the logistic map x 4 x 1 x a usual paradigm of chaotic systems through finite time exponents we scrutinize the lattice dynamics in the vicinity of the threshold of complete synchronization we connect dynamical features such as relaxation to the coherent state and intermittency with the statistics of finite time exponents focusing on the implications of the particular statistics related to the logistic map although numerical examples are given for lattice couplings decaying with distance as a power law our results are expected to be valid for a wider class of schemes coupling logistic maps

statistical mechanics of red blood cell aggregation the distribution of rouleaux in thermal equilibrium when placed in suspension red blood cells adhere face to face and form long cylindrical and sometimes branched structures called rouleaux we use methods developed in statistical mechanics to compute various statistical properties describing the size and shape of rouleaux in thermodynamic equilibrium this leads to analytical expressions for 1 the average number of rouleaux consisting ofn cells and havingm branch points 2 the average number of cells per rouleau 3 the average number of branch points per rouleau and 4 the number of rouleaux withn cells in a system containing a total ofn cells we also derive asymptotic formulas that simplify these analytic expressions and present numerical comparisons of the exact and asymptotic results

synchronized clusters in coupled map networks i numerical studies we study the synchronization of coupled maps on a variety of networks including regular one and two dimensional networks scale free networks small world networks tree networks and random networks for small coupling strengths nodes show turbulent behavior but form phase synchronized clusters as coupling increases when nodes show synchronized behavior we observe two interesting phenomena first there are some nodes of the floating type that show intermittent behavior between getting attached to some clusters and evolving independently second we identify two different ways of cluster formation namely self organized clusters which have mostly intracluster couplings and driven clusters which have mostly intercluster couplings the synchronized clusters may be of dominant self organized type dominant driven type or mixed type depending on the type of network and the parameters of the dynamics we define different states of the coupled dynamics by considering the number and type of synchronized clusters for the local dynamics governed by the logistic map we study the phase diagram in the plane of the coupling constant and the logistic map parameter ensuremath mu for large coupling strengths and nonlinear coupling we find that the scale free networks and the caley tree networks lead to better cluster formation than the other types of networks with the same average connectivity for most of our study we use the number of connections of the order of the number of nodes as the number of connections increases the number of nodes forming clusters and the size of the clusters in general increase

fractal models for diffusion controlled aggregation a two dimensional fractal model is constructed for diffusion controlled deposition on a surface the fractal geometry of the deposit and the power law behaviour of the quantities characterising the non equilibrium cluster size distribution are shown to be consequences of the competition generally present in a nonlinear growth process a qualitative agreement with previous numerical results is found and the scaling laws for the critical exponents of the problem are shown to be satisfied exactly

scaling of average receiving time and average weighted shortest path on weighted koch networks abstract in this paper we present weighted koch networks based on classic koch networks a new method is used to determine the average receiving time art whose key step is to write the sum of mean first passage times mfpts for all nodes to absorption at the trap located at a hub node as a recursive relation we show that the art exhibits a sublinear or linear dependence on network order thus the weighted koch networks are more efficient than classic koch networks in receiving information moreover average weighted shortest path awsp is calculated in the infinite network order limit the awsp depends on the scaling factor the weighted koch network grows unbounded but with the logarithm of the network size while the weighted shortest paths stay bounded

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

extended vicsek fractals laplacian spectra and their applications extended vicsek fractals evf are the structures constructed by introducing linear spacers into traditional vicsek fractals here we study the laplacian spectra of the evf in particularly the recurrence relations for the laplacian spectra allow us to obtain an analytic expression for the sum of all inverse nonvanishing laplacian eigenvalues this quantity characterizes the large scale properties such as the gyration radius of the polymeric structures or the global mean first passage time for the random walk processes introduction of the linear spacers leads to local heterogeneities which reveal themselves for example in the dynamics of evf under external forces

pattern formation in diffusive advective coupled map lattices we investigate pattern formation and evolution in coupled map lattices when advection is incorporated inaddition to the usual diffusive term all patterns may be suitably grouped into ve classes three periodic supporting static patterns and traveling waves and two nonperiodic relative frequencies are determined as afunction of all model parameters diffusion advection local nonlinearity and lattice size advection plays animportant role in coupled map lattices being capable of considerably altering pattern evolution for instance advection may induce synchronization making chaotic patterns evolve periodically as a byproduct we de scribe a practical algorithm for classifying generic pattern evolutions and for measuring velocities of travelingwaves doi 10 1103 physreve 69 066206 pacs number s 89 75 kd 05 45 xt 05 45 rai introduction

relaxation heuristics for a generalized assignment problem abstract we propose relaxation heuristics for the problem of maximum profit assignment of n tasks to m agents n m such that each task is assigned to only one agent subject to capacity constraints on the agents using lagrangian or surrogate relaxation the heuristics perform a subgradient search obtaining feasible solutions relaxation considers a vector of multipliers for the capacity constraints the resolution of the lagrangian is then immediate for the surrogate the resulting problem is a multiple choice knapsack that is again relaxed for continuous values of the variables and solved in polynomial time relaxation multipliers are used with an improved heuristic of martello and toth or a new constructive heuristic to find good feasible solutions six heuristics are tested with problems of the literature and random generated problems best results are less than 0 5 from the optimal with reasonable computational times for an at 386 computer it seems promising even for problems with correlated coefficients

an algorithm for set covering problem in this paper we present an algorithm for the set covering problem that combines problem reduction tests with dual ascent subgradient optimisation and linear programming computational results are presented for problems involving up to 400 rows and 4000 columns

a surrogate heuristic for set covering problems abstract the purpose of this paper is to present a new heuristic for set covering problems based upon continuous surrogate relaxations and subgradient optimization the algorithm combines problem reduction tests an adequate step size control and avoid preliminary sorting in solving the continuous surrogate relaxations computational tests for large scale set covering problems up to 1 000 rows and 12 000 columns indicate better quality results than algorithms based on lagrangian relaxations in terms of final solutions and mainly in computer times although the solving of a single surrogate optimization problem is slower than a corresponding lagrangian optimization the overall performance is almost twice as fast this is due to the smaller number of iterations which is a result of faster convergence and less oscillation

an adaptation of sh heuristic to the location set covering problem abstract in a recent paper a new surrogate heuristic sh has been proposed for the set covering problem here we present an adaptation of it in order to solve more efficiently the location set covering problem we will show that our new version not only outperforms algorithm sh but that it is more accurate than the pair cma fmc its power is experimentally tested over a set of 65 randomly generated problems

pattern formation on trees networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes a tree is characterized by two parameters its ramification and its depth the local dynamics at the nodes of a tree is described by a nonlinear map giving rise to a coupled map lattice system the coupling is expressed by a matrix whose eigenvectors constitute a basis on which spatial patterns on trees can be expressed by linear combination the spectrum of eigenvalues of the coupling matrix exhibit a nonuniform distribution that manifests itself in the bifurcation structure of the spatially synchronized modes these models may describe reaction diffusion processes and several other phenomena occurring on heterogeneous media with hierarchical structure