on the multifractal nature of fully developed turbulence and chaotic systems it is generally argued that the energy dissipation of three dimensional turbulent flow is concentrated on a set with non integer hausdorff dimension recently in order to explain experimental data it has been proposed that this set does not possess a global dilatation invariance it can be considered to be a multifractal set the authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta model

counterexamples to the kawamata viehweg vanishing on ruled surfaces in positive characteristic we give counterexamples to the kawamata viehweg vanishing theorem on ruled surfaces in positive characteristic and prove that if there is a counterexample to the kawamata viehweg vanishing theorem on a geometrically ruled surface f x c then either c is a tango curve or all of sections of f are ample

anomaly of fractal dimensions observed in stochastically switched systems we studied an anomaly in fractal dimensions measured from the attractors of dynamical systems driven by stochastically switched inputs we calculated the dimensions for different switching time lengths in two dimensional linear dynamical systems and found that changes in the dimensions due to the switching time length had a singular point when the system matrix had two different real eigenvalues using partial dimensions along each eigenvector we explicitly derived a generalized dimension d q and a multifractal spectrum f alpha to explain this anomalous property the results from numerical calculations agreed well with those from analytical equations we found that this anomaly is caused by linear independence inhomogeneity of eigenvalues and overlapping conditions the mechanism for the anomaly could be identified for various inhomogeneous systems including nonlinear ones and this reminded us of anomalies in some physical values observed in critical phenomena

diffusion on multifractals abstract we introduce a class of random fields with variable mean square regularity order defined on multifractal domains the local singularity order of these random fields then depends on the initial variable mean square regularity order and on the variable local singularity exponent of the multifractal measure defining the local dimension of the domain considered the theory is developed in a generalized framework through the covariance factorization using the tools of reproducing kernel hilbert spaces and fractional sobolev spaces of variable order

how many correlation lengths for multifractals abstract it is shown here in the context of percolation that one can have multifractal behavior and at the same time a single correlation length this length sets the scale below which non trivial scaling behavior occurs and it is controlled by a few relevant operators as in ordinary critical phenomena all other correlation lengths may be obtained from simple metric factors the quantities which lead to an infinite set of exponents are described by a second renormalization group which is slaved to the first one which determines the correlation length the results are relevant also to the problem of noise in percolating systems

generating cuts in integer programming with families of special ordered sets abstract this paper describes families of cuts which can be added to integer programming formulations incorporating special ordered sets ways in which the cuts can be used are discussed and some computational experience is presented

logic applied to integer programming and integer programming applied to logic the many connections between the methods of computational logic and integer programming ip are surveyed it is shown how computational problems arising in formal logic can be solved by ip also it is shown how the methods of logic are applicable both to modelling and solving ip models it is shown how fourier motzkin elimination for linear programming when specialised to 0 1 ip models gives rise to the logic method of resolution finally conventional ip methods are applied to solving logical inference problems

family of solvable generalized random matrix ensembles with unitary symmetry we construct a very general family of characteristic functions describing random matrix ensembles rme having a global unitary invariance and containing an arbitrary one variable probability measure which we characterize by a spread function various choices of the spread function lead to a variety of possible generalized rmes which show deviations from the well known gaussian rme originally proposed by wigner we obtain the correlation functions of such generalized ensembles exactly and show examples of how particular choices of the spread function can describe ensembles with arbitrary eigenvalue densities as well as critical ensembles with multifractality

on the hausdorff dimension of fractal attractors we consider such mappingsx n 1 f xn of an interval into itself for which the attractor is a cantor set for the same class of mappings for which the feigenbaum scaling laws hold we show that the hausdorff dimension of the attractor is universally equal tod 0 538

a set partitioning heuristic for the generalized assignment problem this paper discusses a heuristic for the generalized assignment problem gap the objective of gap is to minimize the costs of assigning j jobs to m capacity constrained machines such that each job is assigned to exactly one machine the problem is known to be np hard and it is hard from a computational point of view as well the heuristic proposed here is based on column generation techniques and yields both upper and lower bounds on a set of relatively hard test problems the heuristic is able to find solutions that are on average within 0 13 from optimality

multifractality and the kauffman model the author simulates the spread of an initial damage in the kauffman cellular automata at its critical point on the square lattice he calculates various moments of the probability that a site has been damaged n times and checks for multifractality in the critical exponents for different ensembles specifically he finds no evidence for multifractality when the moments of the probabilities are evaluated with lattice size l but multifractal behaviour occurs when the moments are monitored as a function of time t

fractal dimensions and homeomorphic conjugacies we investigate the behavior of the spectrum of singularities associated with the invariant measure of some dynamical systems under nonsmooth coordinate changes when the homeomorphic conjugacy is not lipschitz continuous we discuss how its singularities can affect the whole set of generalized fractal dimensions we give applications to homeomorphisms that conjugate critical circle maps with irrational golden mean winding numbers we present numerical studies corroborating the theoretical predictions

extended instability criteria in isotropic and anisotropic energy avalanches abstract we demonstrate that adding extended instability criteria to 3d critical slope sand pile models has the effect of considerably enhancing the self organized critical state displayed by these models we present two extended models an isotropic one which displays large energy avalanches and an anisotropic one which shows much shorter and much more frequent energy bursts we illuminate the multifractal nature of the self organised critical state in both extended models by finding a nontrivial spectrum of generalised correlation dimensions from the time series and by showing that the power law regions of the distributions functions for different lattice sizes show a scaling behaviour which is ruled by a generalised multifractal scaling transformation

subadditivity of kodaira dimensions for fibrations of three folds in positive characteristics abstract in this paper we will prove subadditivity of kodaira dimensions for a fibration with possibly singular geometric generic fiber under certain nefness and relative semi ampleness conditions as an application for a fibration f x y of a smooth projective threefold over an algebraically closed field of characteristic p 5 under the assumption that y is of general type and non uniruled we prove subadditivity of kodaira dimensions when general fibers are smooth or when k x y is relatively big over y

correlations in multifractals we present an analysis of the implicit assumptions that lie at the basis of the scaling relations for fractal measures proposed by cates et al 1 furthermore the scaling relations which have been shown to hold for trivial multifractals like the generalized cantor set 2 are tested numerically for critical wave functions of an incommensurate system

universal multifractal properties of circle maps from the point of view of critical phenomena ii analytical results the multifractal properties of maps of the circle exhibited in the preceding paper are analyzed from a simplified approach to the renormalization group of kadanoff this second renormalization group transformation whose formulation and interpretation are discussed here acts on the space of one time differentiable coordinate changes which associate a map on the critical manifold to the fixed point of the usual renormalization group while the dependence of the multifractal moments on the starting point can be described statistically and in particular through universal amplitude ratios as in paper i it is shown that fourier analysis is another possible approach for all multifractal moments the low frequency fourier coefficients have a universal self similar scaling behavior analogous to that found for the usual spectrum of circle maps in the case of the first moment it is demonstrated that the fourier coefficients are within constants equal to the usual spectrum the relation between amplitude ratios and fourier coefficients is established and it is demonstrated that the universal values of the ratios come from the universal low frequency fourier coefficients since for the universal ratios arising in the statistical description the scaling regime is much more easily accessible than for the spectrum the statistical approach described in paper i should be more convenient for experiments and could become an alternative to the usual spectral description the universal statistical description of the multifractal moments adopted here is possible because the choice of thea priori probability for the starting point is demonstrated to be irrelevant

multifractal amplitude fluctuations in the transfer matrix approach to the statistics of disordered lattice models it is shown that the amplitude fluctuations of vector iterates in the transfer matrix approach to the statistics of the one dimensional random ising chain correspond to an exact strange set characterised by a multifractal spectrum the temperature and disorder dependence of the spectrum are also investigated

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

two point statistics of multifractal measures abstract the relationship between the function of a multifractal and the spatial correlations of its singularity strengths is examined an expression to compute the probability of observing two different singularities and within a distance r is derived for measures arising from isotropic random multiplicative processes the correlation of s is shown to decay logarithmically with distance possible applications to turbulence models are discussed and the results are illustrated for a binomial measure where the scaling of two point correlation functions is shown to exhibit a phase transition

properties of border states of transient chaos transient chaos with absolutely continuous conditionally invariant measure is studied and a general solution of the frobenius perron equation is presented for complete one dimensional maps in particular properties of borderline situations exhibiting phase transitions within the framework of thermodynamical formalism are investigated

measuring statistical evenness a panoramic overview motivated by the question how equal is the distribution of wealth within a given human population economics devised an impressive toolbox of quantitative measures of societal egalitarianism including the lorenz curve and the following indices gini pietra hoover amato hirschman theil and atkinson these quantitative measures considered in the broader context of general data sets with positive values are in effect general gauges of statistical evenness while the application of gini s index grew beyond economics and reached diverse fields of science the aforementioned evenness toolbox has largely remained within the confines of the social sciences the aim of this paper is to expose this evenness toolbox to the physics community by presenting a comprehensive evenness based approach to a fundamental problem in science the measurement of statistical heterogeneity

tabu search for the multilevel generalized assignment problem abstract the multilevel generalized assignment problem mgap differs from the classical gap in that agents can perform tasks at more than one efficiency level important manufacturing problems such as lot sizing can be formulated as mgaps however the large number of variables in the related 0 1 integer program makes the use of commercial optimization packages impractical in this paper we present a heuristic approach to the solution of the mgap which consists of a novel application of tabu search ts our ts method employs neighborhoods defined by ejection chains that produce moves of greater power without significantly increasing the computational effort

a hybrid heuristic for the generalized assignment problem abstract the objective of this study is to develop a hybrid heuristic hh for solving the generalized assignment problem gap and conduct a computational comparison with the leading alternative heuristic approaches hh is designed around the two best known heuristics heuristic gap hgap and variable depth search heuristic vdsh previous performance characteristic studies have shown that hgap dominates vdsh in terms of solution cpu time while vdsh obtains solutions of 13 to 300 better quality within a reasonable time the main idea in this paper is to hybridize the two approaches such that the inherent values of both heuristics are realized

a branch and price algorithm for the multilevel generalized assignment problem the multilevel generalized assignment problem mgap is a variation of the generalized assignment problem in which agents can execute tasks at different efficiency levels with different costs we present a branch and price algorithm that is the first exact algorithm for the mgap it is based on a decomposition into a master problem with set partitioning constraints and a pricing subproblem that is a multiple choice knapsack problem we report on our computational experience with randomly generated instances with different numbers of agents tasks and levels and with different correlations between cost and resource consumption for each agent task level assignment experimental results show that our algorithm is able to solve instances larger than those of the maximum size considered in the literature to proven optimality

absorption probability distribution for rough surfaces the authors calculate the absorption probability distribution for particles diffusing onto perfectly absorbing boundaries the boundaries studied are rough but not fractal nevertheless non classical behaviour is evident in the singularities of the measure and their distribution

heavy particles in incompressible flows the large stokes number asymptotics abstract the dynamics of very heavy particles suspended in incompressible flows is studied in the asymptotics in which their response time is much larger than any characteristic time of fluid motion in this limit of very large stokes numbers particles behave as if suspended in a correlated in time gaussian flow at those spatial scales where the fluid velocity field is smooth following piterbarg l i piterbarg the top lyapunov exponent for stochastic flow modeling the upper ocean turbulence siam j appl math 62 2002 777 and mehlig et al b mehlig m wilkinson k duncan t weber m ljunggren aggregation of inertial particles in random flows phys rev e 72 2005 051104 the two particle dynamics is reduced to a nonlinear system of three stochastic differential equations with additive noise this model is used to single out the mechanisms leading to the preferential concentration of particles scaling arguments are used to predict the large stokes number behavior of the distribution of the stretching rate and of the probability distribution function of the longitudinal velocity difference between two particles as for the fractal character of the particle distribution strong numerical evidence is obtained in favor of saturation of the correlation dimension to the space dimension at large stokes numbers numerical results at finite stokes number values reveal that this model catches some important qualitative features of particle clustering observed in more realistic flows

improved lagrangean decomposition an application to the generalized assignment problem abstract recently two new ways of obtaining improved lagrangean bounds have been suggested lagrangean decomposition and bound improving sequences in this work we will obtain a lagrangean approach combining the two ideas mentioned above theoretical results are provided about the sharpness of the bounds obtained by the combined approach for the general case as well as an application to the generalized assignment problem computational experience is reported

on q non extensive statistics with non tsallisian entropy we combine an axiomatics of renyi with the qq deformed version of khinchin axioms to obtain a measure of information i e entropy which accounts both for systems with embedded self similarity and non extensivity we show that the entropy thus obtained is uniquely solved in terms of a one parameter family of information measures the ensuing maximal entropy distribution is phrased in terms of a special function known as the lambert w function we analyze the corresponding high and low temperature asymptotics and reveal a non trivial structure of the parameter space salient issues such as concavity and schur concavity of the new entropy are also discussed

kawamata viehweg vanishing on rational surfaces in positive characteristic we prove that the kawamata viehweg vanishing theorem holds on rational surfaces in positive characteristic by means of the lifting property to w2 k of certain log pairs on smooth rational surfaces as a corollary the kawamata viehweg vanishing theorem holds on log del pezzo surfaces in positive characteristic

on the fractal characterization of paretian poisson processes abstract paretian poisson processes are poisson processes which are defined on the positive half line have maximal points and are quantified by power law intensities paretian poisson processes are elemental in statistical physics and are the bedrock of a host of power law statistics ranging from pareto s law to anomalous diffusion in this paper we establish evenness based fractal characterizations of paretian poisson processes considering an array of socioeconomic evenness based measures of statistical heterogeneity we show that amongst the realm of poisson processes which are defined on the positive half line and have maximal points paretian poisson processes are the unique class of fractal processes exhibiting scale invariance the results established in this paper are diametric to previous results asserting that the scale invariance of poisson processes with respect to physical randomness based measures of statistical heterogeneity is characterized by exponential poissonian intensities

a survey of algorithms for the generalized assignment problem abstract this paper surveys algorithms for the well known problem of finding the minimum cost assignment of jobs to agents so that each job is assigned exactly once and agents are not overloaded all approaches seem to be based on branch and bound with bound supplied through heuristics and through relaxations of the primal problem formulation from the survey one can select building blocks for the design of one s own tailor made algorithm the survey also reveals that although just about every mathematical programming technique was tried on this problem there is still a lack of a representative set of test problems on which competing enumeration algorithms can be compared as well as a shortage of effective heuristics

multifractal wavefunctions at the mobility edge the author describes the critical behaviour of wavefunctions at the anderson metal insulator transition in terms of fractal measures at the mobility edge the wavefunctions have structure on all lengths and they scale with a continuous set of non related exponents dq the results are compared with field theoretic calculations by wegner 1980 in d 2 in

influence of boundary conditions on level statistics and eigenstates at the metal insulator transition abstract we investigate the influence of the boundary conditions on the scale invariant critical level statistics at the metal insulator transition of disordered three dimensional orthogonal and two dimensional unitary and symplectic tight binding models the distribution of the spacings between consecutive eigenvalues is calculated numerically and shown to be different for periodic and dirichlet boundary conditions whereas the critical disorder remains unchanged the peculiar correlations of the corresponding critical eigenstates leading to anomalous diffusion seem not to be affected by the change of the boundary conditions

critical weight statistics of the random energy model and of the directed polymer on the cayley tree we consider the critical point of two mean field disordered models i the random energy model rem introduced by derrida as a mean field spin glass model of n spins and ii the directed polymer of length n on a cayley tree dpct with random bond energies both models are known to exhibit a freezing transition between a high temperature phase where the entropy is extensive and a low temperature phase of finite entropy where the weight statistics coincides with the weight statistics of l evy sums with index ensuremath mu t t c l1 in this paper we study the weight statistics at criticality via the entropy s ensuremath ensuremath sum w i phantom rule 0 2em 0ex mathrm ln phantom rule 0 2em 0ex w i and the generalized moments y k ensuremath sum w i k where the w i are the boltzmann weights of the 2 n configurations in the rem we find that the critical weight statistics is governed by the finite size exponent ensuremath nu 2 the entropy scales as overline s n t c ensuremath sim n 1 2 the typical values e overline mathrm ln phantom rule 0 2em 0ex y k decay as n ensuremath k 2 and the disorder averaged values overline y k are governed by rare events and decay as n ensuremath 1 2 for any kg1 for the dpct we find that the entropy scales similarly as overline s n t c ensuremath sim n 1 2 whereas another exponent ensuremath nu ensuremath 1 governs the y k statistics the typical values e overline mathrm ln phantom rule 0 2em 0ex y k decay as n ensuremath k and the disorder averaged values overline y k decay as n ensuremath 1 for any kg1 as a consequence the asymptotic probability distribution overline ensuremath pi n ensuremath infty q of the overlap q in addition to the delta function ensuremath delta q which bears the whole normalization contains an isolated point at q 1 as a memory of the delta peak 1 ensuremath t t c ensuremath delta q ensuremath 1 of the low temperature phase tl t c the associated value overline ensuremath pi n ensuremath infty q 1 is finite for the dpct and diverges as overline ensuremath pi n ensuremath infty q 1 ensuremath sim n 1 2 for the rem

scaling properties of disordered multifractals abstract in turbulence the simplest phenomenological models of the energy cascade are multiplicative processes constructed on a regular grid in short m p g they have been used mostly for their simplicity allowing many of their properties to be derived analytically and their capacity to reproduce the scale invariance properties of various geophysical fields however these m p g s suffer from the drawback of lacking translation invariance in their spatial statistics spatial homogeneity and therefore they cannot be fully satisfactory models for geophysical fields in this paper we are interested in finding new construction methods for spatially homogeneous random multifractals we investigate the scaling properties of a new family of gridless models of multifractals

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

technical note an improved dual based algorithm for the generalized assignment problem the generalized assignment problem gap determines the minimum cost assignment of n jobs to m agents such that each job is assigned to exactly one agent subject to an agent s capacity existing solution algorithms have not solved problems with more than 100 decision variables this paper designs an optimization algorithm for the gap that effectively solves problems with up to 500 variables compared with existing procedures this algorithm requires fewer enumeration nodes and shorter running times improved performance stems from an enhanced lagrangian dual ascent procedure that solves a lagrangian dual at each enumeration node adding a surrogate constraint to the lagrangian relaxed model and an elaborate branch and bound scheme an empirical investigation of various problem structures not considered in existing literature is also presented

a branch and price algorithm for the generalized assignment problem the generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents a new algorithm for the generalized assignment problem is presented that employs both column generation and branch and bound to obtain optimal integer solutions to a set partitioning formulation of the problem

the dimension spectrum of some dynamical systems we analyze the dimension spectrum previously introduced and measured experimentally by jensen kadanoff and libchaber using large deviation theory we prove for some invariant measures of expanding markov maps that the hausdorff dimensionf of the set on which the measure has a singularity is a well defined concave and regular function in particular we show that this is the case for the accumulation of period doubling and critical mappings of the circle with golden rotation number we also show in these particular cases that the functionf is universal

statistics of wave functions in mesoscopic systems we review the results of a recent study of fluctuations of wave functions in confined chaotic systems the fluctuations can be due to a random potential or be a consequence of a chaotic scattering by the walls the entire distribution function of the local amplitudes of the wave functions f 1 and the joint two point distribution are calculated in various situations the computation is performed using the supersymmetry technique and employs the studies of a reduced version of the non linear supersymmetric model developed especially for investigating the properties of a single eigenstate in a discrete spectrum of a chaotic quantum system for not very large amplitudes the complete description can be achieved using the zero dimensional approximation of the model the distribution function calculated in the limit of various symmetry classes shows the universal behavior known as the porter thomas statistics and fluctuations at distant points do not correlate in the crossover regime between the ensembles the distribution of local amplitudes shows a somewhat more sophisticated behavior the fluctuations in this case are correlated over distances exceeding the mean free path for large amplitudes generated by the states the most affected by the localization we call them prelocalized the zero dimensional approximation is no longer valid instead the statistics of their wave functions is determined by nontrivial vacua of the reduced model which is quite similar to the liouville model known in conformal field theory in particular the vacuum state of the reduced model obeys the liouville equation which indicates that in two dimensions the prelocalized states have nearly critical properties we prove their multifractality and power law statistically averaged envelope r 2 r 2 at the intermediate range of distances below the localization length with a spectrum of exponents 1 as well as obtain a logarithmically normal tail of the distribution functionf 1 we also find an evidence of prelocalized states in quasi one dimensional wires with the length shorter than the localization length their statistically averaged envelope has power law asymptotics x 2 x 2 and the tail of the distribution function is similar to that describing localized states in the infinite wires

rational dynamical zeta functions for birational transformations we propose a conjecture for the exact expression of the unweighted dynamical zeta function for a family of birational transformations of two variables depending on two parameters this conjectured function is a simple rational expression with integer coecients this yields an algebraic value for the topological entropy furthermore the generating function for the arnold complexity is also conjectured to be a rational expression with integer coecients with the same singularities as for the dynamical zeta function this leads at least in this example to an equality between the asymptotic of the arnold complexity and the exponential of the topological entropy we also give a semi numerical method to eectively compute the arnold complexity c 1999 published by elsevier science b v all rights reserved

on the upper critical dimension in anderson localisation the authors show that the anomalous scaling behaviour of the moments of the wavefunction at the threshold of anderson localisation implies a log normal distribution for the probability mod psi mod 2 at first order in epsilon d 2 they discuss this result and its implications critically and are led to conclude that the upper critical dimension of anderson localisation is infinity

a hierarchical model for scaling structure in generalised diffusion limited aggregations deterministic fractal models are presented to be exactly solvable for the growth probability distribution on the surface of the cluster in a hierarchical lattice the recursion relations of the electric field on the growth bond are obtained for diffusion limited aggregation and the dielectric breakdown models a hierarchy of generalised dimensions d q is calculated to describe the growth probability by using the recursion relations the partition of q 1 d q into a density of singularities f q with singularity strength alpha q is made and the alpha f spectra are studied for different dielectric breakdown models the scaling of the highest growth probability pmax on the growth bond is analytically derived and the dependence of the fractal dimensions is found on the parameter eta describing the different dielectric breakdown models

some results on the behavior and estimation of the fractal dimensions of distributions on attractors the strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation in this paper we first provide a rigorous mathematical framework for the study of dimension focusing on pointwise dimension x and the generalized renyi dimensionsd q and give a rigorous proof of inequalities first derived by grassberger and procaccia and hentschel and procaccia we then specialize to the problem of statistical estimation of the correlation dimension and information dimension it has been recognized for some time that the error estimates accompanying the usual procedures which generally involve least squares methods and nearest neighbor calculations grossly underestimate the true statistical error involved in least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates we then develop an estimation procedure for which corrects for an important bias term the local measure density and provides confidence intervals for the general applicability of this method is illustrated with various numerical examples

characterisation of intermittency in chaotic systems the authors discuss the characterisation of intermittency in chaotic dynamical systems by means of the time fluctuations of the response to a slight perturbation on the trajectory a set of exponents is introduced which generalise the maximum lyapunov characteristic exponent the link with the statistical mechanics formalism is emphasised and they show that the exponents are connected to a free energy formally defined for chaotic systems they perform some analytical computations in simple cases and give a few numerical examples

effective non vanishing for algebraic surfaces in positive characteristic abstract we give a theorem on the effective non vanishing problem for algebraic surfaces in positive characteristic for the kawamata viehweg vanishing the logarithmic kollar vanishing and the logarithmic semipositivity we give their counterexamples on ruled surfaces in positive characteristic

multifractal wavefunction at the localisation threshold the authors point out that the field theoretical description of the localisation transition exhibits anomalous scaling for the moments of the probability density at the localisation threshold this property hints at a multifractal structure of the wavefunction they attempt an analysis of the corresponding singularity distribution

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

small scale turbulence in the plankton low order deterministic chaos or high order stochasticity abstract almost all regions of the oceans are heavily influenced by the effects of physical processes such as turbulence which in turn influence the distribution and ecology of organisms that occupy these regions there is a real need for additional focus placed on the precise knowledge of both physical and biological processes which is often difficult using basic time series analysis in that way we applied nonlinear analysis techniques to high frequency time series of temperature salinity and phytoplankton concentrations recorded in different hydrodynamical regimes related to tidal forcing in a tidally mixed coastal ecosystem techniques devoted to the identification of low order deterministic chaos cannot find evidence of chaos while a lower dimensionality was identified in low hydrodynamic conditions the results rather suggest stochastic time series with many degrees of freedom no obvious attractor in phase space trajectory lle indistinguishable from zero absence of convergence of the correlation integral we then applied to these data specific multifractal analysis techniques and showed that these time series clearly exhibit high order stochasticity in addition the stochastic structure of purely passive scalars i e temperature and salinity remained invariant while the one of phytoplankton biomass must be regarded as highly structured in time by both hydrodynamic and advective processes

universal multifractal properties of circle maps from the point of view of critical phenomena i phenomenology the strange attractor for maps of the circle at criticality has been shown to be characterized by a remarkable infinite set of exponents this characterization by an infinite set of exponents has become known as the multifractal approach the present paper reformulates the multifractal properties of the strange attractor in a way more akin to critical phenomena this new approach allows one to study the universal properties of both the critical point and of its vicinity within the same framework and it allows universal properties to be extracted from experimental data in a straightforward manner obtaining feigenbaum s scaling function from the experimental data is by contrast much more difficult in addition to the infinite set of exponents universal amplitude ratios here appear naturally to study the crossover region near criticality a correlation time which plays a role analogous to the correlation length in critical phenomena is introduced this new approach is based on the introduction of a joint probability distribution for the positive integer moments of the closest return distances this joint probability distribution is physically motivated by the large fluctuations of the multifractal moments with respect to the choice of origin the joint probability distribution has scaling properties analogous to those of the free energy close to a critical point

mixed generalized dimensions of self similar measures abstract classical multifractal analysis studies the local scaling behaviour of a single measure however recently mixed multifractal has generated interest mixed multifractal analysis studies the simultaneous scaling behaviour of finitely many measures and provides the basis for a significantly better understanding of the local geometry of fractal measures the purpose of this paper is twofold firstly we define and develop a general and unifying mixed multifractal theory of mixed renyi dimensions also sometimes called the generalized dimensions mixed l q dimensions and mixed coarse multifractal spectra for arbitrary doubling measures secondly as an application of the general theory developed in this paper we provide a complete description of the mixed multifractal theory of finitely many self similar measures

logic cuts for multilevel generalized assignment problems abstract in the multilevel generalized assignment problem mgap agents can perform tasks at more than one efficiency level important manufacturing problems such as lot sizing can be easily formulated as mgaps however the large number of variables in the related 0 1 integer program makes it hard to find optimal solutions to these problems even when using powerful commercial optimization packages the mgap includes a set of knapsack constraints one per agent that can be useful for generating simple logical constraints or logic cuts we exploit the fact that logic cuts can be generated in linear time and can be easily added to the model before solving it with classical branch and bound methodology we generate all contiguous 1 cuts for every knapsack in large mgap s problems and report the effect of adding these cuts in our experimental results

some results on multifractal correlations abstract we have performed a numerical and analytical study of multifractal correlations in a two scale random cantor set at large distances for not very large we find qualitative agreement between canonical simulation results also counting results and the formula recently proposed by meneveau and chhabra following work of cates and deutsch for large a new correlation scaling function which is linear in log r is obtained due to a transition of the moment scaling function from cates and deutsch behavior to a differing behavior for some part of its domain this linear is consistent with numerical results

renormalization group analysis of the global properties of a strange attractor this paper considers the circle map at the special point the one at which there is a trajectory with a golden mean winding number and at which the map just fails to be invertable at one point on the circle the invariant density of this trajectory has fractal properties previous work has suggested that the global behavior of this fractal can be effectively analyzed using a kind of partition function formalism to generate anf versus curve in this paper the partition function is obtained by using a renormalization group approach

factorization of joint multifractality abstract complex systems often exhibit multifractal characteristics in various forms the study of the joint fluctuation of multifractal objects referred to as joint multifractality is presented in this work we use the joint partition function approach c meneveau et al phys rev a 41 1990 894 to show that joint multifractality admits a factorization into a common factor related to the notion of relative multifractality studied by riedi and scheuring r h riedi i scheuring fractals 5 1997 153 and a remainder term related to the individual multifractality we demonstrated our ideas using binomial measures and applied to the fluctuation of financial data

multiscaling transformation in dynamical systems and turbulence abstract multiscaling is a scaling law where the exponent is slowing varying with the length scale pseudo algebraic law we discuss its origin as a consequences of multifractility and the existence of a lower cutoff in the calculation of correlation functions in different contexts we derive some exact results in the case of two scale cantor sets which can be extended to other fractal structures such as strange attractors of chaotic systems in fully developed turbulence the cutoff is naturally introduced by the viscosity and our approach leads to the prediction of an intermediate dissipation range which can be tested experimentally

a multiplier adjustment method for the generalized assignment problem we describe a branch and bound algorithm for the generalized assignment problem in which bounds are obtained from a lagrangian relaxation with the multipliers set by a heuristic adjustment method the algorithm was tested on a large sample of small random problems and a number of large problems derived from a vehicle routing application computation times were reasonable in all cases and the branch and bound trees generated had nearly two orders of magnitude fewer nodes than for competing algorithms although comparison of running times on different machines is difficult the multiplier adjustment method appears to be about one order of magnitude faster than the best previously existing algorithms for this problem

multifractal structure of clusters and growing aggregates abstract various phenomena on a given fractal object have different critical behavior this is related to the underlying multifractal structure of the aggregate here we discuss the problem with particular emphasis on a scaling approach which leads to a simple real space renormalization group a mechanism which generates multifractality based on a multiplicative process is also illustrated the multifractal structure of the incipient infinite cluster in percolation and diffusion limited aggregation is discussed in detail