a hybrid dynamic programming branch and bound algorithm for the multiple choice knapsack problem abstract dynamic programming and branch and bound methodologies are combined to produce a hybrid algorithm for the multiple choice knapsack problem lagrangian duality is used in a computationally efficient manner to compute tight bounds on every active node in the search tree the use of lagrangian duality also enables the use of a reduction procedure to reduce the size of the problem for the enumeration phase computational experience with up to 200 multiple choice sets and 20000 zero one variables is reported the computational experience indicates that the resulting algorithm is faster than the best published algorithm and is simpler to code

intensity approximation of random fluctuation in complex systems abstract the markov and non markov processes in complex systems are examined with the help of dynamical information shannon entropy method here we consider the essential role of two mutually independent channels of entropy involving creation of correlation and annihilation of correlation the developed method has been used to analyze the intensity fluctuation of the complex systems of various nature in psychology to analyze numerical and pattern short time human memory to study the effect of stress on the parameters of the dynamical taping test and in cardiology to analyze the random dynamics of rr intervals in human ecg s and to diagnose various diseases of human cardiovascular systems the received results show that the application of intensity approximation allows to improve essentially the diagnostics of parameters in the evolution of human dynamic states

random matrix ensembles from nonextensive entropy the classical gaussian ensembles of random matrices can be constructed by maximizing boltzmann gibbs shannon s entropy s text bgs ensuremath ensuremath int d mathbf h p mathbf h mathrm ln p mathbf h with suitable constraints here we construct and analyze random matrix ensembles arising from the generalized entropy s q 1 ensuremath ensuremath int d mathbf h p mathbf h q q ensuremath 1 thus s 1 s text bgs the resulting ensembles are characterized by a parameter q measuring the degree of nonextensivity of the entropic form making q ensuremath rightarrow 1 recovers the gaussian ensembles if q ensuremath ne 1 the joint probability distributions p mathbf h cannot be factorized i e the matrix elements of mathbf h are correlated in the limit of large matrices two different regimes are observed when ql1 p mathbf h has compact support and the fluctuations tend asymptotically to those of the gaussian ensembles anomalies appear for qg1 both p mathbf h and the marginal distributions p h ij show power law tails numerical analyses reveal that the nearest neighbor spacing distribution is also long tailed not wigner dyson and after proper scaling very close to the result for the 2 ifmmode times else texttimes fi 2 case char22 a generalization of wigner s surmise we discuss connections of these nonextensive ensembles with other non gaussian ones such as the so called l evy ensembles and those arising from soft confinement

levy walks for turbulence a numerical study we present a numerical study of enhanced diffusion for which the mean squared displacement follows asymptotically r2 t t 1 we simulate continuous time random walks with waiting time distributions which couple the spatial and temporal parameters this gives rise to levy walks our results confirm the theoretically predicted long time behavior and demonstrate its temporal regime of validity furthermore the simulations document the appearance of parameter dependent transitions between regular and enhanced diffusion regimes

nonextensive foundation of levy distributions a deep connection between the ubiquity of l evy distributions in nature and the nonextensive thermal statistics introduced a decade ago has been established recently tsallis et al phys rev lett 75 3589 1995 by using unnormalized q expectation values it has just been argued on physical grounds that normalized q expectation values should be used instead we revisit within this more appropriate scheme the l evy problem and verify that the relevant analytic results become sensibly simplified whereas the basic physics remains unchanged

a multi interacting agent model for financial markets abstract microscopic models which resemble random magnetic systems have been used recently in the literature for the description of financial markets in the present work a model with many interacting agents similar to an ising random magnet with infinite range interactions is investigated the introduction of a local field term depending on the absolute value of a magnetization like parameter which measures the volatility of a financial market leads to a significant improvement with respect to previously studied models in the literature by investigating the return time series we show that several features characteristic of real financial markets are better reproduced by the present model in particular within this approach one is able to provide a proper behavior for the following properties i the power law tails and the nonzero skewness of the probability distribution of returns ii the exponential decay of the two time autocorrelation function of returns typical of high frequency financial data iii the so called leverage effect which corresponds to a negative correlation between past returns and future volatility

auxiliary tool allocation in flexible manufacturing systems abstract this paper analyses a new approach to the machine loading problem arising in flexible manufacturing systems fmss this approach allows the operations to be assigned to machines assuming that machines have access to all the tools required for their operations this exploits the flexibility of the fms completely next an allocation of tools to machines is determined which satisfies the tool requirements for each machine and minimizes the total number of tools thus this approach minimizes the unnecessary tool duplications in the system and maximizes the tool utilization the problem is modeled as an integer linear program ilp we notice that the main problem has a block diagonal structure which is decomposable by relaxing a set of linking constraints each separated sub problem represents a problem of allocation of a single type of tools we develop a branch and bound based exact solution procedure and three heuristic procedures to solve the sub problems our lower bounding approach uses lanrangean relaxation the solutions to the lagrangean relaxation are further used to determine the branching sequences and to develop heuristic approaches since finding even a feasible solution to the main problem is np hard we develop only enumerative procedures to solve the main problem finally these solution procedures are tested on randomly generated test problems

on the most algebraic k3 surfaces and the most extremal log enriques surfaces we shall characterize the unique k3 surface of discriminant 3 or 4 called the most algebraic k3 surfaces by vinberg in terms of the fixed locus of an automorphism on it based on this result we show that there is up to isomorphisms only one rational log eriques surface of type d 19 and one of type a 19

what should a statistical mechanics satisfy to reflect nature there is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual boltzmann gibbs prescriptions more specifically ubiquitous natural and artificial systems exhibit generic stationary states which are not ergodic nor close to it in any geometrically simple subset of the a priori allowed phase space in any even extended trivial sense a vast class of such systems appears nevertheless to be tractable within thermostatistical methods completely analogous to the usual ones the question posed in the title arises then naturally some answer to this complex question is advanced in the present review of nonextensive statistical mechanics and its recent connections

relaxation in heterogeneous systems a rare events dominated phenomenon abstract we have derived a general two power law relaxation function for heterogeneous materials using the maximum entropy principle for nonextensive systems the power law exponents of the relaxation function are simply related to a global fractal parameter and for large time to the entropy nonextensivity parameter q for intermediate times the relaxation follows a stretched exponential behavior the asymptotic power law behaviors both in the time and the frequency domains coincide with those of the weron generalized dielectric function derived in the stochastic theory from an extension of the levy central limit theorem these results are in full agreement with the jonscher universality principle and trace the origin of the large t power law universality with system dependent exponent and q to the scaling behavior of the extreme value distribution function of the effective macroscopic waiting time and the fluctuation of the number of relaxing entities

law of error in tsallis statistics in order to theoretically explain the ubiquitous existence of power law behavior such as chaos and fractals in nature tsallis entropy has been successfully applied to the generalization of the traditional boltzmann gibbs statistics the fundamental information measure of which is shannon entropy tsallis entropy s sub q is a one parameter generalization of shannon entropy s sub 1 in the sense that lim sub q spl rarr 1 s sub q s sub 1 the generalized statistics using tsallis entropy are referred to as tsallis statistics in order to present the law of error in tsallis statistics as a generalization of gauss law of error and prove it mathematically we apply the new multiplication operation determined by q logarithm and q exponential the fundamental functions in tsallis statistics to the definition of the likelihood function in gauss law of error the present maximum likelihood principle mlp leads us to determine the so called q gaussian distribution which coincides with one of the tsallis distributions derived from the maximum entropy principle for tsallis entropy under the second moment constraint

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

heuristic allocation based on a dynamic programming state space representation in this paper we focus on the lower level allocation problem of a hierarchical time constrained product development situation commonly found in the industrial practice the type of product development process we consider is the radical experiential model of product development of eisenhardt and tabrizi administr sci q 40 1995 84 the description of the main characteristics of the process follows the line of the recent research of bowers et al in m t brannick e salas c prince eds team performance assessment and measurement theory research and applications lawrence erlbaum associates inc publishers new jersey 1997 pp 85 108 and oorschot analysing radical npd projects from an operational control perspective ph d thesis eindhoven university of technology the netherlands 2001 starting from the dynamic programming techniques we propose a solution to this optimization problem by employing an a monotonic heuristic evaluation function for best search algorithms this function is based on aggregate information on the design task set we discuss the efficiency of the general best first search algorithm using an a evaluation function and of an rbfs variant of it which also searches in best first order using the same a evaluation function we prove that the algorithms find an optimal feasible allocation provided that there exists a feasible allocation we conclude by commenting upon some experimental results

on the gaussian q distribution we present a study of the gaussian q measure introduced by diaz and teruel from a probabilistic and from a combinatorial viewpoint a main motivation for the introduction of the gaussian q measure is that its moments are exactly the q analogues of the double factorial numbers we show that the gaussian q measure interpolates between the uniform measure on the interval 1 1 and the gaussian measure on the real line 2009 elsevier inc all rights reserved

a generalization of the cumulant expansion application to a scale invariant probabilistic model as well known cumulant expansion is an alternative way to moment expansion to fully characterize probability distributions provided all the moments exist if this is not the case the so called escort mean values or q moments have been proposed to characterize probability densities with divergent moments c tsallis et al j math phys 50 043303 2009 we introduce here a new mathematical object namely the q cumulants which in analogy to the cumulants provide an alternative characterization to that of the q moments for the probability densities to illustrate the technical details of the procedure we apply this new scheme to further study a recently proposed family of scale invariant discrete probabilistic models a rodriguez et al j stat mech theory exp 2008 p09006 r hanel et al eur phys j b 72 263 2009 having q gaussians as limiting probability distributions

tsallis distributions and 1 f noise from nonlinear stochastic differential equations probability distributions that emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems in this article we unite modeling of such distributions with the model of widespread 1 f noise we propose a class of nonlinear stochastic differential equations giving both the q exponential or q gaussian distributions of signal intensity revealing long range correlations and 1 f behavior of the power spectral density the superstatistical framework to get 1 f noise with q exponential and q gaussian distributions of the signal intensity is proposed as well

rates of convergence of non extensive statistical distributions to levy distributions in full and half spaces the levy type distributions are derived using the principle of maximum tsallis non extensive entropy both in the full and half spaces the rates of convergence to the exact levy stable distributions are determined by taking the n fold convolutions of these distributions the marked difference between the problems in the full and half spaces is elucidated analytically it is found that the rates of convergence depend on the ranges of the levy indices an important result emerging from the present analysis is deduced if interpreted in terms of random walks implying the dependence of the asymptotic long time behaviours of the walks on the ranges of the levy indices if n is identified with the total time of the walks

linear space best first search abstract best first search is a general heuristic search algorithm that always expands next a frontier node of lowest cost it includes as special cases breadth first search dijkstra s single source shortest path algorithm and the a algorithm its applicability however is limited by its exponential memory requirement previous approaches to this problem such as iterative deepening do not expand nodes in best first order if the cost function can decrease along a path we present a linear space best first search algorithm rbfs that always explores new nodes in best first order regardless of the cost function and expands fewer nodes than iterative deepening with a nondecreasing cost function on the sliding tile puzzles rbfs with a nonmonotonic weighted evaluation function dramatically reduces computation time with only a small penalty in solution cost in general rbfs reduces the space complexity of best first search from exponential to linear at the cost of only a constant factor in time complexity in our experiments

tsallis threshold analysis of digital speckle patterns generated by rough surfaces abstract in this work we report on a study of entropic threshold of digital speckle patterns images produced by rough surfaces using tsallis entropy the speckle pattern images were obtained in the diffraction plane at the normal direction and they are the outcome of the incidence of a laser beam in the rough metallic surfaces the speckle pattern images were segmented in order to verify the sensitivity of the optimal tsallis entropic threshold value as a function of the surface roughness we show that the surface roughness can be sensed and tuned by this method

new trends in exact algorithms for the 0 1 knapsack problem abstract while the 1980s were focused on the solution of large sized easy knapsack problems kps this decade has brought several new algorithms which are able to solve hard large sized instances we will give an overview of the recent techniques for solving hard kps with special emphasis on the addition of cardinality constraints dynamic programming and rudimentary divisibility computational results comparing all recent algorithms are presented

quantitative approach to multifractality induced by correlations and broad distribution of data abstract we analyze quantitatively the effect of spurious multifractality induced by the presence of fat tailed symmetric and asymmetric probability distributions of fluctuations in time series in the presented approach different kinds of symmetric and asymmetric broad probability distributions of synthetic data are examined starting from levy regime up to those with finite variance we use nonextensive tsallis statistics to construct all considered data in order to have good analytical description of frequencies of fluctuations in the whole range of their magnitude and simultaneously the full control over exponent of power law decay for tails of probability distribution the semi analytical compact formulas are then provided to express the level of spurious multifractality generated by the presence of fat tails in terms of tsallis parameter q and the scaling exponent of the asymptotic decay of cumulated probability density function cdf the results are presented in hurst and holder languages more often used in study of multifractal phenomena according to the provided semi analytical relations it is argued how one can make a clear quantitative distinction for any real data between true multifractality caused by the presence of nonlinear correlations spurious multifractality generated by fat tailed shape of distributions eventually with their asymmetry and the correction due to linear autocorrelations in analyzed time series of finite length in particular the spurious multifractal effect of fat tails is found basic for proper quantitative estimation of all spurious multifractal effects examples from stock market data are presented to support these findings

levy decoupled random walks a diffusion model based on a continuous time random walk scheme with a separable transition probability density is introduced the probability density for long jumps is proportional to x 1 a levy like probability density even when the probability density for the walker position at time t p x t has not a finite second moment when 0 2 it is possible to consider alternative estimators for the width of the distribution it is then found that any reasonable width estimator will exhibit the same long time behaviour since in this limit p x t goes to the distribution l x t a levy distribution the scaling property is verified numerically by means of monte carlo simulations we find that if the waiting time density has a finite first moment then 1 while for densities with asymptotic behaviour t 1 with 0 1 long tail densities it is verified that this scaling property ensures that any reasonable estimator of the distribution width will grow as t in the long time limit based on this long time behaviour we propose a generalized criterion for the classification in superdiffusive and subdiffusive processes according to the value of

fractional nonlinear diffusion equation solutions and anomalous diffusion abstract we devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms the presence of external forces and absorbent terms is also considered the solutions found here can have a compact or long tail behavior and in particular for the last case in the asymptotic limit we relate these solutions to the levy or tsallis distributions in addition from the results presented here a rich class of diffusive processes including normal and anomalous ones can be obtained

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

generalized best first search strategies and the optimality of a this paper reports several properties of heuristic best first search strategies whose scoring functions depend on all the information available from each candidate path not merely on the current cost g and the estimated completion cost h it is shown that several known properties of a retain their form with the minmax of f playing the role of the optimal cost which helps establish general tests of admissibility and general conditions for node expansion for these strategies on the basis of this framework the computational optimality of a in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that a uses is examined a hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered computational performances relative to these algorithms and domains are appraised for each class domain combination we then identify the strongest type of optimality that exists and the algorithm for achieving it the main results of this paper relate to the class of algorithms that like a return optimal solutions i e admissible when all cost estimates are optimistic i e h h on this class a is shown to be not optimal and it is also shown that no optimal algorithm exists but if the performance tests are confirmed to cases in which the estimates are also consistent then a is indeed optimal additionally a is also shown to be optimal over a subset of the latter class containing all best first algorithms that are guided by path dependent evaluation functions

boundedness vs unboundedness of a noise linked to tsallis q statistics the role of the overdamped approximation an apparently ideal way to generate continuous bounded stochastic processes is to consider the stochastically perturbed motion of a point of small mass in an infinite potential well under overdamped approximation here however we show that the aforementioned procedure can be fallacious and lead to incorrect results we indeed provide a counter example concerning one of the most employed bounded noises hereafter called tsallis stariolo borland tsb noise which admits the well known tsallis q statistics as stationary density in fact we show that for negative values of the tsallis parameter q corresponding to sufficiently large diffusion coefficient of the stochastic force the motion resulting from the overdamped approximation is unbounded we then investigate the cause of the failure of kramers first type approximation and we formally show that the solutions of the full newtonian non approximated model are bounded following the physical intuition finally we provide a new family of bounded noi

on a q generalization of circular and hyperbolic functions a generalization of the circular and hyperbolic functions is proposed based on the tsallis statistics and on a consistent generalization of the euler formula some properties of the presently proposed q trigonometry are then investigated the generalized functions are exact solutions of a nonlinear oscillator original circular and hyperbolic relations are recovered as the limiting case