taylor s power law and fluctuation scaling explained by a central limit like convergence a power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins this taylor s law or fluctuation scaling has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states this hypothesis is predicated on physical quantities like free energy and an external field the correspondence of these quantities with biological systems though remains unproven questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with taylor s law we note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the tweedie exponential dispersion models these latter models are characterized by variance to mean power functions their phenomenological basis rests with a central limit theorem like property that causes many statistical systems to converge mathematically toward a tweedie form we review evaluations of the tweedie poisson gamma model for taylor s law and provide three further cases to test the clustering of single nucleotide polymorphisms snps within the horse chromosome 1 the clustering of genes within human chromosome 8 and the mertens function this latter case is a number theoretic function for which a thermodynamic model cannot explain taylor s law but where tweedie convergence remains applicable the tweedie models are applicable to diverse biological physical and mathematical phenomena that express power variance functions over a wide range of measurement scales they provide a probabilistic description for taylor s law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism

soft constraint abstraction based on semiring homomorphism the semiring based constraint satisfaction problems semiring csps proposed by bistarelli montanari and rossi s bistarelli u montanari f rossi semiring based constraints solving and optimization journal of the acm 44 2 1997 201 236 is a very general framework of soft constraints in this paper we propose an abstraction scheme for soft constraints that uses semiring homomorphism to find optimal solutions of the concrete problem we first work in the abstract problem and find its optimal solutions and then use them to solve the concrete problem in particular we show that a mapping preserves optimal solutions if and only if it is an order reflecting semiring homomorphism moreover for a semiring homomorphism a and a problem p over s if t is optimal in a p then there is an optimal solution email protected of p such that email protected has the same value as t in a p

qualitative choice logic qualitative choice logic qcl is a propositional logic for representing alternative ranked options for problem solutions the logic adds to classical propositional logic a new connective called ordered disjunction a b intuitively means if possible a but if a is not possible then at least b the semantics of qualitative choice logic is based on a preference relation among models consequences of qcl theories can be computed through a compilation to stratified knowledge bases which in turn can be compiled to classical propositional theories we also discuss potential applications of the logic several variants of qcl based on alternative inference relations and their relation to existing nonmonotonic formalisms

the complexity of some polynomial network consistency algorithms for constraint satisfaction problems abstract constraint satisfaction problems play a central role in artificial intelligence a class of network consistency algorithms for eliminating local inconsistencies in such problems has previously been described we analyze the time complexity of several node arc and path consistency algorithms and prove that arc consistency is achievable in time linear in the number of binary constraints the waltz filtering algorithm is a special case of the arc consistency algorithm in the edge labelling computational vision application the constraint graph is planar and so the time complexity is linear in the number of variables

a wavelet based approach to revealing the tweedie distribution type in sparse data abstract we propose two approaches to the analysis of sparse stochastic data which exhibit a power law dependence between their first and second moments taylor s law and determining the respective power index when it has a value between 1 and 2 they are based on the analysis of components of the haar wavelet expansion the first method uses a dependence between the first iterations of averaging and wavelet coefficients with the subsequent studying the statistics of zero paddings on the line which corresponds the linear dependence between two first moments of the analysed distributions the second method refers to taylor s plot formed by the full set of wavelet coefficients it is discussed that such representations provide also an opportunity to check time scale stability of analysed data and distinguish between particular cases of the tweedie probabilistic distribution both simulated series and real marine species abundance data for five spatial regions of the pacific are used as example illustrating an applicability of these approaches

self organized criticality attributed to a central limit like convergence effect abstract self organized criticality is a hypothesis used to explain the origin of 1 f noise and other scaling behaviors despite being proposed nearly 30 years ago no consensus exists as to its exact definition or mathematical mechanism s recently a model for 1 f noise was proposed based on a family of statistical distributions known as the tweedie exponential dispersion models these distributions are characterized by an inherent scale invariance that manifests as a variance to mean power law called fluctuation scaling they also serve as foci of convergence in a limit theorem on independent and identically distributed distributions fluctuation scaling can be modeled by self similar stochastic processes that relate the variance to mean power law to 1 f noise through their correlation structure a hypothesis is proposed whereby the effects of self organized criticality are mathematically modeled by the tweedie distributions and their convergence behavior as applied to self similar stochastic processes sandpile model fluctuations are shown to manifest 1 f noise fluctuation scaling and to conform to the tweedie compound poisson distribution the tweedie models and their convergence theorem allow for a mechanistic explanation of 1 f noise and fluctuation scaling in phenomena conventionally attributed to self organized criticality thus providing a paradigm shift in our understanding of these phenomena

combining vns with constraint programming for solving anytime optimization problems abstract this paper presents an hybrid search method for solving on line optimization problems that are modelled using the vcsp valued constraint satisfaction problems framework to each constraint is associated a valuation representing the cost to pay when this constraint will be violated by a solution our method vns lds cp uses principles of vns variable neighborhood search and combines a partial tree search limited discrepancy search with constraint propagation in order to compute local optima experiments on the celar benchmarks demonstrate significant improvements on other competing methods lns cp gr lobjois l lemaitre m verfaillie g 2000 large neighbourhood search using constraint propagation and greedy reconstruction for valued csp resolution in proceedings of the ecai2000 workshop on modelling and solving problems with constraints another hybrid method using vcsp s and two standard versions of simulated annealing li y h 1997 directed annealing search in constraint satisfaction and optimization ph d thesis imperial college of science department of computing quick and medium moreover vns lds cp clearly satisfies the key properties of anytime algorithms finally vns lds cp has been successfully applied to a real life on line resource allocation problem in computer networks

epsilon transformation exploiting phase transitions to solve combinatorial optimization problems abstract it has been shown that there exists a transition in the average case complexity of tree search problems from exponential to polynomial in the search depth we develop a new method called e transformation which makes use of this complexity transition to find a suboptimal solution with a random tree model we show that as the tree depth approaches infinity the expected number of nodes expanded by branch and bound bnb using e transformation is at most cubic in the search depth and that the relative error of the solution cost found with respect to the optimal solution cost is bounded above by a small constant we also present an iterative version of e transformation that can be used to find both suboptimal and optimal goal nodes depth first bnb dfbnb using iterative e transformation significantly improves upon dfbnb on random trees with large branching factors and deep goal nodes finding a better solution sooner we then present experimental results for e transformation and iterative e transformation on the asymmetric traveling salesman problem atsp and the maximum boolean satisfiability problem and identify the conditions under which these two methods are effective on the atsp dfbnb using e transformation outperforms a well known local search method and dfbnb using iterative e transformation improves upon dfbnb

solving weighted csp by maintaining arc consistency recently a general definition of arc consistency ac for soft constraint frameworks has been proposed by t schiex proc cp 2000 singapore 2000 pp 411 424 in this paper we specialize this definition to weighted csp and introduce two o ed3 enforcing algorithms then we refine the definition and introduce a stronger form of arc consistency ac along with two o n2d2 ed3 algorithms as in the csp case an important application of ac is to combine it with search we empirically demonstrate that a branch and bound algorithm that maintains either ac or ac is a state of the art general solver for weighted csp our experiments cover binary max csp and max sat problems

clique inference process for solving max csp abstract few works on problems csp max csp and weighted csp was carried out in the field of combinatorial optimization whereas this field contains many algorithmic tools which can be used for the resolution of these problems in this paper we introduce the binary clique concept clique which expresses incompatibilities between values of two csp variables we propose a linear formulation for any binary clique and we present several ways to exploit it in order to compute lower bounds or to solve max csp we also show that the binary clique concept can be exploited in the weighted csp framework the obtained theoretical and experimental results are very interesting and they open new prospects to exploit the combinatorial optimization algorithmic tools for the resolution of csp max csp and weighted csp

dynamics of an impulsive predator prey logistic population model with state dependent in this paper the dynamics for a class of state dependent impulsive predator prey models with the logistic growth for the predator and prey species are analyzed by a direct calculation the existence of a semi trivial periodic solution is obtained based on the geometrical analysis and biological background the strict threshold value conditions for the existence of positive periodic solutions are depicted the stabilities of the semi trivial periodic solution and positive order 1 periodic solutions are proved due to the analogue of poincare criterion numerical results are carried out to illustrate the feasibility of our main results

sample and population exponents of generalized taylor s law has been verified extensively in ecology where it applies to population abundance physics and other natural sciences its ubiquitous empirical verification suggests a context independent mechanism sample exponents b measured empirically via the scaling of sample mean and variance typically cluster around the value b 2 some theoretical models of population growth however predict a broad range of values for the population exponent b pertaining to the mean and variance of population density depending on details of the growth process is the widely reported sample exponent b 2 the result of ecological processes or could it be a statistical artifact here we apply large deviations theory and finite sample arguments to show exactly that in a broad class of growth models the sample exponent is b 2 regardless of the underlying population exponent we derive a generalized tl in terms of sample and population exponents bjk for the scaling of the kth vs the jth cumulants the sample exponent bjk depends predictably on the number of samples and for finite samples we obtain bjk k j asymptotically in time a prediction that we verify in two empirical examples thus the sample exponent b 2 may indeed be a statistical artifact and not dependent on population dynamics under conditions that we specify exactly given the broad class of models investigated our results apply to many fields where tl is used although inadequately understood

and or branch and bound search for combinatorial optimization in graphical models this is the first of two papers presenting and evaluating the power of a new framework for combinatorial optimization in graphical models based on and or search spaces we introduce a new generation of depth first branch and bound algorithms that explore the and or search tree using static and dynamic variable orderings the virtue of the and or representation of the search space is that its size may be far smaller than that of a traditional or representation which can translate into significant time savings for search algorithms the focus of this paper is on linear space search which explores the and or search tree in the second paper we explore memory intensive and or search algorithms in conjunction with the and or search space we investigate the power of the mini bucket heuristics in both static and dynamic setups we focus on two most common optimization problems in graphical models finding the most probable explanation in bayesian networks and solving weighted csps in extensive empirical evaluations we demonstrate that the new and or branch and bound approach improves considerably over the traditional or search strategy and show how various variable ordering schemes impact the performance of the and or search scheme

maintaining reversible dac for max csp abstract we introduce an exact algorithm for maximizing the number of satisfied constraints in an overconstrained csp max csp the algorithm which can also solve weighted csp probabilistic csp and other similar problems is based on directed arc inconsistency counts dac the usage of dac increases the lower bound of branch and bound based algorithms for max csp improving their efficiency originally dac were defined following a static variable ordering in this paper we relax this condition showing how dac can be defined from a directed constraint graph these new graph based dac can be effectively used for lower bound computation interestingly any directed constraint graph of the considered problem is suitable for dac computation so the selected graph can change dynamically during search aiming at optimizing the exploitation of directed arc inconsistencies in addition directed arc inconsistencies are maintained during search propagating the effect of value pruning with these new elements we present the pfc maintaining reversible dac algorithm pfc mrdac a natural successor of pfc dac for max csp we provide experimental evidence for the superiority of pfc mrdac on random and real overconstrained csp instances including problems with weighted constraints

enhancement schemes for constraint processing backjumping learning and cutset decomposition abstract researchers in the areas of constraint satisfaction problems logic programming and truth maintenance systems have suggested various schemes for enhancing the performance of the backtracking algorithm this paper defines and compares the performance of three such schemes backjumping learning and cycle cutset the backjumping and the cycle cutset methods work best when the constraint graph is sparse while the learning scheme mostly benefits problem instances with dense constraint graphs an integrated strategy is described which utilizes the distinct advantages of each scheme experiments show that in hard problems the average improvement realized by the integrated scheme is 20 25 higher than any of the individual schemes

the complexity of soft constraint satisfaction over the past few years there has been considerable progress in methods to systematically analyse the complexity of constraint satisfaction problems with specified constraint types one very powerful theoretical development in this area links the complexity of a set of constraints to a corresponding set of algebraic operations known as polymorphisms in this paper we extend the analysis of complexity to the more general framework of combinatorial optimisation problems expressed using various forms of soft constraints we launch a systematic investigation of the complexity of these problems by extending the notion of a polymorphism to a more general algebraic operation which we call a multimorphism we show that many tractable sets of soft constraints both established and novel can be characterised by the presence of particular multimorphisms we also show that a simple set of np hard constraints has very restricted multimorphisms finally we use the notion of multimorphism to give a complete classification of complexity for the boolean case which extends several earlier classification results for particular special cases

families of distributions for repeated samples of animal counts the criterion of flexibility perry and taylor 1985 journal of animal ecology 54 931 953 that families of distributions with n 2 parameters should fit adequately to all n samples of animal counts over the full range of population densities usually encountered was misinterpreted by kemp 1987 biometrics 43 693 699 this criterion of goodness of fit is examined here for perry and taylor s ades family and one of kemp s alternatives a family of constrained negative binomial c n b distributions using extensive literature data while the ades fitted better than the c n b in 15 of 22 sets the evidence is not overwhelming because in 13 sets the difference was negligible or both families fitted adequately however of the remainder the ades fitted notably better to seven sets these mainly comprised long tailed distributions with large means typical of pest species its use in practical applications with such data is discussed and the importance of its superior reliability stressed kemp s method of fitting is not recommended

multifractality attributed to dual central limit like convergence effects abstract multifractals can be defined as fractal systems that express a range of fractal dimensions the origins of multifractality in time series data have conventionally been attributed to fat tailed probability distributions and to long range correlations multifractal sequences can be generated from the eigenvalue deviations of the gaussian unitary and orthogonal ensembles of random matrix theory these deviations can be resolved into component monofractal sequences governed by the tweedie compound poisson distribution a statistical model that expresses a variance to mean power law related to long range correlations fully multifractal descriptions of these deviations can be constructed provided that the parameter of the compound poisson model related to fractal dimension varies in accordance with an asymmetric laplace distribution both the tweedie compound poisson distribution and the asymmetric laplace distribution serve as foci of convergence in limit theorems on independent and identically distributed random variables the hypothesis that multifractal sequences can be attributed to mathematical convergence effects that have as their focus these two statistical models is proposed

refinements of the maximin approach to decision making in a fuzzy environment abstract the most popular approach to decision making in the setting of fuzzy sets is the maximin ranking of solutions this method is natural when interpreting the fuzzy sets as flexible constraints that cannot compensate with one another however the obtained ranking of solutions is very coarse two kinds of refinements to this ordering are introduced a partial ordering according to the least satisfied discriminating constraint and a lexicographical ranking the latter refines the former and combines utilitarist and egalitarist points of view on the aggregation of feasibility degrees these orderings are characterized in several ways and their representation by means of two place numerical functions is studied dual refinements of the maximax ranking are provided

configuration landscape analysis and backbone guided local search part i satisfiability and maximum satisfiability boolean satisfiability sat and maximum satisfiability max sat are difficult combinatorial problems that have many important real world applications in this paper we first investigate the configuration landscapes of local minima reached by the walksat local search algorithm one of the most effective algorithms for sat a configuration landscape of a set of local minima is their distribution in terms of quality and structural differences relative to an optimal or a reference solution our experimental results show that local minima from walksat form large clusters and their configuration landscapes constitute big valleys in that high quality local minima typically share large partial structures with optimal solutions inspired by this insight into walksat and the previous research on phase transitions and backbones of combinatorial problems we propose and develop a novel method that exploits the configuration landscapes of such local minima the new method termed as backbone guided search can be embedded in a local search algorithm such as walksat to improve its performance our experimental results show that backbone guided local search is effective on overconstrained random max sat instances moreover on large problem instances from a sat library satlib the backbone guided walksat algorithm finds satisfiable solutions more often than walksat on sat problem instances and obtains better solutions than walksat on max sat problem instances improving solution quality by 20 on average

tree clustering for constraint networks research note abstract the paper offers a systematic way of regrouping constraints into hierarchical structures capable of supporting search without backtracking the method involves the formation and preprocessing of an acyclic database that permits a large variety of queries and local perturbations to be processed swiftly either by sequential backtrack free procedures or by distributed constraint propagation processes

image interpretation with a conceptual graph labeling over segmented images and detection of unexpected objects the labeling of the regions of a segmented image according to a semantic representation ontology is usually associated with the notion of understanding the high combinatorial aspect of this problem can be reduced with local checking of constraints between the elements of the ontology in the classical definition of finite domain constraint satisfaction problem it is assumed that the matching problem between regions and labels is bijective unfortunately in image interpretation the matching problem is often non univocal indeed images are often over segmented one object is made up of several regions this non univocal matching between data and a conceptual graph was not possible until a decisive step was accomplished by the introduction of arc consistency with bilevel constraint fdcsp b c however this extension is only adequate for a matching corresponding to surjective functions in medical image analysis the case of non functional relations is often encountered for example when an unexpected object like a tumor appears in this case the data cannot be mapped to the conceptual graph with a classical approach in this paper we propose an extension of the fdcsp b c to solve the constraint satisfaction problem for non functional relations

semiring based constraint satisfaction and optimization we introduce a general framework for constraint satisfaction and optimization where classical csps fuzzy csps weighted csps partial constraint satisfaction and others can be easily cast the framework is based on a semiring structure where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain and the two semiring operations and x model constraint projection and combination respectively local consistency algorithms as usually used for classical csps can be exploited in this general framework as well provided that certain conditions on the semiring operations are satisfied we then show how this framework can be used to model both old and new constraint solving and optimization schemes thus allowing one to both formally justify many informally taken choices in existing schemes and to prove that local consistency techniques can be used also in newly defined schemes

families of discrete distributions satisfying taylor s power law count data in entomological studies can often be described by some form of contagious distribution such as the negative binomial neyman type a or polya aeppli these are all clustered poisson distributions their distributional forms are given in section 2 arising when groups of individuals occur at random i e are poissonian and individuals within a group have their own distribution whilst pahl 1969 found strong evidence that the negative binomial distribution gives good fits to his 35 samples of data on the chrysomelid beetle paropsis atomaria martin and katti 1965 fitted a number of distributions to a variety of insect plant and animal data and observed for instance that mcguire brindley and bancroft s 1957 data on the european cornborer pyrausta nubilalis and beall s 1940 data on the beet webworm loxostege sticticalis are fitted well not only by the negative binomial but also by the neyman type a and other distributions in such circumstances the fits given by different distributions are often very similar and the exact choice is not critical see kemp and kemp 1965 the recent work of tripathi gurland and bhalerao 1986 gives further guidance on the choice of an appropriate distribution when this is not clearly indicated by the ecological context the negative binomial neyman type a and polya aeppli distributions all have two parameters when there are many samples of data in one data set anscombe 1949 and bliss and owen 1958 suggested fitting a model that is parsimonious in parameters by keeping one of them constant from sample to sample their use of a common exponent parameter k when fitting families of negative binomials was criticised by taylor woiwod and perry 1979 who considered that k is an unstable parameter whose relationship with aggregation is doubtful much empirical evidence has accumulated in support of taylor s power law

1 f noise and multifractality from bristlecone pine growth explained by the statistical convergence of random data tree ring growth records from bristlecone pines reveal an irregular pattern of fluctuations that have been linked to climatic change but otherwise have remained poorly understood we find within th

arc consistency for soft constraints the notion of arc consistency plays a central role in constraint satisfaction r dechter constraint processing morgan kaufmann san mateo ca 2003 it is known since the introduction of valued and semi ring constraint networks in 1995 that the notion of local consistency can be extended to constraint optimisation problems defined by soft constraint frameworks based on an idempotent cost combination operator this excludes non idempotent operators such as which define problems which are very important in practical applications such as max csp where the aim is to minimise the number of violated constraints in this paper we show that using a weak additional axiom satisfied by most existing soft constraints proposals it is possible to define a notion of soft arc consistency that extends the classical notion of arc consistency and this even in the case of non idempotent cost combination operators a polynomial time algorithm for enforcing this soft arc consistency exists and its space and time complexities are identical to that of enforcing arc consistency in csps when the cost combination operator is strictly monotonic for example max csp a directional version of arc consistency first introduced by m c cooper reduction operations in fuzzy or valued constraint satisfaction fuzzy sets and systems 134 3 2003 311 342 is potentially even stronger than the non directional version since it allows non local propagation of penalties we demonstrate the utility of directional arc consistency by showing that it not only solves soft constraint problems on trees but that it also implies a form of local optimality which we call arc irreducibility

random sampling of skewed distributions implies taylor s power law of fluctuation scaling taylor s law tl a widely verified quantitative pattern in ecology and other sciences describes the variance in a species population density or other nonnegative quantity as a power law function of the mean density or other nonnegative quantity approximately variance a mean b a 0 multiple mechanisms have been proposed to explain and interpret tl here we show analytically that observations randomly sampled in blocks from any skewed frequency distribution with four finite moments give rise to tl we do not claim this is the only way tl arises we give approximate formulae for the tl parameters and their uncertainty in computer simulations and an empirical example using basal area densities of red oak trees from black rock forest our formulae agree with the estimates obtained by least squares regression our results show that the correlated sampling variation of the mean and variance of skewed distributions is statistically sufficient to explain tl under random sampling without the intervention of any biological or behavioral mechanisms this finding connects tl with the underlying distribution of population density or other nonnegative quantity and provides a baseline against which more complex mechanisms of tl can be compared

partial constraint satisfaction abstract a constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed in some cases it may be impossible or impractical to solve these problems completely we may seek to partially solve the problem in particular by satisfying a maximal number of constraints standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with and take advantage of the differences between partial and complete constraint satisfaction extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods a general model of partial constraint satisfaction is proposed