measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

on the k tuple domination of generalized de brujin and kautz digraphs a vertex u in a digraph g v a is said to dominate itself and vertices v such that u v a for a positive integer k a k tuple dominating set of g is a subset d of vertices such that every vertex in g is dominated by at least k vertices in d the k tuple domination number of g is the minimum cardinality of a k tuple dominating set of g this paper deals with the k tuple domination problem on generalized de bruijn and kautz digraphs we establish bounds on the k tuple domination number for the generalized de bruijn and kautz digraphs and we obtain some conditions for the k tuple domination number attaining the bounds

single step searching in weighted block graphs in this paper three types of problems for single step searching weighted graphs are investigated the summation minimization s type for short bottleneck minimization b type for short and hybrid h type for short weighted single step graph searching problems all three types are shown to be np hard but polynomial solvable for block graphs the s type problem is proved to be linearly equivalent to the optimum weight 2 independent set problem then we solve the s type problem on a block graph g in linear time by solving the optimum weight 2 independent set problem on g to solve the b type problem the first phase computes the bottleneck cost and the second phase constructs the searching plan by applying the s type algorithm using the bottleneck cost derived in the first phase finally an o e log v time algorithm for solving the h type problem on weighted block graphs is proposed

refined composite multiscale weighted permutation entropy of financial time series abstract for quantifying the complexity of nonlinear systems multiscale weighted permutation entropy mwpe has recently been proposed mwpe has incorporated amplitude information and been applied to account for the multiple inherent dynamics of time series however mwpe may be unreliable because its estimated values show large fluctuation for slight variation of the data locations and a significant distinction only for the different length of time series therefore we propose the refined composite multiscale weighted permutation entropy rcmwpe by comparing the rcmwpe results with other methods results on both synthetic data and financial time series rcmwpe method shows not only the advantages inherited from mwpe but also lower sensitivity to the data locations more stable and much less dependent on the length of time series moreover we present and discuss the results of rcmwpe method on the daily price return series from asian and european stock markets there are significant differences between asian markets and european markets and the entropy values of hang seng index hsi are close to but higher than those of european markets the reliability of the proposed rcmwpe method has been supported by simulations on generated and real data it could be applied to a variety of fields to quantify the complexity of the systems over multiple scales more accurately

some np hard polygon decomposition problems the inherent computational complexity of polygon decomposition problems is of theoretical interest to researchers in the field of computational geometry and of practical interest to those working in syntactic pattern recognition three polygon decomposition problems are shown to be np hard and thus unlikely to admit efficient algorithms the problems are to find minimum decompositions of a polygonal region into perhaps overlapping convex star shaped or spiral subsets we permit the polygonal region to contain holes the proofs are by transformation from boolean three satisfiability a known np complete problem several open problems are discussed

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

planar formulae and their uses we define the set of planar boolean formulae and then show that the set of true quantified planar formulae is polynomial space complete and that the set of satisfiable planar formulae is np complete using these results we are able to provide simple and nearly uniform proofs of np completeness for planar node cover planar hamiltonian circuit and line geometric connected dominating set and of polynomial space completeness for planar generalized geography the np completeness of planar node cover and planar hamiltonian circuit and line were first proved elsewhere m r garey and d s johnson the rectilinear steiner tree is np complete siam j appl math 32 1977 pp 826 834 and m r garey d s johnson and r e tarjan the planar hamilton circuit problem is np complete siam j comp 5 1976 pp 704 714

empirical and counterfactual conditions for sufficient cause interactions summary sufficient component causes are discussed within the deterministic potential outcomes framework so as to formalize notions of sufficient causes synergism and sufficient cause in teractions doing so allows for the derivation of counterfactual and empirical conditions for detecting the presence of sufficient cause interactions the conditions are novel in that unlike other conditions in the literature they make no assumption about monotonicity the conditions can also be generalized and the conditions for three way sufficient cause interactions are given explicitly the statistical tests derived for sufficient cause interactions are compared with and contrasted to interaction terms in standard statistical models

forbidden patterns permutation entropy and stock market inefficiency abstract in this paper we introduce two new quantifiers for the stock market inefficiency the number of forbidden patterns and the normalized permutation entropy they are model independent measures thus they have more general applicability we find robust evidence that degree of market inefficiency is positively correlated with the number of forbidden patterns and negatively correlated with the permutation entropy our empirical results suggest that these two physical tools are useful to discriminate the stage of stock market development and can be easily implemented

signed directed acyclic graphs for causal inference formal rules governing signed edges on causal directed acyclic graphs are described in this paper and it is shown how these rules can be useful in reasoning about causality specifically the notions of a monotonic effect a weak monotonic effect and a signed edge are introduced results are developed relating these monotonic effects and signed edges to the sign of the causal effect of an intervention in the presence of intermediate variables the incorporation of signed edges into the directed acyclic graph causal framework furthermore allows for the development of rules governing the relationship between monotonic effects and the sign of the covariance between two variables it is shown that when certain assumptions about monotonic effects can be made then these results can be used to draw conclusions about the presence of causal effects even when data is missing on confounding variables

an investigation of oil water two phase flow instability using multivariate multi scale weighted permutation entropy abstract the present study is devoted to the investigation of oil water two phase flow instability using multivariate multi scale weighted permutation entropy mwmpe four typical multivariate multi scale entropies namely mwmpe multivariate multi scale permutation entropy mmpe multivariate multi scale sample entropy mmse and multivariate multi scale approximate entropy mmae are applied in lorenz system with the addition of different kinds of noises the comparison results indicate that mwmpe presents the superiorities of being sensitive to the variation in scale showing a monotonous increasing trend as well as the best anti noise ability accordingly with the fluctuating signals from an eight electrode rotating electrical field conductance sensor used for the measurement of oil water flows we extract mwmpe for the whole experimental flow conditions in terms of which the effects of mixture velocity and water cut on oil water two phase flow instability are illuminated our research provides an effective method for uncovering the underlying evolution instability of the flow structures in oil water flows

semiparametric tests for sufficient cause interaction a sufficient cause interaction between two exposures signals the presence of individuals for whom the outcome would occur only under certain values of the two exposures when the outcome is dichotomous and all exposures are categorical then under certain no confounding assumptions empirical conditions for sufficient cause interactions can be constructed based on the sign of linear contrasts of conditional outcome probabilities between differently exposed subgroups given confounders it is argued that logistic regression models are unsatisfactory for evaluating such contrasts and that bernoulli regression models with linear link are prone to misspecification we therefore develop semiparametric tests for sufficient cause interactions under models which postulate probability contrasts in terms of a finite dimensional parameter but which are otherwise unspecified estimation is often not feasible in these models because it would require nonparametric estimation of auxiliary conditional expectations given high dimensional variables we therefore develop multiply robust tests under a union model that assumes at least one of several working submodels holds in the special case of a randomized experiment or a family based genetic study in which the joint exposure distribution is known by design or mendelian inheritance the procedure leads to asymptotically distribution free tests of the null hypothesis of no sufficient cause interaction

the computational complexity of probabilistic inference using bayesian belief networks research note abstract bayesian belief networks provide a natural efficient method for representing probabilistic dependencies among a set of variables for these reasons numerous researchers are exploring the use of belief networks as a knowledge representation in artificial intelligence algorithms have been developed previously for efficient probabilistic inference using special classes of belief networks more general classes of belief networks however have eluded efforts to develop efficient inference algorithms we show that probabilistic inference using belief networks is np hard therefore it seems unlikely that an exact algorithm can be developed to perform probabilistic inference efficiently over all classes of belief networks this result suggests that research should be directed away from the search for a general efficient probabilistic inference algorithm and toward the design of efficient special case average case and approximation algorithms

the bottleneck independent domination on the classes of bipartite graphs and block graphs let g v e w denote a graph with vertex set v and edge set e and each vertex v is associated with a cost w v for any set v v the bottleneck cost of v is defined as max w x x v this paper considers the bottleneck independent dominating set problem the bids problem which determines an independent dominating set of g such that its bottleneck cost is minimized this paper studies the problem on the classes of bipartite graphs and block graphs this paper first proves that the problem is np hard on chordal bipartite graphs second a linear time algorithm on convex bipartite graphs is proposed next a linear time algorithm on trees is designed then we generalize the algorithmic result to block graphs all algorithms are designed by the dynamic programming strategy

the tractability of segmentation and scene analysis one of the fundamental problems in computer vision is the segmentation of an image into semantically meaningful regions based only on image characteristics a single segmentation can be determined using a linear number of evaluations of a uniformity predicate however minimising the number of regions is shown to be an np complete problem we also show that the variational approach to segmentation based on minimising a criterion combining the overall variance of regions and the number of regions also gives rise to an np complete problem when a library of object models is available segmenting the image becomes a problem of scene analysis a sufficient condition for the reconstruction of a 3d scene from a 2d image to be solvable in polynomial time is that the scene contains no cycles of mutually occluding objects and that no range information can be deduced from the image it is known that relaxing the no cycles condition renders the problem np complete we show that relaxing the no range information condition also produces an np complete problem

the complexity of the residual node connectedness reliability problem this paper considers a probabilistic network in which the edges are perfectly reliable but the nodes fail with some known probabilities the network is in an operational state if the surviving nodes induce a connected graph the residual node connectedness reliability r g of a network g is the probability that the graph induced by the surviving nodes is connected this reliability measure is very different from the widely studied k terminal network reliability measure it is proven that the problem of computing the residual connectedness reliability is np hard by showing that the problem of counting the number of node induced connected subgraphs of a given graph is bf p complete the problem remains bf p complete for split graphs as well as planar and bipartite graphs

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

on rainbow domination numbers of graphs given a graph g and a set of t colors assume that we assign an arbitrary subset of these colors to each vertex of g if we require that each vertex to which an empty set is assigned has in its neighborhood all t colors then this assignment is called a t rainbow dominating function of the graph g the corresponding invariant c r t g which is the minimum sum of numbers of assigned colors over all vertices of g is called the t rainbow domination number of g in this paper bounds for the t rainbow domination number of an arbitrary graph for an arbitrary positive integer t are given the 3 rainbow domination numbers of several classes of graphs such as paths cycles and the generalized petersen graphs p n k are investigated the 3 rainbow domination number of p n 1 is determined and the upper bounds for p n 2 and p n 3 are provided by computer search we obtain that the upper bounds for p n 2 match their exact values for n 17

power domination in block graphs the problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known domination problem in graphs in 2002 haynes et al considered the graph theoretical representation of this problem as a variation of the domination problem they defined a set s to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set s following a set of rules for power system monitoring the power domination number p g of a graph g is the minimum cardinality of a power dominating set of g this problem was proved np complete even when restricted to bipartite graphs and chordal graphs in this paper we present a linear time algorithm for solving the power domination problem in block graphs as an application of the algorithm we establish a sharp upper bound for power domination number in block graphs and characterize the extremal graphs

causal inference with generalized structural mean models summary we estimate cause effect relationships in empirical research where exposures are not completely controlled as in observational studies or with patient non compliance and self selected treatment switches in randomized clinical trials additive and multiplicative structural mean models have proved useful for this but suffer from the classical limitations of linear and log linear models when accommodating binary data we propose the generalized structural mean model to overcome these limitations this is a semiparametric two stage model which extends the structural mean model to handle non linear average exposure effects the first stage structural model describes the causal effect of received exposure by contrasting the means of observed and potential exposure free outcomes in exposed subsets of the population for identification of the structural parameters a second stage nuisance model is introduced this takes the form of a classical association model for expected outcomes given observed exposure under the model we derive estimating equations which yield consistent asymptotically normal and efficient estimators of the structural effects we examine their robustness to model misspecification and construct robust estimators in the absence of any exposure effect the double logistic structural mean model is developed in more detail to estimate the effect of observed exposure on the success of treatment in a randomized controlled blood pressure reduction trial with self selected non compliance

probabilistic causality and detecting collections of interdependence patterns summary interdependent effects are usually distinguished from statistical interaction by using the sufficient causes framework this almost always involves expressing probability distributions as deterministic logic functions where certain conditions invariably produce or prevent an outcome using an idea from the philosophy literature that a cause is defined as an event which increases the probability of an outcome a probabilistic sufficient causes framework is developed here it expresses distributions with probabilistic logic functions and is used to define interdependence without determinism the connections between probabilistic logic and the inequalities which define convex polytopes in the space of the distribution parameters are given interdependence is defined for the response behaviour of individuals defined by latent variables and is not directly observable it is shown that the formulation of the models as geometric objects enables the use of algebraic tools to compute observable constraints for detecting interdependence novel constraints are derived for detecting causal interdependence patterns and the corresponding statistical tests are described

radiocoloring in planar graphs complexity and approximations the frequency assignment problem fap in radio networks is the problem of assigning frequencies to transmitters by exploiting frequency reuse while keeping signal interference to acceptable levels the fap is usually modelled by variations of the graph coloring problem a radiocoloring rc of a graph g v e is an assignment function v n such that u v 2 when u v are neighbors in g and u v 1 when the distance of u v in g is two the number of discrete frequencies and the range of frequencies used are called order and span respectively the optimization versions of the radiocoloring problem rcp are to minimize the span or the order in this paper we prove that the radiocoloring problem for general graphs is hard to approximate unless np zpp within a factor of n1 2 e for any e 0 where n is the number of vertices of the graph however when restricted to some special cases of graphs the problem becomes easier we prove that the min span rcp is np complete for planar graphs next we provide an o n time algorithm v n which obtains a radiocoloring of a planar graph g that approximates the minimum order within a ratio which tends to 2 where the maximum degree of g finally we provide a fully polynomial randomized approximation scheme fpras for the number of valid radiocolorings of a planar graph g with colors in the case where 4 50

the summation and bottleneck minimization for single step searching on weighted graphs abstract in this paper three types of problems for single step searching weighted graphs are defined they are the summation cost minimization the bottleneck cost minimization and a hybrid to minimize the maximum of the summation cost and the bottleneck cost all three are shown to be np hard but polynomially solvable for trees the bottleneck minimization is shown to be reducible to the summation minimization problem

multiscale entropy analysis of complex physiologic time series there has been considerable interest in quantifying the complexity of physiologic time series such as heart rate however traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long range correlations this paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics we introduce a method to calculate multiscale entropy mse for complex time series we find that mse robustly separates healthy and pathologic groups and consistently yields higher values for simulated long range correlated noise compared to uncorrelated noise

an annotated bibliography on guaranteed graph searching graph searching encompasses a wide variety of combinatorial problems related to the problem of capturing a fugitive residing in a graph using the minimum number of searchers in this annotated bibliography we give an elementary classification of problems and results related to graph searching and provide a source of bibliographical references on this field

randomness and degrees of irregularity the fundamental question are sequential data random arises in myriad contexts often with severe data length constraints furthermore there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness e g to evaluate the efficacy of therapy in medicine we address both these issues from a computable framework via a quantification of regularity apen approximate entropy defining maximal randomness for sequences of arbitrary length indicating the applicability to sequences as short as n 5 points an infinite sequence formulation of randomness is introduced that retains the operational and computable features of the finite case in the infinite sequence setting we indicate how the foundational definition of independence in probability theory and the definition of normality in number theory reduce to limit theorems without rates of convergence from which we utilize apen to address rates of convergence of a deficit from maximal randomness refining the aforementioned concepts in a computationally essential manner representative applications among many are indicated to assess i random number generation output ii well shuffled arrangements and iii the quality of bootstrap replicates

general theory for interactions in sufficient cause models with dichotomous exposures the sufficient component cause framework assumes the existence of sets of sufficient causes that bring about an event for a binary outcome and an arbitrary number of binary causes any set of potential outcomes can be replicated by positing a set of sufficient causes typically this representation is not unique a sufficient cause interaction is said to be present if within all representations there exists a sufficient cause in which two or more particular causes are all present a singular interaction is said to be present if for some subset of individuals there is a unique minimal sufficient cause empirical and counterfactual conditions are given for sufficient cause interactions and singular interactions between an arbitrary number of causes conditions are given for cases in which none some or all of a given set of causes affect the outcome monotonically the relations between these results interactions in linear statistical models and pearl s probability of causation are discussed

following a curve with the discrete frechet distance finding the similarity between curves is an important problem that comes up in many areas such as 3d modeling gis applications ordering and reachability a related problem is to find one of the curves given a measure of similarity and another curve given a set of points s a polygonal curve p and an e 0 the discrete set chain matching problem is to find another polygonal curve q such that the nodes of q are points in s and d f p q e here d f is the discrete frechet distance between the two polygonal curves for the first time we study the set chain matching problem based on the discrete frechet distance rather than the continuous frechet distance we further extend the problem based on unique or non unique nodes and on limiting the number of points used we prove that three of the variations of the set chain matching problem are np complete for the version of the problem that is polynomial we give an o p s time greedy solution