on the directional dynamics of additive cellular automata we continue the study of cellular automata ca directional dynamics i e the behavior of the joint action of ca and shift maps this notion has been investigated for general ca in the case of expansive dynamics by boyle and lind and by sablik for sensitivity and equicontinuity in this paper we give a detailed classification for the class of additive ca providing non trivial examples for some classes of sablik s classification moreover we extend the directional dynamics studies by considering also factor languages and attractors

nondeterministic cellular automata abstract using purely topological concepts we characterize the class of nondeterministic mappings between shift spaces that give rise to nondeterministic sliding block codes we use such topological notions to investigate basic properties of surjective and reversible nondeterministic cellular automata

conservation of some dynamical properties for operations on cellular automata we consider the family of all the cellular automata ca sharing the same local rule but having different memories this family contains also all ca with memory m 0 one sided ca which can act both on a z and on a n we study several set theoretical and topological properties for these classes in particular we investigate whether the properties of a given ca are preserved when considering the ca obtained by changing the memory of the original one shifting operation furthermore we focus our attention on the one sided ca acting on a z starting from the one sided ca acting on a n and having the same local rule lifting operation as a particular consequence of these investigations we prove that the long standing conjecture surjectivity dense periodic orbits dpo can be restated in several different but equivalent ways furthermore we give some results on properties conserved under the iteration of the ca global map

partial auc estimation and regression accurate diagnosis of disease is a critical part of health care new diagnostic and screening tests must be evaluated based on their abilities to discriminate diseased from nondiseased states the partial area under the receiver operating characteristic roc curve is a measure of diagnostic test accuracy we present an interpretation of the partial area under the curve auc which gives rise to a nonparametric estimator this estimator is more robust than existing estimators which make parametric assumptions we show that the robustness is gained with only a moderate loss in efficiency we describe a regression modeling framework for making inference about covariate effects on the partial auc such models can refine knowledge about test accuracy model parameters can be estimated using binary regression methods we use the regression framework to compare two prostate specific antigen biomarkers and to evaluate the dependence of biomarker accuracy on the time prior to clinical diagnosis of prostate cancer

on the undecidability of the limit behavior of cellular automata cellular automata ca are discrete dynamical systems and an abstract model of parallel computation the limit set of a cellular automaton is its maximal topological attractor a well known result due to kari says that all nontrivial properties of limit sets are undecidable in this paper we consider the properties of limit set dynamics i e properties of the dynamics of ca restricted to their limit sets there can be no equivalent of kari s theorem for limit set dynamics anyway we show that there is a large class of undecidable properties of limit set dynamics namely all properties of limit set dynamics which imply stability or the existence of a unique subshift attractor as a consequence we have that it is undecidable whether the cellular automaton map restricted to the limit set is the identity map and whether it is closing injective expansive positively expansive and transitive

non uniform cellular automata classes dynamics and decidability the dynamical behavior of non uniform cellular automata is compared with the one of classical cellular automata several differences and similarities are pointed out by a series of examples decidability of basic properties like surjectivity and injectivity is also established the final part studies a strong form of equicontinuity property specially suited for non uniform cellular automata

analysis of decision boundaries in linearly combined neural classifiers combining or integrating the outputs of several pattern classifiers has led to improved performance in a multitude of applications this paper provides an analytical framework to quantify the improvements in classification results due to combining we show that combining networks linearly in output space reduces the variance of the actual decision region boundaries around the optimum boundary this result is valid under the assumption that the a posteriori probability distributions for each class are locally monotonic around the bayes optimum boundary in the absence of classifier bias the error is shown to be proportional to the boundary variance resulting in a simple expression for error rate improvements in the presence of bias the error reduction expressed in terms of a bias reduction factor is shown to be less than or equal to the reduction obtained in the absence of bias the analysis presented here facilitates the understanding of the relationships among error rates classifier boundary distributions and combining in output space

an online auc formulation for binary classification the area under the roc curve auc provides a good scalar measure of ranking performance without requiring a specific threshold for performance comparison among classifiers auc is useful for imprecise environments since it operates independently with respect to class distributions and misclassification costs a direct optimization of this auc criterion thus becomes a natural choice for binary classifier design however a direct formulation based on the auc criterion would require a high computational cost due to the drastically increasing input pair features in this paper we propose an online learning algorithm to circumvent this computational problem for binary classification different from those conventional recursive formulations the proposed formulation involves a pairwise cost function which pairs up a newly arrived data point with those of opposite class in stored data moreover with incorporation of a sparse learning into the online formulation the computational effort can be significantly reduced our empirical results on three different scales of public databases show promising potential in terms of classification auc accuracy and computational efficiency

sequential exploration of complex surfaces using minimum energy designs a new space filling design called minimum energy design med is proposed to explore unknown regions of the design space of particular interest to an experimenter the key ideas involved in constructing the med are the visualization of each design point as a charged particle inside a box and minimization of the total potential energy of these particles it is shown through theoretical arguments and simulations that with a proper choice of the charge function the med can asymptotically generate any arbitrary probability density function a version of the med which adaptively updates the design by learning about the unknown response surface sequentially is proposed and implemented two potential applications of med in simulation of complex probability densities and optimization of complex response surfaces are discussed and demonstrated with examples this article has supplementary material online

unsupervised learning of finite mixture models this paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data the adjective unsupervised is justified by two properties of the algorithm 1 it is capable of selecting the number of components and 2 unlike the standard expectation maximization em algorithm it does not require careful initialization the proposed method also avoids another drawback of em for mixture fitting the possibility of convergence toward a singular estimate at the boundary of the parameter space the novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models instead we seamlessly integrate estimation and model selection in a single algorithm our technique can be applied to any type of parametric mixture model for which it is possible to write an em algorithm in this paper we illustrate it with experiments involving gaussian mixtures these experiments testify for the good performance of our approach

likelihood ratio based biometric score fusion multibiometric systems fuse information from different sources to compensate for the limitations in performance of individual matchers we propose a framework for the optimal combination of match scores that is based on the likelihood ratio test the distributions of genuine and impostor match scores are modeled as finite gaussian mixture model the proposed fusion approach is general in its ability to handle 1 discrete values in biometric match score distributions 2 arbitrary scales and distributions of match scores 3 correlation between the scores of multiple matchers and 4 sample quality of multiple biometric sources experiments on three multibiometric databases indicate that the proposed fusion framework achieves consistently high performance compared to commonly used score fusion techniques based on score transformation and classification

linear combinations of multiple diagnostic markers abstract the receiver operating characteristic roc curve is a simple and meaningful measure to assess the usefulness of diagnostic markers to use the information carried by multiple markers we note that fisher s linear discriminant function provides a linear combination of markers to maximize the sensitivity over the entire specificity range uniformly under the multivariate normal distribution model with proportional covariance matrices with no restriction on covariance matrices we also provide a solution of the best linear combination of markers in the sense that the area under the roc curve of this combination is maximized among all possible linear combinations we illustrate both situations discussed in the article with a cancer clinical trial data

partial auc maximization in a linear combination of dichotomizers classifier combination is a useful and common methodology to design an effective classification system a large number of combination rules has been proposed hitherto mostly aimed at minimizing the error rate recently some methods have been presented that are devoted to maximize the area under the roc curve auc a more suitable performance measure when dealing with two class problems with imprecise environment and or imbalanced class priors however there are several applications that do not operate in the complete range of the roc curve but only in particular regions of it in these cases it is better to analyze the performance only in a part of the curve and to use the partial auc pauc this paper presents a new method that aims at maximizing the pauc by means of linear combination of classifiers the effectiveness of the proposed method has been proved on two biometric databases

exploiting the relationships among several binary classifiers via data transformation the structural resemblance among several existing classifiers has motivated us to investigate their underlying relationships by exploring into the mapping solutions of these classifiers we found that they can be linked by simple feature data scaling in other words the key to these relationships lies upon how the replica of feature data are being scaled this finding leads us directly to an exploration of novel classifiers beyond existing settings based on an extensive empirical evaluation we show that the proposed formulation facilitates a tuning capability beyond existing settings for classifier generalization highlightsestablishment of relationship among several binary classifiers exploration of a random projection network for such classifier learning proposal of novel classifier which exploits the established relationship observe the performance of novel classifier on several performance measures

fundamental study directional dynamics for cellular automata a sensitivity to initial condition approach a cellular automaton is a continuous function f defined on a full shift a z which commutes with the shift s often to study the dynamics of f one only considers implicitly s however it is possible to emphasize the spatio temporal structure produced by considering the dynamics of the zxn action induced by s f in this purpose we study the notion of directional dynamics in particular we are interested in directions of equicontinuity and expansivity which generalize the concepts introduced by gilman robert h gilman classes of linear automata ergodic theory dynam systems 7 1 1987 105 118 and p kurka petr kurka languages equicontinuity and attractors in cellular automata ergodic theory dynam systems 17 2 1997 417 433 we study the sets of directions which exhibit this special kind of dynamics showing that they induce a discrete geometry in space time diagrams

on the statistical analysis of roc curves we introduce a new accuracy index for receiver operating characteristic roc curves namely the partial area under the binormal roc graph over any specified region of interest we propose a simple but general procedure based on a conventional analysis of variance for comparing accuracy indices derived from two or more different modalities the proposed method is related to and compared with existing methodology and is illustrated by results from an experiment on optimization of density and contrast yielded by multiform photographic images used for scintigraphy

the nilpotency problem of one dimensional cellular automata the limit set of a celullar automaton consists of all the configurations of the automaton that can appear after arbitrarily long computations it is known that the limit set is never empty it contains at least one homogeneous configuration a ca is called nilpotent if its limit set contains just one configuration the present work proves that it is algorithmically undecidable whether a given one dimensional cellular automaton is nilpotent the proof is based on a generalization of the well known result about the undecidability of the tiling problem of the plane the generalization states that the tiling problem remains undecidable even if one considers only so called nw deterministic tile sets that is tile sets in which the left and upper neighbors of each tile determine the tile uniquely the nilpotency problem is known to be undecidable for d dimensional ca for d geq 2 the result is the basis of the proof of rice s theorem for ca limit sets which states that every nontrivial property of limit set

a graphical analysis of cost sensitive regression problems several efforts have been done to bring roc analysis beyond binary classification especially in regression however the mapping and possibilities of these proposals do not correspond to what we expect from the analysis of operating conditions dominance hybrid methods etc in this paper we present a new representation of regression models in the so called regression roc rroc space the basic idea is to represent over estimation on the x axis and under estimation on the y axis the curves are just drawn by adjusting a shift a constant that is added or subtracted to the predictions and plays a similar role as a threshold in classification from here we develop the notions of optimal operating condition convexity dominance and explore several evaluation metrics that can be shown graphically such as the area over the rroc curve aoc in particular we show a novel and significant result the aoc is equal to the error variance multiplied by a factor which does not depend on the model the derivation of rroc curves with non constant shifts and soft regression models and the relation with cost plots is also discussed

roc curves for regression receiver operating characteristic roc analysis is one of the most popular tools for the visual assessment and understanding of classifier performance in this paper we present a new representation of regression models in the so called regression roc rroc space the basic idea is to represent over estimation against under estimation the curves are just drawn by adjusting a shift a constant that is added or subtracted to the predictions and plays a similar role as a threshold in classification from here we develop the notions of optimal operating condition convexity dominance and explore several evaluation metrics that can be shown graphically such as the area over the rroc curve aoc in particular we show a novel and significant result the aoc is equivalent to the error variance we illustrate the application of rroc curves to resource estimation namely the estimation of software project effort

an interpretation for the roc curve and inference using glm procedures the accuracy of a medical diagnostic test is often summarized in a receiver operating characteristic roc curve this paper puts forth an interpretation for each point on the roc curve as being a conditional probability of a test result from a random diseased subject exceeding that from a random nondiseased subject this interpretation gives rise to new methods for making inference about roc curves it is shown that inference can be achieved with binary regression techniques applied to indicator variables constructed from pairs of test results one component of the pair being from a diseased subject and the other from a nondiseased subject within the generalized linear model glm binary regression framework roc curves can be estimated and we highlight a new semiparametric estimator covariate effects can also be evaluated with the glm models the methodology is applied to a pancreatic cancer dataset where we use the regression framework to compare two different serum biomarkers asymptotic distribution theory is developed to facilitate inference and to provide insight into factors influencing variability of estimated model parameters

a proposed design and analysis for comparing digital and analog mammography because randomized trials have shown a reduction in breast cancer mortality analog mammography for the early detection of breast cancer has gained widespread use recently several manufacturers have developed digital mammography which promises great advantages in the storage and transmission of images we were asked to design a study to compare the two types of mammography in terms of their performance for the early detection of breast cancer a standard measure of mammography performance is the receiver operating characteristic roc curve which is a plot of false and true positive rates for each ordered classification of the mammography images methods for study design and data analysis based on roc curves have been well developed for diagnostic tests particularly in radiology but for comparing the performance of mammography for the early detection of breast cancer among asymptomatic women special considerations motivate new designs and methodology first digital mammography may cost substantia

maximum likelihood estimation of receiver operating characteristic roc curves from continuously distributed data we show that truth state runs in rank ordered data constitute a natural categorization of continuously distributed test results for maximum likelihood ml estimation of roc curves on this basis we develop two new algorithms for fitting binormal roc curves to continuously distributed data a true ml algorithm labroc4 and a quasi ml algorithm labroc5 that requires substantially less computation with large data sets simulation studies indicate that both algorithms produce reliable estimates of the binormal roc curve parameters a and b the roc area index az and the standard errors of those estimates

local rule distributions language complexity and non uniform cellular automata this paper investigates a variant of cellular automata namely n ca indeed n ca are cellular automata which can have different local rules at each site of their lattice the assignment of local rules to sites of the lattice completely characterizes n ca in this paper sets of assignments sharing some interesting properties are associated with languages of bi infinite words the complexity classes of these languages are investigated providing an initial rough classification of n ca

rice s theorem for the limit sets of cellular automata abstract rice s theorem is a well known result in the theory of recursive functions a corresponding theorem for cellular automata limit sets is proved all nontrivial properties of limit sets of cellular automata cas are shown undecidable the theorem remains valid even if only one dimensional cas are considered