parity effect of the initial capital based on parrondo s games and the quantum interpretation abstract in our previous study zhu et al quantum game interpretation for a special case of parrondo s paradox physica a 390 2011 579 the capital dependent parrondo s game where one game depends on the capital modulus m 4 was shown not to have a definite stationary probability distribution and that payoffs of the game depended on the parity of the initial capital this paper presents a generalization of these results to even m greater than 4 an intuitive explanation for producing this phenomenon is that the discrete time markov chain of the game is divided into two completely unrelated inner and outer rings the process taking the inner ring or outer ring of the game is determined by the initial capital of parity and then a win or loss of the game is determined quantum game theory is used to further analyze the phenomenon the results show that the explanation of the game corresponding to a stationary probability distribution is that the probability of the initial capital has reached parity

a novel feature selection approach combining feature wrappers and filters abstract feature selection is one of the most important issues in the research fields such as system modelling data mining and pattern recognition in this study a new feature selection algorithm that combines feature wrapper and feature filter approaches is proposed in order to identify the significant input variables in systems with continuous domains the proposed method utilizes functional dependency concept correlation coefficients and k nearest neighbourhood knn method to implement the feature filter and feature wrappers four feature selection methods independently select the significant input variables and the input variable combination which yields best result with respect to their corresponding evaluation function is selected as the winner this is similar to the basic information fusion notion of integrating the information collected from different sources all of the four feature selection methods are performed in two stages i pre selection ii selection two of the four feature selection methods utilize knn method for evaluating the candidates these two methods use sequential forward and sequential backward search mechanism respectively in pre selection stage whereas the third feature selection method uses correlation coefficients in the pre selection stage it is common to have outliers and noise in real life data in order to make the proposed feature selection algorithm noise and outlier resistant approximate functional dependencies are used by utilizing membership values that inherently cope with uncertainty in the data thus the fourth feature selection method makes use of approximate functional dependencies to evaluate candidates in pre selection stage all of these four methods apply knn method with exhaustive search strategy in order to find the most suitable input variable combination with respect to a performance measure

a revision of the lyapunov exponent in 1d quadratic maps abstract only misiurewicz points strictly have a lyapunov exponent positive measure in one dimensional 1d quadratic maps hence we represent here the lyapunov exponent of all the misiurewicz points which were found and inventoried by us in a former work as a result of this representation an infinity of alignments of misiurewicz points are obtained and two types of jumps in the values of are found

drift conditions for matrix analytic models in his seminal work neuts gave drift criteria by which one can determine whether processes of gi m i or m g i type are positive recurrent recently a different drift condition to determine the ergodic character of a quasi birth and death process qbd appeared in the literature although its justification does not seem to have been formally established in this paper we provide a proof for this new drift condition in a general context we also give a simple proof for neuts original condition and establish a number of new drift conditions for the ergodic character of matrix analytic models

a fast heuristic attribute reduction approach to ordered decision systems abstract rough set theory has shown success in being a filter based feature selection approach for analyzing information systems one of its main aims is to search for a feature subset called a reduct which preserves the classification ability of the original system in this paper we consider ordered decision systems where the preference order a fundamental concept in dominance based rough set approach plays a critical role in recent literature based on the greedy hill climbing method many heuristic attribute reduction algorithms are proposed by utilizing significance measures of attributes and they are extended to deal with ordered decision systems unfortunately they are often time consuming especially when applied to deal with large scale data sets with high dimensions to reduce the complexity a novel accelerator is introduced in heuristic algorithms from the perspectives of objects and criteria based on the new accelerator the number of objects and the dimension of criteria are lessened thus making the accelerated algorithms faster than their original counterparts while maintaining the same reducts experimental analysis shows the validity and efficiency of the proposed methods

quantum field theory of treasury bonds the heath jarrow morton hjm formulation of treasury bonds in terms of forward rates is recast as a problem in path integration the hjm model is generalized to the case where all the forward rates are allowed to fluctuate independently the resulting theory is shown to be a two dimensional gaussian quantum field theory the no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract

genetic algorithm based feature set partitioning for classification problems feature set partitioning generalizes the task of feature selection by partitioning the feature set into subsets of features that are collectively useful rather than by finding a single useful subset of features this paper presents a novel feature set partitioning approach that is based on a genetic algorithm as part of this new approach a new encoding schema is also proposed and its properties are discussed we examine the effectiveness of using a vapnik chervonenkis dimension bound for evaluating the fitness function of multiple oblivious tree classifiers the new algorithm was tested on various datasets and the results indicate the superiority of the proposed algorithm to other methods

randomly chosen chaotic maps can give rise to nearly ordered behavior abstract parrondo s paradox j m r parrondo g p harmer d abbott new paradoxical games based on brownian ratchets phys rev lett 85 2000 5226 5229 see also o e percus j k percus can two wrongs make a right coin tossing games and parrondo s paradox math intelligencer 24 3 2002 68 72 states that two losing gambling games when combined one after the other either deterministically or randomly can result in a winning game that is a losing game followed by a losing game a winning game inspired by this paradox a recent study j almeida d peralta salas m romera can two chaotic systems give rise to order physica d 200 2005 124 132 asked an analogous question in discrete time dynamical system can two chaotic systems give rise to order namely can they be combined into another dynamical system which does not behave chaotically numerical evidence is provided in j almeida d peralta salas m romera can two chaotic systems give rise to order physica d 200 2005 124 132 that two chaotic quadratic maps when composed with each other create a new dynamical system which has a stable period orbit the question of what happens in the case of random composition of maps is posed in j almeida d peralta salas m romera can two chaotic systems give rise to order physica d 200 2005 124 132 but left unanswered in this note we present an example of a dynamical system where at each iteration a map is chosen in a probabilistic manner from a collection of chaotic maps the resulting random map is proved to have an infinite absolutely continuous invariant measure acim with spikes at two points from this we show that the dynamics behaves in a nearly ordered manner when the foregoing maps are applied one after the other deterministically as in o e percus j k percus can two wrongs make a right coin tossing games and parrondo s paradox math intelligencer 24 3 2002 68 72 the resulting composed map has a periodic orbit which is stable

positive line bundles on arithmetic varieties p 5 u integers is defined to count the volume of the lattice i l n of integral sections in the space j7 lon of real sections with supremum norm we want to prove that the leading term of this hilbert function as n f oo is given in terms of the height of x in as 1 this is known as a theorem of gillet and soule gs2 if x has a regular generic fiber beside this known result our proof uses hironaka s theorem on resolutions of singularities and minkowski s theorem on successive minima by hironaka s theorem we may construct

parrondo effect in quantum coin toss simulations game a game b game c parrondo s games follow this basic structure where a and b are losing games and c is a winning game a phenomenon called parrondo s paradox these games can take on a wider class of definitions and exhibit these paradoxical results in this paper we show three paradoxical cases i the successive tossing of a single fair quantum coin gives a biased result a previously known result ii the random tossing of two quantum coins each with successive biased expectations gives an average random walk position of approximately zero iii the sequential periodic tossing of two quantum coins each with successive negative biased expectations gives an average random walk with positive expectation using these results we then propose a protocol for identifying and classifying quantum operations that span the same hilbert space for a two level quantum system

quantum walks with history dependence we introduce a multi coin discrete quantum walk where the amplitude for a coin flip depends upon previous tosses although the corresponding classical random walk is unbiased a bias can be introduced into the quantum walk by varying the history dependence by mixing the biased walk with an unbiased one the direction of the bias can be reversed leading to a new quantum version of parrondo s paradox

computable examples of the maximal lyapunov exponent some new examples are given of sequences of matrix valued random variables for which it is possible to compute the maximal lyapunov exponent the examples are constructed by using a sequence of stopping times to group the original sequence into commuting blocks if the original sequence is the outcome of independent bernoulli trials with success probability p then the maximal lyapunov exponent may be expressed in terms of power series in p with explicit formulae for the coefficients the convexity of the maximal lyapunov exponent as a function of p is discussed as is an application to branching processes in a random environment

semianalytical solution of the random product problem of matrices and discrete time random evolution we consider the product of a large number of matrices chosen randomly with some correlation as a or b we introduce an exact functional equation whose solution gives the limiting distribution and the lyapunov exponent for the product of large number of matrices thus we suggest new semianalytical method to solve the random product problem of correlated matrices the method can be easily generalized to high order matrices as we deal with a larger systems of functional equations we have provided a known numerical algorithm for the solution of the matrix product problem we have also applied our method for a solution of discrete time random evolution our functional equation method provides exact transition point

the paradox of parrondo s games we introduce parrondo s paradox that involves games of chance we consider two fair games a and b both of which can be made to lose by changing a biasing parameter an apparently paradoxical situ

dynamic parrondo s paradox abstract this paper is focused on studying parrondo s paradox in non linear dynamics specifically how the periodic combination of the individual maps f and g can give rise to chaos or order we construct dynamical systems exhibiting the paradox for several notions of chaos derived from topological dynamics the effect of altering the order of the combination i e considering f g or g f is analyzed as well as the robustness of the parrondo effect under small perturbations conditions for avoiding parrondian dynamics are also obtained placing special emphasis on the notion of chaos given by turbulence

on the rational approximations to the powers of an algebraic number solution of two problems of mahler and mendes france about fifty years ago mahler ma proved that i f 1 is rational but not an integer and i f 0 l all of whose conjugates different from cr have absolute value less than 1 note that rational integers larger than 1 are pisot numbers according to our definition mahler also added that it would be of some interest to know which algebraic numbers have the same property as the rationals in the theorem now it seems that even replacing ridout s theorem with the modern versions of roth s theorem valid for several valuations and approximations in any given number field the method of mahler does not lead to a complete solution to his question one of the objects of the present paper is to answer mahler s question completely our methods will involve a suitable version of the schmidt subspace theorem which may be considered as a multi dimensional extension of the results mentioned by roth mahler and ridout we state at once our first theorem where as usual we denote by iix the distance of the complex number x from the nearest integer in z i e

gp coach genetic programming based learning of compact and accurate fuzzy rule based classification systems for high dimensional problems in this paper we propose gp coach a genetic programming based method for the learning of compact and accurate fuzzy rule based classification systems for high dimensional problems gp coach learns disjunctive normal form rules generated by means of a context free grammar coded as one rule per tree the population constitutes the rule base so it is a genetic cooperative competitive learning approach gp coach uses a token competition mechanism to maintain the diversity of the population and this obliges the rules to compete and cooperate among themselves and allows the obtaining of a compact set of fuzzy rules the results obtained have been validated by the use of non parametric statistical tests showing a good performance in terms of accuracy and interpretability

occurrence of complementary processes in parrondo s paradox abstract parrondo s paradox involves two losing processes producing a winning outcome we analyze the paradox with an original and novel method in which we start with one process and seek to construct a complementary process to achieve the paradox we then derive a general condition for the classical parrondo game to have a complementary process numerical simulation predicts that approximately two thirds of such losing games satisfy the required condition this suggests the common occurrence of the paradox indicative of many potentially undiscovered applications in real life scenarios involving stochastic processes

a quantitative version of the absolute subspace theorem the celebrated subspace theorem of w m schmidt 12 says the following subspace theorem let l1 ln be linearly independent linear forms in n variables with real or complex algebraic coefficients suppose 0 consider the inequality 1 1 l1 x ln x 0 put 1 5 q c x r li x qi 1 i n then the parametric subspace theorem can be stated as follows parametric subspace theorem let c be a fixed tuple satisfying 1 3 let 0 then there are finitely many proper linear subspaces t1 tb of q n such that for any q which is sufficiently large there exists a subspace ti t1 tb with 1 6 q q c z ti

stochastic dynamics and parrondo s paradox abstract the spanish physicist juan parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game if a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures the appropriate abstract setting is as follows there is given a compact metric space m d and m is written as the union of certain closed subsets a 1 a r for every 1 r there is prescribed a strict contraction a m a random walk x m m n 0 on m is then defined as follows the starting position is x 0 x 0 where x 0 m is fixed and if the walk at the m th step is at position x m m then one chooses a among the with x m a with equal probability say and defines x m 1 as x m associated with the walk is a gain x m in every round where m r is a continuous function the aim of the present investigations is the study of the expectation g m of x m as a function of m our main result states that the sequence g m is eventually approximately periodic provided that all a are not only closed but also open in m for every e there is an l 0 n such that g m is l 0 periodic up to an error of at most e for sufficiently large m in fact it turns out that the behaviour of our process can be described well with a finite markov chain in the general case however the process might behave rather chaotically we give an example where m is the unit interval m is written as the union of two closed subsets a 1 a 2 the contractions 1 2 are rather simple but the expectations of the gains are not even cesaro convergent

the coupling effect of the process sequence and the parity of the initial capital on parrondo s games abstract based on the original parrondo s game and on the case where game a and game b are played randomly with modulo m 4 the processes of the game are divided into odd and even numbered plays where the probability of playing game a in odd numbers is 1 and the probability of playing game a in even numbers is 2 by using the discrete time markov chain we find that the stationary probability distribution and mathematical expectation are not definite when 1 2 while they are definite when 1 2 meanwhile we perform a more in depth analysis according to the residue values divided by an integer n that is 1 2 3 n 1 0 we divide the process of the game into 1 2 3 n 1 n times where the probability of playing game a at each time is i i 1 2 n 1 n the general conclusions we obtain through analysis are 1 when the modulo m is odd whatever odd or even number n is and whatever value i is the stationary probability distribution is definite and the profit of the game does not depend on the initial value and 2 when the modulo m is even if n is odd then whatever value i is the stationary probability distribution is definite if n is even 1 2 n 1 n must be satisfied and then the stationary probability distribution is definite otherwise the stationary probability distribution has infinite solutions and the profit of the game depends on the initial value

periodic sequences of simple maps can support chaos abstract in this paper we explore the parrondo s paradox when several dynamically simple maps are combined in a periodic way producing chaotic dynamics we show that the paradox is not commutative that is it depends on the way that the maps are iterated we also see that the paradox happens more frequently when the number of maps that we iterate increases

pattern formation induced by nonequilibrium global alternation of dynamics we recently proposed a mechanism for pattern formation based on the alternation of two dynamics neither of which exhibits patterns here we analyze the mechanism in detail showing by means of numerical simulations and theoretical calculations how the nonequilibrium process of switching between dynamics either randomly or periodically may induce both stationary and oscillatory spatial structures our theoretical analysis by means of mode amplitude equations shows that all features of the model can be understood in terms of the nonlinear interactions of a small number of fourier modes

quantum parrondo s games parrondo s paradox arises when two losing games are combined to produce a winning one a history dependent quantum parrondo game is studied where the rotation operators that represent the toss of a classical biased coin are replaced by general su 2 operators to transform the game into the quantum domain in the initial state a superposition of qubits can be used to couple the games and produce interference leading to quite different payoffs to those in the classical case

a q deformed logistic map and its implications a new q deformed logistic map is proposed and it is found to have concavity in parts of the x space its one cycle and two cycle non trivial fixed points are obtained which are found to be qualitatively and quantitatively different from those of the usual logistic map the stability of the proposed q logistic map is studied using the lyapunov exponent and with a change in the value of the deformation parameter q one is able to go from the chaotic to regular dynamical regime the implications of this q logistic map on parrondo s paradox are examined

quantum models of parrondo s games abstract a parrondo s paradox is an effect where two losing games when combined can produce a net winning result we provide a short introduction to quantum versions of parrondo s games and review the current status of the work

parrondo games as lattice gas automata parrondo games are coin flipping games with the surprising property that alternating plays of two losing games can produce a winning game we show that this phenomenon can be modelled by probabilistic lattice gas automata furthermore motivated by the recent introduction of quantum coin flipping games we show that quantum lattice gas automata provide an interesting definition for quantum parrondo games

quantum game interpretation for a special case of parrondo s paradox abstract by using the discrete markov chain method parrondo s paradox is studied by means of theoretical analysis and computer simulation built on the case of game ab played in alternation with modulus m 4 we find that such a case does not have a definite stationary probability distribution and that payoffs of the game depend on the parity of the initial capital besides this paper reveals the phenomenon that processing in order produces non deterministic results while a random process produces deterministic results the quantum game method is used in a further study the results show that the explanation of the game corresponding to a stationary probability distribution is that the probability of the initial capital has reached parity

quantum auctions facts and myths abstract quantum game theory whatever opinions may be held due to its abstract physical formalism have already found various applications even outside the orthodox physics domain in this paper we introduce the concept of a quantum auction its advantages and drawbacks then we describe the models that have already been put forward a general model involves wigner formalism and infinite dimensional hilbert spaces we envisage that the implementation might not be an easy task but a restricted model advocated by the hewlett packard group hogg et al seems to be much easier to implement we focus on problems related to combinatorial auctions and technical assumptions that are made powerful quantum algorithms for finding solutions would extend the range of possible applications quantum strategies being qubits can be teleported but are immune from cloning therefore extreme privacy of the agent s activity could in principle be guaranteed then we point out some key problems that have to be solved before commercial use would be possible with present technology optical networks single photon sources and detectors seems to be sufficient for an experimental realization in the near future

discrete time ratchets the fokker planck equation and parrondo s paradox parrondo s games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature here we review two recent approaches based on the fokker planck equation that rigorously establish the connection between parrondo s games and a physical model known as the flashing brownian ratchet this gives rise to a new set of parrondo s games of which the original games are a special case for the first time we perform a complete analysis of the new games via a discrete time markov chain analysis producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs

strange attractors that are not chaotic abstract it is shown that in certain types of dynamical systems it is possible to have attractors which are strange but not chaotic here we use the word strange to refer to the geometry or shape of the attracting set while the word chaotic refers to the dynamics of orbits on the attractor in particular the exponential divergence of nearby trajectories we first give examples for which it can be demonstrated that there is a strange nonchaotic attractor these examples apply to a class of maps which model nonlinear oscillators continuous time which are externally driven at two incommensurate frequencies it is then shown that such attractore are persistent under perturbations which preserve the original system type i e there are two incommensurate external driving frequencies this suggests that for systems of the typw which we have considered nonchaotic strange attractors may be expected to occur for a finite interval of parameter values on the other hand when small perturbations which do not preserve the system type are numerically introduced the strange nonchaotic attractor is observed to be converted to a periodic or chaotic orbit thus we conjecture that in general continuous time systems flows which are not externally driven at two incommensurate frequencies should not be expected to have strange nonchaotic attractors except possibly on a set of measure zero in the parameter space

gender classification from unaligned facial images using support subspaces rough face alignments result in suboptimal performance of face identification in this study we present an approach for identifying the gender based on facial images without proper face alignments instead of just using only the detected face patch for identification a set of patches is randomly cropped around the face detection region each patch set is represented by a linear subspace and compared with other linear subspaces by measuring their canonical correlations a similarity matrix comprised of the canonical correlations is then incorporated into an indefinite kernel support vector machine svm formulation the number of support vectors which we call support subspaces can be decided automatically hence we can avoid the dimension selection problem observed in our previous work our experimental results demonstrate that the proposed approach outperforms state of the art methods

winning combinations of history dependent games the parrondo effect describes the seemingly paradoxical situation in which two losing games can when combined become a winning game parrondo harmer and abbott phys rev lett 85 24 2000 here we generalize this analysis to the case where both games are history dependent i e there is an intrinsic memory in the dynamics of each game results are presented for the cases of both random and periodic switching between the two games

double linear regressions for single labeled image per person face recognition recently the underlying sparse representation structure in high dimensional data has received considerable attention in pattern recognition and computer vision in this paper we propose a novel semi supervised dimensionality reduction sdr method named double linear regressions dlr to tackle the single labeled image per person slip face recognition problem dlr simultaneously seeks the best discriminating subspace and preserves the sparse representation structure specifically a subspace assumption based label propagation salp method which is accomplished using linear regressions lr is first presented to propagate the label information to the unlabeled data then based on the propagated labeled dataset a sparse representation regularization term is constructed via linear regressions lr finally dlr takes into account both the discriminating efficiency and the sparse representation structure by using the learned sparse representation regularization term as a regularization term of linear discriminant analysis lda the extensive and encouraging experimental results on three publicly available face databases cmu pie extended yale b and ar demonstrate the effectiveness of the proposed method

subspace based feature selection for pattern recognition feature selection is an essential topic in the field of pattern recognition the feature selection strategy has a direct influence on the accuracy and processing time of pattern recognition applications features can be evaluated with either univariate approaches which examine features individually or multivariate approaches which consider possible feature correlations and examine features as a group although univariate approaches do not take the correlation among features into consideration they can provide the individual discriminatory power of the features and they are also much faster than multivariate approaches since it is crucial to know which features are more or less informative in certain pattern recognition applications univariate approaches are more useful in these cases this paper therefore proposes subspace based separability measures to determine the individual discriminatory power of the features these measures are then employed to sort and select features in a multi class manner the feature selection performances of the proposed measures are evaluated and compared with the univariate forms of classic separability measures divergence bhattacharyya transformed divergence and jeffries matusita on several datasets the experimental results clearly indicate that the new measures yield comparable or even better performance than the classic ones in terms of classification accuracy and dimension reduction rate

a switching scheme for synthesizing attractors of dissipative chaotic systems in this paper a periodic parameter switching scheme is proposed for synthesizing a large class of hyperbolic attractors of continuous time and autonomous dissipative chaotic systems depending linearly on a single real bifurcation parameter it is illustrated by numerical simulations that a wide range of hyperbolic attractors can be obtained by this new scheme the scheme can also be considered as an effective way for control and anticontrol of chaos

a unified methodology for the efficient computation of discrete orthogonal image moments a novel methodology is proposed in this paper to accelerate the computation of discrete orthogonal image moments the computation scheme is mainly based on a new image representation method the image slice representation isr method according to which an image can be expressed as the outcome of an appropriate combination of several non overlapped intensity slices this image representation decomposes an image into a number of binary slices of the same size whose pixels come in two intensities black or any other gray level value therefore the image block representation can be effectively applied to describe the image in a more compact way once the image is partitioned into intensity blocks the computation of the image moments can be accelerated as the moments can be computed by using decoupled computation forms the proposed algorithm constitutes a unified methodology that can be applied to any discrete moment family in the same way and produces similar promising results as has been concluded through a detailed experimental investigation

optimal potentials for temperature ratchets in a spatially periodic temperature profile directed transport of an overdamped brownian particle can be induced along a periodic potential with a load force applied to the particle this setup can perform as a heat engine for a given load the optimal potential maximizes the current and thus the power output of the heat engine we calculate the optimal potential for different temperature profiles and show that in the limit of a periodic piecewise constant temperature profile alternating between two temperatures the optimal potential leads to a divergent current this divergence being an effect of both the overdamped limit and the infinite temperature gradient at the interface would be cut off in any real experiment

random walks with absolute negative mobility we introduce simple non markovian modifications to the standard random walk resulting in absolute negative mobility i e the response to an external force is always opposite to the direction of the force

can two chaotic systems give rise to order abstract the recently discovered parrondo s paradox claims that two losing games can result under random or periodic alternation of their dynamics in a winning game losing losing winning in this paper we follow parrondo s philosophy of combining different dynamics and we apply it to the case of one dimensional quadratic maps we prove that the periodic mixing of two chaotic dynamics originates an ordered dynamics in certain cases this provides an explicit example theoretically and numerically tested of a different parrondian paradoxical phenomenon chaos chaos order

lyapunov exponents noise induced synchronization and parrondo s paradox we show that lyapunov exponents of a stochastic system when computed for a specific realization of the noise process are related to conditional lyapunov exponents in deterministic systems we propose to use the term stochastically induced regularity instead of noise induced synchronization and explain the reason why the nature of stochastically induced regularity is discussed in some instances it is a dynamical analog of parrondo s paradox

counterintuitive behaviour in games based on spin models a large class of games based on spin models is analysed for these games the long time gain can be calculated exactly it is shown that the mixing of two losing strategies may lead to a winning one but also that the mixing of two winning ones may lead to a loss also the mixing of a losing and a winning strategy may give unexpected results this behaviour is due to two general features i the class of games is such that mixing the playing of two games is equivalent to playing a third one and ii the break even boundaries for these games are curved

finiteness of integral values for the ratio of two linear recurrences let f n n n g n n n be linear recurrent sequences in this paper we are concerned with the well known diophantine problem of the finiteness of the set of natural numbers n such that f n g n is an integer in this direction we have for instance a deep theorem of van der poorten solving a conjecture of pisot he established that if coincides with n then f n g n n n is itself a linear recurrence sequence here we shall prove that if is an infinite set then there exists a nonzero polynomial p such that p n f n g n coincides with a linear recurrence for all n in a suitable arithmetic progression examples like f n 2n 2 g n n 2n 2 n show that our conclusion is in a sense best possible in the proofs we introduce a new method to cope with a notorious crucial difficulty related to the existence of a so called dominant root in an appendix we shall also prove a zero density result for in the cases when the polynomial p cannot be taken a constant

adaptive nonlinear manifolds and their applications to pattern recognition dimensionality reduction has long been associated with retinotopic mapping for understanding cortical maps multisensory information is processed fused and mapped to an essentially 2 d cortex in an information preserving manner data processing and projection techniques inspired by this biological mechanism are playing an increasingly important role in pattern recognition computational intelligence data mining information retrieval and image recognition dimensionality reduction involves reduction of features or volume of data and has become an essential step of information processing in many fields the topic of manifold learning has recently attracted a great deal of attention and a number of advanced techniques for extracting nonlinear manifolds and reducing data dimensions have been proposed from statistics geometry theory and adaptive neural networks this paper provides an overview of this challenging and emerging topic and discusses various recent methods such as self organizing map som kernel pca principal manifold isomap local linear embedding and laplacian eigenmap many of them can be considered in a learning manifold framework the paper further elaborates on the biologically inspired som model and its metric preserving variant visom under the framework of adaptive manifold and their applications in dimensionality reduction with face recognition are investigated the experiments demonstrate that adaptive visom based methods produce markedly improved performance over the others due to their metric scaling and preserving properties along the nonlinear manifold

misiurewicz points in one dimensional quadratic maps abstract misiurewicz points are constituted by the set of unstable or repellent points sometimes called the set of exceptional points these points which are preperiodic and eventually periodic play an important role in the ordering of hyperbolic components of one dimensional quadratic maps in this work we use graphic tools to analyse these points by measuring their preperiods and periods and by ordering and classifying them

deterministic and random synthesis of discrete chaos in this paper two anticontrol algorithms for synthesis of discrete chaos are introduced in these algorithms the control parameter of a discrete dynamical system is switched either randomly or in a deterministic way between two or more values corresponding to periodic motions the result being chaotic behavior these algorithms require no knowledge of specific mathematical properties of the underlying map modeling the system the existence of chaos is demonstrated using various tools including graphical iteration histogram lyapunov exponent and surrogate tests in this paper these very simple and implementable chaotifiers are applied to the logistic map

construction of novel stochastic matrices for analysis of parrondo s paradox abstract in parrondo s paradox a winning strategy is formed either by playing two losing games randomly or alternating them periodically the paradox is commonly analyzed using stochastic matrices in this paper we modify the stochastic matrices to allow a more systematic introduction of bias into fair processes while retaining the use of simple matrix operations throughout the analysis

artificial immune multi objective sar image segmentation with fused complementary features artificial immune systems ais are the computational systems inspired by the principles and processes of the vertebrate immune system ais based algorithms typically mimic the human immune system s characteristics of learning and adaptability to solve some complicated problems here an artificial immune multi objective optimization framework is formulated and applied to synthetic aperture radar sar image segmentation the important innovations of the framework are listed as follows 1 an efficient and robust immune multi objective optimization algorithm is proposed which has the features of adaptive rank clones and diversity maintenance by k nearest neighbor list 2 besides two conflicting fuzzy clustering validity indices are incorporated into this framework and optimized simultaneously and 3 moreover an effective fused feature set for texture representation and discrimination is constructed and researched which utilizes both the gabor filter s ability to precisely extract texture features in low and mid frequency components and the gray level co occurrence probability s glcp ability to measure information in high frequency two experiments with synthetic texture images and sar images are implemented to evaluate the performance of the proposed framework in comparison with other five clustering algorithms fuzzy c means fcm single objective genetic algorithm soga self organizing map som wavelet domain hidden markov models hmtseg and spectral clustering ensemble sce experimental results show the proposed framework has obtained the better performance in segmenting sar images than other five algorithms and behaves insensitive to the speckle noise

switching induced turing instability we propose a mechanism for inducing a turing instability in systems whose only stable state is pattern free and homogeneous global alternation between two dynamics each of which has the same homogeneous stable state may induce a turing instability that leads to pattern formation we determine what kind of alternation can drive the system to a turing instability and show that the appearance of the induced spatiotemporal structure depends on the ratio of two characteristic times one determined by the external forcing and the other by the instability that drives the system at short times the mechanism is illustrated by means of theoretical calculations and numerical simulations on two well known biological models that are relevant in morphogenesis

influence functions for a linear subspace method a linear subspace method which is one of discriminant methods was proposed as a pattern recognition method and was studied because the method and its extensions do not encounter the situation of singular covariance matrix we need not consider extensions such as generalized ridge discrimination even when treating a high dimensional and sparse dataset in addition classifiers based on a multi class discrimination method can function faster because of the simple decision procedure therefore they have been widely used for face and speech recognition however it seems that sufficient studies have not been conducted about the statistical assessment of training data performance for classifier in terms of prediction accuracy in statistics influence functions for statistical discriminant analysis were derived and the assessments for analysis result were performed these studies indicate that influence functions are useful for detecting large influential observations for analysis results by using discrimination methods and they contribute to enhancing the performance of a target classifier in this paper we propose the statistical diagnostics of a classifier on the basis of an influence function by using the linear subspace method we first propose the discriminant score for the linear subspace method next we derive the sample and empirical influence functions for the average of the discriminant scores to detect large influential observations for the misclassification rate finally through a simulation study and a real data analysis we detect the outliers in the training dataset using the derived influence function and develop a highly sophisticated classifier in the linear subspace method highlightswe propose the discriminant score for a clafic method we derive the influence functions for the score and its average because we can enhance the classifier in the clafic method with them we show the effectiveness of our approach through a clear simulation study

parrondo s paradox and complementary parrondo processes abstract parrondo s paradox has gained a fair amount of attention due to it being counter intuitive given two stochastic processes both of which are losing in nature it is possible to have an overall net increase in capital by periodically or randomly alternating between the two processes in this paper we analyze the paradox with a different approach in which we start with one process and seek to derive its complementary process we will also state the conditions required for this to occur possible applications of our results include the development of future models based on the paradox