numerical solution of compartmental models by meshless and finite difference methods abstract in this paper an operator splitting method based on meshless and finite difference procedures is being considered for numerical solution of compartmental epidemiological population models with and without diffusion a one step explicit meshless procedure is also applied for the numerical solution of the nonlinear model the compartmental model contains susceptible vaccinated exposed infected and recovered sveir classes of the population effects of the diffusion on the simulation results of the model are being studied stability of endemic equilibrium point along with bifurcation analysis has also been investigated due to non availability of the exact solution the numerical results obtained are mutually compared and their correctness is being verified by the theoretical results as well

a combinatorial problem on trapezoidal words in this paper we investigate some combinatorial properties concerning the family of the so called trapezoidal words trapezoidal words considered in de luca theoret comput sci 218 1999 13 39 are finite words over the two letter alphabet a a b whose subword complexity has the same behaviour as that of finite sturmian words in de luca theoret comput sci 218 1999 13 39 it has been proved that the family of finite sturmian words is properly contained in that one of trapezoidal words we carry on with the studying of the family of trapezoidal words and in particular of its relation with that one of finite sturmian words

the analysis of a fractional factorial experiment with censored data using iterative least squares schmee and hahn 1979 suggested iterative least squares as a simple method for analyzing censored data the application of this method to the analysis of the results of a fractional factorial experiment with censored observations is described and illustrated in this paper

computing the error linear complexity spectrum of a binary sequence of period 2 sup n binary sequences with high linear complexity are of interest in cryptography the linear complexity should remain high even when a small number of changes are made to the sequence the error linear complexity spectrum of a sequence reveals how the linear complexity of the sequence varies as an increasing number of the bits of the sequence are changed we present an algorithm which computes the error linear complexity for binary sequences of period spl lscr 2 sup n using o spl lscr log spl lscr sup 2 bit operations the algorithm generalizes both the games chan 1983 and stamp martin 1993 algorithms which compute the linear complexity and the k error linear complexity of a binary sequence of period spl lscr 2 sup n respectively we also discuss an application of an extension of our algorithm to decoding a class of linear subcodes of reed muller codes

asymptotic subword complexity of fixed points of group substitutions the subword complexity of fixed points of some types of substitutions was studied by various authors here we introduce a family of substitutions arising from multiplication tables of finite groups and other similar structures and analyze their subword complexity

pattern formation of a spatial predator prey system abstract there are random and directed movements of predator and prey populations in many natural systems which are strongly influenced and modified by spatial factors to investigate how these migration directed movement and diffusion random movement affect predator prey systems we have studied the spatiotemporal complexity in a predator prey system with holling tanner form a theoretical analysis of emerging spatial pattern is presented and wavelength and pattern speed are calculated at the same time we present the properties of pattern solutions the results of numerical simulations show that migration has prominent effect on the pattern formation of the population i e changing turing pattern into traveling pattern this study suggests that modelling by migration and diffusion in predator prey systems can account for the dynamical complexity of ecosystems

numerical study of an influenza epidemic model with diffusion abstract a diffusive epidemic model is investigated with a view to describe the transmission of influenza as an epidemic the equations are solved numerically using the splitting method under different initial distribution of population density it is shown that the initial population distribution and diffusion play an important role for spread of disease it is also shown that interventions medical and nonmedical significantly slow down the spread of disease stability of equilibria of the numerical solutions are also established

analysis of censored data from fractionated experiments a bayesian approach abstract censored data arise naturally in industrial experiments whose observations are failure times or measurements with mixed continuous categorical outcomes when censored data are observed from a fractionated experiment likelihood based estimates quite often do not exist especially when the opportunity for improvement is great to circumvent this problem we propose a bayesian analysis strategy that has a straightforward implementation using the data augmentation and monte carlo em algorithms for nonregular designs with complex aliasing patterns a modified analysis strategy is proposed that substantially reduces the computation needed for model selection the proposed strategy is illustrated using data from three real industrial experiments for these data sets the analysis results are fairly insensitive to the specification of the prior

alternating subspace spanning resampling to accelerate markov chain monte carlo simulation this article provides a simple method to accelerate markov chain monte carlo sampling algorithms such as the data augmentation algorithm and the gibbs sampler via alternating subspace spanning resampling assr the assr algorithm often shares the simplicity of its parent sampler but has dramatically improved efficiency the methodology is illustrated with bayesian estimation for analysis of censored data from fractionated experiments the relationships between assr and existing methods are also discussed

lee metric bch codes and their application to constrained and partial response channels shows that each code in a certain class of bch codes over gf p specified by a code length n spl les p sup m 1 and a runlength r spl les p 1 2 of consecutive roots in gf p sup m has minimum lee distance spl ges 2r for the very high rate range these codes approach the sphere packing bound on the minimum lee distance furthermore for a given r the length range of these codes is twice as large as that attainable by berlekamp s 1984 extended negacyclic codes the authors present an efficient decoding procedure based on euclid s algorithm for correcting up to r 1 errors and detecting r errors that is up to the number of lee errors guaranteed by the designed minimum lee distance 2r bounds on the minimum lee distance for r spl ges p 1 2 are provided for the reed solomon case i e when the bch code roots are in gf p the authors present two applications first lee metric bch codes can be used for protecting against bitshift errors and synchronization errors caused by insertion and or deletion of zeros in d k constrained channels second the code construction with its decoding algorithm can be formulated over the integer ring providing an algebraic approach to correcting errors in partial response channels where matched spectral null codes are used

words and special factors in this paper we consider sets of factors of a given finite word over a finite alphabet which permit us to reconstruct the entire word this analysis is based on the notion of special factor a factor u of a finite word w is called right resp left special if there exist two distinct letters x and y such that ux uy resp xu yu are factors of w a factor is bispecial if it is right and left special a proper box of w is any factor of w of the kind asb with a b letters and s a bispecial factor of w the initial resp terminal box of w is the shortest prefix resp suffix of w which is an unrepeated factor a box is called maximal if it is not a proper factor of another box the main result of the paper is the following theorem maximal box theorem any finite word w is uniquely determined by the initial box the terminal box and the set of maximal boxes a consequence is that a finite word w is uniquely determined by the knowledge of its factors up to the length n max rw kw 1 where kw is the length of the terminal box and rw is the minimal natural number for which there is no right special factor of length rw some structural properties of boxes are studied another important combinatorial notion is that of superbox a superbox is any factor of w of the kind asb with a b letters and such that s is a repeated factor whereas as and sb are unrepeated factors a theorem for superboxes similar to the maximal box theorem is proved some algorithms allowing us to construct boxes and superboxes and conversely to reconstruct the word are given in this combinatorial frame we give an upper and a lower bound to the number of states of a minimal deterministic automaton recognizing the set of the factors of w these bounds are sharper than the known bounds

analysis of interval censored data from fractionated experiments using covariance adjustment censored data are commonly observed in industrial experiments such as for life testing and reliability improvement analyzing censored data from highly fractionated experiments presents a challenging problem to experimenters because many traditional methods become inadequate motivated by the data from a fluorescent lamp experiment we consider in this article analyzing censored data from highly fractionated experiments using covariance adjustment based on multivariate multiple regression models which make use of the joint distribution of multivariate response variables the bayesian approach is taken for the main statistical inference the posterior distribution of the parameters is obtained using the data augmentation algorithm we illustrate the methodology with the fluorescent lamp experiment data with the real example and a simulation study we show that covariance adjustment can lead to both dramatic variance reduction and possible bias reduction

some combinatorial properties of sturmian words abstract in this paper we give a characterization of finite sturmian words by palindrome words which generalizes a property of the fibonacci words we prove that the set st of finite sturmian words coincides with the set of the factors of all the words w such that w ab cxy with a b c palindromes x y a b and x y moreover using this result we prove that st is equal to the set of the factors of all words w having two periods p and q which are coprimes and such that w p q 2 several other combinatorial properties concerning special and bispecial elements of st are shown as a consequence we give a new and purely combinatorial proof of the enumeration formula of st

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

sturmian words structure combinatorics and their arithmetics abstract we prove some new results concerning the structure the combinatorics and the arithmetics of the set per of all the words w having two periods p and q p q which are coprimes and such that w p q 2 a basic theorem relating per with the set of finite standard sturmian words was proved in de luca and mignosi 1994 the main result of this paper is the following simple inductive definition of per the empty word belongs to per if w is an already constructed word of per then also aw and bw belong to per where denotes the operator of palindrome left closure i e it associates to each word u the smallest palindrome word u having u as a suffix we show that by this result one can construct in a simple way all finite and infinite standard sturmian words we prove also that up to the automorphism which interchanges the letter a with the letter b any element of per can be codified by the irreducible fraction p q this allows us to construct for any n 0 a natural bijection that we call farey correspondence of the set of the farey series of order n 1 and the set of special elements of length n of the set st of all finite sturmian words finally we introduce the concepts of farey tree and farey monoid this latter is obtained by defining a suitable product operation on the developments in continued fractions of the set of all irreducible fractions p q

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

reliable communication over channels with insertions deletions and substitutions a new block code is introduced which is capable of correcting multiple insertion deletion and substitution errors the code consists of nonlinear inner codes which we call watermark codes concatenated with low density parity check codes over nonbinary fields the inner code allows probabilistic resynchronization and provides soft outputs for the outer decoder which then completes decoding we present codes of rate 0 7 and transmitted length 5000 bits that can correct 30 insertion deletion errors per block we also present codes of rate 3 14 and length 4600 bits that can correct 450 insertion deletion errors per block

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea

pseudopalindrome closure operators in free monoids we consider involutory antimorphisms of a free monoid a and their fixed points called palindromes or pseudopalindromes a palindrome reduces to a usual palindrome when is the reversal operator for any word w a the right resp left palindrome closure of w is the shortest palindrome having w as a prefix resp suffix we prove some results relating palindrome closure operators with periodicity and conjugacy and derive some interesting closure properties for the languages of finite sturmian and episturmian words in particular a finite word w is sturmian if and only if both its palindromic closures are so moreover in such a case both the palindromic closures of w share the same minimal period of w a new characterization of finite sturmian words follows in terms of periodicity and special factors of their palindromic closures some weaker results can be extended to the episturmian case by using the right palindrome closure we extend the construction of standard episturmian words via directive words in this way one obtains a family of infinite words called standard words which are morphic images of episturmian words as well as a wider family of infinite words including the thue morse word on two symbols

a note on double insertion deletion correcting codes by using a run length representation of sequences ways to determine suband supersequences are discussed this is then used in determining the number of sub and supersequences of a sequence after double insertions or deletions it is also used in creating subsequence supersequence books that are searched to find new double insertion deletion correcting code books with higher cardinalities than those already known

lower bounds for restricted read once parity branching programs we prove the first lower bounds for restricted read once parity branching programs with unlimited parity nondeterminism where for each input the variables may be tested according to several orderings namely sums of k graph driven bp1s with polynomial size graph orderings are under consideration we prove lower bounds for the characteristic function of linear codes we generalize a lower bound by savick and sieling see p savick d sieling a hierarchy result for read once branching programs with restricted parity nondeterminism theoret comput sci 340 2005 594 605 and recent results on graph driven parity branching programs

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

insertion deletion correction with spectral nulls levenshtein 1966 proposed a class of single insertion deletion correcting codes based on the number theoretic construction due to varshamov and tenengolt s 1965 we present several interesting results on the binary structure of these codes and their relation to constrained codes with nulls in the power spectral density function one surprising result is that the higher order spectral null codes of immink and beenker 1987 are sub codes of balanced levenshtein codes other spectral null sub codes with similar coding rates may also be constructed we furthermore present some coding schemes and spectral shaping markers which alleviate the fundamental restriction on levenshtein s codes that the boundaries of each codeword should be known before insertion deletion correction can be effected

on the number of subsequences when deleting symbols from a string we consider the problem of finding the number of subsequences when deleting symbols from a string we present a framework to find closed form expressions for the number of subsequences and use it to prove the first explicit formulas for and the first formulas for nonbinary alphabets we also present the first efficient algorithm to compute the number of subsequences for any string number of deletions and alphabet size

complexity for finite factors of infinite sequences abstract we define several notions of language complexity for finite words and use them to define and compute some new complexity functions for infinite sequences in particular they give a new characterization of sturmian sequences and discriminate between sturmian sequences with bounded or unbounded partial quotients

on the state complexity of closures and interiors of regular languages with subwords and superwords the downward and upward closures of a regular language l are obtained by collecting all the subwords and superwords of its elements respectively the downward and upward interiors of l are obtained dually by collecting words having all their subwords and superwords in l respectively we provide lower and upper bounds on the size of the smallest automata recognizing these closures and interiors we also consider the computational complexity of decision problems for closures of regular languages

sturmian words lyndon words and trees abstract we prove some new combinatorial properties of the set per of all words w having two periods p and q which are coprimes and such that w p q 2 4 3 we show that aperb a b st lynd where st is the set of the finite factors of all infinite sturmian words and lynd is the set of the lyndon words on the alphabet a b it is also shown that aperb a b cp where cp is the set of christoffel primitive words such words can be defined in terms of the slope of the words and of their prefixes 1 from this result one can derive in a different way by using a theorem of borel and laubie that the elements of the set aperb are lyndon words we prove the following correspondence between the ratio p q of the periods p q p q of w per a a b and the slope w b 1 w a 1 of the corresponding christoffel primitive word awb if p q has the development in continued fractions 0 h 1 h n 1 h n 1 then has the development in continued fractions 0 h n h 2 h 1 1 this and other related results can be also derived by means of a theorem which relates the developments in continued fractions of the stern brocot and the raney numbers of a node in a complete binary tree however one needs some further results more precisely we label the binary tree with standard pairs standard tree christoffel pairs christoffel tree and the elements of per farey tree the main theorem is the following if the node w is labeled by the standard pair u v by the christoffel pair x y and by w per then uv wab xy awb the stern brocot number sb w is equal to the slope of the standard word uv and of the christoffel word xy while the raney number ra w is equal to the ratio of the minimal period of wa and the minimal period of wb some further auxiliary results are also derived

algorithms for subsequence combinatorics a subsequence is obtained from a string by deleting any number of characters thus in contrast to a substring a subsequence is not necessarily a contiguous part of the string counting subsequences under various constraints has become relevant to biological sequence analysis to machine learning to coding theory to the analysis of categorical time series in the social sciences and to the theory of word complexity we present theorems that lead to efficient dynamic programming algorithms to count 1 distinct subsequences in a string 2 distinct common subsequences of two strings 3 matching joint embeddings in two strings 4 distinct subsequences with a given minimum span and 5 sequences generated by a string allowing characters to come in runs of a length that is bounded from above

some characterizations of finite sturmian words in this paper we give some new characterizations of words which are finite factors of sturmian words an enumeration formula for primitive finite sturmian words is given moreover we provide two linear time algorithms to recognize whether a finite word is sturmian

concordance and consensus this paper deals with the measurement of concordance and the construction of consensus in preference data either in the form of preference rankings or in the form of response distributions with likert items we propose a set of axioms of concordance in preference orderings and a new class of concordance measures the measures outperform classic measures like kendall s t and w and spearman s r in sensitivity and apply to large sets of orderings instead of just to pairs of orderings for sets of n orderings of n items we present very efficient and flexible algorithms that have a time complexity of only o nn 2 remarkably the algorithms also allow for fast calculation of all longest common subsequences of the full set of orderings we experimentally demonstrate the performance of the algorithms a new and simple measure for assessing concordance on likert items is proposed

analysis of censored data from highly fractionated experiments although censored including interval censored data may be easier or less costly to collect than complete data they contain less information and are harder to analyze existing methodology is inadequate for analyzing such data from highly fractionated experiments we propose an iterative method that provides a simple and flexible way to consider many models simultaneously the method s simplicity makes it easy to implement with existing software results in computational savings and promotes experimenter involvement we demonstrate the procedure by reanalyzing data from two real experiments a simulation study also demonstrates its superiority over some existing methods including taguchi s minute accumulating analysis

local periods and binary partial words an algorithm the study of the combinatorial properties of strings of symbols from a finite alphabet also referred to as words is profoundly connected to numerous fields such as biology computer science mathematics and physics research in combinatorics on words goes back roughly a century there is a renewed interest in combinatorics on words as a result of emerging new application areas such as molecular biology partial words were recently introduced in this context the motivation behind the notion of a partial word is the comparison of genes or proteins alignment of two genes or two proteins can be viewed as a construction of partial words that are said to be compatible while a word can be described by a total function a partial word can be described by a partial function more precisely a partial word of length n over a finite alphabet a is a partial function from 1 n into a elements of 1 n without an image are called holes a word is just a partial word without holes the notion of period of a word is central in combinatorics on words in the case of partial words there arc two notions one is that of period the other is that of local period this paper extends to partial words with one hole the well known result of guibas and odlyzko which states that for every word u there exists a word v of same length as u over the alphabet 0 1 such that the set of all periods of u coincides with the set of all periods of v our result states that for every partial word u with one hole there exists a partial word v of same length as u with at most one hole over the alphabet 0 1 such that the set of all periods of u coincides with the set of all periods of v and the set of all local periods of u coincides with the set of all local periods of v to prove our result we use the technique of halava harju and ilie which they used to characterize constructively the set of periods of a given word as a consequence of our constructive proof we obtain a linear time algorithm which given a partial word with one hole computes a partial word with at most one hole over the alphabet 0 1 with the same length and the same sets of periods and local periods a world wide web server interface at http www uncg edu mat algbin has been established for automated use of the program

a periodicity result of partial words with one hole abstract the study of the combinatorial properties of strings of symbols from a finite alphabet also referred to as words is profoundly connected to numerous fields such as biology computer science mathematics and physics partial words have long been known they have been around in information and coding theory as well as molecular biology while a word can be described by a total function a partial word can be described by a partial function more precisely a partial word of length n over a finite alphabet a is a partial function from 0 n 1 into a elements of n 1 without an image are called holes a word is just a partial word without holes the notion of period of a word is central in combinatorics on words in the case of partial words there are two notions one is that of period and the other is that of local period there are many fundamental results on periods of words among them is the well known periodicity result of fine and wilf which intuitively determines how far two periodic events have to match in order to guarantee a common period this result was extended to partial words with one hole by berstel and boasson we can define the set per o of all words of maximal length for which fine and wilf s result does not apply similarly we can define the set per 1 of all partial words with one hole of maximal length for which berstel and boasson s result does not apply it is well known that per o contains a unique word up to a renaming that is binary in this note we extend this result to per 1

versatile string kernels this paper proposes a class of string kernels that can handle a variety of subsequence based features slight adaptations of the basic algorithm allow for weighing subsequence lengths restricting or soft penalizing gap size character weighing and soft matching of characters an easy extension of the kernels allows for comparing run length encoded strings with a time complexity that is independent of the length of the original strings such kernels have applications in image processing computational biology in demography and in comparing partial rankings

graph connectivity partial words and a theorem of fine and wilf the problem of computing periods in words or finite sequences of symbols from a finite alphabet has important applications in several areas including data compression string searching and pattern matching algorithms the notion of period of a word is central in combinatorics on words there are many fundamental results on periods of words among them is the well known and basic periodicity result of fine and wilf which intuitively determines how far two periodic events have to match in order to guarantee a common period more precisely any word with length at least p q gcd p q having periods p and q has also period the greatest common divisor of p and q gcd p q moreover the bound p q gcd p q is optimal since counterexamples can be provided for words of smaller length partial words or finite sequences that may contain a number of do not know symbols or holes appear in natural ways in several areas of current interest such as molecular biology data communication dna computing etc any long enough partial word with h holes and having periods p q has also period gcd p q in this paper we give closed formulas for the optimal bounds l h p q in the case where p 2 and also in the case where q is large in addition we give upper bounds when q is small and h 3 4 5 6 or 7 no closed formulas for l h p q were known except for the cases where h 0 1 or 2 our proofs are based on connectivity in graphs associated with partial words a world wide web server interface has been established at www uncg edu mat research finewilf3 for automated use of a program which given a number of holes h and two periods p and q computes the optimal bound l h p q and an optimal word for that bound a partial word u with h holes of length l h p q 1 is optimal if p and q are periods of u but gcd p q is not a period of u

neighborhood counting measure and minimum risk metric the neighborhood counting measure is a similarity measure based on the counting of all common neighborhoods in a data space the minimum risk metric mrm is a distance measure based on the minimization of the risk of misclassification the paper by argentini and blanzieri refutes a remark about the time complexity of mrm and presents an experimental comparison of mrm and ncm this paper is a response to the paper by argentini and blanzieri the original remark is clarified by a combination of theoretical analysis of different implementations of mrm and experimental comparison of mrm and ncm using straightforward implementations of the two measures

an improvement to levenshtein s upper bound on the cardinality of deletion correcting codes we consider deletion correcting codes over a q ary alphabet it is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions to obtain asymptotic upper bounds on code size we apply a packing argument to channels that perform different mixtures of insertions and deletions even though the set of codes is identical for all of these channels the bounds that we obtain vary prior to this paper only the bounds corresponding to the all insertion case and the all deletion case were known we recover these as special cases the bound from the all deletion case due to levenshtein has been the best known for more than 45 years our generalized bound is better than levenshtein s bound whenever the number of deletions to be corrected is larger than the alphabet size

some aspects of analysis of covariance an account from first principles is given of a number of aspects of analysis of covariance six different meanings of analysis of covariance are outlined and the history of this technique is sketched briefly the development of the key formulae from the method of least squares is described and generalizations to other distributions in the exponential family are mentioned special problems of application in randomized experiments and in observational studies are discussed finally the decomposition of regression relations is considered along with components of covariance

subword complexity of uniform d0l words over finite groups we deal with the subword complexity of uniform d0l words obtained from group substitutions our main interest is whether the subword complexity is almost proportional to the length of the factor we find necessary and sufficient conditions for that for some cases we show that this is impossible

rich sturmian and trapezoidal words in this paper we explore various interconnections between rich words sturmian words and trapezoidal words rich words first introduced by the second and third authors together with j justin and s widmer constitute a new class of finite and infinite words characterized by having the maximal number of palindromic factors every finite sturmian word is rich but not conversely trapezoidal words were first introduced by the first author in studying the behavior of the subword complexity of finite sturmian words unfortunately this property does not characterize finite sturmian words in this note we show that the only trapezoidal palindromes are sturmian more generally we show that sturmian palindromes can be characterized either in terms of their subword complexity the trapezoidal property or in terms of their palindromic complexity we also obtain a similar characterization of rich palindromes in terms of a relation between palindromic complexity and subword complexity

on average sequence complexity in this paper we study the average behavior of the number of distinct substrings in a text of size n over an alphabet of cardinality k this quantity is called the complexity index and it captures the richness of the language used in a sequence for example sequences with low complexity index contain a large number of repeated substrings and they eventually become periodic e g tandem repeats in a dna sequence in order to identify unusually low or high complexity strings one needs to determine how far are the complexities of the strings under study from the average or maximum string complexity while the maximum string complexity was studied quite extensively in the past to the best of our knowledge there are no results concerning the average complexity we first prove that for a sequence generated by a mixing model which includes markov sources the average complexity is asymptotically equal to n2 2 which coincides with the maximum string complexity however for a memoryless source we establish a more precise result namely the average string complexity is n2 2 n logk n 1 1 ln k k logkn o 1 n where 0 577 and k x is a periodic function with a small amplitude for small alphabet size

some combinatorial properties of the thue morse sequence and a problem in semigroups abstract some combinatorial properties of the special factors of the thue morse sequence in a two letter alphabet are considered an application of this analysis to a problem in semigroups is given

semiperiodic words and root conjugacy a factor u of a word w is called right special if there exist two distinct letters a and b such that both ua and ub are factors of w left special factors are defined symmetrically by rw resp lw we denote the minimal natural number such that there is no right resp left special factor of w of length rw resp lw moreover hw resp kw denotes the length of the shortest prefix resp suffix which cannot be extended on the left resp right in w the parameters rw lw hw and kw give interesting information on the structure of the word w we consider the class of all finite words w such that rw hw these words are called semiperiodic any periodic word is semiperiodic whereas the converse is not generally true several characterizations of semiperiodic words can be given in particular a word w is semiperiodic if and only if it has a period p w rw a further characterization of semiperiodic words relates with their infinite extensions from this characterization one derives the following result deeply related to the theorem of fine and wilf if w is a semiperiodic word having two periods p q w rw then also d gcd p q is a period of w the root rw of a word w is its prefix whose length is equal to the minimal period of w two words u and v are root conjugate if their roots ru and rv are conjugate one of the main results of the paper is the following let w be a semiperiodic word a word v has the same set of factors of length 1 rw of w if and only if v is semiperiodic and root conjugate with w some applications and extensions of this result are proved

regular hilberg processes an example of processes with a vanishing entropy rate a regular hilberg process is a stationary process that satisfies both a hyperlogarithmic growth of maximal repetition and a power law growth of topological entropy which are a kind of dual conditions the hyperlogarithmic growth of maximal repetition has been experimentally observed for texts in natural language whereas the power law growth of topological entropy implies a vanishing shannon entropy rate and thus probably does not hold for natural language in this paper we provide a constructive example of regular hilberg processes which we call random hierarchical association rha processes our construction does not apply the standard cutting and stacking method for the constructed rha processes we demonstrate that the expected length of any uniquely decodable code is the orders of magnitude larger than the shannon block entropy of the ergodic component of the rha process our proposition supplements the classical result by shields concerning nonexistence of universal redundancy rates

on the subword complexity of thue morse polynomial extractions let the subword complexity of a sequence u u n n 0 over a finite set s be the function m p u m where p u m is the number of distinct blocks of length m in u let t t n n 0 denote the thue morse sequence in this paper we study the complexity of the sequences t h t h n n 0 when h n q n is a polynomial with h n n in particular we solve an open problem of allouche and shallit regarding t n 2 n 0 we also study the vector space over z 2z spanned by the sequences t h

construction of fixed length insertion deletion correcting runlength limited codes an algorithm is presented for the construction of fixed length insertion deletion correcting runlength limited rll codes in this construction binary d k constrained codewords are generated by codewords of a q ary lee metric based code it is shown that this new construction always yields better codes than known constructions the use of a q ary lee 1987 metric code q odd is based on the assumption that an error insertion deletion or peak shift has maximal size q 1 2 it is shown that a decoding algorithm for the lee metric code can be extended so that it can also be applied to insertion deletion correcting rll codes furthermore such an extended algorithm can also correct some error patterns containing errors of size more than q 1 2 as a consequence if s denotes the maximal size of an error then in some cases the alphabet size of the generating code can be s 1 instead of 2 spl middot s 1

diffusion has no influence on the global asymptotical stability of the lotka volterra prey predator model incorporating a constant number of prey refuges by constructing a suitable lyapunov function we obtain the global asymptotical stability of the lotka volterra prey predator model incorporating a constant number of prey refuges and diffusion it is shown that diffusion has no influence on the global asymptotical stability of the system with homogeneous neumann boundary condition

partial words and a theorem of fine and wilf revisited a word of length n over a finite alphabet a is a map from 0 n 1 into a a partial word of length n over a is a partial map from 0 n 1 into a in the latter case elements of 0 n1 without image are called holes a word is just a partial word without holes in this paper we extend a fundamental periodicity result on words due to fine and wilf to partial words with two or three holes this study was initiated by berstel and boasson for partial words with one hole partial words are motivated by molecular biolog

enumeration and structure of trapezoidal words trapezoidal words are words having at most n 1 distinct factors of length n for every n 0 they therefore encompass finite sturmian words we give combinatorial characterizations of trapezoidal words and exhibit a formula for their enumeration we then separate trapezoidal words into two disjoint classes open and closed a trapezoidal word is closed if it has a factor that occurs only as a prefix and as a suffix otherwise it is open we investigate open and closed trapezoidal words in relation with their special factors we prove that sturmian palindromes are closed trapezoidal words and that a closed trapezoidal word is a sturmian palindrome if and only if its longest repeated prefix is a palindrome we also define a new class of words semicentral words and show that they are characterized by the property that they can be written as uxyu for a central word u and two different letters x y finally we investigate the prefixes of the fibonacci word with respect to the property of being open or closed trapezoidal words and show that the sequence of open and closed prefixes of the fibonacci word follows the fibonacci sequence

a generalized palindromization map in free monoids the palindromization map j in a free monoid a was introduced in 1997 by the first author in the case of a binary alphabet a and later extended by other authors to arbitrary alphabets acting on infinite words j generates the class of standard episturmian words including standard arnoux rauzy words in this paper we generalize the palindromization map starting with a given code x over a the new map j x maps x to the set pal of palindromes of a in this way some properties of j are lost and some are saved in a weak form when x has a finite deciphering delay one can extend j x to x w generating a class of infinite words much wider than standard episturmian words for a finite and maximal code x over a we give a suitable generalization of standard arnoux rauzy words called x ar words we prove that any x ar word is a morphic image of a standard arnoux rauzy word and we determine some suitable linear lower and upper bounds to its factor complexity for any code x we say that j x is conservative when j x x x we study conservative maps j x and conditions on x assuring that j x is conservative we also investigate the special case of morphic conservative maps j x i e maps such that email protected email protected email protected email protected email protected for an injective morphism f finally we generalize j x by replacing palindromic closure with q palindromic closure where q is any involutory antimorphism of a this yields an extension of the class of q standard words introduced by the authors in 2006

special factors and the combinatorics of suffix and factor automata the suffix automaton resp factor automaton of a finite word w is the minimal deterministic automaton recognizing the set of suffixes resp factors of w we study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w we derive formulae for the number of states of these automata we also characterize the languages l s a and l f a of words having respectively suffix automaton and factor automaton with the minimal possible number of states

bayesian analysis of systems of seemingly unrelated regression equations under a recursive extended natural conjugate prior density abstract a recursive extended natural conjugate prior density is proposed for systems of seemingly unrelated regression equations compared to other classes of extended natural conjugate prior densities it offers the advantage that analytical expressions are available for the prior covariance matrix of the regression coefficients the posterior analysis combines analytical and numerical techniques numerical integration is based on monte carlo importance sampling an application to a system of four wage equations for eec countries serves to evaluate different techniques discussed in the paper

palindrome complexity we study the palindrome complexity of infinite sequences on finite alphabets i e the number of palindromic factors blocks of given length occurring in a given sequence we survey the known results and obtain new results for some sequences in particular for rote sequences and for fixed points of primitive morphisms of constant length belonging to class p of hof knill simon we also give an upper bound for the palindrome complexity of a sequence in terms of its block complexity

on the combinatorics of finite words in this paper we consider a combinatorial method for the analysis of finite words recently introduced in colosimo and de luca special factors in biological strings preprint 97 42 dipt matematica univ di roma for the study of biological macromolecules the method is based on the analysis of right special factors of a given word a factor u of a word w is special if there exist at least two occurrences of the factor u in w followed on the right by two distinct letters we show that in the combinatorics of finite words two parameters play an essential role the first denoted by r represents the minimal integer such that there do not exist special factors of w of length r the second that we denote by k is the minimal length of a factor of w which cannot be extended on the right in a factor of w some new results are proved in particular a new characterization in terms of special factors and of r and k is given for the set per of all words w having two periods p and q which are coprimes and such that w p q 2

existence of traveling wave solutions for influenza model with treatment abstract to investigate the spreading speed of influenza and the influence of treatment on the spreading speed a reaction diffusion influenza model with treatment is established the existence of traveling wave solutions is shown by introducing an auxiliary system and applying the schauder fixed point theorem the non existence of traveling wave solutions is proved by a two sided laplace transform which needs a new approach for the prior estimate of exponential decay of traveling wave solutions

maximal repetition and zero entropy rate maximal repetition of a string is the maximal length of a repeated substring this paper investigates maximal repetition of strings drawn from stochastic processes strengthening previous results two new bounds for the almost sure growth rate of maximal repetition are identified an upper bound in terms of conditional renyi entropy of order gamma 1 given a sufficiently long past and a lower bound in terms of unconditional shannon entropy gamma 1 both the upper and the lower bound can be proved using an inequality for the distribution of recurrence time we also supply an alternative proof of the lower bound which makes use of an inequality for the expectation of subword complexity in particular it is shown that a power law logarithmic growth of maximal repetition with respect to the string length recently observed for texts in natural language may hold only if the conditional renyi entropy rate given a sufficiently long past equals zero according to this observation natural language cannot be faithfully modeled by a typical hidden markov process which is a class of basic language models used in computational linguistics

asymptotically good codes correcting insertions deletions and transpositions we present simple polynomial time encodable and decodable codes which are asymptotically good for channels allowing insertions deletions and transpositions as a corollary they achieve exponential error probability in a stochastic model of insertion deletion

conjugacy on partial words the study of the combinatorial properties of strings of symbols from a finite alphabet also referred to as words is profoundly connected to numerous fields such as biology computer science mathematics and physics in this paper we examine to which extent some fundamental combinatorial properties of words such as conjugacy remain true for partial words the motivation behind the notion of a partial word is the comparison of two genes alignment of two such strings can be viewed as a construction of two partial words that are said to be compatible this study on partial words was initiated by berstel and boasson

hierarchical structures in sturmian dynamical systems the paper is concerned with hierarchical stuctures in subshifis over a finite alphabet in particular we present a hierarchy based approach to sturmian systems this approach is then used to characterize the linearly repetitive sturmian systems among the sturmian systems by uniform positivity of certain weights more generally we discuss various bounds on weights and their relationship finally we combine hierarchies and bounds on a weights to study a thermodynamic formalism for lattice gas models associated to arbitrary linearly repetitive subshifts