leaf languages and string compression tight connections between leaf languages and strings compressed by straight line programs slps are established it is shown that the compressed membership problem for a language l is complete for the leaf language class defined by l via logspace machines a more difficult variant of the compressed membership problem for l is shown to be complete for the leaf language class defined by l via polynomial time machines as a corollary it is shown that there exists a fixed linear visibly pushdown language for which the compressed membership problem is pspace complete for xml languages it is shown that the compressed membership problem is conp complete furthermore it is shown that the embedding problem for slp compressed strings is hard for pp probabilistic polynomial time

interpolation of precipitation under topographic influence at different time scales 1 in this paper new methodologies for interpolating rainfall data in individual time intervals ranging from a day to a year using gaussian copulas and unsymmetrical v copulas with a variety of treatments of altitude as an exogenous variable are described for shorter time aggregations zeros were treated as censored variables for each selected time step the marginal distributions of precipitation amounts were modeled using nonparametric density estimators while the spatial dependence structures were estimated using a maximum likelihood methodology the methodology was compared to other common geostatistical interpolators such as ordinary kriging and external drift kriging several measures of bias and error structure have been used to assess the efficacy of the methods in a range of comparative split sampling studies the data set chosen for the study comprises daily precipitation time series over 41 years in three regions in germany measured at more than 1200 locations over a large area 126 144 km2 among the many findings in the paper the ones that stand out are i correlation between precipitation and topography increases with the length of time interval and is significantly improved by directional smoothing of topography ii the copula methods are superior to kriging methods in terms of quality of interpolation bias and uncertainty estimation iii the treatment of zeros as censored variables improves interpolation quality for daily and pentad values monthly and annual data in this region present no dry periods iv the copula methods yield full conditional distributions of estimates at a target point in an interval improving substantially on the simple uncertainty estimates derived from kriging and v the gauss copula in particular performs best overall in terms of computational efficiency combined with useful error profiles in the interpolations and of all methods is the most realistic in its error estimates

stochastic reconstruction and interpolation of precipitation fields using combined information of commercial microwave links and rain gauges for the reconstruction and interpolation of precipitation fields we present the application of a stochastic approach called random mixing generated fields are based on a data set consisting of rain gauge observations and path averaged rain rates estimated using commercial microwave link cml derived information precipitation fields are received as linear combination of unconditional spatial random fields where the spatial dependence structure is described by copulas the weights of the linear combination are optimized such that the observations and the spatial structure of the precipitation observations are reproduced the innovation of the approach is that this strategy enables the simulation of ensembles of precipitation fields of any size each ensemble member is in concordance with the observed path averaged cml derived rain rates and additionally reflects the observed rainfall variability along the cml paths the ensemble spread allows additionally an estimation of the uncertainty of the reconstructed precipitation fields the method is demonstrated both for a synthetic data set and a real world data set in south germany while the synthetic example allows an evaluation against a known reference the second example demonstrates the applicability for real world observations generated precipitation fields of both examples reproduce the spatial precipitation pattern in good quality a performance evaluation of random mixing compared to ordinary kriging demonstrates an improvement of the reconstruction of the observed spatial variability random mixing is concluded to be a beneficial new approach for the provision of precipitation fields and ensembles of them in particular when different measurement types are combined

compression of low entropy strings with lempel ziv algorithms we compare the compression ratio of the lempel ziv algorithms with the empirical entropy of the input string this approach makes it possible to analyze the performance of these algorithms without any assumption on the input and to obtain worst case results we show that in this setting the standard definition of optimal compression algorithm is not satisfactory in fact although lempel ziv algorithms are optimal according to the standard definition there exist families of low entropy strings which are not compressed optimally more precisely the compression ratio achieved by lz78 resp lz77 can be much higher than the zeroth order entropy h0 resp the first order entropy h1 for this reason we introduce the concept of lambda optimal algorithm an algorithm is lambda optimal with respect to hk if loosely speaking its compression ratio is asymptotically bounded by lambda times the kth order empirical entropy hk we prove that lz78 cannot be lambda optimal with respect to any hk with k geq 0 then we describe a new algorithm which combines lz78 with run length encoding rle and is 3 optimal with respect to h0 finally we prove that lz77 is 8 optimal with respect to h0 and that it cannot be lambda optimal with respect to hk for any k geq 1

constant delay traversal of grammar compressed graphs with bounded rank abstract we present a pointer based data structure for constant time traversal of the edges of an edge labeled alphabet directed hypergraph a graph where edges can be incident to more than two vertices and the incident vertices are ordered given as hyperedge replacement grammar g it is assumed that the grammar has a fixed rank maximal number of vertices connected to a nonterminal hyperedge and that each vertex of the represented graph is incident to at most one edge per direction precomputing the data structure needs o g r h space and o g r h 2 time where h is the height of the derivation tree of g and r is the maximal rank of a terminal edge occurring in the grammar

copula based geostatistical models for groundwater quality parameters 1 groundwater quality parameters exhibit considerable spatial variability geostatistical methods including the assessment of variograms are usually used to characterize this variability copulas offer an interesting opportunity to describe dependence structures for multivariate distributions bivariate empirical copulas can be used as an alternative to variograms and covariance functions for the description of the spatial variability rank correlations of these copulas express the strength of the dependence independently of the marginal distributions and thus offer an alternative to the variograms empirical copulas for four quality parameters chloride sulfate ph and nitrate obtained from a large scale groundwater quality measurement network in baden wurttemberg germany are calculated they indicate that the spatial dependence structure of the investigated parameters is not gaussian two theoretical copula based models are presented in this paper a gaussian and a non gaussian bootstrap based statistical tests using stochastic simulation of the multivariate distributions are used to investigate the appropriateness of the models according to the test results the gaussian copula is rejected for most of the parameters while the non gaussian alternative is not rejected in most cases

beyond the poisson renewal process a tutorial survey after sketching the basic principles of renewal theory and recalling the classical poisson process we discuss two renewal processes characterized by waiting time laws with the same power asymptotics defined by special functions of mittag leffler and of wright type we compare these three processes with each other

tree compression with top trees we introduce a new compression scheme for labeled trees based on top trees our compression scheme is the first to simultaneously take advantage of internal repeats in the tree as opposed to the classical dag compression that only exploits rooted subtree repeats while also supporting fast navigational queries directly on the compressed representation we show that the new compression scheme achieves close to optimal worst case compression can compress exponentially better than dag compression is never much worse than dag compression and supports navigational queries in logarithmic time

a really simple approximation of smallest grammar in this paper we present a really simple linear time algorithm constructing a context free grammar of size 4 g log 3 2 n g for the input string where n is the size of the input string and g the size of the optimal grammar generating this string the algorithm works for arbitrary size alphabets but the running time is linear assuming that the alphabet of the input string can be identified with numbers from 1 n c for some constant c algorithms with such an approximation guarantee and running time are known however all of them were non trivial and their analyses were involved the here presented algorithm computes the lz77 factorisation and transforms it in phases to a grammar in each phase it maintains an lz77 like factorisation of the word with at most factors as well as additional o letters where was the size of the original lz77 factorisation in one phase in a greedy way by a left to right sweep and a help of the factorisation we choose a set of pairs of consecutive letters to be replaced with new symbols i e nonterminals of the constructed grammar we choose at least 2 3 of the letters in the word and there are o many different pairs among them hence there are o log n phases each of them introduces o nonterminals to a grammar a more precise analysis yields a bound 4 log n as g this yields the desired bound g 4 g log n g

improved spatial prediction a combinatorial approach 1 this paper presents a combinatorial approach for improving spatial predictions first copulas are used to interpolate a spatially distributed point rainfall field to a uniform spatial grid it is observed that results vary substantially depending on the parameters chosen for interpolation leading to the hypothesis that it may be advantageous to estimate copula parameters locally or to combine local and global copula predictions it is found that by modifying the method of forecast combinations prediction errors in the spatial interpolation of rainfall can be reduced although this method of combining predictions is applied in the context of rainfall interpolation using local and global copula predictions it can be used on other spatial variables and interpolation methods

particle tracking for fractional diffusion with two time scales abstract previous work y zhang m m meerschaert b baeumer particle tracking for time fractional diffusion phys rev e 78 2008 036705 showed how to solve time fractional diffusion equations by particle tracking this paper extends the method to the case where the order of the fractional time derivative is greater than one a subordination approach treats the fractional time derivative as a random time change of the corresponding cauchy problem with a first derivative in time one novel feature of the time fractional case of order greater than one is the appearance of clustering in the operational time subordinator which is non markovian solutions to the time fractional equation are probability densities of the underlying stochastic process the process models movement of individual particles the evolution of an individual particle in both space and time is captured in a pair of stochastic differential equations or langevin equations monte carlo simulation yields particle location and the ensemble density approximates the solution to the variable coefficient time fractional diffusion equation in one or several spatial dimensions the particle tracking code is validated against inverse transform solutions in the simplest cases further applications solve model equations for fracture flow and upscaling flow in complex heterogeneous porous media these variable coefficient time fractional partial differential equations in several dimensions are not amenable to solution by any alternative method so that the grid free particle tracking approach presented here is uniquely appropriate

the smallest grammar problem this paper addresses the smallest grammar problem what is the smallest context free grammar that generates exactly one given string spl sigma this is a natural question about a fundamental object connected to many fields such as data compression kolmogorov complexity pattern identification and addition chains due to the problem s inherent complexity our objective is to find an approximation algorithm which finds a small grammar for the input string we focus attention on the approximation ratio of the algorithm and implicitly the worst case behavior to establish provable performance guarantees and to address shortcomings in the classical measure of redundancy in the literature our first results are concern the hardness of approximating the smallest grammar problem most notably we show that every efficient algorithm for the smallest grammar problem has approximation ratio at least 8569 8568 unless p np we then bound approximation ratios for several of the best known grammar based compression algorithms including lz78 b isection sequential longest match greedy and re pair among these the best upper bound we show is o n sup 1 2 we finish by presenting two novel algorithms with exponentially better ratios of o log sup 3 n and o log n m sup where m sup is the size of the smallest grammar for that input the latter algorithm highlights a connection between grammar based compression and lz77

a cauchy type problem involving a weighted sequential derivative in the space of integrable functions a cauchy type nonlinear problem for a class of fractional differential equations involving sequential derivatives is considered some properties and composition identities are derived the equivalence with the associated integral equation is established the existence and uniqueness of global solutions in the space of lebesgue integrable functions are proved

the complexity of tree automata and xpath on grammar compressed trees the complexity of various membership problems for tree automata on compressed trees is analyzed two compressed representations are considered dags which allow to share identical subtrees in a tree and straight line context free tree grammars which moreover allow to share identical intermediate parts in a tree several completeness results for the classes nl p and pspace are obtained finally the complexity of the evaluation problem for structural xpath queries on trees that are compressed via straight line context free tree grammars is investigated

boosting textual compression in optimal linear time we provide a general boosting technique for textual data compression qualitatively it takes a good compression algorithm and turns it into an algorithm with a better compression performance guarantee it displays the following remarkable properties a it can turn any memoryless compressor into a compression algorithm that uses the best possible contexts b it is very simple and optimal in terms of time and c it admits a decompression algorithm again optimal in time to the best of our knowledge this is the first boosting technique displaying these properties technically our boosting technique builds upon three main ingredients the burrows wheeler transform the suffix tree data structure and a greedy algorithm to process them specifically we show that there exists a proper partition of the burrows wheeler transform of a string s that shows a deep combinatorial relation with the kth order entropy of s that partition can be identified via a greedy processing of the suffix tree of s with the aim of minimizing a proper objective function over its nodes the final compressed string is then obtained by compressing individually each substring of the partition by means of the base compressor we wish to boost our boosting technique is inherently combinatorial because it does not need to assume any prior probabilistic model about the source emitting s and it does not deploy any training parameter estimation and learning various corollaries are derived from this main achievement among the others we show analytically that using our booster we get better compression algorithms than some of the best existing ones that is lz77 lz78 ppmc and the ones derived from the burrows wheeler transform further we settle analytically some long standing open problems about the algorithmic structure and the performance of bwt based compressors namely we provide the first family of bwt algorithms that do not use move to front or symbol ranking as a part of the compression process

the general time fractional wave equation for a vibrating string the solution of a general time fractional wave equation for a vibrating string is obtained in terms of the mittag leffler type functions and complete set of eigenfunctions of the sturm liouville problem the time fractional derivative used is taken in the caputo sense and the method of separation of variables and the laplace transform method are used to solve the equation some results for special cases of the initial and boundary conditions are obtained and it is shown that the corresponding solutions of the integer order equations are special cases of those of time fractional equations the proposed general equation may be used for modeling different processes in complex or viscoelastic media disordered materials etc

fractional calculus with an integral operator containing a generalized mittag leffler function in the kernel in this paper we introduce and investigate a fractional calculus with an integral operator which contains the following family of generalized mittag leffler functions e a b c k z email protected n 0 c k email protected email protected z nn z b email protected c r a max 0 r k 1 r k 0 in its kernel l n being the familiar pochhammer symbol a number of corollaries and consequences of the main results presented here are also considered

convergence of the grunwald letnikov scheme for time fractional diffusion using bivariate generating functions we prove convergence of the grunwald letnikov difference scheme for the fractional diffusion equation in one space dimension with and without central linear drift in the fourier laplace domain as the space and time steps tend to zero in a well scaled way this implies convergence in distribution weak convergence of the discrete solution towards the probability of sojourn of a diffusing particle the difference schemes allow also interpretation as discrete random walks for fractional diffusion with central linear drift we show that in the fourier laplace domain the limiting ordinary differential equation coincides with that for the solution of the corresponding diffusion equation

almost sure optimality of sliding window lempel ziv algorithm and variants revisited the sliding window lempel ziv swlz algorithm has been studied extensively in the information theory literature and has been used in several commercial compression packages the asymptotic behavior of this algorithm has been studied by wyner and ziv and by shields using different approaches shields results proving asymptotic optimality for all individual sequences with respect to the class of all finite state encoders is known to imply the almost sure asymptotic optimality for the class of stationary and ergodic sources we establish the almost sure asymptotic optimality without any mixing conditions by extending the ideas of wyner and ziv using results on recurrence times from ergodic theory a nonuniversal fixed shift version of the algorithm is introduced to gain more insight into its behavior pointwise optimality results are also obtained for several variants based on match length functions introduced by gavish and lempel we also propose variants of the algorithm for sources with countable alphabet and demonstrate their pointwise optimality

succinct representation of balanced parentheses and static trees we consider the implementation of abstract data types for the static objects binary tree rooted ordered tree and a balanced sequence of parentheses our representations use an amount of space within a lower order term of the information theoretic minimum and support in constant time a richer set of navigational operations than has previously been considered in similar work in the case of binary trees for instance we can move from a node to its left or right child or to the parent in constant time while retaining knowledge of the size of the subtree at which we are positioned the approach is applied to produce a succinct representation of planar graphs in which one can test adjacency in constant time

geostatistical interpolation using copulas 1 in many applications of geostatistical methods the dependence structure of the investigated parameter is described solely with the variogram or covariance functions which are susceptible to measurement anomalies and implies the assumption of gaussian dependence moreover the kriging variance respects only observation density data geometry and the variogram model to address these problems we borrow the idea from copulas to depict the dependence structure without the influence of the marginal distribution the methodology and basic hypotheses for application of copulas as geostatistical methods are discussed and the gaussian copula as well as a non gaussian copula are used in this paper copula parameters are estimated using a division of the observations into multipoint subsets and a subsequent maximization of the corresponding likelihood function the interpolation is carried out with two different copulas where the expected and median values are calculated from the copulas conditioned with the nearby observations the full conditional copulas provide the estimation distributions for the unobserved locations and can be used to define confidence intervals which depend on both the observation geometry and values observations of a large scale groundwater quality measurement network in baden wurttemberg are used to demonstrate the methodology five groundwater quality parameters chloride nitrate ph sulfate and dissolved oxygen are investigated all five parameters show non gaussian dependence the copula based interpolation results of the five parameters are compared to the results of conventional ordinary and indicator kriging different statistical measures including mean squared error relative differences and probability scores are used to compare cross validation and split sampling results of the interpolation methods the non gaussian copulas give better results than the geostatistical interpolations validation of the confidence intervals shows that they are more realistic than the estimation variances obtained by ordinary kriging

a spatial markov model for the evolution of the joint distribution of groundwater age arrival time and velocity in heterogeneous media the evolution of the joint distribution of groundwater age velocity and arrival times based on a markov model for the velocities of fluid particles in heterogeneous porous media has been quantified an explicit evolution equation for the joint distribution of age arrival time and particle velocity is derived which is equivalent to a continuous time random walk for age velocity and arrival time the approach is fully parameterized by the correlation model and the distribution of groundwater flow velocities the transition probability for subsequent particle velocities along streamlines is implemented by a copula which is an efficient method to generate a correlated velocity series with prescribed marginal distribution we discuss different solution methods based on finite differences and random walk particle tracking the latter is based on continuous time random walks whose transition times are obtained kinematically from the flow velocities specifically we discuss a renormalization scheme to accelerate the particle tracking simulations based on the definition of aggregate particle transitions while at the same time renormalizing velocity correlation the impact of velocity correlation and velocity distribution on the evolution of age at different distances from the inlet plane is also studied at distances of the order of the correlation length persistent particle velocities give the same behavior as stochastic streamtube models for velocity distributions which give rise to transition times with finite variance the age distributions evolve toward an inverse gaussian for heavy tailed weighting times they evolve toward stable distribution as the distance from the inlet increases

an inverse problem for a generalized fractional diffusion we propose a method for determining the solution and source term of a generalized time fractional diffusion equation the method is based on selecting a bi orthogonal basis of l 2 space corresponding to a nonself adjoint boundary value problem uniqueness is proven and an existence result is obtained for smooth initial and final conditions the asymptotic behavior of the generalized mittag leffler function is used to relax the smoothness requirement on these conditions

modeling complex geological structures with elementary training images and transform invariant distances 1 we present a new framework for multiple point simulation involving small and simple training images the use of transform invariant distances by applying random transformations expands the range of structures available in the simple patterns of the training image the training image is no longer regarded as a global conceptual geological model but rather a basic structural element of the subsurface complex geological structures are obtained whose spatial structure can be parameterized by adjusting the statistics of the random transformations on the basis of field data or geological context in most cases such parameterization is possible by adjusting two numbers only this method allows us to build models that 1 reproduce shapes corresponding to a desired prior geological concept and 2 are in phase with different types of field observations such as orientation hydrofacies or geophysical measurements the main advantage is that the training images are so simple that they can be easily built even in 3 d we apply the method on a synthetic example involving seismic data where the transformation parameters are data driven we also show examples where realistic 2 and 3 d structures are built from simplistic training images with transformation parameters inferred using a small number of orientation data

universal lossless compression via multilevel pattern matching a universal lossless data compression code called the multilevel pattern matching code mpm code is introduced in processing a finite alphabet data string of length n the mpm code operates at o log log n levels sequentially at each level the mpm code detects matching patterns in the input data string substrings of the data appearing in two or more nonoverlapping positions the matching patterns detected at each level are of a fixed length which decreases by a constant factor from level to level until this fixed length becomes one at the final level the mpm code represents information about the matching patterns at each level as a string of tokens with each token string encoded by an arithmetic encoder from the concatenated encoded token strings the decoder can reconstruct the data string via several rounds of parallel substitutions a o 1 log n maximal redundancy sample upper bound is established for the mpm code with respect to any class of finite state sources of uniformly bounded complexity we also show that the mpm code is of linear complexity in terms of time and space requirements the results of some mpm code compression experiments are reported

the nearest colored node in a tree abstract we start a systematic study of data structures for the nearest colored node problem on trees given a tree with colored nodes and weighted edges we want to answer queries v c asking for the nearest node to node v that has color c this is a natural generalization of the well known nearest marked ancestor problem we give an o n space o log log n query solution and show that this is optimal we also consider the dynamic case where updates can change a node s color and show that in o n space we can support both updates and queries in o log n time we complement this by showing that o polylog n update time implies log n log log n query time finally we consider the case where updates can change the edges of the tree link cut operations there is a known top tree based solution that requires update time that is roughly linear in the number of colors we show that this solution is probably optimal by showing that a strictly sublinear update time implies a strictly subcubic time algorithm for the classical all pairs shortest paths problem on a general graph we also consider versions where the tree is rooted and the query asks for the nearest ancestor descendant of node v that has color c and present efficient data structures for both variants in the static and the dynamic setting

biased search trees we consider the problem of storing items from a totally ordered set in a search tree so that the access time for a given item depends on a known estimate of the access frequency of the item we describe two related classes of biased search trees whose average access time is within a constant factor of the minimum and that are easy to update under insertions deletions and more radical update operations we present and analyze efficient update algorithms for biased search trees we list several applications of such trees

approximate string matching a simpler faster algorithm we give two algorithms for finding all approximate matches of a pattern in a text where the edit distance between the pattern and the matching text substring is at most k the first algorithm which is quite simple runs in time o frac nk 3 m n m on all patterns except k break periodic strings defined later the second algorithm runs in time o frac nk 4 m n m on k break periodic patterns the two classes of patterns are easily distinguished in o m time

entropy copula method for single site monthly streamflow simulation 1 an entropy copula method is proposed for single site monthly streamflow simulation in this method the joint distribution of adjacent monthly streamflows is constructed using the copula method whereas the marginal distribution of streamflow for each month is derived using the entropy method then the conditional distribution is derived from which monthly streamflow is generated moment statistics of monthly streamflow such as mean standard deviation and skewness can be modeled by the entropy based marginal distribution while the dependence structure between streamflows of adjacent months can be modeled by the copula based joint distribution the proposed entropy copula method can be extended by incorporating an aggregate variable for modeling the interannual dependence application to the simulation of monthly streamflow from the colorado river illustrates the effectiveness of the proposed method

approximate pattern matching on elastic degenerate text an elastic degenerate string is a sequence of n sets of strings of total length n it has been introduced to represent a multiple alignment of several closely related sequences e g pan genome compactly in this representation substrings of these sequences that match exactly are collapsed while in positions where the sequences differ all possible variants observed at that location are listed the natural problem that arises is finding all matches of a deterministic pattern of length m in an elastic degenerate text there exists a non combinatorial o nm1 381 n time algorithm to solve this problem on line 1 in this paper we study the same problem under the edit distance model and present an o k2mg kn time and o m space algorithm where g is the total number of strings in the elastic degenerate text and k is the maximum edit distance allowed we also present a simple o kmg kn time and o m space algorithm for solving the problem under hamming distance

generalized viscoelastic models their fractional equations with solutions recently fractional calculus fc has encountered much success in the description of complex dynamics in particular fc has proved to be a valuable tool to handle viscoelastic aspects in this paper we construct fractional rheological constitutive equations on the basis of well known mechanical models especially the maxwell the kelvin voigt the zener and the poynting thomson model to this end we introduce a fractional element in addition to the standard purely elastic and purely viscous elements as we proceed to show many of the fractional differential equations which we obtain by this construction method admit closed form analytical solutions in terms of fox h functions of the minag leffler type

a subquadratic sequence alignment algorithm for unrestricted scoring matrices given two strings of size n over a constant alphabet the classical algorithm for computing the similarity between two sequences d sankoff and j b kruskal eds time warps string edits and macromolecules addison wesley reading ma 1983 t f smith and m s waterman j molec biol 147 1981 pp 195 197 uses a dynamic programming matrix and compares the two strings in o n2 time we address the challenge of computing the similarity of two strings in subquadratic time for metrics which use a scoring matrix of unrestricted weights our algorithm applies to both local and global similarity computations the speed up is achieved by dividing the dynamic programming matrix into variable sized blocks as induced by lempel ziv parsing of both strings and utilizing the inherent periodic nature of both strings this leads to an o n 2 log n algorithm for an input of constant alphabet size for most texts the time complexity is actually o h n 2 log n where h le 1 is the entropy of the text we also present an algorithm for comparing two run length encoded strings of length m and n compressed into m and n runs respectively in o m n n m complexity this result extends to all distance or similarity scoring schemes that use an additive gap penalty

parameter estimation by ensemble kalman filters with transformed data approach and application to hydraulic tomography 1 ensemble kalman filters enkfs are a successful tool for estimating state variables in atmospheric and oceanic sciences recent research has prepared the enkf for parameter estimation in groundwater applications enkfs are optimal in the sense of bayesian updating only if all involved variables are multivariate gaussian subsurface flow and transport state variables however generally do not show gaussian dependence on hydraulic log conductivity and among each other even if log conductivity is multi gaussian to improve enkfs in this context we apply nonlinear monotonic transformations to the observed states rendering them gaussian gaussian anamorphosis ga similar ideas have recently been presented by beal et al 2010 in the context of state estimation our work transfers and adapts this methodology to parameter estimation additionally we address the treatment of measurement errors in the transformation and provide several multivariate analysis tools to evaluate the expected usefulness of ga beforehand for illustration we present a first time application of an enkf to parameter estimation from 3 d hydraulic tomography in multi gaussian log conductivity fields results show that 1 ga achieves an implicit pseudolinearization of drawdown data as a function of log conductivity and 2 this makes both parameter identification and prediction of flow and transport more accurate combining enkfs with ga yields a computationally efficient tool for nonlinear inversion of data with improved accuracy this is an attractive benefit given that linearization free methods such as particle filters are computationally extremely demanding

fully functional suffix trees and optimal text searching in bwt runs bounded space indexing highly repetitive texts such as genomic databases software repositories and versioned text collections has become an important problem since the turn of the millennium a relevant compressibility measure for repetitive texts is r the number of runs in their burrows wheeler transforms bwts one of the earliest indexes for repetitive collections the run length fm index used o r space and was able to efficiently count the number of occurrences of a pattern of length m in a text of length n in o m log log n time with current techniques however it was unable to locate the positions of those occurrences efficiently within a space bounded in terms of r in this article we close this long standing problem showing how to extend the run length fm index so that it can locate the occ occurrences efficiently in o occ log log n time within o r space by raising the space to o r log log n our index counts the occurrences in optimal time o m and locates them in optimal time as well o m occ by further raising the space by an o w log factor where is the alphabet size and w e log n is the ram machine size in bits we support count and locate in o m log w and o m log w occ time which is optimal in the packed setting and had not been obtained before in compressed space we also describe a structure using o r log n r space that replaces the text and extracts any text substring of length e in the almost optimal time o log n r e log w within that space we similarly provide access to arbitrary suffix array inverse suffix array and longest common prefix array cells in time o log n r and extend these capabilities to full suffix tree functionality typically in o log n r time per operation our experiments show that our o r space index outperforms the space competitive alternatives by 1 2 orders of magnitude in time competitive implementations of the original fm index are outperformed by 1 2 orders of magnitude in space and or 2 3 in time

document listing on repetitive collections with guaranteed performance abstract we consider document listing on string collections that is finding in which strings a given pattern appears in particular we focus on repetitive collections a collection of size n over alphabet 1 is composed of d copies of a string of size n and s edits are applied on ranges of copies we introduce the first document listing index with size o n s precisely o n lg s lg 2 n lg d bits and with useful worst case time guarantees given a pattern of length m the index reports the ndoc 0 strings where it appears in time o m lg 1 n ndoc for any constant 0 and tells in time o m lg n if ndoc 0 our technique is to augment a range data structure that is commonly used on grammar based indexes so that instead of retrieving all the pattern occurrences it computes useful summaries on them we show that the idea has independent interest we introduce the first grammar based index that on a text t 1 n with a grammar of size r uses o r lg n bits and counts the number of occurrences of a pattern p 1 m in time o m 2 m lg 2 r for any constant 0 we also give the first index using o z lg n z lg n bits where t is parsed by lempel ziv into z phrases counting occurrences in time o m lg 2 n

approximation of grammar based compression via recompression in this paper we present a simple linear time algorithm constructing a context free grammar of size o g log n g for the input string where n is the size of the input string and g the size of the optimal grammar generating this string the algorithm works for arbitrary size alphabets but the running time is linear assuming that the alphabet of the input string can be identified with numbers from 1 n c for some constant c otherwise additional cost of o n log is needed algorithms with such an approximation guarantee and running time are known the novelty of this paper is a particular simplicity of the algorithm as well as the analysis of the algorithm which uses a general technique of recompression recently introduced by the author furthermore contrary to the previous results this work does not use the lz representation of the input string in the construction nor in the analysis

analytical relationship between gaussian and transformed gaussian spatially distributed fields 1 a transformation of a gaussian random field results in a change of the spatial dependence in simple terms the range and the shape of a variogram are different between an underlying gaussian and a transformed gaussian field there is a relationship between the underlying and the transformed spatial dependence this paper shows how this relationship can be expressed analytically rather than generating multidimensional random fields and conducting spatial statistical analysis we develop an accurate and efficient approach based on a unique mapping of the correlation coefficients of the original multi gaussian fields to the transformed correlation coefficients to evaluate the spatial correlation of transformed non gaussian random fields for any type of geostatistical parameterization such a mapping can also yield accurate estimation of the spatial correlation of the underlying gaussian field given the spatial correlation of the transformed field results indicate that 1 a nonlinear transformation of spatially distributed fields usually changes the spatial dependence structure and 2 the relationship between the dependence structures of the underlying and the transformed field can be expressed analytically and it is sufficient to do this in one dimension we use the developed approach to investigate the change of correlations of connected random fields generated by the absolute value transformation results show 1 the correlation lengths of the underlying gaussian fields are 1 67 and 2 64 times of those of transformed non gaussian fields for gaussian and exponential covariance models respectively 2 the anisotropic ratio does not change and 3 the anticorrelation in hole effect correlation models disappear

random access to grammar compressed strings and trees grammar based compression where one replaces a long string by a small context free grammar that generates the string is a simple and powerful paradigm that captures sometimes with slight reduction in efficiency many of the popular compression schemes including the lempel ziv family run length encoding byte pair encoding sequitur and re pair in this paper we present a novel grammar representation that allows efficient random access to any character or substring without decompressing the string let s be a string of length n compressed into a context free grammar mathcal s of size n we present two representations of mathcal s achieving o log n random access time and either o n cdot alpha k n construction time and space on the pointer machine model or o n construction time and space on the ram here alpha k n is the inverse of the k th row of ackermann s function our representations also efficiently support decompression of any substring in s we can decompres

compressed range minimum queries abstract given a string s of n integers in 0 a range minimum query rmq i j asks for the index of the smallest integer in s i j it is well known that the problem can be solved with a succinct data structure of size 2 n o n and constant query time in this paper we show how to preprocess s into a compressed representation that allows fast range minimum queries this allows for sublinear size data structures with logarithmic query time the most natural approach is to use string compression and construct a data structure for answering range minimum queries directly on the compressed string we investigate this approach in the context of grammar compression we then consider an alternative approach instead of compressing s using string compression we compress the cartesian tree of s using tree compression we show that this approach can be exponentially better than the former is never worse by more than an o factor i e for constant alphabets it is never asymptotically worse and can in fact be worse by an factor

on the compressibility of finite languages and formal proofs abstract we consider the minimal number of productions needed for a grammar to cover a finite language l as the grammatical complexity of l we study this measure for several types of word and tree grammars and show that it is closely connected to well known measures for the complexity of formal proofs in first order predicate logic we construct an incompressible sequence of finite word languages and transfer this and several other results about the complexity of word and tree languages to formal proofs

gaussian and non gaussian inverse modeling of groundwater flow using copulas and random mixing this paper presents a new copula based methodology for gaussian and non gaussian inverse modeling of groundwater flow the presented approach is embedded in a monte carlo framework and it is based on the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function the target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields the corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability and honors all the observations of hydraulic transmissivities the constraints related to hydraulic head observations are nonlinear in order to fulfill these constraints a connected domain in the weight space inside which all linear constraints are fulfilled is identified this domain is defined analytically and includes an infinite number of conditional fields i e conditioned on the observed hydraulic transmissivities and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads this procedure enables the simulation of a great number of solutions for the inverse problem allowing a reasonable quantification of the associated uncertainties the methodology can be used for fields with gaussian copula dependence and fields with specific non gaussian copula dependence further arbitrary marginal distributions can be considered

repair and all irreducible grammars are upper bounded by high order empirical entropy irreducible grammars are a class of context free grammars with well known representatives such as repair with a few tweaks longest match greedy and sequential we show that a grammar based compression method described by kieffer and yang 2000 is upper bounded by the high order empirical entropy of the string when the underlying grammar is irreducible specifically given a string s over an alphabet of size sigma we prove that if the underlying grammar is irreducible then the length of the binary code output by this grammar based compression method is bounded by s h k s o s log sigma for any k in o log sigma s where h k s is the k order empirical entropy of s this is the first bound encompassing the whole class of irreducible grammars in terms of the high order empirical entropy with coefficient 1

approximation of smallest linear tree grammar a simple linear time algorithm for constructing a linear context free tree grammar of size o r g r g log n r g for a given input tree t of size n is presented where g is the size of a minimal linear context free tree grammar for t and r is the maximal rank of symbols in t which is a constant in many applications this is the first example of a grammar based tree compression algorithm with a good i e logarithmic in terms of the size of the input tree approximation ratio the analysis of the algorithm uses an extension of the recompression technique from strings to trees

fractional master equations and fractal time random walks fractional master equations containing fractional time derivatives of order 0 ensuremath le 1 are introduced on the basis of a recent classification of time generators in ergodic theory it is shown that fractional master equations are contained as a special case within the traditional theory of continuous time random walks the corresponding waiting time density ensuremath psi t is obtained exactly as ensuremath psi t mathit t mathrm ensuremath omega mathrm ensuremath 1 c mathit e mathrm ensuremath omega mathrm ensuremath omega mathit t mathrm ensuremath omega c where mathit e mathrm ensuremath omega mathrm ensuremath omega x is the generalized mittag leffler function this waiting time distribution is singular both in the long time as well as in the short time limit

collage system a unifying framework for compressed pattern matching we introduce a general framework which is suitable to capture the essence of compressed pattern matching according to various dictionary based compressions it is a formal system to represent a string by a pair of dictionary d and sequence s of phrases in d the basic operations are concatenation truncation and repetition we also propose a compressed pattern matching algorithm for the framework the goal is to find all occurrences of a pattern in a text without decompression which is one of the most active topics in string matching our framework includes such compression methods as lempel ziv family lz77 lzss lz78 lzw re pair sequitur and the static dictionary based method the proposed algorithm runs in o d s height d m2 r time with o d m2 space where d is the size of d s is the number of tokens in s height d is the maximum dependency of tokens in d m is the pattern length and r is the number of pattern occurrences for a subclass of the framework that contains no truncation the time complexity is o d s m2 r

fast algorithms for finding nearest common ancestors we consider the following problem given a collection of rooted trees answer on line queries of the form what is the nearest common ancester of vertices x and y we show that any pointer machine that solves this problem requires omega log log n time per query in the worst case where n is the total number of vertices in the trees on the other hand we present an algorithm for a random access machine with uniform cost measure and a bound of omega log n on the number of bits per word that requires o 1 time per query and o n preprocessing time assuming that the collection of trees is static for a version of the problem in which the trees can change between queries we obtain an almost linear time and linear space algorithm

sequential codes lossless compression of individual sequences and kolmogorov complexity a general class of sequential codes for lossless compression of individual sequences on a finite alphabet is defined including many types of codes that one would want to implement the principal requirement for membership in the class is that the encoding and decoding operations be performable on a computer the opta function for the class of codes is then considered which is the function that assigns to each individual sequence the infimum of the rates at which the sequence can be compressed over this class of sequential codes two results about the opta function are obtained 1 it is shown that any sequential code in the class compresses some individual sequence at a rate strictly greater than the rate for that sequence given by the opta function and 2 it is shown that the opta function takes a value strictly greater than that of the kolmogorov 1965 complexity rate function for some individual sequences

efficient pairwise composite likelihood estimation for spatial clustered data spatial clustered data refer to high dimensional correlated measurements collected from units or subjects that are spatially clustered such data arise frequently from studies in social and health sciences we propose a unified modeling framework termed as geocopula to characterize both large scale variation and small scale variation for various data types including continuous data binary data and count data as special cases to overcome challenges in the estimation and inference for the model parameters we propose an efficient composite likelihood approach in that the estimation efficiency is resulted from a construction of over identified joint composite estimating equations consequently the statistical theory for the proposed estimation is developed by extending the classical theory of the generalized method of moments a clear advantage of the proposed estimation method is the computation feasibility we conduct several simulation studies to assess the performance of the proposed models and estimation methods for both gaussian and binary spatial clustered data results show a clear improvement on estimation efficiency over the conventional composite likelihood method an illustrative data example is included to motivate and demonstrate the proposed method

factor copula models for replicated spatial data abstractwe propose a new copula model that can be used with replicated spatial data unlike the multivariate normal copula the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all measurements of the process moreover the proposed copula can model tail dependence and tail asymmetry the model is parameterized in terms of a covariance function that may be chosen from the many models proposed in the literature such as the matern model for some choice of common factors the joint copula density is given in closed form and therefore likelihood estimation is very fast in the general case one dimensional numerical integration is needed to calculate the likelihood but estimation is still reasonably fast even with large datasets we use simulation studies to show the wide range of dependence structures that can be generated by the proposed model with different choices of common factors we apply the proposed model to spatial temperature data and com

bayesian assessment of the expected data impact on prediction confidence in optimal sampling design 1 incorporating hydro geo logical data such as head and tracer data into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty because of financial limitations for investigation campaigns information needs toward modeling or prediction goals should be satisfied efficiently and rationally optimal design techniques find the best one among a set of investigation strategies they optimize the expected impact of data on prediction confidence or related objectives prior to data collection we introduce a new optimal design method called predia gnosis preposterior data impact assessor predia derives the relevant probability distributions and measures of data utility within a fully bayesian generalized flexible and accurate framework it extends the bootstrap filter bf and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values predia is a strictly formal information processing scheme free of linearizations it works with arbitrary simulation tools provides full flexibility concerning measurement types linear nonlinear direct indirect allows for any desired task driven formulations and can account for various sources of uncertainty e g heterogeneity geostatistical assumptions boundary conditions measurement values model structure uncertainty a large class of model errors via bayesian geostatistics and model averaging existing methods fail to simultaneously provide these crucial advantages which our method buys at relatively higher computational costs we demonstrate the applicability and advantages of predia over conventional linearized methods in a synthetic example of subsurface transport in the example we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence hence predia will often lead to substantially better sampling designs finally we extend our example to specifically highlight the consideration of conceptual model uncertainty

multivariate hydrological frequency analysis using copulas 1 this article presents the modeling of multivariate extreme values using copulas our approach allows us to model the dependence structure independently of the marginal distributions which is not possible with standard classical methods the methodology has been applied on two different problems in hydrology the first application is concerned with the combined risk in the framework of frequency analysis four copulas have been tested on peak flows from the watershed of peribonka in quebec canada the second application relates to the joint modeling of peak flows and volumes three copulas have been applied to the watershed of the rimouski river in quebec canada this approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology

on the vocabulary of grammar based codes and the logical consistency of texts this paper presents a new interpretation for zipf mandelbrot s law in natural language which rests on two areas of information theory firstly we construct a new class of grammar based codes and secondly we investigate properties of strongly nonergodic stationary processes the motivation for the joint discussion is to prove a proposition with a simple informal statement if a text of length n describes n independent facts in a repetitive way then the text contains at least n log n different words under suitable conditions on n in the formal statement two modeling postulates are adopted firstly the words are understood as nonterminal symbols of the shortest grammar based encoding of the text secondly the text is assumed to be emitted by a finite energy strongly nonergodic source whereas the facts are binary iid variables predictable in a shift invariant way

time space trade offs for lempel ziv compressed indexing abstract given a string s the compressed indexing problem is to preprocess s into a compressed representation that supports fast substring queries the goal is to use little space relative to the compressed size of s while supporting fast queries we present a compressed index based on the lempel ziv 1977 compression scheme we obtain the following time space trade offs for constant sized alphabets i o m occ lg lg n time using o z lg n z lg lg z space or ii o m 1 lg z lg n z occ lg lg n lg z time using o z lg n z space for integer alphabets polynomially bounded by n iii o m 1 lg z lg n z occ lg lg n lg z time using o z lg n z lg lg z space or iv o m occ lg lg n lg z time using o z lg n z lg z space where n and m are the length of the input string and query string respectively z is the number of phrases in the lz77 parse of the input string occ is the number of occurrences of the query in the input and 0 is an arbitrarily small constant in particular i improves the leading term in the query time of the previous best solution from o m lg m to o m at the cost of increasing the space by a factor lg lg z alternatively ii matches the previous best space bound but has a leading term in the query time of o m 1 lg z lg n z however for any polynomial compression ratio i e z o n 1 for constant 0 this becomes o m our index also supports extraction of any substring of length l in o l lg n z time technically our results are obtained by novel extensions and combinations of existing data structures of independent interest including a new batched variant of weak prefix search

compact q gram profiling of compressed strings we consider the problem of computing the q gram profile of a string t of size n compressed by a context free grammar with n production rules we present an algorithm that runs in o email protected expected time and uses o n q k t q space where email protected qn is the exact number of characters decompressed by the algorithm and k t email protected email protected is the number of distinct q grams in t this simultaneously matches the current best known time bound and improves the best known space bound our space bound is asymptotically optimal in the sense that any algorithm storing the grammar and the q gram profile must use w n q k t q space to achieve this we introduce the q gram graph that space efficiently captures the structure of a string with respect to its q grams and show how to construct it from a grammar

computing sequences with addition chains given a sequence n 1 cdots n m of positive integers what is the smallest number of additions needed to compute all m integers starting with 1 this generalization of the addition chain m 1 problem will be called the addition sequence problem we show that the sequence 2 0 2 1 cdots 2 n 1 2 n 1 can be computed with n 2 13 sqrt n log n additions and that n sqrt n 2 is a lower bound this lower bound result is applied to show that the addition sequence problem is np complete

efficient generation of minimal length addition chains an addition chain for a positive integer n is a set 1 a0 a1 ar n of integers such that for each i ge 1 a i a j a k for some k le j i this paper is concerned with some of the computational aspects of generating minimal length addition chains for an integer n particular attention is paid to various pruning techniques that cut down the search time for such chains certain of these techniques are influenced by the multiplicative structure of n later sections of the paper present some results that have been uncovered by searching for minimal length addition chains