dehornoy like left orderings and isolated left orderings abstract we introduce a dehornoy like ordering of groups which is a generalization of the dehornoy ordering of the braid groups under an assumption which we call property f we show that dehornoy like orderings have properties similar to the dehornoy ordering and produce isolated left orderings we also construct new examples of dehornoy like orderings and isolated orderings and study their more precise properties

the fine structure of ld equivalence abstract we introduce new algebraic techniques for the study of left self distributivity we establish a self similarity propriety for the terms k t which are counterparts to garside s fundamental braids k n and deduce partial answers to several long standing open questions convergence of the polish algorithm computation of the normal form existence of a lattice structure on ld equivalence classes

nonlinear extraction of independent components of natural images using radial gaussianization we consider the problem of efficiently encoding a signal by transforming it to a new representation whose components are statistically independent a widely studied linear solution known as independent component analysis ica exists for the case when the signal is generated as a linear transformation of independent nongaussian sources here we examine a complementary case in which the source is nongaussian and elliptically symmetric in this case no invertible linear transform suffices to decompose the signal into independent components but we show that a simple nonlinear transformation which we call radial gaussianization rg is able to remove all dependencies we then examine this methodology in the context of natural image statistics we first show that distributions of spatially proximal bandpass filter responses are better described as elliptical than as linearly transformed independent sources consistent with this we demonstrate that the reduction in dependency achieved by applying rg to either nearby pairs or blocks of bandpass filter responses is significantly greater than that achieved by ica finally we show that the rg transformation may be closely approximated by divisive normalization which has been used to model the nonlinear response properties of visual neurons

finite left distributive algebras and embedding algebras we consider algebras with one binary operation and one generator monogenic and satisfying the left distributive lawa b c a b a c one can define a sequence of finite left distributive algebrasan and then take a limit to get an infinite monogenic left distributive algebraa results of laver and steel assuming a strong large cardinal axiom imply thata is free it is open whether the freeness ofa can be proved without the large cardinal assumption or even in peano arithmetic the main result of this paper is the equivalence of this problem with the existence of a certain algebra of increasing functions on natural numbers called anembedding algebra using this and results of the first author we conclude that the freeness ofa is unprovable in primitive recursive arithmetic

traditional analysis of aquifer tests comparing apples to oranges 1 traditional analysis of aquifer tests uses the observed drawdown at one well induced by pumping at another well for estimating the transmissivity t and storage coefficient s of an aquifer the analysis relies on theis solution or jacob s approximate solution which assumes aquifer homogeneity aquifers are inherently heterogeneous at different scales if the observation well is screened in a low permeability zone while the pumping well is located in a high permeability zone the resulting situation contradicts the homogeneity assumption in the traditional analysis as a result what does the traditional interpretation of the aquifer test tell us using numerical experiments and a first order correlation analysis we investigate this question results of the investigation suggest that the effective t and s for an equivalent homogeneous aquifer of gaussian random t and s fields vary with time as well as the principal directions of the effective t the effective t and s converge to the geometric and arithmetic means respectively at large times analysis of the estimated t and s using drawdown from a single observation well shows that at early time both estimates vary with time the estimated s stabilizes rapidly to the value dominated by the storage coefficient heterogeneity in between the pumping and the observation wells at late time the estimated t approaches but does not equal the effective t it represents an average value over the cone of depression but influenced by the location size and degree of heterogeneity as the cone of depression evolves

nonlinear image representation for efficient perceptual coding image compression systems commonly operate by transforming the input signal into a new representation whose elements are independently quantized the success of such a system depends on two properties of the representation first the coding rate is minimized only if the elements of the representation are statistically independent second the perceived coding distortion is minimized only if the errors in a reconstructed image arising from quantization of the different elements of the representation are perceptually independent we argue that linear transforms cannot achieve either of these goals and propose instead an adaptive nonlinear image representation in which each coefficient of a linear transform is divided by a weighted sum of coefficient amplitudes in a generalized neighborhood we then show that the divisive operation greatly reduces both the statistical and the perceptual redundancy amongst representation elements we develop an efficient method of inverting this transformation and we demonstrate through simulations that the dual reduction in dependency can greatly improve the visual quality of compressed images

a geometric characterization of vassiliev invariants it is a well known paradigm to consider vassiliev invariants as polynomials on the set of knots we prove the following characterization a rational knot invariant is a vassiliev invariant of degree m if and only if it is a polynomial of degree m on every geometric sequence of knots here a sequence kz with z 2 z is called geometric if the knots kz coincide outside a ball b inside of which they satisfy kz b z for all z and some pure braid as an application we show that the torsion in the braid group over the sphere induces torsion at the level of vassiliev invariants there exist knots in s 1 s 2 that can be distinguished by z 2 invariants of finite type but not by rational invariants of finite type in order to obtain such torsion invariants we construct over z a universal vassiliev invariant of degree 1 for knots in s 1 s 2

right l groups geometric garside groups and solutions of the quantum yang baxter equation abstract right lattice ordered groups are introduced and studied as a general framework for garside groups and related groups without a garside element every right l group g has a two sided partially ordered subgroup n g which generalizes the quasi centre of an artin tits group the group n g splits into copies of z if g is noetherian the positive cone of a right l group is described as a structure that is known from algebraic logic a pair of left and right self similar hoops for noetherian right l groups g modularity of the lattice structure is characterized in terms of an operation on the set x g of atoms it is proved that modular garside groups are equivalent to finite projective spaces with a non degenerate labelling a concept of duality for x g is introduced and applied in the distributive case this gives a one to one correspondence between noetherian right l groups with duality and non degenerate unitary set theoretic solutions of the quantum yang baxter equation the description of garside groups via garside germs is extended to right l groups which yields a one sided enhancement and a new proof of dvurecenskij s non commutative extension of mundici s correspondence between abelian l groups and mv algebras

dependency reduction with divisive normalization justification and effectiveness efficient coding transforms that reduce or remove statistical dependencies in natural sensory signals are important for both biology and engineering in recent years divisive normalization dn has been advocated as a simple and effective nonlinear efficient coding transform in this work we first elaborate on the theoretical justification for dn as an efficient coding transform specifically we use the multivariate t model to represent several important statistical properties of natural sensory signals and show that dn approximates the optimal transforms that eliminate statistical dependencies in the multivariate t model second we show that several forms of dn used in the literature are equivalent in their effects as efficient coding transforms third we provide a quantitative evaluation of the overall dependency reduction performance of dn for both the multivariate t models and natural sensory signals finally we find that statistical dependencies in the multivariate t model and natural sensory signals are increased by the dn transform with low input dimensions this implies that for dn to be an effective efficient coding transform it has to pool over a sufficiently large number of inputs

the language of geodesics for garside groups we prove that the language of all geodesics of any garside group with respect to the generating set of divisors of the garside element forms a regular language in particular the braid groups admit generating sets where the associated language of geodesics is regular

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

right veering diffeomorphisms of compact surfaces with boundary we initiate the study of the monoid of right veering diffeomorphisms on a compact oriented surface with nonempty boundary the monoid strictly contains the monoid of products of positive dehn twists we explain the relationship to tight contact structures and open book decompositions

radially convergent flow in heterogeneous porous media we present an analytical solution for apparent effective transmissivity under radially convergent steady state flow conditions produced by constant pumping from a single well of finite radius rw apparent effective transmissivity te is defined as the value that relates the expected values of flow and head gradient at a certain location the domain is two dimensional of annular shape and the size of the pumping well is explicitly taken into account the solution for the steady state heads is obtained by solving the perturbed flow equation and substituting it into darcy s law to obtain a consistent second order expansion for te we show that apparent effective transmissivity is a scalar for any choice of isotropic covariance model with an expression given in integral form our main result is that te in a heterogeneous statistically isotropic random field under radial steady state flow conditions is a monotonie increasing function of r distance from the well that rises from the harmonic mean of the point transmissivity values close to the well and tends asymptotically towards the geometric mean far from the well the asymptotic value is reached at a distance of a few integral scales 1 5 2 for the gaussian model and 3 5 for the exponential one the apparent effective transmissivity versus normalized r curves are in excellent agreement with previously published numerical work carried out using monte carlo method

dual braid monoids mikado braids and positivity in hecke algebras we study the rational permutation braids that is the elements of an artin tits group of spherical type which can be written x 1 y where x and y are prefixes of the garside element of the braid monoid we give a geometric characterization of these braids in type a n and b n and then show that in spherical types different from d n the simple elements of the dual braid monoid for arbitrary choice of coxeter element embedded in the braid group are rational permutation braids we conjecture this to hold also in type d n this property implies positivity properties of the polynomials arising in the linear expansion of their images in the iwahori hecke algebra when expressed in the kazhdan lusztig basis in type a n it implies positivity properties of their images in the temperley lieb algebra when expressed in the diagram basis

the left distributive law and the freeness of an algebra of elementary embeddings the left distributive law for a single binary operation is the law a a it has been studied in universal algebra stein s kepka and nemec kn kepka kl k2 see also jezek et al jkn for a bibliography on the two sided distributive law and it has been studied more recently by set theorists because of its connection with elementary embeddings for e a limit ordinal let 6 be the collection of all j i i j an elementary embedding of v e into itself j not the identity then the existence of a 3 such that c is a large cardinal axiom see gaifman g and kanamori et ul krs for jo let k cr j the critical point of j and ti i j then 1 must equal sup ii w kunen ku martin ml woodin m2 martin and steel msl ms2 and woodin w in deep work showed that slight strengthenings of this axiom imply determinacy properties of the real line and subsequently that considerable weakenings suffice making the axiom unnecessary for those determinacy properties there is a natural operation on 8 write ul for u t in this and similar contexts below for jo gj j extends to a map j v i by defining for a s v j a u j a n i then j may or may not be an elementary embedding of vi e into itself but at least j is elementary from vi e a into v e ja in the special case that a as a set of ordered pairs is a k e we have that j k e j s let j k j k then the operation on j is nonassociative noncommutative and left distributive another operation on 4 is composition if k ie then k ie let z be the set of laws a b c u b c ucb c u bc u b c ub uc a b ub 0 a then j satisfies z and zimplies the left distributive law u bc u b c uboa c ub uc for jo c let 4 be the closure of j under let q the set of polynomials in j be the closure of jj under and 3 results in which 4 9j and their governing equations are involved appear in ml m2 l dougherty

nonlocal properties of nonuniform averaged flows in heterogeneous media the properties of nonuniform average potential flows in media of stationary random conductivity are studied the mathematical model of average flow is derived as a system of governing equations to be satisfied by mean velocity and mean head the averaged darcy s law determines the effective conductivity as an integral operator of the convolution type relating the mean velocity to the mean head gradient in a nonlocal way in fourier domain the mean velocity is proportional to the mean head gradient the coefficient of proportionality is referred to as the effective conductivity tensor and is derived by perturbation methods in terms of functionals of the conductivity spatial moments it is shown that the effective conductivity cannot be defined uniquely for potential flows however this nonuniqueness does not affect the spatial distribution of the mean head and velocity analytical expressions of the effective conductivity tensor are derived for two and three dimensional flows and for exponential and gaussian correlations of isotropic conductivity the fundamental solution of the governing equations in effective media mean green function is calculated for the same cases two new asymptotic models of the averaged darcy s law are developed to be applicable to large and small scales of heterogeneity several asymptotic expansions of tue two dimensional and three dimensional mean green functions are derived for exponential and gaussian correlations

effective groundwater model parameter values influence of spatial variability of hydraulic conductivity leakance and recharge a stochastic simulation approach was used to inspect the influence of spatial variability in aquifer and recharge properties on effective averaged groundwater model parameters a two dimensional unconfined aquifer model was set up for an area similar to that near livermore california monte carlo simulations were generated for different sets of spatial correlation structures assuming stationarity and an exponential semivariogram for each monte carlo realization groundwater flow was simulated and estimates of the means and standard deviations of the hydraulic head were obtained nine different cases were studied involving different correlation lengths of hydraulic conductivity conditional simulations parameter zonation and spatial recharge distributions results indicate that there is no single uniform value of the hydraulic conductivity that reproduces the expected head values spatial averaging to obtain effective values was based on the p norm power norm which ranges from 1 for the arithmetic mean to 1 for the harmonic mean with 0 representing the geometric mean for the unconditional case the 0 4 p norm seems to best reproduce the expected values the 0 2 p norm gave the best result for the conditional simulation case if the geometric mean were used instead the heads would deviate from the expected heads by about 2 m near the wells some value between the arithmetic and the geometric means of riverbed leakance will give results close to the expected head values the arithmetic mean of aerially distributed recharge produced results with small deviations from the expected head values these particular results may only apply to this modeled system as the pumping pattern and magnitudes exhibited strong influences on zones of maximum head deviation the implication of this work is that if an effective hydraulic conductivity is used in a simulation model it must be selected for a particular set of wells and pumping rates in an aquifer with significant pumping centers the best effective value for a two dimensional unconfined flow model is most likely between the geometric and harmonic mean if the wells are turned off the effective hydraulic conductivity for that flow model reverts to the geometric mean

iterative gaussianization from ica to random rotations most signal processing problems involve the challenging task of multidimensional probability density function pdf estimation in this paper we propose a solution to this problem by using a family of rotation based iterative gaussianization rbig transforms the general framework consists of the sequential application of a univariate marginal gaussianization transform followed by an orthonormal transform the proposed procedure looks for differentiable transforms to a known pdf so that the unknown pdf can be estimated at any point of the original domain in particular we aim at a zero mean unit covariance gaussian for convenience rbig is formally similar to classical iterative projection pursuit algorithms however we show that unlike in pp methods the particular class of rotations used has no special qualitative relevance in this context since looking for interestingness is not a critical issue for pdf estimation the key difference is that our approach focuses on the univariate part marginal gaussianization of the problem rather than on the multivariate part rotation this difference implies that one may select the most convenient rotation suited to each practical application the differentiability invertibility and convergence of rbig are theoretically and experimentally analyzed relation to other methods such as radial gaussianization one class support vector domain description and deep neural networks is also pointed out the practical performance of rbig is successfully illustrated in a number of multidimensional problems such as image synthesis classification denoising and multi information estimation

an evaluation of jacob s method for the interpretation of pumping tests in heterogeneous formations most pumping tests are interpreted using the classical theis assumption of large scale homogeneity with various corrections to account for early time behavior of drawdown curves when drawdowns are plotted versus log time late time data often delineate a straight line which is consistent with jacob s approximation of theis solution but may seem surprising in view of the heterogeneity of natural media the aim of our work is to show that jacob s method leads to a good approximation of the effective transmissivity of heterogeneous media when constrained to late time data a review of several multiwell pumping tests demonstrates that when drawdown curves from each observation well are interpreted separately they produce very similar transmissivity t estimates however the corresponding estimates for storativity span a broad range this behavior is verified numerically for several models of formation heterogeneity a very significant finding of the numerical investigation is that t values estimated using simulated drawdown from individual observation wells are all very close to the effective t value for parallel flow this was observed even in nonmultigaussian t fields where high t zones are well connected and where the effective t is larger than the geometric average of point values this implies that jacob s method can be used for estimating effective t values in many if not most formations

two dimensional characterization of hydraulic heterogeneity by multiple pumping tests 1 the conventional analysis of pumping tests by type curve methods is based on the assumption of a homogeneous aquifer applying these techniques to pumping test data from real heterogeneous aquifers leads to estimates of the hydraulic parameters that depend on the choice of the pumping and observation well positions in this paper we test whether these values may be viewed as pseudo local values of transmissivity and storativity which can be interpolated by kriging we compare such estimates to those obtained by geostatistical inverse modeling where heterogeneity is assumed in all stages of estimation we use drawdown data from multiple pumping tests conducted at the test site in krauthausen germany the geometric mean values of transmissivity and storativity determined by type curve analysis are very close to those obtained by geostatistical inversion but the conventional approach failed to resolve the spatial variability of transmissivity in contrast the estimate from geostatistical inversion reveals more structure this indicates that the estimates of the type curve approaches can not be treated as pseudo local values concerning storativity both analysis methods show strong fluctuations because the variability of all terms making up the storativity is small we believe that the estimated variability of storativity is biased we examine the influence of measurement error on estimating structural parameters of covariance functions in the inversion we obtain larger correlation lengths and smaller prior variances if we trust the measured data less

pumping tests in heterogeneous aquifers an analytical study of what can be obtained from their interpretation using jacob s method interpretation of pumping tests to estimate hydraulic parameter values is typically based on the assumption of aquifer homogeneity the applicability of the traditional methods of interpretation in real aquifers can be questioned since the evaluation of the drawdown curves observed at different locations in a single test may not result in one consistent set of hydraulic parameters thus most hydrogeologists tend to look at estimated transmissivities t as some average property of the medium while estimated storativities s are disregarded in some cases particularly when they are obtained from data measured at the pumping well an analytical study of drawdown under radially convergent flow toward a single point in heterogeneous aquifers shows that large time drawdown values form a straight line on a drawdown versus log time plot jacob s method consists of obtaining estimates for t and s from the slope and intercept of this line we find that even in a heterogeneous field these estimates provide valuable information about the aquifer estimated t values for different observation points tend to converge to a single value which corresponds to the effective t derived under parallel flow conditions estimated storativities however display higher variability but the geometric mean of the sest values can be used as an unbiased estimator of the actual s thus it appears that although jacob s method was originally derived for homogeneous media it can provide valuable information in real aquifers

non crossing partitions of type e e r abstract we investigate a new lattice of generalised non crossing partitions constructed using the geometry of the complex reflection group g e e r for the particular case e 2 resp r 2 our lattice coincides with the lattice of simple elements for the type d n resp i 2 e dual braid monoid using this lattice we construct a garside structure for the braid group b e e r as a corollary one may solve the word and conjugacy problems in this group

a higher order approximation to effective conductivity in media of anisotropic random structure properties of the effective conductivity tensor keff are studied by deriving the second order terms in its expansion in the variance 2 of normally distributed log conductivity it is shown that for media of anisotropic structure the components of the effective conductivity tensor are expressed by a functional of the log conductivity covariance that is it depends on the shape of the correlation function and not only on anisotropy ratios variance 2 and space dimensions however the trace of keff is independent of the log conductivity autocovariance and for a given mean conductivity depends only on 2 the dependence of the effective conductivity on the correlation structure is illustrated for gaussian and exponential autocovariances of log conductivity and for two and three dimensional flows

sparse code shrinkage denoising of nongaussian data by maximum likelihood estimation sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active such a representation is closely related to redundancy reduction and independent component analysis and has some neurophysiological plausibility in this article we show how sparse coding can be used for denoising using maximum likelihood estimation of nongaussian variables corrupted by gaussian noise we show how to apply a soft thresholding shrinkage operator on the components of sparse coding so as to reduce noise our method is closely related to the method of wavelet shrinkage but it has the important benefit over wavelet methods that the representation is determined solely by the statistical properties of the data the wavelet representation on the other hand relies heavily on certain mathematical properties like self similarity that may be only weakly related to the properties of natural data

word problems in free sheaves resume on descrit un algorithme effectif conjectural pour resoudre le probleme de mots dans les structures autodistributives libres et on discute la validite de cet algorithme et les consequences de celle ci notamment en termes de formes normales dans un monoide etendant un groupe de tresses infini

novel perceptually uniform chromatic space chromatically perceptive observers are endowed with a sense of similarity between colors for example two shades of green that are only slightly discriminable are perceived as similar whereas oth

representation of grid block permeability in coarse scale models of randomly heterogeneous porous media the two basic approaches for the assignment of coarse scale grid block permeabilities from highly detailed permeability descriptions are sampling where the permeability of the coarse scale grid block is simply specified as the fine scale permeability evaluated at the grid block center no averaging is performed and scaleup or homogenization where the coarse scale permeability is determined through some procedure which appropriately averages the fine scale data the intent of this paper is to quantitatively compare these two approaches through extensive numerical calculations for the modeling of single phase flow through two dimensional realizations of randomly heterogeneous porous media with heterogeneity quantified through the correlation length and the variance of the log of permeability 2 several different flow scenarios and two scaleup techniques local and global are considered over a range of l and it is seen that for flows driven by smoothly varying boundary conditions a sampling procedure is more accurate than global scaleup when the length scale of a typical grid block is less than l independent of for flows driven by source terms by contrast more resolution is required for a sampling approach to be preferable to global scaleup particularly at high variances local scaleup is shown to be preferable to either sampling or global scaleup in essentially all cases though its use for more general permeability fields requires additional numerical calculations

gaussian groups are torsion free abstract assume thatgis a group of fractions of a cancellative monoid where lower common multiples exist and divisibility has no infinite descending chain thengis torsion free the result applies in particular to all finite coxeter type artin groups

a bayesian approach for inverse modeling data assimilation and conditional simulation of spatial random fields 1 this paper addresses the inverse problem in spatially variable fields such as hydraulic conductivity in groundwater aquifers or rainfall intensity in hydrology common to all these problems is the existence of a complex pattern of spatial variability of the target variables and observations the multiple sources of data available for characterizing the fields the complex relations between the observed and target variables and the multiple scales and frequencies of the observations the method of anchored distributions mad that we propose here is a general bayesian method of inverse modeling of spatial random fields that addresses this complexity the central elements of mad are a modular classification of all relevant data and a new concept called anchors data types are classified by the way they relate to the target variable as either local or nonlocal and as either direct or indirect anchors are devices for localization of data they are used to convert nonlocal indirect data into local distributions of the target variables the target of the inversion is the derivation of the joint distribution of the anchors and structural parameters conditional to all measurements regardless of scale or frequency of measurement the structural parameters describe large scale trends of the target variable fields whereas the anchors capture local inhomogeneities following inversion the joint distribution of anchors and structural parameters is used for generating random fields of the target variable s that are conditioned on the nonlocal indirect data through their anchor representation we demonstrate mad through a detailed case study that assimilates point measurements of the conductivity with head measurements from natural gradient flow the resulting statistical distributions of the parameters are non gaussian similarly the moments of the estimates of the hydraulic head are non gaussian we provide an extended discussion of mad vis a vis other inversion methods including maximum likelihood and maximum a posteriori with an emphasis on the differences between mad and the pilot points method

a new algorithm for solving the word problem in braid groups abstract one of the most interesting questions about a group is whether its word problem can be solved and how the word problem in the braid group is of particular interest to topologists algebraists and geometers and is the target of intensive current research we look at the braid group from a topological point of view rather than a geometric one the braid group is defined by the action of diffeomorphisms on the fundamental group of a punctured disk we exploit the topological definition in order to give a new approach for solving its word problem our algorithm although not better in complexity is faster in comparison with known algorithms for short braid words and it is almost independent of the number of strings in the braids moreover the algorithm is based on a new computer presentation of the elements of the fundamental group of a punctured disk this presentation can be used also for other algorithms

an isoperimetric inequality for artin groups of finite type we show that artin groups of finite type satisfy a quadratic isoperimetric inequality moreover we describe an explicit algorithm to solve the word problem in quadratic time

steady flow toward wells in heterogeneous formations mean head and equivalent conductivity we consider steady flow of water in a confined aquifer toward a fully penetrating well of radius rw figure 1 the hydraulic conductivity k is modeled as a three dimensional stationary random space function the two point covariance of y in k kg is of axisymmetric anisotropy with i and i the horizontal and vertical integral scales respectively and kg the geometric mean of k unlike previous studies which assumed constant flux the well boundary condition is of given constant head figure 1 the aim of the study is to derive the mean head h and the mean specific discharge q as functions of the radial coordinate r and of the parameters y2 e i i and rw i an approximate solution is obtained at first order in y2 by replacing the well by a line source of strength proportional to k and by assuming ergodicity i e equivalence between space averages over the vertical and h q ensemble means an equivalent conductivity keq is defined as the fictitious one of a homogeneous aquifer which conveys the same discharge q as the actual one for the given head hw in the well and a given head in a piezometer at distance r from the well this definition corresponds to the transmissivity determined in a pumping test by an observer that measures hw andq the main result of the study is the relationship 19 keq ka 1 kefu where ka is the conductivity arithmetic mean and kefu is the effective conductivity for mean uniform flow in the horizontal direction in the same aquifer the weight coefficient 10 has the simple approximate expression ln r i in r rw near the well 0 and keq ka which is easily understood since for rw i 1 the formation behaves locally like a stratified one in contrast far from the well 1 and keq kefu the flow being slowly varying there since ka kefu our result indicates that the transmissivity is overestimated in a pumping test in a steady state and it decreases with the distance from the well however the difference between ka and kefu is small for highly anisotropic formations for which e 1 a nonlocal effective conductivity which depends only on the heterogeneous structure is derived in appendix a along the lines of indelman and abramovich 1994

conditional stochastic mapping of transport connectivity 1 we present a method for the stochastic simulation of point to point transport connectivity honoring data from three types of information 1 travel time estimates obtained from field tracer tests 2 estimates of flow connectivity indicators obtained from the relatively fast or slow flow response that is observed at a point location given the flow impulse at another location and 3 measurements of transmissivity at a local scale the method thus efficiently integrates data obtained from different hydraulic tests each sampling different areas within the aquifer to achieve this we first extend the concept of point to point flow connectivity and transport connectivity mathematically formulated by trinchero et al 2008 for pumping conditions to support a more general flow configuration interestingly point to point flow connectivity can be generally seen as a weighted integral of transmissivity over the entire domain the weighting function being proportional to the sensitivity of heads with respect to the natural log of transmissivity per unit of aquifer volume on the contrary point to point transport connectivity is a weighted integral along the particle path of the solute mass that involves two variables transmissivity and flow connectivity each variable has its own distinct weighting function the weighting function of transmissivity is inversely proportional to both the homogeneous travel time and the point velocity sampled along the travel path on this basis we show how to generate conditional point to point transport connectivity maps the method avoids the inference of cross covariance functions between variables measured over different scales and sampled areas which cannot be otherwise estimated with a few data measurements by expressing them as a function of the local transmissivity covariance function an example of the method is provided to evaluate the worth of including tracer data to delineate capture zones of abstraction wells originally defined from local transmissivity measurements monte carlo simulations reveal that the impact of including tracer data is a maximum when the travel time data are obtained at a location different than that of transmissivity measurements the reason is that weighting functions give larger weights to the injection location so introducing tracer test data at points where transmissivity is already known is somewhat redundant

in search of minimal random braid configurations a geometric braid consists of n curves stretching between two parallel planes a group structure may be defined on a geometric braid yielding an algebraic braid braids provide information on the structure of knots and links and have many practical applications for example in fluid mechanics and astrophysics a well known problem in braid theory consists of finding minimal crossing number braids no efficient algorithm which solves this problem using group theory seems to be possible for n 3 here we investigate several different approaches to obtaining minimal configurations we employ three different relaxation techniques and compare them with each other and with an algebraic heuristic algorithm in terms of minimization of energy and crossing number and time efficiency by energy we mean total string length of the braid it is found that more than half of the crossings of a sufficiently large braid in terms of crossing number and number of strings are redundant we analyse the different methods and say in what circumstances which method is to be favoured and conclude that minimum braid energy and minimum braid crossing number are substantially different measures of topological complexity for braids

regularization operators for natural images based on nonlinear perception models image restoration requires some a priori knowledge of the solution some of the conventional regularization techniques are based on the estimation of the power spectrum density simple statistical models for spectral estimation just take into account second order relations between the pixels of the image however natural images exhibit additional features such as particular relationships between local fourier or wavelet transform coefficients biological visual systems have evolved to capture these relations we propose the use of this biological behavior to build regularization operators as an alternative to simple statistical models the results suggest that if the penalty operator takes these additional features in natural images into account it will be more robust and the choice of the regularization parameter is less critical

a new approach to the word and conjugacy problems in the braid groups abstract a new presentation of the n string braid group b n is studied using it a new solution to the word problem in b n is obtained which retains most of the desirable features of the garside thurston solution and at the same time makes possible certain computational improvements we also give a related solution to the conjugacy problem but the improvements in its complexity are not clear at this writing

a dual braid monoid for the free group abstract we construct a quasi garside monoid structure for the free group this monoid should be thought of as a dual braid monoid for the free group generalising the constructions by birman ko lee and by the author of new garside monoids for artin groups of spherical type

schur rings over infinite groups ii abstract we construct non traditional schur rings over various infinite groups including surface groups some free products with amalgamation psl 2 z and some groups related to crystallographic groups here non traditional means that the schur rings are not direct products wedge products or orbit schur rings in certain cases we are able to investigate eigenvalues and eigenvectors for these schur rings

the group of parenthesized braids we investigate a group b that includes artin s braid group b8 and thompson s group f the elements of b are represented by braids diagrams in which the distances between the strands are not uniform and besides the usual crossing generators new rescaling operators shrink or stretch the distances between the strands we prove that b is a group of fractions that it is orderable admits a nontrivial self distributive structure i e one involving the law x yz xy xz it embeds in the mapping class group of a sphere with a cantor set of punctures and that artin s representation of b8 into the automorphisms of a free group extends to b

flow to a well in a multiaquifer system solutions are calculated for both steady and unsteady flow to a well in a multiaquifer system with n horizontal aquifers aquifer and aquitard properties may vary from one layer to the next but are assumed constant in the horizontal direction the solutions which are expressed in closed form require the solution of generalized eigenvalue problems for their numerical evaluation it is shown that the matrices appearing in these eigenvalue problems are symmetric and positive definite which means that the eigenvalues are real and positive and that the solution always exists finally a solution is calculated for a numerical example

random walks on three strand braids and on related hyperbolic groups we investigate the statistical properties of random walks on the simplest nontrivial braid group b3 and on related hyperbolic groups we provide a method using cayley graphs of groups allowing us to compute explicitly the probability distribution of the basic statistical characteristics of random trajectories the drift and the return probability the action of the groups under consideration in the hyperbolic plane is investigated and the distribution of a geometric invariant the hyperbolic distance is analysed it is shown that a random walk on b3 can be viewed as a magnetic random walk on the group psl 2

equivalent transmissivity of heterogeneous leaky aquifers for steady state radial flow 1 the purpose of this study is to estimate the equivalent transmissivity for two dimensional steady state radial flow toward a fully penetrating well in a heterogeneous leaky aquifer the log transmissivity of the pumped aquifer is modeled as a multivariate random spatial function with stationary mean and exponential semivariogram while the aquitard conductance is assumed to be spatially uniform an approximate expression for the upscaled or block transmissivity defined as the transmissivity of an equivalent homogeneous leaky aquifer system with the same pumping is proposed the proposed relation expresses the upscaled transmissivity as a weighted average of the log transforms of the point transmissivity values monte carlo simulations are used to numerically validate the proposed upscaling expression for wide ranges of aquifer parameters the relation of the weighing function to the statistical parameters of the transmissivity field is discussed the first and second moments of the upscaled transmissivity are also estimated as a function of the problem parameters the expected value of the equivalent transmissivity is shown to increase from the geometric mean to the arithmetic mean as the aquitard conductance increases from zero to infinity

geostatistical inverse modeling of transient pumping tests using temporal moments of drawdown 1 pumping tests belong to the most common techniques of hydrogeological site assessment while the steady state drawdown is determined by the distribution of transmissivity alone the transient behavior is also influenced by the storativity field in geostatistical inverse modeling the spatial distributions of both transmissivity and storativity are inferred from the drawdown curves and prior information on the spatial correlation of the parameter fields so far however transient data have hardly been analyzed by geostatistical inverse methods because the computational effort is rather high in the present study we characterize the drawdown by its temporal moments we present moment generating equations and corresponding equations to compute the sensitivity of the temporal moments of drawdown with respect to the distributions of transmissivity and storativity we utilize these equations to infer the transmissivity and storativity fields from transient pumping tests using the quasi linear geostatistical approach of inverse modeling considering temporal moments rather than full drawdown curves drastically reduces the computational effort of the estimation procedure in test cases we show that the first two temporal moments are sufficient to characterize the drawdown curves we investigate how erroneous assumptions regarding the spatial variability of storativity affect the estimate of the transmissivity field and we analyze the effect of truncating the measured drawdown curves

dual garside structure and reducibility of braids abstract benardete gutierrez and nitecki showed an important result which relates the geometrical properties of a braid as a homeomorphism of the punctured disk to its algebraic garside theoretical properties namely they showed that if a braid sends a standard curve to another standard curve then the image of this curve under the action of each factor of the left normal form of the braid with the classical garside structure is also standard we provide a new simple geometric proof of the result by benardete gutierrez nitecki which can be easily adapted to the case of the dual garside structure of braid groups with the appropriate definition of standard curves in the dual setting this yields a new algorithm for determining the nielsen thurston type of braids

type curve interpretation of late time pumping test data in randomly heterogeneous aquifers 1 the properties of heterogeneous media vary spatially in a manner that can seldom be described with certainty it may however be possible to describe the spatial variability of these properties in terms of geostatistical parameters such as mean integral spatial correlation scale and variance neuman et al 2004 proposed a graphical method to estimate the geostatistical parameters of natural log transmissivity on the basis of quasi steady state head data when a randomly heterogeneous confined aquifer is pumped at a constant rate from a fully penetrating well they conjectured that a quasi steady state during which heads vary in space time while gradients vary only in space develops in a statistically homogeneous and horizontally isotropic aquifer as it does in a uniform aquifer we confirm their conjecture numerically for gaussian log transmissivities show that time drawdown data from randomly heterogeneous aquifers are difficult to interpret graphically and demonstrate that quasi steady state distance drawdown data are amenable to such interpretation by the type curve method of neuman et al the method yields acceptable estimates of statistical log transmissivity parameters for fields having either an exponential or a gaussian spatial correlation function these estimates are more robust than those obtained using the graphical time drawdown method of copty and findikakis 2003 2004a we apply the method of neuman et al 2004 simultaneously to data from a sequence of pumping tests conducted in four wells in an aquifer near tubingen germany and compare our transmissivity estimate with estimates obtained from 312 flowmeter measurements of hydraulic conductivity in these and eight additional wells at the site we find that 1 four wells are enough to provide reasonable estimates of lead log transmissivity statistics for the tubingen site using this method and 2 the time drawdown method of cooper and jacob 1946 underestimates the geometric mean transmissivity at the site by 30 40

the rotating normal form of braids is regular abstract defined on birman ko lee monoids the rotating normal form has strong connections with the dehornoy s braid ordering it can be seen as a process for selecting between all the representative words of a birman ko lee braid a particular one called rotating word in this paper we construct for all n 2 a finite state automaton which recognizes rotating words on n strands proving that the rotating normal form is regular as a consequence we obtain the regularity of a definite normal form defined on the whole braid group

psychophysically tuned divisive normalization approximately factorizes the pdf of natural images the conventional approach in computational neuroscience in favor of the efficient coding hypothesis goes from image statistics to perception it has been argued that the behavior of the early stages of biological visual processing e g spatial frequency analyzers and their nonlinearities may be obtained from image samples and the efficient coding hypothesis using no psychophysical or physiological information in this work we address the same issue in the opposite direction from perception to image statistics we show that psychophysically fitted image representation in v1 has appealing statistical properties for example approximate pdf factorization and substantial mutual information reduction even though no statistical information is used to fit the v1 model these results are complementary evidence in favor of the efficient coding hypothesis

uniform measures on braid monoids and dual braid monoids we aim at studying the asymptotic properties of typical positive braids respectively positive dual braids denoting by mu k the uniform distribution on positive dual braids of length k we prove that the sequence mu k k converges to a unique probability measure mu infty on infinite positive dual braids the key point is that the limiting measure mu infty has a markovian structure which can be described explicitly using the combinatorial properties of braids encapsulated in the mobius polynomial as a by product we settle a conjecture by gebhardt and tawn j algebra 2014 on the shape of the garside normal form of large uniform braids

a simple algorithm for finding short sigma definite representatives abstract we describe a new algorithm which for each braid returns a quasi geodesic definite word representative defined as a braid word in which the generator i with maximal index i appears either only positively or only negatively

prediction of steady state flow in nonuniform geologic media by conditional moments exact nonlocal formalism effective conductivities and weak approximation we consider the effect of measuring randomly varying local hydraulic conductivities k x on one s ability to predict steady state flow within a bounded domain driven by random source and boundary functions more precisely we consider the prediction of local hydraulic head h x and darcy flux q x by means of their unbiased ensemble moments h x and q x conditioned on measurements of k x these predictors satisfy a deterministic flow equation in which q x x h x r x where x is a relatively smooth unbiased estimate of k x and r x is a residual flux we derive a compact integral expression for r x which is rigorously valid for a broad class of k x fields including fractals it demonstrates that q x is nonlocal and non darcian so that an effective hydraulic conductivity does not generally exist we show analytically that under uniform mean flow the effective conductivity may be a scalar a symmetric or a nonsymmetric tensor or a set of directional scalars which do not form a tensor we demonstrate numerically that in two dimensional mean radial flow it may increase from the harmonic mean of k x near interior and boundary sources to the geometric mean far from such sources for cases where r x can neither be expressed nor approximated by a local expression we propose a weak integral approximation closure which appears to work well in media with pronounced heterogeneity and improves as the quantity and quality of k x measurements increase the nonlocal deterministic flow equation can be solved numerically by standard methods our theory shows clearly how the scale of grid discretization should relate to the scale quantity and quality of available data after providing explicit approximations for the second moments of head and flux prediction errors we conclude by discussing practical methods to compute x from noisy measurements of k x and to calculate required second moments of the associated estimation errors when k x is lognormal

average contaminant concentration and mass flow in aquifers from time dependent pumping well data analytical framework 1 conventional water samples are representative for small subsurface volumes relative to the scale of many natural geological heterogeneities we present an analytical framework for estimation of representative field scale average concentrations and mass flows on the basis of much larger sampling volumes that are obtained through so called integral pumping tests the contaminant concentration is then measured as a function of time in a pumping well and used for estimation of the conditions in the aquifer prior to and after pumping increasing the observation scale to the size of the well capture zone this method complements and provides an alternative to conventional monitoring grids where mass flow and concentration may be misinterpreted or plumes even missed because of problems related to grid spacing the not measured initial spatial concentration distribution and the time dependent concentration measured at the well are related through a volterra integral equation of the first kind for limiting cases of short and long dimensionless pumping duration two closed form analytical solutions are given from which the mass flow and average concentration can be evaluated furthermore a new solution for evaluating integral pumping tests of any duration is provided and used for investigating the applicability of the simple analytical closed form solutions for interpreting test results from seven large scale contaminated sites in europe

ergodicity of pumping tests 1 standard interpretations of pumping tests in heterogeneous formations rely on effective representations of porous media which replace spatially varying hydraulic properties with their constant counterparts averaged over the support volume of a test rigorous approaches for deriving representative effective apparent upscaled etc parameters employ either ensemble or spatial averaging we derive a set of conditions under which these two paradigms yield identical results we refer to them as conditions for the ergodicity of pumping tests this allows one to use stochastic approaches to estimate the statistics of the spatial variability of hydraulic parameters on scales smaller than the support volume of a pumping test

a stochastic analysis of pumping tests in laterally nonuniform media conventional pumping test analysis methodology assumes that aquifer transmissivity is invariant in space the ramifications of this assumption are examined for hypothetical units whose variations in transmissivity are considered to be reasonable representations of variations possible in natural systems the dependence of pumping test transmissivity on spatial angular and radial and temporal location of observations and the method of drawdown analysis is assessed the dependence on the angular position of an observation well appears of little significance dependence on radial position however can be strong the dependence on the interval of time used in the pumping test analysis is only important in highly variable systems methods of drawdown analysis that yield identical estimates in uniform units yield differing estimates in nonuniform ones as a result of a difference in data fitting procedures a reasonable estimate of transmissivity at a regional scale can be obtained from a cooper jacob analysis applied at a large duration of pumpage in general conventional approaches for pumping test analysis should be viable in the nonuniform aquifers of the type considered here

on krammer s representation of the braid group a connection is made between the krammer representation and the birman murakami wenzl algebra inspired by a dimension argument a basis is found for a certain irrep of the algebra and relations which generate the matrices are found following a rescaling and change of parameters the matrices are found to be identical to those of the krammer representation the two representations are thus the same proving the irreducibility of one and the faithfulness of the other

a fast method for comparing braids abstract we describe a new method for comparing braid words which relies both on the automatic structure of the braid groups and on the existence of a linear ordering on braids this syntactical algorithm is a direct generalization of the classical words reduction used in the description of free groups and is more efficient in practice than all previously known methods

bayesian identification of the local transmissivity using time drawdown data from pumping tests 1 conventional pumping test analysis techniques focus mostly on estimating the effective transmissivity of the perturbed subsurface volume surrounding the extraction and observation wells ignoring the existing local scale heterogeneity the purpose of this paper is to explore whether transient drawdown data derived from pumping tests can also be used to identify the statistical spatial structure of the local transmissivity field the log transmissivity is modeled as a multivariate random spatial function with stationary mean and exponential semivariogram monte carlo simulations are used to compute the transient drawdown for different values of the log transmissivity variance and integral scale on the basis of these simulations a bayesian procedure is developed to estimate the probability density functions of these two statistical parameters the main benefit of using a bayesian approach is that it readily accounts for the uncertainty of the estimated parameters application of the proposed procedure to simulated drawdown data shows that it is possible to characterize the local transmissivity from pumping test data and that the reliability of the estimates increases with an increase in the number of available tests

braid groups and left distributive operations the decidability of the word problem for the free left distributive law is proved by introducing a structure group which describes the underlying identities this group is closely connected with artin s braid group b braid colourings associated with free left distributive structures are used to show the existence of a unique ordering on the braids which is compatible with left translation and such that every generator ai is preponderant over all ak with k i this ordering is a linear ordering the first goal of the present paper is to give a proof of the following result which had been conjectured for several years theorem there is an effective algorithm for deciding whether a given identity is or is not a consequence of the left distributivity identity x yz xy xz until recently this question has had a rather unusual status conditional solutions were given independently in 6 and 24 where the decision problem was reduced to a specific algebraic hypothesis one which had been shown by richard laver to be a consequence of a very strong set theoretical axiom of a type which certainly cannot be derived from the usual axioms of set theory namely a large cardinal axiom the question as to whether a strong axiom of this type was actually needed remained open opinions were in fact divided a connection between large cardinals and a purely finitistic problem of this caliber would seem paradoxical but it is well known that problems of a combinatorial type can embody surprisingly strong proof principles see for instance 28 and some work on free distributive structures has shown that they do give rise to intrinsically complex objects typically nonprimitive recursive ones cf 12 13 we will show that in the present case a solution which is purely algebraic in terms of the methods employed and the spirit of the argument can in fact be given in particular no unusual set theoretical axioms are required for this argument the decision method described in 6 was fully effective but the proof of the correctness of the algorithm amounted to a direct invocation of this specific algebraic hypothesis which followed from a large cardinal axiom with no hint of a direct proof we shall refine this decision method below introducing uniqueness at each step of the process and the correctness will then be seen to follow very naturally received by the editors february 5 1993 1991 mathematics subject classification primary 20f36 1 7a30 1 7a50

image compression via joint statistical characterization in the wavelet domain we develop a probability model for natural images based on empirical observation of their statistics in the wavelet transform domain pairs of wavelet coefficients corresponding to basis functions at adjacent spatial locations orientations and scales are found to be non gaussian in both their marginal and joint statistical properties specifically their marginals are heavy tailed and although they are typically decorrelated their magnitudes are highly correlated we propose a markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties and show that it accounts for the statistics of a wide variety of images including photographic images graphical images and medical images in order to directly demonstrate the power of the model we construct an image coder called epwic embedded predictive wavelet image coder in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model bitplanes are ordered using a greedy algorithm that considers the mse reduction per encoded bit the decoder uses the statistical model to predict coefficient values based on the bits it has received despite the simplicity of the model the rate distortion performance of the coder is roughly comparable to the best image coders in the literature

gaussian groups and garside groups two generalisations of artin groups it is known that a number of algebraic properties of the braid groups extend to arbitrary finite coxeter type artin groups here we show how to extend the results to more general groups that we call garside groups define a gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths and where left and right lowest common multiples exist a garside monoid is a gaussian monoid in which the left and right lowest common multiples satisfy an additional symmetry condition a gaussian group is the group of fractions of a gaussian monoid and a garside group is the group of fractions of a garside monoid braid groups and more generally finite coxeter type artin groups are garside groups we determine algorithmic criteria in terms of presentations for recognizing gaussian and garside monoids and groups and exhibit infinite families of such groups we describe simple algorithms that solve the word problem in a gaussian group show that these algorithms have a quadratic complexity if the group is a garside group and prove that garside groups have quadratic isoperimetric inequalities we construct normal forms for gaussian groups and prove that in the case of a garside group the language of normal forms is regular symmetric and geodesic has the 5 fellow traveller property and has the uniqueness property this shows in particular that garside groups are geodesically fully biautomatic finally we consider an automorphism of a finite coxeter type artin group derived from an automorphism of its defining coxeter graph and prove that the subgroup of elements fixed by this automorphism is also a finite coxeter type artin group that can be explicitly determined 1991 mathematics subject classification primary 20f05 20f36 secondary 20b40 20m05

generic case complexity decision problems in group theory and random walks abstract we give a precise definition of generic case complexity and show that for a very large class of finitely generated groups the classical decision problems of group theory the word conjugacy and membership problems all have linear time generic case complexity we prove such theorems by using the theory of random walks on regular graphs

algorithmic recognition of quasipositive braids of algebraic length two abstract we give an algorithm to decide if a given braid is a product of two factors which are conjugates of given powers of standard generators of the braid group the same problem is solved in a certain class of garside groups including artin tits groups of spherical type the solution is based on the garside theory and especially on the theory of cyclic sliding developed by gebhardt and gonzalez meneses we show that if a braid is of the required form then any cycling orbit in its sliding circuit set in the dual garside structure contains an element for which this fact is immediately seen from the left normal form

complete positive group presentations abstract a combinatorial property of positive group presentations called completeness is introduced with an effective criterion for recognizing complete presentations and an iterative method for completing an incomplete presentation we show how to directly read several properties of the associated monoid and group from a complete presentation cancellativity or existence of common multiples in the case of the monoid or isoperimetric inequality in the case of the group in particular we obtain a new criterion for recognizing that a monoid embeds in a group of fractions typical presentations eligible for the current approach are the standard presentations of the artin tits groups and the heisenberg group