spherical functions on symmetric cones in this note we obtain a recursive formula for the spherical functions associated with the symmetric cone of a formally real jordan algebra we use this formula as an inspiration for a similar recursive formula involving the jack polynomials

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

chaotic systems counting the number of periods abstract characterization of chaotic motion may proceed both at an averaged macroscopic level using such notions as lyapunov exponents dimensions and entropies and at a microscopic level in the latter case the number of periodic orbits being a topological invariant plays an important role for various one dimensional mappings the counting problem itself has many interesting facets and may be solved more or less completely in different ways recent progress in this counting problem is summarized with the hope that the explicit results obtained may be useful for classification of higher dimensional dissipative chaotic systems

a bi hamiltonian structure for the integrable discrete non linear schrodinger system abstract this paper shows that the al ablowitz ladik hierarchy of integrable equations can be explicitly viewed as a hierarchy of commuting flows which a are hamiltonian with respect to both a standard local poisson operator j and a new non local skew almost poisson operator k on the appropriate space b can be recursively generated from a recursion operator r k j 1 in addition the proof of these facts relies upon two new pivotal resolvent identities which suggest a general method for uncovering bi hamiltonian structures for other families of discrete integrable equations

on the calculation of misiurewicz patterns in one dimensional quadratic maps abstract in this work we give for the first time a table with all misiurewicz points m n p for low values of the preperiod and period 2 n 8 1 p 5 in one dimensional quadratic maps in the particular case of m n 1 important misiurewicz points which are all placed in the period 1 chaotic band the preperiod values are 2 n 11 a brute force algorithm to obtain all the symbolic sequences patterns of the m n p and a more efficient algorithm to obtain the patterns of m n 1 are also shown

invariant functions on lie groups and hamiltonian flows of surface group representations si est le groupe fondamental d une surface orientee fermee s et g est un groupe de lie satisfaisant des conditions tres generales alors l espace hom g g des classes de conjugaison de representation g a une structure symplectique naturelle on etudie la geometrie de cette structure symplectique a l aide d une famille naturelle de fonctions sur hom g g

point set lattice theoretic topology this essay attempts to survey in a coherent way certain aspects of point set lattice theoretic or poslat topology by which we mean fuzzy topology grounded in notions of sets functions powersets and powerset operators the latter two being lattice theoretic in nature and examined from a lattice theoretic point of view using methods of category theory connections with other related issues and developments are frequently given

universal scaling law for the largest lyapunov exponent in coupled map lattices coupled map lattices cmls 1 as discrete analogs tocoupled oscillators and partial differential equations havein recent years become the model of choice for developingintuitions and concepts in the study of spatiotemporalchaotic systems among the variety of quantities appliedto characterize the dynamics of a cml the spectrum oflyapunov exponents stands out for its ease of numericalevaluation and for the wealth of information that derivesfrom it for example from pesin s formula 2 thesum of all positive lyapunov exponents provides anestimate of the kolmogorov sinai entropy meanwhile one obtains the information dimension of the chaoticattractor by employing the kaplan yorke conjecture 3 moreover the largest lyapunov exponent lle denotedhenceforth by l quanti es the sensitive dependence oninitial conditions a hallmark of chaos 4 by yieldingthe rate of exponential divergence of two typical nearbytrajectories in this letter we focus on the scaling behavior of lnear certain limiting situations consider a diffusivelycoupled map lattice of the form

on douady earle extension and the contractibility of the vmo teichmuller space abstract douady earle extension provides a quasiconformal extension of a quasisymmetric homeomorphism to the unit disk and induces a continuous self map of beltrami coefficients in this note we show that is also continuous under a stronger topology on those beltrami coefficients which induce vanishing carleson measures and thus project to the vmo teichmuller space an immediate consequence is that the vmo teichmuller space is contractible

on a likelihood approach for monte carlo integration the use of estimating equations has been a common approach for constructing monte carlo estimators recently kong et al proposed a formulation of monte carlo integration as a statistical model making explicit what information is ignored and what is retained about the baseline measure from simulated data the baseline measure is estimated by maximum likelihood and then integrals of interest are estimated by substituting the estimated measure for two different situations in which independent observations are simulated from multiple distributions we show that this likelihood approach achieves the lowest asymptotic variance possible by using estimating equations in the first situation the normalizing constants of the design distributions are estimated and meng and wong s bridge sampling estimating equation is considered in the second situation the values of the normalizing constants are known thereby imposing linear constraints on the baseline measure estimating equations including hesterberg s

a general bahadur representation of m estimators and its application to linear regression with nonstochastic designs we obtain strong bahadur representations for a general class of m estimators that satisfies sigma i psi x i theta o delta n where the x i s are independent but not necessarily identically distributed random variables the results apply readily to m estimators of regression with nonstochastic designs more specifically we consider the minimum l p distance estimators bounded influence gm estimators and regression quantiles under appropriate design conditions the error ratesobtained for the first order approximations are sharp in these cases we also provide weaker and more easily verifiable conditions that suffice for an error rate that is suboptimal but strong enough for deriving the asymptotic distribution of m estimators in a wide variety of problems

the moderate deviation principle for minimizers of convex processes abstract this paper mainly discusses the asymptotic behaviors on the minimizers of convex processes in view of the convexity argument it is proved that the minimizers of convex processes with parameterized objective functions satisfy the functional moderate deviation principle as some applications the estimators in two basic models threshold regression models and stochastic dynamical systems are studied in particular the exponential convergence principles on the estimators converging to true parameters are proved

strong representations for lad estimators in linear models consider the standard linear modely i z i e i i 1 2 n where zi denotes theith row of ann x p design matrix p is an unknown parameter to be estimated andei are independent random variables with a common distribution functionf the least absolute deviation lad estimate tilde beta of is defined as any solution of the minimization problem sum limits i 1 n left y i z i tilde beta right inf left sum limits i 1 n left y i z i beta right beta in mathbb r p right

l filters and lf topologies abstract for a complete quasi monoidal lattice l with some additional properties we consider the category of l filtered sets with fixed basis l and we find out a functorial relation from this category to that of the l fuzzy topological spaces on the other hand a morphism in the category of complete quasi monoidal lattices allows us to establish a pair of adjoint functors change of basis between the corresponding categories of l filterd sets

skewness for multivariate distributions two approaches this paper presents two approaches for qualitative quantitative and comparative concepts of skewness to be defined with respect to the spatial median for multivariate distributions they extend the known quantile based notions defined for real distributions the main tool for such extensions consists of a family of central parts that provide suitable generalizations of the real interquantile intervals

the strong law of large numbers for sequential decisions under uncertainty combines optimization and ergodic theory to characterize the optimum long run average performance that can be asymptotically attained by nonanticipating sequential decisions let x sub t be a stationary ergodic process and suppose an action b sub t must be selected in a space spl bscr with knowledge of the t past x sub 0 spl middot spl middot spl middot x sub t 1 at the beginning of every period t spl ges 0 action b sub t will incur a loss l b sub t x sub t at the end of period t when the random variable x sub t is revealed the author proves under mild integrability conditions that the optimum strategy is to select actions that minimize the conditional expected loss given the currently available information at each step the minimum long run average loss per decision can be approached arbitrarily closely by strategies that are finite order markov and under certain continuity conditions it is equal to the minimum expected loss given the infinite past if the loss l b x is bounded and continuous and if the space spl bscr is compact then the minimum can be asymptotically attained even if the distribution of the process x sub t is unknown a priori and must be learned from experience

on a geometric notion of quantiles for multivariate data abstract an extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered the approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles both of which have been extensively studied in the literature these geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other l estimates of multivariate location and they lead to a directional notion of central and extreme points in a multidimensional setup such quantiles can be defined as meaningful and natural objects even in infinite dimensional hilbert and banach spaces and they yield an effective generalization of quantile regression in multiresponse linear model problems desirable equivariance properties are shown to hold for these multivariate quantiles and issues related to their computation for data in finite dimensional spaces are discussed n 1 2 consistenc

comment on adaptive confidence intervals for the test error in classification inspired by the non regular framework studied in laber and murphy 2011 we propose a family of adaptive classifiers we discuss briefly their asymptotic properties and show that under the non regular framework these classifiers have an oracle property and consequently have smaller asymptotic variance and smaller asymptotic test error variance than those of the original classifier we also show that confidence intervals for the test error of the adaptive classifiers based on either normal approximation or centered percentile bootstrap are consistent

multivariate quantiles and multiple output regression quantiles from l1 optimization to halfspace depth a new multivariate concept of quantile based on a directional version of koenker and bassett s traditional regression quantiles is introduced for multivariate location and multiple output regression problems in their empirical version those quantiles can be computed efficiently via linear programming techniques consistency bahadur representation and asymptotic normality results are established most importantly the contours generated by those quantiles are shown to coincide with the classical halfspace depth contours associated with the name of tukey this relation does not only allow for efficient depth contour computations by means of parametric linear programming but also for transferring from the quantile to the depth universe such asymptotic results as bahadur representations finally linear programming duality opens the way to promising developments in depth related multivariate rank based inference

bahadur representation of m sb m estimates we take a unified approach to asymptotic properties of m m estimates based on i i d observations defined through the minimization of a real valued criterion function of one or more variables our results are applicable to a host of location and scale estimators found in the literature

an integrable discretization of the rational mathfrak su 2 gaudin model and related systems the first part of the present paper is devoted to a systematic construction of continuous time finite dimensional integrable systems arising from the rational su 2 gaudin model through certain contraction procedures in the second part we derive an explicit integrable poisson map discretizing a particular hamiltonian flow of the rational su 2 gaudin model then the contraction procedures enable us to construct explicit integrable discretizations of the continuous systems derived in the first part of the paper

multiple bumping of components of deformation spaces of hyperbolic 3 manifolds let m be a hyperbolizable 3 manifold with nonempty incompressible boundary of negative euler characteristic suppose that b 1 b k is a collection of components of the interior of the space of complete marked hyperbolic 3 manifolds homotopy equivalent to m such that for any i j inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i we prove that there is a geometrically finite hyperbolic structure on int m which is in the closure of each b i moreover we show that this structure can be constructed so as to admit quasiconformal deformations which also lie in the closure of every b i

m estimation of linear models with dependent errors we study asymptotic properties of m estimates of regression parameters in linear models in which errors are dependent weak and strong bahadur representations of the m estimates are derived and a central limit theorem is established the results are applied to linear models with errors being short range dependent linear processes heavy tailed linear processes and some widely used nonlinear time series

semiclassical mechanics of the wigner 6j symbol the semiclassical mechanics of the wigner 6j symbol is examined from the standpoint of wkb theory for multidimensional integrable systems to explore the geometrical issues surrounding the ponzano regge formula the relations among the methods of roberts and others for deriving the ponzano regge formula are discussed and a new approach based on the recoupling of four angular momenta is presented a generalization of the yutsis type of spin network is developed for this purpose special attention is devoted to symplectic reduction the reduced phase space of the 6j symbol the 2 sphere of kapovich and millson and the reduction of poisson bracket expressions for semiclassical amplitudes general principles for the semiclassical study of arbitrary spin networks are laid down some of these were used in our recent derivation of the asymptotic formula for the wigner 9j symbol

applications of localic separation axioms compactness axioms representations and compactifications to poslat topological spaces fuzzy topology first appeared about twenty seven years ago with chang s initial paper 1968 yet the fundamental issues of compactness and low order separation axioms remain unresolved this paper resolves these issues with respect to topological compactification categorical compactification and stone representation theorems using the theory of locales and previous work of the author in fuzzy sobriety our results give the first compactification reflectors for all traditional fuzzy topology construct classes of generalized stone representations of boolean algebras and distributive lattices and show categorically that the fuzzy analogue of classical compact hausdorff spaces is the categories of chang compact localic regular sober fuzzy topological spaces

prediction functions for categorical panel data prediction of categorical responses in panel studies is considered prediction functions based on general conditional log linear models are investigated for statistical properties both from a population perspective and a sampling perspective problems such as existence and uniqueness of optimal prediction functions are addressed and basic properties of measures of prediction quality are examined estimation consistency and asymptotic normality are studied for the proposed parameter estimates and measures of prediction quality

absolutely continuous invariant measures for one parameter families of one dimensional maps given a one parameter familyf x of maps of the interval 0 1 we consider the set of parameter values for whichf has an invariant measure absolutely continuous with respect to lebesgue measure we show that this set has positive measure for two classes of maps i f x f x where 0 4 andf x is a functionc3 near the quadratic mapx 1 x and ii f x f x mod 1 wheref isc3 f 0 f 1 0 andf has a unique nondegenerate critical point in 0 1

a new approach for fuzzy topology ii abstract we point out a new approach for fuzzy topology with fuzzy logic and discuss the neighborhood structure of a point and the convergence of nets and filters in this new framework

deformations of polyhedra and polygons by the unitary group we introduce the set of framed convex polyhedra with n faces as the symplectic quotient c2n su 2 a framed polyhedron is then parametrized by n spinors living in c2 satisfying suitable closure constraints and defines a usual convex polyhedron plus extra u 1 phases attached to each face we show that there is a natural action of the unitary group u n on this phase space which changes the shape of faces and allows to map any framed polyhedron onto any other with the same total boundary area this identifies the space of framed polyhedra to the grassmannian space u n su 2 u n 2 we show how to write averages of geometrical observables polynomials in the faces area and the angles between them over the ensemble of polyhedra distributed uniformly with respect to the haar measure on u n as polynomial integrals over the unitary group and we provide a few methods to compute these integrals systematically we also use the itzykson zuber formula from matrix models as the generating function

conditional log linear models for analyzing categorical panel data abstract conditional log linear models are developed for panel data and used to predict sequences of categorical responses the class of models considered includes conventional markov models and independence models as well as distance models in which all previous responses and present and past values of covariates are used to predict the current response the approach taken in this article has some advantages over the marginal modeling approach that has become popular for longitudinal studies quality of prediction is measured by using a logarithmic penalty function given a model conditional probabilities of responses consistent with the model are selected to provide the smallest expected penalty this minimum expected penalty provides a measure of the predictive power of a model models are compared through their predictive power as measured by the proportional reduction in expected penalty ways of incorporating the number of parameters of the competing models are discussed this emphasis on predicti

a kahler structure on the moduli space of isometric maps of a circle into euclidean space we study the spaces and and lip of smooth resp non degenerate lipschitz isometric maps of a circle into euclidean space modulo orientation preserving euclidean motions we prove that and lip are infinite dimensional kahler manifolds in particular they are complex frechet resp banach manifolds this is proved by an infinite dimensional version of the kirwan kempf ness theorem kir84 kn78 nes84 relating symplectic quotients to holomorphic quotients applied to the action ofpsl2 on the free loop space ofs2

geometric and algebraic reduction for singular momentum maps this paper concerns the reduction of singular constraint sets of symplectic manifolds it develops a geometric reduction procedure as well as continues the work of sniatycki and patrick on reduction a la dirac the relationships among the dirac geometric and sniatycki weinstein algebraic reduction procedures are studied primary emphasis is placed on the case where the constraints are given by the vanishing of a singular momentum map associated to the hamiltonian action of a compact lie group specifically an explicit local normal form is given for the momentum map which is used to show that these various reductions are all well defined and a necessary and sufficient condition for them to agree is derived related conditions are investigated and shown to be sufficient in the case of torus actions numerous examples are computed illustrating the results some discussion and examples are given for the noncompact case

the cohomology ring of weight varieties and polygon spaces we use a theorem of s tolman and j weitsman the cohomology rings of abelian symplectic quotients math dg 9807173 to find explicit formulae for the rational cohomology rings of the symplectic reduction of flag varieties in cn or generic coadjoint orbits of su n by maximal torus actions we also calculate the cohomology ring of the moduli space of n points in cpk which is isomorphic to the grassmannian of k planes in cn by realizing it as a degenerate coadjoint orbit

the generation of random equilateral polygons freely jointed random equilateral polygons serve as a common model for polymer rings reflecting their statistical properties under theta conditions to generate equilateral polygons researchers employ many procedures that have been proved or at least are believed to be random with respect to the natural measure on the space of polygonal knots as a result the random selection of equilateral polygons as well as the statistical robustness of this selection is of particular interest in this research we study the key features of four popular methods the polygonal folding the crankshaft rotation the hedgehog and the triangle methods in particular we compare the implementation and efficacy of these procedures especially in regards to the population distribution of polygons in the space of polygonal knots the distribution of edge vectors the local curvature and the local torsion in addition we give a rigorous proof that the crankshaft rotation method is ergodic

intersection numbers of polygon spaces we study the intersection ring of the space m 1 m of polygons in r 3 we find homology cycles dual to generators of this ring and prove a recursion relation in m the number of edges for their intersection numbers this result is an analog of the recursion relation appearing in the work of witten and kontsevich on moduli spaces of punctured curves and in the work of weitsman on moduli spaces of flat connections on two manifolds of genus g with m marked points based on this recursion formula we obtain an explicit expression for the computation of the intersection numbers of polygon spaces and use it in several examples among others we study the special case of equilateral polygon spaces where all i s are the same and compare our results with the expressions for these particular spaces that have been determined by kamiyama and tezuka finally we relate our explicit formula for the intersection numbers with the generating function for intersection pairings of the moduli space of flat connections of yoshida as well as with equivalent expressions for polygon spaces obtained by takakura and konno through different techniques

around polygons in ℝ3 and s3 we survey certain moduli spaces in low dimensions and some of the geometric structures that they carry and then construct identifications among all of these spaces in particular we identify the moduli spaces of polygons in 3 and s 3 the moduli space of restricted representations of the fundamental group of a punctured 2 sphere the moduli space of flat connections on a punctured sphere the moduli space of parabolic bundles on a sphere the moduli space of weighted points on 1 and the symplectic quotient of so 3 acting diagonally on s 2 n all of these spaces depend on parameters and some the above identifications require the parameters to be small one consequence of this work is that these spaces are all biholomorphic with respect to the most natural complex structures they can each be given

uniqueness of the spatial median on montre que si une mesure de probabilite sur un espace euclidien n est pas concentree sur une droite alors sa mediane spatiale est unique

a fast direct sampling algorithm for equilateral closed polygons sampling equilateral closed polygons is of interest in the statistical study of ring polymers over the past 30 years previous authors have proposed a variety of simple markov chain algorithms but have not been able to show that they converge to the correct probability distribution and complicated direct samplers which require extended precision arithmetic to evaluate numerically unstable polynomials we present a simple direct sampler which is fast and numerically stable and analyze its runtime using a new formula for the volume of equilateral polygon space as a dirichlet type integral

adaptive confidence intervals for the test error in classification the estimated test error of a learned classifier is the most commonly reported measure of classifier performance however constructing a high quality point estimator of the test error has proved to be very difficult furthermore common interval estimators e g confidence intervals are based on the point estimator of the test error and thus inherit all the difficulties associated with the point estimation problem as a result these confidence intervals do not reliably deliver nominal coverage in contrast we directly construct the confidence interval by using smooth data dependent upper and lower bounds on the test error we prove that for linear classifiers the proposed confidence interval automatically adapts to the nonsmoothness of the test error is consistent under fixed and local alternatives and does not require that the bayes classifier be linear moreover the method provides nominal coverage on a suite of test problems using a range of classification algorithms and sample sizes this ar

on ranking and generalization bounds the problem of ranking is to predict or to guess the ordering between objects on the basis of their observed features in this paper we consider ranking estimators that minimize the empirical convex risk we prove generalization bounds for the excess risk of such estimators with rates that are faster than 1 n we apply our results to commonly used ranking algorithms for instance boosting or support vector machines moreover we study the performance of considered estimators on real data sets

the equations for the moduli space of n points on the line a central question in invariant theory is that of determining the relations among invariants geometric invariant theory git quotients come with a natural ample line bundle and hence often a natural projective embedding this question translates to determining the equations of the moduli space under this embedding this article deals with one of the most classical quotients the space of ordered points on the projective line we show that under any weighting of the points this quotient is cut out scheme theoretically by a particularly simple set of quadric relations with the single exception of the segre cubic threefold the space of six points with equal weight we also show that the ideal of relations is generated in degree at most four and we give an explicit description of the generators if all the weights are even e g in the case of equal weight for odd n then we show that the ideal of relations is generated by quadrics

the classification of punctured torus groups thurston s ending lamination conjecture proposes that a flnitely generated kleinian group is uniquely determined up to isometry by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends we present a proof of this conjecture for punctured torus groups these are free two generator kleinian groups with parabolic commutator which should be thought of as representations of the fundamental group of a punctured torus as a consequence we verify the conjectural topological description of the deformation space of punctured torus groups including bers conjecture that the quasi fuchsian groups are dense in this space and prove a rigidity theorem two punctured torus groups are quasi conformally conjugate if and only if they are topologically conjugate

mating non renormalizable quadratic polynomials in this paper we prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1 2 limb of mathcal m is non renormalizable and does not have any non repelling periodic orbits

hyperpolygon spaces and moduli spaces of parabolic higgs bundles abstract given an n tuple of positive real numbers we consider the hyperpolygon space x the hyperkahler quotient analogue to the kahler moduli space of polygons in r 3 we prove the existence of an isomorphism between hyperpolygon spaces and moduli spaces of stable rank 2 holomorphically trivial parabolic higgs bundles over c p 1 with fixed determinant and trace free higgs field this isomorphism allows us to prove that hyperpolygon spaces x undergo an elementary transformation in the sense of mukai as crosses a wall in the space of its admissible values we describe the changes in the core of x as a result of this transformation as well as the changes in the nilpotent cone of the corresponding moduli spaces of parabolic higgs bundles moreover we study the intersection rings of the core components of x in particular we find generators of these rings prove a recursion relation in n for their intersection numbers and use it to obtain explicit formulas for the computation of these numbers using our isomorphism we obtain similar formulas for each connected component of the nilpotent cone of the corresponding moduli spaces of parabolic higgs bundles thus determining their intersection rings as a final application of our isomorphism we describe the cohomology ring structure of these moduli spaces of parabolic higgs bundles and of the components of their nilpotent cone

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

fuchsian groups quasiconformal groups and conical limit sets we construct examples showing that the normalized lebesgue measure of the conical limit set of a uniformly quasiconformal group acting discontinuously on the disc may take any value between zero and one this is in contrast to the cases of fuchsian groups acting on the disc conformal groups acting discontinuously on the ball in dimension three or higher uniformly quasiconformal groups acting discontinuously on the ball in dimension three or higher and discrete groups of biholomorphic mappings acting on the ball in several complex dimensions in these cases the normalized lebesgue measure is either zero or one

an overview of asymptotic properties of lp regression under general classes of error distributions we survey the asymptotic properties of regression lp estimators under general classes of error distributions it is found that the asymptotic distributions of lp estimators depend crucially on p and the shape of the error distribution near the origin a number of important features arise as a result among which are a use of a small p may yield accelerated convergence rates for lp estimators under certain classes of error distributions b for p 1 lp regression should under some circumstances be undertaken by locally maximizing rather than minimizing the sum of the pth powers of the absolute deviations and c consistent estimation of the sampling distributions of the lp estimators can be achieved by the m out of n bootstrap in general numerical examples are provided to illustrate our theoretical findings and a computational algorithm is suggested for local maximization as may sometimes be required by the lp procedure

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

m estimation convexity and quantiles the paper develops a class of extensions of the univariate quantile function to the multivariate case m quantiles related in a certain way to m parameters of a probability distribution and their m estimators the spatial geometric quantiles recently introduced by koltchinskii and dudley and by chaudhuri as well as the regression quantiles of koenker and basset are the examples of the m quantile function discussed in the paper we study the main properties of m quantiles and develop the asymptotic theory of empirical m quantiles we use m quantiles to extend l parameters and l estimators to the multivariate case to introduce a bootstrap test for spherical symmetry of a multivariate distribution and to extend the notion of regression quantiles to multiresponse linear regression models

so 2n coherent states for loop quantum gravity a su 2 intertwiner with n legs can be interpreted as the quantum state of a convex polyhedron with n faces when working in 3d we show that the intertwiner hilbert space carries a representation of the non compact group so 2n this group can be viewed as the subgroup of the symplectic group sp 4n r which preserves the su 2 invariance we construct the associated perelomov coherent states and discuss the notion of semi classical limit which is more subtle than we could expect our work completes the work by freidel and livine j math phys 51 082502 2010 and j math phys 52 052502 2011 which focused on the u n subgroup of so 2n

lattice valued fuzzy frames in this paper we aim to introduce the concept of lattice valued fuzzy frame or l fuzzy frame related to traditional frames analogously to how l fuzzy resp l fuzzifying topological spaces related to l topological spaces resp traditional topological spaces some properties of l fuzzy frames are introduced

real polarization of the moduli space of flat connections on a riemann surface we prove that the moduli space of flatsu 2 connections on a riemann surface has a real polarization that is a foliation by lagrangian subvarieties this polarization may provide an alternative quantization of the chern simons gauge theory in higher genus in line with the results of 11 for genus one

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

on a generalization of fuzzy algebras and congruences abstract partially ordered fuzzy algebras are mappings from an algebra to a partially ordered set with the property that every level subset is an ordinary subalgebra similar definitions are induced for p valued congruences and weak congruences necessary and sufficient conditions under which an arbitrary collection of subalgebras congruences enables construction of a p valued fuzzy subalgebra congruence are given any p valued weak congruence uniquely determines a p valued subalgebra of the same algebra finally any collection of subalgebras or congruences of a given algebra can be used for the construction of a relational valued fuzzy algebra or congruence this seems to be the most general way to obtain a fuzzy algebra congruence out of the collection of the ordinary subalgebras congruences

dynamic assortment optimization with a multinomial logit choice model and capacity constraint we consider an assortment optimization problem where a retailer chooses an assortment of products that maximizes the profit subject to a capacity constraint the demand is represented by a multinomial logit choice model we consider both the static and dynamic optimization problems in the static problem we assume that the parameters of the logit model are known in advance we then develop a simple algorithm for computing a profit maximizing assortment based on the geometry of lines in the plane and derive structural properties of the optimal assortment for the dynamic problem the parameters of the logit model are unknown and must be estimated from data by exploiting the structural properties found for the static problem we develop an adaptive policy that learns the unknown parameters from past data and at the same time optimizes the profit numerical experiments based on sales data from an online retailer indicate that our policy performs well

two stage importance sampling with mixture proposals for importance sampling is multiple proposals can be combined to address different aspects of a target distribution there are various methods for is with multiple proposals including hesterberg s stratified is estimator owen and zhou s regression estimator and tan s maximum likelihood estimator for the problem of efficiently allocating samples to different proposals it is natural to use a pilot sample to select the mixture proportions before the actual sampling and estimation however most current discussions are in an empirical sense for such a two stage procedure in this article we establish a theoretical framework of applying the two stage procedure for various methods including the asymptotic properties and the choice of the pilot sample size by our simulation studies these two stage estimators can outperform estimators with naive choices of mixture proportions furthermore while owen and zhou s and tan s estimators are designed for estimating normalizing constants we extend their usa

a distributional approach for causal inference using propensity scores drawing inferences about the effects of treatments and actions is a common challenge in economics epidemiology and other fields we adopt rubin s potential outcomes framework for causal inference and propose two methods serving complementary purposes one can be used to estimate average causal effects assuming no confounding given measured covariates the other can be used to assess how the estimates might change under various departures from no confounding both methods are developed from a nonparametric likelihood perspective the propensity score plays a central role and is estimated through a parametric model under the assumption of no confounding the joint distribution of covariates and each potential outcome is estimated as a weighted empirical distribution expectations from the joint distribution are estimated as weighted averages or equivalently to first order regression estimates the likelihood estimator is at least as efficient and the regression estimator is at least as efficient and r

gorenstein semigroup algebras of weighted trees and ordered points on the projective line abstract we determine exactly which semigroup algebras of weighted trees are gorenstein these algebras arise as toric degenerations of projective coordinate rings of moduli of weighted points on the projective line as a corollary we find exactly when these families of algebras are gorenstein as well

concavity and estimation on donne des conditions simplifiees pour la consistance et la normalite asymptotique d estimations m deduites par maximisation de moyennes de fonctions concaves aleatoires identiquement distribuees et independantes des applications sont donnees pour l estimation de maximum de vraisemblance

gaudin models and bending flows a geometrical point of view in this paper we discuss the bi hamiltonian formulation of the rational xxx gaudin models of spin spin interaction generalized to the case of sl r valued spins we only consider the classical case using recent results concerning the quantum models as guiding principles in particular we focus on the so called homogeneous xxx models we find a pencil of poisson brackets that recursively define a complete set of integrals of the motion alternative to the set of integrals associated with the standard lax representation of the gaudin model these integrals in the case of su 2 coincide with the hamiltonians of the bending flows in the moduli space of polygons in the euclidean space introduced by kapovich and millson we finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the sl 2 case

misiurewicz point patterns generation in one dimensional quadratic maps abstract in a family of one dimensional quadratic maps misiurewicz points are unstable and the orbits of such a points are repulsive on the contrary the orbits of superstable periodic points are attractive here we study the patterns of the symbolic sequences of both misiurewicz and superstable periodic points and show that a misiurewicz point pattern can be obtained as the limit of the sum of a superstable periodic orbit pattern plus itself or some of its heredity transmitters repeated an infinite number of times inversely when a misiurewicz point pattern is given we also show that it is possible to find both the superstable periodic orbit pattern and the heredity transmitters that generate such a pattern