gleason s theorem for rectangular jbw triples a jbw triple b is said to be rectangular if there exists a w algebra a and a pair p q of centrally equivalent elements of the complete orthomodular lattice of projections in a such that b is isomorphic to the jbw triple paq any weak closed injective operator space provides an example of a rectangular jbw triple the principal order ideal of the complete lattice of centrally equivalent pairs of projections in a w algebra a generated by p q forms a complete lattice that is order isomorphic to the complete lattice of weak closed inner ideals in b and to the complete lattice of structural projections on b although not itself in general orthomodular possesses a complementation that allows for definitions of orthogonality centre and central orthogonality to be given a less familiar notion in lattice theory that is well known in the theory of jordan algebras and jordan triple systems is that of rigid collinearity of a pair e2 f2 and e2 f2 of elements of this is defined and characterized in terms of properties of a w algebra a is sometimes thought of as providing a model for a statistical physical system in this case b or equivalently paq may be thought of as providing a model for a fixed sub system of that represented by a therefore may be considered to represent the set consisting of a particular kind of sub system of that represented by paq central orthogonality and rigid collinearity of pairs of elements of may be regarded as representing two different types of disjointness the former classical disjointness and the latter decoherence of the two sub systems it is therefore natural to consider bounded measures m on that are additive on centrally orthogonal and rigidly collinear pairs of elements using results of j d m wright it is shown that provided that neither of the two hereditary sub w algebras pap and qaq of a has a weak closed ideal of type i2 such measures are precisely those that are the restrictions of bounded sesquilinear functionals m on pap qaq with the property that the action of the centroid z b of b commutes with the adjoint operation when b is a complex hilbert space of dimension greater than two this result reduces to gleason s theorem

the central hull and central kernel in jbw triples abstract the complete lattice i a of weak closed inner ideals in a jbw triple a has as its centre the complete boolean algebra z i a of weak closed ideals in a the annihilator l of the subset l of a consists of elements b of a for which l b a is equal to zero and the kernel ker l of l consists of those elements b in a for which l b l is equal to zero for each element j of i a j also lies in i a and a enjoys the generalized peirce decomposition a j m j j 1 where j 1 is the intersection of the kernels of j and j to investigate the properties of the weak closed subspace j 1 of a which is not in general a subtriple the notions of the central hull c l and central kernel k l of a subspace l are introduced these are respectively the smallest element of z i a containing l and the largest element of z i a contained in l for any element j of i a the relationships that exist between the central hull and central kernel of j and j are examined and it is shown that j 1 j is the weak closed ideal k j that j 1 j is the weak closed ideal k j and when j is a peirce inner ideal that j 1 is the weak closed ideal k j m k j

orthogonality preservers in c algebras jb algebras and jb triples abstract we study orthogonality preserving operators between c algebras jb algebras and jb triples let t a e be an orthogonality preserving bounded linear operator from a c algebra to a jb triple satisfying that t 1 d is a von neumann regular element then t a e 2 r d every element in t a and d operator commute in the jb algebra e 2 r d and there exists a triple homomorphism s a e 2 r d such that t l d r d s where r d denotes the range tripotent of d in e an analogous result for a being a jb algebra is also obtained when t a b is an operator between two c algebras we show that denoting h t 1 then t orthogonality preserving if and only if there exists a triple homomorphism s a b satisfying h s z s z h h s z s z h and t z l h r h s z 1 2 h r h s z s z r h h this allows us to prove that a bounded linear operator between two c algebras is orthogonality preserving if and only if it preserves zero triple products

on the mazur ulam property for the space of hilbert space valued continuous functions abstract let k be a compact hausdorff space and let h be a real or complex hilbert space with dim h r 2 we prove that the space c k h of all h valued continuous functions on k equipped with the supremum norm satisfies the mazur ulam property that is if y is any real banach space every surjective isometry from the unit sphere of c k h onto the unit sphere of y admits a unique extension to a surjective real linear isometry from c k h onto y our strategy relies on the structure of c k module of c k h and several results in jb triple theory for this purpose we determine the facial structure of the closed unit ball of a real jb triple and its dual space

a linear least squares version of the algorithm of mode isolation for identifying modal properties part i conceptual development the algorithm of mode isolation ami is an iterative procedure for identifying the number of modes contributing to a frequency response function frf concurrently with identifying the complex eigenvalues and eigenvectors of those modes the latest modifications obtain these modal properties solely by using linear least squares fits of the frf data to canonical forms the algorithmic operations are explained in a detailed sequence of steps that are illustrated by some sample data the computational efficiency of ami relative to other modal identification algorithms that fit response data to multi degree of freedom model equations is discussed

weakly compact orthogonality preservers on c algebras we establish a complete description of weakly compact orthogonality preserving operators from a c algebra a or a jb algebra to a jb triple e we prove that any such operator is the sum of a series of mutually orthogonal triple homomorphisms from a to a certain peirce 2 subspace of e multiplied by a mutually orthogonal norm null sequence in e which enjoy certain operator commutativity relations

classification of homogeneous data with large alphabets given training sequences generated by two distinct but unknown distributions on a common alphabet we study the problem of determining whether a third sequence was generated according to the first or second distribution to model sources such as natural language for which the underlying distributions are difficult to learn from realistic amounts of data we allow the alphabet size to grow and therefore the probability distributions to change with the block length our primary focus is the situation in which the underlying probabilities are all of the same order and in this regime we show that consistent classification is possible if and only if the alphabet grows subquadratically with the block length we also show that some commonly used statistical tests are suboptimal in that they are consistent only if the alphabet grows sublinearly

automatic continuity of derivations on c algebras and jb triples abstract we introduce the notion of banach jordan triple modules and determine the precise conditions under which every derivation from a jb triple e into a banach jordan triple e module is continuous in particular every derivation from a real or complex jb triple into its dual space is automatically continuous motivating the study which we have carried out elsewhere of weakly amenable jb triples specializing to c algebras leads to a unified treatment of derivations and jordan derivations into modules shedding light on a celebrated theorem of barry johnson

on the facial structure of the unit ball in the dual space of a jb triple it is shown that every proper weak closed face of the closed unit ball e 1 in the dual space of a jb triple e coincides with set of all elements in the unit sphere of e attaining their norm at a unique compact tripotent in e in particular every proper weak closed face of the closed unit ball e 1 is weak semi exposed this result provides an affirmative answer to a conjecture posed over 20 years ago

projective completions of jordan pairs part i the generalized projective geometry of a lie algebra abstract we prove that the projective completion x x of the jordan pair g 1 g 1 corresponding to a 3 graded lie algebra g g 1 g 0 g 1 can be realized inside the space f of inner 3 filtrations of g in such a way that the remoteness relation on x x corresponds to transversality of flags this realization is used to give geometric proofs of structure results which will be used in part ii of this work in order to define on x and x the structure of a smooth manifold in arbitrary dimension and over general base fields or rings

tingley s problem for spaces of trace class operators abstract we prove that every surjective isometry between the unit spheres of two trace class spaces admits a unique extension to a surjective complex linear or conjugate linear isometry between the spaces this provides a positive solution to tingley s problem in a new class of operator algebras

geometric characterization of tripotents in real and complex jb triples abstract we establish a geometric characterization of tripotents in real and complex jb triples as a consequence we obtain an alternative proof of kaup s banach stone theorem for jb triples

state spaces of jb triples an atomic decomposition is proved for banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process this is then applied to yield under appropriate assumptions geometric characterizations up to isometry of the unit ball of the dual space of a jb triple and up to complete isometry of one sided ideals in c algebras

low rank compact operators and tingley s problem abstract let e and b be arbitrary weakly compact jb triples whose unit spheres are denoted by s e and s b respectively we prove that every surjective isometry f s e s b admits an extension to a surjective real linear isometry t e b this is a complete solution to tingley s problem in the setting of weakly compact jb triples among the consequences we show that if k h k denotes the space of compact operators between arbitrary complex hilbert spaces h and k then every surjective isometry f s k h k s k h k admits an extension to a surjective real linear isometry t k h k k h k

trace order and a distortion theorem for linearly invariant families on the unit ball of a finite dimensional jb triple abstract we give a distortion theorem for linearly invariant families on the unit ball b of a finite dimensional jb triple x by using the trace order the exponents in the distortion bounds depend on the bergman metric at 0 further we introduce a new definition for the trace order of a linearly invariant family on b based on a jacobian argument we also construct an example of a linearly invariant family on b which has minimum trace order and is not a subset of the normalized convex mappings of b for dim x 2 finally we prove a regularity theorem for linearly invariant families on b all four types of classical cartan domains are the open unit balls of jb triples and the same holds for any finite product of these domains thus the unit balls of jb triples are natural generalizations of the unit disc in c and we have a setting in which a large number of bounded symmetric homogeneous domains may be studied simultaneously

a min max theorem for complex symmetric matrices abstract we optimize the form re x t tx to obtain the singular values of a complex symmetric matrix t we prove that for 0 k n 2 min codim v k max x v x 1 re x t tx 2 k 1 where t is an n n complex symmetric matrix having singular values 1 n we also show that the singular values missed in this theorem i e 2 4 are obtained by a similar optimization over real subspaces

the daugavet property of c algebras jb triples and of their isometric preduals a banach space x is said to have the daugavet property if every rank one operator t x x satisfies id t 1 t we give geometric characterizations of this property in the settings of c algebras jb triples and their isometric preduals we also show that in these settings the daugavet property passes to ultrapowers and thus it is equivalent to an stronger property called the uniform daugavet property

estimating entropy on m bins given fewer than m samples consider a sequence p sub n of discrete probability measures supported on m sub n points and assume that we observe n independent and identically distributed i i d samples from each p sub n we demonstrate the existence of an estimator of the entropy h p sub n which is consistent even if the ratio n m sub n is bounded and as a corollary even if this ratio tends to zero albeit at a sufficiently slow rate

aron berner extensions of triple maps with application to the bidual of jordan banach triple systems abstract by extending the notion of arens regularity of bilinear mappings we say that a bounded trilinear map on the cartesian product of banach spaces is aron berner regular when all its six aron berner extensions to the cartesian product of the bidual spaces coincide we give some results on the aron berner regularity of certain trilinear maps we then focus on the bidual e of a jordan banach triple system e and investigate those conditions under which e is itself a jordan banach triple system under each of the aron berner extensions of the triple product we also compare these six triple products with those arising from certain ultrafilters based on the ultrapower formulation of the principle of local reflexivity in particular we examine the aron berner triple products on the bidual of a jb triple in relation with the so called dineen s theorem some illuminating examples are included and some questions are also left undecided

jordan structures in harmonic functions and fourier algebras on homogeneous spaces we study the jordan structures and geometry of bounded matrix valued harmonic functions on a homogeneous space and their analogue the harmonic functionals in the setting of fourier algebras of homogeneous spaces

unit free contractive projection theorems for c jb and jb algebras abstract we prove that if a is a possibly non unital non commutative j b algebra and if a a is a positive contractive linear projection then a endowed with the product x y x y becomes naturally a non commutative j b algebra and moreover the equality a b a b holds for all a b a the appropriate variant of this result with jb algebra instead of non commutative j b algebra is also obtained in the non commutative j b case the requirement of positiveness for can be relaxed to the one that the equality holds in general this relaxing is strict but it is not strict if is bicontractive actually positive bicontractive linear projections on non commutative j b algebras are fully described and a structure theorem for bicontractive linear projections without any extra requirement on non commutative j b w algebras is proved finally bicontractive linear projections on c algebras are studied in detail

grothendieck s inequalities for real and complex jbw triples we prove that if m 4 1 2 3 and e 0 if v and w are complex jbw triples with preduals v andw respectively and if u is a separately weak continuous bilinear form on v w then there exist norm one functionals 1 2 v and 1 2 w satisfying u x y m u x 2 2 e 2 x 2 1 1 2 y 2 2 e 2 y 2 1 1 2 for all x y v w here for a norm one functional on a complex jb triple v stands for the prehilertian seminorm on v associated to in bf1 we arrive in this grothendieck s inequality through results of c h chu b iochum and g loupias cil and a corrected version of the little grothendieck s inequality for complex jb triples due to t barton and y friedman bf1 we also obtain extensions of these results to the setting of real jb triples 2000 mathematics subject classification 17c65 46k70 46l05 46l10 and 46l70

distortion of locally biholomorphic bloch mappings on bounded symmetric domains abstract we generalize bonk s distortion theorem on the unit disc in the complex plane to locally biholomorphic mappings on finite dimensional bounded symmetric domains as an application we obtain a lower bound for the bloch constant for various classes of locally biholomorphic bloch mappings

an efron stein inequality for nonsymmetric statistics on etablit l analogue d un resultat d efron et stein 1981 que l on demontre a l aide d une technique d espace de hilbert introduite par vitale 1984

generalised f algebras as predual algebras of jbw triples and characterisations of the fourier algebras on locally compact groups abstract we introduce the notion of a generalised f algebra as a banach algebra a whose banach space dual is a j b w triple with a certain additional condition on a distinguished character of a this generalises the well known notion of f algebras which in turn includes as special cases many important classes of banach algebras on locally compact groups and semigroups our main use of this new notion is to give some axiomatic characterisations of the fourier algebras on locally compact groups strengthening our previous work 37 but we also quickly review some well known results in f algebras that can be extended to the context of generalised f algebras

weak convergence analysis of asymptotically optimal hypothesis tests in recent years solutions to various hypothesis testing problems in the asymptotic setting have been proposed using the results from large deviation theory such tests are optimal in terms of appropriately defined error exponents for the practitioner however error probabilities in the finite sample size setting are more important in this paper we show how results on weak convergence of the test statistic can be used to obtain better approximations for the error probabilities in the finite sample size setting while this technique is popular among statisticians for common tests we demonstrate its applicability for several recently proposed asymptotically optimal tests including tests for robust goodness of fit homogeneity tests outlier hypothesis testing and graphical model estimation

on grassmannians associated with jb triples then is a complex lie group that has precisely n 1 orbits e0 en in e each er is the locally closed complex submanifold of all matrices of rank r clearly er 1 is in the closure of er for every 1 r n and en is the unique open orbit for every pair of integers p q 0 let gp q be the grassmannian of all p planes in cp q then gp q is a compact symmetric hermitian manifold of dimension pq holomorphically equivalent to gq p every er is in a canonical way a equivariant holomorphic fibre bundle

some inertia theorems in euclidean jordan algebras abstract this paper deals with some inertia theorems in euclidean jordan algebras first based on the continuity of eigenvalues we give an alternate proof of kaneyuki s generalization of sylvester s law of inertia in simple euclidean jordan algebras as a consequence we show that the cone spectrum of any quadratic representation with respect to a symmetric cone is finite second we present ostrowski schneider type inertia results in euclidean jordan algebras in particular we relate the inertias of objects a and x in a euclidean jordan algebra when l a x 0 or s a x 0 where l a and s a denote lyapunov and stein transformations respectively

perturbation of spectral subspaces and solution of linear operator equations abstract let a and b be normal operators on a hilbert space let k a and k b be subsets of the complex plane at distance at least from each other let e be the spectral projector for a belonging to k a and let f be the spectral projector for b belonging to k b our main results are estimates of the form ef c e a b f in some special situations the constant c is as low as 1 as an application we prove for an absolute constant d that if the space is finite dimensional and if a and b are normal with a b d then the spectrum of b can be obtained from that of a multiplicities counted by moving each eigenvalue by at most our main results have equivalent formulations as statements about the operator equation aq qb s let a and b be normal operators on perhaps different hilbert spaces assume a k a and b k b where k a k b and are as before then we give estimates of the forms q c aq qb

facial structure in operator algebra theory we give a complete description of the closed faces in twelve kinds of convex sets that appear in operator algebra theory these consist of positive parts of unit balls for c algebras and their dual spaces and for von neumann algebras and their pre duals of self adjoint parts of unit balls in the same four classes and finally of general unit balls in the four classes all these faces are shown to be semi exposed and naturally paired with a polar face in the dual or pre dual space

testing closeness of discrete distributions given samples from two distributions over an n element set we wish to test whether these distributions are statistically close we present an algorithm which uses sublinear in n specifically o n2 3e 8 3 log n independent samples from each distribution runs in time linear in the sample size makes no assumptions about the structure of the distributions and distinguishes the cases when the distance between the distributions is small less than e4 3n 1 3 32 en 1 2 4 or large more than e in e1 distance this result can be compared to the lower bound of n2 3e 2 3 for this problem given by valiant 2008 our algorithm has applications to the problem of testing whether a given markov process is rapidly mixing we present sublinear algorithms for several variants of this problem as well

local facial structure and norm exposed faces of the unit ball in a jb triple abstract each tripotent u in the bidual a of a jb triple a compact relative to a gives rise to a complex banach space p 2 u a with bidual the jbw algebra a 2 u that is a weak closed subtriple of a using the fact that the family of tripotents in the jbw algebra a 2 u compact relative to p 2 u a coincides with the family of tripotents in a 2 u compact relative to a the facial structure of the unit balls in p 2 u a and its dual a 2 u the predual of a 2 u is revealed the jbw algebra b u that is the self adjoint part of the jbw algebra a 2 u is the bidual of the unital gm space b u that consists of the space of all real valued weak continuous affine functions on the normal state space of a 2 u it is therefore possible to investigate the real local facial structure of the unit balls in b u b u and b u some of the results obtained are applied to the problem of identifying the norm exposed faces of the unit ball a 1 in a it is shown that both locally and globally the norm exposed faces of a 1 are those corresponding to compact support tripotents of elements of norm one in the dual space a of a

tingley s problem through the facial structure of an atomic jbw triple abstract we prove that every surjective isometry between the unit spheres of two atomic jbw triples e and b admits a unit extension to a surjective real linear isometry from e into b this result constitutes a new positive answer to tingley s problem in the jordan setting

isometries of non self adjoint operator algebras abstract we study isometries of certain non self adjoint operator algebras by means of the structure of the complete holomorphic vector fields on their unit balls and the associated partial jordan triple products we show that isometries of nest sub algebras of b h are of the form t utw or t ujt jw where u w are suitable unitary operators and j a fixed involution of h

the alternative dunford pettis property on projective tensor products a banach space x has the dunford pettis property dpp if and only if whenever xn and pn are weakly null sequences in x and x respectively we have pn xn 0 freedman introduced a stricly weaker version of the dpp called the alternative dunford pettis property dp1 a banach space x has the dp1 if whenever xn x weakly in x with kxnk kxk and xn is weakly null in x we have that xn xn 0 the authors study the dp1 on projective tensor products of c algebras and jb triples their main result theorem 3 5 states that if x and y are banach spaces such that x contains an isometric copy of c0 and y contains an isometric copy of c 0 1 then x y the projective tensor product of x and y does not have the dp1 as a corollary they get that if x and y are jb triples such that x is not reflexive and y contains 1 then x y does not have the dp1 furthermore if a and b are infinite dimensional c algebras then a b has the dpp if and only if a b has the dp1 if and only if both a and b have the dpp and do not contain 1

measures of weak non compactness in preduals of von neumann algebras and jbw triples abstract we prove among other results that three standard measures of weak non compactness coincide in preduals of jbw triples this result is new even for preduals of von neumann algebras we further provide a characterization of jbw triples with strongly wcg predual and describe the order of seminorms defining the strong topology as a byproduct we improve a characterization of weakly compact subsets of a jbw triple predual providing so a proof for a conjecture open for almost eighteen years on weakly compact operators from a jb triple into a complex banach space

testing probability distributions using conditional samples we study a new framework for property testing of probability distributions by considering distribution testing algorithms that have access to a conditional sampling oracle this is an oracle that takes as input a subset s subseteq n of the domain n of the unknown probability distribution cal d and returns a draw from the conditional probability distribution cal d restricted to s this new model allows considerable flexibility in the design of distribution testing algorithms in particular testing algorithms in this model can be adaptive we study a wide range of natural distribution testing problems in this new framework and some of its variants giving both upper and lower bounds on query complexity these problems include testing whether cal d is the uniform distribution cal u testing whether cal d cal d ast for an explicitly provided cal d ast testing whether two unknown distributions cal d 1 and cal d 2 are equivalent and estimating the va

generalized error exponents for small sample universal hypothesis testing the small sample universal hypothesis testing problem is investigated in this paper in which the number of samples n is smaller than the number of possible outcomes m the goal of this paper is to find an appropriate criterion to analyze statistical tests in this setting a suitable model for analysis is the high dimensional model in which both n and m increase to infinity and n o m a new performance criterion based on large deviations analysis is proposed and it generalizes the classical error exponent applicable for large sample problems in which m o n this generalized error exponent criterion provides insights that are not available from asymptotic consistency or central limit theorem analysis the following results are established for the uniform null distribution 1 the best achievable probability of error pe decays as pe exp n2 m j 1 o 1 for some j 0 2 a class of tests based on separable statistics including the coincidence based test attains the optimal generalized error exponents 3 pearson s chi square test has a zero generalized error exponent and thus its probability of error is asymptotically larger than the optimal test

mode isolation a new algorithm for modal parameter identification multiple degree of freedom mdof algorithms are the dominant methods for extracting modal parameters from measured data these methods are founded on the notion that because the response of a linear dynamic system is the sum of many modal contributions the extraction technique must deal with all of the modal parameters in a simultaneous fashion the mode isolation algorithm mia described here is a frequency domain formulation that takes an alternative viewpoint it extracts the modal parameters of each mode in an iterative search and then refines the estimation of each mode by isolating its effect from the other modal contributions the first iteration estimates modes in a hierarchy of their dominance as each mode is estimated its contribution is subtracted from the data set until all that remains is noise the second and subsequent iterations subtract the current estimates for all other modes to identify the properties of the mode under consideration the various operations are described in detail and then illustrated using data from a four degree of freedom system that was previously used to assess the eigensystem realization algorithm era and enhanced era eigenvalues and mode shapes are compared for each algorithm another example analyzes simulated data for a cantilever beam with three suspended one degree of freedom subsystems in which the parameters are adjusted to bring two natural frequencies into close proximity the results suggest that mia is more accurate and more robust in the treatment of noisy data than either era version and that it is able to identify modes whose bandwidth is comparable to the difference of adjacent natural frequencies

a linear least squares version of the algorithm of mode isolation for identifying modal properties part ii application and assessment the latest modifications of the algorithm of mode isolation ami for identification of modal properties from frequency response data are tested with synthetic data derived from an analytical model of an elastic frame in which flexure and torsion are coupled the parameters of this model are selected to cause the occurrence of localized modal patterns in two modes having close natural frequencies the response data is contaminated with white noise at a level sufficient to almost mask the two close modes results for the real and imaginary part of the eigenvalues are tabulated the analytical modal patterns of displacement and torsional rotation are depicted graphically accompanied by the discrete values obtained from ami excellent agreement is found to occur for each mode other than one of the pair of close modes the poorer quality of that mode s identified properties is shown to be a consequence of its localized modal pattern results for the eigenvalues obtained by the rational fraction polynomial algorithm which is an alternative modal identification technique are found to be substantially less accurate as a consequence of difficulty in the presence of noise

estimating renyi entropy of discrete distributions it was shown recently that estimating the shannon entropy h p of a discrete k symbol distribution p requires theta k log k samples a number that grows near linearly in the support size in many applications h p can be replaced by the more general renyi entropy of order alpha and h alpha p we determine the number of samples needed to estimate h alpha p for all alpha showing that alpha requires a super linear roughly k 1 alpha samples noninteger alpha 1 requires a near linear k samples but perhaps surprisingly integer alpha 1 requires only theta k 1 1 alpha samples furthermore developing on a recently established connection between polynomial approximation and estimation of additive functions of the form sum x f p x we reduce the sample complexity for noninteger values of alpha by a factor of log k compared with the empirical estimator the estimators achieving these bounds are simple and run in time linear in the number of samples our lower bounds provide explicit constructions of distributions with different renyi entropies that are hard to distinguish

the minimax principle and related topics in the jordan setting abstract we prove a minimax principle for weakly compact jb triples characterizing geometrically the singular values of an element among the consequences of this principle we present a weyl inequality on the perturbation of the singular values and a cauchy poincare interlacing theorem we also obtain a version of the ky fan maximum principle in the setting of weakly compact jb triples we study perturbations of the spectral resolutions showing that small perturbations of an element produces small perturbations of the corresponding spectral resolutions as a consequence we obtain that weakly compact jb triples satisfy the property that perturbations of a convex combination of elements in the closed unit ball coincide with a convex combination of perturbations of the elements also in the closed unit ball all these results hold true when particularized to weakly compact jb algebras

inference under information constraints i lower bounds from chi square contraction multiple players are each given one independent sample about which they can only provide limited information to a central referee each player is allowed to describe its observed sample to the referee using a channel from a family of channels mathcal w which can be instantiated to capture among others both the communication and privacy constrained settings the referee uses the players messages to solve an inference problem on the unknown distribution that generated the samples we derive lower bounds for the sample complexity of learning and testing discrete distributions in this information constrained setting underlying our bounds is a characterization of the contraction in chi square distance between the observed distributions of the samples when information constraints are placed this contraction is captured in a local neighborhood in terms of chi square and decoupled chi square fluctuations of a given channel two quantities we introduce the former captures the average distance between distributions of channel output for two product distributions on the input and the latter for a product distribution and a mixture of product distribution on the input our bounds are tight for both public and private coin protocols interestingly the sample complexity of testing is order wise higher when restricted to private coin protocols

on the structure of c0 semigroups of holomorphic caratheodory isometries in hilbert space abstract we establish closed formulas for all strongly continuous one parameter semigroups of holomorphic caratheodory isometries of the unit ball of a hilbert space in terms of spectral resolutions of skew self adjoint dilations related to the reich shoikhet nonlinear infinitesimal generator

geometrizing rates of convergence ii consider estimating a functional t f of an unknown distribution f in mathbf f from data x 1 cdots x n i i d f let omega varepsilon denote the modulus of continuity of the functional t over mathbf f computed with respect to hellinger distance for well behaved loss functions l t we show that inf t n sup mathbf f e fl t n t f is equivalent to l omega n 1 2 to within constants whenever t is linear and mathbf f is convex the same conclusion holds in three nonlinear cases estimating the rate of decay of a density estimating the mode and robust nonparametric regression we study the difficulty of testing between the composite infinite dimensional hypotheses h 0 t f leq t and h 1 t f geq t delta our results hold in the cases studied because the difficulty of the full infinite dimensional composite testing problem is comparable to the difficulty of the hardest simple two point testing subproblem

a coincidence based test for uniformity given very sparsely sampled discrete data how many independent samples n do we need from a distribution p to decide that p is epsiv distant from uniform in an l1 sense sigmai 1 m p i 1 m epsiv here m is the number of bins on which the distribution is supported and is assumed known a priori somewhat surprisingly we only need n epsiv2 gt m 1 2 to make this decision reliably this condition is both sufficient and necessary the test for uniformity introduced here is based on the number of observed ldquocoincidencesrdquo samples that fall into the same bin the mean and variance of which may be computed explicitly for the uniform distribution and bounded nonparametrically for any distribution that is known to be epsiv distant from uniform some connections to the classical birthday problem are noted

a unified matrix polynomial approach to modal identification abstract one important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single consistent mathematical formulation with a corresponding set of definitions and unifying concepts particularly a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least squares complex exponential lsce the polyreference time domain ptd ibrahim time domain itd eigensystem realization algorithm era rational fraction polynomial rfp polyreference frequency domain pfd and the complex mode indication function cmif methods using this unified matrix polynomial approach umpa allows a discussion of the similarities and differences of the commonly used methods the use of least squares ls total least squares tls double least squares dls and singular value decomposition svd methods is discussed in order to take advantage of redundant measurement data eigenvalue and svd transformation methods are utilized to reduce the effective size of the resulting eigenvalue eigenvector problem as well

non commutative generalisations of urysohn s lemma and hereditary inner ideals abstract we establish several generalisations of urysohn s lemma in the setting of jb triples which provide full answers to problems 1 12 and 1 13 in fernandez polo and peralta 2007 22 these results extend the previous generalisations obtained by c a akemann g k pedersen and l g brown in the setting of c algebras a generalised kadison s transitivity theorem is established for finite sums of pairwise orthogonal compact tripotents in jbw triples we introduce the notion of positively open tripotent in the bidual of a jb triple as an extension of a concept which was already considered in the setting of ternary rings of operators we investigate the connections appearing between positively open tripotents and hereditary inner ideals