nonparametric tests of stochastic dominance in income distributions tests for stochastic dominance based upon extensions of the goodness of fit test to the nonparametric comparison of income distributions are proposed implemented and compared with indirect tests of second order stochastic dominance currently utilized in income distribution studies

stable bundles and integrable systems on considere la geometrie symplectique des fibres cotangents aux espaces de modules de fibres vectoriels stables sur une surface de riemann on montre que ce sont des systemes dynamiques hamiltoniens algebriquement completement integrables

integrable xyz spin chain with boundaries we consider a general class of boundary terms of the open xyz spin 1 2 chain compatible with integrability we have obtained the general elliptic solution of a k matrix obeying the boundary yang baxter equation using the r matrix of the eight vertex model and derived the associated integrable spin chain hamiltonian

unitary events in multiple single neuron spiking activity ii nonstationary data in order to detect members of a functional group cell assembly in simultaneously recorded neuronal spiking activity we adopted the widely used operational definition that membership in a common assembly is expressed in near simultaneous spike activity unitary event analysis a statistical method to detect the significant occurrence of coincident spiking activity in stationary data was recently developed see the companion article in this issue the technique for the detection of unitary events is based on the assumption that the underlying processes are stationary in time this requirement however is usually not fulfilled in neuronal data here we describe a method that properly normalizes for changes of rate the unitary events by moving window analysis uemwa analysis for unitary events is performed separately in overlapping time segments by sliding a window of constant width along the data in each window stationarity is assumed performance and sensitivity are demonstrated by use of simulated spike trains of independently firing neurons into which coincident events are inserted if cortical neurons organize dynamically into functional groups the occurrence of near simultaneous spike activity should be time varying and related to behavior and stimuli uemwa also accounts for these potentially interesting nonstationarities and allows locating them in time the potential of the new method is illustrated by results from multiple single unit recordings from frontal and motor cortical areas in awake behaving monkey

noncommutative extensions of elliptic integrable euler arnold tops and painleve vi equation in this paper we suggest generalizations of elliptic integrable tops to matrix valued variables our consideration is based on the r matrix description which provides lax pairs in terms of quantum and classical r matrices first we prove that for relativistic and non relativistic tops such lax pairs with spectral parameters follow from the associative yang baxter equation and its degenerations then we proceed to matrix extensions of the models and find out that some additional constraints are required for their construction we describe a matrix version of the reduced elliptic top and verify that the latter constraints are fulfilled in this case the construction of matrix extensions is naturally generalized to the monodromy preserving equation in this way we get matrix extensions of the painleve vi equation and its multidimensional analogues written in the form of non autonomous elliptic tops finally it is mentioned that the matrix valued variables can be replaced by elements of noncommutative associative algebra at the end of the paper we also describe special elliptic gaudin models which can be considered as matrix extensions of the reduced elliptic top

decompositions of pearson s chi squared test we study the properties of pearson s goodness of fit test and show that the components of chi squared or pearson analog tests of anderson j econometrics 62 1994 265 are less generally applicable than was originally claimed

holomorphic bundles and many body systems we show that spin generalization of elliptic calogero moser system elliptic extension of gaudin model and their cousins are the degenerations of hitchin systems applications to the constructions of integrals of motion angle action variables and quantum systems are discussed the constructions of classical systems are motivated by conformal field theory and their quantum counterparts can be thought of as being the degenerations of the critical level knizhnik zamolodchikov bernard equations

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

bihamiltonian structures and quadratic algebras in hydrodynamics and on non commutative torus we demonstrate the common bihamiltonian nature of several integrable systems the first one is an elliptic rotator that is an integrable euler arnold top on the complex group gl n open image in new window for any n whose inertia ellipsiod is related to a choice of an elliptic curve its bihamiltonian structure is provided by the compatible linear and quadratic poisson brackets both of which are governed by the belavin drinfeld classical elliptic r matrix we also generalize this bihamiltonian construction of integrable euler arnold tops to several infinite dimensional groups appearing as certain large n limits of gl n open image in new window these are the group of a non commutative torus nct and the group of symplectomorphisms sdiff t2 of the two dimensional torus the elliptic rotator on symplectomorphisms gives an elliptic version of an ideal 2d hydrodynamics which turns out to be an integrable system in particular we define the quadratic poisson algebra on the space of hamiltonians on t2 depending on two irrational numbers in conclusion we quantize the infinite dimensional quadratic poisson algebra in a fashion similar to the corresponding finite dimensional case

analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity analyzing the dependencies between spike trains is an important step in understanding how neurons work in concert to represent biological signals usually this is done for pairs of neurons at a time using correlation based techniques chornoboy schramm and karr 1988 proposed maximum likelihood methods for the simultaneous analysis of multiple pair wise interactions among an ensemble of neurons one of these methods is an iterative continuous time estimation algorithm for a network likelihood model formulated in terms of multiplicative conditional intensity functions we devised a discrete time version of this algorithm that includes a new efficient computational strategy a principled method to compute starting values and a principled stopping criterion in an analysis of simulated neural spike trains from ensembles of interacting neurons the algorithm recovered the correct connectivity matrices and interaction parameters in the analysis of spike trains from an ensemble of rat hippocampal place cells the algorithm identified a connectivity matrix and interaction parameters consistent with the pattern of conjoined firing predicted by the overlap of the neurons spatial receptive fields these results suggest that the network likelihood model can be an efficient tool for the analysis of ensemble spiking activity

elliptic schlesinger system and painleve vi we consider an elliptic generalization of the schlesinger system ess with positions of marked points on an elliptic curve and its modular parameter as independent variables the parameters in the moduli space of the complex structure this system was originally discovered by takasaki hep th 9711095 in the quasi classical limit of the sl n vertex model our derivation is purely classical ess is defined as a symplectic quotient of the space of connections of bundles of degree 1 over the elliptic curves with marked points the ess is a non autonomous hamiltonian system with pairwise commuting hamiltonians the system is bi hamiltonian with respect to the linear and introduced here quadratic poisson brackets the latter are the multi colour form of the sklyanin feigin odesski classical algebras the ess is the monodromy independence condition on the complex structure for the linear systems related to the flat bundle the case of four points for a special initial data is reduced to the painleve vi equation in the form of the zhukovsky volterra gyrostat proposed in our previous paper

asymptotic expansions of the information matrix test statistic the information matrix im test is shown to have a finite sample distribution which is poorly approximated by its asymptotic x 2 distribution in models and sample sizes commonly encountered in applied econometric research the quality of the x2 approximation depends upon the method chosen to compute the test failure to exploit restrictions on the covariance matrix of the test can lead to a test with appalling finite sample properties order o n 1 approximations to the exact distribution of an efficient form of the im test are reported these are developed from asymptotic expansions of the edgeworth and cornish fisher types they are compared with monte carlo estimates of the finite sample distribution of the test and are found to be superior to the usual x2 approximations in sample sizes of the magnitude found in applied micro econometric work the methods developed in the paper are applied to normal and exponential models and to normal regression models results are provided for the full im test and for heteroskedasticity and nonnormality diagnostic tests which are special cases of the im test in geieral the quality of alternative approximations is sensitive to covariate design however commonly used nonnormality tests are found to have distributions which to order o n 1 are invariant under changes in covariate design this leads to simple design and parameter invariant size corrections for nonnormality tests

characteristic classes and hitchin systems general construction we consider topologically non trivial higgs g bundles over riemann surfaces g with marked points and the corresponding hitchin systems we show that if g is not simply connected then there exists a finite number of different sectors of the higgs bundles endowed with the hitchin hamiltonians they correspond to different characteristic classes of the underlying bundles defined as elements of h 2 sigma g mathcal z g mathcal z g is a center of g we define the conformal version cg of g an analog of gl n for sl n and relate the characteristic classes with degrees of cg bundles we describe explicitly bundles in the genus one g 1 case if 1 has one marked point and the bundles are trivial then the hitchin systems coincide with calogero moser cm systems for the nontrivial bundles we call the corresponding systems the modified calogero moser mcm systems their phase space has the same dimension as the phase space of the cm systems with spin variables but less number of particles and greater number of spin variables starting with these bundles we construct lax operators quadratic hamiltonians and define the phase spaces and the poisson structure using dynamical r matrices the latter are completion of the classification list of etingof varchenko corresponding to the trivial bundles to describe the systems we use a special basis in the lie algebras that generalizes the basis of t hooft matrices for sl n we find that the mcm systems contain the standard cm subsystems related to some unbroken subalgebras the configuration space of the cm particles is the moduli space of the stable holomorphic bundles with non trivial characteristic classes

the small sample performance of the information matrix test abstract this paper reviews the information matrix im test procedure see white 1982 it investigates the size performance of several variants of the im test statistic and in particular exposes the nr2 variant of the test as proposed by chesher 1983 and lancaster 1984 as being extremely poor alternative nr2 im test statistics are considered and it appears that substantial improvements can be made by incorporating expected values of third derivatives of the log density into the im test calculation procedure interestingly these are exactly the sort of calculations that the chesher 1983 and lancaster 1984 variant avoids

simple tests of distributional form abstract this paper discusses a class of tests based upon modifications to the goodness of fit test for examining the accord between distributional assumptions and the data generating process they are easy to compute flexible and applicable in a wide range of circumstances and have intuitive appeal a monte carlo study comparing them to a widely used test for normality is presented

new boundary conditions for integrable lattices new boundary conditions for classical integrable nonlinear lattices of the xxx type such as the heisenberg chain and the toda lattice are presented these integrable extensions are formulated in terms of a generic xxx heisenberg magnet interacting with two additional spins at each end of the chain the construction uses the most general rank 1 ansatz for the 2 2 l operator satisfying the reflection equation algebra with rational r matrix the associated quadratic algebra is shown to be that of dynamical symmetry for the a1 and bc2 calogero moser problems other physical realizations of our quadratic algebra are also considered

on the behavior of inconsistent instrumental variable estimators abstract some theoretical results published recently in hendry 1979 for the limiting distribution of inconsistent instrumental variable estimators in misspecified dynamic systems are incorrect in particular the derivations there involve the use of an inappropriate control variate and lead to an expression for the covariance matrix of the limiting distribution which in general omits many additional terms correct formulae are given in the present paper further the accuracy of the asymptotic distribution in finite samples is investigated in a simple case using the known exact small sample distribution on the basis of our exact results and in view of other strong theoretical and practical considerations we argue for caution in the use of response surface regressions of the type recommended by hendry in monte carlo experiments and we emphasize the need for qualifying statements concerning the parameter environments in which the adequacy of these regressions has been substantiated

painleve vi rigid tops and reflection equation we show that the painleve vi equation has an equivalent form of the non autonomous zhukovsky volterra gyrostat this system is a generalization of the euler top in mathbb c 3 and includes the additional constant gyrostat momentum the quantization of its autonomous version is achieved by the reflection equation the corresponding quadratic algebra generalizes the sklyanin algebra as by product we define integrable xyz spin chain on a finite lattice with new boundary conditions

hitchin systems symplectic hecke correspondence and two dimensional version the aim of this paper is two fold first we define symplectic maps between hitchin systems related to holomorphic bundles of different degrees we call these maps the symplectic hecke correspondence shc of the corresponding higgs bundles they are constructed by means of the modification of the underlying holomorphic bundles shc allows to construct backlund transformations in the hitchin systems defined over riemann curves with marked points we apply the general scheme to the elliptic calogero moser cm system and construct shc to an integrable sl n euler arnold top the elliptic sl n rotator next we propose a generalization of the hitchin approach to 2d integrable theories related to the higgs bundles of infinite rank the main example is an integrable two dimensional version of the two body elliptic cm system the previous construction allows us to define shc between the two dimensional elliptic cm system and the landau lifshitz equation

improvements to the sensitivity of gravitational clustering for multiple neuron recordings we outline two improvements to the technique of gravitational clustering for detection of neuronal synchrony which are capable of improving the method s detection of weak synchrony with limited data the advantages of the enhancements are illustrated using data with known levels of synchrony and different interspike interval distributions the novel simulation method described can easily generate such test data an important dependence of the sensitivity of gravitational clustering to the interspike interval distribution of the analysed spike trains is described

ruijsenaars commuting difference operators as commuting transfer matrices for belavin s elliptic quantum r matrix we construct an l operator as a set of difference operators acting on functions on the type a weight space according to the fundamental relation rll llr taking the trace of the l operator gives a set of commuting difference operators we show that for the above mentioned l operator this approach gives macdonald type operators with elliptic theta function coefficient actually equivalent to ruijsenaars operators the relationship between the difference l operator and krichever s lax matrix is given and an explicit formula for elliptic commuting differential operators is derived we also study the invariant subspace for the system which is spanned by symmetric theta functions on the weight space

a generalisation of the calogero moser system abstract a generalised calogero moser many body system in which the particles possess extra internal degrees of freedom is introduced and solved by the method of olshanetsky and perelomov further the hierarchy of flows commuting with this system is obtained from a hierarchy of linear systems possessing sl n symmetry by the usual method of reduction thus they are shown to be integrable

separation of variables in the elliptic gaudin model for the elliptic gaudin model a degenerate case of the xyz integrable spin chain a separation of variables is constructed in the classical case the corresponding separated coordinates are obtained as the poles of a suitably normalized baker akhiezer function the classical results are generalized to the quantum case where the kernel of the separating integral operator is constructed the simplest one degree of freedom case is studied in detail