estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

grassmann gaussian integrals and generalized star products in quantum scattering on networks there is a nonlinear composition rule for on shell scattering matrices which serves as a replacement for the multiplicative rule of transfer matrices valid in other physical contexts in this paper we show how this composition rule is obtained using berezin integration theory with grassmann variables

is pitman closeness a reasonable criterion the criterion of pitman closeness has been proposed as an alternative comparison criterion to quadratic losses and more generally to decision theory however it may lead to quite paradoxical phenomena the most dramatic being a possible nontransitivity the criterion takes into consideration the joint distribution of the compared estimators but this consideration may be misleading in the selection of the best estimator we show through examples that this criterion is not consistent with a decision theoretic analysis and that it should be used very cautiously if ever

heuristics of instability and stabilization in model selection in model selection usually a best predictor is chosen from a collection hat mu cdot s of predictors where hat mu cdot s is the minimum least squares predictor in a collection mathsf u s of predictors here s is a complexity parameter that is the smaller s the lower dimensional smoother the models in mathsf u s if mathsf l is the data used to derive the sequence hat mu cdot s the procedure is called unstable if a small change in mathsf l can cause large changes in hat mu cdot s with a crystal ball one could pick the predictor in hat mu cdot s having minimum prediction error without prescience one uses test sets cross validation and so forth the difference in prediction error between the crystal ball selection and the statistician s choice we call predictive loss for an unstable procedure the predictive loss is large this is shown by some analytics in a simple case and by simulation results in a more complex comparison of four different linear regression methods unstable procedures can be stabilized by perturbing the data getting a new predictor sequence hat mu cdot s and then averaging over many such predictor sequences

distribution theory for discontinuous test functions and differential operators with generalized coefficients investigation of the differential operators with the generalized coefficients having singular support on a disjoint set of points requires the consideration of the distribution theory with the set of discontinuous test functions such a distribution theory for test functions having discontinuity at one point is developed a four parameter family of schrodinger operators formed by the operators with singular potential singular metrics and singular gauge field is considered it is proved that this family of singular interactions describes all possible selfadjoint extensions of the second derivative operator defined on the functions vanishing in a neighbourhood of the point approximation by operators with smooth coefficients is discussed c 1996 academic press inc

zeta functions of quantum graphs in this paper we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle we start by considering the special case of the star graph with neumann matching conditions at the center of the star we then extend the technique to allow any matching conditions at the center for which the laplace operator is self adjoint and finally obtain an expression for the zeta function of any graph with general vertex matching conditions in the process it is convenient to work with new forms for the secular equation of a quantum graph that extend the well known secular equation of the neumann star graph in the second half of this paper we apply the zeta function to obtain new results for the spectral determinant vacuum energy and heat kernel coefficients of quantum graphs these have all been topics of current research in their own right and in each case this unified approach significantly expands results in the literature

a consistent model coupling adhesion friction and unilateral contact a model considering both unilateral contact coulomb friction and adhesion is presented in the framework of continuum thermodynamics the contact zone is considered as a material boundary and the local constitutive laws are derived by choosing two specific surface potentials the free energy and the dissipation potential because of the non regular properties of these potentials convex analysis is used to derive the local behavior laws from the state and the complementary laws the adhesion is characterized by an internal variable introduced by fremond which represents the intensity of adhesion the continuous transition from a total adhesive condition to a possible pure frictional one is enforced by using elasticity coupled with damage for the interface non penetration conditions and coulomb law are strictly imposed without using any penalty the variational formulation for quasistatic problems is written as the coupling between an implicit variational inequality a variational inequality and a differential equation an increment formulation is proposed an existence result under a condition on the friction coefficient is given a numerical method is derived from the incremental formulation and various algorithms are implemented they solve a sequence of minimization problems under constraints the model is used to simulate a micro indentation experiment conducted to characterize the behavior of fiber matrix interface in a ceramic composite identification of the constitutive parameters is discussed

the berry keating operator on l 2 mathbb r _ gt rm d x and on compact quantum graphs with general self adjoint realizations the berry keating operator berry and keating 1999 siam rev 41 236 governing the schrodinger dynamics is discussed in the hilbert space and on compact quantum graphs it has been proved that the spectrum of hbk defined on is purely continuous and thus this quantization of hbk cannot yield the hypothetical hilbert polya operator possessing as eigenvalues the nontrivial zeros of the riemann zeta function a complete classification of all self adjoint extensions of hbk acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of hbk in addition an exact trace formula and the weyl asymptotics of the eigenvalue counting function are derived furthermore we introduce the squared berry keating operator which is a special case of the black scholes operator used in financial theory of option pricing again all self adjoint extensions the corresponding secular equation the trace formula and the weyl asymptotics are derived for h2bk on compact quantum graphs while the spectra of both hbk and h2bk on any compact quantum graph are discrete their weyl asymptotics demonstrate that neither hbk nor h2bk can yield as eigenvalues the nontrivial riemann zeros some simple examples are worked out in detail

the generalized star product and the factorization of scattering matrices on graphs in this article we continue our analysis of schrodinger operators on arbitrary graphs given as certain laplace operators in the present article we give the proof of the composition rule for the scattering matrices this composition rule gives the scattering matrix of a graph as a generalized star product of the scattering matrices corresponding to its subgraphs we perform a detailed analysis of the generalized star product for arbitrary unitary matrices the relation to the theory of transfer matrices is also discussed

hermitian symplectic geometry and the factorization of the scattering matrix on graphs hermitian symplectic spaces provide a natural framework for the extension theory of symmetric operators here we show that hermitian symplectic spaces may also be used to describe the solution to the factorization problem for the scattering matrix on a graph i e we derive a formula for the scattering matrix of a graph in terms of the scattering matrices of its subgraphs the solution of this problem is shown to be given by the intersection of a lagrange plane and a coisotropic subspace which in an appropriate hermitian symplectic space forms a new lagrange plane the scattering matrix is given by a distinguished basis to the lagrange plane using our construction we are also able to give a simple proof of the unitarity of the scattering matrix as well as provide a characterization of the discrete eigenvalues embedded in the continuous spectrum

characteristic functions of quantum graphs in this paper we give a reduction formula for the characteristic functions of the sturm liouville boundary value problems defined on a tree we also discuss the multiplicity of the eigenvalues and interlacing properties between two spectral sets associated with different boundary conditions

combining estimators to improve structural model estimation and inference under quadratic loss asymptotically semi parametric estimators of the parameters in linear structural models have the same sampling properties in finite samples the sampling properties of these estimators vary and large biases may result for sample sizes often found in practice with a goal of improving asymptotic risk performance and finite sample efficiency properties we investigate the idea of combining correlated structural equation estimators with different finite and asymptotic sampling characteristics based on a quadratic loss measure we present evidence that the finite sample performance of the resulting combination estimator can be notably superior to that of a leading traditional moment based estimator

james stein type estimators in large samples with application to the least absolute deviations estimator we explore the extension of james stein type estimators in a direction that enables them to preserve their superiority when the sample size goes to infinity instead of shrinking a base estimator toward a fixed point we shrink it toward a data dependent point we provide an analytic expression for the asymptotic risk and bias of james stein type estimators shrunk toward a data dependent point and prove that they have smaller asymptotic risk than the base estimator shrinking an estimator toward a data dependent point turns out to be equivalent to combining two random variables using the james stein rule we propose a general combination scheme that includes random combination the james stein combination and the usual nonrandom combination as special cases as an example we apply our method to combine the least absolute deviations estimator and the least squares estimator our simulation study indicates that the resulting combination estimators have desirable finite sample properties when errors are dr

imaging geometric graphs using internal measurements abstract this article presents two topologically motivated algorithms for reconstructing a metric graph from solutions to a wave equation on it our algorithms rely on narrowband and visibility measurements and are therefore of considerable value to urban sensing applications this is an advancement over the wideband methods traditionally used to study metric graphs our methodology exposes and separates the impact of the graph topology and geometry and is driven by a complete cohomological characterization of the space of wave equation solutions

elastic beam in adhesive contact abstract dynamic and quasistatic processes of contact with adhesion between an elastic or viscoelastic beam and a foundation are considered the contact is modeled with the signorini condition when the foundation is rigid and with normal compliance when it is deformable the adhesion is modeled by introducing the bonding function the evolution of which is described by an ordinary differential equation the existence and uniqueness of the weak solution for each of the problems is established using the theory of variational inequalities fixed point arguments and the existence and uniqueness result in commun contemp math 1 1 1999 87 123 the numerical approximations of the quasistatic problem with normal compliance are considered based on semi discrete and fully discrete schemes the convergence of the solutions of the discretized schemes is proved and error estimates for these approximate solutions are derived

four parameter point interaction in 1d quantum systems the author constructs a four parameter point interaction for a nonrelativistic particle moving on a line as the limit of a short range interaction with a range tending toward zero for particular choices of the parameters one can obtain a delta interaction or the so called delta interaction the hamiltonian corresponding to the four parameter point interaction is shown to correspond to the four parameter self adjoint hamiltonian of the free particle moving on the line with the origin excluded

a single mode quantum transport in serial structure geometric scatterers we study transport in quantum systems consisting of a finite array of n identical single channel scatterers a general expression of the s matrix in terms of the individual element data obtained recently for potential scattering is rederived in this wider context it shows in particular how the band spectrum of the infinite periodic system arises in the limit n we illustrate the result on two kinds of examples the first are serial graphs obtained by chaining loops or t junctions another example concerns geometric scatterers where the individual element consists of a surface with a pair of leads we show that apart from the resonances coming from the decoupled surface eigenvalues such scatterers exhibit the high energy behavior typical for the interaction for the physically interesting couplings

preliminary test and stein estimations in simultaneous linear equations abstract in modeling of an economic system there may occur some stochastic constraints that can cause some changes in the estimators and their respective behaviors in this approach we formulate the simultaneous equation models into the problem of estimating the regression parameters of a multiple regression model under elliptical errors we define five different sorts of estimators for the vector parameter their exact risk expressions are also derived under the balanced loss function comparisons are then made to clarify the performance of the proposed estimators it is shown that the shrinkage factor of the stein estimator is robust with respect to departures from normality assumption

index theorems for quantum graphs in geometric analysis an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned sometimes using the heat kernels of two higher order differential operators as an intermediary in this paper the case of quantum graphs is addressed a quantum graph is a graph considered as a singular one dimensional variety and equipped with a second order differential hamiltonian h a laplacian with suitable conditions at vertices for the case of scale invariant vertex conditions i e conditions that do not mix the values of functions and of their derivatives the constant term of the heat kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph this observation is placed into the index theory context by factoring the laplacian into two first order operators h a a and relating the constant term to the index of a an independent consideration provides an index formula for any differential operator on a finite quantum graph in terms of the vertex conditions it is also found that the algebraic multiplicity of 0 as a root of the secular determinant of h is the sum of the nullities of a and a

a remark on discrete wave scattering we consider the spectral problem for the adjacency matrix of a discrete star graph composed of a compact cluster and a few semi infinite periodic leads attached based on the spectral properties of the adjacency matrix we develop the lax phillips scattering theory for the corresponding discrete wave equation

a factorization of the scattering matrix for the schrodinger equation and for the wave equation in one dimension for the one dimensional schrodinger equation with a potential decaying at both ends of the real axis the scattering matrix of the potential is given explicitly in terms of the scattering matrices corresponding to the fragments of this potential a similar result also holds for the wave equation in a nonhomogeneous nondispersive medium where the wave speed has the same asymptotics at both ends of the real line

inverse eigenvalue problems on directed graphs the differential operators id and d2 p are constructed on certain finite directed weighted graphs two types of inverse spectral problems are considered first information about the graph weights and boundary conditions is extracted from the spectrum of d2 second the compactness of isospectral sets for d2 p is established by computation of the residues of the zeta function

spectral properties of matrices associated with some directed graphs we study the spectral properties of certain non self adjoint matrices associated with large directed graphs asymptotically the eigenvalues converge to certain curves apart from a finite number that have limits not on these curves

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

can one hear the shape of a graph we show that the spectrum of the schroperator on a finite metric graph determines uniquely the connectivity matrix and the bond lengths provided that the lengths are non commensurate and the connectivity is simple no parallel bonds between vertices and no loops connecting a vertex to itself that is one can hear the shape of the graph we also consider a related inversion problem a compact graph can be converted into a scattering system by attaching to its vertices leads to infinity we show that the scattering phase determines uniquely the compact part of the graph under similar conditions as above

green function approach for general quantum graphs we present a recursive prescription to calculate the exact green function for general quantum graphs for the closed case the expression for the poles of g which gives the individual eigenstates has the structure of a semiclassical formula where the sum over the periodic orbit is already performed as applications we discuss eigenstate localization for a three arm closed star and filter like mechanisms for transmission throughout an open trident graph

estimation in contingency tables using prior information summary prior beliefs of association and independence in a two way contingency table are discussed and estimators of the cell probabilities are proposed which can incorporate this prior information in the 2 x 2 table where the cell counts are assumed to have a multinomial distribution estimators are developed which can incorporate prior beliefs about the correlation coefficient and the cross product ratio in the i x 2 table in which one set of marginal totals is fixed estimators are developed which reflect prior information about the similarity of a set of cell probabilities numerical examples are given to illustrate the use of these estimators

numerical analysis of a hyperbolic hemivariational inequality arising in dynamic contact in this paper a fully dynamic viscoelastic contact problem is studied the contact is assumed to be bilateral and frictional where the friction law is described by a nonmonotone relation between the tangential stress and the tangential velocity a weak formulation of the problem leads to a second order nonmonotone subdifferential inclusion also known as a second order hyperbolic hemivariational inequality we study both semidiscrete and fully discrete approximation schemes and bound the errors of the approximate solutions under some regularity assumptions imposed on the true solution optimal order error estimates are derived for the linear element solution this theoretical result is illustrated numerically

on the spectrum of the laplace operator of metric graphs attached at a vertex spectral determinant approach we consider a metric graph made of two graphs and attached at one point we derive a formula relating the spectral determinant of the laplace operator in terms of the spectral determinants of the two subgraphs the result is generalized to describe the attachment of n graphs the formulae are also valid for the spectral determinant of the schrodinger operator

the spectrum of the hilbert space valued second derivative with general self adjoint boundary conditions abstract we consider a large class of self adjoint elliptic problems associated with the second derivative acting on a space of vector valued functions we present and survey several results that can be obtained by means of two different approaches to the study of the associated eigenvalues problems the first more general one allows to replace a secular equation which is well known in some special cases by an abstract rank condition the second one though available in general seems to apply particularly well to a specific boundary condition the sometimes dubbed anti kirchhoff condition in the literature that arises in the theory of differential operators on graphs it also permits to discuss interesting and more direct connections between the spectrum of the differential operator and some graph theoretical quantities in particular some results on the symmetry of the spectrum in either case

on the number of states bound by one dimensional finite periodic potentials bound states and zero energy resonances of one dimensional finite periodic potentials are investigated by means of levinson s theorem for finite range potentials supporting no bound states a lower bound for the reduced time delay at threshold is derived

jump start in the analytic perturbation procedure for the friedrichs model for the friedrichs model obtained as a one dimensional perturbation of the orthogonal sum of the momentum and a finite hermitian matrix the scattering matrix is presented as s p i i m p 1 i i m p the rational nevanlinna class krein weyl function m is associated with the operator a and has poles at the eigenvalues of a it is proven that for any eigenvalue 0 of a there exists an intermediate operator which is constructed as a one dimensional perturbation of the orthogonal sum of the momentum and an appropriate one dimensional operator a solvable model which plays the role of an intermediate operator in the scattering problem to the pair the scattering matrix s0 to the pair is an analytic function of and the total scattering matrix to the pair can be factorized as a product where s 0 is the scattering matrix to the pair it is represented by a single blaschke factor with a pole and zero approaching 0 when 0 the non analytic factor describes creation of the resonance from the eigenvalue 0 of the operator a

universal domination and stochastic domination estimation simultaneously under a broad class of loss functions several theoretical questions are resolved in this paper in particular the criterion of universal domination is shown to be equivalent to the criterion of stochastic domination that compares the estimators by the stochastic ordering of their euclidean distances from the estimators to the true parameter concrete results about universal domination relating to the usual estimator are also established in particular when x 0 has a p variate t distribution and p 1 2 there exists no estimator for 0 that universally dominates x however for p 2 3 estimators of the type of james stein positive part estimators that universally dominate x are specified when x has a p variate normal distribution with mean 0 and identity covariance matrix we show that for any dimension p no james stein positive part estimators universally dominate x however under slightly smaller classes of losses some jamesstein positive part estimators are shown to simultaneously dominate x these hitherto unstudied losses are bounded and fairly practical

variational and numerical analysis of a dynamic frictionless contact problem with adhesion we study a dynamic frictionless contact problem between a viscoelastic body and an obstacle the so called foundation the contact is subjected to an adhesion effect whose evolution is described by an ordinary differential equation for the variational formulation of the contact problem we present and prove an existence and uniqueness result a fully discrete scheme is introduced to solve the problem under certain solution regularity assumptions we derive an optimal order error estimate some numerical examples are included to show the performance of the method

focused information criterion and model averaging for generalized additive partial linear models we study model selection and model averaging in generalized additive partial linear models gaplms polynomial spline is used to approximate nonparametric functions the corresponding estimators of the linear parameters are shown to be asymptotically normal we then develop a focused information criterion fic and a frequentist model average fma estimator on the basis of the quasi likelihood principle and examine theoretical properties of the fic and fma the major advantages of the proposed procedures over the existing ones are their computational expediency and theoretical reliability simulation experiments have provided evidence of the superiority of the proposed procedures the approach is further applied to a real world data example

improved estimation in a contingency table independence structure abstract estimation of the cell probabilities in a two way contingency table is considered when it is plausible that the table might have an independence structure relating to the two traits in a classical nonparametric setup the unrestricted maximum likelihood estimators of the cell probabilities are the corresponding sample proportions under the assumption of independence the restricted estimators are the product of the respective row and column sample proportions the latter estimators behave better than the former when independence actually holds but a different picture may emerge for possible departure from the assumed independence structure the restricted estimators may be heavily biased inefficient and even inconsistent for this reason a preliminary test on independence based on the classical contingency chi squared statistic may be conveniently incorporated in the formulation of a preliminary test estimator of the matrix of cell probabilities since typically we have a multiparameter e

on the inverse scattering problem on branching graphs the inverse scattering problem on branching graphs is studied the definition of the schrodinger operator on such graphs is discussed the operator is defined with real potentials with finite first momentum and using special boundary conditions connecting values of the functions at the vertices it is shown that in general the scattering matrix does not determine the topology of the graph the potentials on the edges and the boundary conditions uniquely

comparison of linear estimators using pitman s measure of closeness abstract a method is given for the comparison of two linear forms of a common random vector under the criterion of pitman s measure of closeness assuming multivariate normality of the random vector one can determine exact expressions for the closeness probabilities the applicability of the theory is illustrated on the comparison of ridge regression estimators

variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion a model for the adhesive quasistatic and frictionless contact between a viscoelastic body and a deformable foundation is described the adhesion process is modelled by a bonding field on the contact surface and contact is described by a modified normal compliance condition the problem is formulated as a coupled system of a variational equality for the displacements and a differential equation for the bonding field the existence of a unique weak solution for the problem and its continuous dependence on the adhesion parameters are established then the numerical analysis of the problem is conducted for the fully discrete approximation the convergence of the scheme is established and error estimates derived finally representative numerical simulations are presented depicting the evolution of the state of the system and in particular the evolution of the bonding field

some inverse scattering problems on star shaped graphs having in mind applications to the fault detection diagnosis of lossless electrical networks here we consider some inverse scattering problems for schrodinger operators over star shaped graphs we restrict ourselves to the case of minimal experimental setup consisting in measuring at most two reflection coefficients when an infinite homogeneous potential less branch is added to the central node first by studying the asymptotic behavior of only one reflection coefficient in the high frequency limit we prove the identiability of the geometry of this star shaped graph the number of edges and their lengths next we study the potential identification problem by inverse scattering noting that the potentials represent the inhomogeneities due to the soft faults in the network wirings potentials with bounded h1 norms the main result states that under some assumptions on the geometry of the graph the measurement of two reflection coefficients associated to two different sets of boundary conditions at the external vertices of the tree determines uniquely the potentials it can be seen as a generalization of the theorem of the two boundary spectra on an interval

a topological state sum model for fermions on the circle a simple state sum model for fermions on a 1 manifold is constructed the model is independent of the triangulation and gives exactly the same partition function as the dirac functional integral with zeta function regularization some implications for more realistic physical models are discussed

kirchhoff s rule for quantum wires we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the hamiltonian to be minus the laplace operator with general boundary conditions at the vertices this results in a scattering theory with n channels the corresponding on shell s matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy e 0 is given explicitly in terms of the boundary conditions and the lengths of the internal lines it is shown to be unitary which may be viewed as the quantum version of kirchhoff s law we exhibit covariance and symmetry properties it is symmetric if the boundary conditions are real also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low energy behaviour of one theory gives the high energy behaviour of the transformed theory finally we provide a composition rule by which the on shell s matrix of a graph is factorizable in terms of the s matrices of its subgraphs all proofs use only known facts from the theory of self adjoint extensions standard linear algebra complex function theory and elementary arguments from the theory of hermitian symplectic forms

nodal domains on isospectral quantum graphs the resolution of isospectrality we present and discuss isospectral quantum graphs which are not isometric these graphs are the analogues of the isospectral domains in which were introduced recently in gordon et al 1992 bull am math soc 27 134 8 chapman 1995 am math mon 102 124 buser et al 1994 int math res not 9 391 400 okada and shudo 2001 j phys a math gen 34 5911 22 jakobson et al 2006 j comput appl math 194 141 55 and levitin et al 2006 j phys a math gen 39 2073 82 all based on sunada s construction of isospectral domains sunada t 1985 ann math 121 196 86 after presenting some of the properties of these graphs we discuss a few examples which support the conjecture that by counting the nodal domains of the corresponding eigenfunctions one can resolve the isospectral ambiguity

asymptotically isospectral quantum graphs and generalised trigonometric polynomials abstract the theory of almost periodic functions is used to investigate spectral properties of schrodinger operators on metric graphs also known as quantum graphs in particular we prove that two schrodinger operators may have asymptotically close spectra if and only if the corresponding reference laplacians are isospectral our result implies that a schrodinger operator is isospectral to the standard laplacian on a may be different metric graph only if the potential is identically equal to zero

median unbiasedness and pitman closeness abstract under certain conditions a median unbiased estimator of a parameter is shown to be the pitman closest estimator within a certain class of estimators for location scale or location scale families of distributions the class of equivariant estimators possesses some desirable properties the median unbiasedness of equivariant estimators is explored in the characterization of the pitman closeness property illustrative examples bear fruitful implications of this characterization

optimal weight choice for frequentist model average estimators there has been increasing interest recently in model averaging within the frequentist paradigm the main benefit of model averaging over model selection is that it incorporates rather than ignores the uncertainty inherent in the model selection process one of the most important yet challenging aspects of model averaging is how to optimally combine estimates from different models in this work we suggest a procedure of weight choice for frequentist model average estimators that exhibits optimality properties with respect to the estimator s mean squared error mse as a basis for demonstrating our idea we consider averaging over a sequence of linear regression models building on this base we develop a model weighting mechanism that involves minimizing the trace of an unbiased estimator of the model average estimator s mse we further obtain results that reflect the finite sample as well as asymptotic optimality of the proposed mechanism a monte carlo study based on simulated and real data evaluates

scattering on graphs and one dimensional approximations to n dimensional schrodinger operators in the present article we develop the spectral analysis of schrodinger operators on lattice type graphs for the basic example of a cubic periodic graph the problem is reduced to the spectral analysis of certain regular differential operators on a fundamental star like subgraph with a selfadjoint condition at the central node and quasiperiodic conditions at the boundary vertices using an explicit expression for the resolvent of lattice type operator we develop in the second section appropriate lippmann schwinger techniques for the perturbed periodic operator and construct the corresponding scattering matrix it serves as a base for the approximation of the multi dimensional schrodinger operator by a one dimensional operator on the graph in the third section of the paper for given n dimensional schrodinger operators with rapidly decreasing potential we construct a lattice type operator on a cubic graph embedded into rn and show that the original n dimensional scattering problem can be approximated in a p

convergence of spectra of mesoscopic systems collapsing onto a graph abstract let m be a finite graph in the plane and let me be a domain that looks like the e fattened graph m exact conditions on the domain are given it is shown that the spectrum of the neumann laplacian on me converges when e 0 to the spectrum of an ode problem on m the presence of an electromagnetic field is also allowed considerations of this kind arise naturally in mesoscopic physics and other areas of physics and chemistry the results of the paper extend the ones previously obtained by j rubinstein and m schatzman

improved biased estimation in an anova model abstract the problem of simultaneous estimation of means in one way analysis of variance anova is considered when it is suspected that the mean parameters are equal but with some degree of uncertainty improved estimators using stein rule and preliminary test approach are proposed the explicit forms of the biases and risk functions of the proposed estimators are derived the relative performance of the positive part stein rule estimator pse and the usual stein rule estimator se is critically assessed with the aid of the quadratic loss function it is shown analytically as well as computationally that pse dominates the classical se in the whole parameter space also the improved preliminary test estimator ipe is shown to have smaller risk than that of the classical pe in the entire parameter space

a normal compliance contact problem in viscoelasticity an a posteriori error analysis and computational experiments in this work the numerical approximation of a viscoelastic contact problem is studied the classical kelvin voigt constitutive law is employed and contact is assumed with a deformable obstacle and modelled using the normal compliance condition the variational formulation leads to a nonlinear parabolic variational equation an existence and uniqueness result is recalled then a fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and the implicit euler scheme to discretize time derivatives a priori error estimates recently proved for this problem are recalled then an a posteriori error analysis is provided extending some preliminary results obtained in the study of the heat equation and other parabolic equations upper and lower error bounds are proved finally some numerical experiments are presented to demonstrate the accuracy and the numerical behaviour of the error estimates

classifying the general family of 1d point interactions a scattering approach we propose a classification scheme for the complete family of 1d point interactions to do so we first review the solutions of the wavefunctions and green functions of the problem second we derive the exact time dependent propagators in such a way that we can write the expressions for the k s in a very compact form as they should such expressions do reduce to the known results in the literature according to the potential parameter values then we analyse in general terms how the different point interactions scatter off arbitrary initially localized wave packets finally we show that the physical features associated with the scattering process can be used to establish a classification procedure moreover these physical characteristics are directly related to the potential parameters leading to the many formulae for the k s as an application we present numerical calculations for gaussian wave packets

a semiparametric basis for combining estimation problems under quadratic loss when there is uncertainty concerning the appropriate statistical model estimator to use in representing the data sampling process we consider a basis for optimally combining estimation problems the objective is to produce natural adaptive estimators that are free of subjective choices and tuning parameters in the context of two competing multivariate linear statistical models estimators we demonstrate a semiparametric stein like spsl estimator that under quadratic loss has superior risk performance relative to the conventional least squares estimator the relationship of the spsl estimator to the family of stein estimators is noted and asymptotic and analytic finite sample risk properties of the estimator are developed for some special cases as an application we consider the problem of combining two polar linear models and demonstrate a corresponding spsl estimator an extensive sampling experiment is used to investigate the finite sample performance of the spsl estimator over a wide range of

ridge estimation in semi parametric regression models under the stochastic restriction and correlated elliptically contoured errors abstract some linear stochastic constraints may occur during real data set modeling based on either additional information or prior knowledge these stochastic constraints often cause some changes in the behaviors of estimators in this research shrinkage ridge estimators as well as their positive parts are proposed in the semi parametric model when some stochastic constrains are imposed under a multicollinearity setting also it is assumed that the error terms are dependent and distributed according to the elliptically contoured models the bias and risk expressions of the proposed estimators for comparison purposes are derived finally the monte carlo simulation studies and a real application related to electricity consumption data are conducted to support our theoretical discussion

nodal statistics on quantum graphs it has been suggested that the distribution of the suitably normalized number of zeros of laplacian eigenfunctions contains information about the geometry of the underlying domain we study this distribution more precisely the distribution of the nodal surplus for laplacian eigenfunctions of a metric graph the existence of the distribution is established along with its symmetry one consequence of the symmetry is that the graph s first betti number can be recovered as twice the average nodal surplus of its eigenfunctions furthermore for graphs with disjoint cycles it is proven that the distribution has a universal form it is binomial over the allowed range of values of the surplus to prove the latter result we introduce the notion of a local nodal surplus and study its symmetry and dependence properties establishing that the local nodal surpluses of disjoint cycles behave like independent bernoulli variables

global bounds for the lyapunov exponent and the integrated density of states of random schrodinger operators in one dimension in this paper we prove an upper bound for the lyapunov exponent e and a two sided bound for the integrated density of states n e at an arbitrary energy e 0 of random schrodinger operators in one dimension these schrodinger operators are given by potentials of identical shape centred at every lattice site but with non overlapping supports and with randomly varying coupling constants both types of bounds only involve scattering data for the single site potential they show in particular that both e and n e e 1 2 decay at infinity at least like 1 e 1 2 as an example we consider the random kronig penney model

bayesian estimation methods for 2 2 contingency tables using mixtures of dirichlet distributions abstract in the estimation of cell probabilities from a 2 2 table a prior distribution is developed that can reflect prior beliefs about the cross classification structure in the table the posterior means using this prior shrink the classical estimates towards the association structure specified a priori by the user closed form approximations to the posterior means and credible regions are developed in the special case where the two variables of the table are believed independent

simple regression in view of elliptical models abstract for the simple linear model y 1 x where the error vector follows the elliptically contoured distribution we consider the unrestricted restricted preliminary test and shrinkage estimators for the intercept parameter when it is suspected that the slope parameter may be o the exact bias and mse expressions are derived and the mean square relative efficiency is taken to determine the relative dominance properties of the proposed estimators in comparison in the continuation the optimal level of significance of the preliminary test estimator is tabulated and some graphical result are also displayed

mathematical aspects of vacuum energy on quantum graphs we use quantum graphs as a model to study various mathematical aspects of the vacuum energy such as convergence of periodic path expansions consistency among different methods trace formulae versus method of images and the possible connection with the underlying classical dynamics in our study we derive an expansion for the vacuum energy in terms of periodic paths on the graph and prove its convergence and smooth dependence on the bond lengths of the graph for an important special case of graphs with equal bond lengths we derive a simpler explicit formula with minor changes this formula also applies to graphs with rational up to a common factor bond lengths the main results are derived using the trace formula we also discuss an alternative approach using the method of images and prove that the results are consistent this may have important consequences for other systems since the method of images unlike the trace formula includes a sum over special bounce paths we succeed in showing that in our model bounce paths do not contribute to the vacuum energy finally we discuss the proposed possible link between the magnitude of the vacuum energy and the type chaotic versus integrable of the underlying classical dynamics within a random matrix model we calculate the variance of the vacuum energy over several ensembles and find evidence that the level repulsion leads to suppression of the vacuum energy