multivariate product shot noise cox point process models we introduce a new multivariate product shot noise cox process which is useful for modeling multi species spatial point patterns with clustering intra specific interactions and neutral negative or positive inter specific interactions the auto and cross pair correlation functions of the process can be obtained in closed analytical forms and approximate simulation of the process is straightforward we use the proposed process to model interactions within and among five tree species in the barro colorado island plot

a combined estimating function approach for fitting stationary point process models a composite likelihood technique based on pairwise contributions provides a computationally simple but potentially inefficient approach for fitting spatial point process models we propose a new estimation procedure that improves the efficiency our approach combines estimating functions derived from pairwise composite likelihood estimation and estimating functions that account for correlations among the pairwise contributions our method can be used to fit a variety of parametric spatial point process models and can yield more efficient estimators for the clustering parameters than pairwise composite likelihood estimation we demonstrate the efficacy of our proposed method through a simulation study and an application to the longleaf pine data

free vibrations and sensitivity analysis of a defective two degree of freedom system free oscillations of a two degree of freedom system with honproportional damping are analyzed by a suitable choice of parameters a family of defective systems having a noncomplete set of eigenvectors is selected free motions of underdamped and overdamped defective systems are studied in the four dimensional state space and their main characteristics are discussed in particular the rate at which the trajectories are attracted by the eigenvectors is determined small perturbations of order e of the parameters are then considered and asymptotic expressions for the modified system eigensolutions are obtained these allow qualitative discussion of the effects of modifications on the mechanical behavior of nearly defective systems marked sensitivities of order 2 or e are found these depend strongly on the damping magnitude an extensive numerical analysis is performed n structural dynamics it is by no means rare to encounter systems having multiple eigenvalues this does not pose any substantial difficulties when the system is conservative but it involves specific problems when the system is nonconservative very often indeed the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity and so the system has an incomplete set of eigenvectors insufficient to form a base for the state space systems of this type are called defective the free evolution of defective systems is well known to persons working in the automatic control or system theory field moreover basic notions can be found in any good book on linear algebra however in the author s opinion the problem is not sufficiently known to the structural analyst indeed it is common practice to assume damping of proportional type so that the eigenvectors coincide with those of the corresponding undamped system always forming a complete set and defective systems cannot occur

two step estimation for inhomogeneous spatial point processes summary the paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second order properties k function regression parameters are estimated by using a poisson likelihood score estimating function and in the second step minimum contrast estimation is applied for the residual clustering parameters asymptotic normality of parameter estimates is established under certain mixing conditions and we exemplify how the results may be applied in ecological studies of rainforests

on the subgroup structure of classical groups in this paper we establish a result on the subgroup structure of classical groups over algebraically closed elds and use this to give a new proof of a fundamental theorem of m aschbacher on subgroups of nite classical groups let v be a nite dimensional vector space over an algebraically closed eld k and let g be one of the classical algebraic groups sl v sp v or so v our result is a reduction theorem concerning the subgroups of g we de ne a certain collection c of natural proper subgroups of g and prove that any closed nite or in nite subgroup of g either lies in a member of c or is roughly speaking a simple group acting irreducibly on v aschbacher s result is an analogous reduction theorem for subgroups of nite classical groups we obtain this as a relatively easy consequence of our main result by taking xed points under the action of a frobenius morphism using a standard process involving lang s theorem the proof of the main result uses elementary linear algebra together with a few basic facts from the theory of algebraic groups various complications which arise in the nite group setting in as become much more straightforward in the algebraic group setting in particular questions involving extension elds do not occur and issues of conjugacy are easily settled when we descend to nite invent math 134 427 453 1998

going off grid computationally efficient inference for log gaussian cox processes this paper introduces a new method for performing computational inference on log gaussian cox processes the likelihood is approximated directly by making novel use of a continuously specified gaussian random field we show that for sufficiently smooth gaussian random field prior distributions the approximation can converge with arbitrarily high order while an approximation based on a counting process on a partition of the domain only achieves first order convergence the given results improve on the general theory of convergence of the stochastic partial differential equation models introduced by lindgren et al 2011 the new method is demonstrated on a standard point pattern data set and two interesting extensions to the classical log gaussian cox process framework are discussed the first extension considers variable sampling effort throughout the observation window and implements the method of chakraborty et al 2011 the second extension constructs a log gaussian cox process on the world s oceans the analysis is performed using integrated nested laplace approximation for fast approximate inference

an estimating function approach to inference for inhomogeneous neyman scott processes this article is concerned with inference for a certain class of inhomogeneous neyman scott point processes depending on spatial covariates regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the mother intensity for the neyman scott process tends to infinity clustering parameter estimates are obtained using minimum contrast estimation based on the k function the approach is motivated and illustrated by applications to point pattern data from a tropical rain forest plot

computation of eigenvector derivatives with repeated eigenvalues using a complete modal space this paper presents a complete modal space cms method that is an exact modal expansion method there is no modal truncation error existing in the derivation

on nonparametric variance estimation for second order statistics of inhomogeneous spatial point processes with a known parametric intensity form we introduce new variance estimation procedures for second order statistics that are computed from a single realization of intensity reweighted stationary spatial point processes the statistics are defined either on a subset b of the observation window or on the whole window for the former we use subblocks that have the same size and shape as b as replicates of b in order to estimate the target variance for the latter we develop a subsampling estimator for a key component in the target variance and estimate its other components by method of moment methods under some suitable conditions we prove that the proposed variance estimators are consistent for the target variances in both cases simulations and an application to a real data example are used to demonstrate the usefulness of the proposed methods this article has supplementary material online

eigensolutions sensitivity for nonsymmetric matrices with repeated eigenvalues a perturbation algorithm is developed for evaluating eigenvalue and eigenvector directional derivatives of nonsymmetric defective matrices some properties are recalled in particular chains of generalized right and left eigenvectors and their orthogonal properties are defined small perturbations of the matrix are then considered an asymptotic expansion of the eigensolutions of the perturbed problem is obtained in terms of noninteger powers of the perturbation parameter particular attention is devoted to the eigenvectors of the perturbed system and to the strong coupling that occurs between the chains

approximate method for eigensensitivity analysis of a defective matrix based on the exact modal expansion method an arbitrary high order approximate method is developed for calculating the second order eigenvalue derivatives and the first order eigenvector derivatives of a defective matrix the numerical example shows the validity of the method if the different eigenvalues m 1 m q of the matrix are arranged so that m 1 m q and satisfy the condition that m q 1 m q 1 1 for some q 1

can a semi simple eigenvalue admit fractional sensitivities we perform high order sensitivity analysis of eigenvalues and eigenvectors of linear systems depending on parameters attention is focused on double not semi simple and semi simple eigenvalues undergoing perturbations either of regular or singular type the use of integer taylor or fractional puiseux series expansions is discussed and the analysis carried out both on the characteristic polynomial and on the eigenvalue problem it is shown that semi simple eigenvalues can admit fractional sensitivities when the perturbations are singular conversely to the not semi simple case however such occurrence only manifests itself when a second order perturbation analysis is carried out as a main result it is found that such over degenerate case spontaneously emerges in bifurcation analysis when one looks for the boundaries of the stability domain of circulatory mechanical systems possessing symmetries a four degree of freedom system under a follower force is studied as an illustrative example

partial derivatives of repeated eigenvalues and their eigenvectors the analysis of inverse problems in linear modeling often require the sensitivities of the eigenvalues and eigenvectors the calculation of these sensitivities is mathematically related to the corresponding partial derivatives which do not exist for any parameterization inasmuch as eigenvalues and eigenvectors are coupled by the constitutional equation of the general eigenvalue problem their derivatives are coupled too conditions on the parameterization are derived and formulated as theorems which ensure the existence of the partial derivatives of the eigenvalues and eigenvectors with respect to these parameters the application of the theorems is demonstrated by examples

combined method for calculating eigenvector derivatives with repeated eigenvalues a combined method for calculating particular solutions of eigenvector derivative governing equations in the generalized eigenproblem with groups of repeated eigenvalues is presented which finds the first set of the particular solutions by a direct method and the other particular solutions by a family of modal methods the direct method is based on gauss elimination by which the constraint generalized inverse of the frequency shift stiffness matrix can be obtained as well as the particular solution and the method is applicable to all nondefective systems a formula for finding a constraint generalized inverse from another is derived by which the total calculation can be reduced a simple calculating example is included

restriction of irreducible modules for spin 2n 1 k to spin 2n k abstract let k be an algebraically closed field of characteristic p 0 and let y spin 2 n 1 k n 3 be a simply connected simple algebraic group of type b n over k also let x be the subgroup of type d n embedded in y in the usual way as the derived subgroup of the stabilizer of a non singular one dimensional subspace of the natural module for y in this paper we give a complete set of isomorphism classes of finite dimensional irreducible rational ky modules on which x acts with exactly two composition factors completing the work of ford in 12

simplified calculation of eigenvector derivatives with repeated eigenvalues an efficient and practical procedure based on the generalized schmidt orthogonalization is presented to compute the eigenvector derivatives when repeated eigenvalues exist

eigenvector derivatives with repeated eigenvalues in this paper an algorithm is derived for computing the derivatives of eigenvalues and eigenvectors for real symmetric matrices in the case of repeated eigenvalues where the matrices are functions of real parameters such as mass density or moment of inertia the algorithm is an extension of recent work by i u ojalvo the key step in this extended derivation is to differentiate the eigenvalue equation twice the algorithm preserves the symmetry and band structure of the matrices allowing efficient computer storage and solution techniques applications include sensitivity analysis and optimization of the normal modes of finite element modeled structures such as large space structures a cantilever beam finite element example is included

estimating functions for inhomogeneous spatial point processes with incomplete covariate data the r package spatstat provides a very flexible and useful framework for analysing spatial point patterns a fundamental feature is a procedure for fitting spatial point process models depending on covariates however in practice one often faces incomplete observation of the covariates and this leads to parameter estimation error which is difficult to quantify in this paper we introduce a monte carlo version of the estimating function used in spatstat for fitting inhomogeneous poisson processes and certain inhomogeneous cluster processes for this modified estimating function it is feasible to obtain the asymptotic distribution of the parameter estimators in the case of incomplete covariate information this allows a study of the loss of efficiency due to the missing covariate data

a construction of certain maximal subgroups of the algebraic groups e6 and f4 keywords maximal closed connected subgroup exceptional algebraic groups irreducible embeddings of semisimple algebraic groups rational modules irreducible representations embeddings of parabolic subgroups reference ctg article 1989 002doi 10 1016 0021 8693 89 90218 4 record created on 2008 12 16 modified on 2017 05 12

a thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns when modeling inhomogeneous spatial point patterns it is of interest to fit a parametric model for the first order intensity function foif of the process in terms of some measured covariates estimates for the regression coefficients say can be obtained by maximizing a poisson maximum likelihood criterion little work has been done on the asymptotic distribution of except in some special cases in this article we show that is asymptotically normal for a general class of mixing processes to estimate the variance of we propose a novel thinned block bootstrap procedure that assumes that the point process is second order reweighted stationary to apply this procedure only the foif and not any high order terms of the process needs to be estimated we establish the consistency of the resulting variance estimator and demonstrate its efficacy through simulations and an application to a real data example

a1 type overgroups of elements of order p in semisimple algebraic groups and the associated finite groups keywords semisimple algebraic groups closed connected subgroups finite groups fixed point subgroups reference ctg article 1995 001doi 10 1006 jabr 1995 1285 record created on 2008 12 16 modified on 2017 05 12

quasi likelihood for spatial point processes fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates when cox or cluster process models are used to accommodate clustering not accounted for by the available covariates likelihood based inference becomes computationally cumbersome due to the complicated nature of the likelihood function and the associated score function it is therefore of interest to consider alternative more easily computable estimating functions we derive the optimal estimating function in a class of first order estimating functions the optimal estimating function depends on the solution of a certain fredholm integral equation which in practise is solved numerically the derivation of the optimal estimating function has close similarities to the derivation of quasi likelihood for standard data sets the approximate solution is further equivalent to a quasi likelihood score for binary spatial data we therefore use the term quasi likelihood for our optimal estimating function approach we demonstrate in a simulation study and a data example that our quasi likelihood method for spatial point processes is both statistically and computationally efficient

derivatives of complex eigenvectors with distinct and repeated eigenvalues in this paper we investigate the computation of the first order derivatives of complex eigenvectors for general non defective eigensystems a new normalization condition is proposed with which we can compute unique first order derivatives of arbitrary differentiable eigenvectors of systems with distinct and repeated eigenvalues we also present an efficient algorithm to compute the particular solutions to the governing equations of the first order derivatives of eigenvectors finally numerical examples are included to demonstrate the validity of the proposed method copyright 2007 john wiley sons ltd

on least squares fitting for stationary spatial point processes summary the k function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability in this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the k function by using subsampling we demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures this is done through asymptotic theory simulation experiments and an application to a data set on long leaf pine trees

eigensolutions of perturbed nearly defective matrices abstract perturbation methods for approximating eigenvalues and eigenvectors of perturbed nearly defective mistuned systems have been discussed it is shown that the mistuning causes taylor expansions to be not uniformly valid even in small intervals of the perturbation parameter subsequently rendering them useless for practical purposes the problem is overcome by starting the perturbation expansion from an exactly defective tuned system close to the mistuned one asymptotic expansions are then obtained in terms of fractional powers of two parameters the modification and the mistuning parameter however as the tuned system is unknown an inverse problem has to be solved in order to determine it an algorithm valid for the particular but frequent case of several couples of nearly coincident eigenvalues has been detailed for this problem an outline of a more general case is also given illustrative examples are presented

bayesian semiparametric intensity estimation for inhomogeneous spatial point processes summary in this work we propose a fully bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process the basic idea is to first convert intensity estimation into a poisson regression setting via binning data points on a regular grid and then model the log intensity semiparametrically using an adaptive version of gaussian markov random fields to smooth the corresponding counts the inference is carried by an efficient markov chain monte carlo simulation algorithm compared to existing methods for intensity estimation for example parametric modeling and kernel smoothing the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates but also uses information from the data to adaptively determine the amount of smoothing at the local level the effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset

irreducible disconnected subgroups of exceptional algebraic groups this dissertation is concerned with the study of irreducible embeddings of simple algebraic groups of exceptional type it is motivated by the role of such embeddings in the study of positive dimensional closed subgroups of classical algebraic groups the classification of the maximal closed connected subgroups of simple algebraic groups was carried out by e b dynkin g m seitz and d m testerman their analysis for the classical groups was based primarily on a striking result if g is a simple algebraic group and o g sl v is a tensor indecomposable irreducible rational representation then with specified exceptions the image of g is maximal among closed connected subgroups of one of the classical groups sl v sp v or so v in the case of closed not necessarily connected subgroups of the classical groups one is interested in considering irreducible embeddings of simple algebraic groups and their automorphism groups given a simple algebraic group y defined over an algebraically closed field k one is led to study the embeddings g 0 g is a closed non connected positive dimensional subgroup of y and v is a nontrivial irreducible rational ky module such that v g is irreducible we obtain a precise description of such triples g y v

new method for eigenvector sensitivity analysis with repeated eigenvalues and eigenvalue derivatives this paper proposes a new method of eigenvector sensitivity analysis for real symmetric systems with repeated eigenvalues and eigenvalue derivatives the derivation is completed by using information from the second and third derivatives of the eigenproblem and is applicable to the case of repeated eigenvalue derivatives the extended systems with a nonsingular coefficient matrix are constructed to calculate the particular solutions an efficient approach is developed to compute the homogeneous solutions associated with the repeated eigenvalue derivatives different constraints for calculating the eigenvector sensitivities are derived and discussed four numerical examples are presented to demonstrate the validity of the proposed method

on the central limit theorem for stationary mixing random fields a simple proof of a central limit theorem for stationary random fields under mixing conditions is given generalizing some results obtained by more complicated methods e g bernstein s method

irreducible modules and parabolic subgroups summary it seems desirable from the point of view of finite group theorists to develop further the representation theory of finite chevalley groups in the characteristic of their definition say p by focusing attention on the full array of p local subgroups that is the parabolics rather than the usual single borel or cartan subgroup the following observation may be regarded as a generalization to arbitrary parabolic subgroups of the standard result 3 theorem 39 d for a borel subgroup namely that in an irreducible module the subspace fixed by a maximal unipotent subgroup is 1 dimensional and so affords an irreducible module for a levi complement which is an abelian cartan subgroup it seems natural to state the result first for algebraic groups

on irreducible subgroups of simple algebraic groups let g be a simple algebraic group over an algebraically closed field k of characteristic p geqslant 0 let h be a proper closed subgroup of g and let v be a nontrivial irreducible kg module which is p restricted tensor indecomposable and rational assume that the restriction of v to h is irreducible in this paper we study the triples g h v of this form when g is a classical group and h is positive dimensional combined with earlier work of dynkin seitz testerman and others our main theorem reduces the problem of classifying the triples g h v to the case where g is an orthogonal group v is a spin module and h normalizes an orthogonal decomposition of the natural kg module

improved nelson s method for computing eigenvector derivatives with distinct and repeated eigenvalues t he computation of derivatives of eigenvalues and eigenvectors with respect to model parameters is crucial for many applications 1 nelson 2 proposed an approach for general real eigensystemswith distinct eigenvalueswhere only the eigenvector of interest was required ojalvo 3 mills curran 4 dailey 5 and shaw and jayasuriya 6 developed nelson s method for real symmetric eigensystems with repeated eigenvalues for computation of a particular solution themethods described in 3 5 may fail in some circumstances other methods have been suggested by millscurran 4 and song et al 7 but they are difficult to implement when a system of linear equations is solved one hopes that the calculated solution is a close representation of the true solution the computed solution for a system with a large condition number may be inexact due to extreme sensitivity of the solution to small changes in its coefficient matrix and right column vectors 8 because some diagonal elements in the coefficient matrix for particular solutions are set to units its coefficients are not all of the same order of magnitude so the coefficient matrix has a large condition number in this note nelson s method is first extended to the case of repeated eigenvalues for the symmetric real eigensystems and its improvements are then presented the condition number of the coefficient matrix of the improved method is considerably reduced