on interval routing schemes and treewidth abstract in this paper we investigate which processor networks allow k label interval routing schemes under the assumption that costs of edges may vary we show that for each fixed k 1 the class of graphs allowing such routing schemes is closed under minor taking in the domain of connected graphs and hence has a linear time recognition algorithm this result connects the theory of compact routing with the theory of graph minors and treewidth we show that every graph that does not contain k 2 r as a minor has treewidth at most 2 r 2 as a consequence graphs that allow k label interval routing schemes under dynamic cost edges have treewidth at most 4 k similar results are shown for other types of interval routing schemes

on local smoothing of nonparametric curve estimators abstract we develop new local versions of familiar smoothing methods such as cross validation and smoothed cross validation in the contexts of density estimation and regression these new methods are locally adaptive in the sense that they capture smooth local fluctuations in the curve by using smoothly varying bandwidths that change as the character of the curve changes moreover the new methods are accurate easy to apply and computationally expedient

on the polar decomposition of the quantum su 2 algebra polar decomposition of the generators of the su 2 q algebra is performed and its contraction limit to the deformed oscillator algebra is considered using the phase operator occurring in the decomposition and its conjugate the authors write a realisation of the su 2j 1 algebra into which they embed the deformed su 2 realisation finally they discuss the classical limit of the polar decomposition and the case of the quantum su 2 dynamics

symplectic geometry of suq h 0 2 and suq h 2 algebras the authors give a complete description of q deformation of su 2 algebra in terms of symplectic geometry the geometric meanings of such a deformation are manifestly shown at classical as well as at quantum level as a model they study the classical and quantum dynamics of a particle with q spin moving in electromagnetic fields in detail

studying school size effects in line transect sampling using the kernel method when conducting line transect sampling to estimate the abundance of a clustered wildlife population detection of a school depends not only on the perpendicular distance of the school to the transect line but also on the size of school larger size schools are easier to detect than smaller schools thus a bivariate detection function with distance and size as covariates should be considered this paper considers using the kernel smoothing method to fit the bivariate line transect data in order to estimate both abundance and the mean school size two kernel estimators are studied the fixed kernel estimator which uses the same smoothing bandwidth for all data points and the adaptive kernel estimator which allows the bandwidth to vary across the data points

confidence intervals for densities in line transect sampling we consider the problem of estimating the density d of a population of objects or animals with ungrouped data from line transect sampling we present a method of deriving an approximate confidence interval for d this confidence interval requires the estimation of a certain standard deviation by the bootstrap method it also requires the estimation with negligible bias of the value f o of a density functions we present a method of bias reduction in the case wheref o is estimated by the fourier series method monte carlo simulations indicate that the coverage rates are smaller than their nominal values but the bias reduction offers an improvement especially when f is peaked at 0 or when it is long tailed

horvitz thompson estimators for double platform line transect surveys summary horvitz thompson estimators based on estimated inclusion probabilities are developed for line transect surveys in which some of the central assumptions of conventional line transect theory fail the estimators are designed to accommodate uncertain detection of animals in the observers path simultaneously with dependence of detection probabilities on explanatory variables other than perpendicular distance they require that data be collected by two observer teams simultaneously searching the survey region recording for each detection both positional data and details of any other variables that may affect detectability one of the estimators is designed to correct for responsive animal movement this method requires that the primary observer team searches independently of the secondary team whereas the second estimator requires both observer teams to search independently of each other the methods can be viewed as specific forms of mark recapture experiments in which individual capture probabilities are modelled as functions of observable explanatory variables and in which animals detected by both observer teams correspond to recaptures they differ from existing mark recapture horvitz thompson estimators primarily in that they use an assumption about the distribution of perpendicular distances that is implicit in conventional

hopf algebraic structures of suq h cross to 0 2 and suq h cross 2 algebras monopoles and symplectic geometry on 2d manifolds from the symplectic structure on the q deformed manifold sq2 of s2 the classical and quantum q deformed algebras suq h cross to 0 2 and suq h cross 2 of su 2 are discussed in detail and their hopf structures are constructed it is also shown that the symplectic geometry of s2 describes the properties of monopoles for the su 2 algebra the q deformed monopoles are studied from the symplectic geometry of sq2 and a relation between generic 2d manifold and algebraic structures is established

tannaka krein duality for compact matrix pseudogroups twisted su n groups the notion of concrete monoidalw category is introduced and investigated a generalization of the tannaka krein duality theorem is proved it leads to new examples of compact matrix pseudogroups among them we have twistedsu n groups denoted bys u n it is shown that the representation theory fors u n is similar to that ofsu n irreducible representations are labeled by young diagrams and formulae for dimensions and multiplicity are the same as in the classical case

suq h cross to 0 2 and suq h cross 2 the classical and quantum q deformations of the su 2 algebra iii when q is a root of unity for pt ii see ibid vol 23 p 5371 1990 the q oscillator of type one and the classical and the quantum q deformations of su 2 algebra realized through the q oscillators are studied in the case of q being roots of unity i e qk 1 the q excitations are found to be non bosonic in particular when k is of rank 4 and 6 the q excitations are shown to be fermionic and parafermionic respectively

on the complexity of multi dimensional interval routing schemes abstract multi dimensional interval routing schemes mirs have been introduced in flammini et al 5 as an extension of interval routing schemes irs defined by santoro and khatib 21 and van leeuwen and tan 16 in this paper we study the efficiency of multi dimensional interval routing schemes with respect to the space complexity and the congestion we bring certain comparative complexity results for general graphs as well as for specific networks in the first part of the paper we present three main contributions to the complexity of shortest path mirs for certain hypercube like graphs there are efficient multi dimensional interval routing schemes despite of provable nonexistence of efficient deterministic interval routing schemes we compare the dis mirs and the con mirs models introduced in 5 and prove that the dis mirs model is asymptotically stronger than the con mirs model when considering space requirements of the full information shortest path routing schemes we introduce a powerful lower bound technique on the con mirs model and prove that not for every cayley graph there exists space efficient shortest path mirs on the contrary there does not exist a powerful space lower bound technique for dis mirs model the congestion is a common phenomenon in networks which can completely degrade their performance therefore it is reasonable to study routing schemes which are not necessarily shortest path but allow high network throughput in the second part of the paper we present congestion results for mirs we show that there exists a multipath 2 n 2 dis mirs of n dimensional cube connected cycles with asymptotically optimal congestion we give a tradeoff between the congestion and the space complexity of multipath mirs on general graphs for any graph g and given 1 s v there exists a multipath 2 v 2s 1 mirs with congestion v s where is the forwarding index of the graph g and is the maximum degree of vertices in the graph g for planar graphs of constant bounded degree there exist a multipath o v 1 mirs and a deterministic o v log v irs both with asymptotically optimal congestion

comment on the q analogues of the harmonic oscillator the heisenberg relation for the q analogues of the quantum harmonic oscillator introduced independently by macfarlane and biedenharn 1989 for the quantum group su 2 q is derived by a method analogous to that used by schwinger 1968 for the su 2 case the author also speculates on the possible use of the quantum group as a generalisation of quantum mechanics

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

on the hardness of minimizing space for all shortest path interval routing schemes k interval routing scheme k irs is a compact routing method that allows up to k interval labels to be assigned to an arc and global k irs allows not more than a total of k interval labels in the whole network a fundamental problem is to characterize the networks that admit k irs or global k irs many of the problems related to single shortest path k irs have already been shown to be np complete for all shortest path k irs the characterization problem remains open for k 1 in this paper we study the time complexity of devising minimal space all shortest path k irss and show that it is np complete to decide whether a graph admits an all shortest path k irs for every integer k 3 and so is that of deciding whether a graph admits an all shortest path k strict irs for every integer k 4 these are the first np completeness results for all shortest path k irs where k is a constant and the graph is unweighted the np completeness holds also for the linear case we also prove that it is np complete to decide whether an unweighted graph admits an all shortest path irs with global compactness of at most k which also holds for the linear and strict cases

line transect sampling with unknown probability of detection along the transect summary a model is given for line transect sampling for the purpose of estimating animal population density which makes no assumption about the value of the detection probability along the transect or about the form of the detection probability function other than continuity in addition animals are permitted to be available or not according to a process that is independent of the sampling process the model requires sampling at two effort levels either by varying the speed of the observers and or their number the unconditional maximum likelihood estimate does not exist whereas the maximum likelihood estimate given the total numbers detected at each effort level exists but does very poorly a generalization of a moment like estimator given by cooke 1985 report of the international whaling commission 35 319 323 is proposed instead asymptotic and small sample behavior is examined the estimator is also applied to a field experiment

perpendicular distance models for line transect sampling summary perpendicular distance line transect models are examined to assess whether any single model can provide a general procedure for analysing line transect data of the two parameter models considered the hazard rate model appears promising whereas the exponential power series and exponential quadratic models do not of the nonparametric models the fourier series is the best developed and is favoured by many researchers as a general model however for a given data set the fourier series estimate may be highly dependent on the number of terms selected and so the model is not a clear improvement over the hazard rate model a similar variable term model using hermite polynomials is considered and is shown to be less dependent on the number of terms selected there has been some debate about whether the derivative of the density function of perpendicular distances evaluated at 0 should be 0 so that the function has a shoulder the problem is examined in detail and it is argued that reliable estimation is not possible from line transect data unless a shoulder exists many data sets appear to exhibit no shoulder possible reasons are examined

local bandwidth selection for kernel estimation of population densities with line transect sampling summary seber 1986 biometrics42 267 292 suggested an approach to biological population density estimation using kernel estimates of the probability density of detection distances in line transect sampling chen 1996a applied statistics45 135 150 and others have employed cross validation to choose a global bandwidth for the kernel estimator or have suggested adaptive kernel estimation chen 1996b biometrics52 1283 1294 because estimation of the density is required at only a single point we investigate a local bandwidth selection procedure that is a modification of the method of schucany 1995 journal of the american statistical association90 535 540 for nonparametric regression we report on simulation results comparing the proposed method and a local normal scale rule with cross validation and adaptive estimation the local bandwidths and normal scale rule produce estimates with mean squares that are half the size of the others in most cases consistency results are also provided

bayesian analyses for a multiple capture recapture model summary in multiple capture recapture surveys the probability of capture can vary between sampling occasions the model accounting for this variation is known as at bayes empirical bayes and bayes empirical bayes solutions are given to the problems of interval estimation decision making and point estimation of the population size n when the number of sampling occasions is small to moderate and the number of recaptured units observed on each sampling occasion is moderate estimates obtained from empirical bayes and bayes empirical bayes methods compare closely to bayesian methods using a reference prior distribution for the capture probabilities however when the number of sampling occasions is large and the number of recaptured units observed on each sampling occasion is small inferences obtained using different reference priors can differ considerably

an adaptive procedure for sampling animal populations summary we consider an adaptive stratified sampling procedure for animal populations in which the sample size in a given stratum or primary unit depends on the observations obtained in previous strata or primary units this method provides a more efficient way of sampling sparse but highly clustered populations two sampling approaches are considered the first is a design unbiased strategy as the estimate of population density is unbiased through design induced factors such as the random selection of sites in each stratum the second is called a model unbiased strategy as the density estimate is unbiased under the model assumed for the spatial distribution of the population the theory is demonstrated by reference to sampling from a shrimp population

detectability in conventional and adaptive sampling in this paper a simple but very general method is given for estimating a population total with any sampling design when objects in sampled units are observed with imperfect detectability a problem characteristic of many surveys of natural and human populations in the most general case the method consists of dividing the value of the variable of interest associated with each detected object by the detection probability for that object and then proceeding to use the estimation method that would ordinarily be used under the design if there were no detectability problems examples illustrating the method include simple random sampling conventional unequal probability sampling and adaptive cluster sampling

nonparametric estimators for variable circular plot surveys a non parametric estimator of animal density d is proposed for variable circular plot surveys under the assumption that perfect radial detectability occurs at the station the estimation of d requires estimating the derivative at zero of the probability density function of the detected radial distances kernel techniques are used for that purpose

a survey on interval routing we survey in this paper the classical results and also the most recent results in the field of interval routing a well known strategy to code in a compact way distributed routing algorithms these results are classified in several themes characterization compactness and shortest path dilation and stretch factor specific class of graphs interconnection networks bounded degree planar chordal rings random graphs etc and the other recent extensions proposed in the literature dead lock free congestion non deterministic and distributed problems related to interval routing for each of these themes we review the state of the art and propose several open problems

kernel methods in line and point transect sampling we consider kernel estimation of population density based on size and distance data in line and point transect sampling asymptotic normality of the estimators is established in each setting with very weak assumptions imposed on the random sample size it is pointed out that the kernel approach does not require specifying a horizon a severe shortcoming in the fourier series method some numerical examples based on simulated and real data are presented the results suggest that the kernel method is a viable alternative to other existing estimators

on the space requirement of interval routing interval routing is a space efficient method for point to point networks it is based on labeling the edges of a network with intervals of vertex numbers called interval labels an m label scheme allows up to m labels to be attached on an edge for arbitrary graphs of size m n the number of vertices the problem is to determine the minimum rp necessary for achieving optimality in the length of the longest routing path the longest routing path resulted from a labeling is an important indicator of the performance of any algorithm that runs on the network we prove that there exists a graph with d spl omega n sup 1 3 such that if m spl les n 18d o spl radic n d the longest path is no shorter than d spl theta d spl radic m as a result for any m label 1rs if the longest path is to be shorter than d spl theta d spl radic m at least m spl theta n d labels per edge would be necessary

on the variable circular plot method of estimating animal density the development by ornithologists of the variable circular plot method of estimating bird densities from observer to bird distances has led to estimation problems similar to those of line transect sampling however to apply line transect methods without modification requires that the distance data be transformed to areas by squaring the implications of this transformation on the assumed shapes for the detection curve have not been investigated in the literature this paper illustrates that application of line transect models to area data may lead to poor model performance and erroneous conclusions developments based on distance data are discussed briefly and binomial models are derived for the special case in which birds are categorised simply according to whether they are within or beyond a specified distance

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

an arma type probability density estimator on etudie les proprietes d un estimateur de densite de probabilite ayant la forme rationnelle d un spectre arma sous diverses conditions sur les coefficients de fourier de la densite on montre que l estimateur arma a une erreur quadratique moyenne integree asymptotiquement plus petite que le meilleur estimateur de serie de fourier effile

adaptive cluster sampling designs with primary and secondary units summary in adaptive cluster sampling designs an initial probability sample is selected and whenever the observed value of the variable of interest satisfies a given condition units in the neighborhood of that observation are added to the sample in this paper the initial design is selected in terms of primary units while subsequent sampling is in terms of secondary units such initial designs include systematic sampling strip sampling and other forms of classical cluster sampling but because of the subsequent addition to the sample of secondary units in the neighborhood of any secondary unit that satisfies the condition of interest the final clusters of units obtained through the procedure may be quite different in shape from the initial primary units the methods described in this paper apply to such sampling situations as whale surveys in which the research vessel temporarily leaves the selected transect to close in on sighted whales surveys of rare bird species in which initial observations are made at systematically selected sites and additional observations are made in the vicinity of any site at which sufficiently high abundance is observed and aerial walrus surveys in which the aircraft searches to either side of the preselected transect line whenever a congregation of animals is encountered because conventional estimators of the population mean and total are biased with such a procedure estimators that are unbiased under the adaptive designs are presented in this paper variance formulae and unbiased estimators of variance are also given the designs are illustrated using a point pattern representing locations of individuals or objects in a spatially aggregated population for such a population the adaptive designs can be substantially more efficient than their conventional counterparts

nonparametric estimates of standard error the jackknife the bootstrap and other methods summary we discuss several nonparametric methods for attaching a standard error to a point estimate the jackknife the bootstrap half sampling subsampling balanced repeated replications the infinitesimal jackknife influence function techniques and the delta method the last three methods are shown to be identical all the methods derive from the same basic idea which is also the idea underlying the common parametric methods extended numerical comparisons are made for the special case of the correlation coefficient

an alternative method of cross validation for the smoothing of density estimates cross validation with kullback leibler loss function has been applied to the choice of a smoothing parameter in the kernel method of density estimation a framework for this problem is constructed and used to derive an alternative method of cross validation based on integrated squared error recently also proposed by rudemo 1982 hall 1983 has established the consistency and asymptotic optimality of the new method for small and moderate sized samples the performances of the two methods of cross validation are compared on simulated data and specific examples

spatially explicit maximum likelihood methods for capture recapture studies live trapping capture recapture studies of animal populations with fixed trap locations inevitably have a spatial component animals close to traps are more likely to be caught than those far away this is not addressed in conventional closed population estimates of abundance and without the spatial component rigorous estimates of density cannot be obtained we propose new flexible capture recapture models that use the capture locations to estimate animal locations and spatially referenced capture probability the models are likelihood based and hence allow use of akaike s information criterion or other likelihood based methods of model selection density is an explicit parameter and the evaluation of its dependence on spatial or temporal covariates is therefore straightforward additional nonspatial variation in capture probability may be modeled as in conventional capture recapture the method is tested by simulation using a model in which capture probability depends only on location relative to traps point estimators are found to be unbiased and standard error estimators almost unbiased the method is used to estimate the density of red eyed vireos vireo olivaceus from mist netting data from the patuxent research refuge maryland u s a estimates agree well with those from an existing spatially explicit method based on inverse prediction a variety of additional spatially explicit models are fitted these include models with temporal stratification behavioral response and heterogeneous animal home ranges

incorporating covariates into standard line transect analyses summary an implicit assumption of standard line transect methodology is that detection probabilities depend solely on the perpendicular distance of detected objects to the transect line heterogeneity in detection probabilities is commonly minimized using stratification but this may be precluded by small sample sizes we develop a general methodology which allows the effects of multiple covariates to be directly incorporated into the estimation procedure using a conditional likelihood approach small sample size properties of estimators are examined via simulations as an example the method is applied to eastern tropical pacific dolphin sightings data

data based optimal smoothing of orthogonal series density estimates let f be a density possessing some smoothness properties and let x 1 cdots x n be independent observations from f some desirable properties of orthogonal series density estimates f n m lambda of f of the form f n m lambda t sum n nu 1 frac hat f nu 1 lambda nu 2m phi nu t where phi nu is an orthonormal sequence and hat f nu 1 n sum n j 1 phi nu x j is an estimate of f nu int phi nu t f t dt are discussed the parameter lambda plays the role of a bandwidth or smoothing parameter and m controls a shape factor the major novel result of this note is a simple method for estimating lambda and m from the data in an objective manner to minimize integrated mean square error the results extend to multivariate estimates

the line transect method a nonparametric estimator based on shape restrictions summary a new estimator for population density based on line transect surveys is presented its sampling behaviour is investigated through simulation studies advantages of the proposed estimator include its simple intuitive base its stable behaviour over a wide variety of detection curves the ease with which it can be computed and the availability of reliable confidence limits the simulation results point to a general improvement in efficiency over existing estimators

multidimensional interval routing schemes interval routing scheme k irs is a compact routing scheme on general networks it has been studied extensively and recently been implemented on the latest generation inmos transputer router chip in this paper we introduce an extension of the interval routing scheme k irs to the multi dimensional case k d mirs where k is the number of intervals and d is the number of dimensions whereas k irs only represents compactly a single shortest path between any two nodes with this new extension we are able to represent all shortest paths compactly this is useful for fault tolerance and traffic distribution in a network we study efficient representations of all shortest paths between any pair of nodes for general network topologies and for specific interconnection networks such as rings grids tori and hypercubes for these interconnection networks we show that for about the same space complexity as k irs we can represent all shortest paths in k d mirs as compared to only a single shortest path in k irs moreover tradeoffs are derived between the dimension d and the number of intervals k in multi dimensional interval routing schemes on hypercubes grids and tori

the g spectral estimator abstract in this article a modified definition of the g spectral estimator is given it is shown that the resulting estimator is a method of moments autoregressive moving average arma spectral estimator that does not require an estimate of the moving average parameters as a result a new formula for the power spectrum of an arma process is given that does not explicitly involve the moving average ma parameters this formula then leads to a closed form expression for the ma parameters and their corresponding moment estimators

empirical bias bandwidths for local polynomial nonparametric regression and density estimation abstract a data based local bandwidth selector is proposed for nonparametric regression by local fitting of polynomials the estimator called the empirical bias bandwidth selector ebbs is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function ebbs minimizes an estimate of mean squared error consisting of a squared bias term plus a variance term the variance term used is exact not asymptotic though it involves the conditional variance of the response given the predictors that must be estimated the bias term is estimated empirically not from an asymptotic expression thus ebbs is similar to the double smoothing approach of hardle hall and marron and a local bandwidth selector of schucany but is developed here for a far wider class of estimation problems than what those authors considered ebbs is tested on simulated data and its performance seems quite satisfactory local polynomial smoothing of a histogram is a high

bayesian estimation of animal abundance for line transect sampling this paper develops a bayesian model for estimating the density of a closed animal population from data obtained by the line transect method the detection function is assumed to be half normal and the data are neither grouped nor truncated a bayes estimator is constructed with respect to a gamma prior density and two loss functions relative squared error and absolute squared error the bayes estimator is compared with the maximum likelihood estimator as well as the fourier series estimator using two data sets

integrable stochastic ladder models a general way to construct ladder models with certain lie algebraic or quantum lie algebraic symmetries is presented these symmetric models give rise to a series of integrable systems it is shown that corresponding to these su 2 symmetric integrable ladder models there are exactly solvable stationary discrete time resp continuous time markov processes with transition matrices resp intensity matrices having spectra which coincide with the ones of the corresponding integrable models

comparison of data driven bandwidth selectors abstract this article compares several promising data driven methods for selecting the bandwidth of a kernel density estimator the methods compared are least squares cross validation biased cross validation and a plug in rule the comparison is done by asymptotic rate of convergence to the optimum and a simulation study it is seen that the plug in bandwidth is usually most efficient when the underlying density is sufficiently smooth but is less robust when there is not enough smoothness present we believe the plug in rule is the best of those currently available but there is still room for improvement

a note on the fourier series model for analysing line transect data the fourier series model offers a powerful procedure for the estimation of animal population density from line transect data the estimate is reliable over a wide range of detection functions in contrast analytic confidence intervals yield at best 90 confidence for nominal 95 intervals three solutions one using monte carlo techniques another making direct use of replicate lines and the third based on the jackknife method are discussed and compared

brst cohomology for uq sl 2 representations a nilpotent brst operator qq is constructed for the q deformation of the universal enveloping algebra of sl 2 an associated operator rq such that qq rq cq is introduced where cq is the q deformed casimir invariant cq fe 1 2h q 1 2h 1 q the related operator qq conjugate to qq is also considered the resulting brst cohomology of uq sl 2 representations is discussed

simulated likelihood methods for complex double platform line transect surveys the conventional line transect approach of estimating effective search width from the perpendicular distance distribution is inappropriate in certain types of surveys e g when an unknown fraction of the animals on the track line is detected the animals can be observed only at discrete points in time there are errors in positional measurements and covariate heterogeneity exists in detectability for such situations a hazard probability framework for independent observer surveys is developed the likelihood of the data including observed positions of both initial and subsequent observations of animals is established under the assumption of no measurement errors to account for measurement errors and possibly other complexities this likelihood is modified by a function estimated from extensive simulations this general method of simulated likelihood is explained and the methodology applied to data from a double platform survey of minke whales in the northeastern atlantic in 1995

extent to which least squares cross validation minimises integrated square error in nonparametric density estimation let ho o and c be the windows which minimise mean integrated square error integrated square error and the least squares cross validatory criterion respectively for kernel density estimates it is argued that o not ho should be the benchmark for comparing different data driven approaches to the determination of window size asymptotic properties of ho o and c o and of differences between integrated square errors evaluated at these windows are derived it is shown that in comparison to the benchmark o the observable window c performs as well as the so called optimal but unattainable window ho to both first and second order

distance sampling methodology we consider the method of distance sampling described by buckland anderson burnham and laake in 1993 we explore the properties of the methodology in simple cases chosen to allow direct and accessible comparisons of distance sampling in the design and model based frameworks in particular we obtain expressions for the bias and variance of the distance sampling estimator of object density and for the expected value of the recommended analytic variance estimator within each framework these results enable us to clarify aspects of the performance of the methodology which may be of interest to users and potential users of distance sampling

monte carlo confidence intervals des intervalles de confiance non parametriques obtenus par la methode de monte carlo sont utiles quand les intervalles obtenus par les methodes analytiques sont indisponibles ou ne correspondent pas au niveau nominal on fournit des formules permettant de generer un intervalle de niveau donne et de quantifier la variation due a la methode de monte carlo

model selection an integral part of inference we argue that model selection uncertainty should be fully incorporated into statistical inference whenever estimation is sensitive to model choice and that choice is made with reference to the data we consider different philosophies for achieving this goal and suggest strategies for data analysis we illustrate our methods through three examples the first is a poisson regression of bird counts in which a choice is to be made between inclusion of one or both of two covariates the second is a line transect data set for which different models yield substantially different estimates of abundance the third is a simulated example in which truth is known

estimating the error rate of a prediction rule improvement on cross validation abstract we construct a prediction rule on the basis of some data and then wish to estimate the error rate of this rule in classifying future observations cross validation provides a nearly unbiased estimate using only the original data cross validation turns out to be related closely to the bootstrap estimate of the error rate this article has two purposes to understand better the theoretical basis of the prediction problem and to investigate some related estimators which seem to offer considerably improved estimation in small samples

suq h cross to 0 2 and suq h cross 2 the classical and quantum q deformations of the su 2 algebra ii the hopf algebra the yang baxter equation and multi deformed algebraic structures for pt i see ibid vol 23 p 4185 1990 the suq 2 algebra is realized by means of both the poisson brackets in classical mechanics and commutators in quantum mechanics in a system with q deformed oscillators of two different types the structures of the hopf algebra and the quantum yang baxter equation are also discussed on a quantum level a set of j representations of the quantum algebra suq 2 is constructed based on the type ii q oscillators multi deformations of the oscillators of the two types and multi deformed algebras expressed in poisson brackets as well as in lie brackets are proposed

new bounds for multi label interval routing interval routing ir is a space efficient routing method for computer networks for longest routing path analysis researchers have focused on lower bounds for many years for any n node graph g of diameter d there exists an upper bound of 2d for ir using one or more labels and an upper bound of 3 2d for ir using o nlogn or more labels we present two upper bounds in the first part of the paper we show that for every integer i 0 every n node graph of diameter d has a k dominating set of size o i 1 n for k 1 1 3i d this result implies a new upper bound of 2 1 3i d for ir using o i 1 n or more labels where i is any positive integer constant we apply the result by kutten and peleg 7 to achieve an upper bound of 1 d for ir using o n d or more labels where is any constant in 0 1 the second part of the paper offers some lower bounds for planar graphs for any m label interval routing scheme m irs where m o 3 n we derive a lower bound of 2m 1 2m d 1 on the longest path for m o n and a lower bound of 2 1 m 1 2 1 m d where 0 1 for m o n the latter result implies a lower bound of n on the number of labels needed to achieve optimality

capture recapture estimation via gibbs sampling capture recapture models are widely used in the estimation of population sizes based on data augmentation considerations we show how gibbs sampling can be applied to calculate bayes estimates in this setting as a result formulations which were previously avoided because of analytical and numerical intractability can now be easily considered for practical application we illustrate this potential by using gibbs sampling to calculate bayes estimates for a hierarchical capture recapture model in a real example

the estimation of extreme quantiles in logit bioassay summary suppose that we administer a low dose of a drug and if no response is observed increase this dose by a fixed amount which is administered to a second experimental subject this procedure continues until at some dose level a response is finally observed this whole sequence may be repeated we investigate the features of an experimental design of this kind for estimating the dose at which the expected response is small this design is highly efficient when the number of responses e g deaths is considered the major portion of the cost of the study and various alternatives having some advantage over maximum likelihood estimation are suggested

q deformed oscillator algebra as a quantum group it is proved that the q deformed oscillator algebra is a quantum group the hopf algebraic structure is set up and verified to be consistent and compatible the universal r matrix and yang baxter equation are constructed the q differential operator algebra is briefly discussed

detectability functions in observing spatial point processes whenever populations modelled as spatial point patterns are sampled the observational methods used influence the form of the associated delectability functions in this paper we show how the properties of estimators of population quantities depend on the delectability functions in combination with the stochastic structure of the point process giving rise to the spatial patterns criteria for optimal delectability functions indicative of the most efficient observational methods are derived for the inference objectives of i estimating expected density and ii predicting or estimating realized density within a study region detectability functions related to observational methods such as plots of various shapes line transects radial transects and aerial surveys are compared numerically for a point process with aggregation tendencies for a given effective area observed constant delectability over the study region is optimal for predicting realized density while some curious doughnut shaped functions are more efficient for estimating the expected density parameter

adaptive bandwidth choice for kernel regression abstract a data based procedure is introduced for local bandwidth selection for kernel estimation of a regression function at a point the estimated bandwidth is shown to be consistent and asymptotically normal as an estimator of the asymptotic optimal value for minimum mean square estimation simulation studies indicate satisfactory behavior of the new bandwidth estimator in finite samples the findings are improvements over a global bandwidth estimator the same methodology works for local linear regression and extends easily to weighted local polynomial fits

the construction of the q analogues of the harmonic oscillator operators from ordinary oscillator operators the q analogues of boson operators are constructed from ordinary boson operators by an embedding approach accordingly the q deformed quantum algebras su n q can be obtained straightforwardly from corresponding universal enveloping algebras of lie algebra su n

double observer line transect methods levels of independence double observer line transect methods are becoming increasingly widespread especially for the estimation of marine mammal abundance from aerial and shipboard surveys when detection of animals on the line is uncertain the resulting data supplement conventional distance sampling data with two sample mark recapture data like conventional mark recapture data these have inherent problems for estimating abundance in the presence of heterogeneity unlike conventional mark recapture methods line transect methods use knowledge of the distribution of a covariate which affects detection probability namely distance from the transect line in inference this knowledge can be used to diagnose unmodeled heterogeneity in the mark recapture component of the data by modeling the covariance in detection probabilities with distance we show how the estimation problem can be formulated in terms of different levels of independence at one extreme full independence is assumed as in the petersen estimator which does not use distance data at the other extreme independence only occurs in the limit as detection probability tends to one between the two extremes there is a range of models including those currently in common use which have intermediate levels of independence we show how this framework can be used to provide more reliable analysis of double observer line transect data we test the methods by simulation and by analysis of a dataset for which true abundance is known we illustrate the approach through analysis of minke whale sightings data from the north sea and adjacent waters

a trade off between space and efficiency for routing tables two conflicting goals play a crucial role in the design of routing schemes for communication networks a routing scheme should use paths that are as short as possible for routing messages in the network while keeping the routing information stored in the processors local memory as succinct as possible the efficiency of a routing scheme is measured in terms of its stretch factor the maximum ratio between the length of a route computed by the scheme and that of a shortest path connecting the same pair of vertices most previous work has concentrated on finding good routing schemes with a small fixed stretch factor for special classes of network topologies in this paper the problem for general networks is studied and the entire range of possible stretch factors is examined the results exhibit a trade off between the efficiency of a routing scheme and its space requirements almost tight upper and lower bounds for this trade off are presented specifically it is proved that any routing scheme for general n vertex networks that achieves a stretch factor k 1 must use a total of o n 1 1 2 k 4 bits of routing information in the networks this lower bound is complemented by a family k k of hierarchical routing schemes for every k l for unit cost general networks which guarantee a stretch factor of o k require storing a total of o k 3 n 1 1 h log n bits of routing information in the network name the vertices with o log 2 n bit names and use o log n bit headers

radial distance models for the line transect method line transect estimation of wildlife populations can be based on either right angle distances or radial distances estimation based on radial distances requires more restrictive assumptions about the mechanism by which observations are generated we examine this mechanism and show that the mean sighting angle may frequently be larger than predicted by hayne s fixed distance model or by eberhardt s variable distance model the modified and generalized hayne s models are also investigated an alternative approach based on hazard rate analysis is suggested but we conclude that a nonparametric right angle distance model will generally result in more reliable estimation than any radial distance model

static and dynamic low congested interval routing schemes interval routing schemes irs have been extensively investigated in the past years with special emphasis on shortest paths besides their theoretical interest irs have practical applications as they have been implemented with wormhole routing in the last generation of inmos transputer router chips in this paper we consider irs that are optimal with respect to the congestion of the induced path system in fact wormhole routing is strongly influenced by the maximum number of paths that share a physical link and from low to moderate congestion it outperforms the packet switching technique we provide a general framework able to deal with the various congestion issues in irs in fact we will distinguish between static cases in which the source destination configurations are fixed and dynamic cases where they vary over time all these situations can be handled in a unified setting thanks to the notion of competitiveness introduced in this paper we first give some general results not related to specific traffic demands then in the one to all communication pattern we show that constructing competitive irs for a given network is an intractable problem both for the static and the dynamic case that is when the root vertex is fixed and when it can change along the time respectively finally both for one to all and all to all communication patterns we provide nicely competitive k irs for relevant topologies networks considered are chains trees rings chordal rings and multi dimensional grids and tori we consider both the directed congestion case in which there are pairwise opposite unidirectional links connecting two neighbor processors and the undirected congestion case in which two neighbors are connected by a single bi directional link

the complexity of shortest path and dilation bounded interval routing abstract interval routing is a popular compact routing method for point to point networks which found industrial applications in novel transputer routing technology may and thompson transputers and routers components for concurrent machines inmos 1991 recently much effort is devoted to relate the efficiency measured by the dilation or the stretch factor to space requirements measured by the compactness or the total number of memory bits in a variety of compact routing methods eilam moran and zaks 10th international workshop on distributed algorithms wdag lecture notes in computer science vol 1151 springer berlin 1996 pp 191 205 fraigniaud and gavoille 8th annual acm symp on parallel algorithms and architectures spaa acm press new york 1996 gavoille and perennes proc sircco 96 carleton press 1996 pp 88 103 kranakis krizanc 13th annual symp on theoretical aspects of computer science stacs lecture notes in computer science vol 1046 springer berlin 1996 pp 529 540 meyer auf der heide and scheideler proc 37th symp on foundations of computer science focs november 1996 peleg and upfal j acm 36 1989 510 530 tse and lau proc sirocco 95 carleton press 1995 pp 123 134 we add new results in this direction for interval routing for the shortest path interval routing we apply a technique from flammini van leeuwen and marchetti spaccamela mfcs 95 lecture notes in computer science vol 969 springer berlin 1995 pp 37 49 to some interconnection networks shuffie exchange se cube connected cycles ccc butterfly bf and star s and get improved lower bounds on compactness in the form n 1 2 e any e 0 for se n log n for ccc and bf and n log log n log n 5 for s where n is the number of nodes in the corresponding network previous lower bounds for these networks were only constant fraigniaud and gavoille conpar 94 lecture notes in computer science vol 854 springer berlin 1994 pp 785 796 for the dilation bounded interval routing we give a routing algorithm with the dilation 1 5d and the compactness o n log n on n node networks with the diameter d it is the first nontrivial upper bound on the dilation bounded interval routing on general networks moreover we construct a network on which each interval routing with the dilation 1 5d 3 needs the compactness at least n it is an asymptotical improvement over the previous lower bounds in tse and lau proc sirocco 95 carleton press 1995 pp 123 134 and it is also better than independently obtained lower bounds in tse and lau proc computing the australasian theory symp cats 97 sydney australia february 1997

the selection of terms in an orthogonal series density estimator abstract we show that kronmal and tarter s well known rule for selecting the terms in an orthogonal series density estimator can lead to poor performance and even inconsistency in certain cases these difficulties arise when the underlying density has a nonmonotone sequence of fourier coefficients as is likely to be the case with sharply peaked or multimodal distributions we suggest a way of overcoming these shortcomings

integrable poisson algebras and two dimensional manifolds the relations between integrable poisson algebras with three generators and two dimensional symplectic manifolds are investigated it is shown that for a given integrable poisson algebra there exists a two dimensional symplectic manifold such that the poisson algebra generated by the coordinates of m coincides with the algebra vice versa the coordinates of a given smooth two dimensional symplectic manifold m embedded in generate an integrable poisson algebra moreover smooth poisson algebraic maps between two integrable poisson algebras are governed by equations involving the symplectic manifolds corresponding to these algebras

suq h 0 2 and suq h 2 the classical and quantum q deformations of the su 2 algebra by means of classical harmonic oscillators and their canonical quantization we show that the q deformation of the su 2 lie algebra can be realized at a classical level in the sense of poisson brackets denoted by suq inf not 0 2 and that the canonical quantization of the system leads to the quantum q deformation of the su 2 algebra denoted by suq 2 this means that the q deformation and the h cross quantization are in general two different concepts

suq h 0 2 and suq h 2 the classical and quantum q deformations of the su 2 algebra 4 geometric quantization and hopf algebraic structures for pt iii see ibid vol 24 p 1427 1991 in the q deformed oscillator system the hopf algebraic structures of suq inf not 0 2 and suq 2 are constructed in the scheme of geometric quantization the classical and quantum representation spaces are analyzed with respect to whether or not q is a root of unity

hazard models for line transect surveys with independent observers summary the likelihood function for data from independent observer line transect surveys is derived and a hazard model is proposed for the situation where animals are available for detection only at discrete time points under the assumption that the time points of availability follow a poisson point process we obtain an analytical expression for the detection function we discuss different criteria for choosing the hazard function and consider in particular two different parametric families of hazard functions discrete and continuous hazard models are compared and the robustness of the discrete model is investigated finally the methodology is applied to data from a survey for minke whales in the northeastern atlantic

distance sampling detection functions 2d or not 2d conventional distance sampling cds methods assume that animals are uniformly distributed in the vicinity of lines or points but when animals move in response to observers before detection or when lines or points are not located randomly this assumption may fail by formulating distance sampling models as survival models we show that using time to first detection in addition to perpendicular distance line transect surveys or radial distance point transect surveys allows estimation of detection probability and hence density when animal distribution in the vicinity of lines or points is not uniform and is unknown we also show that times to detection can provide information about failure of the cds assumption that detection probability is 1 at distance zero we obtain a maximum likelihood estimator of line transect survey detection probability and effective strip half width using times to detection and we investigate its properties by simulation in situations where animals are nonuniformly distributed and their distribution is unknown the estimator is found to perform well when detection probability at distance zero is 1 it allows unbiased estimates of density to be obtained in this case from surveys in which there has been responsive movement prior to animals coming within detectable range when responsive movement continues within detectable range estimates may be biased but are likely less biased than estimates from methods that assuming no responsive movement we illustrate by estimating primate density from a line transect survey in which animals are known to avoid the transect line and a shipboard survey of dolphins that are attracted to it

biased and unbiased cross validation in density estimation abstract nonparametric density estimation requires the specification of smoothing parameters the demands of statistical objectivity make it highly desirable to base the choice on properties of the data set in this article we introduce some biased cross validation criteria for selection of smoothing parameters for kernel and histogram density estimators closely related to one investigated in scott and factor 1981 these criteria are obtained by estimating l 2 norms of derivatives of the unknown density and provide slightly biased estimates of the average squared l 2 error or mean integrated squared error these criteria are roughly the analog of wahba s 1981 generalized cross validation procedure for orthogonal series density estimators we present the relationship of the biased cross validation procedure to the least squares cross validation procedure which provides unbiased estimates of the mean integrated squared error both methods are shown to be based on u statistics we compare the two metho