some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

cored hypergraphs power hypergraphs and their laplacian h eigenvalues abstract in this paper we introduce the class of cored hypergraphs and power hypergraphs and investigate the properties of their laplacian h eigenvalues from an ordinary graph one may generate a k uniform hypergraph called the kth power hypergraph of that graph power hypergraphs are cored hypergraphs but not vice versa sunflowers loose paths and loose cycles are power hypergraphs while squids generalized loose s paths and loose s cycles for 2 s k 2 are cored hypergraphs but not power graphs in general we show that the largest laplacian h eigenvalue of an even uniform cored hypergraph is equal to its largest signless laplacian h eigenvalue especially we find out these largest h eigenvalues for even uniform squids moreover we show that the largest laplacian h eigenvalue of an odd uniform squid loose path and loose cycle is equal to the maximum degree i e 2 we also compute the laplacian h spectra of the class of sunflowers when k is odd the laplacian h spectra of the loose cycle of size 3 and the loose path of length 3 are characterized as well

superstability and rigorous asymptotics in singularly perturbed state dependent delay differential equations abstract we study the singularly perturbed state dependent delay differential equation e x t x t k x t r r r x t 1 x t which is a special case of the equation e x t g x t x t r r r x t one knows that for every sufficiently small e 0 eq possesses at least one so called slowly oscillating periodic solution and moreover the graph of every such solution approaches a specific sawtooth like shape as e 0 in this paper we obtain higher order asymptotics of the sawtooth including the location of the minimum and maximum of the solution with the form of the solution near these turning points and as well an asymptotic formula for the period using these and other asymptotic formulas we further show that the solution enjoys the property of superstability namely the nontrivial characteristic multipliers are of size o e for small e this stability property implies that this solution is unique among all slowly oscillating periodic solutions again for small e

on the spectral radius of uniform hypertrees abstract we determine the unique hypertrees with maximum spectral radius among k uniform non hyper caterpillars with m edges and diameter d for 4 d m 2 among k uniform non hyper caterpillars with m edges for m 6 among k uniform hypertrees with m edges and independence number for m k 1 1 k m among k uniform hypertrees with m edges and matching number for 1 m k 1 1 k and among k uniform hypertrees with m edges and s branch vertices for 0 s m 1 2 respectively

ordering of some uniform supertrees with larger spectral radii abstract a supertree is a connected and acyclic hypergraph we study some uniform supertrees with larger spectral radii we first define a new type of edge moving operation on hypergraphs and study its applications on the comparison of the spectral radii of hypergraphs by using this new operation on some supertrees together with the general edge moving operation introduced by li shao and qi in 2015 and using a result by zhou et al in 2014 about the relation between the spectral radii of an ordinary graph and its power hypergraph we are able to determine the first eight k uniform supertrees on n vertices with the largest spectral radii

criteria for copositive matrices abstract some finite criteria for copositive copositive plus and strictly copositive matrices are proposed and compared with existing determinantal tests the basic mathematical tool is principal pivoting

now comes the time to defuzzify neuro fuzzy models abstract fuzzy models present a singular janus face on the one hand they are knowledge based software environments constructed from a collection of linguistic if then rules and on the other hand they realize nonlinear mappings which have interesting mathematical properties like low order interpolation and universal function approximation neuro fuzzy basically provides fuzzy models with the capacity based on the available data to compensate for the missing human knowledge by an automatic self tuning of the structure and the parameters a first consequence of this hybridization between the architectural and representational aspect of fuzzy models and the learning mechanisms of neural networks has been to progressively increase and fuzzify the contrast between the two janus faces readability or performance

asymptotic optimality of generalized cl cross validation and generalized cross validation in regression with heteroskedastic errors abstract the problem considered here is that of using a data driven procedure to select a good estimate from a class of linear estimates indexed by a discrete parameter in contrast to other papers on this subject we consider models with heteroskedastic errors the results apply to model selection problems in linear regression and to nonparametric regression estimation via series estimators nearest neighbor estimators and local regression estimators among others generalized c l gc l cross validation cv and generalized cross validation gcv procedures are analyzed the gc l and cv criteria are shown to be asymptotically optimal under general conditions a feasible version of gc l however is available only in some applications the gcv criterion is found to be asymptotically optimal only under a condition that is satisfied in some applications but not in others for example it is satisfied in the nearest neighbor estimation context but not in the series estimation local regression estimation or model selection contexts thus the cv criterion is the only feasible criterion of the three that is asymptotically optimal under general conditions the proofs rely heavily on results of li 1987

the maximum spectral radii of uniform supertrees with given degree sequences abstract this paper generalizes the breadth first search ordering on trees to k uniform supertrees by using 2 switch operation and edge moving operation on supertrees we determine the unique k uniform supertree with the maximum spectral radius among all k uniform supertrees with a given degree sequence moreover we generalize the majorization theorem on trees to k uniform supertrees

stability of periodic solutions of state dependent delay differential equations abstract we consider a class of autonomous delay differential equations z t f z t which includes equations of the form z t g z t z t r 1 z t r n r i r i z t for 1 i n with state dependent delays r i z t 0 the functions g and r i satisfy appropriate smoothness conditions we assume there exists a periodic solution z x t which is linearly asymptotically stable namely with all nontrivial characteristic multipliers satisfying 1 we prove that the appropriate nonlinear stability properties hold for x t namely that this solution is asymptotically orbitally stable with asymptotic phase and enjoys an exponential rate of attraction given in terms of the leading nontrivial characteristic multiplier a principal difficulty which distinguishes the analysis of equations such as from ones with constant delays is that even with g and r i smooth the associated function f is not smooth in function space techniques of hartung krisztin walther and wu are employed to resolve these issues

local parametric analysis of hedging in discrete time when continuous time portfolio weights are applied to a discrete time hedging problem errors are likely to occur this paper evaluates the overall importance of the discretization induced tracking error it does so by comparing the performance of black scholes hedge ratios against those obtained from a novel estimation procedure namely local parametric estimation in the latter the weights of the duplicating portfolio are estimated by fitting parametric models in this paper black scholes in the neighborhood of the derivative s moneyness and maturity local parametric estimation directly incorporates the error from hedging in discrete time results are shown where the root mean square tracking error is reduced up to 41 for short maturity options the performance can still be improved by combining locally estimated hedge portfolio weights with standard analysis based on historically estimated parameters the root mean square tracking error is thereby reduced by about 18 for long maturity options plots of the locally estimated volatility parameter against moneyness and maturity reveal the biases of the black scholes model when hedging in discrete time in particular there is a sharp smile effect in the relation between estimated volatility and moneyness for short maturity options as well as a significant wave effect in the relation with maturity for deep out of the money options 1997 elsevier science s a

on differentiability of solutions with respect to parameters in state dependent delay equations in this paper we study differentiability of solutions with respect to parameters in state dependent delay equations in particular we give sufficient conditions for differentiability of solutions in thew1 pnorm 1 p in establishing our main results we make use of a version of the uniform contraction principle for quasi banach spaces

a mathematical model of controlling the growth of tissue in pigs a mathematical model of controlling the growth of tissues in pigs is described in this paper in that sense a method is given by which it is possible to periodically and very accurately estimate live pig weight of backfat based upon measurements done by ultrasound these estimations will be used for the purpose of predicting growth of backfat in live pigs backfat weight is estimated on the basis of measurements done by using the moving total least squares method whereas estimation of live pig backfat growth is done by using a generalized logistic function whose parameters are estimated by means of the least squares method since thereby the hessian of the corresponding minimizing function is very close to a singular matrix an additional problem analysis was necessary

singular hopf bifurcation in a differential equation with large state dependent delay we study the onset of sustained oscillations in a classical state dependent delay sdd differential equation inspired by control theory owing to the large delays considered the hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold using asymptotic techniques we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations the dependence of the delay on the solution can be either linear or nonlinear with at least quadratic dependence in the former case an asymptotic connection is made with the rayleigh oscillator in the latter van der pol s equation is derived for the small amplitude oscillations sdd differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant delay differential equation but explicit analytical construction of solutions are rare this paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for sdd problems with large delays

an improved afriat diewert parkan nonparametric production function estimator abstract recent developments in the production frontier literature include nonparametric estimators with shape constraints a few of these estimators rely on the afriat inequalities to provide piecewise linear approximations to the production function frontier we show in this paper that these afriat diewert parkan adp estimators have deficiencies in the presence of moderate statistical noise including overfitting and a relatively high estimator variance we propose new estimators with lower variance and a relatively low bias we consider such alternative estimators based on weighted averages of random hinge functions with parameter restrictions small sample properties of the estimators are presented that show our new estimators outperform the existing adp estimators when moderate to large amounts of noise are present

linear smoothers and additive models we study linear smoothers and their use in building nonparametric regression models in the first part of this paper we examine certain aspects of linear smoothers for scatterplots examples of these are the running mean and running line kernel and cubic spline smoothers the eigenvalue and singular value decompositions of the corresponding smoother matrix are used to describe qualitatively a smoother and several other topics such as the number of degrees of freedom of a smoother are discussed in the second part of the paper we describe how linear smoothers can be used to estimate the additive model a powerful nonparametric regression model using the backfitting algorithm we show that backfitting is the gauss seidel iterative method for solving a set of normal equations associated with the additive model we provide conditions for consistency and nondegeneracy and prove convergence for the backfitting and related algorithms for a class of smoothers that includes cubic spline smoothers

spectra of uniform hypergraphs abstract we present a spectral theory of uniform hypergraphs that closely parallels spectral graph theory a number of recent developments building upon classical work has led to a rich understanding of symmetric hyperdeterminants of hypermatrices a k a multidimensional arrays symmetric hyperdeterminants share many properties with determinants but the context of multilinear algebra is substantially more complicated than the linear algebra required to address spectral graph theory i e ordinary matrices nonetheless it is possible to define eigenvalues of a hypermatrix via its characteristic polynomial as well as variationally we apply this notion to the adjacency hypermatrix of a uniform hypergraph and prove a number of natural analogs of basic results in spectral graph theory open problems abound and we present a number of directions for further study

multiple transition layers in a singularly perturbed differential delay equation the singularly perturbed differential delay equation is studied for a class of step function nonlinearities f we show that in general the discrete system does not mirror the dynamics of even for small e but that rather a different system does here f is related to but different from f and describes the evolution of transition layers in this context we also study the effects of smoothing out the discontinuities of f

a general product of tensors with applications abstract we study a general product of two n dimensional tensors a and b with orders m 2 and k 1 this product satisfies the associative law and is a generalization of the usual matrix product using this product many concepts and known results of tensors can be simply expressed and or proved and a number of applications of it will be given using the associative law of this tensor product and some properties on the resultant of a system of homogeneous equations on n variables we define the similarity and congruence of tensors which are also the generalizations of the corresponding relations for matrices and prove that similar tensors have the same characteristic polynomials thus the same spectra we study two special kinds of similarity permutational similarity and diagonal similarity and their applications in the study of the spectra of hypergraphs and nonnegative irreducible tensors we also define the direct product of tensors in matrix case it is also called the kronecker product and give its applications in the study of the spectra of two kinds of the products of hypergraphs we also give applications of this general product in the study of nonnegative tensors including a characterization of primitive tensors the upper bounds of primitive degrees and the cyclic indices of some nonnegative irreducible tensors

kriging nonstationary data abstract spatial data modeled to have come from a random function with a nonstationary mean are considered the spatial prediction method known as kriging exploits second order spatial correlation structure to obtain minimum variance predictions of certain average values of the random function but to do so it must be assumed that either the mean function the drift is known up to a constant or the second order structure the variogram is known exactly knowledge of the drift allows the stationary variogram to be estimated and leads to ordinary kriging knowledge of the variogram allows the drift to be estimated and leads to universal kriging more usually neither is known this article shows how median polish of gridded spatial data provides a resistant and relatively bias free way of kriging in the presence of drift yet yields results as good as the mathematically optimal but operationally difficult universal kriging comparisons are performed on two data sets

global hopf bifurcation for differential equations with state dependent delay abstract we develop a global hopf bifurcation theory for a system of functional differential equations with state dependent delay the theory is based on an application of the homotopy invariance of s 1 equivariant degree using the formal linearization of the system at a stationary state our results show that under a set of mild conditions the information about the characteristic equation of the formal linearization with frozen delay can be utilized to detect the local hopf bifurcation and to describe the global continuation of periodic solutions for such a system with state dependent delay

continental scale relationship between bankfull width and drainage area for single thread alluvial channels we explore the bankfull width wbf versus drainage area ada relationship across a range of climatic and geologic environments and ask 1 is the relationship between ln wbf and ln ada best described by a linear function and 2 can a reliable relationship be developed for predicting wbf with ada as the only independent variable the principal data set for this study was compiled from regional curve studies and other reports that represent 1018 sites 1 m wbf 110 m and 0 50 km2 ada 22 000 km2 in the continental united states two additional data sets were used for validation after dividing the data into small medium and large size basins which respectfully correspond to ada 4 95 km2 4 95 km2 ada 337 km2 and ada 337 km2 regression lines from each data set were compared using one way analysis of covariance ancova a second ancova was performed to determine if mean annual precipitation p is an extraneous factor in the wbf versus ada relationship the ancova results reveal that using ada alone does not yield a reliable wbf versus ada relationship that is applicable across a wide range of environments and that p is a significant extraneous factor in the relationship considering data for very small basins ada 0 49 km2 and very large basins ada 1 0 105 km2 we conclude that a two segment linear model is the most probable form of the ln wbf versus ln ada relationship this study provides useful information for building complex multivariate models for predicting wbf

asymptotic theory for a class of functional differential equations with state dependent delays we characterize the asymptotic behavior of a class of functional differential equations with state dependent delays and show that this asymptotic behavior can be numerically observed by computing corresponding solutions of approximating equations with piecewise constant arguments

connections between morse sets for delay differential equations on etudie la dynamique globale de l equation differentielle a retard scalaire x t f x t x t 1 avec des conditions appropriees sur f

bayesian regression with multivariate linear splines summary we present a bayesian analysis of a piecewise linear model constructed using basis functions which generalizes the univariate linear spline to higher dimensions prior distributions are adopted on both the number and the locations of the splines which leads to a model averaging approach to prediction with predictive distributions that take into account model uncertainty conditioning on the data produces a bayes local linear model with distributions on both predictions and local linear parameters the method is spatially adaptive and covariate selection is achieved by using splines of lower dimension than the data

the solution manifold and c1 smoothness for differential equations with state dependent delay abstract let h 0 u c 1 h 0 r n open and f u r n continuously differentiable if f satisfies two mild additional smoothness conditions then the set x u 0 f is a c1 submanifold of codimension n in c 1 h 0 r n the maximal solutions x of the initial value problems x t f x t x 0 x define a continuous semiflow f on x and all operators f t are continuously differentiable their derivatives d2f t are given in the usual way by solutions v to the variational equation along x with segments vt in the tangent spaces tf t x the additional conditions on f are motivated by properties of differential equations with state dependent delay and are verified for an example

existence of periodic solutions for delay differential equations with state dependent delay abstract in this paper we study the existence of periodic solutions of a delay differential equation with delay depending indirectly on the state a fixed point problem related to a poincare operator is constructed and solved using an ejective fixed point theorem

metastable periodic patterns in singularly perturbed state dependent delayed equations abstract we consider the scalar delayed differential equation x t x t f x t r where 0 r r x 1 r x and f represents either a monotone positive feedback d f d x 0 or a monotone negative feedback d f d x 0 plus some other hypotheses when the delay is a constant i e r x 1 this equation can support metastable rapidly oscillating solutions that are transients whose duration is of order exp c for some c 0 in this paper combining analytic and numerical techniques we investigate whether this metastable behavior persists when the delay r x depends non trivially on the state variable x more precisely we proceed in three steps first we explore theoretically and numerically the existence of branches of rapid periodic solutions for these equations then to predict conditions for metastability we introduce transition layer equations that depict the asymptotic shape of transient oscillations when tends to zero and finally these predictions are validated by numerical simulations numerical explorations are also performed for other scalings of with our conclusions are i when 0 0 there are no metastable transients ii when 0 0 and 0 is finite for monotone negative feedback the metastable oscillations exist irrespective of choices of f and r iii for monotone positive feedback they require that the feedback f and the delay r satisfy extra conditions such as f being an odd function and the delay r x an even function one novel result is that state dependent delays may lead to metastable dynamics in equations that cannot support such regimes when the delay is constant

boundary layer phenomena for differential delay equations with state dependent time lags i in this paper we begin a study of the differential delay equation mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0jc9yq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpeps0he9vr0 vr 0 vqpwqaaeaabigaciaacaqabeaadaqaaqaaaoqaaiabew7aljqadi hagaqbaiaacicacawg0bgaaiykaiabg2da9iabgkhitiaadihacagg oagaamidaiaacmcacqghrawkcawgmbgaaiikaiaadihacaggoagaam idaiabgkhitiaadkhacaggpagaaiykaiaacycacaqggagaaeiiaiaa dkhacqgh9aqpcawgybgaaiikaiaadihacaggoagaamidaiaacmcaca ggpaaaaa 5192 varepsilon x t x t f x t r r r x t we prove the existence of periodic solutions for 0 0 where 0 is an optimal positive number we investigate regularity and monotonicity properties of solutions x t which are defined for all t and of associated functions like t t r x t we begin the development of a poincare bendixson theory and phase plane analysis for such equations in a companion paper these results will be used to investigate the limiting profile and corresponding boundary layer phenomena for periodic solutions as approaches zero

morse decompositions for delay differential equations abstract the attractor for the scalar delay differential equation x t f x t x t 1 is shown to possess a morse decomposition under the hypothesis of a negative feedback condition in the delay term using this decomposition we prove results on the asymptotic rate of oscillation of solutions of the initial value problem existence of both slowly and rapidly oscillating periodic solutions is also proved

a variational approach to copositive matrices this work surveys essential properties of the so called copositive matrices the study of which has been spread over more than fifty five years special emphasis is given to variational aspects related to the concept of copositivity in addition some new results on the geometry of the cone of copositive matrices are presented here for the first time

some diagnostics for binary logistic regression via smoothing summary the paper discusses some diagnostic tools for binary logistic regression which use smoothing techniques smoothed binary data are employed to devise a battery of diagnostic plots from simple procedures which indicate only the adequacy or inadequacy of a maximum likelihood logistic fit to partial residual plots and delta local deviance plots which reveal the type of model inadequacy suggesting perhaps the addition of nonlinear terms or interactions properties of the methods are studied by simulation the diagnostic tools are illustrated on a set of data in which the probability of having telephone service is related to the demographic variables income and education

chemical principle and pde of variational electrodynamics abstract the two body problem of variational electrodynamics possesses differential delay equations of motion with state dependent delays of neutral type and solutions that can have velocity discontinuities on countable sets from a periodic orbit possessing some mild properties at breaking points we define a synchronization function in r r 3 which is further used to construct two bounded oscillatory functions vanishing at breaking points and whose first derivatives are continuous and defined everywhere but at breaking points the oscillatory functions are associated with a natural pde identity in w 2 2 r 3 we postulate an asymptotic ordering for a generalized pde identity which defines a fredholm schroedinger operator in w 2 2 r 3 with a forcing term belonging to l 2 r 3 o 1 r 2 as an application we introduce the chemical principle criterion to select orbits with asymptotically vanishing far fields and estimate the bohr radius parameter of the fredholm schroedinger pde using the boundary layers of orbits chosen according to the chemical principle criterion last working backward we derive an orbital property of the chemical principle type from the ordering conditions

boundedness global existence and continuous dependence for nonlinear dynamical systems describing physiologically structured populations abstract the paper is aimed as a contribution to the general theory of nonlinear infinite dimensional dynamical systems describing interacting physiologically structured populations we carry out continuation of local solutions to maximal solutions in a functional analytic setting for maximal solutions we establish global existence via exponential boundedness and by a contraction argument adapted to derive uniform existence time moreover within the setting of dual banach spaces we derive results on continuous dependence with respect to time and initial state to achieve generality the paper is organized top down in the way that we first treat abstract nonlinear dynamical systems under very few but rather strong hypotheses and thereafter work our way down towards verifiable assumptions in terms of more basic biological modelling ingredients that guarantee that the high level hypotheses hold

approximating surfaces by moving total least squares method we suggest a method for generating a surface approximating the given data x i y i z i e r 3 i 1 m assuming that the errors can occur both in the independent variables x and y as well as in the dependent variable z our approach is based on the moving total least squares method where the local approximants local planes are determined in the sense of total least squares the parameters of the local approximants are obtained by finding the eigenvector corresponding to the smallest eigenvalue of a certain symmetric matrix to this end we develop a procedure based on the inverse power method the method is tested on several examples

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

hybridization of intelligent techniques and arima models for time series prediction traditionally the autoregressive moving average arma model has been one of the most widely used linear models in time series prediction recent research activities in forecasting with artificial neural networks anns suggest that anns can be a promising alternative to the traditional arma structure these linear models and anns are often compared with mixed conclusions in terms of the superiority in forecasting performance in this paper we propose a hybridization of intelligent techniques such as anns fuzzy systems and evolutionary algorithms so that the final hybrid arima ann model could outperform the prediction accuracy of those models when used separately more specifically we propose the use of fuzzy rules to elicit the order of the arma or arima model without the intervention of a human expert and the use of a hybrid arima ann model that combines the advantages of the easy to use and relatively easy to tune arima models and the computational power of anns

locally weighted polynomial regression parameter choice and application to forecasts of the great salt lake 1 relationships between hydrologic variables are often nonlinear usually the functional form of such a relationship is not known a priori a multivariate nonparametric regression methodology is provided here for approximating the underlying regression function using locally weighted polynomials locally weighted polynomials consider the approximation of the target function through a taylor series expansion of the function in the neighborhood of the point of estimate cross validatory procedures for the selection of the size of the neighborhood over which this approximation should take place and for the order of the local polynomial to use are provided and shown for some simple situations the utility of this nonparametric regression approach is demonstrated through an application to nonparametric short term forecasts of the biweekly great salt lake volume blind forecasts up to 1 year in the future using the 1847 2004 time series of the great salt lake are presented

on some properties of the α spectral radius of the k uniform hypergraph abstract in this paper we show how the spectral radius changes under the edge grafting operations on connected k uniform hypergraphs we characterize the extremal hypertree for spectral radius among k uniform non caterpillar hypergraphs with given order size and diameter we also characterize the supertree with the second largest spectral radius among all k uniform supertrees on n vertices

acoustic articulatory mapping in vowels by locally weighted regression a method for mapping between simultaneously measured articulatory and acoustic data is proposed the method uses principal components analysis on the articulatory and acoustic variables and mapping between the domains by locally weighted linear regression or loess cleveland w s 1979 j am stat assoc 74 829 836 the latter method permits local variation in the slopes of the linear regression assuming that the function being approximated is smooth the methodology is applied to vowels of four speakers in the wisconsin x ray microbeam speech production database with formant analysis results are examined in terms of 1 examples of forward articulation to acoustics mappings and inverse mappings 2 distributions of local slopes and constants 3 examples of correlations among slopes and constants 4 root mean square error and 5 sensitivity of formant frequencies to articulatory change it is shown that the results are qualitatively correct and that loess performs better than global regression the forward mappings show different root mean square error properties than the inverse mappings indicating that this method is better suited for the forward mappings than the inverse mappings at least for the data chosen for the current study some preliminary results on sensitivity of the first two formant frequencies to the two most important articulatory principal components are presented

regression by local fitting methods properties and computational algorithms abstract local regression is a procedure for estimating regression surfaces by the local fitting of linear or quadratic functions of the independent variables in a moving fashion that is analogous to how a moving average is computed for a time series the advantage of the methodology over the global fitting of parametric functions of the independent variables by least squares the current paradigm in regression studies is that a much wider class of regression functions can be estimated without distortion in this paper we discuss the methods their statistical properties and computational algorithms

a note on the aα spectral radius of graphs abstract let g be a graph with adjacency matrix a g and let d g be the diagonal matrix of the degrees of g for any real 0 1 nikiforov 2017 7 defined the matrix a g as a g d g 1 a g let u and v be two vertices of a connected graph g suppose that u and v are connected by a path w 0 v w 1 w s 1 w s u where d w i 2 for 1 i s 1 let g p s q u v be the graph obtained by attaching the paths p p to u and p q to v let s 0 1 nikiforov and rojo 2018 9 conjectured that g p s q u v g p 1 s q 1 u v if p q 2 in this paper we confirm the conjecture as applications firstly the extremal graph with maximal a spectral radius with fixed order and cut vertices is characterized secondly we characterize the extremal tree which attains the maximal a spectral radius with fixed order and matching number these results generalize some known results

slowly oscillating periodic solutions of autonomous state dependent delay equations more than a dozen years since the peak of activity on the question of the existence of periodic slowly oscillating solutions of autonomous delay differential equations following the early work of jones l wright 2 and grafton 3 the work of nussbaum 4 51 is to be specially noted for providing several new fixed point results and a global bifurcation theorem which are particularly useful for proving the existence of periodic solutions other important works include those of hadeler and tomiuk 6 kaplan and yorke 7 chow 8 chow and hale 9 alt lo 111 and walther 12 131 see hale s book 14 for an overview to the best of our knowledge only nussbaum 5 and alt 1 l considered the question of the existence of periodic solutions of autonomous state dependent delay differential equations nussbaum considered a special equation 0 3 below in 5 but did not prove a general result alt 1 l considered more complicated integral threshold type state dependent delays which have arisen in various models in epidemiology and structured population models alt obtained a theorem for a general class of state dependent equations on which we comment below the lack of results on periodic solutions for state dependent equations is probably explained by the fact that it is not clear what kinds of state dependent delays are interesting or natural and on a lack of compelling examples of such equations arising from plausible mathematical models however some recent papers of belair and mackey 15 and belair 16 contain some interesting state dependent delay equations arising in economics and population biology state dependent delays of threshold type arise naturally in structured population models see lo 111 the motivation for this paper stems from consideration of the innocent looking equation x t kx t r x t 0 1 where r x is bell shaped e g r x 01 emxz 1 01 0 i 01 5 1 if k 7r 2 and r o 1 then the zero solution of 0 1 is unstable a formal linearization would yield z t kz t 1 which is known to be unstable for

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

completely positive matrices abstract an n n real matrix a is called completely positive cp if it can be factored as a b b stands for transpose where b is an m n entrywise nonnegative matrix for some integer m the smallest such number m is called the cprank of a in this paper we present a necessary and sufficient condition for any entrywise nonnegative and positive semidefinite matrix to be cp we also present an expression for the cprank of any cp matrix

the aα spread of a graph abstract let a g and d g be the adjacency matrix and the degree diagonal matrix of a graph g respectively for any real number 0 1 nikiforov defined the a matrix of a graph g as a g d g 1 a g the a spread of a graph is the difference between the largest eigenvalue and the smallest eigenvalue of the a matrix of the graph in this paper we obtain some new lower bounds on a spread and characterize the extremal graphs for certain cases which extend the results of a spread and q spread moreover some graph operations on a spread are presented

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

a tree structured adaptive network for function approximation in high dimensional spaces nonlinear function approximation is often solved by finding a set of coefficients for a finite number of fixed nonlinear basis functions however if the input data are drawn from a high dimensional space the number of required basis functions grows exponentially with dimension leading many to suggest the use of adaptive nonlinear basis functions whose parameters can be determined by iterative methods the author proposes a technique based on the idea that for most of the data only a few dimensions of the input may be necessary to compute the desired output function additional input dimensions are incorporated only where needed the learning procedure grows a tree whose structure depends upon the input data and the function to be approximated this technique has a fast learning algorithm with no local minima once the network shape is fixed and it can be used to reduce the number of required measurements in situations where there is a cost associated with sensing three examples are given controlling the dynamics of a simulated planar two joint robot arm predicting the dynamics of the chaotic mackey glass equation and predicting pixel values in real images from pixel values above and to the left

proportional hazards tests and diagnostics based on weighted residuals summary nonproportional hazards can often be expressed by extending the cox model to include time varying coefficients e g for a single covariate the hazard function for subject i is modelled as exp fl t zi t a common example is a treatment effect that decreases with time we show that the function 3 t can be directly visualized by smoothing an appropriate residual plot also many tests of proportional hazards including those of cox 1972 gill schumacher 1987 harrell 1986 lin 1991 moreau o quigley mesbah 1985 nagelkerke oosting hart 1984 o quigley pessione 1989 schoenfeld 1980 and wei 1984 are related to time weighted score tests of the proportional hazards hypothesis and can be visualized as a weighted least squares line fitted to the residual plot

identifying optimal risk windows for self controlled case series studies of vaccine safety in vaccine safety studies subjects are considered at increased risk for adverse events for a period of time after vaccination known as risk window to our knowledge risk windows for vaccine safety studies have tended to be pre defined and not to use information from the current study inaccurate specification of the risk window can result in either including the true control period in the risk window or including some of the risk window in the control period which can introduce bias we propose a data based approach for identifying the optimal risk windows for self controlled case series studies of vaccine safety the approach involves fitting conditional poisson regression models to obtain incidence rate ratio estimates for different risk window lengths for a specified risk window length l the average time at risk t l is calculated when the specified risk window is shorter than the true the incidence rate ratio decreases with 1 t l increasing but there is no explicit relationship when the specified risk window is longer than the true the incidence rate ratio increases linearly with 1 t l increasing theoretically the risk window with the maximum incidence ratio is the optimal risk window because of sparse data problem we recommend using both the maximum incidence rate ratio and the linear relationship when the specified risk window is longer than the true to identify the optimal risk windows both simulation studies and vaccine safety data applications show that our proposed approach is effective in identifying medium and long risk windows

nondetects detection limits and the probability of detection abstract when chemists cannot quantify the concentration in a field sample they report nondetect instead of a numerical measurement a data analyst faced with environmental data containing nondetects might assume that all nondetects are zeros all nondetects are smaller than the smallest detect numerical measurement or if a detection limit is reported that all nondetects are below the detection limit this article shows that these assumptions can be incorrect and suggests better alternatives the measurements that are likely to be reported as nondetect can be described by a new concept the probability of acceptance where acceptance means that a measurement passes the requirements for being reported as a detect the 90th percentile of the probability of acceptance curve is a reasonable upper bound or censoring limit for a measurement reported as nondetect the probability of acceptance also suggests the complexity of the data analysis task for example assuming that all nondetects are smaller than

a basis theorem for a class of max plus eigenproblems we study the max plus equation p max s m h s s 0 m where h 0 m and 0 m 0 m are given functions the function 0 m and the quantity p are unknown and are respectively an eigenfunction and additive eigenvalue eigensolutions are known to describe the asymptotics of certain solutions of singularly perturbed differential equations with state dependent time lags under general conditions we prove the existence of a finite set a basis of eigensolutions i for 1 i q with the same eigenvalue p such that the general solution to is given by c1 1 c2 2 cq q here ci are arbitrary quantities and denotes the maximum operator in many cases q 1 so the solution is unique up to an additive constant

boundary layer phenomena for differential delay equations with state dependent time lags iii in this paper we begin a study of the differential delay equation varepsilon x t x t f x t r r r x t

on the α index of graphs with pendent paths abstract let g be a graph with adjacency matrix a g and let d g be the diagonal matrix of the degrees of g for every real 0 1 write a g for the matrix a g d g 1 a g this paper presents some extremal results about the spectral radius g of a g that generalize previous results about 0 g and 1 2 g in particular write b p q r be the graph obtained from a complete graph k p by deleting an edge and attaching paths p q and p r to its ends it is shown that if 0 1 and g is a graph of order n and diameter at least k then g b n k 2 k 2 k 2 with equality holding if and only if g b n k 2 k 2 k 2 this result generalizes results of hansen and stevanovic 5 and liu and lu 7

predictive flow field estimation abstract we are considering the problem of real time prediction of 3d turbulent velocity fields based on a small number of scalar measurements the method of proper orthogonal decomposition pod allows for the decomposition of an ensemble of velocity fields into a set of spatial basis functions and a set of temporal coefficients the computation of the temporal coefficients is by no means a trivial matter especially when one is faced with a large number of modes in this paper we discuss the use of radial basis function rbf models to capture the discrete time evolution and nonlinear dynamics of the pod coefficients further we propose the use of regularized regression techniques to generate models that provide mappings between the pod coefficients and scalar measurements as a final step towards real time prediction the state space rbf models and regression measurement models are combined using unscented kalman filters to produce optimal solutions such that a balance between the state models and measurement models is achieved the proposed methods are tested for two specific cases the classical lorenz model is chosen to demonstrate the use and effectiveness of rbf models as a potential candidate for state models flow around a wall mounted cube in a channel at r e 20 000 is considered as the second case the aim for the second case is to be able to accurately predict the pod coefficients outside the ensemble it is shown that a large number of pod coefficients is required to approximate the velocity fields with sufficient accuracy the rbf models are created based on only the temporal information available from the initial ensemble and it is shown that the rbf model is able to correctly approximate the high dimensional phase space combined with the unscented kalman filter it is indeed possible to track the evolution of the pod coefficients for a long time the robustness of the filter is demonstrated by considering the presence of noise in measurements and using measurement information at time steps greater than the evolution time step

symmetric nonnegative tensors and copositive tensors abstract we first prove two new spectral properties for symmetric nonnegative tensors we prove a maximum property for the largest h eigenvalue of a symmetric nonnegative tensor and establish some bounds for this eigenvalue via row sums of that tensor we show that if an eigenvalue of a symmetric nonnegative tensor has a positive h eigenvector then this eigenvalue is the largest h eigenvalue of that tensor we also give a necessary and sufficient condition for this we then introduce copositive tensors this concept extends the concept of copositive matrices symmetric nonnegative tensors and positive semi definite tensors are examples of copositive tensors the diagonal elements of a copositive tensor must be nonnegative we show that if each sum of a diagonal element and all the negative off diagonal elements in the same row of a real symmetric tensor is nonnegative then that tensor is a copositive tensor some further properties of copositive tensors are discussed