integrable equations with ermakov pinney nonlinearities and chiellini damping a new type of dissipative ermakov pinney equations are integrable nonlinear dissipation gain introduced through the chiellini integrable abel equation higher order reid nonlinearities are also considered ermakov invariant is used in the solution method we introduce a special type of dissipative ermakov pinney equations of the form v g v v h v 0 where h v h 0 v cv 3 and the nonlinear dissipation g v is based on the corresponding chiellini integrable abel equation when h 0 v is a linear function h 0 v 2 v general solutions are obtained following the abel equation route based on particular solutions we also provide general solutions containing a factor with the phase of the milne type in addition the same kinds of general solutions are constructed for the cases of higher order reid nonlinearities the chiellini dissipative function is actually a dissipation gain function because it can be negative on some intervals we also examine the nonlinear case h 0 v 0 2 v v 2 and show that it leads to an integrable hyperelliptic case

gossip coverage control for robotic networks dynamical systems on the space of partitions future applications in environmental monitoring delivery of services and transportation of goods motivate the study of deployment and partitioning tasks for groups of autonomous mobile agents these tasks may be achieved by recent coverage algorithms based upon the classic methods by lloyd these algorithms however rely upon critical requirements on the communication network information is exchanged synchronously among all agents and long range communication is sometimes required this work proposes novel coverage algorithms that require only gossip communication i e asynchronous pairwise and possibly unreliable communication which robot pair communicates at any given time may be selected deterministically or randomly a key innovative idea is describing coverage algorithms for robot deployment and environment partitioning as dynamical systems on a space of partitions in other words we study the evolution of the regions assigned to each agent rather than the evolution of the agents positions the proposed gossip algorithms are shown to converge to centroidal voronoi partitions under mild technical conditions our treatment features a broad variety of results in topology analysis and geometry first we establish the compactness of a suitable space of partitions with respect to the symmetric difference metric second with respect to this metric we establish the continuity of various geometric maps including the voronoi diagram as a function of its generators the location of a centroid as a function of a set and the widely known multicenter function studied in facility location problems third we prove two convergence theorems for dynamical systems on metric spaces described by deterministic and stochastic switches

adaptive information collection by robotic sensor networks for spatial estimation this work deals with trajectory optimization for a robotic sensor network sampling a spatio temporal random field we examine the optimal sampling problem of minimizing the maximum predictive variance of the estimator over the space of network trajectories this is a high dimensional multi modal nonsmooth optimization problem known to be np hard even for static fields and discrete design spaces under an asymptotic regime of near independence between distinct sample locations we show that the solutions to a novel generalized disk covering problem are solutions to the optimal sampling problem this result effectively transforms the search for the optimal trajectories into a geometric optimization problem constrained versions of the latter are also of interest as they can accommodate trajectories that satisfy a maximum velocity restriction on the robots we characterize the solution for the unconstrained and constrained versions of the geometric optimization problem as generalized multicircumcenter trajectories and provide algorithms which enable the network to find them in a distributed fashion several simulations illustrate our results

bias in estimation of misclassification rates when a simple random sample of size n is employed to establish a classification rule for prediction of a polytomous variable by an independent variable the best achievable rate of misclassification is higher than the corresponding best achievable rate if the conditional probability distribution is known for the predicted variable given the independent variable in typical cases this increased misclassification rate due to sampling is remarkably small relative to other increases in expected measures of prediction accuracy due to samplings that are typically encountered in statistical analysis

front propagation into unstable states universal algebraic convergence towards uniformly translating pulled fronts fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes pulled fronts and pushed fronts the term pulled front expresses that these fronts are pulled along by the spreading of linear perturbations about the unstable state accordingly their asymptotic speedv equals the spreading speed of perturbations whose dynamics is governed by the equations linearized about the unstable state the central result of this paper is the analysis of the convergence of asymptotically uniformly traveling pulled fronts towardsv we show that when such fronts evolve from sufficiently steep initial conditions which initially decay faster than e x forx 1 t hey have auniversal relaxation behavioras timet 1 the velocity of a pulled front always relaxes algebraically like v t d v 3 2t c 3 p d d 2 t 3 2 c o 1 t 2 the parametersv and d are determined through a saddle point analysis from the equation of motion linearized about the unstable invaded state this front velocity is independent of the precise value of the front amplitude which one tracks to measure the front position the interior of the front is essentially slaved to the leading edge and develops universally as x t d8v t x rt dt 0 v t 0 c o 1 t 2 where8v x vt is a uniformly translating front solution with velocity v v our result which can be viewed as a general center manifold result for pulled front propagation is derived in detail for the well known nonlinear diffusion equation of type t d 2 x c 3 where the invaded unstable state is d 0 even for this simple case the subdominant t 3 2 term extends an earlier result of bramson our analysis is then generalized to more general sets of partial differential equations with higher spatial or temporal derivatives to pdes with memory kernels and also to difference equations such as those that occur in numerical finite difference codes our universal result for pulled fronts thus implies independence i of the level curve which is used to track the front position ii of the precise nonlinearities iii of the precise form of the linear operators in the dynamical equation and iv of the precise initial conditions as long as they are sufficiently steep the only remainders of the explicit form of the dynamical equation are the nonlinear solutions 8v and the three saddle point parameters v and d as our simulations confirm all our analytical predictions in every detail it can be concluded that we have a complete analytical understanding of the propagation mechanism and relaxation behavior of pulled fronts if they are uniformly translating for t 1 an immediate consequence of the slow algebraic relaxation is that the standard moving boundary approximation breaks down for weakly curved pulled fronts in two or three dimensions in addition to our main result for pulled fronts we also discuss the propagation and convergence of fronts emerging from

distributed learning and cooperative control for multi agent systems this paper presents an algorithm and analysis of distributed learning and cooperative control for a multi agent system so that a global goal of the overall system can be achieved by locally acting agents we consider a resource constrained multi agent system in which each agent has limited capabilities in terms of sensing computation and communication the proposed algorithm is executed by each agent independently to estimate an unknown field of interest from noisy measurements and to coordinate multiple agents in a distributed manner to discover peaks of the unknown field each mobile agent maintains its own local estimate of the field and updates the estimate using collective measurements from itself and nearby agents each agent then moves towards peaks of the field using the gradient of its estimated field while avoiding collision and maintaining communication connectivity the proposed algorithm is based on a recursive spatial estimation of an unknown field we show that the closed loop dynamics of the proposed multi agent system can be transformed into a form of a stochastic approximation algorithm and prove its convergence using ljung s ordinary differential equation ode approach we also present extensive simulation results supporting our theoretical results

new method for generating general solution of abel differential equation abstract a new method for generating a general solution of the nonlinear first kind abel type differential equation from a particular one is presented

improper solutions in the analysis of covariance structures their interpretability and a comparison of alternate respecifications a monte carlo approach was employed to investigate the interpretability of improper solutions caused by sampling error in maximum likelihood confirmatory factor analysis four models were studied with two sample sizes of the overall goodness of fit indices provided by the lisrel vi program significant differences between improper and proper solutions were found only for the root mean square residual as expected indicators of the factor on which the negative uniqueness estimate occurred had biased loadings and the correlations of its factor with other factors were also biased in contrast the loadings of indicators on other factors and those factor intercorrelations did not have any bias of practical significance for initial solutions with one negative uniqueness estimate three respecifications were studied fix the uniqueness at 00 fix it at 20 or constrain the domain of the solution to be proper for alternate respecified solutions that were converged and proper the constrained solutions and uniqueness fixed at 00 solutions were equivalent the mean goodness of fit and pattern coefficient values for the original improper solutions were not meaningfully different from those obtained under the constrained and uniqueness fixed at 00 respecifications

solutions generating technique for abel type nonlinear ordinary differential equations abstract a second order nonlinear differential equation describing the dynamics of a bulk viscous fluid filled general relativistic friedmann robertson walker universe is considered by means of appropriate transformations the evolution equation of the space time is transformed into a third order polynomial abel differential equation with the use of some particular solutions of this equation repeated classes of exact solutions are generated

coordination and geometric optimization via distributed dynamical systems this paper discusses dynamical systems for disk covering and sphere packing problems we present facility location functions from geometric optimization and characterize their differentiable properties we design and analyze a collection of distributed control laws that are related to nonsmooth gradient systems the resulting dynamical systems promise to be of use in coordination problems for networked robots in this setting the distributed control laws correspond to local interactions between the robots the technical approach relies on concepts from computational geometry nonsmooth analysis and the dynamical system approach to algorithms

a family of analytical solutions of a nonlinear diffusion convection equation abstract despite its popularity in many engineering fields the nonlinear diffusion convection equation has no general analytical solutions this work presents a family of closed form analytical traveling wave solutions for the nonlinear diffusion convection equation with power law nonlinearities this kind of equations typically appears in nonlinear problems of flow and transport in porous media the solutions that are addressed are simple and fully analytical three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient increasing decreasing or constant it has shown that the structure of the traveling wave solution is strongly related to the diffusion term the main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters the proposed closed form solutions are simple to use do not require any numerical implementation and may be implemented in a simple spreadsheet the analytical expressions are also useful to mathematically analyze the structure and properties of the solutions

the asymptotic covariance matrix of maximum likelihood estimates in factor analysis the case of nearly singular matrix of estimates of unique variances this paper is concerned with the asymptotic covariance matrix acm of maximum likelihood estimates mles of factor loadings and unique variances when one element of mles of unique variances is nearly zero i e the matrix of mles of unique variances is nearly singular in this situation standard formulas break down we give explicit formulas for the acm of mles of factor loadings and unique variances that could be used even when an element of mles of unique variances is very close to zero we also discuss an alternative approach using the augmented information matrix under a nearly singular matrix of mles of unique variances and derive the partial derivatives of the alternative constraint functions with respect to the elements of factor loadings and unique variances 2000 elsevier science inc all rights reserved ams classification 62h25 62f12

necessary conditions for mean square convergence of the best linear factor predictor several sufficient conditions are available for mean square convergence of factor predictors a necessary and sufficient condition is given in the heywood case with respect to confirmatory factor analysis this condition generalizes that of krijnen 2006 and performs better than a signal to noise type of condition schneeweiss mathes 1995

dynamical systems that sort lists diagonalize matrices and solve linear programming problems abstract we establish a number of properties associated with the dynamical system h h h n where h and n are symmetric n by n matrices and a b ab ba the most important of these come from the fact that this equation is equivalent to a certain gradient flow on the space of orthogonal matrices we are especially interested in the role of this equation as an analog computer for example we show how to map the data associated with a linear programming problem into h 0 and n in such a way as to have h h h n evolve to a solution of the linear programming problem this result can be applied to find systems which solve a variety of genetic combinatorial optimization problems and it even provides an algorithm for diagonalizing symmetric matrices

hedonic coalition formation for optimal deployment this paper presents a distributed algorithmic solution termed coalition formation and deployment algorithm to achieve network configurations where agents cluster into coincident groups that are distributed optimally over the environment the motivation for this problem comes from spatial estimation tasks executed with unreliable sensors we propose a probabilistic strategy that combines a repeated game governing the formation of coalitions with a spatial motion component governing their location for a class of probabilistic coalition switching laws we establish the convergence of the agents to coincident groups of a desired size in finite time and the asymptotic convergence of the overall network to the optimal deployment both with probability 1 we also investigate the algorithm s time and communication complexity specifically we upper bound the expected completion time of executions that use the proportional to number of unmatched agentscoalition switching law under arbitrary and complete communication topologies we also upper bound the number of messages required per timestep to execute our strategy the proposed algorithm is robust to agent addition and subtraction from a coalitional game perspective the algorithm is novel in that the players information is limited to the neighboring clusters from a motion coordination perspective the algorithm is novel because it brings together the basic tasks of rendezvous individual agents into clusters and deployment clusters in the environment simulations illustrate the correctness robustness and complexity results

on the jacobi last multipliers and lagrangians for a family of linard type equations we study a family of the linard type equations which can be transformed via the generalized sundman transformations into a particular case of painlevgambier equation xxvii we show that this equation of the painlevgambier type admits an autonomous lagrangian jacobi last multiplier and first integral as a consequence we obtain that the corresponding family of linard type equations also admits a time independent lagrangian jacobi last multiplier and first integral we also construct the general analytical and singular solutions for members of this family of linard type equations by virtue of the generalized sundman transformations to demonstrate applications of our results we consider several examples of the linard type equations with a generalization of the modified emden equation among them and construct their autonomous lagrangians jacobi last multipliers and first integral as well as their general analytical solutions

exact analytical solutions of the susceptible infected recovered sir epidemic model and of the sir model with equal death and birth rates abstract in this paper the exact analytical solution of the susceptible infected recovered sir epidemic model is obtained in a parametric form by using the exact solution we investigate some explicit models corresponding to fixed values of the parameters and show that the numerical solution reproduces exactly the analytical solution we also show that the generalization of the sir model including births and deaths described by a nonlinear system of differential equations can be reduced to an abel type equation the reduction of the complex sir model with vital dynamics to an abel type equation can greatly simplify the analysis of its properties the general solution of the abel equation is obtained by using a perturbative approach in a power series form and it is shown that the general solution of the sir model with vital dynamics can be represented in an exact parametric form

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

nonsmooth coordination and geometric optimization via distributed dynamical systems emerging applications for networked and cooperative robots motivate the study of motion coordination for groups of agents for example it is envisioned that groups of agents will perform a variety of useful tasks including surveillance exploration and environmental monitoring this paper deals with basic interactions among mobile agents such as move away from the closest other agent or move toward the furthest vertex of your own voronoi polygon these simple interactions amount to distributed dynamical systems because their implementation requires only minimal information about neighboring agents we characterize the close relationship between these distributed dynamical systems and the disk covering and sphere packing cost functions from geometric optimization our main results are as follows i we characterize the smoothness properties of these geometric cost functions ii we show that the interaction laws are variations of the nonsmooth gradient of the cost functions and iii we establish various asymptotic convergence properties of the laws the technical approach relies on concepts from computational geometry nonsmooth analysis and nonsmooth stability theory

the characterization of reaction convection diffusion processes by travelling waves it has long been known that the heat equation displays infinite speed of propagation this is to say that if the initial data are nonnegative and have nonempty compact support the solution of an initial value problem is positive everywhere after any infinitesimal time however since the nineteen fifties it has also been known that certain nonlinear diffusion equations of degenerate parabolic type do not display this phenomenon for these equations the generalized solution of an initial value problem with compactly supported initial data will have bounded support with respect to the spatial variable at all times in this paper the necessary and sufficient criterion for finite speed of propagation for the general nonlinear reaction convection diffusion equation formula is determined the assumptions on the coefficientsa bandcare such that the classification unifies and generalizes previously known results the technique employed is comparision of an arbitrary solution of the equation with suitably constructed travelling wave solutions and subsolutions basically the central conclusion is that the equation exhibits finite speed of propagation if and only if it admits a travelling wave solution with bounded support concurrently the search for a travelling wave solution with bounded support can be reduced to the study of a singular nonlinear integral equation whose solution must satisfy a certain constraint

asymptotic optimality of multicenter voronoi configurations for random field estimation this technical note deals with multi agent networks performing estimation tasks consider a network of mobile agents with sensors that can take measurements of a spatial stochastic process using the kriging statistical technique a field estimate may be calculated over the environment with an associated error variance at each point we study a single snapshot scenario in which the spatial process mean is known and each agent can only take one measurement we consider two optimization problems with respect to the measurement locations using as objective functions the maximum error variance and the extended prediction variance as the correlation between distinct locations vanishes we show that circumcenter and incenter voronoi configurations become network configurations that optimize the maximum error variance and the extended prediction variance respectively we also present distributed coordination algorithms that steer the network towards these configurations

exact travelling wave solutions of non linear reaction convection diffusion equations an abel equation based approach we consider quasi stationary travelling wave type solutions to a general nonlinear reaction convection diffusion equation with arbitrary autonomous coefficients the second order nonlinear equation describing one dimensional travelling waves can be reduced to a first kind first order abel equation by using two integrability conditions for the abel equation the chiellini lemma and the lemke transformation several classes of exact travelling wave solutions of the general reaction convection diffusion equation are obtained corresponding to different functional relations imposed between the diffusion convection and reaction functions in particular we obtain travelling wave solutions for two non linear second order partial differential equations representing generalizations of the standard diffusion equation and of the classical fisher kolmogorov equation to which they reduce for some limiting values of the model parameters the models correspond to some specific power law type choices of the reaction and convection functions respectively the travelling wave solutions of these two classes of differential equation are investigated in detail by using both numerical and semi analytical methods

some results on mean square error for factor score prediction for the confirmatory factor model a series of inequalities is given with respect to the mean square error mse of three main factor score predictors the eigenvalues of these mse matrices are a monotonic function of the eigenvalues of the matrix p 1 2 p p 1 p 1 2 this matrix increases with the number of observable variables p a necessary and sufficient condition for mean square convergence of predictors is divergence of the smallest eigenvalue of p or equivalently divergence of signal to noise schneeweiss mathes 1995 the same condition is necessary and sufficient for convergence to zero of the positive definite mse differences of factor predictors convergence to zero of the distance between factor predictors and convergence to the unit value of the relative efficiencies of predictors various illustrations and examples of the convergence are given as well as explicit recommendations on the problem of choosing between the three main factor score predictors

a gauss newton algorithm for exploratory factor analysis it is shown that the scoring algorithm for maximum likelihood estimation in exploratory factor analysis can be developed in a way that is many times more efficient than a direct development based on information matrices and score vectors the algorithm offers a simple alternative to current algorithms and when used in one step mode provides the simplest and fastest method presently available for moving from consistent to efficient estimates perhaps of greater importance is its potential for extension to the confirmatory model the algorithm is developed as a gauss newton algorithm to facilitate its application to generalized least squares and to maximum likelihood estimation

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments