spinning gas clouds iii solutions of minimal energy with precession we consider the model of rotating and expanding gas cloud originally proposed by ovsiannikov 1956 dokl akad nauk sssr 111 47 and dyson 1968 j math mech 18 91 under the restricting assumptions of an adiabatic index 5 3 and of vorticity free motion this has been shown gaffet 2001 j phys a math gen 34 2097 to be a liouville integrable hamiltonian system in the present work we consider the precessing solutions where the cloud does not retain a fixed rotation axis choosing for definiteness a particular set of constants of motion which corresponds to a minimum of the energy we show that a separation of variables occurs and that the equations of motion are reducible to the form of a riccati equation whose integration merely involves an elliptic integral

the resistant line and related regression methods abstract in a bivariate x y scatterplot the three group resistant line is that line for which the median residual in each outer third of the data ordered on x is zero it was proposed by tukey as an exploratory method resistant to outliers in x and y and suited to hand calculation a dual plot representation of the procedure yields a fast convergent algorithm nonparametric confidence intervals for the slope consistency influence function and asymptotic normality results monte carlo results show that small sample efficiencies exceed their asymptotic values in important cases both breakdown and efficiency are adequate for exploratory work replacing medians by other m estimators of location increases efficiency substantially without affecting breakdown or computational complexity the method thus combines bounded influence and acceptable efficiency with conceptual and computational simplicity

efficient scores variance decompositions and monte carlo swindles abstract monte carlo swindles or variance reduction techniques exploit the experimenter s knowledge of the stochastic structure governing the simulated data to construct more precise estimates of unknown parameters alternatively one can reduce the number of replications and thus the cost needed to gain a desired level of precision this article reviews the common case of swindles based on variance decompositions for estimating efficiencies and variances of location and regression estimators we then propose a new swindle based on fisher s efficient score function that can be applied profitably to a much wider range of situations than can the gaussian over independent swindles used in many studies of robust estimators we compare these methods by performing simulations for the efficiencies of location estimates and by placing them in a simple geometric framework as an illustration the score function swindle is used to estimate the variances of pitman estimates of location for samples from selected

distributed continuous time convex optimization on weight balanced digraphs this technical note studies the continuous time distributed optimization of a sum of convex functions over directed graphs contrary to what is known in the consensus literature where the same dynamics works for both undirected and directed scenarios we show that the consensus based dynamics that solves the continuous time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting this study sets the basis for the design of an alternative distributed dynamics which we show is guaranteed to converge on any strongly connected weight balanced digraph to the set of minimizers of a sum of convex differentiable functions with globally lipschitz gradients our technical approach combines notions of invariance and cocoercivity with the positive definiteness properties of graph matrices to establish the results

on a class of quartic surfaces and an associated integrable differential system given a unicursal quartic in a plane and four bi tangential straight lines there exist a pair of conics four times tangential to it choosing an arbitrary point k0 outside the plane the lines and either one of the conics determine four planes and a cone and a quartic surface can be found that stays tangential to them and presents 15 conic point singularities including k0 we introduce a one parameter family of symmetric tensors which are polynomial functions of degree 7 of the cartesian coordinates each of them determines two families of curves on the surface which are the null curves of the associated metric and are the integral curves of a differential system which turns out to possess the painleve property and to be integrable by quadratures differential systems of that form have been found gaffet 2006 j phys a math gen 39 99 to represent the rotating motion with precession of gas clouds expanding into a vacuum

efficient bounded influence regression estimation abstract the least squares estimator for in the classical linear regression model is strongly efficient under certain conditions however in the presence of heavy tailed errors and or anomalous data the least squares efficiency can be markedly reduced in this article we propose an estimator that limits the influence of any small subset of the data and show that it satisfies a first order condition for strong efficiency subject to the constraint we then show that the estimator is asymptotically normal the article concludes with an outline of an algorithm for computing a bounded influence regression estimator and with an example comparing least squares robust regression as developed by huber and the estimator proposed in this article

on distributed convex optimization under inequality and equality constraints we consider a general multi agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint a global equality constraint and a global constraint set the objective function is defined by a sum of local objective functions while the global constraint set is produced by the intersection of local constraint sets in particular we study two cases one where the equality constraint is absent and the other where the local constraint sets are identical we devise two distributed primal dual subgradient algorithms based on the characterization of the primal dual optimal solutions as the saddle points of the lagrangian and penalty functions these algorithms can be implemented over networks with dynamically changing topologies but satisfying a standard connectivity property and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the slater s condition

gas clouds rotating around a principal axis ii the separation of variables we present a new formulation of the spinning gas cloud model of ovsiannikov and dyson in the case of rotation around a fixed axis in terms of a 4 4 symmetric matrix which is a linear function of four coordinates xi we obtain a pair of separable variables l1 l2 related to the xi by a simple transformation and discuss their geometrical meaning

an integrable hamiltonian motion on a sphere ii the separation of variables we consider the motions on the unit sphere in a potential which have been shown earlier to derive from a completely integrable hamiltonian the separation of variables is completed in terms of an independent variable u which differs from the canonical time t where m and are the two integrals of motion s is the action and is the integration constant constant along each trajectory finally a lax pair is deduced from a separable form of the system lax p d 1968 commun pure appl math 21 467

spinning gas clouds with precession non degenerate cases we extend here our earlier treatment gaffet b 2003 j phys a math gen 36 5211 gaffet b 2005 phil trans r soc a accepted of the evolution of spinning gas clouds with precession to the non degenerate cases where the last integral of motion l6 is non vanishing the liouville torus is still found to be transformable into a quartic surface on which there are 15 conic point singularities the differential system governing the evolution is integrable by quadratures there is an integrating factor and the independent variable u which is the thermasy of the cloud admits an exact differential formulation on the liouville torus as well this integrable system is conjectured to have the painleve property with respect to the independent variable u as in the degenerate cases

time and space efficient algorithms for least median of squares regression abstract the least median of squared residuals regression line or lms line is that line y ax b for which the median of the residuals yi axi b 2 is minimized over all choices of a and b if we rephrase the traditional ordinary least squares ols problem as finding the a and b that minimize the mean of yi axi b 2 one can see that in a formal sense lms just replaces a mean by a median this way of describing lms regression does not do justice to the remarkable properties of lms in fact lms regression behaves in ways that distinguish it greatly from ols as well as from many other methods for robustifying ols see e g rousseeuw 1984 as illustrations given here show the lms regression line should provide a valuable tool for studying those data sets in which the usual linear model assumptions are violated by the presence of some not too small groups of data values that behave distinctly from the bulk of the data this feature of lms regression is illustrated by the fit given in

the hough transform estimator this paper pursues a statistical study of the hough transform the celebrated computer vision algorithm used to detect the presence of lines in a noisy image we first study asymptotic properties of the hough transform estimator whose objective is to find the line that best fits a set of planar points in particular we establish strong consistency rates of convergence and characterize the limiting distribution of the hough transform estimator while the convergence rates are seen to be slower than those found in some standard regression methods the hough transform estimator is shown to be more robust as measured by its breakdown point we next study the hough transform in the context of the problem of detecting multiple lines this is addressed via the framework of excess mass functionals and modality testing throughout several numerical examples help illustrate various properties of the estimator relations between the hough transform and more mainstream statistical paradigms and methods are discussed as well short title the hough transform estimator

a randomized incremental subgradient method for distributed optimization in networked systems we present an algorithm that generalizes the randomized incremental subgradient method with fixed stepsize due to nedic and bertsekas siam j optim 12 2001 pp 109 138 our novel algorithm is particularly suitable for distributed implementation and execution and possible applications include distributed optimization e g parameter estimation in networks of tiny wireless sensors the stochastic component in the algorithm is described by a markov chain which can be constructed in a distributed fashion using only local information we provide a detailed convergence analysis of the proposed algorithm and compare it with existing both deterministic and randomized incremental subgradient methods

an assumption free exact test for fixed design linear models with exchangeable errors we propose the cyclic permutation test cpt to test general linear hypotheses for linear models this test is non randomized and valid in finite samples with exact type i error alpha for an arbitrary fixed design matrix and arbitrary exchangeable errors whenever 1 alpha is an integer and n p ge 1 alpha 1 the test involves applying the marginal rank test to 1 alpha linear statistics of the outcome vector where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a non standard cyclic permutation group under the null hypothesis the power can be further enhanced by solving a secondary non linear travelling salesman problem for which the genetic algorithm can find a reasonably good solution extensive simulation studies show that the cpt has comparable power to existing tests when testing for a single contrast of coefficients an exact confidence interval can be obtained by inverting the test furthermore we provide a selective yet extensive literature review of the century long efforts on this problem highlighting the novelty of our test

distributed convex optimization via continuous time coordination algorithms with discrete time communication this paper proposes a novel class of distributed continuous time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents we establish the exponential convergence of the proposed algorithm under i strongly connected and weight balanced digraph topologies when the local costs are strongly convex with globally lipschitz gradients and ii connected graph topologies when the local costs are strongly convex with locally lipschitz gradients when the local cost functions are convex and the global cost function is strictly convex we establish asymptotic convergence under connected graph topologies we also characterize the algorithm s correctness under time varying interaction topologies and study its privacy preservation properties motivated by practical considerations we analyze the algorithm implementation with discrete time communication we provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication building on this result we design a provably correct centralized event triggered communication scheme that is free of zeno behavior finally we develop a distributed asynchronous event triggered communication scheme that is also free of zeno with asymptotic convergence guarantees several simulations illustrate our results

the change of variance curve and optimal redescending m estimators abstract we define the change of variance curve cvc of location m estimators in order to investigate the infinitesimal stability of the asymptotic variance we also construct the so called hyperbolic tangent estimators proving their existence and performing certain numerical computations of their defining constants their introduction is motivated by a theorem that shows they are the optimally robust redescending m estimators in the sense of the cvc

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

distributed optimal in network resource allocation algorithm design via a control theoretic approach abstract in this paper we consider an in network optimal resource allocation problem with multiple demand equations we propose a novel distributed continuous time algorithm that solves the problem over strongly connected and weight balanced digraph network topologies when the local cost functions are strongly convex we also discuss the extension of our convergence guarantees to dynamically changing topologies finally we show that if the network is an undirected connected graph we can guarantee stability and convergence of our algorithm for problems involving local convex functions this convergence guarantee is to a point in the set of minimizers of our optimal resource allocation problem the design and analysis of our algorithm are carried out using a control theoretic approach we demonstrate our results through a numerical example

robust regression using repeated medians abstract the repeated median algorithm is a robustified u statistic in which nested medians replace the single mean unlike many generalizations of the univariate median repeated median estimates maintain the high 50 breakdown value and can resist the effects of outliers even when they comprise nearly half of the data because they are calculated directly not iteratively repeated median procedures can be used as starting values for iterative robust estimation methods for bivariate linear regression with symmetric errors repeated median estimates are unbiased and fisher consistent and their efficiency under gaussian sampling can be comparable to the efficiency of the univariate median author

zero gradient sum algorithms for distributed convex optimization the continuous time case this technical note presents a set of continuous time distributed algorithms that solve unconstrained separable convex optimization problems over undirected networks with fixed topologies the algorithms are developed using a lyapunov function candidate that exploits convexity and are called zero gradient sum zgs algorithms as they yield nonlinear networked dynamical systems that evolve invariantly on a zero gradient sum manifold and converge asymptotically to the unknown optimizer we also describe a systematic way to construct zgs algorithms show that a subset of them actually converge exponentially and obtain lower and upper bounds on their convergence rates in terms of the network topologies problem characteristics and algorithm parameters including the algebraic connectivity laplacian spectral radius and function curvatures the findings of this technical note may be regarded as a natural generalization of several well known algorithms and results for distributed consensus to distributed convex optimization

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given