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Sample records for convex functions ii

  1. Differential analysis of matrix convex functions II

    DEFF Research Database (Denmark)

    Hansen, Frank; Tomiyama, Jun

    2009-01-01

    We continue the analysis in [F. Hansen, and J. Tomiyama, Differential analysis of matrix convex functions. Linear Algebra Appl., 420:102--116, 2007] of matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divide...

  2. Global approximation of convex functions

    CERN Document Server

    Azagra, D

    2011-01-01

    We show that for every (not necessarily bounded) open convex subset $U$ of $\\R^n$, every (not necessarily Lipschitz or strongly) convex function $f:U\\to\\R$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded sets to results on uniform approximation on unbounded sets, in such a way that not only convexity and $C^k$ smoothness, but also local Lipschitz constants, minimizers, order, and strict or strong convexity, are preserved. This transfer method is quite general and it can also be used to obtain new results on approximation of convex functions defined on Riemannian manifolds or Banach spaces. We also provide a characterization of the class of convex functions which can be uniformly approximated on $\\R^n$ by strongly convex functions.

  3. Covering Numbers for Convex Functions

    CERN Document Server

    Guntuboyina, Adityanand

    2012-01-01

    In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the $\\epsilon$-covering number of $\\C([a, b]^d, B)$, in the $L_p$-metric, $1 \\le p 0$, and $\\C([a,b]^d, B)$ denotes the set of all convex functions on $[a, b]^d$ that are uniformly bounded by $B$. We summarize previously known results on covering numbers for convex functions and also provide alternate proofs of some known results. Our results have direct implications in the study of rates of convergence of empirical minimization procedures as well as optimal convergence rates in the numerous convexity constrained function estimation problems.

  4. Uniformly convex-transitive function spaces

    OpenAIRE

    Rambla-Barreno, Fernando; Talponen, Jarno

    2009-01-01

    We introduce a property of Banach spaces called uniform convex-transitivity, which falls between almost transitivity and convex-transitivity. We will provide examples of uniformly convex-transitive spaces. This property behaves nicely in connection with some Banach-valued function spaces. As a consequence, we obtain new examples of convex-transitive Banach spaces.

  5. Relations between Lipschitz functions and convex functions

    Institute of Scientific and Technical Information of China (English)

    RUAN Yingbin

    2005-01-01

    We discuss the relationship between Lipschitz functions and convex functions.By these relations, we give a sufficient condition for the set of points where Lipschitz functions on a Hilbert space is Frechet differentiable to be residual.

  6. Generalized geometrically convex functions and inequalities.

    Science.gov (United States)

    Noor, Muhammad Aslam; Noor, Khalida Inayat; Safdar, Farhat

    2017-01-01

    In this paper, we introduce and study a new class of generalized functions, called generalized geometrically convex functions. We establish several basic inequalities related to generalized geometrically convex functions. We also derive several new inequalities of the Hermite-Hadamard type for generalized geometrically convex functions. Several special cases are discussed, which can be deduced from our main results.

  7. CONVEX CLASS OF STARLIKE FUNCTIONS

    OpenAIRE

    Gupta, V. P.

    1984-01-01

    Let $S$ denote the class of functions of the form $f(z)=z-¥sum_{n=2}^{¥infty}|a_{n}|z^{n}$ that are analytic and univalent in the unit disk $U$. Let $S(¥alpha, ¥beta)$ and $K(¥alpha, ¥beta)$ denote the subclasses of $S$ consisting respectively, of starlike and close-to-convex functions of order $¥alpha(0¥leqq¥alpha

  8. Convex trace functions of several variables

    DEFF Research Database (Denmark)

    Hansen, Frank

    2002-01-01

    We prove that the function (x1,...,xk)¿Tr(f(x1,...,xk)), defined on k-tuples of symmetric matrices of order (n1,...,nk) in the domain of f, is convex for any convex function f of k variables. The matrix f(x1,...,xk) is defined by the functional calculus for functions of several variables, and it ...

  9. Relations between Lipschitz functions and convex functions

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    [1]Zajicek, J., On the differentation of convex functions in finite and infinite dimensional spaces, Czech J. Math.,1979, 29: 340-348.[2]Hu, T. C., Klee, V. L., Larman, D. G., Optimization of globally convex functions, SIAM J. Control Optim., 1989,27: 1026-1047.[3]Cepedello Boiso, M., Approximation of Lipschitz functions by △-convex functions in Banach spaces, Israel J.Math., 1998, 106: 269-284.[4]Asplund, E., Frechet differentiability of convex functions, Acta Math., 1968, 121: 31-47.[5]Johnson, J. A., Lipschitz spaces, Pacific J. Math, 1974, 51: 177-186.[6]Stromberg, T., The operation of infimal convolution, Dissert. Math., (Rozprawy Mat.), 1996, 325: 58.[7]Kadison, R. V., Ringrose, J. R., Fundamentals of the theory of operator algebras, volume Ⅰ: Elementary Theory,Graduate Studies in Math., vol. 15, Amer. Math. Soc., 1997.[8]Phelps, R. R., Convex functions,monotone operators and differentiability, Lect. Notes in Math., vol. 1364,Springer-Verlag, 1977.[9]Lindenstrauss, J., On operators which attain their norm, Israel J. Math., 1963, 1: 139-148.[10]Press, D., Gateaux differentiable functions are somewhere Frechet differentiable, Rend. Circ. Mat. Palermo,1984, 33: 122-133.[11]Press, D., Differentiability of Lipschitz functions on Banach spaces, J. Funct. Anal., 1990, 91:312-345.[12]Lindenstrauss, J., Press, D., On Frechet differentiability of Lipschitz maps between Banach spaces, Annals of Math., 2003, 157: 257-288.[13]Press, D., Gateaux differentiable Lipschitz functions need not be Frechet differentiable on a residual set, Supplemento Rend. Circ. Mat. Palermo, Serie Ⅱ, 1982, 2: 217-222.

  10. Efficient Line Searching for Convex Functions

    NARCIS (Netherlands)

    den Boef, E.; den Hertog, D.

    2004-01-01

    In this paper we propose two new line search methods for convex functions. These new methods exploit the convexity property of the function, contrary to existing methods.The worst method is an improved version of the golden section method.For the second method it is proven that after two evaluations

  11. Strictly convex functions on complete Finsler manifolds

    Indian Academy of Sciences (India)

    YOE ITOKAWA; KATSUHIRO SHIOHAMA; BANKTESHWAR TIWARI

    2016-10-01

    The purpose of the present paper is to investigate the influence of strictly convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss the properties of the group of isometries and the exponential maps on a complete Finsler manifold admitting strictly convex functions.

  12. Convex functions, monotone operators and differentiability

    CERN Document Server

    Phelps, Robert R

    1993-01-01

    The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition. Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space. The startlingly simple proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for subdifferentials of convex functions. The exciting new version of the useful Borwein-Preiss smooth variational principle due to Godefroy, Deville and Zizler. The material is accessible to students who have had a course in Functional Analysis; indeed, the first edition has been used in numerous graduate seminars. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational princ...

  13. Quasi-convex Functions in Carnot Groups

    Institute of Scientific and Technical Information of China (English)

    Mingbao SUN; Xiaoping YANG

    2007-01-01

    In this paper, the authors introduce the concept of h-quasiconvex functions on Carnot groups G. It is shown that the notions of h-quasiconvex functions and h-convex sets are equivalent and the L∞ estimates of first derivatives of h-quasiconvex functions are given. For a Carnot group G of step two, it is proved that h-quasiconvex functions are locally bounded from above. Furthermore, the authors obtain that h-convex functions are locally Lipschitz continuous and that an h-convex function is twice differentiable almost everywhere.

  14. Some integral inequalities for logarithmically convex functions

    Directory of Open Access Journals (Sweden)

    Mevlüt Tunç

    2014-07-01

    Full Text Available The main aim of the present note is to establish new Hadamard like integral inequalities involving log-convex function. We also prove some Hadamard-type inequalities, and applications to the special means are given.

  15. DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES

    Institute of Scientific and Technical Information of China (English)

    CHENG LIXIN; TENG YANMEI

    2005-01-01

    This paper presents a type of variational principles for real valued w* lower semicon tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces.

  16. Convex functions and the rolling circle criterion

    OpenAIRE

    1995-01-01

    Given 0≤R1≤R2≤∞, CVG(R1,R2) denotes the class of normalized convex functions f in the unit disc U, for which ∂f(U) satisfies a Blaschke Rolling Circles Criterion with radii R1 and R2. Necessary and sufficient conditions for R1=R2, growth and distortion theorems for CVG(R1,R2) and rotation theorem for the class of convex functions of bounded type, are found.

  17. Optimal convex shapes for concave functionals

    CERN Document Server

    Bucur, Dorin; Lamboley, Jimmy

    2011-01-01

    Motivated by a long-standing conjecture of Polya and Szeg\\"o about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application to isoperimetriclike inequalities. As a byproduct of this approach we also obtain a quantitative version of the Kneser-S\\"uss inequality. Finally, for a large class of functionals involving Dirichlet energies and the surface measure, we perform a local analysis of strictly convex portions of the boundary via second order shape derivatives. This allows in particular to exclude the presence of smooth regions with positive Gauss curvature in an optimal shape for Polya-Szeg\\"o problem.

  18. Minimizing convex functions by continuous descent methods

    Directory of Open Access Journals (Sweden)

    Sergiu Aizicovici

    2010-01-01

    Full Text Available We study continuous descent methods for minimizing convex functions, defined on general Banach spaces, which are associated with an appropriate complete metric space of vector fields. We show that there exists an everywhere dense open set in this space of vector fields such that each of its elements generates strongly convergent trajectories.

  19. Differential analysis of matrix convex functions

    DEFF Research Database (Denmark)

    Hansen, Frank; Tomiyama, Jun

    2007-01-01

    We analyze matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus [F. Kraus, Über konvekse Matrixfunktionen, Math. Z. 41 (1936) 18-42]. We obtain for each order conditions for ma...

  20. The Identification of Convex Function on Riemannian Manifold

    Directory of Open Access Journals (Sweden)

    Li Zou

    2014-01-01

    Full Text Available The necessary and sufficient condition of convex function is significant in nonlinear convex programming. This paper presents the identification of convex function on Riemannian manifold by use of Penot generalized directional derivative and the Clarke generalized gradient. This paper also presents a method for judging whether a point is the global minimum point in the inequality constraints. Our objective here is to extend the content and proof the necessary and sufficient condition of convex function to Riemannian manifolds.

  1. DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS

    Institute of Scientific and Technical Information of China (English)

    Jacek DZIOK; Ravinder Krishna RAINA; Janusz SOK(O)L

    2013-01-01

    This article presents some new results on the class SLMα of functions that are analytic in the open unit discu ={z:[z[< 1} satisfying the conditions that f(0)=0,f'(0)=1,and α (1+ zf"(z)/f'(z)) + (1-α)zf'(z)/f(x) ∈(p)(u)for all z ∈ u,where α is a real number and (p)(z) =1 + τ2z2/ 1-τz-τ2z2 (z ∈ u).The number τ =(1-√5)/2 is such that τ2 =1 + T.The class SLMα introduced by J.Dziok,R.K.Raina,and J.Sokól [3,Appl.Math.Comput.218 (2011),996-1002] is closely related to the classes of starlike and convex functions.The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.

  2. Convex functions, monotone operators and differentiability

    CERN Document Server

    Phelps, Robert R

    1989-01-01

    These notes start with an introduction to the differentiability of convex functions on Banach spaces, leading to the study of Asplund spaces and their intriguing relationship to monotone operators (and more general set-values maps) and Banach spaces with the Radon-Nikodym property. While much of this is classical, some of it is presented using streamlined proofs which were not available until recently. Considerable attention is paid to contemporary results on variational principles and perturbed optimization in Banach spaces, exhibiting their close connections with Asplund spaces. An introductory course in functional analysis is adequate background for reading these notes which can serve as the basis for a seminar of a one-term graduate course. There are numerous excercises, many of which form an integral part of the exposition.

  3. ANALYSIS TO NEYMAN-PEARSON CLASSIFICATION WITH CONVEX LOSS FUNCTION

    Institute of Scientific and Technical Information of China (English)

    Min Han; Dirong Chen; Zhaoxu Sun

    2008-01-01

    Neyman-Pearson classification has been studied in several articles before.But they all proceeded in the classes of indicator functions with indicator function as the loss function,which make the calculation to be difficult.This paper investigates NeymanPearson classification with convex loss function in the arbitrary class of real measurable functions.A general condition is given under which Neyman-Pearson classification with convex loss function has the same classifier as that with indicator loss function.We give analysis to NP-ERM with convex loss function and prove it's performance guarantees.An example of complexity penalty pair about convex loss function risk in terms of Rademacher averages is studied,which produces a tight PAC bound of the NP-ERM with convex loss function.

  4. Foundations of complex analysis in non locally convex spaces function theory without convexity condition

    CERN Document Server

    Bayoumi, A

    2003-01-01

    All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field. Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-convex and

  5. Trace-Inequalities and Matrix-Convex Functions

    Directory of Open Access Journals (Sweden)

    Ando Tsuyoshi

    2010-01-01

    Full Text Available Abstract A real-valued continuous function on an interval gives rise to a map via functional calculus from the convex set of Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provided with the order structure induced by the cone of positive semidefinite matrices, one can consider convexity of this map. We will characterize its convexity by the following trace-inequalities: for . A related topic will be also discussed.

  6. Convex functions and optimization methods on Riemannian manifolds

    CERN Document Server

    Udrişte, Constantin

    1994-01-01

    This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...

  7. Simple sufficient conditions for starlikeness and convexity for meromorphic functions

    Directory of Open Access Journals (Sweden)

    Goswami Pranay

    2016-01-01

    Full Text Available In this paper we investigate some extensions of sufficient conditions for meromorphic multivalent functions in the open unit disk to be meromorphic multivalent starlike and convex of order α. Our results unify and extend some starlikeness and convexity conditions for meromorphic multivalent functions obtained by Xu et al. [2], and some interesting special cases are given.

  8. Gradient of the Value Function in Parametric Convex Optimization Problems

    OpenAIRE

    Baotić, Mato

    2016-01-01

    We investigate the computation of the gradient of the value function in parametric convex optimization problems. We derive general expression for the gradient of the value function in terms of the cost function, constraints and Lagrange multipliers. In particular, we show that for the strictly convex parametric quadratic program the value function is continuously differentiable at every point in the interior of feasible space for which the Linear Independent Constraint Qualification holds.

  9. Differential subordination for meromorphic multivalent quasi-convex functions

    OpenAIRE

    R. W. Ibrahim; M. Darus

    2010-01-01

    We introduce new classes of meromorphic multivalent quasi-convex functions and find some sufficient differential subordination theorems for such classes in punctured unit disk with applications in fractional calculus.

  10. Differential subordination for meromorphic multivalent quasi-convex functions

    Directory of Open Access Journals (Sweden)

    R. W. Ibrahim

    2010-02-01

    Full Text Available We introduce new classes of meromorphic multivalent quasi-convex functions and find some sufficient differential subordination theorems for such classes in punctured unit disk with applications in fractional calculus.

  11. Lipschitz estimates for convex functions with respect to vector fields

    Directory of Open Access Journals (Sweden)

    Valentino Magnani

    2012-12-01

    Full Text Available We present Lipschitz continuity estimates for a class of convex functions with respect to Hörmander vector fields. These results have been recently obtained in collaboration with M. Scienza, [22].

  12. Properties of distance functions on convex surfaces and Alexandrov spaces

    CERN Document Server

    Rataj, Jan

    2009-01-01

    If $X$ is a convex surface in a Euclidean space, then the squared (intrinsic) distance function $\\dist^2(x,y)$ is d.c. (DC, delta-convex) on $X\\times X$ in the only natural extrinsic sense. For the proof we use semiconcavity (in an intrinsic sense) of $\\dist^2(x,y)$ on $X \\times X$ if $X$ is an Alexandrov space with nonnegative curvature. Applications concerning $r$-boundaries (distance spheres) and the ambiguous locus (exoskeleton) of a closed subset of a convex surface are given.

  13. Nonparametric estimation of a convex bathtub-shaped hazard function.

    Science.gov (United States)

    Jankowski, Hanna K; Wellner, Jon A

    2009-11-01

    In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of n(2/5) at points x(0) where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. One notable feature of the nonparametric MLE studied here is that no arbitrary choice of tuning parameter (or complicated data-adaptive selection of the tuning parameter) is required.

  14. Nonparametric Least Squares Estimation of a Multivariate Convex Regression Function

    CERN Document Server

    Seijo, Emilio

    2010-01-01

    This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. Mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided. We also consider a regression function which is known to be convex and componentwise nonincreasing and discuss the characterization, computation and consistency of its least squares estimator.

  15. Schur convexity for a class of symmetric functions

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    The Schur convexity and concavity of a class of symmetric functions are discussed, and an open problem proposed by Guan in "Some properties of a class of symmetric functions" is answered. As consequences, some inequalities are established by use of the theory of majorization.

  16. On Certain Subclass of Meromorphic Close-to-Convex Functions

    Directory of Open Access Journals (Sweden)

    Goyal S.P.

    2013-05-01

    Full Text Available In this paper we introduce and investigate a certain subclass of functions which are analytic in the punctured unit disk and meromorphically close-to-convex. The sub-ordination property, inclusion relationship, coefficient inequalities, distortion theorem and a sufficient condition for our subclass of functions are derived. The results presented here would provide extensions of those given in earlier works.

  17. Trace-Inequalities and Matrix-Convex Functions

    Directory of Open Access Journals (Sweden)

    Tsuyoshi Ando

    2010-01-01

    Full Text Available A real-valued continuous function f(t on an interval (α,β gives rise to a map X↦f(X via functional calculus from the convex set of n×n Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provided with the order structure induced by the cone of positive semidefinite matrices, one can consider convexity of this map. We will characterize its convexity by the following trace-inequalities: Tr(f(B−f(A(C−B≤Tr(f(C−f(B(B−A for A≤B≤C. A related topic will be also discussed.

  18. Widths of some classes of convex functions and bodies

    Science.gov (United States)

    Konovalov, V. N.; Maiorov, Vitalii E.

    2010-02-01

    We consider classes of uniformly bounded convex functions defined on convex compact bodies in \\mathbb{R}^d and satisfying a Lipschitz condition and establish the exact orders of their Kolmogorov, entropy, and pseudo-dimension widths in the L_1-metric. We also introduce the notions of pseudo-dimension and pseudo-dimension widths for classes of sets and determine the exact orders of the entropy and pseudo-dimension widths of some classes of convex bodies in \\mathbb{R}^drelative to the pseudo-metric defined as the d-dimensional Lebesgue volume of the symmetric difference of two sets. We also find the exact orders of the entropy and pseudo-dimension widths of the corresponding classes of characteristic functions in L_p-spaces, 1\\le p\\le\\infty.

  19. A subclass of close-to-convex functions

    Directory of Open Access Journals (Sweden)

    Zheng- Lv Zhang

    2013-03-01

    Full Text Available In this paper, we introduce and investigate an interesting subclass $\\mathcal {J}_\\alpha(h$ of analytic and close-to-convex function in the open unit disk D. several coefficient inequalities, growth, and distortion theorem for this class are proved. The various results presented here would generalize many know results.

  20. Parametric R-norm directed-divergence convex function

    Science.gov (United States)

    Garg, Dhanesh; Kumar, Satish

    2016-06-01

    In this paper, we define parametric R-norm directed-divergence convex function and discuss their special cases and prove some properties similar to Kullback-Leibler information measure. From R-norm divergence measure new information measures have also been derived and their relations with different measures of entropy have been obtained and give its application in industrial engineering.

  1. A parameter-dependent refinement of the discrete Jensen's inequality for convex and mid-convex functions

    Directory of Open Access Journals (Sweden)

    Horváth László

    2011-01-01

    Full Text Available Abstract In this paper, a new parameter-dependent refinement of the discrete Jensen's inequality is given for convex and mid-convex functions. The convergence of the introduced sequences is also studied. One of the proofs requires an interesting convergence theorem with probability theoretical background. We apply the results to define some new quasi-arithmetic and mixed symmetric means and study their monotonicity and convergence.

  2. Some Hermite–Hadamard Type Inequalities for Geometrically Quasi-Convex Functions

    Indian Academy of Sciences (India)

    Feng Qi; Bo-Yan Xi

    2014-08-01

    In the paper, we introduce a new concept ‘geometrically quasi-convex function’ and establish some Hermite–Hadamard type inequalities for functions whose derivatives are of geometric quasi-convexity.

  3. APPROXIMATION OF CONVEX TYPE FUNCTION BY PARTIAL SUMS OF FOURIER SERIES

    Institute of Scientific and Technical Information of China (English)

    YuGuohua

    2004-01-01

    The concept of convex type function is introduced in this paper,from which a kind of convex-decomposition approach is proposed. As one of applications of this approach, the approximation of the convex type function by the partial sum of its Fourier series is investigated. Moreover,the order of approximation is described with the 2th continuous modulus.

  4. Undergraduate Convexity

    DEFF Research Database (Denmark)

    Lauritzen, Niels

    -Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point...

  5. An efficient method for minimizing a convex separable logarithmic function subject to a convex inequality constraint or linear equality constraint

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available We consider the problem of minimizing a convex separable logarithmic function over a region defined by a convex inequality constraint or linear equality constraint, and two-sided bounds on the variables (box constraints. Such problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems as well as in various practical problems such as problems of production planning and scheduling, allocation of resources, decision making, facility location problems, and so forth. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.

  6. A Generalization on Weighted Means and Convex Functions with respect to the Non-Newtonian Calculus

    Directory of Open Access Journals (Sweden)

    Uğur Kadak

    2016-01-01

    Full Text Available This paper is devoted to investigating some characteristic features of weighted means and convex functions in terms of the non-Newtonian calculus which is a self-contained system independent of any other system of calculus. It is shown that there are infinitely many such useful types of weighted means and convex functions depending on the choice of generating functions. Moreover, some relations between classical weighted mean and its non-Newtonian version are compared and discussed in a table. Also, some geometric interpretations of convex functions are presented with respect to the non-Newtonian slope. Finally, using multiplicative continuous convex functions we give an application.

  7. Off-Grid DOA Estimation Based on Analysis of the Convexity of Maximum Likelihood Function

    Science.gov (United States)

    LIU, Liang; WEI, Ping; LIAO, Hong Shu

    Spatial compressive sensing (SCS) has recently been applied to direction-of-arrival (DOA) estimation owing to advantages over conventional ones. However the performance of compressive sensing (CS)-based estimation methods decreases when true DOAs are not exactly on the discretized sampling grid. We solve the off-grid DOA estimation problem using the deterministic maximum likelihood (DML) estimation method. In this work, we analyze the convexity of the DML function in the vicinity of the global solution. Especially under the condition of large array, we search for an approximately convex range around the ture DOAs to guarantee the DML function convex. Based on the convexity of the DML function, we propose a computationally efficient algorithm framework for off-grid DOA estimation. Numerical experiments show that the rough convex range accords well with the exact convex range of the DML function with large array and demonstrate the superior performance of the proposed methods in terms of accuracy, robustness and speed.

  8. Applications of fractional calculus to $ k $-uniformly starlike and $ k $-uniformly convex functions of order $ \\alpha $

    Directory of Open Access Journals (Sweden)

    Ajab Akbarally

    2007-06-01

    Full Text Available A new subclass of analytic functions $ k-SP_\\lambda(\\alpha $ is introduced by applying certain operators of fractional calculus to $k$-uniformly starlike and $ k $-uniformly convex functions of order $ \\alpha $. Some theorems on coefficient bounds and growth and distortion theorems for this subclass are found. The radii of close to convexity, starlikeness and convexity for this subclass is also derived.

  9. Matrix convex functions with applications to weighted centers for semidefinite programming

    NARCIS (Netherlands)

    J. Brinkhuis (Jan); Z-Q. Luo; S. Zhang (Shuzhong)

    2005-01-01

    textabstractIn this paper, we develop various calculus rules for general smooth matrix-valued functions and for the class of matrix convex (or concave) functions first introduced by Loewner and Kraus in 1930s. Then we use these calculus rules and the matrix convex function -log X to study a new

  10. Shape Preserving Positive and Convex Data Visualization using Rational Bi-cubic Functions

    Directory of Open Access Journals (Sweden)

    Tahira Sumbal Shaikh

    2012-01-01

    Full Text Available This paper is concerned with the problem of positive and convex data visualization in the form of positive and convex surfaces. A rational bi-cubic partially blended function with eight free parameters in its description is introduced and applied to visualize the shape of positive data and convex data. The developed schemes in this paper have unique representations. Visual models of surfaces attain  smoothness.  

  11. Hermite-Hadamard type inequalities for GA-s-convex functions

    Directory of Open Access Journals (Sweden)

    İmdat İşcan

    2014-10-01

    Full Text Available In this paper, The author introduces the concepts of the GA-s-convex functions in the first sense and second sense and establishes some integral inequalities of Hermite-Hadamard type related to the GA-s-convex functions. Some applications to special means of real numbers are also given.

  12. Inequalities of Hadamard Type for r-Convex Functions in Carnot Groups

    Institute of Scientific and Technical Information of China (English)

    Ming-bao Sun; Xiao-ping Yang

    2004-01-01

    For a Carnot group G,we establish the relationship between extended mean values and r-convex functions which is introduced in this paper,which is a class of inequalities of Hadamard type for r-convex function on G.

  13. On the minima and convexity of Epstein zeta function

    Science.gov (United States)

    Lim, S. C.; Teo, L. P.

    2008-07-01

    Let Zn(s ;a1,…,an) be the Epstein zeta function defined as the meromorphic continuation of the function ∑k εZn{0}(∑i =1n[aiki]2)-s, Re s>n/2 to the complex plane. We show that for fixed s ≠n/2, the function Zn(s ;a1,…,an) as a function of (a1,…,an)ε(R+)n with fixed ∏i =1nai has a unique minimum at the point a1=⋯=an. When ∑i =1nci is fixed, the function (c1,…,cn)↦Zn(s ;ec1,…,ecn) can be shown to be a convex function of any (n -1) of the variables {c1,…,cn}. These results are then applied to the study of the sign of Zn(s ;a1,…,an) when s is in the critical range (0,n/2). It is shown that when 1≤n≤9, Zn(s ;a1,…,an) as a function of (a1,…,an)ε(R+)n can be both positive and negative for every s ε(0,n/2). When n ≥10, there are some open subsets In,+ of s ε(0,n/2), where Zn(s ;a1,…,an) is positive for all (a1,…,an)ε(R+)n. By regarding Zn(s ;a1,…,an) as a function of s, we find that when n ≥10, the generalized Riemann hypothesis is false for all (a1,…,an).

  14. Calibration of Field II using a Convex Ultrasound Transducer

    DEFF Research Database (Denmark)

    Bæk, David; Jensen, Jørgen Arendt; Willatzen, Morten

    2010-01-01

    Field II is an ultrasound simulation program capable of simulating the pressure scattering from inhomogeneous tissue. The simulations are based on a convolution between spatial impulse responses from the field in front of the transducer and the volt-to-surface acceleration impulse response...... of the transducer. For such simulations to reflect actual measured intensities and pressure levels, the transducer impulse response is to be known. This work presents the results of combining a modified form of a 1D linear transducer model originally suggested by Willatzen with the Field II program to calibrate...... BK-Medical (Herlev, Denmark). As input waveform for the Field model we measured the output voltage of the research amplifier, which peak voltage was limited to 31 V to avoid too high non linear effects. We measured the hydrophone output from three transducer front elements by averaging 40 shoot...

  15. On Convex Hull of Orthogonal Scalar Spectral Functions of a Carleman Operator

    Directory of Open Access Journals (Sweden)

    S. M. Bahri

    2008-11-01

    Full Text Available In this paper we describe the closed convex hull of orthogonal resolvents of an abstract symmetric operator of defect indices (1; 1, then we study the convex hull of orthogonal spectral functions of a Carleman operator in the Hilbert space L^2(X;mu.

  16. On Certain New Subclass of Meromorphic Close-to-Convex Functions

    Directory of Open Access Journals (Sweden)

    Jing-Ping Yi

    2013-01-01

    Full Text Available We introduce a certain new subclass of meromorphic close-to-convex functions. Such results as inclusion relationship, coefficient inequalities, distortion, and growth theorems for this class of functions are derived.

  17. Some Fejer Type Inequalities for Harmonically-Convex Functions with Applications to Special Means

    Directory of Open Access Journals (Sweden)

    M. A. Latif

    2017-01-01

    Full Text Available In this paper, the notion of harmonic symmetricity of functions is introduced. A new identity involving harmonically symmetric functions is established and some new Fejer type integral inequalities are presented for the class of harmonically convex functions. The results presented in this paper are better than those established in recent literature concerning harmonically convex functions. Applications of our results to special means of positive real numbers are given as well.

  18. A Generalization on Weighted Means and Convex Functions with respect to the Non-Newtonian Calculus

    OpenAIRE

    Uğur Kadak; Yusuf Gürefe

    2016-01-01

    This paper is devoted to investigating some characteristic features of weighted means and convex functions in terms of the non-Newtonian calculus which is a self-contained system independent of any other system of calculus. It is shown that there are infinitely many such useful types of weighted means and convex functions depending on the choice of generating functions. Moreover, some relations between classical weighted mean and its non-Newtonian version are compared and discussed in a table...

  19. On Convex Quadratic Approximation

    NARCIS (Netherlands)

    den Hertog, D.; de Klerk, E.; Roos, J.

    2000-01-01

    In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

  20. On Convex Quadratic Approximation

    NARCIS (Netherlands)

    den Hertog, D.; de Klerk, E.; Roos, J.

    2000-01-01

    In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

  1. Assessing 3-D Uncertain System Stability by Using MATLAB Convex Hull Functions

    OpenAIRE

    Mohammed Tawfik Hussein

    2011-01-01

    This paper is dealing with the robust stability of an uncertain three dimensional (3-D) system using existence MATLAB convex hull functions. Hence, the uncertain model of plant will be simulated by INTLAB Toolbox; furthermore, the root loci of the characteristic polynomials of the convex hull are obtained to judge whether the uncertain system is stable or not. A design third order example for uncertain parameters is given to validate the proposed approach.

  2. Local Uniform Convexity and Kadec-Klee Type Properties in K-interpolation spaces II

    Directory of Open Access Journals (Sweden)

    Peter G. Dodds

    2004-01-01

    Full Text Available We study local uniform convexity and Kadec-Klee type properties in K-interpolation spaces of Lorentz couples. We show that a wide class of Banach couples of (commutative and non-commutative Lorentz spaces possess the (so-alled (DGL-property originally introduced by Davis, Ghoussoub and Lindenstrauss in the context of renorming order continuous Banach latties. This property is used as a key tool to show that local uniform convexity and certain Kadec-Klee type properties in non-commutative symmetric spaces of measurable operators may be inferred from corresponding properties of the parameter space of the K-interpolation method. Further applications are given to renorming properties of separable symmetric Banach function spaces and their non-commutative counterparts.

  3. On the convex hull of the simple integer recourse objective function

    NARCIS (Netherlands)

    Klein Haneveld, Willem K.; Stougie, L.; van der Vlerk, Maarten H.

    1995-01-01

    We consider the objective function of a simple integer recourse problem with fixed technology matrix. Using properties of the expected value function, we prove a relation between the convex hull of this function and the expected value function of a continuous simple recourse program. We present an

  4. On the convex hull of the simple integer recourse objective function

    NARCIS (Netherlands)

    Klein Haneveld, Willem K.; Stougie, L.; van der Vlerk, Maarten H.

    1995-01-01

    We consider the objective function of a simple integer recourse problem with fixed technology matrix. Using properties of the expected value function, we prove a relation between the convex hull of this function and the expected value function of a continuous simple recourse program. We present an a

  5. An O(n invariant rank 1 convex function that is not polyconvex

    Directory of Open Access Journals (Sweden)

    Silhavy M.

    2002-01-01

    Full Text Available An O(n invariant nonnegative rank 1 convex function of linear growth is given that is not polyconvex. This answers a recent question [8, p. 182] and [5]. The polyconvex hull of the function is calculated explicitly if n = 2: .

  6. Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions

    Directory of Open Access Journals (Sweden)

    İmdat İşcan

    2014-01-01

    Full Text Available A new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite-Hadamard and Simpson-like types for functions whose derivatives in absolute value at certain power are harmonically convex. Some applications to special means of real numbers are also given.

  7. Applying GG-Convex Function to Hermite-Hadamard Inequalities Involving Hadamard Fractional Integrals

    Directory of Open Access Journals (Sweden)

    Zhi Zhang

    2014-01-01

    Full Text Available By virtue of fractional integral identities, incomplete beta function, useful series, and inequalities, we apply the concept of GG-convex function to derive new type Hermite-Hadamard inequalities involving Hadamard fractional integrals. Finally, some applications to special means of real numbers are demonstrated.

  8. Parameter sensitivity study of a Field II multilayer transducer model on a convex transducer

    DEFF Research Database (Denmark)

    Bæk, David; Jensen, Jørgen Arendt; Willatzen, Morten

    2009-01-01

    .ResultsPredictions using the ZR give a pressure pulse error (PPE) and an intensity error (IE) of 32 % and 23 %, respectively, relative to the measured. Altering the piezoelectric permittivity +12 % from ZR decreases the PPE to 30 % and the IE to 2 % relative to the measured. Changing the stiffness constant of the lens -4......A multilayer transducer model for predicting a transducer impulse response has in earlier works been developed and combined with the Field II software. This development was tested on current, voltage, and intensity measurements on piezoceramics discs (Bæk et al. IUS 2008) and a convex 128 element...... ultrasound imaging transducer (Bæk et al. ICU 2009). The model benefits from its 1D simplicity and hasshown to give an amplitude error around 1.7‐2 dB. However, any prediction of amplitude, phase, and attenuation of pulses relies on the accuracy of manufacturer supplied material characteristics, which may...

  9. Domains of variability of Laurent coefficients and the convex hull for the family of concave univalent functions

    CERN Document Server

    Bhowmik, B; Wirths, K-J

    2010-01-01

    Let $\\ID$ denote the open unit disc and let $p\\in (0,1)$. We consider the family $Co(p)$ of functions $f:\\ID\\to \\overline{\\IC}$ that satisfy the following conditions: \\bee \\item[(i)] $f$ is meromorphic in $\\ID$ and has a simple pole at the point $p$. \\item[(ii)] $f(0)=f'(0)-1=0$. \\item[(iii)] $f$ maps $\\ID$ conformally onto a set whose complement with respect to $\\overline{\\IC}$ is convex. \\eee We determine the exact domains of variability of some coefficients $a_n(f)$ of the Laurent expansion

  10. Schur-Convexity for a Class of Symmetric Functions and Its Applications

    Directory of Open Access Journals (Sweden)

    Wei-Feng Xia

    2009-01-01

    Full Text Available For x=(x1,x2,…,xn∈R+n, the symmetric function ϕn(x,r is defined by ϕn(x,r=ϕn(x1,x2,…,xn;r=∏1≤i1convexity, Schur multiplicative convexity and Schur harmonic convexity of ϕn(x,r are discussed. As applications, some inequalities are established by use of the theory of majorization.

  11. The Distortion Theorems for Harmonic Mappings with Analytic Parts Convex or Starlike Functions of Order β

    Directory of Open Access Journals (Sweden)

    Mengkun Zhu

    2015-01-01

    Full Text Available Some sharp estimates of coefficients, distortion, and growth for harmonic mappings with analytic parts convex or starlike functions of order β are obtained. We also give area estimates and covering theorems. Our main results generalise those of Klimek and Michalski.

  12. Phase retrieval for characteristic functions of convex bodies and reconstruction from covariograms

    DEFF Research Database (Denmark)

    Bianchi, Gabriele; Gardner, Richard; Kiderlen, Markus

    2011-01-01

    We propose strongly consistent algorithms for reconstructing the characteristic function $ 1_K$ of an unknown convex body $ K$ in $ \\mathbb{R}^n$ from possibly noisy measurements of the modulus of its Fourier transform $ \\widehat{1_K}$. This represents a complete theoretical solution to the Phase...

  13. A Generalized Hermite-Hadamard Inequality for Coordinated Convex Function and Some Associated Mappings

    Directory of Open Access Journals (Sweden)

    Atiq Ur Rehman

    2016-01-01

    Full Text Available We have discussed the generalization of Hermite-Hadamard inequality introduced by Lupaş for convex functions on coordinates defined in a rectangle from the plane. Also we define that mappings are related to it and their properties are discussed.

  14. Convexity of the integral operator involving normalized Mittag-Leffler function

    Science.gov (United States)

    Ćaǧlar, Murat; Yılmaz, Saip Emre; Deniz, Erhan

    2017-04-01

    The main object of this paper is to give sufficient condition for a certain family of integral operator which are defined by means of the normalized form of the Mittag-Leffler function to be convex of given order in the open unit disk.

  15. Neighborhoods of Starlike and Convex Functions Associated with Parabola

    Directory of Open Access Journals (Sweden)

    Ravichandran V

    2008-01-01

    Full Text Available Abstract Let be a normalized analytic function defined on the unit disk and for . For , a function if lies in the parabolic region . Let be the corresponding class consisting of functions such that lies in the region . For an appropriate , the -neighbourhood of a function is shown to consist of functions in the class .

  16. Convexity properties of generalized trigonometric and hyperbolic functions

    OpenAIRE

    Baricz, Árpád; Bhayo, Barkat Ali; Klén, Riku

    2013-01-01

    We study the power mean inequality of the generalized trigonometric and hyperbolic functions with two parameters. The generalized $p$-trigonometric and $(p, q)$-trigonometric functions were introduced by P. Lindqvist and S. Takeuchi, respectively.

  17. On subclasses of close-to-convex functions of higher order

    Directory of Open Access Journals (Sweden)

    Khalida Inayat Noor

    1992-01-01

    Full Text Available The classes Tk(ρ, 0≤ρ<1, k≥2, of analytic functions, using the class Vk(ρ of functions of bounded boundary rotation, are defined and it is shown that the functions in these classes are close-to-convex of higher order. Covering theorem, arc-length result and some radii problems are solved. We also discuss some properties of the class Vk(ρ including distortion and coefficient results.

  18. Convexity of Energy-Like Functions: Theoretical Results and Applications to Power System Operations

    Energy Technology Data Exchange (ETDEWEB)

    Dvijotham, Krishnamurthy [California Inst. of Technology (CalTech), Pasadena, CA (United States); Low, Steven [California Inst. of Technology (CalTech), Pasadena, CA (United States); Chertkov, Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-01-12

    Power systems are undergoing unprecedented transformations with increased adoption of renewables and distributed generation, as well as the adoption of demand response programs. All of these changes, while making the grid more responsive and potentially more efficient, pose significant challenges for power systems operators. Conventional operational paradigms are no longer sufficient as the power system may no longer have big dispatchable generators with sufficient positive and negative reserves. This increases the need for tools and algorithms that can efficiently predict safe regions of operation of the power system. In this paper, we study energy functions as a tool to design algorithms for various operational problems in power systems. These have a long history in power systems and have been primarily applied to transient stability problems. In this paper, we take a new look at power systems, focusing on an aspect that has previously received little attention: Convexity. We characterize the domain of voltage magnitudes and phases within which the energy function is convex in these variables. We show that this corresponds naturally with standard operational constraints imposed in power systems. We show that power of equations can be solved using this approach, as long as the solution lies within the convexity domain. We outline various desirable properties of solutions in the convexity domain and present simple numerical illustrations supporting our results.

  19. Convexity of Energy-Like Functions: Theoretical Results and Applications to Power System Operations

    Energy Technology Data Exchange (ETDEWEB)

    Dvijotham, Krishnamurthy [California Inst. of Technology (CalTech), Pasadena, CA (United States); Chertkov, Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Low, Steven [California Inst. of Technology (CalTech), Pasadena, CA (United States)

    2015-01-22

    Power systems are undergoing unprecedented transformations with increased adoption of renewables and distributed generation, as well as the adoption of demand response programs. All of these changes, while making the grid more responsive and potentially more efficient, pose significant challenges for power systems operators. Conventional operational paradigms are no longer sufficient as the power system may no longer have big dispatchable generators with sufficient positive and negative reserves. This increases the need for tools and algorithms that can efficiently predict safe regions of operation of the power system. In this paper, we study energy functions as a tool to design algorithms for various operational problems in power systems. These have a long history in power systems and have been primarily applied to transient stability problems. In this paper, we take a new look at power systems, focusing on an aspect that has previously received little attention: Convexity. We characterize the domain of voltage magnitudes and phases within which the energy function is convex in these variables. We show that this corresponds naturally with standard operational constraints imposed in power systems. We show that power of equations can be solved using this approach, as long as the solution lies within the convexity domain. We outline various desirable properties of solutions in the convexity domain and present simple numerical illustrations supporting our results.

  20. Special function related to the concave-convex boundary problem of the diffraction theory

    CERN Document Server

    Kazakov, A Y

    2003-01-01

    The concave-convex boundary problem of the diffraction theory is studied. It corresponds to the scattering of a whispering gallery mode on the point of inflection of the boundary. A new special function related to this boundary problem is introduced and its particular properties are discussed. This special function is defined as a contour integral on the complex plane and its behaviour in different domains of parameters is considered.

  1. Neighborhoods of Starlike and Convex Functions Associated with Parabola

    Directory of Open Access Journals (Sweden)

    Om P. Ahuja

    2008-09-01

    Full Text Available Let f be a normalized analytic function defined on the unit disk and fλ(z:=(1−λz+λf(z for 00, a function f∈𝒮𝒫(α,λ if zf′(z/fλ(z lies in the parabolic region Ω:={w:|w−α|0, the δ-neighbourhood of a function f∈𝒞𝒫(α,λ is shown to consist of functions in the class 𝒮𝒫(α,λ.

  2. ON α-CONVEX FUNCTIONS WITH MISSING COEFFICIENTS

    Institute of Scientific and Technical Information of China (English)

    杨定恭

    1990-01-01

    Let Jn(α,A,B),α≥0,-1≤Bfunctions f(z)=z+∑k=n+1∞αkZk which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))-<1+Az/1+Bz for z∈E.In this paper we obtain incluion relations,distortion properties and estimates of |αn+2-λα2n+1| for the class Jn(α,A,B),where λ is complex.

  3. Supply Chain Coordination with Demand Disruptions under Convex Production Cost Function

    Institute of Scientific and Technical Information of China (English)

    XU Ming-hui; GAO Cheng-xiu

    2005-01-01

    This paper investigates the problem of how to handling demand disruptions in a one-supplier-one-retailer supply chain, where production cost is a convex function of production quantity andprice-demand relationship is linear. Our results show that, if demand is disrupted, under the new price-demand relationship, all-unit wholesale quantity discount policies combining capacitated linear pricingpolicies can also fully coordinate the supply chain.

  4. Finsler geodesics in the presence of a convex function and their applications

    Energy Technology Data Exchange (ETDEWEB)

    Caponio, Erasmo; Masiello, Antonio [Dipartimento di Matematica, Politecnico di Bari, Via Orabona 4, 70125 Bari (Italy); Javaloyes, Miguel Angel [Departamento de GeometrIa y TopologIa, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva s/n, 18071 Granada (Spain)], E-mail: caponio@poliba.it, E-mail: ma.javaloyes@gmail.com, E-mail: majava@ugr.es, E-mail: masiello@poliba.it

    2010-04-24

    In this paper, we obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.

  5. Some Convex Functions Based Measures of Independence and Their Application to Strange Attractor Reconstruction

    Directory of Open Access Journals (Sweden)

    Kazuyuki Aihara

    2011-04-01

    Full Text Available The classical information-theoretic measures such as the entropy and the mutual information (MI are widely applicable to many areas in science and engineering. Csiszar generalized the entropy and the MI by using the convex functions. Recently, we proposed the grid occupancy (GO and the quasientropy (QE as measures of independence. The QE explicitly includes a convex function in its definition, while the expectation of GO is a subclass of QE. In this paper, we study the effect of different convex functions on GO, QE, and Csiszar’s generalized mutual information (GMI. A quality factor (QF is proposed to quantify the sharpness of their minima. Using the QF, it is shown that these measures can have sharper minima than the classical MI. Besides, a recursive algorithm for computing GMI, which is a generalization of Fraser and Swinney’s algorithm for computing MI, is proposed. Moreover, we apply GO, QE, and GMI to chaotic time series analysis. It is shown that these measures are good criteria for determining the optimum delay in strange attractor reconstruction.

  6. Functional analysis and applied optimization in Banach spaces applications to non-convex variational models

    CERN Document Server

    Botelho, Fabio

    2014-01-01

    This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.

  7. Convex objective function-based design method developed for minimizing side lobe.

    Science.gov (United States)

    Liu, Jian; Tan, Jiubin; Zhao, Chenguang

    2008-08-01

    The existence of multiple local solutions makes it very difficult to search for filter parameters to achieve a desired side lobe level during the design of superresolution pupil filters. To deal with the difficult issue of side lobe control in the designing process, a convex objective function-based design method is developed through phase rotation and variable replacement to transform the complicated solving process with multiextreme subintervals into a simple optimization process with a convex interval. A group of constant annular complex superresolving filters are designed using the developed method. The comparison of the superresolving filters designed in this way with the well-known continuous phase filter and 3-zone multiphase diffractive superresolution filters proves the validity of the developed method.

  8. APPROXIMATION OF CONVEX TYPE FUNCTION BY PARTIAL SUMS OF FOURIER SERIES%Fourier级数部分和对凸型函数的逼近

    Institute of Scientific and Technical Information of China (English)

    俞国华

    2004-01-01

    The concept of convex type function is introduced in this paper,from which a kind of convex-decomposition approach is proposed. As one of applications of this approach, the approximation of the convex type function by the partial sum of its Fourier series is investigated. Moreover,the order of approximation is described with the 2th continuous modulus.

  9. Generalizations on Some Hermite-Hadamard Type Inequalities for Differentiable Convex Functions with Applications to Weighted Means

    Directory of Open Access Journals (Sweden)

    Banyat Sroysang

    2014-01-01

    Full Text Available Some new Hermite-Hadamard type inequalities for differentiable convex functions were presented by Xi and Qi. In this paper, we present new generalizations on the Xi-Qi inequalities.

  10. Coefficient Estimates for Certain Subclasses of Bi-Univalent Ma-Minda Mocanu-Convex Functions

    Institute of Scientific and Technical Information of China (English)

    C.Selvaraj; O.S.Babu; G.Murugusundaramoorthy

    2014-01-01

    In this paper, we introduce and investigate a new subclass of the function classΣof bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Sev-eral (known or new) consequences of the results are also pointed out.

  11. Characterization of subdifferentials of a singular convex functional in Sobolev spaces of order minus one

    CERN Document Server

    Kashima, Yohei

    2011-01-01

    Subdifferentials of a singular convex functional representing the surface free energy of a crystal under the roughening temperature are characterized. The energy functional is defined on Sobolev spaces of order -1, so the subdifferential mathematically formulates the energy's gradient which formally involves 4th order spacial derivatives of the surface's height. The subdifferentials are analyzed in the negative Sobolev spaces of arbitrary spacial dimension on which both a periodic boundary condition and a Dirichlet boundary condition are separately imposed. Based on the characterization theorem of subdifferentials, the smallest element contained in the subdifferential of the energy for a spherically symmetric surface is calculated under the Dirichlet boundary condition.

  12. An inequality for convex functionals and its application to a maxwellian gas

    Directory of Open Access Journals (Sweden)

    G. Toscani

    1991-05-01

    Full Text Available We study the trend towards equilibrium of the solution of the spatially homogeneous Boltzmann equation for a gas of Maxwellian molecules. The cases of axially symmetric and plane initial densities are investigated. In these situations, the strong L1 convergence to equilibrium follows by a suitable use of some convex and isotropic functionals, with monotonic behaviour in time along the solution. The initial density is required to have finite energy and entropy. It is shown that the functionals satisfy a common convolution inequality.

  13. Construction of convex solutions for the second type of Feigenbaum’s functional equations

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    In this paper, convex solutions for the second type of Feigenbaum’s equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1-convex solutions and C2-convex solutions of the above equation.

  14. Convex functions and some inequalities in terms of the Non-Newtonian Calculus

    Science.gov (United States)

    Unluyol, Erdal; Salas, Seren; Iscan, Imdat

    2017-04-01

    Differentiation and integration are basic operations of calculus and analysis. Indeed, they are many versions of the subtraction and addition operations on numbers, respectively. From 1967 till 1970 Michael Grossman and Robert Katz [1] gave definitions of a new kind of derivative and integral, converting the roles of subtraction and addition into division and multiplication, and thus establish a new calculus, called Non-Newtonian Calculus. So, in this paper, it is investigated to the convex functions and some inequalities in terms of Non-Newtonian Calculus. Then we compare with the Newtonian and Non-Newtonian Calculus.

  15. Convexity Adjustments

    DEFF Research Database (Denmark)

    M. Gaspar, Raquel; Murgoci, Agatha

    2010-01-01

    of particular importance to practitioners: yield convexity adjustments, forward versus futures convexity adjustments, timing and quanto convexity adjustments. We claim that the appropriate way to look into any of these adjustments is as a side effect of a measure change, as proposed by Pelsser (2003...

  16. Strict convexity and C 1, α regularity of potential functions in optimal transportation under condition A3w

    Science.gov (United States)

    Chen, Shibing; Wang, Xu-Jia

    2016-01-01

    In this paper we prove the strict c-convexity and the C 1, α regularity for potential functions in optimal transportation under condition (A3w). These results were obtained by Caffarelli [1,3,4] for the cost c (x, y) =| x - y | 2, by Liu [11], Loeper [15], Trudinger and Wang [20] for costs satisfying the condition (A3). For costs satisfying the condition (A3w), the results have also been proved by Figalli, Kim, and McCann [6], assuming that the initial and target domains are uniformly c-convex, see also [21]; and by Guillen and Kitagawa [8], assuming the cost function satisfies A3w in larger domains. In this paper we prove the strict c-convexity and the C 1, α regularity assuming either the support of source density is compactly contained in a larger domain where the cost function satisfies A3w, or the dimension 2 ≤ n ≤ 4.

  17. A Novel Gradient Vector Flow Snake Model Based on Convex Function for Infrared Image Segmentation.

    Science.gov (United States)

    Zhang, Rui; Zhu, Shiping; Zhou, Qin

    2016-10-21

    Infrared image segmentation is a challenging topic because infrared images are characterized by high noise, low contrast, and weak edges. Active contour models, especially gradient vector flow, have several advantages in terms of infrared image segmentation. However, the GVF (Gradient Vector Flow) model also has some drawbacks including a dilemma between noise smoothing and weak edge protection, which decrease the effect of infrared image segmentation significantly. In order to solve this problem, we propose a novel generalized gradient vector flow snakes model combining GGVF (Generic Gradient Vector Flow) and NBGVF (Normally Biased Gradient Vector Flow) models. We also adopt a new type of coefficients setting in the form of convex function to improve the ability of protecting weak edges while smoothing noises. Experimental results and comparisons against other methods indicate that our proposed snakes model owns better ability in terms of infrared image segmentation than other snakes models.

  18. Pseudo minimum translational distance between convex polyhedra (II) ——Robot collision-free path planning

    Institute of Scientific and Technical Information of China (English)

    ZHU; Xiangyang; DING; Han; XIONG; Youlun

    2001-01-01

    By using the pseudo minimum translational distance between convex objects, this paper presents two algorithms for robot path planning. First, an analytically tractable potential field is defined in the robot configuration space, and the concept of virtual obstacles is introduced and incorporated in the path planner to handle the local minima of the potential function. Second, based on the Lipschitz continuity and differentiability of the pseudo minimum translational distance, the flexible-trajectory approach is implemented. Simulation examples are given to show the effectiveness and efficiency of the path planners for both mobile robots and manipulators.

  19. An L0(F,R)-valued Function's Intermediate Value Theorem and Its Applications to Random Uniform Convexity

    Institute of Scientific and Technical Information of China (English)

    Tie Xin GUO; Xiao Lin ZENG

    2012-01-01

    Let (Ω,F,P) be a probability space and L0(F,R) the algebra of equivalence classes of realvalued random variables on (Ω,F,P).When L0(F,R) is endowed with the topology of convergence in probability,we prove an intermediate value theorem for a continuous local function from L0(F,R) to L0(F,R).As applications of this theorem,we first give several useful expressions for modulus of random convexity,then we prove that a complete random normed module (S,‖· ‖) is random uniformly convex itf LF(S) is uniformly convex for each fixed positive number p such that 1 < p < +oo.

  20. 由Γ-截面函数确定凸体%Determination of convex bodies from Γ-section functions

    Institute of Scientific and Technical Information of China (English)

    熊革; 马艳伟; CHEUNG Wing-sum

    2008-01-01

    In this paper, we prove that any polygon P in R2 containing a fixed smooth. strictly convex and origin-symmetric body Γ whose boundary is real analytic in its interior, can be determined by its Γ-section functions among the polygons.

  1. Carnot群上凸函数的比较原理%Comparison Principles for Convex Functions on the Carnot Group

    Institute of Scientific and Technical Information of China (English)

    李虎俊; 王彦林; 徐飞

    2011-01-01

    The monotonicity properties of convex functions on the Carnot group are important in studying the regularity of fully nonlinear subelliptic equations. Firstly, the (H)r-convex function class was introduced on the Carnot group. Then, the comparison principle of the (H). Convex functions was established by constructing auxiliary functions and using divergence theorem based on the group structure. Moreover,as an application of the result, the comparison principle of the convex functions on the higher - dimension Heisenberg group was obtained. These results are expected to provide some theoretical basis for the further study of the properties of convex functions and of the regularity of fully nonlinear equations on the Carnot group.%Carnot群上凸函数的单调性质对研究完全非线性次椭圆方程的正则性理论起关键作用.通过在Carnot群上引入(H)r-凸函数类,利用辅助函数方法并结合基于群结构的散度定理,建立了关于(H)2-凸函数的比较原理.此外,作为该结论的应用,得到了高维Heisenberg群上关于凸函数的比较原理.这些结果有望为进一步研究Carnot群上凸函数的性质和完全非线性方程的正则性提供理论基础.

  2. Application of Convex Function in Microeconomics%凸函数在微观经济学中的应用

    Institute of Scientific and Technical Information of China (English)

    陈秋涵

    2014-01-01

    先介绍了凸函数的概念与主要性质,再分析了生产函数及效用函数的特征,并对一些相关经济现象用凸函数理论作出解释。最后研究了凸函数在消费者效用最大化问题中的应用。%This paper introduces the defined notions and main properties of convex function firstly. Then there is an analysis of the characteristics of production function and utility function. Also, the paper makes explanation about some economic phenomena. Finally, study the application of convex functions in the utility maximization problem.

  3. 一个精细的Bishop-Phelps定理%An Extended and Unified Sharp Bishop-Phelps Theorem by the Subdifferential Mapping of a Convex Function

    Institute of Scientific and Technical Information of China (English)

    陈晓锋

    2003-01-01

    讨论了凸函数的次微分映射和凸集的支撑点集之间的内在关系,由此本文给出了由凸函数的次微分映射所刻划的一个精细的Bishop-Phelps定理.%Through investigating support points and support functional of a convex set and the behavior of the subdifferential mappings of convex functions, this note presents a sharp Bishop-Phelps theorem unified by the subdifferential mapping of a convex function.

  4. Equivalent Conditions for E-Convex Functions and E-Quasi Convex Functions%E-凸函数和E-拟凸函数的等价条件

    Institute of Scientific and Technical Information of China (English)

    韦丽兰; 黄雪燕

    2011-01-01

    在更弱的连续假设下研究集合Ax,y={λ∈[0,1]|f(λE(x)+(1-λ)E(y))≤λf(E(x))+(1-λ)f(E(y))}和集合Ax,y={λ∈[0,1]{f(λE(x)+(1-λ)E(y))≤max{f(E(x)),f(E(y))}}的稠密性、闭性、(弱)近似凸性,得到E-凸函数和E-拟凸函数的等价条件.%In this paper, the density,closeness and (weak) nearly convexity of the sets Ax,y = {λ ∈ [0,1] | f(λE(x) + (1 - λ)E(y)) ≤ λf(E(x)) + (1 - λ)f(E(y))} and A'x,y = {λ ∈ [0,1] | f(λE(x) + (1 - λ)E(y)) ≤ max{f(E(x), f(E(y)}} are investigated, some equivalent conditions for E-convex functions and E-quasi convex functions are derived under the weaker continuity assumptions.

  5. On new inequalities of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex with applications

    Directory of Open Access Journals (Sweden)

    Shahid Qaisar

    2014-04-01

    Full Text Available We establish some new inequalities of Hermite-Hadamard type for functions whose third derivatives absolute values are quasi-convex. Applications to special means have also been presented.

  6. Carnpt群上的r-凸函数与广义加权平均值%Generalized Weighted Mean Values and r-Convex Functions in Carnots Groups

    Institute of Scientific and Technical Information of China (English)

    孙明保; 杨孝平

    2011-01-01

    In this paper, we establish the relationship between generalized weighted mean values and r-convex functions on Carnot group G, which is a generalization of the classical Hadamard's inequality for convex functions.%该文建立了Carnot群上的r-凸函数与广义加权平均值间的关系,它们是经典凸函数的Hadamard不等式的推广.

  7. On Properties of Quasi-semi-(E, F)-Convex Functions and Quasi-semi- (E, F)-Convex Programming%拟半(E,F)-凸函数及拟半(E,F)-凸规划的性质

    Institute of Scientific and Technical Information of China (English)

    简金宝; 胡庆娟; 马鹏飞; 黎健玲

    2012-01-01

    In 2004,Jian,Hu and Tang et al (Int. J.Pure Appl. Math.,2004,14(4):439-454) introduced the concept of quasi-semi-(E,F)-convex functions.In this paper,some important properties of quasi-semi-(E,F)-convex function and the associated quasi-semi-(E,F)-convex programming are further discussed.As a result,some important results for this generalized convexity are established.%简、胡及唐等(Int.J.Pure Appl.Math.,2004,14(4):439-454)于2004年提出了拟半(E,F)-凸函数的概念.本文进一步深入讨论拟半(E,F)-凸函数及与之相应的拟半(E,F)-凸规划的一些重要性质,建立了此类广义凸性的若干重要结论.

  8. Notions of convexity

    CERN Document Server

    Hörmander, Lars

    1994-01-01

    The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed, leading up to Trépreau’s theorem on sufficiency of condition (capital Greek letter Psi) for microlocal solvability in the analytic category. At the beginning of the book, no prerequisites are assumed beyond calculus and linear algebra. Later on, basic facts from distribution theory and functional analysis are needed. In a few places, a more extensive background in differential geometry or pseudodiffer...

  9. A simple view on convex analysis and its applications

    NARCIS (Netherlands)

    J. Brinkhuis (Jan); V. Tikhomirov

    2005-01-01

    textabstractOur aim is to give a simple view on the basics and applications of convex analysis. The essential feature of this account is the systematic use of the possibility to associate to each convex object---such as a convex set, a convex function or a convex extremal problem--- a cone, without

  10. Introducing the Adaptive Convex Enveloping

    CERN Document Server

    Yu, Sheng

    2011-01-01

    Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an accurate, fast and reliable algorithm for solving convex dynamic programs with multivariate continuous states and actions, called Adaptive Convex Enveloping. This is a short introduction of the core technique created and used in my dissertation, so it is less formal, and misses some parts, such as literature review and reference, compared to a full journal paper.

  11. On the existence of convex classical solutions to a generalized Prandtl-Batchelor free-boundary problem-II

    Science.gov (United States)

    Acker, A.

    We give an analytical proof of the existence of convex classical solutions for the (convex) Prandtl-Batchelor free boundary problem in fluid dynamics. In this problem, a convex vortex core of constant vorticity μ >0 is embedded in a closed irrotational flow inside a closed, convex vessel in ℜ 2. The unknown boundary of the vortex core is a closed curve Γ along which (v+)^2-(v^-)^2=Λ , where v+ and v- denote, respectively, the exterior and interior flow-speeds along Γ and Λ is a given constant. Our existence results all apply to the natural multidimensional mathematical generalization of the above problem. The present existence theorems are the only ones available for the Prandtl-Batchelor problem for Λ >0, because (a) the author's prior existence treatment was restricted to the case where Λ <0, and because (b) there is no analytical existence theory available for this problem in the non-convex case, regardless of the sign of Λ .

  12. Cubes convexes

    CERN Document Server

    Nedjar, Sebastien; Cicchetti, Rosine; Lakhal, Lotfi; 10.3166/isi.11.6.11-31

    2010-01-01

    In various approaches, data cubes are pre-computed in order to answer efficiently OLAP queries. The notion of data cube has been declined in various ways: iceberg cubes, range cubes or differential cubes. In this paper, we introduce the concept of convex cube which captures all the tuples of a datacube satisfying a constraint combination. It can be represented in a very compact way in order to optimize both computation time and required storage space. The convex cube is not an additional structure appended to the list of cube variants but we propose it as a unifying structure that we use to characterize, in a simple, sound and homogeneous way, the other quoted types of cubes. Finally, we introduce the concept of emerging cube which captures the significant trend inversions. characterizations.

  13. Convex Optimization without Projection Steps

    CERN Document Server

    Jaggi, Martin

    2011-01-01

    We study the general problem of minimizing a convex function over a compact convex domain. We will investigate a simple iterative approximation algorithm that does not need projection steps in order to stay inside the optimization domain. Instead of a projection step, the linearized problem defined by a current subgradient is solved, which gives a step direction that will naturally stay in the domain. The approach generalizes the sparse greedy algorithm of Clarkson (and the low-rank SDP solver by Hazan) to arbitrary convex domains, and to using subgradients for the case of non-differentiable convex functions. Analogously, we give a convergence proof guaranteeing {\\epsilon}-small duality gap after O(1/{\\epsilon}) iterations. The framework allows us understand the sparsity of approximate solutions for any l1-regularized convex optimization problem, expressed as a function of the approximation quality. We obtain matching upper and lower bounds of {\\Theta}(1/{\\epsilon}) for the sparsity for l1-problems. The same ...

  14. Convex polytopes

    CERN Document Server

    Klee, Victor; Ziegler, Günter

    2003-01-01

    "The appearance of Grünbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way." (Gil Kalai, The Hebrew University of Jerusalem) "The original book of Grünbaum has provided the central reference for work in this active area of mathematics for the past 35 years...I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day." (Louis J. Billera, Cornell University) "The or...

  15. A forward backward splitting algorithm for the minimization of non-smooth convex functionals in Banach space

    Science.gov (United States)

    Bredies, Kristian

    2009-01-01

    We consider the task of computing an approximate minimizer of the sum of a smooth and a non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert space, we propose a generalization which involves the iterative solution of simpler subproblems. Descent and convergence properties of this new algorithm are studied. Furthermore, the results are applied to the minimization of Tikhonov-functionals associated with linear inverse problems and semi-norm penalization in Banach spaces. With the help of Bregman-Taylor-distance estimates, rates of convergence for the forward-backward splitting procedure are obtained. Examples which demonstrate the applicability are given, in particular, a generalization of the iterative soft-thresholding method by Daubechies, Defrise and De Mol to Banach spaces as well as total-variation-based image restoration in higher dimensions are presented.

  16. Multiple functions of photosystem II

    NARCIS (Netherlands)

    Rensen, van J.J.S.; Curwiel, V.B.

    2000-01-01

    The most important function of photosystem II (PSII) is its action as a water-plastoquinone oxido-reductase. At the expense of light energy, water is split, and oxygen and plastoquinol are formed. In addition to this most important activity, PSII has additional functions, especially in the

  17. Convex Graph Invariants

    Science.gov (United States)

    2010-12-02

    evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in

  18. Convexity Adjustments for ATS Models

    DEFF Research Database (Denmark)

    Murgoci, Agatha; Gaspar, Raquel M.

    Practitioners are used to value a broad class of exotic interest rate derivatives simply by preforming for what is known as convexity adjustments (or convexity corrections). We start by exploiting the relations between various interest rate models and their connections to measure changes. As a re......Practitioners are used to value a broad class of exotic interest rate derivatives simply by preforming for what is known as convexity adjustments (or convexity corrections). We start by exploiting the relations between various interest rate models and their connections to measure changes....... As a result we classify convexity adjustments into forward adjustments and swaps adjustments. We, then, focus on affine term structure (ATS) models and, in this context, conjecture convexity adjustments should be related of affine functionals. In the case of forward adjustments, we show how to obtain exact...... formulas. Concretely for LIBOR in arrears (LIA) contracts, we derive the system of Riccatti ODE-s one needs to compute to obtain the exact adjustment. Based upon the ideas of Schrager and Pelsser (2006) we are also able to derive general swap adjustments useful, in particular, when dealing with constant...

  19. Theory of function spaces II

    CERN Document Server

    Triebel, Hans

    1992-01-01

    Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as Hölder-Zygmund spaces, (fractional) Sobolev spaces, Besov spaces, inhomogeneous Hardy spaces, spaces of BMO-type and local approximation spaces which are closely connected with Morrey-Campanato spaces. Theory of Function Spaces II is self-contained, although it may be considered an update of the author’s earlier book of the same title. The book’s 7 chapters start with a historical survey of the subject, and then analyze the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds. ------ Reviews The first chapter deserves special attention. This chapter is both an outstanding historical survey of function spaces treated in the book and a remarkable survey of rather different techniques developed in the last 50 years. It is s...

  20. When is multidimensional screening a convex program?

    CERN Document Server

    Figalli, Alessio; McCann, Robert J

    2009-01-01

    A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis and that agents can choose only pure strategies, we identify a structural condition on the preference b(x,y) of agent type x for product type y -- and on the principal's costs c(y) -- which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal's problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal's optimum strategy -- and similarly of the strategy maximizing the expected welfare of the agents when the principal's profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under r...

  1. Various Expressions for Modulus of Random Convexity

    Institute of Scientific and Technical Information of China (English)

    Xiao Lin ZENG

    2013-01-01

    We first prove various kinds of expressions for modulus of random convexity by using an Lo(F,R)-valued function's intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals,then establish some basic properties including continuity for modulus of random convexity.In particular,we express the modulus of random convexity of a special random normed module Lo(F,X) derived from a normed space X by the classical modulus of convexity of X.

  2. Uniformly convex and strictly convex Orlicz spaces

    Science.gov (United States)

    Masta, Al Azhary

    2016-02-01

    In this paper we define the new norm of Orlicz spaces on ℝn through a multiplication operator on an old Orlicz spaces. We obtain some necessary and sufficient conditions that the new norm to be a uniformly convex and strictly convex spaces.

  3. Oracle Inequalities for Convex Loss Functions with Non-Linear Targets

    DEFF Research Database (Denmark)

    Caner, Mehmet; Kock, Anders Bredahl

    of the same order as that of the oracle. If the target is linear we give sufficient conditions for consistency of the estimated parameter vector. Next, we briefly discuss how a thresholded version of our estimator can be used to perform consistent variable selection. We give two examples of loss functions...... is linear this inequality also provides an upper bound of the estimation error of the estimated parameter vector. These are new results and they generalize the econometrics and statistics literature. Next, we use the non-asymptotic results to show that the excess loss of our estimator is asymptotically...

  4. Convexity and the translational-invariance constraint on the exchange-correlation functional

    Science.gov (United States)

    Joubert, Daniel; Levy, Mel

    1996-07-01

    Knowledge of the properties of the exchange-correlation functional in the form 1/λvxc([ρλ],r/λ), where ρλ(r)= λ3ρ(λr), is important when expressing the exchange-correlation energy as a line integral Exc[ρ]=∫10dλ∫dr1/λvxc([ρλ],r/λ) [3ρ(r)+r.∇ρ(r)] [R. van Leeuwen and E. J. Baerends, Phys. Rev. A 51, 170 (1995)]. With this in mind, it is shown that in the low-density limit limλ-->0∫ρ(r)∇21/λvxc([ρλ],r/λ)d3 r<=4π∫ρ(r)2d3r. This inequality is violated in the local-density approximation.

  5. The genealogy of convex solids

    CERN Document Server

    Domokos, Gabor; Szabó, Timea

    2012-01-01

    The shape of homogeneous, smooth convex bodies as described by the Euclidean distance from the center of gravity represents a rather restricted class M_C of Morse-Smale functions on S^2. Here we show that even M_C exhibits the complexity known for general Morse-Smale functions on S^2 by exhausting all combinatorial possibilities: every 2-colored quadrangulation of the sphere is isomorphic to a suitably represented Morse-Smale complex associated with a function in M_C (and vice versa). We prove our claim by an inductive algorithm, starting from the path graph P_2 and generating convex bodies corresponding to quadrangulations with increasing number of vertices by performing each combinatorially possible vertex splitting by a convexity- preserving local manipulation of the surface. Since convex bodies carrying Morse-Smale complexes isomorphic to P_2 exist, this algorithm not only proves our claim but also defines a hierarchical order among convex solids and general- izes the known classification scheme in [35], ...

  6. Generalized convexity, generalized monotonicity recent results

    CERN Document Server

    Martinez-Legaz, Juan-Enrique; Volle, Michel

    1998-01-01

    A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo­ metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man­ agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized conve...

  7. Analysis of Conformational B-Cell Epitopes in the Antibody-Antigen Complex Using the Depth Function and the Convex Hull.

    Directory of Open Access Journals (Sweden)

    Wei Zheng

    Full Text Available The prediction of conformational b-cell epitopes plays an important role in immunoinformatics. Several computational methods are proposed on the basis of discrimination determined by the solvent-accessible surface between epitopes and non-epitopes, but the performance of existing methods is far from satisfying. In this paper, depth functions and the k-th surface convex hull are used to analyze epitopes and exposed non-epitopes. On each layer of the protein, we compute relative solvent accessibility and four different types of depth functions, i.e., Chakravarty depth, DPX, half-sphere exposure and half space depth, to analyze the location of epitopes on different layers of the proteins. We found that conformational b-cell epitopes are rich in charged residues Asp, Glu, Lys, Arg, His; aliphatic residues Gly, Pro; non-charged residues Asn, Gln; and aromatic residue Tyr. Conformational b-cell epitopes are rich in coils. Conservation of epitopes is not significantly lower than that of exposed non-epitopes. The average depths (obtained by four methods for epitopes are significantly lower than that of non-epitopes on the surface using the Wilcoxon rank sum test. Epitopes are more likely to be located in the outer layer of the convex hull of a protein. On the benchmark dataset, the cumulate 10th convex hull covers 84.6% of exposed residues on the protein surface area, and nearly 95% of epitope sites. These findings may be helpful in building a predictor for epitopes.

  8. Integral inequalities of Herimite-Hadamard type for log-convex functions%对数凸函数的 Herimite-Hadamard 型积分不等式

    Institute of Scientific and Technical Information of China (English)

    春玲

    2013-01-01

    引进了新的二元对数凸函数的定义,建立了积分等式,并利用 Hölder不等式得到了一些新的关于对数凸函数的Herimite-Hadamard型积分不等式。%Convex function is an important concept of modern mathematics and plays an important role in mathematics and other subject fields . Herimite-Hadamard type integral inequalitiy , the first basic conclusion of convex function with a natural geometric interpretation , is widely applied in cybernetics theory ,and so on .In this paper , the definition of a new log-convex function in two variables has been introduced ,an integral equality has been established , and some new Herimite-Hadamard type integral inequalities concerned with log-convex function have been obtained from Hölder inequality .

  9. Bornological Locally Convex Cones

    Directory of Open Access Journals (Sweden)

    Davood Ayaseh

    2014-10-01

    Full Text Available In this paper we define bornological and b-bornological cones and investigate their properties. We give some characterization for these cones. In the special case of locally convex topological vector space both these concepts reduce to the known concept  of bornological spaces. We introduce and investigate the  convex quasiuniform   structures U_{tau}, U_{sigma}(P,P* and \\U_{beta}(P,P* on locally convex cone (P,U.

  10. Uniformly Convex Metric Spaces

    OpenAIRE

    Kell Martin

    2014-01-01

    In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology called co-convex topology agrees with the usualy weak topology in Banach spaces. An example of a $CAT(0)$-spaces with weak topology which is not Hausdorff is given. This answers questions raised b...

  11. Theory of convex structures

    CERN Document Server

    van de Vel, MLJ

    1993-01-01

    Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear si

  12. ON THE PRODUCT OF GATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

    Institute of Scientific and Technical Information of China (English)

    Shen Xisheng; Cheng Lixin

    2005-01-01

    A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Frechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.

  13. On convexity in complex networks

    CERN Document Server

    Marc, Tilen

    2016-01-01

    Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity. We analyze the expansion of convex subsets of nodes in empirical networks and also convexity of small subgraphs known as graphlets. We demonstrate that convexity is an inherent property of complex networks not present in a random graph. According to our perception of convexity, a convex network is such in which every connected subset of nodes induces a convex subgraph. Especially convex are technological networks and social collaboration graphs, whereas food webs are the only networks studied that are truly non-convex. Many other networks can be divided into a non-convex core surrounded by a convex periphery. We interpret convexity in terms of redundancy of shortest paths in a network and discuss possible applications.

  14. Applications of Fitzpatrick functions for solving optimization problems II

    Science.gov (United States)

    Nashed, Z.; Raykov, I.

    2015-10-01

    This paper is a continuation of the paper [8] and presents more applications of Fitzpatrick functions for solving optimization problems. The main purpose of the present work is to introduce some new properties of Fitzpatrick functions useful for solving optimization problems, using also their already presented specific properties, as the maximal monotonicity, proper, convex and lower semi-continuity.

  15. Dynamic Planar Convex Hull

    DEFF Research Database (Denmark)

    Jacob, Riko

    We determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage of the data structure...... is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects the convex hull......, and the tangent queries to determine whether a given point is inside the convex hull. The space usage of the data structure is O(n). We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure....

  16. Dynamic Planar Convex Hull

    DEFF Research Database (Denmark)

    Brodal, Gerth Stølfting; Jacob, Rico

    2002-01-01

    In this paper we determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage...... of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects...... the convex hull, and the tangent queries to determine whether a given point is inside the convex hull. We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure....

  17. Deformation in locally convex topological linear spaces

    Institute of Scientific and Technical Information of China (English)

    DING; Yanheng

    2004-01-01

    We are concerned with a deformation theory in locally convex topological linear spaces. A special "nice" partition of unity is given. This enables us to construct certain vector fields which are locally Lipschitz continuous with respect to the locally convex topology. The existence, uniqueness and continuous dependence of flows associated to the vector fields are established. Deformations related to strongly indefinite functionals are then obtained. Finally, as applications, we prove some abstract critical point theorems.

  18. Statistical properties of convex clustering

    OpenAIRE

    Tan, Kean Ming; Witten, Daniela

    2015-01-01

    In this manuscript, we study the statistical properties of convex clustering. We establish that convex clustering is closely related to single linkage hierarchical clustering and $k$-means clustering. In addition, we derive the range of the tuning parameter for convex clustering that yields a non-trivial solution. We also provide an unbiased estimator of the degrees of freedom, and provide a finite sample bound for the prediction error for convex clustering. We compare convex clustering to so...

  19. Estimates for Solutions of the $\\partial$-Equation and Application to the Characterization of the Zero Varieties of the Functions of the Nevanlinna Class for Lineally Convex Domains of Finite Type

    CERN Document Server

    Charpentier, Philippe; Mounkaila, Modi

    2011-01-01

    In the late ten years, the resolution of the equation $\\bar\\partial u=f$ with sharp estimates has been intensively studied for convex domains of finite type by many authors. In this paper, we consider the case of lineally convex domains. As the method used to obtain global estimates for a support function cannot be carried out in this case, we use a kernel that does not gives directly a solution of the $\\bar\\partial$-equation but only a representation formula which allows us to end the resolution of the equation using Kohn's $L^2$ theory. As an application we give the characterization of the zero sets of the functions of the Nevanlinna class for lineally convex domains of finite type.

  20. Convergence of Algorithms for Reconstructing Convex Bodies and Directional Measures

    DEFF Research Database (Denmark)

    Gardner, Richard; Kiderlen, Markus; Milanfar, Peyman

    2006-01-01

    We investigate algorithms for reconstructing a convex body K in Rn from noisy measurements of its support function or its brightness function in k directions u1, . . . , uk. The key idea of these algorithms is to construct a convex polytope Pk whose support function (or brightness function) best ...

  1. Inductance and hypergeometric functions. II

    DEFF Research Database (Denmark)

    Karlsson, Per W.

    2000-01-01

    A previously obtained integral for the self-inductance of a solenoid is further transformed. The resulting formula involves double Kampé de Fériet functions which are analytic continuations rather than power series.......A previously obtained integral for the self-inductance of a solenoid is further transformed. The resulting formula involves double Kampé de Fériet functions which are analytic continuations rather than power series....

  2. Quantal Density Functional Theory II

    CERN Document Server

    Sahni, Viraht

    2009-01-01

    Discusses approximation methods and applications of Quantal Density Functional Theory (QDFT), a local effective-potential-energy theory of electronic structure. This book describes approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT

  3. Convex Geometry and Stoichiometry

    CERN Document Server

    Jer-Chin,

    2011-01-01

    We demonstrate the benefits of a convex geometric perspective for questions on chemical stoichiometry. We show that the balancing of chemical equations, the use of "mixtures" to explain multiple stoichiometry, and the half-reaction for balancing redox actions all yield nice convex geometric interpretations. We also relate some natural questions on reaction mechanisms with the enumeration of lattice points in polytopes. Lastly, it is known that a given reaction mechanism imposes linear constraints on observed stoichiometries. We consider the inverse question of deducing reaction mechanism consistent with a given set of linear stoichiometric restrictions.

  4. Error bound results for convex inequality systems via conjugate duality

    CERN Document Server

    Bot, Radu Ioan

    2010-01-01

    The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. We deal first of all with systems described via one convex inequality and extend the achieved results, by making use of a celebrated scalarization function, to convex inequality systems expressed by means of a general vector function. We also propose a second approach for guaranteeing the existence of global error bounds of the latter, which meanwhile sharpens the classical result of Robinson.

  5. Recovery of Sparse Probability Measures via Convex Programming

    OpenAIRE

    Pilanci, Mert; El Ghaoui, Laurent; Chandrasekaran, Venkat

    2012-01-01

    We consider the problem of cardinality penalized optimization of a convex function over the probability simplex with additional convex constraints. The classical ℓ_1 regularizer fails to promote sparsity on the probability simplex since ℓ_1 norm on the probability simplex is trivially constant. We propose a direct relaxation of the minimum cardinality problem and show that it can be efficiently solved using convex programming. As a first application we consider recovering a spa...

  6. SMOOTHING BY CONVEX QUADRATIC PROGRAMMING

    Institute of Scientific and Technical Information of China (English)

    Bing-sheng He; Yu-mei Wang

    2005-01-01

    In this paper, we study the relaxed smoothing problems with general closed convex constraints. It is pointed out that such problems can be converted to a convex quadratic minimization problem for which there are good programs in software libraries.

  7. Locally uniformly convex norms in Banach spaces and their duals

    OpenAIRE

    Haydon, Richard

    2006-01-01

    It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by C^1 functions.

  8. (Average-) convexity of common pool and oligopoly TU-games

    NARCIS (Netherlands)

    Driessen, T.S.H.; Meinhardt, H.

    2000-01-01

    The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the rele

  9. Egalitarianism in Convex Fuzzy Games

    NARCIS (Netherlands)

    Brânzei, R.; Dimitrov, D.A.; Tijs, S.H.

    2002-01-01

    In this paper the egalitarian solution for convex cooperative fuzzy games is introduced.The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game.This adjusted algorithm is also a f

  10. Average Convexity in Communication Situations

    NARCIS (Netherlands)

    Slikker, M.

    1998-01-01

    In this paper we study inheritance properties of average convexity in communication situations. We show that the underlying graph ensures that the graphrestricted game originating from an average convex game is average convex if and only if every subgraph associated with a component of the underlyin

  11. A Mean Point Based Convex Hull Computation Algorithm

    Directory of Open Access Journals (Sweden)

    Digvijay Singh

    2016-11-01

    Full Text Available The optimal solution of a Linear Programming problem (LPP is a basic feasible solution and all basic feasible solutions are extreme or boundary points of a convex region formed by the constraint functions of the LPP. In fact, the feasible solution space is not always a convex set so the verification of extreme points for optimality is quite difficult. In order to cover the non-convex feasible points within a convex set, a convex hull is imagined so that the extreme or boundary points may be checked for evaluation of the optimum solution in the decision-making process. In this article a computer assisted convex hull computation algorithm using the Mean Point and Python code verified results of the designed algorithm are discussed.

  12. Non-convex multi-objective optimization

    CERN Document Server

    Pardalos, Panos M; Žilinskas, Julius

    2017-01-01

    Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions. Multi-objective optimization methods facilitate designers, engineers, and researchers to make decisions on appropriate trade-offs between various conflicting goals. A variety of deterministic and stochastic multi-objective optimization methods are developed in this book. Beginning with basic concepts and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach. Detailed descriptions of new algorithms for non-convex multi-objective optimization, their theoretical substantiation, and examples for practical applications to the cell formation problem in manufacturing engineering, the process design in...

  13. Efficient Approximation of Convex Recolorings

    OpenAIRE

    Moran, Shlomo; Snir, Sagi

    2005-01-01

    A coloring of a tree is convex if the vertices that pertain to any color induce a connected subtree; a partial coloring (which assigns colors to some of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring of trees arise in areas such as phylogenetics, linguistics, etc. eg, a perfect phylogenetic tree is one in which the states of each character induce a convex coloring of the tree. Research on perfect phylogeny is usually focused on finding a tree so t...

  14. Projections onto Convex Sets Super-Resolution Reconstruction Based on Point Spread Function Estimation of Low-Resolution Remote Sensing Images

    Science.gov (United States)

    Fan, Chong; Wu, Chaoyun; Li, Grand; Ma, Jun

    2017-01-01

    To solve the problem on inaccuracy when estimating the point spread function (PSF) of the ideal original image in traditional projection onto convex set (POCS) super-resolution (SR) reconstruction, this paper presents an improved POCS SR algorithm based on PSF estimation of low-resolution (LR) remote sensing images. The proposed algorithm can improve the spatial resolution of the image and benefit agricultural crop visual interpolation. The PSF of the high-resolution (HR) image is unknown in reality. Therefore, analysis of the relationship between the PSF of the HR image and the PSF of the LR image is important to estimate the PSF of the HR image by using multiple LR images. In this study, the linear relationship between the PSFs of the HR and LR images can be proven. In addition, the novel slant knife-edge method is employed, which can improve the accuracy of the PSF estimation of LR images. Finally, the proposed method is applied to reconstruct airborne digital sensor 40 (ADS40) three-line array images and the overlapped areas of two adjacent GF-2 images by embedding the estimated PSF of the HR image to the original POCS SR algorithm. Experimental results show that the proposed method yields higher quality of reconstructed images than that produced by the blind SR method and the bicubic interpolation method. PMID:28208837

  15. Projections onto Convex Sets Super-Resolution Reconstruction Based on Point Spread Function Estimation of Low-Resolution Remote Sensing Images.

    Science.gov (United States)

    Fan, Chong; Wu, Chaoyun; Li, Grand; Ma, Jun

    2017-02-13

    To solve the problem on inaccuracy when estimating the point spread function (PSF) of the ideal original image in traditional projection onto convex set (POCS) super-resolution (SR) reconstruction, this paper presents an improved POCS SR algorithm based on PSF estimation of low-resolution (LR) remote sensing images. The proposed algorithm can improve the spatial resolution of the image and benefit agricultural crop visual interpolation. The PSF of the highresolution (HR) image is unknown in reality. Therefore, analysis of the relationship between the PSF of the HR image and the PSF of the LR image is important to estimate the PSF of the HR image by using multiple LR images. In this study, the linear relationship between the PSFs of the HR and LR images can be proven. In addition, the novel slant knife-edge method is employed, which can improve the accuracy of the PSF estimation of LR images. Finally, the proposed method is applied to reconstruct airborne digital sensor 40 (ADS40) three-line array images and the overlapped areas of two adjacent GF-2 images by embedding the estimated PSF of the HR image to the original POCS SR algorithm. Experimental results show that the proposed method yields higher quality of reconstructed images than that produced by the blind SR method and the bicubic interpolation method.

  16. Convexity-preserving Bernstein–Bézier quartic scheme

    Directory of Open Access Journals (Sweden)

    Maria Hussain

    2014-07-01

    Full Text Available A C1 convex surface data interpolation scheme is presented to preserve the shape of scattered data arranged over a triangular grid. Bernstein–Bézier quartic function is used for interpolation. Lower bound of the boundary and inner Bézier ordinates is determined to guarantee convexity of surface. The developed scheme is flexible and involves more relaxed constraints.

  17. Convex bodies in Euclidean and Weil-Petersson geometries

    CERN Document Server

    Yamada, Sumio

    2011-01-01

    On a convex body in a Euclidean space, we introduce a new variational formulation for its Funk metric, a Finsler metric compatible with the tautological Finsler structure of the convex body. We generalize the metric on Teichmuller spaces with the Weil-Petersson distance function. A set of similarities the resulting metric structure shares with Thurston's asymmetric metric is noted.

  18. Weak Sharp Minima and Finite Termination of the Proximal Point Method for Convex Functions on Hadamard Manifolds

    CERN Document Server

    Bento, G C

    2012-01-01

    In this paper we proved that the sequence generated by the proximal point method, associated to a unconstrained optimization problem in the Riemannian context, has finite termination when the objective function has a weak sharp minima on the solution set of the problem.

  19. Cost Allocation and Convex Data Envelopment

    DEFF Research Database (Denmark)

    Hougaard, Jens Leth; Tind, Jørgen

    This paper considers allocation rules. First, we demonstrate that costs allocated by the Aumann-Shapley and the Friedman-Moulin cost allocation rules are easy to determine in practice using convex envelopment of registered cost data and parametric programming. Second, from the linear programming...... such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output...... problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models...

  20. Cost Allocation and Convex Data Envelopment

    DEFF Research Database (Denmark)

    Hougaard, Jens Leth; Tind, Jørgen

    problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models...... such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output...

  1. An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions

    Directory of Open Access Journals (Sweden)

    Oqlah Al-Refai

    2009-01-01

    Full Text Available Let 𝒜 be the class of analytic functions in the open unit disk . We define Θα,β:𝒜→𝒜 by (Θα,βf(z:=Γ(2−αzαDzα(Γ(2−βzβDzβf(z,(α,β≠2,3,4…, where Dzγf is the fractional derivative of f of order γ. If α,β∈[0,1], then a function f in 𝒜 is said to be in the class SPα,β if Θα,βf is a parabolic starlike function. In this paper, several properties and characteristics of the class SPα,β are investigated. These include subordination, characterization and inclusions, growth theorems, distortion theorems, and class-preserving operators. Furthermore, sandwich theorem related to the fractional derivative is proved.

  2. Allometric relationships between traveltime channel networks, convex hulls, and convexity measures

    Science.gov (United States)

    Tay, Lea Tien; Sagar, B. S. Daya; Chuah, Hean Teik

    2006-06-01

    The channel network (S) is a nonconvex set, while its basin [C(S)] is convex. We remove open-end points of the channel connectivity network iteratively to generate a traveltime sequence of networks (Sn). The convex hulls of these traveltime networks provide an interesting topological quantity, which has not been noted thus far. We compute lengths of shrinking traveltime networks L(Sn) and areas of corresponding convex hulls C(Sn), the ratios of which provide convexity measures CM(Sn) of traveltime networks. A statistically significant scaling relationship is found for a model network in the form L(Sn) ˜ A[C(Sn)]0.57. From the plots of the lengths of these traveltime networks and the areas of their corresponding convex hulls as functions of convexity measures, new power law relations are derived. Such relations for a model network are CM(Sn) ˜ ? and CM(Sn) ˜ ?. In addition to the model study, these relations for networks derived from seven subbasins of Cameron Highlands region of Peninsular Malaysia are provided. Further studies are needed on a large number of channel networks of distinct sizes and topologies to understand the relationships of these new exponents with other scaling exponents that define the scaling structure of river networks.

  3. Subset Selection by Local Convex Approximation

    DEFF Research Database (Denmark)

    Øjelund, Henrik; Sadegh, Payman; Madsen, Henrik

    1999-01-01

    least squares criterion. We propose an optimization technique for the posed probelm based on a modified version of the Newton-Raphson iterations, combined with a backward elimination type algorithm. THe Newton-Raphson modification concerns iterative approximations to the non-convex cost function...

  4. Integral Inequalities of Herimite-Hadamard Type for Co-ordinated s-Convex Functions%协同s-凸函数的Herimite-Hadamard型积分不等式

    Institute of Scientific and Technical Information of China (English)

    春玲; 双叶

    2013-01-01

    Convex function is an important concept of modern mathematics. Herimite-Hadamard inequality is widely applied in cybernetics theory, and so on. In this paper, a new lemma has been introduced and some new Herimite-Had-amard inequalities concerned with co-ordinated s-convex functions in the second sense have been obtained with the help of Holder inequality.%凸函数是现代数学中的重要概念,而凸函数的Hermite-Hadamard型不等式在控制理论等领域内有广泛的应用。本文利用新的引理和Hölder不等式给出了第二种意义下的二元协同s-凸函数的一些新的Heri-mite-Hadamard型不等式。

  5. Nehari manifold for non-local elliptic operator with concave–convex nonlinearities and sign-changing weight functions

    Indian Academy of Sciences (India)

    Sarika Goyal; K Sreenadh

    2015-11-01

    In this article, we study the existence and multiplicity of non-negative solutions of the following p-fractional equation: \\begin{equation*} \\left\\{ \\begin{matrix} -2 {\\displaystyle\\int}_{\\mathbb{R}^n} \\frac{|u(y) - u (x)|^{p-2} (u(y)-u(x))}{|x-y|^{n+p}} dy = h (x) |u|^{q-1} u + b (x)|u|^{r-1} u \\text{ in } ,\\\\ u = 0 \\quad \\text{ in } \\mathbb{R}^n \\setminus , \\quad u \\in W^{,p} (\\mathbb{R}^n) \\end{matrix} \\right. \\end{equation*} where is a bounded domain in $\\mathbb{R}^n$ with continuous boundary, $p ≥ 2$, $n > p $, $ \\in (0,1)$, $0 < q < p -1 < r < p^* - 1$ with $p^* = np (n -p)^{-1}$, $ > 0$ and $h, b$ are signchanging continuous functions. We show the existence and multiplicity of solutions by minimization on the suitable subset of Nehari manifold using the fibering maps. We find that there exists 0 such that for $ \\in (0, _0)$, it has at least two non-negative solutions.

  6. Continuity of Extremal Elements in Uniformly Convex Spaces

    OpenAIRE

    Ferguson, Timothy

    2013-01-01

    In this paper, we study the problem of finding the extremal element for a linear functional over a uniformly convex Banach space. We show that a unique extremal element exists and depends continuously on the linear functional, and vice versa. Using this, we simplify and clarify Ryabykh's proof that for any linear functional on a uniformly convex Bergman space with kernel in a certain Hardy space, the extremal functional belongs to the corresponding Hardy space.

  7. Convex polytopes and quantum states

    Energy Technology Data Exchange (ETDEWEB)

    Wilmott, Colin; Kampermann, Hermann; Bruss, Dagmar [Institut fuer Theoretische Physik III, Heinrich-Heine-Universitaet Duesseldorf (Germany)

    2010-07-01

    A convex polytope is defined as the convex hull of a finite non-empty set of vectors. We present a theorem of Rado (1952) which characterizes the convex hull of the collection of all permutations of a given real d-tuple in terms of the Hardy-Littlewood-Polya spectral order relation prec. We give a necessary and sufficient condition to construct a d-dimensional convex polytope which utilizes Rado's original (d-1)-dimensional characterization, and we describe how the resulting polytope may be placed in a quantum mechanical framework.

  8. CPU timing routines for a CONVEX C220 computer system

    Science.gov (United States)

    Bynum, Mary Ann

    1989-01-01

    The timing routines available on the CONVEX C220 computer system in the Structural Mechanics Division (SMD) at NASA Langley Research Center are examined. The function of the timing routines, the use of the timing routines in sequential, parallel, and vector code, and the interpretation of the results from the timing routines with respect to the CONVEX model of computing are described. The timing routines available on the SMD CONVEX fall into two groups. The first group includes standard timing routines generally available with UNIX 4.3 BSD operating systems, while the second group includes routines unique to the SMD CONVEX. The standard timing routines described in this report are /bin/csh time,/bin/time, etime, and ctime. The routines unique to the SMD CONVEX are getinfo, second, cputime, toc, and a parallel profiling package made up of palprof, palinit, and palsum.

  9. Stability of Class II fixed functional appliance therapy—a systematic review and meta-analysis

    Science.gov (United States)

    von Bremen, Julia; Ruf, Sabine

    2016-01-01

    Summary Objectives: To systematically search for scientific evidence concerning the stability of treatment (Tx) results achieved by means of Class II fixed functional appliance therapy and to assess possible differences between appliances. Search Methods: An electronic search of databases and orthodontic journals was carried out (until December 2013), with supplemental hand searching. In addition to the names of all identified appliances, the term fixed functional was used in combination with each of the following search terms: long-term, post-Tx, relapse, retention, stability. Selection Criteria: To be included in the review, the articles had to contain clear data on: Class II Tx with a fixed functional appliance (>5 patients), post-Tx period ≥ 1 year, assessment of ANB angle, Wits appraisal, molar relationship, soft-tissue profile convexity excluding the nose, overjet and/or overbite. Data Collection and Analysis: The literature search revealed 20 scientific investigations which corresponded to only two of the 76 identified appliances (Herbst and Twin Force Bite Corrector). As only one publication was found for the Twin Force Bite Corrector, a meta-analysis could only be performed for Herbst Tx. The data were extracted, pooled and weighted according to the number of patients in each study. Results: The mean values for post-Tx relapse (percentages relative to the Tx changes) were: ANB angle 0.2 degrees (12.4 per cent), Wits appraisal 0.5mm (19.5 per cent), sagittal molar relationship 1.2mm/0.1 cusp widths (21.8 per cent /6.5 per cent); soft-tissue profile convexity excluding nose less than 0.1 degrees (1.0 per cent), overjet 1.8mm (26.2 per cent), overbite Class II:1 1.4mm (44.7 per cent), overbite Class II:2 1.0mm (22.2 per cent). Conclusions: The scientific evidence concerning the stability of Tx results is inexistent for most fixed functional appliances for Class II correction except for Herbst appliance Tx. Even if the evidence level of most included studies

  10. Stability of Class II fixed functional appliance therapy--a systematic review and meta-analysis.

    Science.gov (United States)

    Bock, Niko C; von Bremen, Julia; Ruf, Sabine

    2016-04-01

    To systematically search for scientific evidence concerning the stability of treatment (Tx) results achieved by means of Class II fixed functional appliance therapy and to assess possible differences between appliances. An electronic search of databases and orthodontic journals was carried out (until December 2013), with supplemental hand searching. In addition to the names of all identified appliances, the term fixed functional was used in combination with each of the following search terms: long-term, post-Tx, relapse, retention, stability. To be included in the review, the articles had to contain clear data on: Class II Tx with a fixed functional appliance (>5 patients), post-Tx period ≥ 1 year, assessment of ANB angle, Wits appraisal, molar relationship, soft-tissue profile convexity excluding the nose, overjet and/or overbite. The literature search revealed 20 scientific investigations which corresponded to only two of the 76 identified appliances (Herbst and Twin Force Bite Corrector). As only one publication was found for the Twin Force Bite Corrector, a meta-analysis could only be performed for Herbst Tx. The data were extracted, pooled and weighted according to the number of patients in each study. The mean values for post-Tx relapse (percentages relative to the Tx changes) were: ANB angle 0.2 degrees (12.4 per cent), Wits appraisal 0.5mm (19.5 per cent), sagittal molar relationship 1.2mm/0.1 cusp widths (21.8 per cent /6.5 per cent); soft-tissue profile convexity excluding nose less than 0.1 degrees (1.0 per cent), overjet 1.8mm (26.2 per cent), overbite Class II:1 1.4mm (44.7 per cent), overbite Class II:2 1.0mm (22.2 per cent). The scientific evidence concerning the stability of Tx results is inexistent for most fixed functional appliances for Class II correction except for Herbst appliance Tx. Even if the evidence level of most included studies is rather low, good dentoskeletal stability without clinically relevant changes was found for most

  11. Decomposability of Abstract and Path-Induced Convexities in Hypergraphs

    Directory of Open Access Journals (Sweden)

    Malvestuto Francesco Mario

    2015-08-01

    Full Text Available An abstract convexity space on a connected hypergraph H with vertex set V (H is a family C of subsets of V (H (to be called the convex sets of H such that: (i C contains the empty set and V (H, (ii C is closed under intersection, and (iii every set in C is connected in H. A convex set X of H is a minimal vertex convex separator of H if there exist two vertices of H that are separated by X and are not separated by any convex set that is a proper subset of X. A nonempty subset X of V (H is a cluster of H if in H every two vertices in X are not separated by any convex set. The cluster hypergraph of H is the hypergraph with vertex set V (H whose edges are the maximal clusters of H. A convexity space on H is called decomposable if it satisfies the following three properties:

  12. Convex Games versus Clan Games

    NARCIS (Netherlands)

    Brânzei, R.; Dimitrov, D.A.; Tijs, S.H.

    2006-01-01

    In this paper we provide characterizations of convex games and total clan games by using properties of their corresponding marginal games.We show that a "dualize and restrict" procedure transforms total clan games with zero worth for the clan into monotonic convex games.Furthermore, each monotonic

  13. Shape preserving rational cubic spline for positive and convex data

    Directory of Open Access Journals (Sweden)

    Malik Zawwar Hussain

    2011-11-01

    Full Text Available In this paper, the problem of shape preserving C2 rational cubic spline has been proposed. The shapes of the positive and convex data are under discussion of the proposed spline solutions. A C2 rational cubic function with two families of free parameters has been introduced to attain the C2 positive curves from positive data and C2 convex curves from convex data. Simple data dependent constraints are derived on free parameters in the description of rational cubic function to obtain the desired shape of the data. The rational cubic schemes have unique representations.

  14. Quadratic growth and stability in convex programming problems

    OpenAIRE

    Bonnans, J. Frederic; Ioffe, Alexander D.

    1994-01-01

    Projet PROMATH; Given a convex program with $C^2$ functions and a convex set $S$ of solutions to the problem, we give a second order condition which guarantees that the problem does not have solutions outside of $S$. This condition is interpreted as a characterization for the quadratic growth of the cost function. The crucial role in the proofs is played by a theorem describing a certain uniform regularity property of critical cones in smooth convex programs. We apply these results to the dis...

  15. Conference on Convex Analysis and Global Optimization

    CERN Document Server

    Pardalos, Panos

    2001-01-01

    There has been much recent progress in global optimization algo­ rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun­ damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon­ vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en­ dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by th...

  16. Two new definitions on convexity and related inequalities

    CERN Document Server

    Tunc, Mevlut

    2012-01-01

    We have made some new definitions using the inequalities of Young' and Nesbitt'. And we have given some features of these new definitions. After, we established new Hadamard type inequalities for convex functions in the Young and Nesbitt sense.

  17. Convex Arrhenius plots and their interpretation

    Science.gov (United States)

    Truhlar, Donald G.; Kohen, Amnon

    2001-01-01

    This paper draws attention to selected experiments on enzyme-catalyzed reactions that show convex Arrhenius plots, which are very rare, and points out that Tolman's interpretation of the activation energy places a fundamental model-independent constraint on any detailed explanation of these reactions. The analysis presented here shows that in such systems, the rate coefficient as a function of energy is not just increasing more slowly than expected, it is actually decreasing. This interpretation of the data provides a constraint on proposed microscopic models, i.e., it requires that any successful model of a reaction with a convex Arrhenius plot should be consistent with the microcanonical rate coefficient being a decreasing function of energy. The implications and limitations of this analysis to interpreting enzyme mechanisms are discussed. This model-independent conclusion has broad applicability to all fields of kinetics, and we also draw attention to an analogy with diffusion in metastable fluids and glasses. PMID:11158559

  18. Coefficient inequalities for starlikeness and convexity

    Directory of Open Access Journals (Sweden)

    Ali Rosihan M.

    2013-06-01

    Full Text Available For an analytic function $f(z=z+\\sum_{n=2}^\\infty a_n z^n$ satisfying the inequality $\\sum_{n=2}^\\infty n(n-1|a_n|\\leq \\beta$, sharp bound on $\\beta$ is determined so that $f$ is either starlike or convex of order $\\alpha$. Several other coefficient inequalities related to certain subclasses are also investigated.

  19. Decision Problems For Convex Languages

    CERN Document Server

    Brzozowski, Janusz; Xu, Zhi

    2008-01-01

    In this paper we examine decision problems associated with various classes of convex languages, studied by Ang and Brzozowski (under the name "continuous languages''). We show that we can decide whether a given language L is prefix-, suffix-, factor-, or subword-convex in polynomial time if L is represented by a DFA, but that the problem is PSPACE-hard if L is represented by an NFA. In the case that a regular language is not convex, we prove tight upper bounds on the length of the shortest words demonstrating this fact, in terms of the number of states of an accepting DFA. Similar results are proved for some subclasses of convex languages: the prefix-, suffix-, factor-, and subword-closed languages, and the prefix-, suffix-, factor-, and subword-free languages.

  20. A Convex Optimization Approach to pMRI Reconstruction

    CERN Document Server

    Zhang, Cishen

    2013-01-01

    In parallel magnetic resonance imaging (pMRI) reconstruction without using estimation of coil sensitivity functions, one group of algorithms reconstruct sensitivity encoded images of the coils first followed by the magnitude only image reconstruction, e.g. GRAPPA, and another group of algorithms jointly compute the image and sensitivity functions by regularized optimization which is a non-convex problem with local only solutions. For the magnitude only image reconstruction, this paper derives a reconstruction formulation, which is linear in the magnitude image, and an associated convex hull in the solution space of the formulated equation containing the magnitude of the image. As a result, the magnitude only image reconstruction for pMRI is formulated into a two-step convex optimization problem, which has a globally optimal solution. An algorithm based on split-bregman and nuclear norm regularized optimizations is proposed to implement the two-step convex optimization and its applications to phantom and in-vi...

  1. Complex Convexity of Orlicz Modular Sequence Spaces

    Directory of Open Access Journals (Sweden)

    Lili Chen

    2016-01-01

    Full Text Available The concepts of complex extreme points, complex strongly extreme points, complex strict convexity, and complex midpoint locally uniform convexity in general modular spaces are introduced. Then we prove that, for any Orlicz modular sequence space lΦ,ρ, lΦ,ρ is complex midpoint locally uniformly convex. As a corollary, lΦ,ρ is also complex strictly convex.

  2. On Fuzzy Simplex and Fuzzy Convex Hull

    Institute of Scientific and Technical Information of China (English)

    Dong QIU; Wei Quan ZHANG

    2011-01-01

    In this paper,we discuss fuzzy simplex and fuzzy convex hull,and give several representation theorems for fuzzy simplex and fuzzy convex hull.In addition,by giving a new characterization theorem of fuzzy convex hull,we improve some known results about fuzzy convex hull.

  3. The Convex Coordinates of the Symmedian Point

    Science.gov (United States)

    Boyd, J. N.; Raychowdhury, P. N.

    2006-01-01

    In this note, we recall the convex (or barycentric) coordinates of the points of a closed triangular region. We relate the convex and trilinear coordinates of the interior points of the triangular region. We use the relationship between convex and trilinear coordinates to calculate the convex coordinates of the symmedian point of the triangular…

  4. Compactly convex sets in linear topological spaces

    CERN Document Server

    Banakh, T; Ravsky, O

    2012-01-01

    A convex subset X of a linear topological space is called compactly convex if there is a continuous compact-valued map $\\Phi:X\\to exp(X)$ such that $[x,y]\\subset\\Phi(x)\\cup \\Phi(y)$ for all $x,y\\in X$. We prove that each convex subset of the plane is compactly convex. On the other hand, the space $R^3$ contains a convex set that is not compactly convex. Each compactly convex subset $X$ of a linear topological space $L$ has locally compact closure $\\bar X$ which is metrizable if and only if each compact subset of $X$ is metrizable.

  5. Convex Modeling of Interactions with Strong Heredity

    Science.gov (United States)

    Haris, Asad; Witten, Daniela; Simon, Noah

    2015-01-01

    We consider the task of fitting a regression model involving interactions among a potentially large set of covariates, in which we wish to enforce strong heredity. We propose FAMILY, a very general framework for this task. Our proposal is a generalization of several existing methods, such as VANISH [Radchenko and James, 2010], hierNet [Bien et al., 2013], the all-pairs lasso, and the lasso using only main effects. It can be formulated as the solution to a convex optimization problem, which we solve using an efficient alternating directions method of multipliers (ADMM) algorithm. This algorithm has guaranteed convergence to the global optimum, can be easily specialized to any convex penalty function of interest, and allows for a straightforward extension to the setting of generalized linear models. We derive an unbiased estimator of the degrees of freedom of FAMILY, and explore its performance in a simulation study and on an HIV sequence data set. PMID:28316461

  6. Powers of Convex-Cyclic Operators

    Directory of Open Access Journals (Sweden)

    Fernando León-Saavedra

    2014-01-01

    Full Text Available A bounded operator T on a Banach space X is convex cyclic if there exists a vector x such that the convex hull generated by the orbit Tnxn≥0 is dense in X. In this note we study some questions concerned with convex-cyclic operators. We provide an example of a convex-cyclic operator T such that the power Tn fails to be convex cyclic. Using this result we solve three questions posed by Rezaei (2013.

  7. A class of free locally convex spaces

    Science.gov (United States)

    Sipacheva, O. V.

    2003-04-01

    Stratifiable spaces are a natural generalization of metrizable spaces for which Dugundji's theorem holds. It is proved that the free locally convex space of a stratifiable space is stratifiable. This means, in particular, that the space of finitely supported probability measures on a stratifiable space is a retract of a locally convex space, and that each stratifiable convex subset of a locally convex space is a retract of a locally convex space.

  8. A novel neural network for nonlinear convex programming.

    Science.gov (United States)

    Gao, Xing-Bao

    2004-05-01

    In this paper, we present a neural network for solving the nonlinear convex programming problem in real time by means of the projection method. The main idea is to convert the convex programming problem into a variational inequality problem. Then a dynamical system and a convex energy function are constructed for resulting variational inequality problem. It is shown that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. Compared with the existing neural networks for solving the nonlinear convex programming problem, the proposed neural network has no Lipschitz condition, no adjustable parameter, and its structure is simple. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.

  9. Entropy and convexity for nonlinear partial differential equations.

    Science.gov (United States)

    Ball, John M; Chen, Gui-Qiang G

    2013-12-28

    Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.

  10. Interior-point Algorithm for Convex Quadratic Programming Based on A New Class of Kernel Functions%基于新的核函数求解凸二次规划的内点算法

    Institute of Scientific and Technical Information of China (English)

    李鑫

    2016-01-01

    Based on a new class of kernel functions,a large-update primal-dual interior-point algorithm for convex quadratic programming is presented.By using new technical results and favorable properties of the kernel function, the study proves that the iteration complexity for the algorithm is On1/2lognlogn/ε, which is identical with the currently best iteration bound for large-update primal-dual interior-point algorithms of convex quadratic programming.%基于一类新的核函数对凸二次规划(CQP)设计了一种大步校正内点算法。通过应用新的技术性结果和这类核函数良好的性质,证明了算法的迭代复杂性为 O(n1/2lognlogn/ε),这与目前凸二次规划的大步校正原始-对偶内点算法最好的迭代复杂性一致。

  11. A capacity scaling algorithm for convex cost submodular flows

    Energy Technology Data Exchange (ETDEWEB)

    Iwata, Satoru [Kyoto Univ. (Japan)

    1996-12-31

    This paper presents a scaling scheme for submodular functions. A small but strictly submodular function is added before scaling so that the resulting functions should be submodular. This scaling scheme leads to a weakly polynomial algorithm to solve minimum cost integral submodular flow problems with separable convex cost functions, provided that an oracle for exchange capacities are available.

  12. NP-completeness of weakly convex and convex dominating set decision problems

    Directory of Open Access Journals (Sweden)

    Joanna Raczek

    2004-01-01

    Full Text Available The convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are \\(NP\\-complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can verify in polynomial time whether a given subset of vertices of a graph is convex or weakly convex.

  13. Local Routing in Convex Subdivisions

    DEFF Research Database (Denmark)

    Bose, Prosenjit; Durocher, Stephane; Mondal, Debajyoti;

    2015-01-01

    In various wireless networking settings, node locations determine a network’s topology, allowing the network to be modelled by a geometric graph drawn in the plane. Without any additional information, local geometric routing algorithms can guarantee delivery to the target node only in restricted...... classes of geometric graphs, such as triangulations. In order to guarantee delivery on more general classes of geometric graphs (e.g., convex subdivisions or planar subdivisions), previous local geometric routing algorithms required Θ(logn) state bits to be stored and passed with the message. We present...... the first local geometric routing algorithm using only one state bit to guarantee delivery on convex subdivisions and the first local geometric memoryless routing algorithm that guarantees delivery on edge-augmented monotone subdivisions (including all convex subdivisions) when the algorithm has knowledge...

  14. Extreme properties of quermassintegrals of convex bodies

    Institute of Scientific and Technical Information of China (English)

    LENG; Gangsong

    2001-01-01

    [1]Ball,K.,Shadows of convex bodies,Trans.Amer.Math.Soc.,1991,327:891-901.[2]Lutwak,E.,Mixed projection inequalities,Trans.Amer.Math.Soc.,1985,287:92-106.[3]Bourgain,J.,Lindenstrauss,J.,Projection bodies,Israel Seminar (G.A.F.A) 1986-1987,Lecture Notes in Math.Vol.1317,Berlin-New York:Springer-Verlag,1988,250-269.[4]Chakerian,G.D.,Lutwak,E.,Bodies with similar projections,Trans.Amer.Math.Soc.,1997,349:1811-1820.[5]Schneider,R.,Weil,W.,Zonoids and related topics,Convexity and its Applications (eds.Gruber,P.M.,Wills,J.M.),Basel:Birkhuser,1983,296-316.[6]Schneider,R.,Convex Bodies:the Brunn-Minkowski Theory,Cambridge:Cambridge University Press,1993.[7]Schneider,R.,On the determination of convex bodies by projection and girth functions,Result Math.,1998,33:155-160.[8]Thompson,A.C.,Minkowski Geometry,Cambridge:Cambridge University Press,1996.[9]Petty,C.M.,Projection bodies,in Proceedings,Coll Convexity,Copenhagen,1965,Kbenhavns Univ.Mat.Inst.,1967,234-241.[10]Schneider,R.,Zu einem problem von Shephard über die projectionen konvexer kirper,Math.Z.,1967,101:71-81.[11]Ball,K.,Volume ratios and a reverse isoprimetric inequalitity,J.London Math.Soc.,1991,44(2):351-359.[12]Gardner,R.J.,Intersection bodies and the Busemann-Petty problem,Trans.Amer.Math.Soc.,1994,342:435-445.[13]Gardner,R.J.,A positive answer to the Busemann-petty problem in three dimensions,Annals of Math.,1994,140:435-447.[14]Grinberg,E.L.,Isoperimetric inequalities and identities fork-dimensional cross-sections of convex bodies,Math.Ann.,1991,291:75-86.[15]Goodey,P.,Schneider,R.,Weil,W.,On the determination of convex bodies by projection functions,Bull.London Math.Soc.,1997,29:82-88.[16]Lutwak,E.,Intersection bodies and dual mixed volumes,Adv.Math.,1988,71:232-261.[17]Zhang,G.,Centered bodies and dual mixed volumes,Trans.Amer.Soc.,1994,345:777-801.[18]Zhang,G.,Dual Kinematic formulas,Trans.Amer.Soc.,1999,351:985-995.[19

  15. Quantum information and convex optimization

    Energy Technology Data Exchange (ETDEWEB)

    Reimpell, Michael

    2008-07-01

    This thesis is concerned with convex optimization problems in quantum information theory. It features an iterative algorithm for optimal quantum error correcting codes, a postprocessing method for incomplete tomography data, a method to estimate the amount of entanglement in witness experiments, and it gives necessary and sufficient criteria for the existence of retrodiction strategies for a generalized mean king problem. (orig.)

  16. Fragile Nucleosomes Influence Pol II Promoter Function.

    Science.gov (United States)

    Pradhan, Suman K; Xue, Yong; Carey, Michael F

    2015-11-05

    In this issue of Molecular Cell, Kubik et al. (2015) describe how the RSC chromatin remodeling complex collaborates with two DNA sequence motifs and sequence-specific general regulatory factors to assemble fragile nucleosomes at highly transcribed yeast Pol II promoters, and they distinguish these from promoters bearing stable nucleosomes.

  17. A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming%凸非线性规划的同伦不可能内点算法

    Institute of Scientific and Technical Information of China (English)

    杨轶华; 吕显瑞; 刘庆怀

    2006-01-01

    In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP)for convex nonlinear programming problems. For any convex nonlinear programming,without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.

  18. A simple randomised algorithm for convex optimisation - Application to two-stage stochastic programming.

    NARCIS (Netherlands)

    M. Dyer; R. Kannan; L. Stougie (Leen)

    2014-01-01

    htmlabstractWe consider maximising a concave function over a convex set by a simplerandomised algorithm. The strength of the algorithm is that it requires only approximatefunction evaluations for the concave function and a weak membership oraclefor the convex set. Under smoothness conditions on the

  19. A Microscopic Convexity Principle for Spacetime Convex Solutions of Fully Nonlinear Parabolic Equations

    Institute of Scientific and Technical Information of China (English)

    Chuan Qiang CHEN; Bo Wen HU

    2013-01-01

    We study microscopic spacetime convexity properties of fully nonlinear parabolic partial differential equations.Under certain general structure condition,we establish a constant rank theorem for the spacetime convex solutions of fully nonlinear parabolic equations.At last,we consider the parabolic convexity of solutions to parabolic equations and the convexity of the spacetime second fundamental form of geometric flows.

  20. Revisiting separation properties of convex fuzzy sets

    Science.gov (United States)

    Separation of convex sets by hyperplanes has been extensively studied on crisp sets. In a seminal paper separability and convexity are investigated, however there is a flaw on the definition of degree of separation. We revisited separation on convex fuzzy sets that have level-wise (crisp) disjointne...

  1. A Note on Permutationally Convex Games

    NARCIS (Netherlands)

    van Velzen, S.; Hamers, H.J.M.; Norde, H.W.

    2005-01-01

    In this paper we generalise marginal vectors and permutational convexity.We show that if a game is generalised permutationally convex, then the corresponding generalised marginal vector is a core element.Furthermore we refine the concept of permutational convexity and show that this refinement yield

  2. On Uniform Convexity of Banach Spaces

    Institute of Scientific and Technical Information of China (English)

    Qing Jin CHENG; Bo WANG; Cui Ling WANG

    2011-01-01

    This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.

  3. Computing farthest neighbors on a convex polytope

    NARCIS (Netherlands)

    Cheong, O.; Shin, C.S.; Vigneron, A.

    2002-01-01

    Let N be a set of n points in convex position in R3. The farthest-point Voronoi diagram of N partitions R³ into n convex cells. We consider the intersection G(N) of the diagram with the boundary of the convex hull of N. We give an algorithm that computes an implicit representation of G(N) in expecte

  4. Computing farthest neighbors on a convex polytope

    NARCIS (Netherlands)

    Cheong, O.; Shin, C.S.; Vigneron, A.

    2002-01-01

    Let N be a set of n points in convex position in R3. The farthest-point Voronoi diagram of N partitions R³ into n convex cells. We consider the intersection G(N) of the diagram with the boundary of the convex hull of N. We give an algorithm that computes an implicit representation of G(N) in

  5. Firey linear combinations of convex bodies

    Institute of Scientific and Technical Information of China (English)

    XIONG Ge; XIAO Qi-ming; CHEUNG Wing-Sum

    2009-01-01

    For convex bodies, the Firey linear combinations were introduced and studied in several papers. In this paper the mean width of the Firey linear combinations of convex bodies is studied, and the lower bound of the mean width of the Firey linear combinations of convex body and its polar body is given.

  6. Blaschke-type conditions in unbounded domains, generalized convexity and applications in perturbation theory

    CERN Document Server

    Favorov, S

    2012-01-01

    We introduce a new geometric characteristic of compact sets on the plane called $r$-convexity, which fits nicely into the concept of generalized convexity and extends essentially the conventional convexity. For a class of subharmonic functions on unbounded domains with $r$-convex compact complement, with the growth governed by the distance to the boundary, we obtain the Blaschke--type condition for their Riesz' measures. The result is applied to the study of the convergence of the discrete spectrum for the Schatten-von Neumann perturbations.

  7. Convexity and the "Pythagorean" metric of space(-time)

    CERN Document Server

    Kalogeropoulos, Nikos

    2016-01-01

    We address the question about the reasons why the "Wick-rotated", positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces providing the kinematic framework for the statistical or quantum treatments of gravity. We rely on particular moduli of convexity and smoothness which are extremized by Hilbert spaces. In the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a functional integral approach. The "Pythagorean" metric of space(-time) is then induced by such Hilbert spaces.

  8. A noncommutative convexity in C*-bimodules

    Directory of Open Access Journals (Sweden)

    Mohsen Kian

    2017-02-01

    Full Text Available Let A and B be C*-algebras. We consider a noncommutative convexity in Hilbert A-B-bimodules, called A-B-convexity, as a generalization of C*-convexity in C*-algebras. We show that if X is a Hilbert A-B-bimodule, then Mn(X is a Hilbert Mn(A-Mn(B-bimodule and apply it to show that the closed unit ball of every Hilbert A-B-bimodule is A-B-convex. Some properties of this kind of convexity and various examples have been given.

  9. The problem of convexity of Chebyshev sets

    Science.gov (United States)

    Balaganskii, V. S.; Vlasov, L. P.

    1996-12-01

    Contents Introduction §1. Definitions and notation §2. Reference theorems §3. Some results Chapter I. Characterization of Banach spaces by means of the relations between approximation properties of sets §1. Existence, uniqueness §2. Prom approximate compactness to 'sun'-property §3. From 'sun'-property to approximate compactness §4. Differentiability in the direction of the gradient is sufficient for Fréchet and Gâteaux differentiability §5. Sets with convex complement Chapter II. The structure of Chebyshev and related sets §1. The isolated point method §2. Restrictions of the type \\vert\\overline{W}\\vert Klee (discrete Chebyshev set) §4. A survey of some other results Conclusion Bibliography

  10. Barrelled locally convex spaces

    CERN Document Server

    Pérez Carreras, P

    1987-01-01

    This book is a systematic treatment of barrelled spaces, and of structures in which barrelledness conditions are significant. It is a fairly self-contained study of the structural theory of those spaces, concentrating on the basic phenomena in the theory, and presenting a variety of functional-analytic techniques.Beginning with some basic and important results in different branches of Analysis, the volume deals with Baire spaces, presents a variety of techniques, and gives the necessary definitions, exploring conditions on discs to ensure that they are absorbed by the barrels of the sp

  11. Evaluating convex roof entanglement measures.

    Science.gov (United States)

    Tóth, Géza; Moroder, Tobias; Gühne, Otfried

    2015-04-24

    We show a powerful method to compute entanglement measures based on convex roof constructions. In particular, our method is applicable to measures that, for pure states, can be written as low order polynomials of operator expectation values. We show how to compute the linear entropy of entanglement, the linear entanglement of assistance, and a bound on the dimension of the entanglement for bipartite systems. We discuss how to obtain the convex roof of the three-tangle for three-qubit states. We also show how to calculate the linear entropy of entanglement and the quantum Fisher information based on partial information or device independent information. We demonstrate the usefulness of our method by concrete examples.

  12. Luminosity function of optically-selected type II QSOs

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    For a sample of 411 type II QSOs with redshifts less then 0.3,we use the Balmer decrements to do the reddening correction of the [O III] luminosities and then derive the intrinsic [O III] luminosity function.We find that the host reddening correction of the [O III] 5007 luminosity for type II QSOs cannot be neglected.The median Balmer decrement of Hα/Hβ=4.0 corresponds to an extinction of 0.94 mag for the [O III] 5007 line,which is consistent with the result derived from the median Hβ/Hγ.Comparing the intrinsic luminosity function of type II QSOs with that of type I QSOs,we find that the upper limit of the type II QSO’s fraction in the total QSOs is 80% for type II QSOs with z < 0.3 and 8.6≤log(L[O III]/L)≤9.4.

  13. Convex Hulls of Algebraic Sets

    CERN Document Server

    Gouveia, João

    2010-01-01

    This article describes a method to compute successive convex approximations of the convex hull of a set of points in R^n that are the solutions to a system of polynomial equations over the reals. The method relies on sums of squares of polynomials and the dual theory of moment matrices. The main feature of the technique is that all computations are done modulo the ideal generated by the polynomials defining the set to the convexified. This work was motivated by questions raised by Lov\\'asz concerning extensions of the theta body of a graph to arbitrary real algebraic varieties, and hence the relaxations described here are called theta bodies. The convexification process can be seen as an incarnation of Lasserre's hierarchy of convex relaxations of a semialgebraic set in R^n. When the defining ideal is real radical the results become especially nice. We provide several examples of the method and discuss convergence issues. Finite convergence, especially after the first step of the method, can be described expl...

  14. Measures of Asymmetry Dual to Mean Minkowski Measures of Asymmetry for Convex Bo dies

    Institute of Scientific and Technical Information of China (English)

    Yao Dan; Guo Qi

    2016-01-01

    We introduce a family of measures (functions) of asymmetry for convex bodies and discuss their properties. It turns out that this family of measures shares many nice properties with the mean Minkowski measures. As the mean Minkowski measures describe the symmetry of lower dimensional sections of a convex body, these new measures describe the symmetry of lower dimensional orthogonal projections.

  15. Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons.

    Science.gov (United States)

    Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

    2013-08-01

    In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π.

  16. On a convex combination of solutions to elliptic variational inequalities

    Directory of Open Access Journals (Sweden)

    Sergiu Aizicovici

    2007-02-01

    Full Text Available We consider continuous descent methods for the minimization of convex functions defined on a general Banach space. In our previous work we showed that most of them (in the sense of Baire category converged. In the present paper we show that convergent continuous descent methods are stable under small perturbations.

  17. Stochastic level-value approximation for quadratic integer convex programming

    Institute of Scientific and Technical Information of China (English)

    PENG Zheng; WU Dong-hua

    2008-01-01

    We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and re-port some numerical results to illuminate its effectiveness.

  18. Use of Convexity in Ostomy Care

    Science.gov (United States)

    Salvadalena, Ginger; Pridham, Sue; Droste, Werner; McNichol, Laurie; Gray, Mikel

    2017-01-01

    Ostomy skin barriers that incorporate a convexity feature have been available in the marketplace for decades, but limited resources are available to guide clinicians in selection and use of convex products. Given the widespread use of convexity, and the need to provide practical guidelines for appropriate use of pouching systems with convex features, an international consensus panel was convened to provide consensus-based guidance for this aspect of ostomy practice. Panelists were provided with a summary of relevant literature in advance of the meeting; these articles were used to generate and reach consensus on 26 statements during a 1-day meeting. Consensus was achieved when 80% of panelists agreed on a statement using an anonymous electronic response system. The 26 statements provide guidance for convex product characteristics, patient assessment, convexity use, and outcomes. PMID:28002174

  19. Finite dimensional convexity and optimization

    CERN Document Server

    Florenzano, Monique

    2001-01-01

    The primary aim of this book is to present notions of convex analysis which constitute the basic underlying structure of argumentation in economic theory and which are common to optimization problems encountered in many applications. The intended readers are graduate students, and specialists of mathematical programming whose research fields are applied mathematics and economics. The text consists of a systematic development in eight chapters, with guided exercises containing sometimes significant and useful additional results. The book is appropriate as a class text, or for self-study.

  20. Systematization of problems on ball estimates of a convex compactum

    Science.gov (United States)

    Dudov, S. I.

    2015-09-01

    We consider a class of finite-dimensional problems on the estimation of a convex compactum by a ball of an arbitrary norm in the form of extremal problems whose goal function is expressed via the function of the distance to the farthest point of the compactum and the function of the distance to the nearest point of the compactum or its complement. Special attention is devoted to the problem of estimating (approximating) a convex compactum by a ball of fixed radius in the Hausdorff metric. It is proved that this problem plays the role of the canonical problem: solutions of any problem in the class under consideration can be expressed via solutions of this problem for certain values of the radius. Based on studying and using the properties of solutions of this canonical problem, we obtain ranges of values of the radius in which the canonical problem expresses solutions of the problems on inscribed and circumscribed balls, the problem of uniform estimate by a ball in the Hausdorff metric, the problem of asphericity of a convex body, the problems of spherical shells of the least thickness and of the least volume for the boundary of a convex body. This makes it possible to arrange the problems in increasing order of the corresponding values of the radius. Bibliography: 34 titles.

  1. Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order

    OpenAIRE

    Balashov, Maxim V.; Repovš, Dušan,

    2011-01-01

    We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius.

  2. Entropy coherent and entropy convex measures of risk

    NARCIS (Netherlands)

    Laeven, R.J.A.; Stadje, M.

    2013-01-01

    We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex measur

  3. Efficiency Loss in a Cournot Oligopoly with Convex Market Demand

    CERN Document Server

    Tsitsiklis, John N

    2012-01-01

    We consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand function is convex. We establish a lower bound on the efficiency of Cournot equilibria in terms of a scalar parameter derived from the inverse demand function, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium to the average slope of the inverse demand function between the Cournot equilibrium and a social optimum. Also, for the case of a single, monopolistic, profit maximizing supplier, or of multiple suppliers who collude to maximize their total profit, we establish a similar but tighter lower bound on the efficiency of the resulting output. Our results provide nontrivial quantitative bounds on the loss of social welfare for several convex inverse demand functions that appear in the economics literature.

  4. First-order Convex Optimization Methods for Signal and Image Processing

    DEFF Research Database (Denmark)

    Jensen, Tobias Lindstrøm

    2012-01-01

    In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can...... be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple......-description problem. We finally present the contributions of the thesis. The remaining parts of the thesis consist of five research papers. The first paper addresses non-smooth first-order convex optimization and the trade-off between accuracy and smoothness of the approximating smooth function. The second and third...

  5. Calculus of Elementary Functions, Part II. Student Text. Revised Edition.

    Science.gov (United States)

    Herriot, Sarah T.; And Others

    This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This text, Part II, contains material designed to follow Part I. Chapters included in this text are: (6) Derivatives of Exponential and Related Functions; (7) Area and…

  6. Introduction to Convex and Quasiconvex Analysis

    NARCIS (Netherlands)

    J.B.G. Frenk (Hans); G. Kassay

    2004-01-01

    textabstractIn the first chapter of this book the basic results within convex and quasiconvex analysis are presented. In Section 2 we consider in detail the algebraic and topological properties of convex sets within Rn together with their primal and dual representations. In Section 3 we apply the re

  7. Stochastic Dominance: Convexity and Some Efficiency Tests

    NARCIS (Netherlands)

    A.M. Lizyayev (Andrey)

    2009-01-01

    textabstractThis paper points out the importance of Stochastic Dominance (SD) efficient sets being convex. We review classic convexity and efficient set characterization results on SD efficiency of a given portfolio relative to a diversified set of assets and generalize them in the following

  8. Polar DuaLs of Convex Bodies

    Science.gov (United States)

    1990-01-01

    to Convex Bodies, Geometriae Dedicata 2" (1973) 225-248. 10. H. Guggenheimer, "The Analytic Geometry of the Unsymmetric Minkowski Plane," Lecture...Mathematics, Vol. 58, No. 2, 1975. 19. E. Lutwak, "On Cross-Sectional Measures of Polar Reciprocal Convex Bodies," Geometriae Dedicata 5, (1976) 79-80

  9. The Band around a Convex Body

    Science.gov (United States)

    Swanson, David

    2011-01-01

    We give elementary proofs of formulas for the area and perimeter of a planar convex body surrounded by a band of uniform thickness. The primary tool is a integral formula for the perimeter of a convex body which describes the perimeter in terms of the projections of the body onto lines in the plane.

  10. A proximal point method for nonsmooth convex optimization problems in Banach spaces

    Directory of Open Access Journals (Sweden)

    Y. I. Alber

    1997-01-01

    Full Text Available In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.

  11. Toric geometry of convex quadrilaterals

    CERN Document Server

    Legendre, Eveline

    2009-01-01

    We provide an explicit resolution of the Abreu equation on convex labeled quadrilaterals. This confirms a conjecture of Donaldson in this particular case and implies a complete classification of the explicit toric K\\"ahler-Einstein and toric Sasaki-Einstein metrics constructed in [6,23,14]. As a byproduct, we obtain a wealth of extremal toric (complex) orbi-surfaces, including K\\"ahler-Einstein ones, and show that for a toric orbi-surface with 4 fixed points of the torus action, the vanishing of the Futaki invariant is a necessary and sufficient condition for the existence of K\\"ahler metric with constant scalar curvature. Our results also provide explicit examples of relative K-unstable toric orbi-surfaces that do not admit extremal metrics.

  12. Convex analysis and global optimization

    CERN Document Server

    Tuy, Hoang

    2016-01-01

    This book presents state-of-the-art results and methodologies in modern global optimization, and has been a staple reference for researchers, engineers, advanced students (also in applied mathematics), and practitioners in various fields of engineering. The second edition has been brought up to date and continues to develop a coherent and rigorous theory of deterministic global optimization, highlighting the essential role of convex analysis. The text has been revised and expanded to meet the needs of research, education, and applications for many years to come. Updates for this new edition include: · Discussion of modern approaches to minimax, fixed point, and equilibrium theorems, and to nonconvex optimization; · Increased focus on dealing more efficiently with ill-posed problems of global optimization, particularly those with hard constraints;

  13. Reconstruction of convex bodies from surface tensors

    DEFF Research Database (Denmark)

    Kousholt, Astrid; Kiderlen, Markus

    The set of all surface tensors of a convex body K (Minkowski tensors derived from the surface area measure of K) determine K up to translation, and hereby, the surface tensors of K contain all information on the shape of K. Here, shape means the equivalence class of all convex bodies...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available....... The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...

  14. A Note on Upper Convex Density

    Institute of Scientific and Technical Information of China (English)

    YIN JIAN-DONG; ZHOU ZUO-LING

    2010-01-01

    For a self-similar set E satisfying the open set condition,upper convex density is an important concept for the computation of its Hausdorff measure,and it is well known that the set of relative interior points with upper convex density 1has a full Hausdorff measure.But whether the upper convex densities of E at all the relative interior points are equal to 1? In other words,whether there exists a relative interior point of E such that the upper convex density of E at this point is less than 1?In this paper,the authors construct a self-similar set satisfying the open set condition,which has a relative interior point with upper convex density less than 1.Thereby,the above problem is sufficiently answered.

  15. A plasticity principle of convex quadrilaterals on a complete convex surface of bounded specific curvature

    CERN Document Server

    Zachos, Anastasios

    2010-01-01

    We obtain the plasticity equations for convex quadrilaterals on a complete convex surface with bounded specific curvature and derive a plasticity principle which states that: Given four shortest arcs which meet at the weighted Fermat-Torricelli point P_F and their endpoints form a convex quadrilateral, an increase of the weight that corresponds to a shortest arc causes a decrease to the two weights that correspond to the two neighboring shortest arcs and an increase to the weight that corresponds to the opposite shortest arc. We show a connection between the plasticity of convex quadrilaterals on a complete convex surface with bounded specific curvature with the plasticity of generalized convex quadrilaterals on a manifold which is composed by triangles located on a complete convex surface of bounded specific curvature and triangles located on a two dimensional sphere whose constant Gaussian curvature equals to the infimum or supremum of the specific curvature. Furthermore, we give some cases of geometrizatio...

  16. Non-differentiable multiobjective mixed symmetric duality under generalized convexity

    Directory of Open Access Journals (Sweden)

    Li Jueyou

    2011-01-01

    Full Text Available Abstract The objective of this paper is to obtain a mixed symmetric dual model for a class of non-differentiable multiobjective nonlinear programming problems where each of the objective functions contains a pair of support functions. Weak, strong and converse duality theorems are established for the model under some suitable assumptions of generalized convexity. Several special cases are also obtained. MS Classification: 90C32; 90C46.

  17. Convex weighting criteria for speaking rate estimation

    Science.gov (United States)

    Jiao, Yishan; Berisha, Visar; Tu, Ming; Liss, Julie

    2015-01-01

    Speaking rate estimation directly from the speech waveform is a long-standing problem in speech signal processing. In this paper, we pose the speaking rate estimation problem as that of estimating a temporal density function whose integral over a given interval yields the speaking rate within that interval. In contrast to many existing methods, we avoid the more difficult task of detecting individual phonemes within the speech signal and we avoid heuristics such as thresholding the temporal envelope to estimate the number of vowels. Rather, the proposed method aims to learn an optimal weighting function that can be directly applied to time-frequency features in a speech signal to yield a temporal density function. We propose two convex cost functions for learning the weighting functions and an adaptation strategy to customize the approach to a particular speaker using minimal training. The algorithms are evaluated on the TIMIT corpus, on a dysarthric speech corpus, and on the ICSI Switchboard spontaneous speech corpus. Results show that the proposed methods outperform three competing methods on both healthy and dysarthric speech. In addition, for spontaneous speech rate estimation, the result show a high correlation between the estimated speaking rate and ground truth values. PMID:26167516

  18. Functional orthopedic magnetic appliance (FOMA) II--modus operandi.

    Science.gov (United States)

    Vardimon, A D; Stutzmann, J J; Graber, T M; Voss, L R; Petrovic, A G

    1989-05-01

    A new functional appliance (FA) to correct Class II dentoskeletal malocclusions is introduced. The functional orthopedic magnetic appliance (FOMA) II uses upper and lower attracting magnetic means (Nd2Fe14B) to constrain the lower jaw in an advanced sagittal posture. In vitro, a special gauge transducer measured the magnetic attractive path and forces. In vivo, 13 prepubertal female Macaca fascicularis monkeys received facial implants and were treated for 4 months with the following appliances: conventional FA (four subjects), FOMA II (five subjects), a combined FOMA II + FA (two subjects), and sham (control) appliance (two subjects). The in vitro results showed the following: vertico-sagitally displaced upper and lower magnets attracted ultimately along an oblique line with a terminal horizonal slide to become fully superimposed; the functional performance improved when the magnetic interface acted as a magnetic inclined plane; and the magnetic force was able to guide and constrain the mandible toward the constructive protrusive closure position (CPCP) (1.2 mm, F = 570 gm) from levels below the habitual rest position (3 mm, F = 219 gm) and the electromyographic (EMG) relaxed position (8.5 mm, F = 45 gm). The in vivo results demonstrated the following: functional performance increased in FOMA II (22%) and in the combined FOMA II + FA (28%) over the conventional FA; mandibular length increased significantly in the treated animals (means = 2.83 +/- 0.70 mm) over the control animals (means = 0.43 +/- 0.08 mm); incisor proclination was lower in magnetic appliances (means = 4.57 +/- 1.76 degrees) than in the conventional FA (means = 8.75 +/- 1.85 degrees); mandibular elongation and condylar posterior inclination resulted from posterosuperior endochondral growth (increased cell proliferation and/or hyperplasia of functional chondroblasts) and by bony remodeling of the condylar neck (apposition posterior border, resorption anterior border), respectively; virtually no

  19. Convexity and the Euclidean Metric of Space-Time

    Directory of Open Access Journals (Sweden)

    Nikolaos Kalogeropoulos

    2017-02-01

    Full Text Available We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.

  20. Convex-set description of quantum phase transitions in the transverse Ising model using reduced-density-matrix theory.

    Science.gov (United States)

    Schwerdtfeger, Christine A; Mazziotti, David A

    2009-06-14

    Quantum phase transitions in N-particle systems can be identified and characterized by the movement of the two-particle reduced density matrix (2-RDM) along the boundary of its N-representable convex set as a function of the Hamiltonian parameter controlling the phase transition [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 74, 012501 (2006)]. For the one-dimensional transverse Ising model quantum phase transitions as well as their finite-lattice analogs are computed and characterized by the 2-RDM movement with respect to the transverse magnetic field strength g. The definition of a 2-RDM "speed" quantifies the movement of the 2-RDM per unit of g, which reaches its maximum at the critical point of the phase transition. For the infinite lattice the convex set of 2-RDMs and the 2-RDM speed are computed from the exact solution of the 2-RDM in the thermodynamic limit of infinite N [P. Pfeuty, Ann. Phys. 57, 79 (1970)]. For the finite lattices we compute the 2-RDM convex set and its speed by the variational 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] in which approximate ground-state 2-RDMs are calculated without N-particle wave functions by using constraints, known as N-representability conditions, to restrict the 2-RDMs to represent quantum system of N fermions. Advantages of the method include: (i) rigorous lower bounds on the ground-state energies, (ii) polynomial scaling of the calculation with N, and (iii) independence of the N-representability conditions from a reference wave function, which enables the modeling of multiple quantum phases. Comparing the 2-RDM convex sets for the finite- and infinite-site lattices reveals that the variational 2-RDM method accurately captures the shape of the convex set and the signature of the phase transition in the 2-RDM movement. From the 2-RDM all one- and two-particle expectation values (or order parameters) of the quantum Ising model can also be computed including the pair correlation function, which

  1. Changes in soft tissue profile using functional appliances in the treatment of skeletal class II malocclusion

    Directory of Open Access Journals (Sweden)

    Stamenković Zorana

    2015-01-01

    Full Text Available Introduction. The effects of orthodontic treatment are considered to be successful if the facial harmony is achieved, while the structures of soft tissue profile are in harmony with skeletal structures of neurocranium and viscerocranium. In patients with skeletal distal bite caused by mandibular retrognathism, facial esthetics is disturbed often, in terms of pronounced convexity of the profile and change in the position and relationship of the lips. Objective. The aim of this study was to determine the extent of soft tissue profile changes in patients with skeletal Class II malocclusion treated with three different orthodontic appliances: Fränkel functional regulator type I (FR-I, Balters’ Bionator type I and Hotz appliance. Methods. The study included 60 patients diagnosed with skeletal Class II malocclusion caused by mandibular retrognathism, in the period of early mixed dentition. Each subgroup of 20 patients was treated with a variety of orthodontic appliances. On the lateral cephalogram, before and after treatment, the following parameters were analyzed: T angle, H angle, the height of the upper lip, the position of the upper and lower lip in relation to the esthetic line. Within the statistical analysis the mean, maximum, minimum, standard deviation, coefficient of variation, two-factor analysis of variance with repeated measures and the factor analysis of variance were calculated using ANOVA, Bonferroni test and Student’s t-test. Results. A significant decrease of angles T and H was noticed in the application of FR-I, from 21.60° to 17.15°, and from 16.45° to 13.40° (p<0.001. FR-I decreased the height of the upper lip from 26.15 mm to 25.85 mm, while Hotz appliance and Balters’ Bionator type I increased the height of the upper lip, thereby deteriorating esthetics of the patient. Conclusion. All used orthodontic appliances lead to changes in soft tissue profile in terms of improving facial esthetics, with the most distinctive

  2. Structural and functional characteristics of plant proteinase inhibitor-II (PI-II) family.

    Science.gov (United States)

    Rehman, Shazia; Aziz, Ejaz; Akhtar, Wasim; Ilyas, Muhammad; Mahmood, Tariq

    2017-02-09

    Plant proteinase inhibitor-II (PI-II) proteins are one of the promising defensive proteins that helped the plants to resist against different kinds of unfavorable conditions. Different roles for PI-II have been suggested such as regulation of endogenous proteases, modulation of plant growth and developmental processes and mediating stress responses. The basic knowledge on genetic and molecular diversity of these proteins has provided significant insight into their gene structure and evolutionary relationships in various members of this family. Phylogenetic comparisons of these family genes in different plants suggested that the high rate of retention of gene duplication and inhibitory domain multiplication may have resulted in the expansion and functional diversification of these proteins. Currently, a large number of transgenic plants expressing PI-II genes are being developed for enhancing the defensive capabilities against insects, bacteria and pathogenic fungi. Much emphasis is yet to be given to exploit this ever expanding repertoire of genes for improving abiotic stress resistance in transgenic crops. This review presents an overview about the current knowledge on PI-II family genes, their multifunctional role in plant defense and physiology with their potential applications in biotechnology.

  3. Combining Convex-Concave Decompositions and Linearization Approaches for solving BMIs, with application to Static Output Feedback

    CERN Document Server

    Dinh, Quoc Tran; Michiels, Wim; Diehl, Moritz

    2011-01-01

    A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem.Applications to various output feedback controller synthesis problems are presented. In these applications the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from COMPleib library.

  4. On the vertex index of convex bodies

    CERN Document Server

    Bezdek, Karoly

    2011-01-01

    We introduce the vertex index, vein(K), of a given centrally symmetric convex body K, which, in a sense, measures how well K can be inscribed into a convex polytope with small number of vertices. This index is closely connected to the illumination parameter of a body, introduced earlier by the first named author, and, thus, related to the famous conjecture in Convex Geometry about covering of a d-dimensional body by 2^d smaller positively homothetic copies. We provide asymptotically sharp estimates (up to a logarithmic term) of this index in the general case. Also, we provide sharp estimates in dimensions 2 and 3.

  5. Fuzzy Clustering Using the Convex Hull as Geometrical Model

    Directory of Open Access Journals (Sweden)

    Luca Liparulo

    2015-01-01

    Full Text Available A new approach to fuzzy clustering is proposed in this paper. It aims to relax some constraints imposed by known algorithms using a generalized geometrical model for clusters that is based on the convex hull computation. A method is also proposed in order to determine suitable membership functions and hence to represent fuzzy clusters based on the adopted geometrical model. The convex hull is not only used at the end of clustering analysis for the geometric data interpretation but also used during the fuzzy data partitioning within an online sequential procedure in order to calculate the membership function. Consequently, a pure fuzzy clustering algorithm is obtained where clusters are fitted to the data distribution by means of the fuzzy membership of patterns to each cluster. The numerical results reported in the paper show the validity and the efficacy of the proposed approach with respect to other well-known clustering algorithms.

  6. Noah, Joseph and Convex Hulls

    Science.gov (United States)

    Watkins, N. W.; Chau, Y.; Chapman, S. C.

    2010-12-01

    The idea of describing animal movement by mathematical models based on diffusion and Brownian motion has a long heritage. It has thus been natural to account for those aspects of motion that depart from the Brownian by the use of models incorporating long memory & subdiffusion (“the Joseph effect”) and/or heavy tails & superdiffusion (“the Noah effect”). My own interest in this problem was originally from a geoscience perspective, and was triggered by the need to model time series in space physics where both effects coincide. Subsequently I have been involved in animal foraging studies [e.g. Edwards et al, Nature, 2007]. I will describe some recent work [Watkins et al, PRE, 2009] which studies how fixed-timestep and variable-timestep formulations of anomalous diffusion are related in the presence of heavy tails and long range memory (stable processes versus the CTRW). Quantities for which different scaling relations are predicted between the two approaches are of particular interest, to aid testability. I will also present some of work in progress on the convex hull of anomalously diffusing walkers, inspired by its possible relevance to the idea of home range in biology, and by Randon-Furling et al’s recent analytical results in the Brownian case [PRL, 2009].

  7. The -Curvature Images of Convex Bodies and -Projection Bodies

    Indian Academy of Sciences (India)

    Songjun Lv; Gangsong Leng

    2008-08-01

    Associated with the -curvature image defined by Lutwak, some inequalities for extended mixed -affine surface areas of convex bodies and the support functions of -projection bodies are established. As a natural extension of a result due to Lutwak, an -type affine isoperimetric inequality, whose special cases are -Busemann–Petty centroid inequality and -affine projection inequality, respectively, is established. Some -mixed volume inequalities involving -projection bodies are also established.

  8. A formulation of combinatorial auction via reverse convex programming

    Directory of Open Access Journals (Sweden)

    Henry Schellhorn

    2005-01-01

    of this problem, where orders are aggregated and integrality constraints are relaxed. It was proved that this problem could be solved efficiently in two steps by calculating two fixed points, first the fixed point of a contraction mapping, and then of a set-valued function. In this paper, we generalize the problem to incorporate constraints on maximum price changes between two auction rounds. This generalized problem cannot be solved by the aforementioned methods and necessitates reverse convex programming techniques.

  9. Revising incompletely specified convex probabilistic belief bases

    CSIR Research Space (South Africa)

    Rens, G

    2016-04-01

    Full Text Available International Workshop on Non-Monotonic Reasoning (NMR), 22-24 April 2016, Cape Town, South Africa Revising Incompletely Specified Convex Probabilistic Belief Bases Gavin Rens CAIR_, University of KwaZulu-Natal, School of Mathematics, Statistics...

  10. Convex analysis and optimization in Hadamard spaces

    CERN Document Server

    Bacak, Miroslav

    2014-01-01

    This book gives a first systematic account on the subject of convex analysis and optimization in Hadamard spaces. It is primarily aimed at both graduate students and researchers in analysis and optimization.

  11. A New Section Theorem in L-convex Spaces and Its Applications%建立在L-凸空间上的截口定理及其应用

    Institute of Scientific and Technical Information of China (English)

    金彩云; 程曹宗

    2007-01-01

    In this paper, the author gives a new section theorem in L-convex spaces. And as its applications, the author proves a coincident theorem and a two-functional minimax theorem established in L-convex spaces.

  12. Linearization functors on real convex sets

    OpenAIRE

    Velasco, Mauricio

    2012-01-01

    We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to efficient computation. These operations are convex analogues of Hom functors, tensor products, symmetric powers, exterior powers and general Schur functors on vector spaces and lead to novel constructions even for polyhedra.

  13. The convexity radius of a Riemannian manifold

    OpenAIRE

    Dibble, James

    2014-01-01

    The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver's method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius.

  14. Convexity conditions and normal structure of Banach spaces

    Science.gov (United States)

    Saejung, Satit

    2008-08-01

    We prove that F-convexity, the property dual to P-convexity of Kottman, implies uniform normal structure. Moreover, in the presence of the WORTH property, normal structure follows from a weaker convexity condition than F-convexity. The latter result improves the known fact that every uniformly nonsquare space with the WORTH property has normal structure.

  15. Entropy Coherent and Entropy Convex Measures of Risk

    NARCIS (Netherlands)

    Laeven, R.J.A.; Stadje, M.A.

    2011-01-01

    We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences, respe

  16. A further characteristic of abstract convexity structures on topological spaces

    Science.gov (United States)

    Xiang, Shu-Wen; Xia, Shunyou

    2007-11-01

    In this paper, we give a characteristic of abstract convexity structures on topological spaces with selection property. We show that if a convexity structure defined on a topological space has the weak selection property then satisfies H0-condition. Moreover, in a compact convex subset of a topological space with convexity structure, the weak selection property implies the fixed point property.

  17. Exact and Approximate Sizes of Convex Datacubes

    Science.gov (United States)

    Nedjar, Sébastien

    In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.

  18. Delivering sound energy along an arbitrary convex trajectory.

    Science.gov (United States)

    Zhao, Sipei; Hu, Yuxiang; Lu, Jing; Qiu, Xiaojun; Cheng, Jianchun; Burnett, Ian

    2014-10-15

    Accelerating beams have attracted considerable research interest due to their peculiar properties and various applications. Although there have been numerous research on the generation and application of accelerating light beams, few results have been published on the generation of accelerating acoustic beams. Here we report on the experimental observation of accelerating acoustic beams along arbitrary convex trajectories. The desired trajectory is projected to the spatial phase profile on the boundary which is discretized and sampled spatially. The sound field distribution is formulated with the Green function and the integral equation method. Both the paraxial and the non-paraxial regimes are examined and observed in the experiments. The effect of obstacle scattering in the sound field is also investigated and the results demonstrate that the approach is robust against obstacle scattering. The realization of accelerating acoustic beams will have an impact on various applications where acoustic information and energy are required to be delivered along an arbitrary convex trajectory.

  19. A Convex Optimization Model and Algorithm for Retinex

    Directory of Open Access Journals (Sweden)

    Qing-Nan Zhao

    2017-01-01

    Full Text Available Retinex is a theory on simulating and explaining how human visual system perceives colors under different illumination conditions. The main contribution of this paper is to put forward a new convex optimization model for Retinex. Different from existing methods, the main idea is to rewrite a multiplicative form such that the illumination variable and the reflection variable are decoupled in spatial domain. The resulting objective function involves three terms including the Tikhonov regularization of the illumination component, the total variation regularization of the reciprocal of the reflection component, and the data-fitting term among the input image, the illumination component, and the reciprocal of the reflection component. We develop an alternating direction method of multipliers (ADMM to solve the convex optimization model. Numerical experiments demonstrate the advantages of the proposed model which can decompose an image into the illumination and the reflection components.

  20. Gauss images of hyperbolic cusps with convex polyhedral boundary

    CERN Document Server

    Fillastre, François

    2009-01-01

    We prove that a 3--dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by its Gauss image. Furthermore, any spherical metric on the torus with cone singularities of negative curvature and all closed contractible geodesics of length greater than $2\\pi$ is the metric of the Gauss image of some convex polyhedral cusp. This result is an analog of the Rivin-Hodgson theorem characterizing compact convex hyperbolic polyhedra in terms of their Gauss images. The proof uses a variational method. Namely, a cusp with a given Gauss image is identified with a critical point of a functional on the space of cusps with cone-type singularities along a family of half-lines. The functional is shown to be concave and to attain maximum at an interior point of its domain. As a byproduct, we prove rigidity statements with respect to the Gauss image for cusps with or without cone-type singularities. In a special case, our theorem is equivalent to existence of a circle pattern on the torus, with prescrib...

  1. Generalizing the Convex Hull of a Sample: The R Package alphahull

    Directory of Open Access Journals (Sweden)

    Beatriz Pateiro-López

    2010-10-01

    Full Text Available This paper presents the R package alphahull which implements the α-convex hull and the α-shape of a finite set of points in the plane. These geometric structures provide an informative overview of the shape and properties of the point set. Unlike the convex hull, the α-convex hull and the α-shape are able to reconstruct non-convex sets. This flexibility make them specially useful in set estimation. Since the implementation is based on the intimate relation of theses constructs with Delaunay triangulations, the R package alphahull also includes functions to compute Voronoi and Delaunay tesselations. The usefulness of the package is illustrated with two small simulation studies on boundary length estimation.

  2. Convex integration theory solutions to the h-principle in geometry and topology

    CERN Document Server

    Spring, David

    1998-01-01

    This book provides a comprehensive study of convex integration theory in immersion-theoretic topology. Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to optimal control theory. Though topological in nature, the theory is based on a precise analytical approximation result for higher order derivatives of functions, proved by M. Gromov. This book is the first to present an exacting record and exposition of all of the basic concepts and technical results of convex integration theory in higher order jet spaces, including the theory of iterated convex hull extensions and the theory of relative h-principles. A second feature of the book is its detailed presentation of applications of the general theory to topics in symplectic topology, divergence free vector fields on 3-manifolds, isometric immersions, totally real embeddings, u...

  3. Convex Clustering: An Attractive Alternative to Hierarchical Clustering

    Science.gov (United States)

    Chen, Gary K.; Chi, Eric C.; Ranola, John Michael O.; Lange, Kenneth

    2015-01-01

    The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its shortcomings in accuracy, hierarchical clustering is the dominant clustering method in bioinformatics. Biologists find the trees constructed by hierarchical clustering visually appealing and in tune with their evolutionary perspective. Hierarchical clustering operates on multiple scales simultaneously. This is essential, for instance, in transcriptome data, where one may be interested in making qualitative inferences about how lower-order relationships like gene modules lead to higher-order relationships like pathways or biological processes. The recently developed method of convex clustering preserves the visual appeal of hierarchical clustering while ameliorating its propensity to make false inferences in the presence of outliers and noise. The solution paths generated by convex clustering reveal relationships between clusters that are hidden by static methods such as k-means clustering. The current paper derives and tests a novel proximal distance algorithm for minimizing the objective function of convex clustering. The algorithm separates parameters, accommodates missing data, and supports prior information on relationships. Our program CONVEXCLUSTER incorporating the algorithm is implemented on ATI and nVidia graphics processing units (GPUs) for maximal speed. Several biological examples illustrate the strengths of convex clustering and the ability of the proximal distance algorithm to handle high-dimensional problems. CONVEXCLUSTER can be freely downloaded from the UCLA Human Genetics web site at http://www.genetics.ucla.edu/software/ PMID:25965340

  4. Amino-functionalized core-shell magnetic mesoporous composite microspheres for Pb(II) and Cd(II) removal.

    Science.gov (United States)

    Tang, Yulin; Liang, Song; Wang, Juntao; Yu, Shuili; Wang, Yilong

    2013-04-01

    Amino-functionalized Fe3O4@mesoporous SiO2 core-shell composite microspheres NH2-MS in created in multiple synthesis steps have been investigated for Pb(II) and Cd(II) adsorption. The microspheres were characterized by transmission electron microscope (TEM), scanning electron microscope (SEM), N2 adsorption-desorption, zeta potential measurements and vibrating sample magnetometer. Batch adsorption tests indicated that NH2-MS exhibited higher adsorption affinity toward Pb(II) and Cd(II) than MS did. The Langmuir model could fit the adsorption isotherm very well with maximum adsorption capacity of 128.21 and 51.81 mg/g for Pb(II) and Cd(II), respectively, implying that adsorption processes involved monolayer adsorption. Pb(II) and Cd(II) adsorption could be well described by the pseudo second-order kinetics model, and was found to be strongly dependent on pH and humic acid. The Pb(II)- and Cd(II)-loaded microspheres were effectively desorbed using 0.01 mol/L HCl or EDTA solution. NH2-MS have promise for use as adsorbents in the removal of Pb(II) and Cd(II) in wastewater treatment processes.

  5. 具有凸资源消耗函数的最小化Makespan的平行机调度问题%Parallel Machine Scheduling Problems with a Convex Resource Consumption Function to Minimize the Makespan

    Institute of Scientific and Technical Information of China (English)

    李凯; 史烨; 马英

    2013-01-01

    研究了一类资源受限的平行机调度问题,其中假定作业的处理时间是其消耗资源量的凸减函数,调度的目标是在限定资源总量的情况下最小化Makespan(最大完工时间).给出了此类NP-hard问题的形式化描述.定义了关键机器与非关键机器,给出了非最优解必定存在非关键机器的论断.尽快缩短非关键机器与关键机器之间工作量的差距能够有效逼近最优解,从而构造了快速的模拟退火算法.设计了一个下界用于衡量解的精度,并用于构造模拟退火算法迭代结束条件.算法性能通过20000组随机数值算例进行了测试,实验结果表明所构造的模拟退火算法能够在0.1秒之内有效求解1000个作业的问题并将相对误差控制在0.01%以内.该算法体现出很高的精度和计算效率.%In most production environments, such as the steel industry, the job processing times may be shortened by using additional resources, e. g. energy, manpower, money and catalyzer. Different from the supposition that processing times are fixed in the traditional scheduling papers, this paper asserts that scheduling problems with changeable processing times can improve not only the production efficiency but also maximize resource consumption. Factories must find a balance between production efficiency and resource consumption. This paper asserts that the parallel machine scheduling problem has changeable job processing times, which has a convex decreasing function of resource consumption. Monma et al. think that the convex decreasing function has practical implications because it can reflect the diminishing marginal return of the production process. This paper supposes that the total resource is limited, and an optimization method ( e. g. minimizing the makespan) is important to improve the production efficiency. The formal description of this NP-hard problem is given. The characteristics of the optimal and non-optimal solutions are

  6. On the convexity of Relativistic Ideal Magnetohydrodynamics

    CERN Document Server

    Ibáñez, José-María; Aloy, Miguel-Ángel; Martí, José-María; Miralles, Juan-Antonio

    2015-01-01

    We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity condition on the magnetic field. The result is expressed in the form of a generalized fundamental derivative written as the sum of two terms. The first one is the generalized fundamental derivative in the case of purely hydrodynamical (relativistic) flow. The second one contains the effects of the magnetic field. The analysis ...

  7. A generalization of the convex Kakeya problem

    KAUST Repository

    Ahn, Heekap

    2012-01-01

    We consider the following geometric alignment problem: Given a set of line segments in the plane, find a convex region of smallest area that contains a translate of each input segment. This can be seen as a generalization of Kakeya\\'s problem of finding a convex region of smallest area such that a needle can be turned through 360 degrees within this region. Our main result is an optimal Θ(n log n)-time algorithm for our geometric alignment problem, when the input is a set of n line segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then the optimum placement is when the midpoints of the segments coincide. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallest-perimeter region containing a translate of any rotated copy of G. © 2012 Springer-Verlag Berlin Heidelberg.

  8. A new method for automatically constructing convexity-preserving interpolatory splines

    Institute of Scientific and Technical Information of China (English)

    PAN Yongjuan; WANG Guojin

    2004-01-01

    Constructing a convexity-preserving interpolating curve according to the given planar data points is a problem to be solved in computer aided geometric design (CAGD). So far, almost all methods must solve a system of equations or recur to a complicated iterative process, and most of them can only generate some function-form convexity-preserving interpolating curves which are unaccommodated with the parametric curves, commonly used in CAGD systems. In order to overcome these drawbacks, this paper proposes a new method that can automatically generate some parametric convexity-preserving polynomial interpolating curves but dispensing with solving any system of equations or going at any iterative computation. The main idea is to construct a family of interpolating spline curves first with the shape parameter a as its family parameter; then, using the positive conditions of Bernstein polynomial to respectively find a range in which the shape parameter a takes its value for two cases of global convex data points and piecewise convex data points so as to make the corresponding interpolating curves convexity-preserving and C2(or G1) continuous. The method is simple and convenient, and the resulting interpolating curves possess smooth distribution of curvature. Numerical examples illustrate the correctness and the validity of theoretical reasoning.

  9. Non-convex onion peeling using a shape hull algorithm

    OpenAIRE

    Fadili, Jalal M.; Melkemi, Mahmoud; Elmoataz, Abderrahim

    2004-01-01

    International audience; The convex onion-peeling of a set of points is the organization of these points into a sequence of interpolating convex polygons. This method is adequate to detect the shape of the “center” of a set of points when this shape is convex. However it reveals inadequate to detect non-convex shapes. Alternatively, we propose an extension of the convex onion-peeling method. It consists in representing a set of points with a sequence of non-convex polylines which are computed ...

  10. Uniform convexity and the splitting problem for selections

    CERN Document Server

    Balashov, Maxim V; 10.1016/j.jmaa.2009.06.045

    2009-01-01

    We continue to investigate cases when the Repov\\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images.

  11. Simple integer recourse models : convexity and convex approximations

    NARCIS (Netherlands)

    Klein Haneveld, W.K.; Stougie, L.; van der Vlerk, M.H.

    We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a

  12. Simple Integer Recourse Models : Convexity and Convex Approximations

    NARCIS (Netherlands)

    Klein Haneveld, Willem K.; Stougie, L; van der Vlerk, Maarten H.

    2004-01-01

    We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a

  13. Reconstruction of convex bodies from surface tensors

    DEFF Research Database (Denmark)

    Kousholt, Astrid; Kiderlen, Markus

    2016-01-01

    We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy...

  14. Reconstruction of convex bodies from surface tensors

    DEFF Research Database (Denmark)

    Kousholt, Astrid; Kiderlen, Markus

    We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based...

  15. A Complete Characterization of the Gap between Convexity and SOS-Convexity

    CERN Document Server

    Ahmadi, Amir Ali

    2011-01-01

    Our first contribution in this paper is to prove that three natural sum of squares (sos) based sufficient conditions for convexity of polynomials via the definition of convexity, its first order characterization, and its second order characterization are equivalent. These three equivalent algebraic conditions, henceforth referred to as sos-convexity, can be checked by semidefinite programming whereas deciding convexity is NP-hard. If we denote the set of convex and sos-convex polynomials in $n$ variables of degree $d$ with $\\tilde{C}_{n,d}$ and $\\tilde{\\Sigma C}_{n,d}$ respectively, then our main contribution is to prove that $\\tilde{C}_{n,d}=\\tilde{\\Sigma C}_{n,d}$ if and only if $n=1$ or $d=2$ or $(n,d)=(2,4)$. We also present a complete characterization for forms (homogeneous polynomials) except for the case $(n,d)=(3,4)$ which is joint work with G. Blekherman and is to be published elsewhere. Our result states that the set $C_{n,d}$ of convex forms in $n$ variables of degree $d$ equals the set $\\Sigma C_{...

  16. Structure/Function/Dynamics of Photosystem II Plastoquinone Binding Sites

    Science.gov (United States)

    Lambreva, Maya D.; Russo, Daniela; Polticelli, Fabio; Scognamiglio, Viviana; Antonacci, Amina; Zobnina, Veranika; Campi, Gaetano; Rea, Giuseppina

    2014-01-01

    Photosystem II (PSII) continuously attracts the attention of researchers aiming to unravel the riddle of its functioning and efficiency fundamental for all life on Earth. Besides, an increasing number of biotechnological applications have been envisaged exploiting and mimicking the unique properties of this macromolecular pigment-protein complex. The PSII organization and working principles have inspired the design of electrochemical water splitting schemes and charge separating triads in energy storage systems as well as biochips and sensors for environmental, agricultural and industrial screening of toxic compounds. An intriguing opportunity is the development of sensor devices, exploiting native or manipulated PSII complexes or ad hoc synthesized polypeptides mimicking the PSII reaction centre proteins as bio-sensing elements. This review offers a concise overview of the recent improvements in the understanding of structure and function of PSII donor side, with focus on the interactions of the plastoquinone cofactors with the surrounding environment and operational features. Furthermore, studies focused on photosynthetic proteins structure/function/dynamics and computational analyses aimed at rational design of high-quality bio-recognition elements in biosensor devices are discussed. PMID:24678671

  17. Functional Implications of Photosystem II Crystal Formation in Photosynthetic Membranes*

    Science.gov (United States)

    Tietz, Stefanie; Puthiyaveetil, Sujith; Enlow, Heather M.; Yarbrough, Robert; Wood, Magnus; Semchonok, Dmitry A.; Lowry, Troy; Li, Zhirong; Jahns, Peter; Boekema, Egbert J.; Lenhert, Steven; Niyogi, Krishna K.; Kirchhoff, Helmut

    2015-01-01

    The structural organization of proteins in biological membranes can affect their function. Photosynthetic thylakoid membranes in chloroplasts have the remarkable ability to change their supramolecular organization between disordered and semicrystalline states. Although the change to the semicrystalline state is known to be triggered by abiotic factors, the functional significance of this protein organization has not yet been understood. Taking advantage of an Arabidopsis thaliana fatty acid desaturase mutant (fad5) that constitutively forms semicrystalline arrays, we systematically test the functional implications of protein crystals in photosynthetic membranes. Here, we show that the change into an ordered state facilitates molecular diffusion of photosynthetic components in crowded thylakoid membranes. The increased mobility of small lipophilic molecules like plastoquinone and xanthophylls has implications for diffusion-dependent electron transport and photoprotective energy-dependent quenching. The mobility of the large photosystem II supercomplexes, however, is impaired, leading to retarded repair of damaged proteins. Our results demonstrate that supramolecular changes into more ordered states have differing impacts on photosynthesis that favor either diffusion-dependent electron transport and photoprotection or protein repair processes, thus fine-tuning the photosynthetic energy conversion. PMID:25897076

  18. Functional Implications of Photosystem II Crystal Formation in Photosynthetic Membranes.

    Science.gov (United States)

    Tietz, Stefanie; Puthiyaveetil, Sujith; Enlow, Heather M; Yarbrough, Robert; Wood, Magnus; Semchonok, Dmitry A; Lowry, Troy; Li, Zhirong; Jahns, Peter; Boekema, Egbert J; Lenhert, Steven; Niyogi, Krishna K; Kirchhoff, Helmut

    2015-05-29

    The structural organization of proteins in biological membranes can affect their function. Photosynthetic thylakoid membranes in chloroplasts have the remarkable ability to change their supramolecular organization between disordered and semicrystalline states. Although the change to the semicrystalline state is known to be triggered by abiotic factors, the functional significance of this protein organization has not yet been understood. Taking advantage of an Arabidopsis thaliana fatty acid desaturase mutant (fad5) that constitutively forms semicrystalline arrays, we systematically test the functional implications of protein crystals in photosynthetic membranes. Here, we show that the change into an ordered state facilitates molecular diffusion of photosynthetic components in crowded thylakoid membranes. The increased mobility of small lipophilic molecules like plastoquinone and xanthophylls has implications for diffusion-dependent electron transport and photoprotective energy-dependent quenching. The mobility of the large photosystem II supercomplexes, however, is impaired, leading to retarded repair of damaged proteins. Our results demonstrate that supramolecular changes into more ordered states have differing impacts on photosynthesis that favor either diffusion-dependent electron transport and photoprotection or protein repair processes, thus fine-tuning the photosynthetic energy conversion.

  19. Functional assessment of feet of patients with type II diabetes

    Directory of Open Access Journals (Sweden)

    Vinicius Saura Cardoso

    2014-09-01

    Full Text Available Objective: To evaluate the incidence of functional changes and risk of developing ulcers in type II diabetic patients seen in Primary Healthcare Units (Unidades Básicas de Saúde- UBS. Methods: A cross-sectional, quantitative and descriptive study comprising 80patients with type II diabetes mellitus (DM aged between 41 to 85 years and attended inthe UBS in the city of Parnaíba-PI. Volunteers responded to the identification form and theMichigan Neuropathy Screening Instrument (MNSI, followed by an evaluation of the lowerlimbs, as follows: achilles and patellar reflex, palpation of arterial pulses (dorsalis pedis and posterior tibial, tactile sensitivity (Monofilament 10g and vibration sensitivity (128Hz tuning fork; identification of the presence of changes such as ingrown toenails, calluses,claw toes and hair loss. Finally, using the information acquired from the assessment, subjects were classified according to the risk of developing wounds. Results: The sample consisted of 76 diabetic patients, with average age of 63.8 ± 10.4 years, 63 (82.8% were female, mean diagnostic time 8.8 ± 7.2 years, average body mass index (BMI 28.2 ± 5.4 kg/m2, with 15.7% of the sample being smokers. The myotatic reflexes and arterial pulses were reduced. Tactile sensitivity was identified in 81.5% and 13.1% did not feel the vibration of the tuning fork. The most dominant changes identified were calluses, 76.3% (n = 58. Risk level 2 of developing ulcers stood out, 52.6% (n = 40. Conclusion: Functional changes were detected in the sample and a classification of risk 2 for developing wounds was found in more than 50% of the assessed patients. doi:http://dx.doi.org/10.5020/18061230.2013.p563

  20. Kr II and Xe II axial velocity distribution functions in a cross-field ion source

    Science.gov (United States)

    Lejeune, A.; Bourgeois, G.; Mazouffre, S.

    2012-07-01

    Laser induced fluorescence measurements were carried out in a cross-field ion source to examine the behaviour of the axial ion velocity distribution functions (VDFs) in the expanding plasma. In the present paper, we focus on the axial VDFs of Kr II and Xe II ions. We examine the contourplots in a 1D-phase space (x,vx) representation in front of the exhaust channel and along the centerline of the ion source. The main ion beam, whose momentum corresponds to the ions that are accelerated through the whole potential drop, is observed. A secondary structure reveals the ions coming from the opposite side of the channel. We show that the formation of the neutralized ion flow is governed by the annular geometry. The assumption of a collisionless shock or a double layer due to supersonic beam interaction is not necessary. A non-negligible fraction of slow ions originates in local ionization or charge-exchange collision events between ions of the expanding plasma and atoms of the background residual gas. Slow ions that are produced near the centerline in the vicinity of the exit plane are accelerated toward the source body with a negative velocity leading to a high sputtering of front face. On the contrary, the ions that are produced in the vicinity of the channel exit plane are partially accelerated by the extended electric field.

  1. Application of mesoporous SBA-15 silica functionalized with 4-amino-2-mercaptopyrimidine for the adsorption of Cu(II), Zn(II), Cd(II), Ni(II), and Pb(II) from water.

    Science.gov (United States)

    Jorgetto, Alexandre de Oliveira; Pereira, Silvana Pontes; Silva, Rafael Innocenti Vieira da; Saeki, Margarida Juri; Martines, Marco Antonio Utrera; Pedrosa, Valber de Albuquerque; Castro, Gustavo Rocha de

    2015-01-01

    This work reports the sol-gel synthesis of a SBA-15 silica, and its functionalization with 4-amino-2-mercaptopyrimidine to perform adsorption of metal species from aqueous media. The functionalization of the material was confirmed by FTIR and superficial area measurements. The final material was tested through batch experiments to uncover its adsorptive properties towards the adsorption of Cu(II), Cd(II), Zn(II), Pb(II) and Ni(II). Contact time and pH conditions were investigated, and the material presented slow adsorption kinetics, which was best described by the pseudo-second order model. In addition, at pH 5 - 6, the adsorption of the metal ions was favored. Under optimized conditions, the material had its maximum adsorption capacities determined for all metal species studied, and the obtained values were 13.0 µmol g(-1) for Zn(II), 12.3 µmol g(-1) for Cu(II), 3.45 µmol g(-1) for Ni(II), 2.45 µmol g(-1) for Pb(II) and 0.60 µmol g(-1) for Cd(II). The capacity differences between each metal ion were discussed in terms of their ionic radii and Person's soft/hard acids/bases concept.

  2. Spectral calibration for convex grating imaging spectrometer

    Science.gov (United States)

    Zhou, Jiankang; Chen, Xinhua; Ji, Yiqun; Chen, Yuheng; Shen, Weimin

    2013-12-01

    Spectral calibration of imaging spectrometer plays an important role for acquiring target accurate spectrum. There are two spectral calibration types in essence, the wavelength scanning and characteristic line sampling. Only the calibrated pixel is used for the wavelength scanning methods and he spectral response function (SRF) is constructed by the calibrated pixel itself. The different wavelength can be generated by the monochromator. The SRF is constructed by adjacent pixels of the calibrated one for the characteristic line sampling methods. And the pixels are illuminated by the narrow spectrum line and the center wavelength of the spectral line is exactly known. The calibration result comes from scanning method is precise, but it takes much time and data to deal with. The wavelength scanning method cannot be used in field or space environment. The characteristic line sampling method is simple, but the calibration precision is not easy to confirm. The standard spectroscopic lamp is used to calibrate our manufactured convex grating imaging spectrometer which has Offner concentric structure and can supply high resolution and uniform spectral signal. Gaussian fitting algorithm is used to determine the center position and the Full-Width-Half-Maximum(FWHM)of the characteristic spectrum line. The central wavelengths and FWHMs of spectral pixels are calibrated by cubic polynomial fitting. By setting a fitting error thresh hold and abandoning the maximum deviation point, an optimization calculation is achieved. The integrated calibration experiment equipment for spectral calibration is developed to enhance calibration efficiency. The spectral calibration result comes from spectral lamp method are verified by monochromator wavelength scanning calibration technique. The result shows that spectral calibration uncertainty of FWHM and center wavelength are both less than 0.08nm, or 5.2% of spectral FWHM.

  3. Characterization of the minimal penalty of a convex risk measure with applications to Levy processes

    CERN Document Server

    Hernández-Hernández, Daniel

    2012-01-01

    The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and closed subset of the absolutely continuous measures with respect to some reference measure $\\mathbb{P}$ to be minimal. When the probability space supports a L\\'{e}vy process, we establish results that guarantee the minimality property of a penalty function described in terms of the coefficients associated with the density processes. The set of densities processes is described and the convergence of its quadratic variation is analyzed.

  4. Scavenger receptor AI/II truncation, lung function and COPD

    DEFF Research Database (Denmark)

    Thomsen, M; Nordestgaard, B G; Tybjaerg-Hansen, A

    2011-01-01

    The scavenger receptor A-I/II (SRA-I/II) on alveolar macrophages is involved in recognition and clearance of modified lipids and inhaled particulates. A rare variant of the SRA-I/II gene, Arg293X, truncates the distal collagen-like domain, which is essential for ligand recognition. We tested whet...

  5. Tropicalized Lambda Lengths, Measured Laminations and Convexity

    DEFF Research Database (Denmark)

    C. Penner, R.

    cell decomposition of a surface is discovered in the limit. Finally, the tropical analogue of the convex hull construction in Minkowski space is formulated as an explicit algorithm that serially simplifies a triangulation with respect to a fixed lamination and has its own independent applications....

  6. Some Characterizations of Convex Interval Games

    NARCIS (Netherlands)

    Brânzei, R.; Tijs, S.H.; Alparslan-Gok, S.Z.

    2008-01-01

    This paper focuses on new characterizations of convex interval games using the notions of exactness and superadditivity. We also relate big boss interval games with concave interval games and obtain characterizations of big boss interval games in terms of exactness and subadditivity.

  7. A generalization of the convex Kakeya problem

    KAUST Repository

    Ahn, Heekap

    2013-09-19

    Given a set of line segments in the plane, not necessarily finite, what is a convex region of smallest area that contains a translate of each input segment? This question can be seen as a generalization of Kakeya\\'s problem of finding a convex region of smallest area such that a needle can be rotated through 360 degrees within this region. We show that there is always an optimal region that is a triangle, and we give an optimal Θ(nlogn)-time algorithm to compute such a triangle for a given set of n segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then placing the segments with their midpoint at the origin and taking their convex hull results in an optimal solution. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallest-perimeter region containing a translate of every rotated copy of G. © 2013 Springer Science+Business Media New York.

  8. Robust Utility Maximization Under Convex Portfolio Constraints

    Energy Technology Data Exchange (ETDEWEB)

    Matoussi, Anis, E-mail: anis.matoussi@univ-lemans.fr [Université du Maine, Risk and Insurance institut of Le Mans Laboratoire Manceau de Mathématiques (France); Mezghani, Hanen, E-mail: hanen.mezghani@lamsin.rnu.tn; Mnif, Mohamed, E-mail: mohamed.mnif@enit.rnu.tn [University of Tunis El Manar, Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT (Tunisia)

    2015-04-15

    We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption–investment strategy by studying the associated quadratic backward stochastic differential equation. We characterize the optimal control by using the duality method and deriving a dynamic maximum principle.

  9. Tropicalized Lambda Lengths, Measured Laminations and Convexity

    DEFF Research Database (Denmark)

    C. Penner, R.

    This work uncovers the tropical analogue for measured laminations of the convex hull construction of decorated Teichmueller theory, namely, it is a study in coordinates of geometric degeneration to a point of Thurston's boundary for Teichmueller space. This may offer a paradigm for the extension...

  10. On fixed points and uniformly convex spaces

    OpenAIRE

    Gelander, Tsachik

    2008-01-01

    The purpose of this note is to present two elementary, but useful, facts concerning actions on uniformly convex spaces. We demonstrate how each of them can be used in an alternative proof of the triviality of the first $L_p$-cohomology of higher rank simple Lie groups, proved in [BFGM].

  11. Dynamic Matchings in Convex Bipartite Graphs

    DEFF Research Database (Denmark)

    Brodal, Gerth Stølting; Georgiadis, Loukas; Hansen, Kristoffer Arnsfelt

    2007-01-01

    We consider the problem of maintaining a maximum matching in a convex bipartite graph G = (V,E) under a set of update operations which includes insertions and deletions of vertices and edges. It is not hard to show that it is impossible to maintain an explicit representation of a maximum matching...

  12. Estimates for oscillatory integrals with convex phase

    Energy Technology Data Exchange (ETDEWEB)

    Chakhkiev, M A [Moscow State Social University, Moscow (Russian Federation)

    2006-02-28

    We consider methods for estimating one-dimensional oscillatory integrals with convex phase and amplitudes of bounded variation or Lipschitz class amplitudes. In particular, we improve the estimate for the Piercey integral with near-caustic parameter values, and also consider estimation methods for n-dimensional oscillatory integrals.

  13. Some Characterizations of Convex Interval Games

    NARCIS (Netherlands)

    Brânzei, R.; Tijs, S.H.; Alparslan-Gok, S.Z.

    2008-01-01

    This paper focuses on new characterizations of convex interval games using the notions of exactness and superadditivity. We also relate big boss interval games with concave interval games and obtain characterizations of big boss interval games in terms of exactness and subadditivity.

  14. Directional Convexity and Finite Optimality Conditions.

    Science.gov (United States)

    1984-03-01

    system, Necessary Conditions for optimality. Work Unit Number 5 (Optimization and Large Scale Systems) *Istituto di Matematica Applicata, Universita...that R(T) is convex would then imply x(u,T) e int R(T). Cletituto di Matematica Applicata, Universita di Padova, 35100 ITALY. Sponsored by the United

  15. Convex bodies of states and maps

    Science.gov (United States)

    Grabowski, Janusz; Ibort, Alberto; Kuś, Marek; Marmo, Giuseppe

    2013-10-01

    We give a general solution to the question of when the convex hulls of orbits of quantum states on a finite-dimensional Hilbert space under unitary actions of a compact group have a non-empty interior in the surrounding space of all density operators. The same approach can be applied to study convex combinations of quantum channels. The importance of both problems stems from the fact that, usually, only sets with non-vanishing volumes in the embedding spaces of all states or channels are of practical importance. For the group of local transformations on a bipartite system we characterize maximally entangled states by the properties of a convex hull of orbits through them. We also compare two partial characteristics of convex bodies in terms of the largest balls and maximum volume ellipsoids contained in them and show that, in general, they do not coincide. Separable states, mixed-unitary channels and k-entangled states are also considered as examples of our techniques.

  16. Convexity properties of Hamiltonian group actions

    CERN Document Server

    Guillemin, Victor

    2005-01-01

    This is a monograph on convexity properties of moment mappings in symplectic geometry. The fundamental result in this subject is the Kirwan convexity theorem, which describes the image of a moment map in terms of linear inequalities. This theorem bears a close relationship to perplexing old puzzles from linear algebra, such as the Horn problem on sums of Hermitian matrices, on which considerable progress has been made in recent years following a breakthrough by Klyachko. The book presents a simple local model for the moment polytope, valid in the "generic&rdquo case, and an elementary Morse-theoretic argument deriving the Klyachko inequalities and some of their generalizations. It reviews various infinite-dimensional manifestations of moment convexity, such as the Kostant type theorems for orbits of a loop group (due to Atiyah and Pressley) or a symplectomorphism group (due to Bloch, Flaschka and Ratiu). Finally, it gives an account of a new convexity theorem for moment map images of orbits of a Borel sub...

  17. Fast approximate convex decomposition using relative concavity

    KAUST Repository

    Ghosh, Mukulika

    2013-02-01

    Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.

  18. On the convexity of N-Chebyshev sets

    Science.gov (United States)

    Borodin, Petr A.

    2011-10-01

    We define N-Chebyshev sets in a Banach space X for every positive integer N (when N=1, these are ordinary Chebyshev sets) and study conditions that guarantee their convexity. In particular, we prove that all N-Chebyshev sets are convex when N is even and X is uniformly convex or N\\ge 3 is odd and X is smooth uniformly convex.

  19. Iterative Schemes for Convex Minimization Problems with Constraints

    Directory of Open Access Journals (Sweden)

    Lu-Chuan Ceng

    2014-01-01

    Full Text Available We first introduce and analyze one implicit iterative algorithm for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: the generalized mixed equilibrium problem, the system of generalized equilibrium problems, and finitely many variational inclusions in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another implicit iterative algorithm for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.

  20. Vector optimization and monotone operators via convex duality recent advances

    CERN Document Server

    Grad, Sorin-Mihai

    2014-01-01

    This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.

  1. Convexity of Spheres in a Manifold without Conjugate Points

    Indian Academy of Sciences (India)

    Akhil Ranjan; Hemangi Shah

    2002-11-01

    For a non-compact, complete and simply connected manifold without conjugate points, we prove that if the determinant of the second fundamental form of the geodesic spheres in is a radial function, then the geodesic spheres are convex. We also show that if is two or three dimensional and without conjugate points, then, at every point there exists a ray with no focal points on it relative to the initial point of the ray. The proofs use a result from the theory of vector bundles combined with the index lemma.

  2. Reverse convex problems: an approach based on optimality conditions

    Directory of Open Access Journals (Sweden)

    Ider Tseveendorj

    2006-01-01

    Full Text Available We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.

  3. On Quasi E-Convex Bilevel Programming Problem

    Directory of Open Access Journals (Sweden)

    E. A. Youness

    2005-01-01

    Full Text Available Bilevel programming problems involve two optimization problems where the data of the first one is implicity determined by the solution of the second. This study introduces the notions of E-convexity and quasi E-convexity in bilevel programming problems to generalize quasi convex bilevel programming problems.

  4. Reverse convex problems: an approach based on optimality conditions

    OpenAIRE

    Ider Tseveendorj

    2006-01-01

    We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.

  5. The Optimality Conditions for Multiobjective Semi-infinite Programming Involving Generalized Unified (C, α, p, d)-convexity

    Institute of Scientific and Technical Information of China (English)

    ZHANG Qing-xiang; ZHANG Yong-zhan

    2013-01-01

    The definition of generalized unified (C,α,p,d)-convex function is given.The concepts of generalized unified (C,α,p,d)-quasiconvexity,generalized unified (C,α,p,d)-pseudoconvexity and generalized unified (C,α,p,d)-strictly pseudoconvex functions are presented.The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.

  6. Nonparametric instrumental regression with non-convex constraints

    Science.gov (United States)

    Grasmair, M.; Scherzer, O.; Vanhems, A.

    2013-03-01

    This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, such as integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition.

  7. Cu(I)/Cu(II) templated functional pseudorotaxanes and rotaxanes

    Indian Academy of Sciences (India)

    Subrata Saha; Pradyut Ghosh

    2012-11-01

    Threaded complexes like pseudorotaxanes, rotaxanes based on Cu(I)/Cu(II) ions have shown to be promising for the construction of mechanically interlocked molecular-level architectures. In this short review, we focus on the synthetic strategies developed to construct pseudorotaxanes and rotaxanes using Cu(I)/Cu(II) ions as template. Further, brief discussions on chemical and mechanical properties associated with some of the selected to Cu(I)/Cu(II) based pseudorotaxanes and rotaxanes are presented.

  8. A sufficient condition for global convergence of the Polak-Ribiére-Polyak method for uniformly convex functions%Polak Ribiére Polyak共轭梯度法对 一致凸函数全局收敛的一个充分条件

    Institute of Scientific and Technical Information of China (English)

    杜学武

    2001-01-01

    已有文献对求解无约束优化问题的Polak Ribiére Polyak(PRP)共轭梯度法进行了研究并得出结论:采用Wolfe线性搜索确定步长的PRP方法对一致凸函数具有全局收敛性.本文对上述问题作了进一步研究,首先通过构造反例,说明了上述文献中的结论是错误的,然后给出了PRP方法对一致凸函数全局收敛的一个充分条件.%In referrence [4],the Polak-Ribiére-Polyak(PRP) conjugate gradient method for unconstrained optimization is considered and the conclusion is obtained that the PRP method is global convergent for uniformly convex functions under the Wolfe line search.The problem in referrence [4] is further investigated.A counter example is constructed to show that the result in referrence [4] is incorrect.A sufficient condition for global convergence of the PRP method for uniformly convex functions is given.

  9. Rationally convex sets on the unit sphere in ℂ2

    Science.gov (United States)

    Wermer, John

    2008-04-01

    Let X be a rationally convex compact subset of the unit sphere S in ℂ2, of three-dimensional measure zero. Denote by R( X) the uniform closure on X of the space of functions P/ Q, where P and Q are polynomials and Q≠0 on X. When does R( X)= C( X)? Our work makes use of the kernel function for the bar{δ}b operator on S, introduced by Henkin in [5] and builds on results obtained in Anderson Izzo Wermer [3]. We define a real-valued function ɛ X on the open unit ball int B, with ɛ X ( z, w) tending to 0 as ( z, w) tends to X. We give a growth condition on ɛ X ( z, w) as ( z, w) approaches X, and show that this condition is sufficient for R( X)= C( X) (Theorem 1.1). In Section 4, we consider a class of sets X which are limits of a family of Levi-flat hypersurfaces in int B. For each compact set Y in ℂ2, we denote the rationally convex hull of Y by widehat{Y}. A general reference is Rudin [8] or Aleksandrov [1].

  10. A recurrent neural network for solving a class of generalized convex optimization problems.

    Science.gov (United States)

    Hosseini, Alireza; Wang, Jun; Hosseini, S Mohammad

    2013-08-01

    In this paper, we propose a penalty-based recurrent neural network for solving a class of constrained optimization problems with generalized convex objective functions. The model has a simple structure described by using a differential inclusion. It is also applicable for any nonsmooth optimization problem with affine equality and convex inequality constraints, provided that the objective function is regular and pseudoconvex on feasible region of the problem. It is proven herein that the state vector of the proposed neural network globally converges to and stays thereafter in the feasible region in finite time, and converges to the optimal solution set of the problem.

  11. Strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives

    OpenAIRE

    Vegh, Laszlo A.

    2011-01-01

    A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\\sum_{ij\\in E} C_{ij}(f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function. We give a strongly polynomial algorithm for the case when all $C_{ij}$'s are convex quadratic functions, settling an open problem raised e.g. by Hochbaum [1994]. We also give strongly polynomial algorithms for computing market equilibria in Fisher markets with linear util...

  12. The universal cut function and type II metrics

    Energy Technology Data Exchange (ETDEWEB)

    Kozameh, Carlos [FaMaF, University of Cordoba, Cordoba (Argentina); Newman, E T [Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 (United States); Santiago-Santiago, J G [Facultad de Ciencias Fisico Matematicas de la Universidad Autonoma de Puebla, Apartado Postal 1152, 72001, Puebla, Pue. (Mexico); Silva-Ortigoza, Gilberto [Facultad de Ciencias Fisico Matematicas de la Universidad Autonoma de Puebla, Apartado Postal 1152, 72001, Puebla, Pue. (Mexico)

    2007-04-21

    In analogy with classical electromagnetic theory, where one determines the total charge and both electric and magnetic multipole moments of a source from certain surface integrals of the asymptotic (or far) fields, it has been known for many years-from the work of Hermann Bondi-that the energy and momentum of gravitational sources could be determined by similar integrals of the asymptotic Weyl tensor. Recently, we observed that there were certain overlooked structures, defined at future null infinity, that allowed one to determine (or define) further properties of both electromagnetic and gravitating sources. These structures, families of complex 'slices' or 'cuts' of Penrose's I{sup +}, are referred to as universal cut functions. In particular, one can define from these structures a (complex) centre of mass (and centre of charge) and its equations of motion-with rather surprising consequences. It appears as if these asymptotic structures contain, in their imaginary part, a well-defined total spin-angular momentum of the source. We apply these ideas to the type II algebraically special metrics, both twisting and twist free.

  13. An algorithm for the construction of convex hulls in simple integer recourse programming

    NARCIS (Netherlands)

    Klein Haneveld, W.K.; Stougie, L.; van der Vlerk, M.H.

    1996-01-01

    We consider the objective function of a simple integer recourse problem with fixed technology matrix and discretely distributed right-hand sides. Exploiting the special structure of this problem, we devise an algorithm that determines the convex hull of this function efficiently. The results are imp

  14. Material Removal Model Considering Influence of Curvature Radius in Bonnet Polishing Convex Surface

    Institute of Scientific and Technical Information of China (English)

    SONG Jianfeng; YAO Yingxue

    2015-01-01

    The bonnet tool polishing is a novel, advanced and ultra-precise polishing process, by which the freeform surface can be polished. However, during the past few years, not only the key technology of calculating the dwell time and controlling the surface form in the bonnet polishing has been little reported so far, but also little attention has been paid to research the material removal function of the convex surface based on the geometry model considering the influence of the curvature radius. Firstly in this paper, for realizing the control of the freeform surface automatically by the bonnet polishing, on the basis of the simplified geometric model of convex surface, the calculation expression of the polishing contact spot on the convex surface considering the influence of the curvature radius is deduced, and the calculation model of the pressure distribution considering the influence of the curvature radius on the convex surface is derived by the coordinate transformation. Then the velocity distribution model is built in the bonnet polishing the convex surface. On the basis of the above research and the semi-experimental modified Preston equation obtained from the combination method of experimental and theoretical derivation, the material removal model of the convex surface considering the influence of the curvature radius in the bonnet polishing is established. Finally, the validity of the model through the simulation method has been validated. This research presents an effective prediction model and the calculation method of material removal for convex surface in bonnet polishing and prepares for the bonnet polishing the free surface numerically and automatically.

  15. A Generalization of Uniformly Extremely Convex Banach Spaces

    OpenAIRE

    Suyalatu Wulede; Wurichaihu Bai; Wurina Bao

    2016-01-01

    We discuss a new class of Banach spaces which are the generalization of uniformly extremely convex spaces introduced by Wulede and Ha. We prove that the new class of Banach spaces lies strictly between either the classes of k-uniformly rotund spaces and k-strongly convex spaces or classes of fully k-convex spaces and k-strongly convex spaces and has no inclusive relation with the class of locally k-uniformly convex spaces. We obtain in addition some characterizations and properties of this ne...

  16. Left ventricle segmentation in MRI via convex relaxed distribution matching.

    Science.gov (United States)

    Nambakhsh, Cyrus M S; Yuan, Jing; Punithakumar, Kumaradevan; Goela, Aashish; Rajchl, Martin; Peters, Terry M; Ayed, Ismail Ben

    2013-12-01

    A fundamental step in the diagnosis of cardiovascular diseases, automatic left ventricle (LV) segmentation in cardiac magnetic resonance images (MRIs) is still acknowledged to be a difficult problem. Most of the existing algorithms require either extensive training or intensive user inputs. This study investigates fast detection of the left ventricle (LV) endo- and epicardium surfaces in cardiac MRI via convex relaxation and distribution matching. The algorithm requires a single subject for training and a very simple user input, which amounts to a single point (mouse click) per target region (cavity or myocardium). It seeks cavity and myocardium regions within each 3D phase by optimizing two functionals, each containing two distribution-matching constraints: (1) a distance-based shape prior and (2) an intensity prior. Based on a global measure of similarity between distributions, the shape prior is intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive a fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed algorithm relaxes the need for costly pose estimation (or registration) procedures and large training sets, and can tolerate shape deformations, unlike template (or atlas) based priors. Our formulation leads to a challenging problem, which is not directly amenable to convex-optimization techniques. For each functional, we split the problem into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Unlike related graph-cut approaches, the proposed convex-relaxation solution can be parallelized to reduce substantially the computational time for 3D domains (or higher), extends directly to high dimensions, and does not have the grid-bias problem. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm

  17. Functional properties of the oxygen evolving complex of photosystem II.

    NARCIS (Netherlands)

    Vliet, van P.H.

    1996-01-01

    This Thesis presents the results of a study by electron paramagnetic resonance (EPR) and measurements of oxygen evolution of the Oxygen Evolving Complex of Photosystem 11 (PS-II) in PS-II enriched membranes from spinach.The experimental part of this Thesis is preceded by a general introduction (Chap

  18. Cd(ii)-MOF-IM: post-synthesis functionalization of a Cd(ii)-MOF as a triphase transfer catalyst.

    Science.gov (United States)

    Wang, Jian-Cheng; Ma, Jian-Ping; Liu, Qi-Kui; Hu, Yu-Hong; Dong, Yu-Bin

    2016-05-19

    A robust and porous Cd(ii)-MOF based on a bent imidazole-bridged ligand was synthesized and post-synthetically functionalized with linear alkyl chains to afford imidazolium salt (IM)-type triphase transfer catalysts for organic transformations. The imidazolium salt decorated Cd(ii)-MOF-IM exhibits typical solid phase transfer catalytic behavior for the azidation and thiolation of bromoalkane between aqueous/organic phases. Moreover, they can be easily recovered and reused under the PTC conditions. Cd(ii)-MOF-IM herein created a versatile family of solid phase transfer catalysts for promoting a broad scope of reactions carried out in a biphasic mixture of two immiscible solvents.

  19. Iminodiacetic acid functionalized cation exchange resin for adsorptive removal of Cr(VI), Cd(II), Ni(II) and Pb(II) from their aqueous solutions.

    Science.gov (United States)

    Misra, R K; Jain, S K; Khatri, P K

    2011-01-30

    Iminodiacetic acid functionality has been introduced on styrene-divinyl benzene co-polymeric beads and characterized by FT-IR in order to develop weak acid based cation exchange resin. This resin was evaluated for the removal of different heavy metal ions namely Cd(II), Cr(VI), Ni(II) and Pb(II) from their aqueous solutions. The results showed greater affinity of resin towards Cr(VI) for which 99.7% removal achieved in optimal conditions following the order Ni(II)>Pb(II)>Cd(II) with 65%, 59% and 28% removal. Experiments were also directed towards kinetic studies of adsorption and found to follow first order reversible kinetic model with the overall rate constants 0.3250, 0.2393, 0.4290 and 0.2968 for Cr(VI), Ni(II), Pb(II) and Cd(II) removal respectively. Detailed studies of Cr(VI) removal has been carried out to see the effect of pH, resin dose and metal ion concentration on adsorption and concluded that complexation enhanced the chromium removal efficacy of resin drastically, which is strongly pH dependent. The findings were also supported by the comparison of FT-IR spectra of neat resin with the chromium-adsorbed resin.

  20. The heart of a convex body

    CERN Document Server

    Brasco, Lorenzo

    2012-01-01

    We investigate some basic properties of the {\\it heart} $\\heartsuit(\\mathcal{K})$ of a convex set $\\mathcal{K}.$ It is a subset of $\\mathcal{K},$ whose definition is based on mirror reflections of euclidean space, and is a non-local object. The main motivation of our interest for $\\heartsuit(\\mathcal{K})$ is that this gives an estimate of the location of the hot spot in a convex heat conductor with boundary temperature grounded at zero. Here, we investigate on the relation between $\\heartsuit(\\mathcal{K})$ and the mirror symmetries of $\\mathcal{K};$ we show that $\\heartsuit(\\mathcal{K})$ contains many (geometrically and phisically) relevant points of $\\mathcal{K};$ we prove a simple geometrical lower estimate for the diameter of $\\heartsuit(\\mathcal{K});$ we also prove an upper estimate for the area of $\\heartsuit(\\mathcal{K}),$ when $\\mathcal{K}$ is a triangle.

  1. Coalescence between two convex liquid surfaces

    Science.gov (United States)

    Yang, Fan; Jian, Zhen; Li, Erqiang; Thoroddsen, S. T.

    2015-11-01

    We study the coalescence of two convex surfaces of the same liquid. One of the convex free surfaces is formed at a circular opening of a closed tank by imposing a negative pressure difference. The other surface is a droplet of larger curvature, which is pendant from a concentric nozzle. The coalescence starts from near-zero velocity, so the configuration can be characterized by two dimensionless numbers: the Ohnesorge number Oh = μ /√{ ργL } and the radius ratio between the two surfaces α =rd /rs . We use high-speed video, PIV and numerical simulations, using the Gerris program, to study the dynamics of the coalescence. Our focus is on the interface shapes, the growth-rate of the neck connecting the two surfaces and the formation of a vortex ring. The growth-rate is compared to earlier models for the coalescence of drops or bubbles.

  2. On the convexity of Relativistic Hydrodynamics

    CERN Document Server

    Ibáñez, José María; Martí, José María; Miralles, Juan Antonio; 10.1088/0264-9381/30/5/057002

    2013-01-01

    The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr 1989 {\\it Rev. Mod. Phys.} {\\bf 61} 75). The classical limit is recovered.

  3. On convex relaxation of graph isomorphism.

    Science.gov (United States)

    Aflalo, Yonathan; Bronstein, Alexander; Kimmel, Ron

    2015-03-10

    We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving n2 equality and n2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic.

  4. The functional performance of the Argus II retinal prosthesis.

    Science.gov (United States)

    Stronks, H Christiaan; Dagnelie, Gislin

    2014-01-01

    Visual prostheses are devices to treat profound vision loss by stimulating nerve cells anywhere along the visual pathway, typically with electrical pulses. The Argus II implant, developed by Second Sight Medical Products (SSMP, Sylmar, CA, USA), targets the retina and features 60 electrodes that electrically stimulate the surviving retinal neurons. Of the approximately 20 research groups that are actively developing visual prostheses, SSMP has the longest track record. The Argus II was the first visual prosthesis to become commercially available: it received the European conformity mark in 2011 and FDA approval was granted in early 2013 for humanitarian use in the USA. Meanwhile, the Argus II safety/benefit study has been extended for research purposes, and is still ongoing. In this review, we will discuss the performance of the Argus II in restoring sight to the blind, and we will shed light on its expected developments in the coming years.

  5. The functional performance of the Argus II retinal prosthesis

    OpenAIRE

    2013-01-01

    Visual prostheses are devices to treat profound vision loss by stimulating secondary nerve cells anywhere along the visual pathway, typically with electrical pulses. The Argus® II implant, developed by Second Sight Medical Products (SSMP, Sylmar, CA, USA), targets the retina and features 60 electrodes that electrically stimulate the surviving retinal neurons. Of the approximately 20 research groups that are actively developing visual prostheses, SSMP has the longest track record. The Argus II...

  6. Cholecystokinin rapidly stimulates CrkII function in vivo in rat pancreatic acini. Formation of CrkII-protein complexes.

    Science.gov (United States)

    Andreolotti, Alberto G; Bragado, Maria J; Tapia, Jose A; Jensen, Robert T; Garcia-Marin, Luis J

    2003-12-01

    Crk belongs to a family of adapter proteins whose structure allows interaction with tyrosine-phosphorylated proteins and is therefore an important modulator of downstream signals, representing a convergence of the actions of numerous stimuli. Recently, it was demonstrated that cholecystokinin (CCK) induced tyrosine phosphorylation of proteins related to fiber stress formation in rat pancreatic acini. Here, we investigated whether CCK receptor activation signals through CrkII and forms complexes with tyrosine-phosphorylated proteins in rat pancreatic acini. We demonstrated that CCK promoted the transient formation of CrkII-paxillin and CrkII-p130Cas complexes with maximal effect at 1 min. Additionally, CCK decreased the electrophoretic mobility of CrkII. This decrease was time- and concentration-dependent and inversely related with its function. Carbachol and bombesin also decreased CrkII electrophoretic mobility, whereas epidermal growth factor, vasoactive intestinal peptide, secretin or pituitary adenylate cyclase-activating polypeptide had no effect. CCK-induced CrkII electrophoretic shift was dependent on the Src family of tyrosine kinases and occurred in the intact animal, suggesting a physiological role of CrkII mediating CCK actions in the exocrine pancreas in vivo.

  7. A New Hybrid Shuffled Frog Leaping Algorithm to Solve Non-convex Economic Load Dispatch Problem

    Directory of Open Access Journals (Sweden)

    Ehsan Bijami

    2011-11-01

    Full Text Available This paper presents a New Hybrid Shuffled Frog Leaping (NHSFL algorithm applied to solve Economic Load Dispatch (ELD problem. Practical ELD has non-convex cost function and various equality and inequality constraints that convert the ELD problem as a nonlinear, non-convex and non-smooth optimization problem. In this paper, a new frog leaping rule is proposed to improve the local exploration and the performance of the conventional SFL algorithm. Also a genetic mutation operator is used for the creation of new frogs instead of random frog creation that improves the convergence. To show the efficiency of the proposed approach, the non-convex ELD problem is solved using conventional SFL and an improved SFL method proposed by other researchers. Then the results of SFL methods are compared to the results obtained by the proposed NHSFL algorithm. Simulation studies show that the results obtained by NHSFL are more effective and better compared with these algorithms.

  8. Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach

    Energy Technology Data Exchange (ETDEWEB)

    Rodman, Leiba [Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795 (United States); Spitkovsky, Ilya M., E-mail: ims2@nyu.edu, E-mail: ilya@math.wm.edu [Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795 (United States); Division of Science and Mathematics, New York University Abu Dhabi, Saadiyat Island, P.O. Box 129188, Abu Dhabi (United Arab Emirates); Szkoła, Arleta, E-mail: szkola@mis.mpg.de; Weis, Stephan, E-mail: maths@stephan-weis.info [Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig (Germany)

    2016-01-15

    We study the continuity of an abstract generalization of the maximum-entropy inference—a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for 3 × 3 matrices.

  9. Widder-Arendt theorem and integrated semigroups in locally convex space

    Institute of Scientific and Technical Information of China (English)

    肖体俊; 梁进

    1996-01-01

    A well-known result established by Arendt in 1987 with regard to the Laplace transforms in Banach spaces is developed. A Widder-Arendt theorem in the setting of sequentially complete locally convex spaces is set up (Theorem 1.1). Moreover, integrated semigroups in such spaces are introduced and generation theorems and some basic properties for semigroups of this type are obtained. As examples, elliptic differential operators on certain classes of function spaces with locally convex topology are shown to be the generators of integrated semigroups under some conditions.

  10. Fixed point theorems in locally convex spaces—the Schauder mapping method

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available In the appendix to the book by F. F. Bonsal, Lectures on Some Fixed Point Theorems of Functional Analysis (Tata Institute, Bombay, 1962 a proof by Singbal of the Schauder-Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping method, is included. The aim of this note is to show that this method can be adapted to yield a proof of Kakutani fixed point theorem in the locally convex case. For the sake of completeness we include also the proof of Schauder-Tychonoff theorem based on this method. As applications, one proves a theorem of von Neumann and a minimax result in game theory.

  11. Convex relaxation for a 3D spatiotemporal segmentation model using the primal-dual method

    Institute of Scientific and Technical Information of China (English)

    Shi-yan WANG; Hui-min YU

    2012-01-01

    A method based on 3D videos is proposed for multi-target segmentation and tracking with a moving viewing system.A spatiotemporal energy functional is built up to perform motion segmentation and estimation simultaneously.To overcome the limitation of the local minimum problem with the level set method,a convex relaxation method is applied to the 3D spatiotemporal segmentation model.The relaxed convex model is independent of the initial condition.A primal-dual algorithm is used to improve computational efficiency.Several indoor experiments show the validity of the proposed method.

  12. Convex foundations for generalized MaxEnt models

    Science.gov (United States)

    Frongillo, Rafael; Reid, Mark D.

    2014-12-01

    We present an approach to maximum entropy models that highlights the convex geometry and duality of generalized exponential families (GEFs) and their connection to Bregman divergences. Using our framework, we are able to resolve a puzzling aspect of the bijection of Banerjee and coauthors between classical exponential families and what they call regular Bregman divergences. Their regularity condition rules out all but Bregman divergences generated from log-convex generators. We recover their bijection and show that a much broader class of divergences correspond to GEFs via two key observations: 1) Like classical exponential families, GEFs have a "cumulant" C whose subdifferential contains the mean: Eo˜pθ[φ(o)]∈∂C(θ) ; 2) Generalized relative entropy is a C-Bregman divergence between parameters: DF(pθ,pθ')= D C(θ,θ') , where DF becomes the KL divergence for F = -H. We also show that every incomplete market with cost function C can be expressed as a complete market, where the prices are constrained to be a GEF with cumulant C. This provides an entirely new interpretation of prediction markets, relating their design back to the principle of maximum entropy.

  13. The relation of executive functioning to CVLT-II learning, memory, and process indexes.

    Science.gov (United States)

    Hill, Benjamin David; Alosco, Michael; Bauer, Lyndsey; Tremont, Geoffrey

    2012-01-01

    Previous research has found that executive functioning plays a role in memory performance. This study sought to determine the amount of variance accounted for in the California Verbal Learning Test-Second Edition (CVLT-II) by a global executive-functioning factor score. Archival data were extracted from 285 outpatients in a mixed neurologic sample. Measures used included: CVLT-II, Wisconsin Card-Sorting Test (Perseverative Errors), Trail-Making Test-Part B, Controlled Oral Word Association Test, Animal Naming, and Wechsler Adult Intelligence Scale-Third Edition Similarities. Executive data were reduced to a single executive-functioning factor score for each individual. Regression was used to determine the amount of variance accounted for by executive functioning in CVLT-II performance. Executive functioning accounted for minimal variance (0%-10%) in the following CVLT-II indexes: Total Learning (Trials 1-5), Semantic Clustering, Repetitions, Intrusions, and False Positives. However, executive functioning accounted for substantial variance (24%-31%) in CVLT-II performance for both Short- and Long-Delay Recall indexes and most discriminability indexes. CVLT-II indexes that would intuitively be associated with executive functioning accounted for a smaller-than-expected amount of variance. Additionally, level of executive functioning was related to level of CVLT-II performance. These results suggest that clinicians should consider executive deficits when interpreting mild-to-moderate memory impairments in recall and discriminability functions but that executive abilities have little effect on other aspects of memory.

  14. Axon extension in the fast and slow lanes: substratum-dependent engagement of myosin II functions.

    Science.gov (United States)

    Ketschek, Andrea R; Jones, Steven L; Gallo, Gianluca

    2007-09-01

    Axon extension involves the coordinated regulation of the neuronal cytoskeleton. Actin filaments drive protrusion of filopodia and lamellipodia while microtubules invade the growth cone, thereby providing structural support for the nascent axon. Furthermore, in order for axons to extend the growth cone must attach to the substratum. Previous work indicates that myosin II activity inhibits the advance of microtubules into the periphery of growth cones, and myosin II has also been implicated in mediating integrin-dependent cell attachment. However, it is not clear how the functions of myosin II in regulating substratum attachment and microtubule advance are integrated during axon extension. We report that inhibition of myosin II function decreases the rate of axon extension on laminin, but surprisingly promotes extension rate on polylysine. The differential effects of myosin II inhibition on axon extension rate are attributable to myosin II having the primary function of mediating substratum attachment on laminin, but not on polylysine. Conversely, on polylysine the primary function of myosin II is to inhibit microtubule advance into growth cones. Thus, the substratum determines the role of myosin II in axon extension by controlling the functions of myosin II that contribute to extension.

  15. A Convex Variational Model for Restoring Blurred Images with Multiplicative Noise

    DEFF Research Database (Denmark)

    Dong, Yiqiu; Tieyong Zeng

    2013-01-01

    In this paper, a new variational model for restoring blurred images with multiplicative noise is proposed. Based on the statistical property of the noise, a quadratic penalty function technique is utilized in order to obtain a strictly convex model under a mild condition, which guarantees...... to multiplicative noise. A comparison with other methods is provided as well....

  16. Implementation of an optimal first-order method for strongly convex total variation regularization

    DEFF Research Database (Denmark)

    Jensen, Tobias Lindstrøm; Jørgensen, Jakob Heide; Hansen, Per Christian;

    2012-01-01

    We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to μ-strongly convex objective functions with L-Lipschitz continuous gradient...

  17. Optimal Energy Consumption in Refrigeration Systems - Modelling and Non-Convex Optimisation

    DEFF Research Database (Denmark)

    Hovgaard, Tobias Gybel; Larsen, Lars F. S.; Skovrup, Morten J.

    2012-01-01

    that is somewhat more efficient than general purpose optimisation algorithms for NMPC and still near to optimal. Since the non-convex cost function has multiple extrema, standard methods for optimisation cannot be directly applied. A qualitative analysis of the system's constraints is presented and a unique...

  18. Continuous solutions for fractional integral inclusion in locally convex topological space

    Institute of Scientific and Technical Information of China (English)

    Rabha W. Ibrahim

    2009-01-01

    The existence of continuous solutions for fractional integral inclusion via its singlevalued problem and fixed point theorem for set-valued function in locally convex topological spaces is discussed. The proof of the single-valued problem will be based on the Leray- Schauder fixed point theorem. Moreover, the controllability of this solution is studied.

  19. -ree vibration analysis of cracked thin plates by quasi-convex coupled isogeometric-meshfree method

    Institute of Scientific and Technical Information of China (English)

    Hanjie ZHANG[1,2; JunzhaoWU[1,2; Dongdong WANG[1,2

    2015-01-01

    The free vibration analysis of cracked thin plates via a quasi-convex coupled isogeometric-meshfree method is presented. This formulation employs the consistently coupled isogeometric-meshfree strategy where a mixed basis vector of the convex B-splines is used to impose the consistency conditions throughout the whole problem domain. Meanwhile, the rigid body modes related to the mixed basis vector and reproducing conditions are also discussed. The mixed basis vector simultaneously offers the consistent isogeometric-meshfree coupling in the coupled region and the quasi-convex property for the meshfree shape functions in the meshfree region, which is particularly attractive for the vibration analysis. The quasi-convex meshfree shape functions mimic the isogeometric basis function as well as offer the meshfree nodal arrangement flexibility. Subsequently, this approach is exploited to study the free vibration analysis of cracked plates, in which the plate geometry is exactly represented by the isogeometric basis functions, while the cracks are discretized by meshfree nodes and highly smoothing approximation is invoked in the rest of the problem domain. The efficacy of the present method is illustrated through several numerical examples.

  20. Consolidation of Military Pay and Personnel Functions (Copper). Volume II

    Science.gov (United States)

    1978-05-01

    as in any system, the commander and staff must perform their roles in providing information in a timely and accurate manner. a. Concepts pertaining to...feminine genders . Exceptions to this use of the words "he" or "his" will be so noted. 8. RECOMMENDED CHANGES AND COMMENTS. Users of this manual are...II-lO-Aq3 S NO CAH TR TION NCL IN 0’ SECTION 2 co P ? PAGE YES YES II-10-A43 MAKE CORRECTIONS LOG IN OTL SEPARATE DOCUMENTS Orl, OTL DOCUMENTS ORIG

  1. Nitrilotriacetic acid functionalized Adansonia digitata biosorbent: Preparation, characterization and sorption of Pb (II and Cu (II pollutants from aqueous solution

    Directory of Open Access Journals (Sweden)

    Adewale Adewuyi

    2016-11-01

    Full Text Available Nitrilotriacetic acid functionalized Adansonia digitata (NFAD biosorbent has been synthesized using a simple and novel method. NFAD was characterized by X-ray Diffraction analysis technique (XRD, Scanning Electron Microscopy (SEM, Brunauer-Emmett-Teller (BET surface area analyzer, Fourier Transform Infrared spectrometer (FTIR, particle size dispersion, zeta potential, elemental analysis (CHNS/O analyzer, thermogravimetric analysis (TGA, differential thermal analysis (DTA, derivative thermogravimetric analysis (DTG and energy dispersive spectroscopy (EDS. The ability of NFAD as biosorbent was evaluated for the removal of Pb (II and Cu (II ions from aqueous solutions. The particle distribution of NFAD was found to be monomodal while SEM revealed the surface to be heterogeneous. The adsorption capacity of NFAD toward Pb (II ions was 54.417 mg/g while that of Cu (II ions was found to be 9.349 mg/g. The adsorption of these metals was found to be monolayer, second-order-kinetic, and controlled by both intra-particle diffusion and liquid film diffusion. The results of this study were compared better than some reported biosorbents in the literature. The current study has revealed NFAD to be an effective biosorbent for the removal of Pb (II and Cu (II from aqueous solution.

  2. Nitrilotriacetic acid functionalized Adansonia digitata biosorbent: Preparation, characterization and sorption of Pb (II) and Cu (II) pollutants from aqueous solution.

    Science.gov (United States)

    Adewuyi, Adewale; Pereira, Fabiano Vargas

    2016-11-01

    Nitrilotriacetic acid functionalized Adansonia digitata (NFAD) biosorbent has been synthesized using a simple and novel method. NFAD was characterized by X-ray Diffraction analysis technique (XRD), Scanning Electron Microscopy (SEM), Brunauer-Emmett-Teller (BET) surface area analyzer, Fourier Transform Infrared spectrometer (FTIR), particle size dispersion, zeta potential, elemental analysis (CHNS/O analyzer), thermogravimetric analysis (TGA), differential thermal analysis (DTA), derivative thermogravimetric analysis (DTG) and energy dispersive spectroscopy (EDS). The ability of NFAD as biosorbent was evaluated for the removal of Pb (II) and Cu (II) ions from aqueous solutions. The particle distribution of NFAD was found to be monomodal while SEM revealed the surface to be heterogeneous. The adsorption capacity of NFAD toward Pb (II) ions was 54.417 mg/g while that of Cu (II) ions was found to be 9.349 mg/g. The adsorption of these metals was found to be monolayer, second-order-kinetic, and controlled by both intra-particle diffusion and liquid film diffusion. The results of this study were compared better than some reported biosorbents in the literature. The current study has revealed NFAD to be an effective biosorbent for the removal of Pb (II) and Cu (II) from aqueous solution.

  3. Calculus of Elementary Functions, Part II. Teacher's Commentary. Revised Edition.

    Science.gov (United States)

    Herriot, Sarah T.; And Others

    This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This teacher's guide is for Part II of the course. It is designed to follow Part I of the text. The guide contains background information, suggested instructional…

  4. On the modulus of U-convexity

    Directory of Open Access Journals (Sweden)

    Satit Saejung

    2005-01-01

    Full Text Available We prove that the moduli of U-convexity, introduced by Gao (1995, of the ultrapower X˜ of a Banach space X and of X itself coincide whenever X is super-reflexive. As a consequence, some known results have been proved and improved. More precisely, we prove that uX(1>0 implies that both X and the dual space X∗ of X have uniform normal structure and hence the “worth” property in Corollary 7 of Mazcuñán-Navarro (2003 can be discarded.

  5. Convex and Radially Concave Contoured Distributions

    Directory of Open Access Journals (Sweden)

    Wolf-Dieter Richter

    2015-01-01

    Full Text Available Integral representations of the locally defined star-generalized surface content measures on star spheres are derived for boundary spheres of balls being convex or radially concave with respect to a fan in Rn. As a result, the general geometric measure representation of star-shaped probability distributions and the general stochastic representation of the corresponding random vectors allow additional specific interpretations in the two mentioned cases. Applications to estimating and testing hypotheses on scaling parameters are presented, and two-dimensional sample clouds are simulated.

  6. Width Distributions for Convex Regular Polyhedra

    CERN Document Server

    Finch, Steven R

    2011-01-01

    The mean width is a measure on three-dimensional convex bodies that enjoys equal status with volume and surface area [Rota]. As the phrase suggests, it is the mean of a probability density f. We verify formulas for mean widths of the regular tetrahedron and the cube. Higher-order moments of f_tetra and f_cube have not been examined until now. Assume that each polyhedron has edges of unit length. We deduce that the mean square width of the regular tetrahedron is 1/3+(3+sqrt(3))/(3*pi) and the mean square width of the cube is 1+4/pi.

  7. Measuring Voting Power in Convex Policy Spaces

    Directory of Open Access Journals (Sweden)

    Sascha Kurz

    2014-03-01

    Full Text Available Classical power index analysis considers the individual’s ability to influence the aggregated group decision by changing its own vote, where all decisions and votes are assumed to be binary. In many practical applications we have more options than either “yes” or “no”. Here we generalize three important power indices to continuous convex policy spaces. This allows the analysis of a collection of economic problems like, e.g., tax rates or spending that otherwise would not be covered in binary models.

  8. Lower Bound for Convex Hull Area and Universal Cover Problems

    CERN Document Server

    Khandhawit, Tirasan; Sriswasdi, Sira

    2011-01-01

    In this paper, we provide a lower bound for an area of the convex hull of points and a rectangle in a plane. We then apply this estimate to establish a lower bound for a universal cover problem. We showed that a convex universal cover for a unit length curve has area at least 0.232239. In addition, we show that a convex universal cover for a unit closed curve has area at least 0.0879873.

  9. Approximation of Convex Bodies by Convex Bodies%凸体间的逼近

    Institute of Scientific and Technical Information of China (English)

    国起; Sten Kaijser

    2003-01-01

    For the affine distance d(C,D)between two convex bodies C,D(∈)Rn,which reduces to the Banach-Mazur distance for symmetric convex bodies, the bounds of d(C,D)have been studied for many years. Some well known estimates for the upper-bounds are as follows: F. John proved d(C,D)≤n1/2 if one is an ellipsoid and another is symmetric,d(C,D)≤n if both are symmetric, and fromF. John's result and d(C1,C2)≤d(C1,C3)d(C2,C3) one has d(C,D)≤n2 for general convex bodies;M.Lassak proved d(C,D)≤(2n-1) if one of them is symmetric.In this paper we get an estimate which includes all the results above as special cases and refines some of them in terms of measures of asymmetry for convex bodies.

  10. Functional characterisation of a putative rhamnogalacturonan II specific xylosyltransferase.

    Science.gov (United States)

    Egelund, Jack; Damager, Iben; Faber, Kirsten; Olsen, Carl-Erik; Ulvskov, Peter; Petersen, Bent Larsen

    2008-09-22

    An Arabidopsis thaliana gene, At1g56550, was expressed in Pichia pastoris and the recombinant protein was shown to catalyse transfer of D-xylose from UDP-alpha-D-xylose onto methyl alpha-L-fucoside. The product formed was shown by 1D and 2D 1H NMR spectroscopy to be Me alpha-D-Xyl-(1,3)-alpha-L-Fuc, which is identical to the proposed target structure in the A-chain of rhamnogalacturonan II. Chemically synthesized methyl L-fucosides derivatized by methyl groups on either the 2-, 3- or 4 position were tested as acceptor substrates but only methyl 4-O-methyl-alpha-L-fucopyranoside acted as an acceptor, although to a lesser extent than methyl alpha-L-fucoside. At1g56550 is suggested to encode a rhamnogalacturonan II specific xylosyltransferase.

  11. Long Wave Dynamics along a Convex Bottom

    CERN Document Server

    Didenkulova, Ira; Soomere, Tarmo

    2008-01-01

    Long linear wave transformation in the basin of varying depth is studied for a case of a convex bottom profile in the framework of one-dimensional shallow water equation. The existence of travelling wave solutions in this geometry and the uniqueness of this wave class is established through construction of a 1:1 transformation of the general 1D wave equation to the analogous wave equation with constant coefficients. The general solution of the Cauchy problem consists of two travelling waves propagating in opposite directions. It is found that generally a zone of a weak current is formed between these two waves. Waves are reflected from the coastline so that their profile is inverted with respect to the calm water surface. Long wave runup on a beach with this profile is studied for sine pulse, KdV soliton and N-wave. Shown is that in certain cases the runup height along the convex profile is considerably larger than for beaches with a linear slope. The analysis of wave reflection from the bottom containing a s...

  12. Molecular Graphics of Convex Body Fluids.

    Science.gov (United States)

    Gabriel, Adrian T; Meyer, Timm; Germano, Guido

    2008-03-01

    Coarse-grained modeling of molecular fluids is often based on nonspherical convex rigid bodies like ellipsoids or spherocylinders representing rodlike or platelike molecules or groups of atoms, with site-site interaction potentials depending both on the distance among the particles and the relative orientation. In this category of potentials, the Gay-Berne family has been studied most extensively. However, conventional molecular graphics programs are not designed to visualize such objects. Usually the basic units are atoms displayed as spheres or as vertices in a graph. Atomic aggregates can be highlighted through an increasing amount of stylized representations, e.g., Richardson ribbon diagrams for the secondary structure of proteins, Connolly molecular surfaces, density maps, etc., but ellipsoids and spherocylinders are generally missing, especially as elementary simulation units. We fill this gap providing and discussing a customized OpenGL-based program for the interactive, rendered representation of large ensembles of convex bodies, useful especially in liquid crystal research. We pay particular attention to the performance issues for typical system sizes in this field. The code is distributed as open source.

  13. 非光滑多目标广义本性凸规划的最优性条件与对偶%Optimality Conditions and Duality for Nonsmooth Multiobjective Programms with Generalized Essential Convexity

    Institute of Scientific and Technical Information of China (English)

    王彩玲; 刘庆怀; 李忠范

    2008-01-01

    In this paper, we introduce generalized essentially pseudoconvex func-tion and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective programming and its saddle point theorem about cone efficient solution.We set up Mond-Weir type duality and Craven type duality for nonsmooth multiobjective programming with generalized essentially convex functions, and prove them.

  14. Ruthenium(II)-Catalyzed C-C Arylations and Alkylations: Decarbamoylative C-C Functionalizations.

    Science.gov (United States)

    Moselage, Marc; Li, Jie; Kramm, Frederik; Ackermann, Lutz

    2017-04-05

    Ruthenium(II)biscarboxylate catalysis enabled selective C-C functionalizations by means of decarbamoylative C-C arylations. The versatility of the ruthenium(II) catalysis was reflected by widely applicable C-C arylations and C-C alkylations of aryl amides, as well as acids with modifiable pyrazoles, through facile organometallic C-C activation.

  15. Robust Nearfield Wideband Beamforming Design Based on Adaptive-Weighted Convex Optimization

    Directory of Open Access Journals (Sweden)

    Guo Ye-Cai

    2017-01-01

    Full Text Available Nearfield wideband beamformers for microphone arrays have wide applications in multichannel speech enhancement. The nearfield wideband beamformer design based on convex optimization is one of the typical representatives of robust approaches. However, in this approach, the coefficient of convex optimization is a constant, which has not used all the freedom provided by the weighting coefficient efficiently. Therefore, it is still necessary to further improve the performance. To solve this problem, we developed a robust nearfield wideband beamformer design approach based on adaptive-weighted convex optimization. The proposed approach defines an adaptive-weighted function by the adaptive array signal processing theory and adjusts its value flexibly, which has improved the beamforming performance. During each process of the adaptive updating of the weighting function, the convex optimization problem can be formulated as a SOCP (Second-Order Cone Program problem, which could be solved efficiently using the well-established interior-point methods. This method is suitable for the case where the sound source is in the nearfield range, can work well in the presence of microphone mismatches, and is applicable to arbitrary array geometries. Several design examples are presented to verify the effectiveness of the proposed approach and the correctness of the theoretical analysis.

  16. Correction of an adult Class II division 2 individual using fixed functional appliance: A noncompliance approach

    Directory of Open Access Journals (Sweden)

    Shrinivas Basavaraddi

    2016-01-01

    Full Text Available This case report describes the application of fixed functional appliance in the treatment of an adult female having Class II division 2 malocclusion with retroclination of upper incisors. Fixed functional appliance was used to correct the overjet after the uprighting of upper incisors. Fixed functional appliance was fitted on a rigid rectangular arch wire. Application of fixed functional appliance achieved a good Class I molar relationship along with Class I canine relationship with normal overjet and overbite. Fixed functional appliance is effective in the treatment of Class II malocclusions, even in adult patients, and can serve as an alternate choice of treatment instead of orthognathic surgery. This is a case; wherein, fixed functional appliance was successfully used to relieve deep bite and overjet that was ensued after leveling and aligning. We demonstrate that fixed functional appliance can act as a “noncompliant corrector” and use of Class II elastics can be avoided.

  17. Correction of an adult Class II division 2 individual using fixed functional appliance: A noncompliance approach.

    Science.gov (United States)

    Basavaraddi, Shrinivas; Gandedkar, Narayan H; Belludi, Anup; Patil, Anand

    2016-01-01

    This case report describes the application of fixed functional appliance in the treatment of an adult female having Class II division 2 malocclusion with retroclination of upper incisors. Fixed functional appliance was used to correct the overjet after the uprighting of upper incisors. Fixed functional appliance was fitted on a rigid rectangular arch wire. Application of fixed functional appliance achieved a good Class I molar relationship along with Class I canine relationship with normal overjet and overbite. Fixed functional appliance is effective in the treatment of Class II malocclusions, even in adult patients, and can serve as an alternate choice of treatment instead of orthognathic surgery. This is a case; wherein, fixed functional appliance was successfully used to relieve deep bite and overjet that was ensued after leveling and aligning. We demonstrate that fixed functional appliance can act as a "noncompliant corrector" and use of Class II elastics can be avoided.

  18. Rocking convex array used for 3D synthetic aperture focusing

    DEFF Research Database (Denmark)

    Andresen, Henrik; Nikolov, Svetoslav; Pedersen, M M

    2008-01-01

    Volumetric imaging can be performed using 1D arrays in combination with mechanical motion. Outside the elevation focus of the array, the resolution and contrast quickly degrade compared to the azimuth plane, because of the fixed transducer focus. The purpose of this paper is to use synthetic...... aperture focusing (SAF) for enhancing the elevation focusing for a convex rocking array, to obtain a more isotropic point spread function. This paper presents further development of the SAF method, which can be used with curved array combined with a rocking motion. The method uses a virtual source (VS...... Kretztechnik, Zipf, Austria). The array has an elevation focus at 60 mm of depth, and the angular rocking velocity is up to 140deg/s. The scan sequence uses an fprf of 4500 - 7000 Hz allowing up to 15 cm of penetration. The full width at half max (FWHM) and main-lobe to side-lobe ratio (MLSL) is used...

  19. Hyperspectral image superresolution: An edge-preserving convex formulation

    CERN Document Server

    Simões, Miguel; Almeida, Luis B; Chanussot, Jocelyn

    2014-01-01

    Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These complementary characteristics have stimulated active research in the inference of images with high spatial and spectral resolutions from HSI-MSI pairs. In this paper, we formulate this data fusion problem as the minimization of a convex objective function containing two data-fitting terms and an edge-preserving regularizer. The data-fitting terms are quadratic and account for blur, different spatial resolutions, and additive noise; the regularizer, a form of vector Total Variation, promotes aligned discontinuities across the reconstructed hyperspectral bands. The optimization described above is rather hard, owing to its non-diagonalizable linear operators, to the non-quadratic and non-smooth nature of the regularizer, and to the very large size of the image to be inferred. We tac...

  20. Convex Relaxations for a Generalized Chan-Vese Model

    KAUST Repository

    Bae, Egil

    2013-01-01

    We revisit the Chan-Vese model of image segmentation with a focus on the encoding with several integer-valued labeling functions. We relate several representations with varying amount of complexity and demonstrate the connection to recent relaxations for product sets and to dual maxflow-based formulations. For some special cases, it can be shown that it is possible to guarantee binary minimizers. While this is not true in general, we show how to derive a convex approximation of the combinatorial problem for more than 4 phases. We also provide a method to avoid overcounting of boundaries in the original Chan-Vese model without departing from the efficient product-set representation. Finally, we derive an algorithm to solve the associated discretized problem, and demonstrate that it allows to obtain good approximations for the segmentation problem with various number of regions. © 2013 Springer-Verlag.

  1. Bankruptcy Problem Allocations and the Core of Convex Games

    Directory of Open Access Journals (Sweden)

    William Olvera-Lopez

    2014-01-01

    Full Text Available A well-known result related to bankruptcy problems establishes that a vector is a bankruptcy allocation if and only if it belongs to the core of the associated O’Neill’s bankruptcy game. In this paper we show that this game is precisely the unique TU-game based on convex functions that satisfies the previous result. In addition, given a bankruptcy problem, we show a way for constructing bankruptcy games such that the set of bankruptcy allocations is a subset of their core or their core is a subset of the set of bankruptcy allocations. Also, we show how these results can be applied for finding new bankruptcy solutions.

  2. Entropies from Coarse-graining: Convex Polytopes vs. Ellipsoids

    Directory of Open Access Journals (Sweden)

    Nikos Kalogeropoulos

    2015-09-01

    Full Text Available We examine the Boltzmann/Gibbs/Shannon SBGS and the non-additive Havrda-Charvát/Daróczy/Cressie-Read/Tsallis Sq and the Kaniadakis κ-entropy Sκ from the viewpoint of coarse-graining, symplectic capacities and convexity. We argue that the functional form of such entropies can be ascribed to a discordance in phase-space coarse-graining between two generally different approaches: the Euclidean/Riemannian metric one that reflects independence and picks cubes as the fundamental cells in coarse-graining and the symplectic/canonical one that picks spheres/ellipsoids for this role. Our discussion is motivated by and confined to the behaviour of Hamiltonian systems of many degrees of freedom. We see that Dvoretzky’s theorem provides asymptotic estimates for the minimal dimension beyond which these two approaches are close to each other. We state and speculate about the role that dualities may play in this viewpoint.

  3. Prenatal cocaine exposure impairs cognitive function of progeny via insulin growth factor II epigenetic regulation.

    Science.gov (United States)

    Zhao, Qian; Hou, Jing; Chen, Bo; Shao, Xue; Zhu, Ruiming; Bu, Qian; Gu, Hui; Li, Yan; Zhang, Baolai; Du, Changman; Fu, Dengqi; Kong, Jueying; Luo, Li; Long, Hailei; Li, Hongyu; Deng, Yi; Zhao, Yinglan; Cen, Xiaobo

    2015-10-01

    Studies have showed that prenatal cocaine exposure (PCOC) can impair cognitive function and social behavior of the offspring; however, the mechanism underlying such effect is poorly understood. Insulin-like growth factor II (Igf-II), an imprinted gene, has a critical role in memory consolidation and enhancement. We hypothesized that epigenetic regulation of hippocampal Igf-II may attribute to the cognitive deficits of PCOC offspring. We used Morris water maze and open-field task to test the cognitive function in PCOC offspring. The epigenetic alteration involved in hippocampal Igf-II expression deficit in PCOC offspring was studied by determining Igf-II methylation status, DNA methyltransferases (DNMT) expressions and L-methionine level. Moreover, IGF-II rescue experiments were performed and the downstream signalings were investigated in PCOC offspring. In behavioral tests, we observed impaired spatial learning and memory and increased anxiety in PCOC offspring; moreover, hippocampal IGF-II mRNA and protein expressions were significantly decreased. Hippocampal methylation of cytosine-phospho-guanine (CpG) dinucleotides in differentially methylated region (DMR) 2 of Igf-II was elevated in PCOC offspring, which may be driven by the upregulation of L-methionine and DNA methyltransferase (DNMT) 1. Importantly, intra-hippocampal injection of recombinant IGF-II reactivated the repressed calcium calmodulin kinase II α (CaMKIIα) and reversed cognitive deficits in PCOC offspring. Collectively, our findings suggest that cocaine exposure during pregnancy impairs cognitive function of offspring through epigenetic modification of Igf-II gene. Enhancing IGF-II signaling may represent a novel therapeutical strategy for cocaine-induced cognitive impairment.

  4. Correlation functions in conformal Toda field theory II

    CERN Document Server

    Fateev, V A

    2009-01-01

    This is the second part of the paper 0709.3806v2. Here we show that three-point correlation function with one semi-degenerate field in Toda field theory as well as four-point correlation function with one completely degenerate and one semi-degenerate field can be represented by the finite dimensional integrals.

  5. Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging

    CERN Document Server

    Girard, Julien N; Starck, Jean Luc; Corbel, Stéphane; Woiselle, Arnaud; Tasse, Cyril; McKean, John P; Bobin, Jérôme

    2015-01-01

    Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we expose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a Forward-Backward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are: i) an improved angular resolution (super resolution of a factor ~2) with point sources as compared to CLEAN on the same data, ii) correct photometry measurements on a field of point sources at high dynamic range and iii) the imaging of extended sources with improved fidelity. SASIR provides better reconstructions (five time less residuals) of the extended emissions as compared to CLEAN. With the advent of large radiotel...

  6. Enhanced removal of Hg(II) from acidic aqueous solution using thiol-functionalized biomass.

    Science.gov (United States)

    Chai, Liyuan; Wang, Qingwei; Li, Qingzhu; Yang, Zhihui; Wang, Yunyan

    2010-01-01

    Spent grain, the low-cost and abundant biomass produced in the brewing industry, was functionalized with thiol groups to be used as an adsorbent for Hg(II) removal from acidic aqueous solution. The adsorbents were characterized by the energy-dispersive X-ray analysis (EDAX) and Fourier transform infrared (FTIR) spectroscopy. Optimum pH for Hg(II) adsorption onto the thiol-functionalized spent grain (TFSG) was 2.0. The equilibrium and kinetics of the adsorption of Hg(II) onto TFSG from acidic aqueous solution were investigated. From the Langmuir isotherm model the maximum adsorption capacity of TFSG for Hg(II) was found to be 221.73 mg g(-1), which was higher than that of most various adsorbents reported in literature. Moreover, the adsorption of Hg(II) onto TFSG followed pseudo-second-order kinetic model.

  7. Finding sets of points without empty convex 6-gons

    NARCIS (Netherlands)

    Overmars, M.H.

    2001-01-01

    Erdös asked whether every large enough set of points in general position in the plane contains six points that form a convex 6-gon without any points from the set in its interior. In this note we show how a set of 29 points was found that contains no empty convex 6-gon. To this end a fast

  8. In-vivo Convex Array Vector Flow Imaging

    DEFF Research Database (Denmark)

    Jensen, Jørgen Arendt; Brandt, Andreas Hjelm; Nielsen, Michael Bachmann

    2014-01-01

    In-vivo VFI scans obtained from the abdomen of a human volunteer using a convex array transducers and trans- verse oscillation vector flow imaging (VFI) are presented. A 3 MHz BK Medical 8820e (Herlev, Denmark) 192-element convex array probe is used with the SARUS experimental ultrasound scanner....

  9. On a-order-convexity of Fuzzy Syntopogenous Spaces

    Institute of Scientific and Technical Information of China (English)

    WANG Hong

    2007-01-01

    In this paper,we combine L-fuzzy syntopogenous structure on X with algebraic structure on X.First,the *-increasing and *-decreasing spaces have been studied.Second,we define a-order-convexity on syntopogenous structures (X,S,≤).some important properties of a-order-convexity have been obtained.

  10. Transverse-Mode Control of VCSELs With Convex Mirror

    Institute of Scientific and Technical Information of China (English)

    2003-01-01

    We propose the transverse-mode control of vertical-cavity surface-emitting lasers (VCSELs) with a convex mirror. A possibility of improvements on single-mode output power and higher-order mode suppression is presented by optimizing a convex mirror.

  11. Infinitesimal nonrigidity of convex surfaces with planar boundary

    Institute of Scientific and Technical Information of China (English)

    LI Chunhe; HONG Jiaxing

    2005-01-01

    In the present paper infinitesimal nonrigidity of a class of convex surfaces with planar boundary is given. This result shows that if the image of the Gauss map of an evolution convex surface with planar boundary covers some hemisphere, this surface may be of infinitesimal nonrigidity for the isometric deformation of planar boundary.

  12. Homotopy Method for Non-convex Programming in Unbonded Set

    Institute of Scientific and Technical Information of China (English)

    徐庆; 于波

    2005-01-01

    In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.

  13. A Localization Method for Multistatic SAR Based on Convex Optimization.

    Directory of Open Access Journals (Sweden)

    Xuqi Zhong

    Full Text Available In traditional localization methods for Synthetic Aperture Radar (SAR, the bistatic range sum (BRS estimation and Doppler centroid estimation (DCE are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function's maximum is on the circumference of the ellipse which is the iso-range for its model function's T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment.

  14. A Localization Method for Multistatic SAR Based on Convex Optimization.

    Science.gov (United States)

    Zhong, Xuqi; Wu, Junjie; Yang, Jianyu; Sun, Zhichao; Huang, Yuling; Li, Zhongyu

    2015-01-01

    In traditional localization methods for Synthetic Aperture Radar (SAR), the bistatic range sum (BRS) estimation and Doppler centroid estimation (DCE) are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R) pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function's maximum is on the circumference of the ellipse which is the iso-range for its model function's T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment.

  15. Functional Implications of Photosystem II Crystal Formation in Photosynthetic Membranes

    NARCIS (Netherlands)

    Tietz, Stefanie; Puthiyaveetil, Sujith; Enlow, Heather M; Yarbrough, Robert; Wood, Magnus; Semchonok, Dmitry A; Lowry, Troy; Li, Zhirong; Jahns, Peter; Boekema, Egbert J; Lenhert, Steven; Niyogi, Krishna K; Kirchhoff, Helmut

    2015-01-01

    The structural organization of proteins in biological membranes can affect their function. Photosynthetic thylakoid membranes in chloroplasts have the remarkable ability to change their supramolecular organization between disordered and semicrystalline states. Although the change to the semicrystall

  16. The inverse moment problem for convex polytopes

    CERN Document Server

    Gravin, Nick; Pasechnik, Dmitrii; Robins, Sinai

    2011-01-01

    The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.

  17. non-Lipschitzian mappings without convexity

    Directory of Open Access Journals (Sweden)

    G. Li

    1999-01-01

    real Hilbert space H, and ℑ={Tt:t∈G} a representation of G as asymptotically nonexpansive type mappings of C into itself. Let L(x={z∈H:infs∈Gsupt∈G‖Tts x−z‖=inft∈G‖Tt x−z‖} for each x∈C and L(ℑ=∩x∈C L(x. In this paper, we prove that ∩s∈Gconv¯{Tts x:t∈G}∩L(ℑ is nonempty for each x∈C if and only if there exists a unique nonexpansive retraction P of C into L(ℑ such that PTs=P for all s∈G and P(x∈conv¯{Ts x:s∈G} for every x∈C. Moreover, we prove the ergodic convergence theorem for a semitopological semigroup of non-Lipschitzian mappings without convexity.

  18. Quantification of small, convex particles by TEM

    Energy Technology Data Exchange (ETDEWEB)

    Andersen, Sigmund J. [SINTEF Materials and Chemistry, Department of Synthesis and Properties, Material Physics, NO-7465 Trondheim (Norway)], E-mail: sigmund.j.andersen@sintef.no; Holme, Borge [SINTEF Materials and Chemistry, P.O. Box 124, Blindern, NO-0314 Oslo (Norway); Marioara, Calin D. [SINTEF Materials and Chemistry, Department of Synthesis and Properties, Material Physics, NO-7465 Trondheim (Norway)

    2008-07-15

    It is shown how size distributions of arbitrarily oriented, convex, non-overlapping particles extracted from conventional transmission electron microscopy (TEM) images may be determined by a variation of the Schwartz-Saltykov method. In TEM, particles cut at the surfaces have diminished projections, which alter the observed size distribution. We represent this distribution as a vector and multiply it with the inverse of a matrix comprising thickness-dependent Scheil or Schwartz-Saltykov terms. The result is a corrected size distribution of the projections of uncut particles. It is shown how the real (3D) distribution may be estimated when particle shape is considered. Computer code to generate the matrix is given. A log-normal distribution of spheres and a real distribution of pill-box-shaped dispersoids in an Al-Mg-Si alloy are given as examples. The errors are discussed in detail.

  19. Weighted composition operators and locally convex algebras

    Institute of Scientific and Technical Information of China (English)

    Edoardo Vesentini

    2005-01-01

    The Gleason-Kahane-Zelazko theorem characterizes the continuous homomorphism of an associative, locally multiplicatively convex, sequentially complete algebra A into the field C among all linear forms on A. This characterization will be applied along two different directions. In the case in which A is a commutative Banach algebra, the theorem yields the representation of some classes of continuous linear maps A: A → A as weighted composition operators, or as composition operators when A is a continuous algebra endomorphism. The theorem will then be applied to explore the behaviour of continuous linear forms on quasi-regular elements, when A is either the algebra of all Hilbert-Schmidt operators or a Hilbert algebra.

  20. Convex Decomposition Based Cluster Labeling Method for Support Vector Clustering

    Institute of Scientific and Technical Information of China (English)

    Yuan Ping; Ying-Jie Tian; Ya-Jian Zhou; Yi-Xian Yang

    2012-01-01

    Support vector clustering (SVC) is an important boundary-based clustering algorithm in multiple applications for its capability of handling arbitrary cluster shapes. However,SVC's popularity is degraded by its highly intensive time complexity and poor label performance.To overcome such problems,we present a novel efficient and robust convex decomposition based cluster labeling (CDCL) method based on the topological property of dataset.The CDCL decomposes the implicit cluster into convex hulls and each one is comprised by a subset of support vectors (SVs).According to a robust algorithm applied in the nearest neighboring convex hulls,the adjacency matrix of convex hulls is built up for finding the connected components; and the remaining data points would be assigned the label of the nearest convex hull appropriately.The approach's validation is guaranteed by geometric proofs.Time complexity analysis and comparative experiments suggest that CDCL improves both the efficiency and clustering quality significantly.

  1. Introducing convex layers to the Traveling Salesman Problem

    CERN Document Server

    Liew, Sing

    2012-01-01

    In this paper, we will propose convex layers to the Traveling Salesman Problem (TSP). Firstly, we will focus on human performance on the TSP. Experimental data shows that untrained humans appear to have the ability to perform well in the TSP. On the other hand, experimental data also supports the hypothesis of convex hull i.e. human relies on convex hull to search for the optimal tour for the TSP. Secondly, from the paper published by Bonabeau, Dorigo and Theraulaz, social insect behavior would be able to help in some of the optimizing problems, especially the TSP. Thus, we propose convex layers to the TSP based on the argument that, by the analogy to the social insect behavior, untrained humans' cognition should be able to help in the TSP. Lastly, we will use Tour Improvement algorithms on convex layers to search for an optimal tour for a 13-cities problem to demonstrate the idea.

  2. Efficient protocols for point-convex hull inclusion decision problems

    Directory of Open Access Journals (Sweden)

    Yun Ye

    2010-05-01

    Full Text Available Secure Multi-party Computation (SMC is dedicated to solve trust problems in cooperative computing with each participant’s private data. Privacy Preserving Computational Geometry (PPCG is a special area in SMC and being widely researched. In the real world, PPCG theories can be found being used in various occasions such as military cooperation, commercial competitions and so on. Point-convex hull inclusion problem is a practical case in PPCG and has its profound values. This paper firstly investigates the point inclusion problem with static convex hull, and then marches on to the cases of active convex hull, including the parallel moving and rotating ones. To solve the problems above, we propose a secure protocol to determine the relative position of a private point and a private convex hull in the first place. Compared with previous solutions, our protocols perform better in efficiency, especially when the number of the convex hull’s point is large.

  3. Misunderstanding that the Effective Action is Convex under Broken Symmetry

    CERN Document Server

    Asanuma, Nobu-Hiko

    2016-01-01

    The widespread belief that the effective action is convex and has a flat bottom under broken global symmetry is shown to be wrong. We show spontaneous symmetry breaking necessarily accompanies non-convexity in the effective action for quantum field theory, or in the free energy for statistical mechanics, and clarify the magnitude of non-convexity. For quantum field theory, it is also explicitly proved that translational invariance breaks spontaneously when the system is in the non-convex region, and that different vacua of spontaneously broken symmetry cannot be superposed. As applications of non-convexity, we study the first-order phase transition which happens at the zero field limit of spontaneously broken symmetry, and we propose a simple model of phase coexistence which obeys the Born rule.

  4. Fundamentals of convex analysis duality, separation, representation, and resolution

    CERN Document Server

    Panik, Michael J

    1993-01-01

    Fundamentals of Convex Analysis offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called convex analysis. In particular, it explores the topics of duality, separation, representation, and resolution. The work is intended for students of economics, management science, engineering, and mathematics who need exposure to the mathematical foundations of matrix games, optimization, and general equilibrium analysis. It is written at the advanced undergraduate to beginning graduate level and the only formal preparation required is some familiarity with set operations and with linear algebra and matrix theory. Fundamentals of Convex Analysis is self-contained in that a brief review of the essentials of these tool areas is provided in Chapter 1. Chapter exercises are also provided. Topics covered include: convex sets and their properties; separation and support theorems; theorems of the alternative; convex cones; dual homogeneous systems; basic solutions and comple...

  5. Stable anisotropic plasma confinement in magnetic configurations with convex-concave field lines

    Science.gov (United States)

    Tsventoukh, M. M.

    2014-02-01

    It is shown that a combination of the convex and the concave part of a field line provides a strong stabilizing action against convective (flute-interchange) plasma instability (Tsventoukh 2011 Nucl. Fusion 51 112002). This results in internal peaking of the stable plasma pressure profile that is calculated from the collisionless kinetic stability criterion for any magnetic confinement system with combination of mirrors and cusps. Connection of the convex and concave field line parts results in a reduction of the space charge that drives the unstable E × B motion, as there is an opposite direction of the particle drift in a non-uniform field at convex and concave field lines. The pressure peaking arises at the minimum of the second adiabatic invariant J that takes place at the ‘middle’ of a tandem mirror-cusp transverse cross-section. The position of the minimum in J varies with the particle pitch angle that results in a shift of the peaking position depending on plasma anisotropy. This allows one to improve a stable peaked pressure profile at a convex-concave field by changing the plasma anisotropy over the trap cross-section. Examples of such anisotropic distribution functions are found that give an additional substantial enhancement in the maximal central pressure. Furthermore, the shape of new calculated stable profiles has a wide central plasma layer instead of a narrow peak.

  6. Polymorphisms of mouse apolipoprotein A-II alter its physical and functional nature.

    Directory of Open Access Journals (Sweden)

    Timothy J Sontag

    Full Text Available ApoA-II is the second most abundant protein on HDL making up ∼ 20% of the total protein but its functions have still only been partially characterized. Recent methodological improvements have allowed for the recombinant expression and characterization of human apoA-II which shares only 55% sequence homology with murine apoA-II. Here we describe the purification of the two most common polymorphic variants of apoA-II found in inbred mouse strains, differing at 3 amino acid sites. C57BL/6 mice having variant apoA-II(a have lower plasma HDL levels than FVB/N mice that have variant apoA-II(b. Characterization of the helical structure of these two variants reveals a more alpha-helical structure for the FVB/N apoA-II. These changes do not alter the lipid or HDL binding of the two apoA-II variants, but significantly increase the ability of the FVB/N variant to promote both ABCA1 and ABCG1 mediated cellular cholesterol efflux. These differences may be differentially altering plasma HDL apoA-II levels. In vivo, neither C57 nor FVB apoA-II protein levels are affected by the absence of apoE, while an apoE/apoA-I double deficiency results in a 50% decrease of plasma FVB apoA-II but results in undetectable levels of C57 apoA-II in the plasma. FVB apoA-II is able to form an HDL particle in the absence of apoE or apoA-I.

  7. The adsorption properties of Pb(II) and Cd(II) on functionalized graphene prepared by electrolysis method

    Energy Technology Data Exchange (ETDEWEB)

    Deng Xiaojiao; Lue Lili; Li Hongwei [Key Laboratory of Polyoxometalates Science of Ministry of Education, College of Chemistry, Northeast Normal University, Changchun 130024 (China); Luo Fang, E-mail: luof746@nenu.edu.cn [Key Laboratory of Polyoxometalates Science of Ministry of Education, College of Chemistry, Northeast Normal University, Changchun 130024 (China)

    2010-11-15

    The functionalized graphene (GNS{sup PF6}) was fabricated by simple and fast method of electrolysis with potassium hexafluorophosphate solution as electrolyte under the static potential of 15 V. The characterization results of transmission electron microscopy, atom force microscopy, X-ray photoelectron spectroscopy, X-ray powder diffraction, Raman spectroscopy and thermogravimetric analysis indicate that graphite rod was completely exfoliated to graphene layer containing 30 wt.% PF{sub 6}{sup -} with the average thickness ca. 1.0 nm. Our sample of GNS{sup PF6} was developed for the removal of Pb(II) or Cd(II) ions from water, and the determined adsorption capacities are 406.6 mg/g (pH = 5.1) for Pb(II) and 73.42 mg/g (pH = 6.2) for Cd(II), which is much higher than that by our previous sample of GNS{sup C8P} and carbon nanotube. The adsorption processes reach equilibrium in just 40 min and the adsorption isotherms are described well by Langmuir and Freundlich classical isotherms models.

  8. The adsorption properties of Pb(II) and Cd(II) on functionalized graphene prepared by electrolysis method.

    Science.gov (United States)

    Deng, Xiaojiao; Lü, Lili; Li, Hongwei; Luo, Fang

    2010-11-15

    The functionalized graphene (GNS(PF6)) was fabricated by simple and fast method of electrolysis with potassium hexafluorophosphate solution as electrolyte under the static potential of 15 V. The characterization results of transmission electron microscopy, atom force microscopy, X-ray photoelectron spectroscopy, X-ray powder diffraction, Raman spectroscopy and thermogravimetric analysis indicate that graphite rod was completely exfoliated to graphene layer containing 30 wt.% PF(6)- with the average thickness ca. 1.0 nm. Our sample of GNS(PF6) was developed for the removal of Pb(II) or Cd(II) ions from water, and the determined adsorption capacities are 406.6 mg/g (pH=5.1) for Pb(II) and 73.42 mg/g (pH=6.2) for Cd(II), which is much higher than that by our previous sample of GNS(C8P) and carbon nanotube. The adsorption processes reach equilibrium in just 40 min and the adsorption isotherms are described well by Langmuir and Freundlich classical isotherms models.

  9. Path Following in the Exact Penalty Method of Convex Programming.

    Science.gov (United States)

    Zhou, Hua; Lange, Kenneth

    2015-07-01

    Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.

  10. Functionalization of conducting polymer with novel Co(II) complex: Electroanalysis of ascorbic acid

    Energy Technology Data Exchange (ETDEWEB)

    Mohan, Swati [School of Materials Science and Technology, Institute of Technology, Banaras Hindu University, Varanasi 221005 (India); Prakash, Rajiv, E-mail: rajivprakash12@yahoo.com [School of Materials Science and Technology, Institute of Technology, Banaras Hindu University, Varanasi 221005 (India)

    2010-06-15

    We report for the first time the functionalization of a conducting polymer with a metal complex in order to develop a new type of catalytic material exhibiting better electronic communication through their delocalized {pi} electrons. The Co(II) complex having hydroxyl group as functional moiety is chemically coupled with carboxyl group of polyanthranilic acid which itself is a self doped conducting polymer. The covalent linkage between Co(II) and -OH group is confirmed using UV-vis, FT-IR and NMR spectroscopic techniques. The Co(II) complex functionalized polymer does exhibit excellent redox behavior and stability with mixed properties of Co(II) complex and {pi}-conjugated polymer. The material possesses potential benefits in sensors/biosensor applications and it is demonstrated for the electroanalysis of ascorbic acid at a level of nano molar concentration.

  11. Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints

    OpenAIRE

    Goberna, Miguel A.; Jeyakumar, Vaithilingam; Li, Guoyin; Linh, Nguyen

    2016-01-01

    The radius of robust feasibility of a convex program with uncertain constraints gives a value for the maximal ‘size’ of an uncertainty set under which robust feasibility can be guaranteed. This paper provides an upper bound for the radius for convex programs with uncertain convex polynomial constraints and exact formulas for convex programs with SOS-convex polynomial constraints (or convex quadratic constraints) under affine data uncertainty. These exact formulas allow the radius to be comput...

  12. Molecular determinants of angiotensin II type 1 receptor functional selectivity

    DEFF Research Database (Denmark)

    Aplin, Mark; Bonde, Marie Mi; Hansen, Jakob Lerche

    2008-01-01

    -independent recruitment of beta-arrestin-scaffolded signalling complexes that activate protein kinase pathways. Different states of receptor activation with preference for individual downstream pathways (functional selectivity) have been demonstrated in mutational studies of the AT(1) receptor and by pharmacological...... that selective blockade of G protein actions and simultaneous activation of G protein-independent signalling will prove to be a feasible strategy for improved cardiovascular therapy. The pharmacological perspectives of functional selectivity by receptors, such as the AT(1) receptor, urge the elucidation...

  13. Optimality and Duality on Fractional Multi-objective Programming Under Semilocal E-convexity%半局部E-凸性下分式多目标规划的最优性条件与对偶

    Institute of Scientific and Technical Information of China (English)

    胡清洁; 肖运海; 陈内萍

    2009-01-01

    In this paper, some necessary and sufficient optimality conditions are obtained for a fractional multiple objective programming involving semilocal E-convex and related functions. Also, some dual results are established under this kind of generalized convex functions. Our results generalize the ones obtained by Preda[J Math Anal Appl, 288(2003) 365-382].

  14. Postlaunch Monitoring of Functional Foods - Methodology development (II)

    NARCIS (Netherlands)

    Jong N de; Buurma-Rethans EJM; Fransen HP; Ocke MC; CVG

    2005-01-01

    Despite the availability of numerous cohort and monitoring studies in different populations in the Netherlands, the available information on functional food and/or supplement use on the whole from these studies is rather limited. Unfortunately, food intake data are vital for Post Launch Monitoring

  15. Universality of the Distribution Functions of Random Matrix Theory. II

    OpenAIRE

    Tracy, Craig A.; Widom, Harold

    1999-01-01

    This paper is a brief review of recent developments in random matrix theory. Two aspects are emphasized: the underlying role of integrable systems and the occurrence of the distribution functions of random matrix theory in diverse areas of mathematics and physics.

  16. Subharmonic functions and electric fields in ball layers. II

    Directory of Open Access Journals (Sweden)

    O. P. Gnatiuk

    2011-03-01

    Full Text Available In this sequel to cite{GK} we study a special case $BL(frac{1}{r},r$, $r>1$. Alsothe explicit representation of a subharmonic extension for a subharmonic function $u(x$ near a removable point is obtained. Moreover, the diverse Nevanlinna characteristics are compared.

  17. Reliability-based design optimization using convex approximations and sequential optimization and reliability assessment method

    Energy Technology Data Exchange (ETDEWEB)

    Cho, Tae Min; Lee, Byung Chai [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of)

    2010-01-15

    In this study, an effective method for reliability-based design optimization (RBDO) is proposed enhancing sequential optimization and reliability assessment (SORA) method by convex approximations. In SORA, reliability estimation and deterministic optimization are performed sequentially. The sensitivity and function value of probabilistic constraint at the most probable point (MPP) are obtained in the reliability analysis loop. In this study, the convex approximations for probabilistic constraint are constructed by utilizing the sensitivity and function value of the probabilistic constraint at the MPP. Hence, the proposed method requires much less function evaluations of probabilistic constraints in the deterministic optimization than the original SORA method. The efficiency and accuracy of the proposed method were verified through numerical examples

  18. Weighted composition operators between growth spaces on circular and strictly convex domain

    Directory of Open Access Journals (Sweden)

    Shayesteh Rezaei

    2015-06-01

    Full Text Available Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X$ is the space of all $finmathcal{H}(Omega_X$ for which $$|f(x|leqslant C omega(r_{Omega_X}(x,quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the Minkowski functional on $Omega_X$ and $omega :[0,1rightarrow(0,infty$ is a nondecreasing, continuous and unbounded function. Boundedness and compactness of weighted composition operators between growth spaces on circular and strictly convex domains were investigated.

  19. On the acceleration of the double smoothing technique for unconstrained convex optimization problems

    CERN Document Server

    Bot, Radu Ioan

    2012-01-01

    In this article we investigate the possibilities of accelerating the double smoothing technique when solving unconstrained nondifferentiable convex optimization problems. This approach relies on the regularization in two steps of the Fenchel dual problem associated to the problem to be solved into an optimization problem having a differentiable strongly convex objective function with Lipschitz continuous gradient. The doubly regularized dual problem is then solved via a fast gradient method. The aim of this paper is to show how do the properties of the functions in the objective of the primal problem influence the implementation of the double smoothing approach and its rate of convergence. The theoretical results are applied to linear inverse problems by making use of different regularization functionals.

  20. Reduction of shock induced noise in imperfectly expanded supersonic jets using convex optimization

    Science.gov (United States)

    Adhikari, Sam

    2007-11-01

    Imperfectly expanded jets generate screech noise. The imbalance between the backpressure and the exit pressure of the imperfectly expanded jets produce shock cells and expansion or compression waves from the nozzle. The instability waves and the shock cells interact to generate the screech sound. The mathematical model consists of cylindrical coordinate based full Navier-Stokes equations and large-eddy-simulation turbulence modeling. Analytical and computational analysis of the three-dimensional helical effects provide a model that relates several parameters with shock cell patterns, screech frequency and distribution of shock generation locations. Convex optimization techniques minimize the shock cell patterns and the instability waves. The objective functions are (convex) quadratic and the constraint functions are affine. In the quadratic optimization programs, minimization of the quadratic functions over a set of polyhedrons provides the optimal result. Various industry standard methods like regression analysis, distance between polyhedra, bounding variance, Markowitz optimization, and second order cone programming is used for Quadratic Optimization.

  1. Correction of an adult Class II division 2 individual using fixed functional appliance: A noncompliance approach

    OpenAIRE

    Shrinivas Basavaraddi; Gandedkar, Narayan H; Anup Belludi; Anand Patil

    2016-01-01

    This case report describes the application of fixed functional appliance in the treatment of an adult female having Class II division 2 malocclusion with retroclination of upper incisors. Fixed functional appliance was used to correct the overjet after the uprighting of upper incisors. Fixed functional appliance was fitted on a rigid rectangular arch wire. Application of fixed functional appliance achieved a good Class I molar relationship along with Class I canine relationship with normal ov...

  2. Immunophilins and their function in photosystem II assembly

    Energy Technology Data Exchange (ETDEWEB)

    Sheng Luan

    2012-11-27

    In the past funding period, the following lines of experiments have been conducted: to identify the partner proteins for FKBP20-2; to identify the mechanism of CYP38 function; studies on other FKBPs in the thylakoid lumen; to identify the partner proteins for FKBP20-2 using yeast two hybrid and transgenic lines expressing HA-FKBP20-2; to identify the partner protein of CYP38; studies on other FKBPs in the chloroplast.

  3. Traveling wavefronts in nonlocal diffusive predator-prey system with Holling type II functional response

    Directory of Open Access Journals (Sweden)

    Shuang Li

    2015-06-01

    Full Text Available This article concerns the existence of traveling wavefronts for a nonlocal diffusive predator-prey system with functional response of Holling type II. We first establish the existence principle for the system with a general functional response by using a fixed point theorem and upper-lower solution technique. We apply this result to a predator-prey model with Holling type II functional response. We deduce the existence of traveling wavefronts that connect the zero equilibrium and the positive equilibrium.

  4. Karst geomorphology: From hydrological functioning to palaeoenvironmental reconstructions. Part II

    Science.gov (United States)

    De Waele, Jo; Gutierrez, Francisco; Audra, Philippe

    2015-10-01

    In January 2015, the first part of the special issue on karst, entitled "Karst geomorphology: From hydrological functioning to palaeoenvironmental reconstructions" was published (Geomorphology, Vol. 229). This second part of the special issue comprises seven research papers covering a broad geographical canvas including Japan, Slovenia, France, Spain, Croatia, and Poland-Ukraine. Both issues mainly emanate from the contributions presented in the Karst session of the 8th International Conference of Geomorphology (International Association of Geomorphologists), held in Paris in August 2013, enriched with some invited papers.

  5. Tin(II)-functionalization of the archetypal {P8W48} polyoxotungstate.

    Science.gov (United States)

    Izarova, N V; Klaß, L; de Oliveira, P; Mbomekalle, I-M; Peters, V; Haarmann, F; Kögerler, P

    2015-11-28

    The synthesis of [K(4.5) ⊂ (ClSn(II))8P8W48O184](17.5-), featuring Sn(II) ions in trigonal-pyramidal SnO2Cl environment coordinating to the two inner rims of the wheel-shaped {P8W48}-type polyoxotungstate(vi) archetype, showcases how high chloride ligand concentrations as well as the control of the polyanion solubility via electrolytes and evaporation rates are essential to prevent numerous competing reactions that can hamper the Sn(ii) functionalization of polyoxometalates.

  6. Functional design criteria for project W-252, phase II liquid effluent treatment and disposal. Revision 2

    Energy Technology Data Exchange (ETDEWEB)

    Hatch, C.E.

    1995-05-01

    This document is the Functional Design Criteria for Project W-252. Project W-252 provides the scope to provide BAT/AKART (best available technology...) to 200 Liquid Effluent Phase II streams (B-Plant). This revision (Rev. 2) incorporates a major descoping of the project. The descoping was done to reflect a combination of budget cutting measures allowed by a less stringent regulatory posture toward the Phase II streams

  7. Relationship between personality disorder functioning styles and the emotional states in bipolar I and II disorders.

    Directory of Open Access Journals (Sweden)

    Jiashu Yao

    Full Text Available Bipolar disorder types I (BD I and II (BD II behave differently in clinical manifestations, normal personality traits, responses to pharmacotherapies, biochemical backgrounds and neuroimaging activations. How the varied emotional states of BD I and II are related to the comorbid personality disorders remains to be settled.We therefore administered the Plutchick - van Praag Depression Inventory (PVP, the Mood Disorder Questionnaire (MDQ, the Hypomanic Checklist-32 (HCL-32, and the Parker Personality Measure (PERM in 37 patients with BD I, 34 BD II, and in 76 healthy volunteers.Compared to the healthy volunteers, patients with BD I and II scored higher on some PERM styles, PVP, MDQ and HCL-32 scales. In BD I, the PERM Borderline style predicted the PVP scale; and Antisocial predicted HCL-32. In BD II, Borderline, Dependent, Paranoid (- and Schizoid (- predicted PVP; Borderline predicted MDQ; Passive-Aggressive and Schizoid (- predicted HCL-32. In controls, Borderline and Narcissistic (- predicted PVP; Borderline and Dependent (- predicted MDQ.Besides confirming the different predictability of the 11 functioning styles of personality disorder to BD I and II, we found that the prediction was more common in BD II, which might underlie its higher risk of suicide and poorer treatment outcome.

  8. Bone morphogenetic protein receptor II regulates pulmonary artery endothelial cell barrier function.

    Science.gov (United States)

    Burton, Victoria J; Ciuclan, Loredana I; Holmes, Alan M; Rodman, David M; Walker, Christoph; Budd, David C

    2011-01-06

    Mutations in bone morphogenetic protein receptor II (BMPR-II) underlie most heritable cases of pulmonary arterial hypertension (PAH). However, less than half the individuals who harbor mutations develop the disease. Interestingly, heterozygous null BMPR-II mice fail to develop PAH unless an additional inflammatory insult is applied, suggesting that BMPR-II plays a fundamental role in dampening inflammatory signals in the pulmonary vasculature. Using static- and flow-based in vitro systems, we demonstrate that BMPR-II maintains the barrier function of the pulmonary artery endothelial monolayer suppressing leukocyte transmigration. Similar findings were also observed in vivo using a murine model with loss of endothelial BMPR-II expression. In vitro, the enhanced transmigration of leukocytes after tumor necrosis factor α or transforming growth factor β1 stimulation was CXCR2 dependent. Our data define how loss of BMPR-II in the endothelial layer of the pulmonary vasculature could lead to a heightened susceptibility to inflammation by promoting the extravasation of leukocytes into the pulmonary artery wall. We speculate that this may be a key mechanism involved in the initiation of the disease in heritable PAH that results from defects in BMPR-II expression.

  9. Relationship between personality disorder functioning styles and the emotional states in bipolar I and II disorders.

    Science.gov (United States)

    Yao, Jiashu; Xu, You; Qin, Yanhua; Liu, Jing; Shen, Yuedi; Wang, Wei; Chen, Wei

    2015-01-01

    Bipolar disorder types I (BD I) and II (BD II) behave differently in clinical manifestations, normal personality traits, responses to pharmacotherapies, biochemical backgrounds and neuroimaging activations. How the varied emotional states of BD I and II are related to the comorbid personality disorders remains to be settled. We therefore administered the Plutchick - van Praag Depression Inventory (PVP), the Mood Disorder Questionnaire (MDQ), the Hypomanic Checklist-32 (HCL-32), and the Parker Personality Measure (PERM) in 37 patients with BD I, 34 BD II, and in 76 healthy volunteers. Compared to the healthy volunteers, patients with BD I and II scored higher on some PERM styles, PVP, MDQ and HCL-32 scales. In BD I, the PERM Borderline style predicted the PVP scale; and Antisocial predicted HCL-32. In BD II, Borderline, Dependent, Paranoid (-) and Schizoid (-) predicted PVP; Borderline predicted MDQ; Passive-Aggressive and Schizoid (-) predicted HCL-32. In controls, Borderline and Narcissistic (-) predicted PVP; Borderline and Dependent (-) predicted MDQ. Besides confirming the different predictability of the 11 functioning styles of personality disorder to BD I and II, we found that the prediction was more common in BD II, which might underlie its higher risk of suicide and poorer treatment outcome.

  10. Exploiting Symmetry in Integer Convex Optimization using Core Points

    CERN Document Server

    Herr, Katrin; Schürmann, Achill

    2012-01-01

    We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. We define a core point of such a symmetry group as an integral point for which the convex hull of its orbit does not contain integral points other than the orbit points themselves. These core points allow us to decompose symmetric integer convex programming problems. Especially for symmetric integer linear programs we describe two algorithms based on this decomposition. Using a characterization of core points for direct products of symmetric groups, we show that prototype implementations can compete with state-of-the art commercial solvers and solve an open MIPLIB problem.

  11. Plane geometry and convexity of polynomial stability regions

    CERN Document Server

    Henrion, Didier

    2008-01-01

    The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however that quite often for benchmark problem instances, the set of stabilizing controllers seems to be convex. In this note we use elementary techniques from real algebraic geometry (resultants and Bezoutian matrices) to explain this phenomenon. As a byproduct, we derive a convex linear matrix inequality (LMI) formulation of two-parameter fixed-order controller design problem, when possible.

  12. Bubbles, convexity and the Black--Scholes equation

    CERN Document Server

    Ekström, Erik; 10.1214/08-AAP579

    2009-01-01

    A bubble is characterized by the presence of an underlying asset whose discounted price process is a strict local martingale under the pricing measure. In such markets, many standard results from option pricing theory do not hold, and in this paper we address some of these issues. In particular, we derive existence and uniqueness results for the Black--Scholes equation, and we provide convexity theory for option pricing and derive related ordering results with respect to volatility. We show that American options are convexity preserving, whereas European options preserve concavity for general payoffs and convexity only for bounded contracts.

  13. A Note on The Convexity of Chebyshev Sets

    Directory of Open Access Journals (Sweden)

    Sangeeta

    2009-07-01

    Full Text Available Perhaps one of the major unsolved problem in Approximation Theoryis: Whether or not every Chebyshev subset of a Hilbert space must be convex. Many partial answers to this problem are available in the literature. R.R. Phelps[Proc. Amer. Math. Soc. 8 (1957, 790-797] showed that a Chebyshev set in an inner product space (or in a strictly convex normed linear space is convex if the associated metric projection is non-expansive. We extend this result to metricspaces.

  14. Global Optimization Approach to Non-convex Problems

    Institute of Scientific and Technical Information of China (English)

    LU Zi-fang; ZHENG Hui-li

    2004-01-01

    A new approach to find the global optimal solution of the special non-convex problems is proposed in this paper. The non-convex objective problem is first decomposed into two convex sub-problems. Then a generalized gradient is introduced to determine a search direction and the evolution equation is built to obtain a global minimum point. By the approach, we can prevent the search process from some local minima and search a global minimum point. Two numerical examples are given to prove the approach to be effective.

  15. Hard convex lens-shaped particles: Densest-known packings and phase behavior

    Energy Technology Data Exchange (ETDEWEB)

    Cinacchi, Giorgio, E-mail: giorgio.cinacchi@uam.es [Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada (IFIMAC), Instituto de Ciencias de Materiales “Nicolás Cabrera,” Universidad Autónoma de Madrid, Campus de Cantoblanco, E-28049 Madrid (Spain); Torquato, Salvatore, E-mail: torquato@princeton.edu [Department of Chemistry, Department of Physics, Institute for the Science and Technology of Materials, Program for Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544 (United States)

    2015-12-14

    By using theoretical methods and Monte Carlo simulations, this work investigates dense ordered packings and equilibrium phase behavior (from the low-density isotropic fluid regime to the high-density crystalline solid regime) of monodisperse systems of hard convex lens-shaped particles as defined by the volume common to two intersecting congruent spheres. We show that, while the overall similarity of their shape to that of hard oblate ellipsoids is reflected in a qualitatively similar phase diagram, differences are more pronounced in the high-density crystal phase up to the densest-known packings determined here. In contrast to those non-(Bravais)-lattice two-particle basis crystals that are the densest-known packings of hard (oblate) ellipsoids, hard convex lens-shaped particles pack more densely in two types of degenerate crystalline structures: (i) non-(Bravais)-lattice two-particle basis body-centered-orthorhombic-like crystals and (ii) (Bravais) lattice monoclinic crystals. By stacking at will, regularly or irregularly, laminae of these two crystals, infinitely degenerate, generally non-periodic in the stacking direction, dense packings can be constructed that are consistent with recent organizing principles. While deferring the assessment of which of these dense ordered structures is thermodynamically stable in the high-density crystalline solid regime, the degeneracy of their densest-known packings strongly suggests that colloidal convex lens-shaped particles could be better glass formers than colloidal spheres because of the additional rotational degrees of freedom.

  16. Stochastic Dynamic Programming Applied to Hydrothermal Power Systems Operation Planning Based on the Convex Hull Algorithm

    Directory of Open Access Journals (Sweden)

    Bruno H. Dias

    2010-01-01

    Full Text Available This paper presents a new approach for the expected cost-to-go functions modeling used in the stochastic dynamic programming (SDP algorithm. The SDP technique is applied to the long-term operation planning of electrical power systems. Using state space discretization, the Convex Hull algorithm is used for constructing a series of hyperplanes that composes a convex set. These planes represent a piecewise linear approximation for the expected cost-to-go functions. The mean operational costs for using the proposed methodology were compared with those from the deterministic dual dynamic problem in a case study, considering a single inflow scenario. This sensitivity analysis shows the convergence of both methods and is used to determine the minimum discretization level. Additionally, the applicability of the proposed methodology for two hydroplants in a cascade is demonstrated. With proper adaptations, this work can be extended to a complete hydrothermal system.

  17. An Effective Branch-and-Bound Algorithm for Convex Quadratic Integer Programming

    Science.gov (United States)

    Buchheim, Christoph; Caprara, Alberto; Lodi, Andrea

    We present a branch-and-bound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints. In a given node of the enumeration tree, corresponding to the fixing of a subset of the variables, a lower bound is given by the continuous minimum of the restricted objective function. We improve this bound by exploiting the integrality of the variables using suitably-defined lattice-free ellipsoids. Experiments show that our approach is very fast on both unconstrained problems and problems with box constraints. The main reason is that all expensive calculations can be done in a preprocessing phase, while a single node in the enumeration tree can be processed in linear time in the problem dimension.

  18. Optimal Orthogonal Graph Drawing with Convex Bend Costs

    CERN Document Server

    Bläsius, Thomas; Wagner, Dorothea

    2012-01-01

    Traditionally, the quality of orthogonal planar drawings is quantified by either the total number of bends, or the maximum number of bends per edge. However, this neglects that in typical applications, edges have varying importance. Moreover, as bend minimization over all planar embeddings is NP-hard, most approaches focus on a fixed planar embedding. We consider the problem OptimalFlexDraw that is defined as follows. Given a planar graph G on n vertices with maximum degree 4 and for each edge e a cost function cost_e : N_0 --> R defining costs depending on the number of bends on e, compute an orthogonal drawing of G of minimum cost. Note that this optimizes over all planar embeddings of the input graphs, and the cost functions allow fine-grained control on the bends of edges. In this generality OptimalFlexDraw is NP-hard. We show that it can be solved efficiently if 1) the cost function of each edge is convex and 2) the first bend on each edge does not cause any cost (which is a condition similar to the posi...

  19. Gauge-independent Wigner functions. II. Inclusion of radiation reaction

    Science.gov (United States)

    Javanainen, J.; Varró, S.; Serimaa, O. T.

    1987-04-01

    We investigate the effects of quantized radiation reaction fields on the motion of a charged particle using the gauge-independent Wigner operator (GIWO) and gauge-independent Wigner function (GIWF) introduced earlier [Phys. Rev. A 33, 2913 (1986)]. To complement the equation of motion of the GIWO, the Heisenberg equations of motion of the quantized electromagnetic fields are solved within the Markov approximation. After considering the operator orderings and orders of magnitude of the radiation reaction terms, we eliminate the quantum fields from the evolution equation of the GIWO, and obtain for the GIWF a closed equation containing relaxation terms. As an example of the formalism we derive a Fokker-Planck equation (FPE) for the GIWF of a particle in a constant magnetic field. To the order ħ 0 the classical radiation damping ensues, and the first quantum correction proportional to ħ emerges as diffusion. The diffusion operator turns out to be indefinite and the FPE consequently defies our attempts at a complete analysis, but we demonstrate that at least the coherent states constructed from the Landau levels exhibit a manifestly physical time evolution under the FPE. We point out that the GIWF calculated with quantized electromagnetic fields is divergent even if the fields are in the vacuum state, and suggest that the GIWF should be associated with the particle state by ignoring the quantized fields altogether.

  20. Prolonging sensor networks lifetime using convex clusters

    Directory of Open Access Journals (Sweden)

    Payam Salehi

    2013-11-01

    Full Text Available Reducing the energy consumption of nodes in sensor networks and prolonging the network life time has been proposed as one of the most important challenges facing researchers in the field of sensor networks. Therefore, designing an energy-aware protocol to gather data from network level and transmitting it to sink is placed on the agenda at this paper. After presenting an analysis of the processes of clustering in sensory networks and investigating the effect of sending interval on the amount of energy consumption, We have shown that if the use of convex static casters be done such as all the communications within the cluster with the sending distance less than the optimal threshold, it Will help to increase the lifetime of nodes. also have shown that if we create a virtual backbone between cluster heads to transfer far cluster heads data from sink to sink , will has a significant impact on increasing the network lifetime. For this reason, a detailed discussion on how to determine the size of clusters and partitioning of the network environment to them is presented in Chapter 4.Simulation results show considerable improvement of the proposed algorithm.

  1. Designing Camera Networks by Convex Quadratic Programming

    KAUST Repository

    Ghanem, Bernard

    2015-05-04

    ​In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport). ​

  2. Flip to Regular Triangulation and Convex Hull.

    Science.gov (United States)

    Gao, Mingcen; Cao, Thanh-Tung; Tan, Tiow-Seng

    2017-02-01

    Flip is a simple and local operation to transform one triangulation to another. It makes changes only to some neighboring simplices, without considering any attribute or configuration global in nature to the triangulation. Thanks to this characteristic, several flips can be independently applied to different small, non-overlapping regions of one triangulation. Such operation is favored when designing algorithms for data-parallel, massively multithreaded hardware, such as the GPU. However, most existing flip algorithms are designed to be executed sequentially, and usually need some restrictions on the execution order of flips, making them hard to be adapted to parallel computation. In this paper, we present an in depth study of flip algorithms in low dimensions, with the emphasis on the flexibility of their execution order. In particular, we propose a series of provably correct flip algorithms for regular triangulation and convex hull in 2D and 3D, with implementations for both CPUs and GPUs. Our experiment shows that our GPU implementation for constructing these structures from a given point set achieves up to two orders of magnitude of speedup over other popular single-threaded CPU implementation of existing algorithms.

  3. Convexity and symmetrization in relativistic theories

    Science.gov (United States)

    Ruggeri, T.

    1990-09-01

    There is a strong motivation for the desire to have symmetric hyperbolic field equations in thermodynamics, because they guarantee well-posedness of Cauchy problems. A generic quasi-linear first order system of balance laws — in the non-relativistic case — can be shown to be symmetric hyperbolic, if the entropy density is concave with respect to the variables. In relativistic thermodynamics this is not so. This paper shows that there exists a scalar quantity in relativistic thermodynamics whose concavity guarantees a symmetric hyperbolic system. But that quantity — we call it —bar h — is not the entropy, although it is closely related to it. It is formed by contracting the entropy flux vector — ha with a privileged time-like congruencebar ξ _α . It is also shown that the convexity of h plus the requirement that all speeds be smaller than the speed of light c provide symmetric hyperbolic field equations for all choices of the direction of time. At this level of generality the physical meaning of —h is unknown. However, in many circumstances it is equal to the entropy. This is so, of course, in the non-relativistic limit but also in the non-dissipative relativistic fluid and even in relativistic extended thermodynamics for a non-degenerate gas.

  4. A projected gradient method with nonmonotonic backtracking technique for solving convex constrained monotone variational inequality problem

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Based on a differentiable merit function proposed by Taji,et al in "Mathematical Programming,1993,58: 369-383",a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented.Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions.The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

  5. Nonlinear Stability of a SIRS Epidemic Model with Convex Incidence Rate

    Science.gov (United States)

    Buonomo, B.; Rionero, S.

    2010-09-01

    We study an epidemic model for infections with non permanent acquired immunity (SIRS). The incidence rate is assumed to be convex respect to the infective class. By using a peculiar Lyapunov function, we obtain necessary and sufficient conditions for the local nonlinear stability of equilibria. Conditions ensuring the global stability of the endemic equilibrium are also obtained. Our procedure allows to enlarge the class of incidence rates ensuring the Lyapunov nonlinear stability of the endemic equilibrium for SIRS models.

  6. A simple convex optimization problem with many applications

    DEFF Research Database (Denmark)

    Vidal, Rene Victor Valqui

    1994-01-01

    This paper presents an algorithm for the solution of a simple convex optimization problem. This problem is a generalization of several other optimization problems which have applications to resource allocation, optimal capacity expansion, and vehicle scheduling. The algorithm is based...

  7. Global optimization over linear constraint non-convex programming problem

    Institute of Scientific and Technical Information of China (English)

    ZHANG Gui-Jun; WU Ti-Huan; YE Rong; YANG Hai-qing

    2005-01-01

    A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programmin g problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.

  8. Subaperture Stitching Interferometry for Large Convex Aspheric Surfaces Project

    Data.gov (United States)

    National Aeronautics and Space Administration — The size and accuracy specifications of telescope mirrors are ever more demanding. This is particularly true for secondary mirrors, as they are convex and thus...

  9. Synthesis, spectroscopic and thermal studies of Mg(II), Ca(II), Sr(II) and Ba(II) diclofenac sodium complexes as anti-inflammatory drug and their protective effects on renal functions impairment and oxidative stress

    Science.gov (United States)

    El-Megharbel, Samy M.; Hamza, Reham Z.; Refat, Moamen S.

    2015-01-01

    The main task of our present study is the preparation of newly complexes of Mg(II), Ca(II), Sr(II) and Ba(II) with diclofenac which succeeded to great extent in alleviating the side effects of diclofenac alone and ameliorating the kidney function parameters and antioxidant capacities with respect to diclofenac treated group alone. The Mg(II), Ca(II), Sr(II) and Ba(II) with diclofenac have been synthesized and characterized using infrared, electronic and 1H NMR spectral, thermogravimetric and conductivity measurements. The diclofenac ligand has been found to act as bidentate chelating agent. Diclofenac complexes coordinate through the oxygen's of the carboxyl group. The molar ratio chelation is 1:2 (M2+-dic) with general formula [M(dic)2(H2O)2]ṡnH2O. Antibacterial screening of the alkaline earth metal complexes against Escherichia coli (Gram - ve), Bacillus subtilis (Gram + ve) and anti-fungal (Asperagillus oryzae, Asperagillus niger, Asperagillus flavus) were investigated. The kidney functions in male albino rats were ameliorated upon treatment with metal complexes of dic, which are represented by decreasing the levels of urea and uric acid to be located within normal values. The other looks bright spot in this article is the assessment of antioxidant defense system including SOD, CAT and MDA with the help of Sr2+, Mg2+ and Ca2+-dic complexes. The hormones related to kidney functions and stresses have been greatly ameliorated in groups treated with dic complexes in comparable with dic treated group.

  10. Synthesis, spectroscopic and thermal studies of Mg(II), Ca(II), Sr(II) and Ba(II) diclofenac sodium complexes as anti-inflammatory drug and their protective effects on renal functions impairment and oxidative stress.

    Science.gov (United States)

    El-Megharbel, Samy M; Hamza, Reham Z; Refat, Moamen S

    2015-01-25

    The main task of our present study is the preparation of newly complexes of Mg(II), Ca(II), Sr(II) and Ba(II) with diclofenac which succeeded to great extent in alleviating the side effects of diclofenac alone and ameliorating the kidney function parameters and antioxidant capacities with respect to diclofenac treated group alone. The Mg(II), Ca(II), Sr(II) and Ba(II) with diclofenac have been synthesized and characterized using infrared, electronic and (1)H NMR spectral, thermogravimetric and conductivity measurements. The diclofenac ligand has been found to act as bidentate chelating agent. Diclofenac complexes coordinate through the oxygen's of the carboxyl group. The molar ratio chelation is 1:2 (M(2+)-dic) with general formula [M(dic)2(H2O)2]⋅nH2O. Antibacterial screening of the alkaline earth metal complexes against Escherichia coli (Gram-ve), Bacillus subtilis (Gram+ve) and anti-fungal (Asperagillus oryzae, Asperagillus niger, Asperagillus flavus) were investigated. The kidney functions in male albino rats were ameliorated upon treatment with metal complexes of dic, which are represented by decreasing the levels of urea and uric acid to be located within normal values. The other looks bright spot in this article is the assessment of antioxidant defense system including SOD, CAT and MDA with the help of Sr(2+), Mg(2+) and Ca(2+)-dic complexes. The hormones related to kidney functions and stresses have been greatly ameliorated in groups treated with dic complexes in comparable with dic treated group.

  11. Convex games, clan games, and their marginal games

    OpenAIRE

    Branzei , Rodica; Dimitrov, Dinko; Tijs, Stef

    2005-01-01

    We provide characterizations of convex games and total clan games by using properties of their corresponding marginal games. As it turns out, a cooperative game is convex if and only if all its marginal games are superadditive, and a monotonic game satisfying the veto player property with respect to the members of a coalition C is a total clan game (with clan C) if and only if all its C-based marginal games are subadditive.

  12. A longitudinal study of emotional adjustment, quality of life and adaptive function in attenuated MPS II.

    Science.gov (United States)

    Shapiro, Elsa G; Rudser, Kyle; Ahmed, Alia; Steiner, Robert D; Delaney, Kathleen A; Yund, Brianna; King, Kelly; Kunin-Batson, Alicia; Eisengart, Julie; Whitley, Chester B

    2016-06-01

    The behavioral, adaptive and quality of life characteristics of attenuated mucopolysaccharidosis type II (MPS II) have not been well studied. Understanding changes over time in the attenuated phenotype may assist in helping achieve better outcomes in long-term function. This longitudinal study investigates these outcomes in relation to age, somatic disease burden, and IQ. Specifically, somatic disease burden is a major challenge for these patients, even with treatment with enzyme replacement therapy. 15 patients, 10 between ages 6 and MPS II patients have increasing somatic disease burden and poor physical quality of life as they develop as well as decreasing self-esteem and sense of adequacy. Psychosocial quality of life, adaptive skills, and attention improve. Recognition of and intervention around these issues will be beneficial to MPS II attenuated patients who have the resources to use such assistance to improve their long-term outcomes.

  13. Functional recombinant MHC class II molecules and high-throughput peptide-binding assays

    DEFF Research Database (Denmark)

    Justesen, Sune; Harndahl, Mikkel; Lamberth, Kasper

    2009-01-01

    of peptide-binding assay were developed including a homogeneous, non-radioactive, high-throughput (HTS) binding assay. Binding isotherms were generated allowing the affinities of interaction to be determined. The affinities of the best binders were found to be in the low nanomolar range. Recombinant MHC...... in the generation of MHC-II molecules as reagents to study and manipulate specific T helper cell responses. Methods to generate functional MHC-II molecules recombinantly, and measure their interaction with peptides, would be highly desirable; however, no consensus methodology has yet emerged. RESULTS: We generated....... CONCLUSION: We have successfully developed versatile MHC-II resources, which may assist in the generation of MHC class II -wide reagents, data, and tools....

  14. Convex Aspherical Surface Testing Using Catadioptric Partial Compensating System

    Science.gov (United States)

    Wang, Jingxian; Hao, Qun; Hu, Yao; Wang, Shaopu; Li, Tengfei; Tian, Yuhan; Li, Lin

    2016-01-01

    Aspheric optical components are the indispensable part of modern optics systems. With the constant development of aspheric optical fabrication technique, the systems with large aperture convex aspheric optical components are widely used in astronomy and space optics. Thus, the measurement of the figure error of the whole convex aspherical surface with high precision comes to be a challenge in the area of optical surface manufacture, and surface testing method is also very important. This paper presents a new partial compensating system by the combination of a refractive lens and a reflective mirror for testing convex aspherical surface. The refractive lens is used to compensate the aberration of the tested convex asphere partially. The reflective mirror is a spherical mirror which is coaxial to the refractive lens and reflecting the lights reflected by the tested convex asphere back to the convex asphere itself. With the long focal length and large aperture system we can realize a lighter and more compact system than the refractive partial compensating system because the spheric reflective mirror is more easily to realize and can bending the light conveniently.

  15. First and second order numerical methods based on a new convex splitting for phase-field crystal equation

    Science.gov (United States)

    Shin, Jaemin; Lee, Hyun Geun; Lee, June-Yub

    2016-12-01

    The phase-field crystal equation derived from the Swift-Hohenberg energy functional is a sixth order nonlinear equation. We propose numerical methods based on a new convex splitting for the phase-field crystal equation. The first order convex splitting method based on the proposed splitting is unconditionally gradient stable, which means that the discrete energy is non-increasing for any time step. The second order scheme is unconditionally weakly energy stable, which means that the discrete energy is bounded by its initial value for any time step. We prove mass conservation, unique solvability, energy stability, and the order of truncation error for the proposed methods. Numerical experiments are presented to show the accuracy and stability of the proposed splitting methods compared to the existing other splitting methods. Numerical tests indicate that the proposed convex splitting is a good choice for numerical methods of the phase-field crystal equation.

  16. [Functional analysis of transforming growth factor-beta type II dominant negative receptor].

    Science.gov (United States)

    Takarada, M

    1996-06-01

    The transforming growth factor-beta (TGF-beta) is a multifunctional homodimeric protein with an apparent molecular weight of 25 KDa. TGF-beta transduces signals by forming heteromeric complexes of their type-I (T beta R-I) and type-II (T beta R-II) serin/threonine kinase receptors. TGF-beta binds first to T beta R-II receptor, and then the ligand in this complex is recognized by T beta R-I, resulting in formation of a heteromeric receptor complex composed of T beta R-I and T beta R-II. Once received, T beta R-I becomes phosphorylated in the GS domain by the associated constitutively active T beta R-II and transmits the downstream signal. It has been reported that formation of the heteromeric complex is indispensible at least in epithelial cells for growth inhibition and extracellular matrix production induced by TGF-beta. In this study, the functional role of T beta R-II for the TGF-beta-induced signals in osteoblastic cells was investigated by using a dominant negative type of T beta R-II mutant receptors (T beta RIIDNR). ROS 17/2.8 and MG 63 cells were found to express T beta R-I, T beta R-II, and T beta R-III, and their cell growth was inhibited by TGF-beta, whereas alkaline phosphatase activity was stimulated. Cells that were stably transfected with the T beta RIIDNR plasmid showed decreased response to TGF-beta during growth and alkaline phosphatase activity. These results indicate that the intracellular serine/threonine kinase domain of T beta R-II is essential for signal transduction of the TGF-beta-induced alkaline phosphatase activity as well as growth inhibition.

  17. Stochastic convex sparse principal component analysis.

    Science.gov (United States)

    Baytas, Inci M; Lin, Kaixiang; Wang, Fei; Jain, Anil K; Zhou, Jiayu

    2016-12-01

    Principal component analysis (PCA) is a dimensionality reduction and data analysis tool commonly used in many areas. The main idea of PCA is to represent high-dimensional data with a few representative components that capture most of the variance present in the data. However, there is an obvious disadvantage of traditional PCA when it is applied to analyze data where interpretability is important. In applications, where the features have some physical meanings, we lose the ability to interpret the principal components extracted by conventional PCA because each principal component is a linear combination of all the original features. For this reason, sparse PCA has been proposed to improve the interpretability of traditional PCA by introducing sparsity to the loading vectors of principal components. The sparse PCA can be formulated as an ℓ1 regularized optimization problem, which can be solved by proximal gradient methods. However, these methods do not scale well because computation of the exact gradient is generally required at each iteration. Stochastic gradient framework addresses this challenge by computing an expected gradient at each iteration. Nevertheless, stochastic approaches typically have low convergence rates due to the high variance. In this paper, we propose a convex sparse principal component analysis (Cvx-SPCA), which leverages a proximal variance reduced stochastic scheme to achieve a geometric convergence rate. We further show that the convergence analysis can be significantly simplified by using a weak condition which allows a broader class of objectives to be applied. The efficiency and effectiveness of the proposed method are demonstrated on a large-scale electronic medical record cohort.

  18. Fixed point theorems in locally convex spaces—the Schauder mapping method

    Directory of Open Access Journals (Sweden)

    S. Cobzaş

    2006-03-01

    Full Text Available In the appendix to the book by F. F. Bonsal, Lectures on Some Fixed Point Theorems of Functional Analysis (Tata Institute, Bombay, 1962 a proof by Singbal of the Schauder-Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping method, is included. The aim of this note is to show that this method can be adapted to yield a proof of Kakutani fixed point theorem in the locally convex case. For the sake of completeness we include also the proof of Schauder-Tychonoff theorem based on this method. As applications, one proves a theorem of von Neumann and a minimax result in game theory.

  19. String-averaging incremental subgradients for constrained convex optimization with applications to reconstruction of tomographic images

    Science.gov (United States)

    Massambone de Oliveira, Rafael; Salomão Helou, Elias; Fontoura Costa, Eduardo

    2016-11-01

    We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed independently along each string, possibly in parallel, by an incremental subgradient method (ISM). The end-points of all strings are averaged to form the next iterate. The method is useful to solve sparse and large-scale non-smooth convex optimization problems, such as those arising in tomographic imaging. A convergence analysis is provided under realistic, standard conditions. Numerical tests are performed in a tomographic image reconstruction application, showing good performance for the convergence speed when measured as the decrease ratio of the objective function, in comparison to classical ISM.

  20. A Total Variation Model Based on the Strictly Convex Modification for Image Denoising

    Directory of Open Access Journals (Sweden)

    Boying Wu

    2014-01-01

    Full Text Available We propose a strictly convex functional in which the regular term consists of the total variation term and an adaptive logarithm based convex modification term. We prove the existence and uniqueness of the minimizer for the proposed variational problem. The existence, uniqueness, and long-time behavior of the solution of the associated evolution system is also established. Finally, we present experimental results to illustrate the effectiveness of the model in noise reduction, and a comparison is made in relation to the more classical methods of the traditional total variation (TV, the Perona-Malik (PM, and the more recent D-α-PM method. Additional distinction from the other methods is that the parameters, for manual manipulation, in the proposed algorithm are reduced to basically only one.

  1. The extension of the Krein-Smulian theorem for Orlicz sequence spaces and convex sets

    Science.gov (United States)

    Granero, Antonio S.

    2007-02-01

    If X is a Banach space and C[subset of]X** a convex subset, for x**[set membership, variant]X** and A[subset of]X** let be the distance from x** to C and . In this paper we prove that if [phi] is an Orlicz function, I an infinite set and X=l[phi](I) the corresponding Orlicz space, equipped with either the Luxemburg or the Orlicz norm, then for every w*-compact subset K[subset of]X** we have if and only if [phi] satisfies the [Delta]2-condition at 0. We also prove that for every Banach space X, every nonempty convex subset C[subset of]X and every w*-compact subset K[subset of]X** then and, if K[intersection]C is w*-dense in K, then .

  2. CELL TRACKING USING PARTICLE FILTERS WITH IMPLICIT CONVEX SHAPE MODEL IN 4D CONFOCAL MICROSCOPY IMAGES

    Science.gov (United States)

    Ramesh, Nisha; Tasdizen, Tolga

    2016-01-01

    Bayesian frameworks are commonly used in tracking algorithms. An important example is the particle filter, where a stochastic motion model describes the evolution of the state, and the observation model relates the noisy measurements to the state. Particle filters have been used to track the lineage of cells. Propagating the shape model of the cell through the particle filter is beneficial for tracking. We approximate arbitrary shapes of cells with a novel implicit convex function. The importance sampling step of the particle filter is defined using the cost associated with fitting our implicit convex shape model to the observations. Our technique is capable of tracking the lineage of cells for nonmitotic stages. We validate our algorithm by tracking the lineage of retinal and lens cells in zebrafish embryos. PMID:27403085

  3. Fixed Points of Single- and Set-Valued Mappings in Uniformly Convex Metric Spaces with No Metric Convexity

    Directory of Open Access Journals (Sweden)

    Rafa Espínola

    2010-01-01

    Full Text Available We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for set-valued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric which makes a big difference when studying the existence of fixed points for set-valued mappings.

  4. Derivative-free generation and interpolation of convex Pareto optimal IMRT plans.

    Science.gov (United States)

    Hoffmann, Aswin L; Siem, Alex Y D; den Hertog, Dick; Kaanders, Johannes H A M; Huizenga, Henk

    2006-12-21

    In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.

  5. MERCURY(II) ADSORPTION FROM WASTEWATERS USING A THIOL FUNCTIONAL ADSORBENT

    Science.gov (United States)

    The removal of mercury(II) from wastewaters (coal-fired utility plant scrubber solutions) using a thiol functional organoceramic composite (SOL-AD-IV) is investigated. A simulant is employed as a surrogate to demonstrate the removal of mercury from real waste solutions. Equilibri...

  6. WISC-IV and WIAT-II Profiles in Children with High-Functioning Autism

    Science.gov (United States)

    Mayes, Susan Dickerson; Calhoun, Susan L.

    2008-01-01

    Children with high-functioning autism earned above normal scores on the Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV) Perceptual Reasoning and Verbal Comprehension Indexes and below normal scores on the Working Memory and Processing Speed Indexes and Wechsler Individual Achievement Test-Second Edition (WIAT-II) Written…

  7. Functional defecation disorders in children: comparing the Rome II with the Rome III criteria.

    Science.gov (United States)

    Burgers, Rosa; Levin, Alon D; Di Lorenzo, Carlo; Dijkgraaf, Marcel G W; Benninga, Marc A

    2012-10-01

    To evaluate the prevalence of pediatric functional defecation disorders (FDD) using the Rome III criteria and to compare these data with those obtained using Rome II criteria. A chart review was performed in patients referred to a tertiary outpatient clinic with symptoms of constipation and/or fecal incontinence. All patients received a standardized bowel questionnaire and physical examination, including rectal examination. The prevalence of pediatric FDD according to both Rome criteria sets was assessed. Patients with FDD (n = 336; 61% boys, mean age 6.3 ± 3.5 SD) were studied: 39% had a defecation frequency ≤ 2/wk, 75% had fecal incontinence, 75% displayed retentive posturing, 60% had pain during defecation, 49% passed large diameter stools, and 49% had a palpable rectal fecal mass. According to the Rome III criteria, 87% had functional constipation (FC) compared with only 34% fulfilling criteria for either FC or functional fecal retention based on the Rome II definitions (P criteria for functional nonretentive fecal incontinence according to both the Rome II and Rome III criteria. The pediatric Rome III criteria for FC are less restrictive than the Rome II criteria. The Rome III criteria are an important step forward in the definition and recognition of FDD in children. Copyright © 2012 Mosby, Inc. All rights reserved.

  8. Optimizing the Structure of Tetracyanoplatinate (II): A Comparison of Relativistic Density Functional Theory Methods

    DEFF Research Database (Denmark)

    Dohn, Asmus Ougaard; Møller, Klaus Braagaard; Sauer, Stephan P. A.

    2013-01-01

    The geometry of tetracyanoplatinate(II) (TCP) has been optimized with density functional theory (DFT) calculations in order to compare different computational strategies. Two approximate scalar relativistic methods, i.e. the scalar zeroth-order regular approximation (ZORA) and non-relativistic ca...

  9. Statistical Mechanics of Optimal Convex Inference in High Dimensions

    Science.gov (United States)

    Advani, Madhu; Ganguli, Surya

    2016-07-01

    A fundamental problem in modern high-dimensional data analysis involves efficiently inferring a set of P unknown model parameters governing the relationship between the inputs and outputs of N noisy measurements. Various methods have been proposed to regress the outputs against the inputs to recover the P parameters. What are fundamental limits on the accuracy of regression, given finite signal-to-noise ratios, limited measurements, prior information, and computational tractability requirements? How can we optimally combine prior information with measurements to achieve these limits? Classical statistics gives incisive answers to these questions as the measurement density α =(N /P )→∞ . However, these classical results are not relevant to modern high-dimensional inference problems, which instead occur at finite α . We employ replica theory to answer these questions for a class of inference algorithms, known in the statistics literature as M-estimators. These algorithms attempt to recover the P model parameters by solving an optimization problem involving minimizing the sum of a loss function that penalizes deviations between the data and model predictions, and a regularizer that leverages prior information about model parameters. Widely cherished algorithms like maximum likelihood (ML) and maximum-a posteriori (MAP) inference arise as special cases of M-estimators. Our analysis uncovers fundamental limits on the inference accuracy of a subclass of M-estimators corresponding to computationally tractable convex optimization problems. These limits generalize classical statistical theorems like the Cramer-Rao bound to the high-dimensional setting with prior information. We further discover the optimal M-estimator for log-concave signal and noise distributions; we demonstrate that it can achieve our high-dimensional limits on inference accuracy, while ML and MAP cannot. Intriguingly, in high dimensions, these optimal algorithms become computationally simpler than

  10. Cu(II) coordination chemistry of patellamide derivatives: possible biological functions of cyclic pseudopeptides.

    Science.gov (United States)

    Comba, Peter; Dovalil, Nina; Gahan, Lawrence R; Haberhauer, Gebhard; Hanson, Graeme R; Noble, Christopher J; Seibold, Björn; Vadivelu, Prabha

    2012-02-27

    Two synthetic derivatives of the naturally occurring cyclic pseudooctapeptides patellamide  A-F and ascidiacyclamide, that is, H(4)pat(2), H(4)pat(3), as well as their Cu(II) complexes are described. These cyclic peptide derivatives differ from the naturally occurring macrocycles by the variation of the incorporated heterocyclic donor groups and the configuration of the amino acids connecting the heterocycles. The exchange of the oxazoline and thiazole groups by dimethylimidazoles or methyloxazoles leads to more rigid macrocycles, and the changes in the configuration of the side chains leads to significant differences in the folding of the cyclic peptides. These variations allow a detailed study of the various possible structural changes on the chemistry of the Cu(II) complexes formed. The coordination of Cu(II) with these macrocyclic species was monitored by high-resolution electrospray mass spectrometry (ESI-MS), spectrophotometric (UV/Vis) and circular dichroic (CD) titrations, and electron paramagnetic resonance (EPR) spectroscopy. Density functional theory (DFT) calculations and molecular mechanics (MM) simulations have been used to model the structures of the Cu(II) complexes and provide a detailed understanding of their geometric preferences and conformational flexibility. This is related to the Cu(II) coordination chemistry and the reactivity of the dinuclear Cu(II) complexes towards CO(2) fixation. The variation observed between the natural and various synthetic peptide systems enables conclusions about structure-reactivity correlations, and our results also provide information on why nature might have chosen oxazolines and thiazoles as incorporated heterocycles.

  11. Overlapping and non-overlapping functions of condensins I and II in neural stem cell divisions.

    Directory of Open Access Journals (Sweden)

    Kenji Nishide

    2014-12-01

    Full Text Available During development of the cerebral cortex, neural stem cells (NSCs divide symmetrically to proliferate and asymmetrically to generate neurons. Although faithful segregation of mitotic chromosomes is critical for NSC divisions, its fundamental mechanism remains unclear. A class of evolutionarily conserved protein complexes, known as condensins, is thought to be central to chromosome assembly and segregation among eukaryotes. Here we report the first comprehensive genetic study of mammalian condensins, demonstrating that two different types of condensin complexes (condensins I and II are both essential for NSC divisions and survival in mice. Simultaneous depletion of both condensins leads to severe defects in chromosome assembly and segregation, which in turn cause DNA damage and trigger p53-induced apoptosis. Individual depletions of condensins I and II lead to slower loss of NSCs compared to simultaneous depletion, but they display distinct mitotic defects: chromosome missegregation was observed more prominently in NSCs depleted of condensin II, whereas mitotic delays were detectable only in condensin I-depleted NSCs. Remarkably, NSCs depleted of condensin II display hyperclustering of pericentric heterochromatin and nucleoli, indicating that condensin II, but not condensin I, plays a critical role in establishing interphase nuclear architecture. Intriguingly, these defects are taken over to postmitotic neurons. Our results demonstrate that condensins I and II have overlapping and non-overlapping functions in NSCs, and also provide evolutionary insight into intricate balancing acts of the two condensin complexes.

  12. Rome II versus Rome III classification of functional gastrointestinal disorders in pediatric chronic abdominal pain.

    Science.gov (United States)

    Baber, Kari F; Anderson, Julia; Puzanovova, Martina; Walker, Lynn S

    2008-09-01

    The updated Rome III criteria for pediatric functional gastrointestinal disorders (FGIDs) include new FGID categories and changes to the Rome II criteria for various FGIDs. To our knowledge, the implications of these revisions for patient classification have not been identified. The purpose of this study was to compare classification results using Rome II versus Rome III criteria for FGIDs associated with chronic abdominal pain. Participants were 368 pediatric patients whose subspecialty evaluations for chronic abdominal pain yielded no evidence of organic disease. The children's gastrointestinal symptoms were assessed with the parent-report version of the Questionnaire on Pediatric Gastrointestinal Symptoms (QPGS). More patients met the criteria for a pediatric pain-related FGID according to the Rome III criteria (86.6%) than the Rome II criteria (68.0%). In comparison with the results from the Rome II criteria, the Rome III criteria classified a greater percentage of children as meeting criteria for Abdominal Migraine (23.1% vs 5.7%) and Functional Abdominal Pain (11.4% vs 2.7%). Irritable Bowel Syndrome was the most common diagnosis according to both Rome II (44.0%) and Rome III (45.1%). Changes to the Rome criteria make the Rome III criteria more inclusive, allowing classification of 86.6% of pediatric patients with medically unexplained chronic abdominal pain.

  13. Functionality of in vitro reconstituted group II intron RmInt1-derived ribonucleoprotein particles

    Directory of Open Access Journals (Sweden)

    María Dolores Molina-Sánchez

    2016-09-01

    Full Text Available The functional unit of mobile group II introns is a ribonucleoprotein particle (RNP consisting of the intron-encoded protein (IEP and the excised intron RNA. The IEP has reverse transcriptase activity but also promotes RNA splicing, and the RNA-protein complex triggers site-specific DNA insertion by reverse splicing, in a process called retrohoming. In vitro reconstituted ribonucleoprotein complexes from the Lactococcus lactis group II intron Ll.LtrB, which produce a double strand break, have recently been studied as a means of developing group II intron-based gene targeting methods for higher organisms. The Sinorhizobium meliloti group II intron RmInt1 is an efficient mobile retroelement, the dispersal of which appears to be linked to transient single-stranded DNA during replication. The RmInt1IEP lacks the endonuclease domain (En and cannot cut the bottom strand to generate the 3’ end to initiate reverse transcription. We used an Escherichia coli expression system to produce soluble and active RmInt1 IEP and reconstituted RNPs with purified components in vitro. The RNPs generated were functional and reverse-spliced into a single-stranded DNA target. This work constitutes the starting point for the use of group II introns lacking DNA endonuclease domain-derived RNPs for highly specific gene targeting methods.

  14. (Prorenin receptor triggers distinct angiotensin II-independent extracellular matrix remodeling and deterioration of cardiac function.

    Directory of Open Access Journals (Sweden)

    Anne-Mari Moilanen

    Full Text Available BACKGROUND: Activation of the renin-angiotensin-system (RAS plays a key pathophysiological role in heart failure in patients with hypertension and myocardial infarction. However, the function of (prorenin receptor ((PRR is not yet solved. We determined here the direct functional and structural effects of (PRR in the heart. METHODOLOGY/PRINCIPAL FINDINGS: (PRR was overexpressed by using adenovirus-mediated gene delivery in normal adult rat hearts up to 2 weeks. (PRR gene delivery into the anterior wall of the left ventricle decreased ejection fraction (P<0.01, fractional shortening (P<0.01, and intraventricular septum diastolic and systolic thickness, associated with approximately 2-fold increase in left ventricular (PRR protein levels at 2 weeks. To test whether the worsening of cardiac function and structure by (PRR gene overexpression was mediated by angiotensin II (Ang II, we infused an AT(1 receptor blocker losartan via osmotic minipumps. Remarkably, cardiac function deteriorated in losartan-treated (PRR overexpressing animals as well. Intramyocardial (PRR gene delivery also resulted in Ang II-independent activation of extracellular-signal-regulated kinase1/2 phosphorylation and myocardial fibrosis, and the expression of transforming growth factor-β1 and connective tissue growth factor genes. In contrast, activation of heat shock protein 27 phosphorylation and apoptotic cell death by (PRR gene delivery was Ang II-dependent. Finally, (PRR overexpression significantly increased direct protein-protein interaction between (PRR and promyelocytic zinc-finger protein. CONCLUSIONS/SIGNIFICANCE: These results indicate for the first time that (PRR triggers distinct Ang II-independent myocardial fibrosis and deterioration of cardiac function in normal adult heart and identify (PRR as a novel therapeutic target to optimize RAS blockade in failing hearts.

  15. Pulmonary function testing in HTLV-I and HTLV-II infected humans: a cohort study

    Directory of Open Access Journals (Sweden)

    Garratty George

    2003-07-01

    Full Text Available Abstract Background HTLV-I infection has been linked to lung pathology and HTLV-II has been associated with an increased incidence of pneumonia and acute bronchitis. However it is unknown whether HTLV-I or -II infection alters pulmonary function. Methods We performed pulmonary function testing on HTLV-I, HTLV-II and HTLV seronegative subjects from the HTLV outcomes study (HOST, including vital capacity (VC, forced expiratory volume in one second (FEV1, and diffusing lung capacity for carbon monoxide (DLCO corrected for hemoglobin and lung volume. Multivariable analysis adjusted for differences in age, gender, race/ethnicity, height and smoking history. Results Mean (standard deviation pulmonary function values among the 257 subjects were as follows: FVC = 3.74 (0.89 L, FEV1 = 2.93 (0.67 L, DLCOcorr = 23.82 (5.89 ml/min/mmHg, alveolar ventilation (VA = 5.25 (1.20 L and DLCOcorr/VA = 4.54 (0.87 ml/min/mmHg/L. There were no differences in FVC, FEV1 and DLCOcorr/VA by HTLV status. For DLCOcorr, HTLV-I and HTLV-II subjects had slightly lower values than seronegatives, but neither difference was statistically significant after adjustment for confounding. Conclusions There was no difference in measured pulmonary function and diffusing capacity in generally healthy HTLV-I and HTLV-II subjects compared to seronegatives. These results suggest that previously described HTLV-associated abnormalities in bronchoalveolar cells and fluid may not affect pulmonary function.

  16. Inhibition of central angiotensin II enhances memory function and reduces oxidative stress status in rat hippocampus.

    Science.gov (United States)

    Bild, Walther; Hritcu, Lucian; Stefanescu, Cristinel; Ciobica, Alin

    2013-06-03

    While it is now well established that the independent brain renin-angiotensin system (RAS) has some important central functions besides the vascular ones, the relevance of its main bioactive peptide angiotensin II (Ang II) on the memory processes, as well as on oxidative stress status is not completely understood. The purpose of the present work was to evaluate the effects of central Ang II administration, as well as the effects of Ang II inhibition with either AT1 and AT 2 receptor specific blockers (losartan and PD-123177, respectively) or an angiotensin-converting enzyme (ACE) inhibitor (captopril). These effects were studied on the short-term memory (assessed through Y-maze) or long-term memory (as determined in passive avoidance) and on the oxidative stress status of the hippocampus. Our results demonstrate memory deficits induced by the administration of Ang II, as showed by the significant decrease of the spontaneous alternation in Y-maze (p=0.015) and latency-time in passive avoidance task (p=0.001) when compared to saline. On the other side, the administration of all the aforementioned Ang II blockers significantly improved the spontaneous alternation in Y-maze task, while losartan also increased the latency time as compared to saline in step-through passive avoidance (p=0.042). Also, increased oxidative stress status was induced in the hippocampus by the administration of Ang II, as demonstrated by increased levels of lipid peroxidation markers (malondialdehyde-MDA concentration) (p0.0001) vs. saline. Moreover, significant correlations were found between all of the memory related behavioral parameters and the main oxidative stress markers from the hippocampus, which is known for its implication in the processes of memory and also where RAS components are well expressed. This could be relevant for the complex interactions between Ang II, behavioral processes and neuronal oxidative stress, and could generate important therapeutic approaches. Copyright

  17. The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities

    Science.gov (United States)

    Cain, George L., Jr.; González, Luis

    2008-02-01

    The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.

  18. Nuclear angiotensin II type 2 (AT2) receptors are functionally linked to nitric oxide production.

    Science.gov (United States)

    Gwathmey, Tanya M; Shaltout, Hossam A; Pendergrass, Karl D; Pirro, Nancy T; Figueroa, Jorge P; Rose, James C; Diz, Debra I; Chappell, Mark C

    2009-06-01

    Expression of nuclear angiotensin II type 1 (AT(1)) receptors in rat kidney provides further support for the concept of an intracellular renin-angiotensin system. Thus we examined the cellular distribution of renal ANG II receptors in sheep to determine the existence and functional roles of intracellular ANG receptors in higher order species. Receptor binding was performed using the nonselective ANG II antagonist (125)I-[Sar(1),Thr(8)]-ANG II ((125)I-sarthran) with the AT(1) antagonist losartan (LOS) or the AT(2) antagonist PD123319 (PD) in isolated nuclei (NUC) and plasma membrane (PM) fractions obtained by differential centrifugation or density gradient separation. In both fetal and adult sheep kidney, PD competed for the majority of cortical NUC (> or =70%) and PM (> or =80%) sites while LOS competition predominated in medullary NUC (> or =75%) and PM (> or =70%). Immunodetection with an AT(2) antibody revealed a single approximately 42-kDa band in both NUC and PM extracts, suggesting a mature molecular form of the NUC receptor. Autoradiography for receptor subtypes localized AT(2) in the tubulointerstitium, AT(1) in the medulla and vasa recta, and both AT(1) and AT(2) in glomeruli. Loading of NUC with the fluorescent nitric oxide (NO) detector DAF showed increased NO production with ANG II (1 nM), which was abolished by PD and N-nitro-l-arginine methyl ester, but not LOS. Our studies demonstrate ANG II receptor subtypes are differentially expressed in ovine kidney, while nuclear AT(2) receptors are functionally linked to NO production. These findings provide further evidence of a functional intracellular renin-angiotensin system within the kidney, which may represent a therapeutic target for the regulation of blood pressure.

  19. [Association of the insulin-like growth factor II (IGF2) gene with human cognitive functions].

    Science.gov (United States)

    Alfimova, M V; Lezheĭko, T V; Gritsenko, I K; Golimbet, V E

    2012-08-01

    Active search for candidate genes whose polymorphisms are associated with human cognitive functions has been in progress in the past years. The study focused on the role that the insulin-like growth factor II (IGF2) gene may play in the variation of cognitive processes related to executive functions. The ApaI polymorphism of the IGF2 gene was tested for association with selective attention during visual search, working memory/mental control, and semantic verbal fluency in a group of 182 healthy individuals. The ApaI polymorphism was associated with the general cognitive index and selective attention measure. Carriers of genotype AA displayed higher values of the two parameters than carriers of genotype GG. It was assumed that the ApaI polymorphism of the IGF2 gene influences the human cognitive functions, acting possibly via modulation of the IGF-II level in the central nervous system.

  20. The long-term functional outcome of type II odontoid fractures managed non-operatively.

    LENUS (Irish Health Repository)

    Butler, J S

    2010-10-01

    Odontoid fractures currently account for 9-15% of all adult cervical spine fractures, with type II fractures accounting for the majority of these injuries. Despite recent advances in internal fixation techniques, the management of type II fractures still remains controversial with advocates still supporting non-rigid immobilization as the definitive treatment of these injuries. At the NSIU, over an 11-year period between 1 July 1996 and 30 June 2006, 66 patients (n = 66) were treated by external immobilization for type II odontoid fractures. The medical records, radiographs and CT scans of all patients identified were reviewed. Clinical follow-up evaluation was performed using the Cervical Spine Outcomes Questionnaire (CSOQ). The objectives of this study were to evaluate the long-term functional outcome of patients suffering isolated type II odontoid fractures managed non-operatively and to correlate patient age and device type with clinical and functional outcome. Of the 66 patients, there were 42 males and 24 females (M:F = 1.75:1) managed non-operatively for type II odontoid fractures. The mean follow-up time was 66 months. Advancing age was highly correlated with poorer long-term functional outcomes when assessing neck pain (r = 0.19, P = 0.1219), shoulder and arm pain (r = 0.41, P = 0.0007), physical symptoms (r = 0.25, P = 0.472), functional disability (r = 0.24, P = 0.0476) and psychological distress (r = 0.41, P = 0.0007). Patients >65 years displayed a higher rate of pseudoarthrosis (21.43 vs. 1.92%) and established non-union (7.14 vs. 0%) than patients <65 years. The non-operative management of type II odontoid fractures is an effective and satisfactory method of treating type II odontoid fractures, particularly those of a stable nature. However, patients of advancing age have been demonstrated to have significantly poorer functional outcomes in the long term. This may be linked to higher rates of non-union.

  1. A proof of convergence of the concave-convex procedure using Zangwill's theory.

    Science.gov (United States)

    Sriperumbudur, Bharath K; Lanckriet, Gert R G

    2012-06-01

    The concave-convex procedure (CCCP) is an iterative algorithm that solves d.c. (difference of convex functions) programs as a sequence of convex programs. In machine learning, CCCP is extensively used in many learning algorithms, including sparse support vector machines (SVMs), transductive SVMs, and sparse principal component analysis. Though CCCP is widely used in many applications, its convergence behavior has not gotten a lot of specific attention. Yuille and Rangarajan analyzed its convergence in their original paper; however, we believe the analysis is not complete. The convergence of CCCP can be derived from the convergence of the d.c. algorithm (DCA), proposed in the global optimization literature to solve general d.c. programs, whose proof relies on d.c. duality. In this note, we follow a different reasoning and show how Zangwill's global convergence theory of iterative algorithms provides a natural framework to prove the convergence of CCCP. This underlines Zangwill's theory as a powerful and general framework to deal with the convergence issues of iterative algorithms, after also being used to prove the convergence of algorithms like expectation-maximization and generalized alternating minimization. In this note, we provide a rigorous analysis of the convergence of CCCP by addressing two questions: When does CCCP find a local minimum or a stationary point of the d.c. program under consideration? and when does the sequence generated by CCCP converge? We also present an open problem on the issue of local convergence of CCCP.

  2. On evolving deformation microstructures in non-convex partially damaged solids

    KAUST Repository

    Gurses, Ercan

    2011-06-01

    The paper outlines a relaxation method based on a particular isotropic microstructure evolution and applies it to the model problem of rate independent, partially damaged solids. The method uses an incremental variational formulation for standard dissipative materials. In an incremental setting at finite time steps, the formulation defines a quasi-hyperelastic stress potential. The existence of this potential allows a typical incremental boundary value problem of damage mechanics to be expressed in terms of a principle of minimum incremental work. Mathematical existence theorems of minimizers then induce a definition of the material stability in terms of the sequential weak lower semicontinuity of the incremental functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of weak convexity notions of the stress potential. Furthermore, the variational setting opens up the possibility to analyze the development of deformation microstructures in the post-critical range of unstable inelastic materials based on energy relaxation methods. In partially damaged solids, accumulated damage may yield non-convex stress potentials which indicate instability and formation of fine-scale microstructures. These microstructures can be resolved by use of relaxation techniques associated with the construction of convex hulls. We propose a particular relaxation method for partially damaged solids and investigate it in one- and multi-dimensional settings. To this end, we introduce a new isotropic microstructure which provides a simple approximation of the multi-dimensional rank-one convex hull. The development of those isotropic microstructures is investigated for homogeneous and inhomogeneous numerical simulations. © 2011 Elsevier Ltd. All rights reserved.

  3. Adsorption characteristics of cadmium(II) onto functionalized poly(hydroxyethylmethacrylate)-grafted coconut coir pith.

    Science.gov (United States)

    Anirudhan, Thayyath Sreenivasan; Divya, Lekshmi; Rijith, Sreenivasan

    2010-07-01

    This study explored the feasibility of utilizing a novel adsorbent, poly(hydroxyethylmethacrylate)-grafted coconut coir pith with carboxyl functionality (PGCP-COOH) for the removal of cadmium(II) from water and wastewater. Maximum removal of 99.9% was observed for an initial concentration of 25 mg/L at pH 6.0 and adsorbent dose of 2.0 g/L. The first-order reversible kinetic model and Langmuir isotherm model were resulted in high correlation coefficients and described well the adsorption of Cd(II) onto PGCP-COOH. The complete removal of 22.4 mg/L Cd(II) from fertilizer industry wastewater was achieved by 2.0 g/L PGCP-COOH. The reusability of the PGCP-COOH for several cycles was demonstrated using 0.1 M HCl solution.

  4. Therapeutic approach to Class II, Division 1 malocclusion with maxillary functional orthopedics

    Science.gov (United States)

    de Bittencourt, Aristeu Corrêa; Saga, Armando Yukio; Pacheco, Ariel Adriano Reyes; Tanaka, Orlando

    2015-01-01

    INTRODUCTION: Interceptive treatment of Class II, Division 1 malocclusion is a challenge orthodontists commonly face due to the different growth patterns they come across and the different treatment strategies they have available. OBJECTIVE: To report five cases of interceptive orthodontics performed with the aid of Klammt's elastic open activator (KEOA) to treat Class II, Division 1 malocclusion. METHODS: Treatment comprehends one or two phases; and the use of functional orthopedic appliances, whenever properly recommended, is able to minimize dentoskeletal discrepancies with consequent improvement in facial esthetics during the first stage of mixed dentition. The triad of diagnosis, correct appliance manufacture and patient's compliance is imperative to allow KEOA to contribute to Class II malocclusion treatment. RESULTS: Cases reported herein showed significant improvement in skeletal, dental and profile aspects, as evinced by cephalometric analysis and clinical photographs taken before, during and after interceptive orthodontics. PMID:26352852

  5. P-cadherin counteracts myosin II-B function: implications in melanoma progression

    Directory of Open Access Journals (Sweden)

    De Wever Olivier

    2010-09-01

    Full Text Available Abstract Background Malignant transformation of melanocytes is frequently attended by a switch in cadherin expression profile as shown for E- and N-cadherin. For P-cadherin, downregulation in metastasizing melanoma has been demonstrated, and over-expression of P-cadherin in melanoma cell lines has been shown to inhibit invasion. The strong invasive and metastatic nature of cutaneous melanoma implies a deregulated interplay between intercellular adhesion and migration-related molecules Results In this study we performed a microarray analysis to compare the mRNA expression profile of an invasive BLM melanoma cell line (BLM LIE and the non-invasive P-cadherin over-expression variant (BLM P-cad. Results indicate that nonmuscle myosin II-B is downregulated in BLM P-cad. Moreover, myosin II-B plays a major role in melanoma migration and invasiveness by retracting the tail during the migratory cycle, as shown by the localization of myosin II-B stress fibers relative to Golgi and the higher levels of phosphorylated myosin light chain. Analysis of P-cadherin and myosin II-B in nodular melanoma sections and in a panel of melanoma cell lines further confirmed that there is an inverse relationship between both molecules. Conclusions Therefore, we conclude that P-cadherin counteracts the expression and function of myosin II-B, resulting in the suppression of the invasive and migratory behaviour of BLM melanoma cells

  6. MHC class II-associated proteins in B-cell exosomes and potential functional implications for exosome biogenesis.

    NARCIS (Netherlands)

    Buschow, S.I.; Balkom, B.W.M. van; Aalberts, M.; Heck, A.J.R. van; Wauben, M.; Stoorvogel, W.

    2010-01-01

    Professional antigen-presenting cells secrete major histocompatibility complex class II (MHC II) carrying exosomes with unclear physiological function(s). Exosomes are first generated as the intraluminal vesicles (ILVs) of a specific type of multivesicular body, and are then secreted by fusion of th

  7. Adsorption of Co(II) by a carboxylate-functionalized polyacrylamide grafted lignocellulosics.

    Science.gov (United States)

    Shibi, I G; Anirudhan, T S

    2005-02-01

    A new adsorbent (PGBS-COOH) having carboxylate functional group at the chain end was synthesized by graft copolymerization of acrylamide onto banana stalk, BS (Musa Paradisiaca) using ferrous ammonium sulphate/H2O2 redox initiator system. The efficiency of the adsorbent in the removal of cobalt [Co(II)] from water was investigated using batch adsorption technique. The adsorbent exhibits very high adsorption potential for Co(II) and under optimum conditions more than 99% removal was achieved. The maximum adsorption capacity was observed at the pH range 6.5-9.0. The equilibrium isotherm data were analysed using three isotherm models, Langmuir, Freundlich and Scatchard, to determine the best fit equation for the sorption of Co(II) on the PGBS-COOH. A comparative study with a commercial cation exchanger, Ceralite IRC-50, having carboxylate functional group showed that PGBS-COOH is 2.8 times more effective compared to Ceralite IRC-50 at 30 degrees C. Synthetic nuclear power plant coolant water samples were also treated by the adsorbent to demonstrate its efficiency in removing Co(II) from water in the presence of other metal ions. Acid regeneration was tried for several cycles to recover the adsorbed metal ions and also to restore the sorbent to its original state.

  8. Fundamentals of Functional Analysis

    CERN Document Server

    Kutateladze, S S; Slovák, Jan

    2001-01-01

    A concise guide to basic sections of modern functional analysis. Included are such topics as the principles of Banach and Hilbert spaces, the theory of multinormed and uniform spaces, the Riesz-Dunford holomorphic functional calculus, the Fredholm index theory, convex analysis and duality theory for locally convex spaces with applications to the Schwartz spaces of distributions and Radon measures.

  9. Cavitation bubbles collapse characteristics behind a convex body

    Institute of Scientific and Technical Information of China (English)

    李瑶; 许唯临; 张亚磊; 张敬威; 陈春祺; 阿蓉

    2013-01-01

    Cavitation bubbles behind a convex body were experimentally studied by a high speed camera and a hydrophone synch- ronously. The experiments were conducted in a circulating water tunnel with five various contraction ratios:b=0.497,b=0.6,b=0.697,b=0.751, andb=0.799. The distributions of the cavitation bubble collapse positions behind the five different convex bodies were obtained by combining the images taken by the high speed camera. According to the collapse positions, it was found that no cavitation bubble was collapsed in the region near the wall until the ratio of the water head loss over the convex body height was larger than 20, which can be used to predict if the cavitation damage would occur in the tunnel with orifice energy dissipaters.

  10. RESEARCH ANNOUNCEMENTS Helly Type Problems for Some Special Convex Polygons

    Institute of Scientific and Technical Information of China (English)

    苑立平; 丁仁

    2001-01-01

    @@In the combinatorial geometry of convex sets the question of how efficiently a family of convex sets can be pierced by points has led to various problems which may be regarded as extensions of the Helly-type problems. A family of sets is said to be n-pierceable (abbreviated as Пn) if there exists a set of n points such that each member of the family contains at least one of them. A family of sets is said to be Пnk if every subfamily of size k or less is Пn. The famous Helly theorem in combinatorial geometry asserts that for finite families of convex sets in the plane П13 implies П1. In a recent paper by M. Katchalski and D. Nashtir[a] the following conjecture of Griinbaum[2] was mentioned again:

  11. Convex minorants of random walks and L\\'evy processes

    CERN Document Server

    Abramson, Josh; Ross, Nathan; Bravo, Gerónimo Uribe

    2011-01-01

    This article provides an overview of recent work on descriptions and properties of the convex minorant of random walks and L\\'evy processes which summarize and extend the literature on these subjects. The results surveyed include point process descriptions of the convex minorant of random walks and L\\'evy processes on a fixed finite interval, up to an independent exponential time, and in the infinite horizon case. These descriptions follow from the invariance of these processes under an adequate path transformation. In the case of Brownian motion, we note how further special properties of this process, including time-inversion, imply a sequential description for the convex minorant of the Brownian meander.

  12. Small sets in convex geometry and formal independence over ZFC

    Directory of Open Access Journals (Sweden)

    Menachem Kojman

    2005-01-01

    Full Text Available To each closed subset S of a finite-dimensional Euclidean space corresponds a σ-ideal of sets  (S which is σ-generated over S by the convex subsets of S. The set-theoretic properties of this ideal hold geometric information about the set. We discuss the relation of reducibility between convexity ideals and the connections between convexity ideals and other types of ideals, such as the ideals which are generated over squares of Polish space by graphs and inverses of graphs of continuous self-maps, or Ramsey ideals, which are generated over Polish spaces by the homogeneous sets with respect to some continuous pair coloring. We also attempt to present to nonspecialists the set-theoretic methods for dealing with formal independence as a means of geometric investigations.

  13. Dose evaluation from multiple detector outputs using convex optimisation.

    Science.gov (United States)

    Hashimoto, Makoto; Iimoto, Takeshi; Kosako, Toshiso

    2011-07-01

    A dose evaluation using multiple radiation detectors can be improved by the convex optimisation method. It enables flexible dose evaluation corresponding to the actual radiation energy spectrum. An application to the neutron ambient dose equivalent evaluation is investigated using a mixed-gas proportional counter. The convex derives the certain neutron ambient dose with certain width corresponding to the true neutron energy spectrum. The range of the evaluated dose is comparable to the error of conventional neutron dose measurement equipments. An application to the neutron individual dose equivalent measurement is also investigated. Convexes of particular dosemeter combinations evaluate the individual dose equivalent better than the dose evaluation of a single dosemeter. The combinations of dosemeters with high orthogonality of their response characteristics tend to provide a good suitability for dose evaluation.

  14. Entanglement Quantification Made Easy: Polynomial Measures Invariant under Convex Decomposition.

    Science.gov (United States)

    Regula, Bartosz; Adesso, Gerardo

    2016-02-19

    Quantifying entanglement in composite systems is a fundamental challenge, yet exact results are available in only a few special cases. This is because hard optimization problems are routinely involved, such as finding the convex decomposition of a mixed state with the minimal average pure-state entanglement, the so-called convex roof. We show that under certain conditions such a problem becomes trivial. Precisely, we prove by a geometric argument that polynomial entanglement measures of degree 2 are independent of the choice of pure-state decomposition of a mixed state, when the latter has only one pure unentangled state in its range. This allows for the analytical evaluation of convex roof extended entanglement measures in classes of rank-2 states obeying such a condition. We give explicit examples for the square root of the three-tangle in three-qubit states, and we show that several representative classes of four-qubit pure states have marginals that enjoy this property.

  15. Polyominoes with nearly convex columns: A model with semidirected blocks

    CERN Document Server

    Feretic, Svjetlan

    2009-01-01

    In most of today's exactly solved classes of polyominoes, either all members are convex (in some way), or all members are directed, or both. If the class is neither convex nor directed, the exact solution uses to be elusive. This paper is focused on polyominoes with hexagonal cells. Concretely, we deal with polyominoes whose columns can have either one or two connected components. Those polyominoes (unlike the well-explored column-convex polyominoes) cannot be exactly enumerated by any of the now existing methods. It is therefore appropriate to introduce additional restrictions, thus obtaining solvable subclasses. In our recent paper, published in this same journal, the restrictions just mentioned were semidirectedness and an upper bound on the size of the gap within a column. In this paper, the semidirectedness requirement is made looser. The result is that now the exactly solved subclasses are larger and have greater growth constants. These new polyomino families also have the advantage of being invariant u...

  16. Prestarlike functions with negative coefficients

    Directory of Open Access Journals (Sweden)

    H. Silverman

    1979-01-01

    Full Text Available The extreme points for prestarlike functions having negative coefficients are determined. Coefficient, distortion and radii of univalence, starlikeness, and convexity theorems are also obtained.

  17. Point-in-convex polygon and point-in-convex polyhedron algorithms with O(1) complexity using space subdivision

    Science.gov (United States)

    Skala, Vaclav

    2016-06-01

    There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees, octrees, kd-trees, bounding volume hierarchies etc. However in some applications a non-orthogonal space subdivision can offer new ways for actual speed up. In the case of convex polygon in E2 a simple Point-in-Polygon test is of the O(N) complexity and the optimal algorithm is of O(log N) computational complexity. In the E3 case, the complexity is O(N) even for the convex polyhedron as no ordering is defined. New Point-in-Convex Polygon and Point-in-Convex Polyhedron algorithms are presented based on space subdivision in the preprocessing stage resulting to O(1) run-time complexity. The presented approach is simple to implement. Due to the principle of duality, dual problems, e.g. line-convex polygon, line clipping, can be solved in a similarly.

  18. Rational trigonometric cubic spline to conserve convexity of 2D data

    Directory of Open Access Journals (Sweden)

    Farheen Ibraheem

    2013-11-01

    Full Text Available Researchers in different fields of study are always in dire need of spline interpolating function that conserve intrinsic trend of the data. In this paper, a rational trigonometric cubic spline with four free parameters has been used to retain convexity of 2D data. For this purpose, constraints on two of free parameters βi and γi in the description of the rational trigonometric function are derived while the remaining two αi and δi are set free. Numerical examples demonstrate that resulting curves using the technique of the underlying paper are C1.

  19. Structure and function of Cu(I)- and Zn(II)-ATPases

    DEFF Research Database (Denmark)

    Sitsel, Oleg; Grønberg, Christina; Autzen, Henriette

    2015-01-01

    membranes at the expense of ATP. Recent biochemical studies and crystal structures have significantly improved our understanding of the transport mechanisms of these proteins, but many details about their structure and function remain elusive. Here we compare the Cu(I)- and Zn(II)-ATPases, scrutinizing......Copper and zinc are micronutrients essential for the function of many enzymes while also being toxic at elevated concentrations. Cu(I)- and Zn(II)-transporting P-type ATPases of subclass 1B are of key importance for the homeostasis of these transition metals, allowing ion transport across cellular...... the molecular differences that allow transport of these two distinct metal types, and discuss possible future directions of research in the field....

  20. Correction of Skeletal Class II Malocclusion using Functional-Fixed Appliance Therapy

    Directory of Open Access Journals (Sweden)

    Ashok Surana

    2012-01-01

    Full Text Available Single-phase treatment started during late mixed dentition using functional followed by fixed appliance therapy has proven to be the most effective approach to achieve correction of Class II malocclusion. This case report demonstrates the use of this treatment approach in an 11-year-old girl with skeletal and dental Class II malocclusion, large overjet, deep overbite, increased incisor exposure and a gummy smile. She was given a functional appliance for 1 year which was immediately followed by fixed mechanotherapy for final finishing and detailing of the occlusion. The magnitude of skeletal and dental correction achieved, along with the dramatic improvement in facial appearance of the patient, provides a strong case for establishing the efficacy of this treatment modality.

  1. AN EFFICIENT ALGORITHM FOR THE CONVEX HULL OF PLANAR SCATTERED POINT SET

    Directory of Open Access Journals (Sweden)

    Z. Fu

    2012-07-01

    Full Text Available Computing the convex hull of a point set is requirement in the GIS applications. This paper studies on the problem of minimum convex hull and presents an improved algorithm for the minimum convex hull of planar scattered point set. It adopts approach that dividing the point set into several sub regions to get an initial convex hull boundary firstly. Then the points on the boundary, which cannot be vertices of the minimum convex hull, are removed one by one. Finally the concave points on the boundary, which cannot be vertices of the minimum convex hull, are withdrew. Experimental analysis shows the efficiency of the algorithm compared with other methods.

  2. Measurement of Cardiac Angiotensin II by Immunoassays, HPLC-Chip/Mass Spectrometry, and Functional Assays.

    Science.gov (United States)

    De Mello, Walmor C; Gerena, Yamil

    2017-01-01

    The molecular mechanisms related to the effect of angiotensin II, its level on cardiac tissues, as well as its overexpression represent an important aspect of cardiovascular pharmacology and pathology. Severe alterations of cardiac functions are induced by hypertension including activation of circulating and local cardiac renin angiotensin systems. In this chapter, we are providing the methods and materials necessary for further investigation of this important topic.

  3. Convex Four Body Central Configurations with Some Equal Masses

    CERN Document Server

    Perez-Chavela, Ernest

    2009-01-01

    We prove that there is a unique convex non-collinear central configuration of the planar Newtonian four-body problem when two equal masses are located at opposite vertices of a quadrilateral and, at most, only one of the remaining masses is larger than the equal masses. Such central configuration posses a symmetry line and it is a kite shaped quadrilateral. We also show that there is exactly one convex non-collinear central configuration when the opposite masses are equal. Such central configuration also posses a symmetry line and it is a rhombus.

  4. A working-set framework for sequential convex approximation methods

    DEFF Research Database (Denmark)

    Stolpe, Mathias

    2008-01-01

    to guarantee global convergence of the method. The algorithm works directly on the nonlinear constraints in the convex sub-problems and solves a sequence of relaxations of the current sub-problem. The algorithm terminates with the optimal solution to the sub-problem after solving a finite number of relaxations.......We present an active-set algorithmic framework intended as an extension to existing implementations of sequential convex approximation methods for solving nonlinear inequality constrained programs. The framework is independent of the choice of approximations and the stabilization technique used...

  5. Finding Convex Hulls Using Quickhull on the GPU

    CERN Document Server

    Tzeng, Stanley

    2012-01-01

    We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of problems. Our framework transforms the recursive splitting step into a permutation step that is well-suited for graphics hardware. Our convex hull algorithm of choice is Quickhull. Our parallel Quickhull implementation (for both 2D and 3D cases) achieves an order of magnitude speedup over standard computational geometry libraries.

  6. Convex Combination of Multiple Statistical Models with Application to VAD

    DEFF Research Database (Denmark)

    Petsatodis, Theodoros; Boukis, Christos; Talantzis, Fotios

    2011-01-01

    This paper proposes a robust Voice Activity Detector (VAD) based on the observation that the distribution of speech captured with far-field microphones is highly varying, depending on the noise and reverberation conditions. The proposed VAD employs a convex combination scheme comprising three...... statistical distributions - a Gaussian, a Laplacian, and a two-sided Gamma - to effectively model captured speech. This scheme shows increased ability to adapt to dynamic acoustic environments. The contribution of each distribution to this convex combination is automatically adjusted based on the statistical...

  7. Closedness type regularity conditions in convex optimization and beyond

    Directory of Open Access Journals (Sweden)

    Sorin-Mihai Grad

    2016-09-01

    Full Text Available The closedness type regularity conditions have proven during the last decade to be viable alternatives to their more restrictive interiority type counterparts, in both convex optimization and different areas where it was successfully applied. In this review article we de- and reconstruct some closedness type regularity conditions formulated by means of epigraphs and subdifferentials, respectively, for general optimization problems in order to stress that they arise naturally when dealing with such problems. The results are then specialized for constrained and unconstrained convex optimization problems. We also hint towards other classes of optimization problems where closedness type regularity conditions were successfully employed and discuss other possible applications of them.

  8. A working-set framework for sequential convex approximation methods

    DEFF Research Database (Denmark)

    Stolpe, Mathias

    2008-01-01

    We present an active-set algorithmic framework intended as an extension to existing implementations of sequential convex approximation methods for solving nonlinear inequality constrained programs. The framework is independent of the choice of approximations and the stabilization technique used...... to guarantee global convergence of the method. The algorithm works directly on the nonlinear constraints in the convex sub-problems and solves a sequence of relaxations of the current sub-problem. The algorithm terminates with the optimal solution to the sub-problem after solving a finite number of relaxations....

  9. L2CXCV: A Fortran 77 package for least squares convex/concave data smoothing

    Science.gov (United States)

    Demetriou, I. C.

    2006-04-01

    , biology and engineering. Distribution material that includes single and double precision versions of the code, driver programs, technical details of the implementation of the software package and test examples that demonstrate the use of the software is available in an accompanying ASCII file. Program summaryTitle of program:L2CXCV Catalogue identifier:ADXM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXM_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer:PC Intel Pentium, Sun Sparc Ultra 5, Hewlett-Packard HP UX 11.0 Operating system:WINDOWS 98, 2000, Unix/Solaris 7, Unix/HP UX 11.0 Programming language used:FORTRAN 77 Memory required to execute with typical data:O(n), where n is the number of data No. of bits in a byte:8 No. of lines in distributed program, including test data, etc.:29 349 No. of bytes in distributed program, including test data, etc.:1 276 663 No. of processors used:1 Has the code been vectorized or parallelized?:no Distribution format:default tar.gz Separate documentation available:Yes Nature of physical problem:Analysis of processes that show initially increasing and then decreasing rates of change (sigmoid shape), as, for example, in heat curves, reactor stability conditions, evolution curves, photoemission yields, growth models, utility functions, etc. Identifying an unknown convex/concave (sigmoid) function from some measurements of its values that contain random errors. Also, identifying the inflection point of this sigmoid function. Method of solution:Univariate data smoothing by minimizing the sum of the squares of the residuals (least squares approximation) subject to the condition that the second order divided differences of the smoothed values change sign at most once. Ideally, this is the number of sign changes in the second derivative of the underlying function. The remarkable property of the smoothed values is that they consist of one separate section of optimal components

  10. Decompositions of Multiattribute Utility Functions Based on Convex Dependence.

    Science.gov (United States)

    1982-03-01

    Angeles, CA 90024 Murray Hill, NJ 07974 Professor Morris H. DeGroot Professor Dennis G. Fryback Department of Statistics Health Systems Engineering...of Business Menlo Park, CA 94025 Administration Duke University Dr. Peter A. Morris Durham, NC 27706 Applied Decision Analysis, Inc. 3000 San Hill

  11. Adsorption behaviors of Hg(II) on chitosan functionalized by amino-terminated hyperbranched polyamidoamine polymers.

    Science.gov (United States)

    Ma, Fang; Qu, Rongjun; Sun, Changmei; Wang, Chunhua; Ji, Chunnuan; Zhang, Ying; Yin, Ping

    2009-12-30

    The adsorption behaviors of Hg(II) on adsorbents, chitosan functionalized by generation 1.0-3.0 of amino-terminated hyperbranched polyamidoamine polymers (denoted as CTS-1.0, CTS-2.0 and CTS-3.0, respectively), were studied. The optimum pH corresponding to the maximum adsorption capacities was found to be 5.0 for the three adsorbents. The experimental equilibrium data of Hg(II) on the three adsorbents were fitted to the Freundlich and the Langmuir models, and it is found that the Langmuir isotherm was the best fitting model to describe the equilibrium adsorption. The kinetics data indicated that the adsorption process of Hg(II) ions on CTS-1.0, CTS-2.0 and CTS-3.0 were governed by the film diffusion and followed pseudo-second-order rate model. Thermodynamic analysis and FTIR analysis revealed that the adsorption behaviors of Hg(II) ions on the three adsorbents could be considered as spontaneous, endothermic and chemical sorption process, resulting in their higher adsorption capacities at higher temperature.

  12. Study on the adsorption of Cu(II) by folic acid functionalized magnetic graphene oxide

    Science.gov (United States)

    Wang, Cuicui; Ge, Heyi; Zhao, Yueying; Liu, Shanshan; Zou, Yu; Zhang, Wenbo

    2017-02-01

    The folic acid functionalized magnetic graphene oxide (FA-mGO) as a new adsorbent has been synthesized in this work for the elimination of Cu(II) from waste water. The as-prepared FA-mGO was tested by SEM, TEM, particle size analyzer, FTIR, XRD, Roman spectrum, TGA and magnetic properties analyzer. Some factors, such as adsorbent dose, pH, contact time, initial concentration of adsorbate and temperature were explored. The results showed that the FA-mGO had the better adsorption performance than mGO. After 40 min, the adsorption equilibrium could be reached. Furthermore, the adsorption property obeyed the pseudo-second order kinetic model and the Temkin isotherms well. The maximum adsorption capacity was 283.29 mg/g for Cu(II) from Pseudo-second-order model at pH=5 and 318 K. The chelation action between FA and Cu(II) along with electrostatic incorporation between GO and Cu(II) determined the favourable adsorption property. Besides, thermodynamic studies results ∆G00, ∆S0>0 suggested that the adsorption mechanism was an endothermic and spontaneous process essentially. Finally, desorption and reusability studies imply FA-mGO has an excellent reproducibility and is benefit to environmental protection and resource conservation.

  13. Re-analysis of the Radio Luminosity Function of Galactic H II Regions

    Science.gov (United States)

    Paladini, R.; De Zotti, G.; Noriega-Crespo, A.; Carey, S. J.

    2009-09-01

    We have re-analyzed continuum and recombination lines radio data available in the literature in order to derive the luminosity function (LF) of Galactic H II regions. The study is performed by considering the first and fourth Galactic quadrants independently. We estimate the completeness level of the sample in the fourth quadrant at 5 Jy, and the one in the first quadrant at 2 Jy. We show that the two samples (fourth or first quadrant) include, as well as giant and supergiant H II regions, a significant number of subgiant sources. The LF is obtained, in each Galactic quadrant, with a generalized Schmidt's estimator using an effective volume derived from the observed spatial distribution of the considered H II regions. The re-analysis also takes advantage of recently published ancillary absorption data allowing to solve the distance ambiguity for several objects. A single power-law fit to the LFs retrieves a slope equal to -2.23 ± 0.07 (fourth quadrant) and to -1.85 ± 0.11 (first quadrant). We also find marginal evidence of a luminosity break at L knee = 1023.45 erg s-1 Hz-1 for the LF in the fourth quadrant. We convert radio luminosities into equivalent Hα and Lyman continuum luminosities to facilitate comparisons with extragalactic studies. We obtain an average total H II regions Lyman continuum luminosity of 0.89 ± 0.23 × 1053 s-1, corresponding to 30% of the total ionizing luminosity of the Galaxy.

  14. Immunological Functions of the Membrane Proximal Region of MHC Class II Molecules [version 1; referees: 3 approved

    Directory of Open Access Journals (Sweden)

    Jonathan Harton

    2016-03-01

    Full Text Available Major histocompatibility complex (MHC class II molecules present exogenously derived antigen peptides to CD4 T cells, driving activation of naïve T cells and supporting CD4-driven immune functions. However, MHC class II molecules are not inert protein pedestals that simply bind and present peptides. These molecules also serve as multi-functional signaling molecules delivering activation, differentiation, or death signals (or a combination of these to B cells, macrophages, as well as MHC class II-expressing T cells and tumor cells. Although multiple proteins are known to associate with MHC class II, interaction with STING (stimulator of interferon genes and CD79 is essential for signaling. In addition, alternative transmembrane domain pairing between class II α and β chains influences association with membrane lipid sub-domains, impacting both signaling and antigen presentation. In contrast to the membrane-distal region of the class II molecule responsible for peptide binding and T-cell receptor engagement, the membrane-proximal region (composed of the connecting peptide, transmembrane domain, and cytoplasmic tail mediates these “non-traditional” class II functions. Here, we review the literature on the function of the membrane-proximal region of the MHC class II molecule and discuss the impact of this aspect of class II immunobiology on immune regulation and human disease.

  15. MHC class II-associated proteins in B-cell exosomes and potential functional implications for exosome biogenesis.

    Science.gov (United States)

    Buschow, Sonja I; van Balkom, Bas W M; Aalberts, Marian; Heck, Albert J R; Wauben, Marca; Stoorvogel, Willem

    2010-01-01

    Professional antigen-presenting cells secrete major histocompatibility complex class II (MHC II) carrying exosomes with unclear physiological function(s). Exosomes are first generated as the intraluminal vesicles (ILVs) of a specific type of multivesicular body, and are then secreted by fusion of this compartment with the plasma membrane. We have previously shown that in contrast to the sorting of MHC II at lysosomally targeted multivesicular bodies, sorting of MHC II into exosomes does not rely on MHC II ubiquitination. In search for proteins that drive the incorporation of MHC II into exosomes or functionally discriminate exosomal from plasma membrane MHC II, we first analyzed the total proteome of highly purified B cell-derived exosomes using sensitive and accurate mass spectrometry (MS), and identified 539 proteins, including known and not previously identified constituents. Using quantitative MS, we then identified a small subset of proteins that were specifically co-immunoprecipitated with MHC II from detergent-solubilized exosomes. These include HSC71, HSP90, 14-3-3ɛ, CD20 and pyruvate kinase type M2 (PKM2), and we speculate on the functionality of their interaction with exosomal MHC II.

  16. Recent horizontal transfer, functional adaptation and dissemination of a bacterial group II intron.

    Science.gov (United States)

    LaRoche-Johnston, Félix; Monat, Caroline; Cousineau, Benoit

    2016-10-20

    Group II introns are catalytically active RNA and mobile retroelements present in certain eukaryotic organelles, bacteria and archaea. These ribozymes self-splice from the pre-mRNA of interrupted genes and reinsert within target DNA sequences by retrohoming and retrotransposition. Evolutionary hypotheses place these retromobile elements at the origin of over half the human genome. Nevertheless, the evolution and dissemination of group II introns was found to be quite difficult to infer. We characterized the functional and evolutionary relationship between the model group II intron from Lactococcus lactis, Ll.LtrB, and Ef.PcfG, a newly discovered intron from a clinical strain of Enterococcus faecalis. Ef.PcfG was found to be homologous to Ll.LtrB and to splice and mobilize in its native environment as well as in L. lactis. Interestingly, Ef.PcfG was shown to splice at the same level as Ll.LtrB but to be significantly less efficient to invade the Ll.LtrB recognition site. We also demonstrated that specific point mutations between the IEPs of both introns correspond to functional adaptations which developed in L. lactis as a response to selective pressure on mobility efficiency independently of splicing. The sequence of all the homologous full-length variants of Ll.LtrB were compared and shown to share a conserved pattern of mutation acquisition. This work shows that Ll.LtrB and Ef.PcfG are homologous and have a common origin resulting from a recent lateral transfer event followed by further adaptation to the new target site and/or host environment. We hypothesize that Ef.PcfG is the ancestor of Ll.LtrB and was initially acquired by L. lactis, most probably by conjugation, via a single event of horizontal transfer. Strong selective pressure on homing site invasion efficiency then led to the emergence of beneficial point mutations in the IEP, enabling the successful establishment and survival of the group II intron in its novel lactococcal environment. The current

  17. Brownian limits, local limits, extreme value and variance asymptotics for convex hulls in the ball

    CERN Document Server

    Calka, Pierre; Yukich, J E

    2009-01-01

    The paper of Schreiber and Yukich [40] establishes an asymptotic representation for random convex polytope geometry in the unit ball $\\B_d, d \\geq 2,$ in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of the so-called generalized paraboloid growth process. This paper further exploits this connection, introducing also a dual object termed the paraboloid hull process. Via these growth processes we establish local functional and measure-level limit theorems for the properly scaled radius-vector and support functions as well as for curvature measures and $k$-face empirical measures of convex polytopes generated by high density Poisson samples. We use general techniques of stabilization theory to establish Brownian sheet limits for the defect volume and mean width functionals, and we provide explicit variance asymptotics and central limit theorems for the $k$-face and intrinsic volume functionals. We establish extreme value theorems for radius-vector and suppo...

  18. A constructive algorithm to solve "convex recursive deletion" (CoRD) classification problems via two-layer perceptron networks.

    Science.gov (United States)

    Cabrelli, C; Molter, U; Shonkwiler, R

    2000-01-01

    A sufficient condition that a region be classifiable by a two-layer feedforward neural net (a two-layer perceptron) using threshold activation functions is that either it be a convex polytope or that intersected with the complement of a convex polytope in its interior, or that intersected with the complement of a convex polytope in its interior or ... recursively. These have been called convex recursive deletion (CoRD) regions.We give a simple algorithm for finding the weights and thresholds in both layers for a feedforward net that implements such a region. The results of this work help in understanding the relationship between the decision region of a perceptron and its corresponding geometry in input space. Our construction extends in a simple way to the case that the decision region is the disjoint union of CoRD regions (requiring three layers). Therefore this work also helps in understanding how many neurons are needed in the second layer of a general three-layer network. In the event that the decision region of a network is known and is the union of CoRD regions, our results enable the calculation of the weights and thresholds of the implementing network directly and rapidly without the need for thousands of backpropagation iterations.

  19. Bounds for Minkowski Billiard Trajectories in Convex Bodies

    CERN Document Server

    Artstein-Avidan, Shiri

    2011-01-01

    In this paper we use the Ekeland-Hofer-Zehnder symplectic capacity to provide several bounds and inequalities for the length of the shortest periodic billiard trajectory in a smooth convex body in ${\\mathbb R}^{n}$. Our results hold both for classical billiards, as well as for the more general case of Minkowski billiards.

  20. Method for solving a convex integer programming problem

    OpenAIRE

    Stefanov, Stefan M.

    2003-01-01

    We consider a convex integer program which is a nonlinear version of the assignment problem. This problem is reformulated as an equivalent problem. An algorithm for solving the original problem is suggested which is based on solving the simple assignment problem via some of known algorithms.