A New Filled Function Method with One Parameter for Global Optimization

Directory of Open Access Journals (Sweden)

Fei Wei

2013-01-01

Full Text Available The filled function method is an effective approach to find the global minimizer of multidimensional multimodal functions. The conventional filled functions are numerically unstable due to exponential or logarithmic term and sensitive to parameters. In this paper, a new filled function with only one parameter is proposed, which is continuously differentiable and proved to satisfy all conditions of the filled function definition. Moreover, this filled function is not sensitive to parameter, and the overflow can not happen for this function. Based on these, a new filled function method is proposed, and it is numerically stable to the initial point and the parameter variable. The computer simulations indicate that the proposed filled function method is efficient and effective.

Undergraduate Convexity

DEFF Research Database (Denmark)

Lauritzen, Niels

Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier-Motzkin elimin...

A new convexity measure for polygons.

Science.gov (United States)

Zunic, Jovisa; Rosin, Paul L

2004-07-01

Abstract-Convexity estimators are commonly used in the analysis of shape. In this paper, we define and evaluate a new convexity measure for planar regions bounded by polygons. The new convexity measure can be understood as a "boundary-based" measure and in accordance with this it is more sensitive to measured boundary defects than the so called "area-based" convexity measures. When compared with the convexity measure defined as the ratio between the Euclidean perimeter of the convex hull of the measured shape and the Euclidean perimeter of the measured shape then the new convexity measure also shows some advantages-particularly for shapes with holes. The new convexity measure has the following desirable properties: 1) the estimated convexity is always a number from (0, 1], 2) the estimated convexity is 1 if and only if the measured shape is convex, 3) there are shapes whose estimated convexity is arbitrarily close to 0, 4) the new convexity measure is invariant under similarity transformations, and 5) there is a simple and fast procedure for computing the new convexity measure.

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....

θ-convex nonlinear programming problems

International Nuclear Information System (INIS)

Emam, T.

2008-01-01

A class of sets and a class of functions called θ-convex sets and θ-convex functions are introduced by relaxing the definitions of convex sets and operator θ on the sets and domain of definition of the functions. The optimally results for θ-convex programming problems are established.

A new corrective technique for adolescent idiopathic scoliosis (Ucar′s convex rod rotation

Directory of Open Access Journals (Sweden)

Bekir Yavuz Ucar

2014-01-01

Full Text Available Study Design: Prospective single-center study. Objective: To analyze the efficacy and safety of a new technique of global vertebral correction with convex rod rotation performed on the patients with adolescent idiopathic scoliosis. Summary of Background Data: Surgical goal is to obtain an optimal curve correction in scoliosis surgery. There are various correction techniques. This report describes a new technique of global vertebral correction with convex rod rotation. Materials and Methods: A total of 12 consecutive patients with Lenke type I adolescent idiopathic scoliosis and managed by convex rod rotation technique between years 2012 and 2013 having more than 1 year follow-up were included. Mean age was 14.5 (range = 13-17 years years at the time of operation. The hospital charts were reviewed for demographic data. Measurements of curve magnitude and balance were made on 36-inch standing anteroposterior and lateral radiographs taken before surgery and at most recent follow up to assess deformity correction, spinal balance, and complications related to the instrumentation. Results: Preoperative coronal plane major curve of 62° (range = 50°-72° with flexibility of less than 30% was corrected to 11.5°(range = 10°-14° showing a 81% scoliosis correction at the final follow-up. Coronal imbalance was improved 72% at the most recent follow-up assessment. No complications were found. Conclusion: The new technique of global vertebral correction with Ucar′s convex rod rotation is an effective technique. This method is a vertebral rotation procedure from convex side and it allows to put screws easily to the concave side.

Relaxation Methods for Strictly Convex Regularizations of Piecewise Linear Programs

International Nuclear Information System (INIS)

Kiwiel, K. C.

1998-01-01

We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that occur in entropy maximization, quadratic programming, and network flows. In particular, it may solve exact penalty versions of such (possibly inconsistent) problems, and subproblems of bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity, and in certain cases is highly parallelizable. Its global convergence is established in the recent framework of B -functions (generalized Bregman functions)

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

Analytic aspects of convexity

CERN Document Server

Colesanti, Andrea; Gronchi, Paolo

2018-01-01

This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016. It offers a collection of selected articles, written by some of the world’s leading experts in the field of Convex Geometry, on recent developments in this area: theory of valuations; geometric inequalities; affine geometry; and curvature measures. The book will be of interest to a broad readership, from those involved in Convex Geometry, to those focusing on Functional Analysis, Harmonic Analysis, Differential Geometry, or PDEs. The book is a addressed to PhD students and researchers, interested in Convex Geometry and its links to analysis.

Convex Interval Games

NARCIS (Netherlands)

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

2008-01-01

In this paper, convex interval games are introduced and some characterizations are given. Some economic situations leading to convex interval games are discussed. The Weber set and the Shapley value are defined for a suitable class of interval games and their relations with the interval core for

Generalized Convexity and Inequalities

OpenAIRE

Anderson, G. D.; Vamanamurthy, M. K.; Vuorinen, M.

2007-01-01

Let R+ = (0,infinity) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 in M, we say that a function f : R+ to R+ is (m1,m2)-convex if f(m1(x,y)) < or = m2(f(x),f(y)) for all x, y in R+ . The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m1,m2)-convexity on m1 and m2 and give sufficient conditions for (m1,m2)-convexity of functions defined...

Neuro-genetic hybrid approach for the solution of non-convex economic dispatch problem

International Nuclear Information System (INIS)

Malik, T.N.; Asar, A.U.

2009-01-01

ED (Economic Dispatch) is non-convex constrained optimization problem, and is used for both on line and offline studies in power system operation. Conventionally, it is solved as convex problem using optimization techniques by approximating generator input/output characteristic. Curves of monotonically increasing nature thus resulting in an inaccurate dispatch. The GA (Genetic Algorithm) has been used for the solution of this problem owing to its inherent ability to address the convex and non-convex problems equally. This approach brings the solution to the global minimum region of search space in a short time and then takes longer time to converge to near optimal results. GA based hybrid approaches are used to fine tune the near optimal results produced by GA. This paper proposes NGH (Neuro Genetic Hybrid) approach to solve the economic dispatch with valve point effect. The proposed approach combines the GA with the ANN (Artificial Neural Network) using SI (Swarm Intelligence) learning rule. The GA acts as a global optimizer and the neural network fine tunes the GA results to the desired targets. Three machines standard test system has been tested for validation of the approach. Comparing the results with GA and NGH model based on back-propagation learning, the proposed approach gives contrast improvements showing the promise of the approach. (author)

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.

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 d......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....

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

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....

A class of free locally convex spaces

International Nuclear Information System (INIS)

Sipacheva, O V

2003-01-01

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

Geometry of isotropic convex bodies

CERN Document Server

Brazitikos, Silouanos; Valettas, Petros; Vritsiou, Beatrice-Helen

2014-01-01

The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lov�sz-Simonovits conjecture. This book prov...

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

Convexity and Marginal Vectors

NARCIS (Netherlands)

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

2002-01-01

In this paper we construct sets of marginal vectors of a TU game with the property that if the marginal vectors from these sets are core elements, then the game is convex.This approach leads to new upperbounds on the number of marginal vectors needed to characterize convexity.An other result is that

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

Deformation patterning driven by rate dependent non-convex strain gradient plasticity

NARCIS (Netherlands)

Yalcinkaya, T.; Brekelmans, W.A.M.; Geers, M.G.D.

2011-01-01

A rate dependent strain gradient plasticity framework for the description of plastic slip patterning in a system with non-convex energetic hardening is presented. Both the displacement and the plastic slip fields are considered as primary variables. These fields are determined on a global level by

Alpha-Concave Hull, a Generalization of Convex Hull

OpenAIRE

Asaeedi, Saeed; Didehvar, Farzad; Mohades, Ali

2013-01-01

Bounding hull, such as convex hull, concave hull, alpha shapes etc. has vast applications in different areas especially in computational geometry. Alpha shape and concave hull are generalizations of convex hull. Unlike the convex hull, they construct non-convex enclosure on a set of points. In this paper, we introduce another generalization of convex hull, named alpha-concave hull, and compare this concept with convex hull and alpha shape. We show that the alpha-concave hull is also a general...

Reconstruction of convex bodies from moments

DEFF Research Database (Denmark)

Hörrmann, Julia; Kousholt, Astrid

We investigate how much information about a convex body can be retrieved from a finite number of its geometric moments. We give a sufficient condition for a convex body to be uniquely determined by a finite number of its geometric moments, and we show that among all convex bodies, those which......- rithm that approximates a convex body using a finite number of its Legendre moments. The consistency of the algorithm is established using the stabil- ity result for Legendre moments. When only noisy measurements of Legendre moments are available, the consistency of the algorithm is established under...

Two generalizations of column-convex polygons

International Nuclear Information System (INIS)

Feretic, Svjetlan; Guttmann, Anthony J

2009-01-01

Column-convex polygons were first counted by area several decades ago, and the result was found to be a simple, rational, generating function. In this work we generalize that result. Let a p-column polyomino be a polyomino whose columns can have 1, 2, ..., p connected components. Then column-convex polygons are equivalent to 1-convex polyominoes. The area generating function of even the simplest generalization, namely 2-column polyominoes, is unlikely to be solvable. We therefore define two classes of polyominoes which interpolate between column-convex polygons and 2-column polyominoes. We derive the area generating functions of those two classes, using extensions of existing algorithms. The growth constants of both classes are greater than the growth constant of column-convex polyominoes. Rather tight lower bounds on the growth constants complement a comprehensive asymptotic analysis.

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,

Duality and calculus of convex objects (theory and applications)

International Nuclear Information System (INIS)

Brinkhuis, Ya; Tikhomirov, V M

2007-01-01

A new approach to convex calculus is presented, which allows one to treat from a single point of view duality and calculus for various convex objects. This approach is based on the possibility of associating with each convex object (a convex set or a convex function) a certain convex cone without loss of information about the object. From the duality theorem for cones duality theorems for other convex objects are deduced as consequences. The theme 'Duality formulae and the calculus of convex objects' is exhausted (from a certain precisely formulated point of view). Bibliography: 5 titles.

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...

Convex surfaces

CERN Document Server

Busemann, Herbert

2008-01-01

This exploration of convex surfaces focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. It also examines intrinsic geometry and the realization of intrinsic metrics. 1958 edition.

Convexity Adjustments for ATS Models

DEFF Research Database (Denmark)

Murgoci, Agatha; Gaspar, Raquel M.

. 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...

Convex games versus clan games

NARCIS (Netherlands)

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

2008-01-01

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

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

An easy path to convex analysis and applications

CERN Document Server

Mordukhovich, Boris S

2013-01-01

Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to cl

On Hadamard-Type Inequalities Involving Several Kinds of Convexity

Directory of Open Access Journals (Sweden)

Dragomir SeverS

2010-01-01

Full Text Available We do not only give the extensions of the results given by Gill et al. (1997 for log-convex functions but also obtain some new Hadamard-type inequalities for log-convex -convex, and -convex functions.

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

ON THE GENERALIZED CONVEXITY AND CONCAVITY

Directory of Open Access Journals (Sweden)

Bhayo B.

2015-11-01

Full Text Available A function ƒ : R+ → R+ is (m1, m2-convex (concave if ƒ(m1(x,y ≤ (≥ m2(ƒ(x, ƒ(y for all x,y Є R+ = (0,∞ and m1 and m2 are two mean functions. Anderson et al. [1] studies the dependence of (m1, m2-convexity (concavity on m1 and m2 and gave the sufficient conditions of (m1, m2-convexity and concavity of a function defined by Maclaurin series. In this paper, we make a contribution to the topic and study the (m1, m2-convexity and concavity of a function where m1 and m2 are identric mean, Alzer mean mean. As well, we prove a conjecture posed by Bruce Ebanks in [2].

Nested convex bodies are chaseable

NARCIS (Netherlands)

N. Bansal (Nikhil); M. Böhm (Martin); M. Eliáš (Marek); G. Koumoutsos (Grigorios); S.W. Umboh (Seeun William)

2018-01-01

textabstractIn the Convex Body Chasing problem, we are given an initial point v0 2 Rd and an online sequence of n convex bodies F1; : : : ; Fn. When we receive Fi, we are required to move inside Fi. Our goal is to minimize the total distance traveled. This fundamental online problem was first

A Genealogy of Convex Solids Via Local and Global Bifurcations of Gradient Vector Fields

Science.gov (United States)

Domokos, Gábor; Holmes, Philip; Lángi, Zsolt

2016-12-01

Three-dimensional convex bodies can be classified in terms of the number and stability types of critical points on which they can balance at rest on a horizontal plane. For typical bodies, these are non-degenerate maxima, minima, and saddle points, the numbers of which provide a primary classification. Secondary and tertiary classifications use graphs to describe orbits connecting these critical points in the gradient vector field associated with each body. In previous work, it was shown that these classifications are complete in that no class is empty. Here, we construct 1- and 2-parameter families of convex bodies connecting members of adjacent primary and secondary classes and show that transitions between them can be realized by codimension 1 saddle-node and saddle-saddle (heteroclinic) bifurcations in the gradient vector fields. Our results indicate that all combinatorially possible transitions can be realized in physical shape evolution processes, e.g., by abrasion of sedimentary particles.

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...

Convexity of the effective potential

International Nuclear Information System (INIS)

Haymaker, R.W.; Perez-Mercader, J.

1978-01-01

The effective potential V(phi) in field theories is a convex function of phi. V(lambda phi 1 + (1 - lambda)phi 2 ) less than or equal to lambdaV(phi 1 ) + (1 - lambda)V(phi 2 ), 0 less than or equal to lambda less than or equal to 1, all phi 1 , phi 2 . A linear interpolation of V(phi) is always larger than or equal to V(phi). There are numerous examples in the tree approximation and in perturbation theory for which this is not the case, the most notorious example being the double dip potential. More complete solutions may or may not show this property automatically. However, a non-convex V(phi) simply indicates that an unstable vacuum state was used in implementing the definition of V(phi). A strict definition will instruct one to replace V(phi) with its linear interpolation in such a way as to make it convex. (Alternatively one can just as well take the view that V(phi) is undefined in these domains.) In this note, attention is called to a very simple argument for convexity based on a construction described by H. Callen in his classic book Thermodynamics

Convex Banding of the Covariance Matrix.

Science.gov (United States)

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

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...

Approximate convex hull of affine iterated function system attractors

International Nuclear Information System (INIS)

Mishkinis, Anton; Gentil, Christian; Lanquetin, Sandrine; Sokolov, Dmitry

2012-01-01

Highlights: ► We present an iterative algorithm to approximate affine IFS attractor convex hull. ► Elimination of the interior points significantly reduces the complexity. ► To optimize calculations, we merge the convex hull images at each iteration. ► Approximation by ellipses increases speed of convergence to the exact convex hull. ► We present a method of the output convex hull simplification. - Abstract: In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy.

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

Decompositions, partitions, and coverings with convex polygons and pseudo-triangles

NARCIS (Netherlands)

Aichholzer, O.; Huemer, C.; Kappes, S.; Speckmann, B.; Tóth, Cs.D.

2007-01-01

We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex

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...

Convex bodies with many elliptic sections

OpenAIRE

Arelio, Isaac; Montejano, Luis

2014-01-01

{We show in this paper that two normal elliptic sections through every point of the boundary of a smooth convex body essentially characterize an ellipsoid and furthermore, that four different pairwise non-tangent elliptic sections through every point of the $C^2$-differentiable boundary of a convex body also essentially characterize an ellipsoid.

Sufficient Descent Conjugate Gradient Methods for Solving Convex Constrained Nonlinear Monotone Equations

Directory of Open Access Journals (Sweden)

San-Yang Liu

2014-01-01

Full Text Available Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large-scale nonsmooth equations.

INdAM Workshop on Analytic Aspects of Convexity

CERN Document Server

Colesanti, Andrea; Gronchi, Paolo

2018-01-01

This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016. It offers a collection of selected articles, written by some of the world’s leading experts in the field of Convex Geometry, on recent developments in this area: theory of valuations; geometric inequalities; affine geometry; and curvature measures. The book will be of interest to a broad readership, from those involved in Convex Geometry, to those focusing on Functional Analysis, Harmonic Analysis, Differential Geometry, or PDEs. The book is a addressed to PhD students and researchers, interested in Convex Geometry and its links to analysis.

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...

Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

International Nuclear Information System (INIS)

Zhao Yunbin

2010-01-01

While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the condition number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.

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 ...

Nonsmooth Mechanics and Convex Optimization

CERN Document Server

Kanno, Yoshihiro

2011-01-01

"This book concerns matter that is intrinsically difficult: convex optimization, complementarity and duality, nonsmooth analysis, linear and nonlinear programming, etc. The author has skillfully introduced these and many more concepts, and woven them into a seamless whole by retaining an easy and consistent style throughout. The book is not all theory: There are many real-life applications in structural engineering, cable networks, frictional contact problems, and plasticity! I recommend it to any reader who desires a modern, authoritative account of nonsmooth mechanics and convex optimiz

Increased dependence on slow filling for left ventricular diastolic filling in patients with coronary artery disease and a depressed systolic function

International Nuclear Information System (INIS)

Yamagishi, Takashi; Ozaki, Masaharu; Furutani, Yuhji; Yamamoto, Kouzo; Saeki, Atsushi; Satoh, Shinichi; Kusukawa, Reizo

1990-01-01

Contributions of rapid filling, slow filling and atrial systole to the left ventricular(LV) filling volume were analyzed with the use of radionuclide ventriculography at rest, both globally and regionally, in 34 patients with isolated disease of the left anterior descending coronary artery. The patients included 17 with a normal ejection fraction (EF≥50%; group 1) and 17 with a depressed EF (<50%; group 2), and the data were compared with those obtained from 13 normal subjects. A computer program subdivided the LV image into 4 regions, and time-activity curves were constructed globally and regionally by reverse-gating from the R wave. In both groups the contribution of rapid filling to the LV filling volume was decreased significantly in the affected septal and apical regions, and in the global left ventricle compared with that in normal subjects. In group 1, the contribution of atrial systole showed an increase in these affected regions and in the global left ventricle. In contrast, in group 2, the atrial contribution was not increased globally or regionally as much as was expected. However, the contribution of slow filling was either increased significantly or tended to increase in the affected regions and in the global left ventricle. There were negative correlations between the contribution of rapid filling and that of slow filling in the global left ventricle (r=-0.73, p<0.001) and in each of the septal, apical and lateral regions (r≥-0.60, p<0.001), which suggested that the contribution of slow filling as well as of atrial systole undergoes an increase as rapid filling is impaired. Thus, in patients with coronary artery disease, the left ventricle relies on slow filling as well as atrial systole to affect diastolic LV filling in the affected regions and in the global left ventricle in the presence of LV systolic dysfunction. (author)

Convexity of oligopoly games without transferable technologies

NARCIS (Netherlands)

Driessen, Theo; Meinhardt, Holger I.

2005-01-01

We present sufficient conditions involving the inverse demand function and the cost functions to establish the convexity of oligopoly TU-games without transferable technologies. For convex TU-games it is well known that the core is relatively large and that it is generically nonempty. The former

Convex stoma appliances: an audit of stoma care nurses.

Science.gov (United States)

Perrin, Angie

2016-12-08

This article observes the complexities surrounding the use of convex appliances within the specialist sphere of stoma care. It highlights some of the results taken from a small audit carried out with 24 stoma care nurses examining the general use of convex appliances and how usage of convex products has evolved, along with specialist stoma care practice.

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 divided...

A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES

Institute of Scientific and Technical Information of China (English)

程立新; 腾岩梅

2003-01-01

This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.

Characterizing Convexity of Games using Marginal Vectors

NARCIS (Netherlands)

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

2003-01-01

In this paper we study the relation between convexity of TU games and marginal vectors.We show that if specfic marginal vectors are core elements, then the game is convex.We characterize sets of marginal vectors satisfying this property, and we derive the formula for the minimum number of marginal

On Difference of Convex Optimization to Visualize Statistical Data and Dissimilarities

DEFF Research Database (Denmark)

Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero

2016-01-01

In this talk we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective...... is the difference of two convex functions (DC). Suitable DC decompositions allow us to use the DCA algorithm in a very efficient way. Our algorithmic approach is used to visualize two real-world datasets....

Displacement Convexity for First-Order Mean-Field Games

KAUST Repository

Seneci, Tommaso

2018-05-01

In this thesis, we consider the planning problem for first-order mean-field games (MFG). These games degenerate into optimal transport when there is no coupling between players. Our aim is to extend the concept of displacement convexity from optimal transport to MFGs. This extension gives new estimates for solutions of MFGs. First, we introduce the Monge-Kantorovich problem and examine related results on rearrangement maps. Next, we present the concept of displacement convexity. Then, we derive first-order MFGs, which are given by a system of a Hamilton-Jacobi equation coupled with a transport equation. Finally, we identify a large class of functions, that depend on solutions of MFGs, which are convex in time. Among these, we find several norms. This convexity gives bounds for the density of solutions of the planning problem.

Convex unwraps its first grown-up supercomputer

Energy Technology Data Exchange (ETDEWEB)

Manuel, T.

1988-03-03

Convex Computer Corp.'s new supercomputer family is even more of an industry blockbuster than its first system. At a tenfold jump in performance, it's far from just an incremental upgrade over its first minisupercomputer, the C-1. The heart of the new family, the new C-2 processor, churning at 50 million floating-point operations/s, spawns a group of systems whose performance could pass for some fancy supercomputers-namely those of the Cray Research Inc. family. When added to the C-1, Convex's five new supercomputers create the C series, a six-member product group offering a performance range from 20 to 200 Mflops. They mark an important transition for Convex from a one-product high-tech startup to a multinational company with a wide-ranging product line. It's a tough transition but the Richardson, Texas, company seems to be doing it. The extended product line propels Convex into the upper end of the minisupercomputer class and nudges it into the low end of the big supercomputers. It positions Convex in an uncrowded segment of the market in the $500,000 to $1 million range offering 50 to 200 Mflops of performance. The company is making this move because the minisuper area, which it pioneered, quickly became crowded with new vendors, causing prices and gross margins to drop drastically.

Hermitian harmonic maps into convex balls

International Nuclear Information System (INIS)

Li Zhenyang; Xi Zhang

2004-07-01

In this paper, we consider Hermitian harmonic maps from Hermitian manifolds into convex balls. We prove that there exist no non-trivial Hermitian harmonic maps from closed Hermitian manifolds into convex balls, and we use the heat flow method to solve the Dirichlet problem for Hermitian harmonic maps when the domain is compact Hermitian manifold with non-empty boundary. The case where the domain manifold is complete(noncompact) is also studied. (author)

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...

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.

Displacement Convexity for First-Order Mean-Field Games

KAUST Repository

Seneci, Tommaso

2018-01-01

Finally, we identify a large class of functions, that depend on solutions of MFGs, which are convex in time. Among these, we find several norms. This convexity gives bounds for the density of solutions of the planning problem.

Strictly convex functions on complete Finsler manifolds

Indian Academy of Sciences (India)

convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss ... map expp at some point p ∈ M (and hence at every point on M) is defined on the whole tangent space Mp to M at ... The influence of the existence of convex functions on the metric and topology of under- lying manifolds has ...

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...

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.

Counting convex polygons in planar point sets

NARCIS (Netherlands)

Mitchell, J.S.B.; Rote, G.; Sundaram, Gopalakrishnan; Woeginger, G.J.

1995-01-01

Given a set S of n points in the plane, we compute in time O(n3) the total number of convex polygons whose vertices are a subset of S. We give an O(m · n3) algorithm for computing the number of convex k-gons with vertices in S, for all values k = 3,…, m; previously known bounds were exponential

Reconstruction of convex bodies from surface tensors

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus

. 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...... 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...... tensors up to rank s. This is used to establish consistency of the developed reconstruction algorithm....

Recovering convexity in non-associated plasticity

Science.gov (United States)

Francfort, Gilles A.

2018-03-01

We quickly review two main non-associated plasticity models, the Armstrong-Frederick model of nonlinear kinematic hardening and the Drucker-Prager cap model. Non-associativity is commonly thought to preclude any kind of variational formulation, be it in a Hencky-type (static) setting, or when considering a quasi-static evolution because non-associativity destroys convexity. We demonstrate that such an opinion is misguided: associativity (and convexity) can be restored at the expense of the introduction of state variable-dependent dissipation potentials.

Conditionally exponential convex functions on locally compact groups

International Nuclear Information System (INIS)

Okb El-Bab, A.S.

1992-09-01

The main results of the thesis are: 1) The construction of a compact base for the convex cone of all conditionally exponential convex functions. 2) The determination of the extreme parts of this cone. Some supplementary lemmas are proved for this purpose. (author). 8 refs

Entropy coherent and entropy convex measures of risk

NARCIS (Netherlands)

Laeven, Roger; Stadje, M.A.

2010-01-01

We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized

The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases

KAUST Repository

Gomes, Diogo A.; Mitake, Hiroyoshi; Tran, Hung V.

2018-01-01

Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton–Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton–Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton–Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not directly apply. In this case, we establish the convergence by a direct approach.

The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases

KAUST Repository

Gomes, Diogo A.

2018-01-26

Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton–Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton–Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton–Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not directly apply. In this case, we establish the convergence by a direct approach.

Stereotype locally convex spaces

International Nuclear Information System (INIS)

Akbarov, S S

2000-01-01

We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis

Stereotype locally convex spaces

Energy Technology Data Exchange (ETDEWEB)

Akbarov, S S

2000-08-31

We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.

Stereotype locally convex spaces

Science.gov (United States)

Akbarov, S. S.

2000-08-01

We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.

CVXPY: A Python-Embedded Modeling Language for Convex Optimization

OpenAIRE

Diamond, Steven; Boyd, Stephen

2016-01-01

CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at http://www.cvxpy.org/ under the GPL license, along with documentation and examples.

CVXPY: A Python-Embedded Modeling Language for Convex Optimization.

Science.gov (United States)

Diamond, Steven; Boyd, Stephen

2016-04-01

CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at http://www.cvxpy.org/ under the GPL license, along with documentation and examples.

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.

Convex Optimization in R

Directory of Open Access Journals (Sweden)

Roger Koenker

2014-09-01

Full Text Available Convex optimization now plays an essential role in many facets of statistics. We briefly survey some recent developments and describe some implementations of these methods in R . Applications of linear and quadratic programming are introduced including quantile regression, the Huber M-estimator and various penalized regression methods. Applications to additively separable convex problems subject to linear equality and inequality constraints such as nonparametric density estimation and maximum likelihood estimation of general nonparametric mixture models are described, as are several cone programming problems. We focus throughout primarily on implementations in the R environment that rely on solution methods linked to R, like MOSEK by the package Rmosek. Code is provided in R to illustrate several of these problems. Other applications are available in the R package REBayes, dealing with empirical Bayes estimation of nonparametric mixture models.

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.

Schur Convexity of Generalized Heronian Means Involving Two Parameters

Directory of Open Access Journals (Sweden)

Bencze Mihály

2008-01-01

Full Text Available Abstract The Schur convexity and Schur-geometric convexity of generalized Heronian means involving two parameters are studied, the main result is then used to obtain several interesting and significantly inequalities for generalized Heronian means.

Chance-Constrained Guidance With Non-Convex Constraints

Science.gov (United States)

Ono, Masahiro

2011-01-01

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of

Inhibitory competition in figure-ground perception: context and convexity.

Science.gov (United States)

Peterson, Mary A; Salvagio, Elizabeth

2008-12-15

Convexity has long been considered a potent cue as to which of two regions on opposite sides of an edge is the shaped figure. Experiment 1 shows that for a single edge, there is only a weak bias toward seeing the figure on the convex side. Experiments 1-3 show that the bias toward seeing the convex side as figure increases as the number of edges delimiting alternating convex and concave regions increases, provided that the concave regions are homogeneous in color. The results of Experiments 2 and 3 rule out a probability summation explanation for these context effects. Taken together, the results of Experiments 1-3 show that the homogeneity versus heterogeneity of the convex regions is irrelevant. Experiment 4 shows that homogeneity of alternating regions is not sufficient for context effects; a cue that favors the perception of the intervening regions as figures is necessary. Thus homogeneity alone does not alone operate as a background cue. We interpret our results within a model of figure-ground perception in which shape properties on opposite sides of an edge compete for representation and the competitive strength of weak competitors is further reduced when they are homogeneous.

Use of Convexity in Ostomy Care: Results of an International Consensus Meeting.

Science.gov (United States)

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

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.

Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes

Energy Technology Data Exchange (ETDEWEB)

Sarıkaya, Mehmet Zeki, E-mail: sarikayamz@gmail.com [Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce (Turkey); Kiriş, Mehmet Eyüp, E-mail: kiris@aku.edu.tr [Department of Mathematics, Institute of Science and Arts, Afyon Kocatepe University, Afyonkarahisar (Turkey); Çelik, Nuri, E-mail: ncelik@bartin.edu.tr [Department of Statistics, Faculty of Science, Bartın University, Bartın-Turkey (Turkey)

2016-04-18

The main aim of the present paper is to introduce φ{sub h}-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φ{sub h}-convex stochastic processes. We also give some new general inequalities for φ{sub h}-convex stochastic processes.

Fast approximate convex decomposition using relative concavity

KAUST Repository

Ghosh, Mukulika; Amato, Nancy M.; Lu, Yanyan; Lien, Jyh-Ming

2013-01-01

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.

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.

Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear-equality constraints

International Nuclear Information System (INIS)

Zhang Yunong; Li Zhan

2009-01-01

In this Letter, by following Zhang et al.'s method, a recurrent neural network (termed as Zhang neural network, ZNN) is developed and analyzed for solving online the time-varying convex quadratic-programming problem subject to time-varying linear-equality constraints. Different from conventional gradient-based neural networks (GNN), such a ZNN model makes full use of the time-derivative information of time-varying coefficient. The resultant ZNN model is theoretically proved to have global exponential convergence to the time-varying theoretical optimal solution of the investigated time-varying convex quadratic program. Computer-simulation results further substantiate the effectiveness, efficiency and novelty of such ZNN model and method.

Generalized Bregman distances and convergence rates for non-convex regularization methods

International Nuclear Information System (INIS)

Grasmair, Markus

2010-01-01

We generalize the notion of Bregman distance using concepts from abstract convexity in order to derive convergence rates for Tikhonov regularization with non-convex regularization terms. In particular, we study the non-convex regularization of linear operator equations on Hilbert spaces, showing that the conditions required for the application of the convergence rates results are strongly related to the standard range conditions from the convex case. Moreover, we consider the setting of sparse regularization, where we show that a rate of order δ 1/p holds, if the regularization term has a slightly faster growth at zero than |t| p

Canonical Primal-Dual Method for Solving Non-convex Minimization Problems

OpenAIRE

Wu, Changzhi; Li, Chaojie; Gao, David Yang

2012-01-01

A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a convex-concave saddle point optimization problem, which is then solved by a quadratically perturbed primal-dual method. %It is proved that the popular SDP method is indeed a special case of the canonical duality theory. Numerical examples are illustrated. Comparing...

Study on IAEA international emergency response exercise convEx-3

International Nuclear Information System (INIS)

Yamamoto, Kazuya

2007-05-01

The International Atomic Energy Agency (IAEA) carried out a large-scale international emergency response exercise in 2005 under the designated name of ConvEx-3(2005), at Romania. This review report summarizes a study about ConvEx-3(2005) based on several related open literature. The ConvEx-3 was conducted in accordance with Agency's safety standard series and requirements in the field of Emergency Preparedness and Response. The study on the preparation, conduct and evaluation of ConvEx-3(2005) exercise is expected to provide very useful knowledge for development of drills and educational programs conducted by Nuclear Emergency Assistance and Training Center (NEAT). Especially, study on the exercise evaluations is instrumental in improving evaluations of drills planned by the national government and local governments. As international cooperation among Asian countries in the field of nuclear emergency preparedness and response is going to realize, it is very useful to survey and consider scheme and methodology about international emergency preparedness, response and exercise referring the knowledge of this ConvEx-3 study. The lessons learned from this study of ConvEx-3(2005) are summarized in four chapters; methodology of exercises and educational programs, exercise evaluation process, amendments/verification of the emergency response plan of NEAT, and technical issues of systems for emergency response and assistance of NEAT relevant to interface for international emergency communication. (author)

Convex geometry of quantum resource quantification

Science.gov (United States)

Regula, Bartosz

2018-01-01

We introduce a framework unifying the mathematical characterisation of different measures of general quantum resources and allowing for a systematic way to define a variety of faithful quantifiers for any given convex quantum resource theory. The approach allows us to describe many commonly used measures such as matrix norm-based quantifiers, robustness measures, convex roof-based measures, and witness-based quantifiers together in a common formalism based on the convex geometry of the underlying sets of resource-free states. We establish easily verifiable criteria for a measure to possess desirable properties such as faithfulness and strong monotonicity under relevant free operations, and show that many quantifiers obtained in this framework indeed satisfy them for any considered quantum resource. We derive various bounds and relations between the measures, generalising and providing significantly simplified proofs of results found in the resource theories of quantum entanglement and coherence. We also prove that the quantification of resources in this framework simplifies for pure states, allowing us to obtain more easily computable forms of the considered measures, and show that many of them are in fact equal on pure states. Further, we investigate the dual formulation of resource quantifiers, which provide a characterisation of the sets of resource witnesses. We present an explicit application of the results to the resource theories of multi-level coherence, entanglement of Schmidt number k, multipartite entanglement, as well as magic states, providing insight into the quantification of the four resources by establishing novel quantitative relations and introducing new quantifiers, such as a measure of entanglement of Schmidt number k which generalises the convex roof-extended negativity, a measure of k-coherence which generalises the \

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.

Probing convex polygons with X-rays

International Nuclear Information System (INIS)

Edelsbrunner, H.; Skiena, S.S.

1988-01-01

An X-ray probe through a polygon measures the length of intersection between a line and the polygon. This paper considers the properties of various classes of X-ray probes, and shows how they interact to give finite strategies for completely describing convex n-gons. It is shown that (3n/2)+6 probes are sufficient to verify a specified n-gon, while for determining convex polygons (3n-1)/2 X-ray probes are necessary and 5n+O(1) sufficient, with 3n+O(1) sufficient given that a lower bound on the size of the smallest edge of P is known

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.

STRICT CONVEXITY THROUGH EQUIVALENT NORMS IN SEPARABLES BANACH SPACES

Directory of Open Access Journals (Sweden)

Willy Zubiaga Vera

2016-12-01

Full Text Available Let E be a separable Banach space with norm || . ||. In the present work, the objective is to construct a norm || . ||1 that is equivalent to || . || in E, such that || . ||1 is strictly convex. In addition it is shown that its dual conjugate norm is also strictly convex.

Some Aspects of Convexity

Indian Academy of Sciences (India)

for all t E [0,1] and all x, y (in the domain of definition of f). ... Proof: (a) is a consequence of the definition. (b) Define conv(S) ... More generally, a set F is said to be a face of the convex .... and bounded, and assume the validity (for a proof, see.

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...

Convergence theorems for quasi-contractive maps in uniformly convex spaces

International Nuclear Information System (INIS)

Chidume, C.E.; Osilike, M.O.

1992-04-01

Let K be a nonempty closed convex and bounded subset of a real uniformly convex Banach space E of modulus of convexity of power type q≥2. Let T by a quasi-contractive mapping of K into itself. It is proved that each of two well known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of T in K. Our theorems generalize important known results. (author). 22 refs

A Fast Algorithm of Convex Hull Vertices Selection for Online Classification.

Science.gov (United States)

Ding, Shuguang; Nie, Xiangli; Qiao, Hong; Zhang, Bo

2018-04-01

Reducing samples through convex hull vertices selection (CHVS) within each class is an important and effective method for online classification problems, since the classifier can be trained rapidly with the selected samples. However, the process of CHVS is NP-hard. In this paper, we propose a fast algorithm to select the convex hull vertices, based on the convex hull decomposition and the property of projection. In the proposed algorithm, the quadratic minimization problem of computing the distance between a point and a convex hull is converted into a linear equation problem with a low computational complexity. When the data dimension is high, an approximate, instead of exact, convex hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples. In addition, the impact of outliers is also considered, and the proposed algorithm is improved by deleting the outliers in the initial procedure. Furthermore, a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems. An upper bound is theoretically proved for the difference between the support vector machines based on the approximate convex hull vertices selected and all the training samples. Experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm.

Convexity, gauge-dependence and tunneling rates

Energy Technology Data Exchange (ETDEWEB)

Plascencia, Alexis D.; Tamarit, Carlos [Institute for Particle Physics Phenomenology, Durham University,South Road, DH1 3LE (United Kingdom)

2016-10-19

We clarify issues of convexity, gauge-dependence and radiative corrections in relation to tunneling rates. Despite the gauge dependence of the effective action at zero and finite temperature, it is shown that tunneling and nucleation rates remain independent of the choice of gauge-fixing. Taking as a starting point the functional that defines the transition amplitude from a false vacuum onto itself, it is shown that decay rates are exactly determined by a non-convex, false vacuum effective action evaluated at an extremum. The latter can be viewed as a generalized bounce configuration, and gauge-independence follows from the appropriate Nielsen identities. This holds for any election of gauge-fixing that leads to an invertible Faddeev-Popov matrix.

Convexity, gauge-dependence and tunneling rates

International Nuclear Information System (INIS)

Plascencia, Alexis D.; Tamarit, Carlos

2016-01-01

We clarify issues of convexity, gauge-dependence and radiative corrections in relation to tunneling rates. Despite the gauge dependence of the effective action at zero and finite temperature, it is shown that tunneling and nucleation rates remain independent of the choice of gauge-fixing. Taking as a starting point the functional that defines the transition amplitude from a false vacuum onto itself, it is shown that decay rates are exactly determined by a non-convex, false vacuum effective action evaluated at an extremum. The latter can be viewed as a generalized bounce configuration, and gauge-independence follows from the appropriate Nielsen identities. This holds for any election of gauge-fixing that leads to an invertible Faddeev-Popov matrix.

Convexity and concavity constants in Lorentz and Marcinkiewicz spaces

Science.gov (United States)

Kaminska, Anna; Parrish, Anca M.

2008-07-01

We provide here the formulas for the q-convexity and q-concavity constants for function and sequence Lorentz spaces associated to either decreasing or increasing weights. It yields also the formula for the q-convexity constants in function and sequence Marcinkiewicz spaces. In this paper we extent and enhance the results from [G.J.O. Jameson, The q-concavity constants of Lorentz sequence spaces and related inequalities, Math. Z. 227 (1998) 129-142] and [A. Kaminska, A.M. Parrish, The q-concavity and q-convexity constants in Lorentz spaces, in: Banach Spaces and Their Applications in Analysis, Conference in Honor of Nigel Kalton, May 2006, Walter de Gruyter, Berlin, 2007, pp. 357-373].

Two examples of non strictly convex large deviations

OpenAIRE

De Marco, Stefano; Jacquier, Antoine; Roome, Patrick

2016-01-01

We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex large deviations. For one of these examples, we show that the rate function of the Cramer-type of large deviations coincides with that of the Freidlin-Wentzell when contraction principles are applied.

Convex Hull Aided Registration Method (CHARM).

Science.gov (United States)

Fan, Jingfan; Yang, Jian; Zhao, Yitian; Ai, Danni; Liu, Yonghuai; Wang, Ge; Wang, Yongtian

2017-09-01

Non-rigid registration finds many applications such as photogrammetry, motion tracking, model retrieval, and object recognition. In this paper we propose a novel convex hull aided registration method (CHARM) to match two point sets subject to a non-rigid transformation. First, two convex hulls are extracted from the source and target respectively. Then, all points of the point sets are projected onto the reference plane through each triangular facet of the hulls. From these projections, invariant features are extracted and matched optimally. The matched feature point pairs are mapped back onto the triangular facets of the convex hulls to remove outliers that are outside any relevant triangular facet. The rigid transformation from the source to the target is robustly estimated by the random sample consensus (RANSAC) scheme through minimizing the distance between the matched feature point pairs. Finally, these feature points are utilized as the control points to achieve non-rigid deformation in the form of thin-plate spline of the entire source point set towards the target one. The experimental results based on both synthetic and real data show that the proposed algorithm outperforms several state-of-the-art ones with respect to sampling, rotational angle, and data noise. In addition, the proposed CHARM algorithm also shows higher computational efficiency compared to these methods.

On convex complexity measures

Czech Academy of Sciences Publication Activity Database

Hrubeš, P.; Jukna, S.; Kulikov, A.; Pudlák, Pavel

2010-01-01

Roč. 411, 16-18 (2010), s. 1842-1854 ISSN 0304-3975 R&D Projects: GA AV ČR IAA1019401 Institutional research plan: CEZ:AV0Z10190503 Keywords : boolean formula * complexity measure * combinatorial rectangle * convexity Subject RIV: BA - General Mathematics Impact factor: 0.838, year: 2010 http://www.sciencedirect.com/science/article/pii/S0304397510000885

The occipital lobe convexity sulci and gyri.

Science.gov (United States)

Alves, Raphael V; Ribas, Guilherme C; Párraga, Richard G; de Oliveira, Evandro

2012-05-01

The anatomy of the occipital lobe convexity is so intricate and variable that its precise description is not found in the classic anatomy textbooks, and the occipital sulci and gyri are described with different nomenclatures according to different authors. The aim of this study was to investigate and describe the anatomy of the occipital lobe convexity and clarify its nomenclature. The configurations of sulci and gyri on the lateral surface of the occipital lobe of 20 cerebral hemispheres were examined in order to identify the most characteristic and consistent patterns. The most characteristic and consistent occipital sulci identified in this study were the intraoccipital, transverse occipital, and lateral occipital sulci. The morphology of the transverse occipital sulcus and the intraoccipital sulcus connection was identified as the most important aspect to define the gyral pattern of the occipital lobe convexity. Knowledge of the main features of the occipital sulci and gyri permits the recognition of a basic configuration of the occipital lobe and the identification of its sulcal and gyral variations.

On approximation and energy estimates for delta 6-convex functions.

Science.gov (United States)

Saleem, Muhammad Shoaib; Pečarić, Josip; Rehman, Nasir; Khan, Muhammad Wahab; Zahoor, Muhammad Sajid

2018-01-01

The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted [Formula: see text]-norm.

Transient disturbance growth in flows over convex surfaces

Science.gov (United States)

Karp, Michael; Hack, M. J. Philipp

2017-11-01

Flows over curved surfaces occur in a wide range of applications including airfoils, compressor and turbine vanes as well as aerial, naval and ground vehicles. In most of these applications the surface has convex curvature, while concave surfaces are less common. Since monotonic boundary-layer flows over convex surfaces are exponentially stable, they have received considerably less attention than flows over concave walls which are destabilized by centrifugal forces. Non-modal mechanisms may nonetheless enable significant disturbance growth which can make the flow susceptible to secondary instabilities. A parametric investigation of the transient growth and secondary instability of flows over convex surfaces is performed. The specific conditions yielding the maximal transient growth and strongest instability are identified. The effect of wall-normal and spanwise inflection points on the instability process is discussed. Finally, the role and significance of additional parameters, such as the geometry and pressure gradient, is analyzed.

Global Asymptotic Stability of Switched Neural Networks with Delays

Directory of Open Access Journals (Sweden)

Zhenyu Lu

2015-01-01

Full Text Available This paper investigates the global asymptotic stability of a class of switched neural networks with delays. Several new criteria ensuring global asymptotic stability in terms of linear matrix inequalities (LMIs are obtained via Lyapunov-Krasovskii functional. And here, we adopt the quadratic convex approach, which is different from the linear and reciprocal convex combinations that are extensively used in recent literature. In addition, the proposed results here are very easy to be verified and complemented. Finally, a numerical example is provided to illustrate the effectiveness of the results.

On approximation and energy estimates for delta 6-convex functions

Directory of Open Access Journals (Sweden)

Muhammad Shoaib Saleem

2018-02-01

Full Text Available Abstract The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted L2 $L^{2}$-norm.

Riemann solvers and undercompressive shocks of convex FPU chains

International Nuclear Information System (INIS)

Herrmann, Michael; Rademacher, Jens D M

2010-01-01

We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space–time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax shocks are replaced by so-called dispersive shocks. For convex–concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave–convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions

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...

Efficiency and Generalized Convex Duality for Nondifferentiable Multiobjective Programs

Directory of Open Access Journals (Sweden)

Bae KwanDeok

2010-01-01

Full Text Available We introduce nondifferentiable multiobjective programming problems involving the support function of a compact convex set and linear functions. The concept of (properly efficient solutions are presented. We formulate Mond-Weir-type and Wolfe-type dual problems and establish weak and strong duality theorems for efficient solutions by using suitable generalized convexity conditions. Some special cases of our duality results are given.

Processing convexity and concavity along a 2-D contour: figure-ground, structural shape, and attention.

Science.gov (United States)

Bertamini, Marco; Wagemans, Johan

2013-04-01

Interest in convexity has a long history in vision science. For smooth contours in an image, it is possible to code regions of positive (convex) and negative (concave) curvature, and this provides useful information about solid shape. We review a large body of evidence on the role of this information in perception of shape and in attention. This includes evidence from behavioral, neurophysiological, imaging, and developmental studies. A review is necessary to analyze the evidence on how convexity affects (1) separation between figure and ground, (2) part structure, and (3) attention allocation. Despite some broad agreement on the importance of convexity in these areas, there is a lack of consensus on the interpretation of specific claims--for example, on the contribution of convexity to metric depth and on the automatic directing of attention to convexities or to concavities. The focus is on convexity and concavity along a 2-D contour, not convexity and concavity in 3-D, but the important link between the two is discussed. We conclude that there is good evidence for the role of convexity information in figure-ground organization and in parsing, but other, more specific claims are not (yet) well supported.

Measures of symmetry for convex sets and stability

CERN Document Server

Toth, Gabor

2015-01-01

This textbook treats two important and related matters in convex geometry: the quantification of symmetry of a convex set—measures of symmetry—and the degree to which convex sets that nearly minimize such measures of symmetry are themselves nearly symmetric—the phenomenon of stability. By gathering the subject’s core ideas and highlights around Grünbaum’s general notion of measure of symmetry, it paints a coherent picture of the subject, and guides the reader from the basics to the state-of-the-art. The exposition takes various paths to results in order to develop the reader’s grasp of the unity of ideas, while interspersed remarks enrich the material with a behind-the-scenes view of corollaries and logical connections, alternative proofs, and allied results from the literature. Numerous illustrations elucidate definitions and key constructions, and over 70 exercises—with hints and references for the more difficult ones—test and sharpen the reader’s comprehension. The presentation includes:...

Generalized vector calculus on convex domain

Science.gov (United States)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Dose evaluation from multiple detector outputs using convex optimisation

International Nuclear Information System (INIS)

Hashimoto, M.; Iimoto, T.; Kosako, T.

2011-01-01

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. (authors)

Global blending optimization of laminated composites with discrete material candidate selection and thickness variation

DEFF Research Database (Denmark)

Sørensen, Søren N.; Stolpe, Mathias

2015-01-01

rate. The capabilities of the method and the effect of active versus inactive manufacturing constraints are demonstrated on several numerical examples of limited size, involving at most 320 binary variables. Most examples are solved to guaranteed global optimality and may constitute benchmark examples...... but is, however, convex in the original mixed binary nested form. Convexity is the foremost important property of optimization problems, and the proposed method can guarantee the global or near-global optimal solution; unlike most topology optimization methods. The material selection is limited...... for popular topology optimization methods and heuristics based on solving sequences of non-convex problems. The results will among others demonstrate that the difficulty of the posed problem is highly dependent upon the composition of the constitutive properties of the material candidates....

On the Moduli of Convexity

Czech Academy of Sciences Publication Activity Database

Guirao, A. J.; Hájek, Petr Pavel

2007-01-01

Roč. 135, č. 10 (2007), s. 3233-3240 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190502 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach spaces * moduli of convexity * uniformly rotund norms Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007

Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and -convexity

Science.gov (United States)

Briec, Walter; Horvath, Charles

2008-05-01

-convexity was introduced in [W. Briec, C. Horvath, -convexity, Optimization 53 (2004) 103-127]. Separation and Hahn-Banach like theorems can be found in [G. Adilov, A.M. Rubinov, -convex sets and functions, Numer. Funct. Anal. Optim. 27 (2006) 237-257] and [W. Briec, C.D. Horvath, A. Rubinov, Separation in -convexity, Pacific J. Optim. 1 (2005) 13-30]. We show here that all the basic results related to fixed point theorems are available in -convexity. Ky Fan inequality, existence of Nash equilibria and existence of equilibria for abstract economies are established in the framework of -convexity. Monotone analysis, or analysis on Maslov semimodules [V.N. Kolokoltsov, V.P. Maslov, Idempotent Analysis and Its Applications, Math. Appl., volE 401, Kluwer Academic, 1997; V.P. Litvinov, V.P. Maslov, G.B. Shpitz, Idempotent functional analysis: An algebraic approach, Math. Notes 69 (2001) 696-729; V.P. Maslov, S.N. Samborski (Eds.), Idempotent Analysis, Advances in Soviet Mathematics, Amer. Math. Soc., Providence, RI, 1992], is the natural framework for these results. From this point of view Max-Plus convexity and -convexity are isomorphic Maslov semimodules structures over isomorphic semirings. Therefore all the results of this paper hold in the context of Max-Plus convexity.

Behavior of Hollow Thin Welded Tubes Filled with Sand Slag Concrete

Directory of Open Access Journals (Sweden)

Noureddine Ferhoune

2016-01-01

Full Text Available This paper presents the axial bearing capacity of thin welded rectangular steel stubs filled with concrete sand. A series of tests was conducted to study the behavior of short composite columns under axial compressive load; the cross section dimensions were 100 × 70 × 2 mm. A total of 20 stubs have been tested, as follows: 4 hollow thin welded tubes were tested to axial and eccentric load compression, 4 were filled with ordinary concrete appointed by BO columns, 6 were filled with concrete whose natural sand was completely substituted by a crystallized sand slag designated in this paper by BSI, and 6 were tucked in concrete whose natural sand was partially replaced by a crystallized sand slag called BSII. The main parameters studied are the height of the specimen (300 mm–500 mm, eccentricity of load and type of filling concrete. Based on test results obtained, it is confirmed that the length of the tubes has a considerable effect on the bearing capacity and the failure mode. In all test tubes, fracture occurred by the convex local buckling of steel section due to the outward thrust of the concrete; it was observed that the sand concrete improves the bearing capacity of tubes compounds compared to those filled with ordinary concrete.

Flat tori in three-dimensional space and convex integration.

Science.gov (United States)

Borrelli, Vincent; Jabrane, Saïd; Lazarus, Francis; Thibert, Boris

2012-05-08

It is well-known that the curvature tensor is an isometric invariant of C(2) Riemannian manifolds. This invariant is at the origin of the rigidity observed in Riemannian geometry. In the mid 1950s, Nash amazed the world mathematical community by showing that this rigidity breaks down in regularity C(1). This unexpected flexibility has many paradoxical consequences, one of them is the existence of C(1) isometric embeddings of flat tori into Euclidean three-dimensional space. In the 1970s and 1980s, M. Gromov, revisiting Nash's results introduced convex integration theory offering a general framework to solve this type of geometric problems. In this research, we convert convex integration theory into an algorithm that produces isometric maps of flat tori. We provide an implementation of a convex integration process leading to images of an embedding of a flat torus. The resulting surface reveals a C(1) fractal structure: Although the tangent plane is defined everywhere, the normal vector exhibits a fractal behavior. Isometric embeddings of flat tori may thus appear as a geometric occurrence of a structure that is simultaneously C(1) and fractal. Beyond these results, our implementation demonstrates that convex integration, a theory still confined to specialists, can produce computationally tractable solutions of partial differential relations.

Convex Hull Abstraction in Specialisation of CLP Programs

DEFF Research Database (Denmark)

Peralta, J.C.; Gallagher, John Patrick

2003-01-01

We introduce an abstract domain consisting of atomic formulas constrained by linear arithmetic constraints (or convex hulls). This domain is used in an algorithm for specialization of constraint logic programs. The algorithm incorporates in a single phase both top-down goal directed propagation...... and bottom-up answer propagation, and uses a widening on the convex hull domain to ensure termination. We give examples to show the precision gained by this approach over other methods in the literature for specializing constraint logic programs. The specialization method can also be used for ordinary logic...

Convex sets in probabilistic normed spaces

International Nuclear Information System (INIS)

Aghajani, Asadollah; Nourouzi, Kourosh

2008-01-01

In this paper we obtain some results on convexity in a probabilistic normed space. We also investigate the concept of CSN-closedness and CSN-compactness in a probabilistic normed space and generalize the corresponding results of normed spaces

Exact generating function for 2-convex polygons

International Nuclear Information System (INIS)

James, W R G; Jensen, I; Guttmann, A J

2008-01-01

Polygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their 'concavity index', m. Such polygons are called m-convex polygons and are characterized by having up to m indentations in their perimeter. We first describe how we conjectured the (isotropic) generating function for the case m = 2 using a numerical procedure based on series expansions. We then proceed to prove this result for the more general case of the full anisotropic generating function, in which steps in the x and y directions are distinguished. In doing so, we develop tools that would allow for the case m > 2 to be studied

Solving ptychography with a convex relaxation

Science.gov (United States)

Horstmeyer, Roarke; Chen, Richard Y.; Ou, Xiaoze; Ames, Brendan; Tropp, Joel A.; Yang, Changhuei

2015-05-01

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that currently solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the ptychographic reconstruction algorithm that is currently in widespread use.

Fast globally optimal segmentation of 3D prostate MRI with axial symmetry prior.

Science.gov (United States)

Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Sun, Yue; Rajchl, Martin; Fenster, Aaron

2013-01-01

We propose a novel global optimization approach to segmenting a given 3D prostate T2w magnetic resonance (MR) image, which enforces the inherent axial symmetry of the prostate shape and simultaneously performs a sequence of 2D axial slice-wise segmentations with a global 3D coherence prior. We show that the proposed challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. With this regard, we introduce a novel coupled continuous max-flow model, which is dual to the studied convex relaxed optimization formulation and leads to an efficient multiplier augmented algorithm based on the modern convex optimization theory. Moreover, the new continuous max-flow based algorithm was implemented on GPUs to achieve a substantial improvement in computation. Experimental results using public and in-house datasets demonstrate great advantages of the proposed method in terms of both accuracy and efficiency.

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

Short Run Profit Maximization in a Convex Analysis Framework

Directory of Open Access Journals (Sweden)

Ilko Vrankic

2017-03-01

Full Text Available In this article we analyse the short run profit maximization problem in a convex analysis framework. The goal is to apply the results of convex analysis due to unique structure of microeconomic phenomena on the known short run profit maximization problem where the results from convex analysis are deductively applied. In the primal optimization model the technology in the short run is represented by the short run production function and the normalized profit function, which expresses profit in the output units, is derived. In this approach the choice variable is the labour quantity. Alternatively, technology is represented by the real variable cost function, where costs are expressed in the labour units, and the normalized profit function is derived, this time expressing profit in the labour units. The choice variable in this approach is the quantity of production. The emphasis in these two perspectives of the primal approach is given to the first order necessary conditions of both models which are the consequence of enveloping the closed convex set describing technology with its tangents. The dual model includes starting from the normalized profit function and recovering the production function, and alternatively the real variable cost function. In the first perspective of the dual approach the choice variable is the real wage, and in the second it is the real product price expressed in the labour units. It is shown that the change of variables into parameters and parameters into variables leads to both optimization models which give the same system of labour demand and product supply functions and their inverses. By deductively applying the results of convex analysis the comparative statics results are derived describing the firm's behaviour in the short run.

Global affine differential geometry of hypersurfaces

CERN Document Server

Li, An-Min; Zhao, Guosong; Hu, Zejun

2015-01-01

This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.

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.

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.

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.

Designing Camera Networks by Convex Quadratic Programming

KAUST Repository

Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao

2015-01-01

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

On convexity and Schoenberg's variation diminishing splines

International Nuclear Information System (INIS)

Feng, Yuyu; Kozak, J.

1992-11-01

In the paper we characterize a convex function by the monotonicity of a particular variation diminishing spline sequence. The result extends the property known for the Bernstein polynomial sequence. (author). 4 refs

Distribution functions of sections and projections of convex bodies

OpenAIRE

Kim, Jaegil; Yaskin, Vladyslav; Zvavitch, Artem

2015-01-01

Typically, when we are given the section (or projection) function of a convex body, it means that in each direction we know the size of the central section (or projection) perpendicular to this direction. Suppose now that we can only get the information about the sizes of sections (or projections), and not about the corresponding directions. In this paper we study to what extent the distribution function of the areas of central sections (or projections) of a convex body can be used to derive ...

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.)

Quantum information and convex optimization

International Nuclear Information System (INIS)

Reimpell, Michael

2008-01-01

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.)

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

Preconditioning 2D Integer Data for Fast Convex Hull Computations.

Science.gov (United States)

Cadenas, José Oswaldo; Megson, Graham M; Luengo Hendriks, Cris L

2016-01-01

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.

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...... 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 on measurements subject to noise is established under certain assumptions on the noise...

Effect of dental arch convexity and type of archwire on frictional forces

NARCIS (Netherlands)

Fourie, Zacharias; Ozcan, Mutlu; Sandham, John

Introduction: Friction measurements in orthodontics are often derived from models by using brackets placed on flat models with various straight wires. Dental arches are convex in some areas. The objectives of this study were to compare the frictional forces generated in conventional flat and convex

Subordination by convex functions

Directory of Open Access Journals (Sweden)

Rosihan M. Ali

2006-01-01

Full Text Available For a fixed analytic function g(z=z+∑n=2∞gnzn defined on the open unit disk and γ<1, let Tg(γ denote the class of all analytic functions f(z=z+∑n=2∞anzn satisfying ∑n=2∞|angn|≤1−γ. For functions in Tg(γ, a subordination result is derived involving the convolution with a normalized convex function. Our result includes as special cases several earlier works.

A One-Layer Recurrent Neural Network for Constrained Complex-Variable Convex Optimization.

Science.gov (United States)

Qin, Sitian; Feng, Jiqiang; Song, Jiahui; Wen, Xingnan; Xu, Chen

2018-03-01

In this paper, based on calculus and penalty method, a one-layer recurrent neural network is proposed for solving constrained complex-variable convex optimization. It is proved that for any initial point from a given domain, the state of the proposed neural network reaches the feasible region in finite time and converges to an optimal solution of the constrained complex-variable convex optimization finally. In contrast to existing neural networks for complex-variable convex optimization, the proposed neural network has a lower model complexity and better convergence. Some numerical examples and application are presented to substantiate the effectiveness of the proposed neural network.

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...

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...

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.

A parallel Discrete Element Method to model collisions between non-convex particles

Directory of Open Access Journals (Sweden)

Rakotonirina Andriarimina Daniel

2017-01-01

Full Text Available In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called “glued-convex method” (in the sense clumping convex bodies together, as an extension of the popular “glued-spheres” method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i the collapse of a granular column made of convex particles and (i the microstructure of a heap of non-convex particles in a cylindrical reactor.

Global Optimization of Nonlinear Blend-Scheduling Problems

Directory of Open Access Journals (Sweden)

Pedro A. Castillo Castillo

2017-04-01

Full Text Available The scheduling of gasoline-blending operations is an important problem in the oil refining industry. This problem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but also non-convex nonlinear behavior, due to the blending of various materials with different quality properties. In this work, a global optimization algorithm is proposed to solve a previously published continuous-time mixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimization, the distribution problem, and several important operational features and constraints. The algorithm employs piecewise McCormick relaxation (PMCR and normalized multiparametric disaggregation technique (NMDT to compute estimates of the global optimum. These techniques partition the domain of one of the variables in a bilinear term and generate convex relaxations for each partition. By increasing the number of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates of the global solution. The algorithm is compared to two commercial global solvers and two heuristic methods by solving four examples from the literature. Results show that the proposed global optimization algorithm performs on par with commercial solvers but is not as fast as heuristic approaches.

linear time algorithm for finding the convex ropes between two vertices of a simple polygon without triangulation

International Nuclear Information System (INIS)

Phan Thanh An

2008-06-01

The convex rope problem, posed by Peshkin and Sanderson in IEEE J. Robotics Automat, 2 (1986) pp. 53-58, is to find the counterclockwise and clockwise convex ropes starting at the vertex a and ending at the vertex b of a simple polygon, where a is on the boundary of the convex hull of the polygon and b is visible from infinity. In this paper, we present a linear time algorithm for solving this problem without resorting to a linear-time triangulation algorithm and without resorting to a convex hull algorithm for the polygon. The counterclockwise (clockwise, respectively) convex rope consists of two polylines obtained in a basic incremental strategy described in convex hull algorithms for the polylines forming the polygon from a to b. (author)

The Concept of Convexity in Fuzzy Set Theory | Rauf | Journal of the ...

African Journals Online (AJOL)

The notions of convex analysis are indispensable in theoretical and applied Mathematics especially in the study of Calculus where it has a natural generalization for the several variables case. This paper investigates the concept of Fuzzy set theory in relation to the idea of convexity. Some fundamental theorems were ...

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...

Diameter 2 properties and convexity

Czech Academy of Sciences Publication Activity Database

Abrahamsen, T. A.; Hájek, Petr Pavel; Nygaard, O.; Talponen, J.; Troyanski, S.

2016-01-01

Roč. 232, č. 3 (2016), s. 227-242 ISSN 0039-3223 R&D Projects: GA ČR GA16-07378S Institutional support: RVO:67985840 Keywords : diameter 2 property * midpoint locally uniformly rotund * Daugavet property Subject RIV: BA - General Mathematics Impact factor: 0.535, year: 2016 https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia- mathematica /all/232/3/91534/diameter-2-properties-and-convexity

A generalization of the convex Kakeya problem

KAUST Repository

Ahn, Heekap; Bae, Sangwon; Cheong, Otfried; Gudmundsson, Joachim; Tokuyama, Takeshi; Vigneron, Antoine E.

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

Multi-objective convex programming problem arising in multivariate ...

African Journals Online (AJOL)

user

Multi-objective convex programming problem arising in ... However, although the consideration of multiple objectives may seem a novel concept, virtually any nontrivial ..... Solving multiobjective programming problems by discrete optimization.

Cost Allocation and Convex Data Envelopment

DEFF Research Database (Denmark)

Hougaard, Jens Leth; Tind, Jørgen

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...

Convex Optimization for the Energy Management of Hybrid Electric Vehicles Considering Engine Start and Gearshift Costs

Directory of Open Access Journals (Sweden)

Tobias Nüesch

2014-02-01

Full Text Available This paper presents a novel method to solve the energy management problem for hybrid electric vehicles (HEVs with engine start and gearshift costs. The method is based on a combination of deterministic dynamic programming (DP and convex optimization. As demonstrated in a case study, the method yields globally optimal results while returning the solution in much less time than the conventional DP method. In addition, the proposed method handles state constraints, which allows for the application to scenarios where the battery state of charge (SOC reaches its boundaries.

On the Lasserre hierarchy of semidefinite programming relaxations of convex polynomial optimization problems

NARCIS (Netherlands)

de Klerk, E.; Laurent, M.

2011-01-01

The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization problems is known to converge finitely under some assumptions. [J. B. Lasserre, Convexity in semialgebraic geometry and polynomial optimization, SIAM J. Optim., 19 (2009), pp. 1995–2014]. We give a

On the stretch factor of convex Delaunay graphs

Directory of Open Access Journals (Sweden)

Prosenjit Bose

2010-06-01

Full Text Available Let C be a compact and convex set in the plane that contains the origin in its interior, and let S be a finite set of points in the plane. The Delaunay graph DGC(S of S is defined to be the dual of the Voronoi diagram of S with respect to the convex distance function defined by C. We prove that DGC(S is a t-spanner for S, for some constant t that depends only on the shape of the set C. Thus, for any two points p and q in S, the graph DGC(S contains a path between p and q whose Euclidean length is at most t times the Euclidean distance between p and q.

A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions

KAUST Repository

Fowkes, Jaroslav M.

2012-06-21

We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. Unlike other branch and bound algorithms, lower bounds are obtained via nonconvex underestimators of the function. For a numerical example, we apply the proposed branch and bound algorithm to radial basis function approximations. © 2012 Springer Science+Business Media, LLC.

Learning Convex Inference of Marginals

OpenAIRE

Domke, Justin

2012-01-01

Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this paper, the inference process is first defined to be the minimization of a convex function, inspired by free energy approximations. Learning is then done directly in terms of the performance of the inference process at univariate marginal prediction. The main ...

Quantum logics and convex geometry

International Nuclear Information System (INIS)

Bunce, L.J.; Wright, J.D.M.

1985-01-01

The main result is a representation theorem which shows that, for a large class of quantum logics, a quantum logic, Q, is isomorphic to the lattice of projective faces in a suitable convex set K. As an application we extend our earlier results, which, subject to countability conditions, gave a geometric characterization of those quantum logics which are isomorphic to the projection lattice of a von Neumann algebra or a JBW-algebra. (orig.)

Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

Science.gov (United States)

Hernandez, Monica

2017-12-01

This paper proposes a method for primal-dual convex optimization in variational large deformation diffeomorphic metric mapping problems formulated with robust regularizers and robust image similarity metrics. The method is based on Chambolle and Pock primal-dual algorithm for solving general convex optimization problems. Diagonal preconditioning is used to ensure the convergence of the algorithm to the global minimum. We consider three robust regularizers liable to provide acceptable results in diffeomorphic registration: Huber, V-Huber and total generalized variation. The Huber norm is used in the image similarity term. The primal-dual equations are derived for the stationary and the non-stationary parameterizations of diffeomorphisms. The resulting algorithms have been implemented for running in the GPU using Cuda. For the most memory consuming methods, we have developed a multi-GPU implementation. The GPU implementations allowed us to perform an exhaustive evaluation study in NIREP and LPBA40 databases. The experiments showed that, for all the considered regularizers, the proposed method converges to diffeomorphic solutions while better preserving discontinuities at the boundaries of the objects compared to baseline diffeomorphic registration methods. In most cases, the evaluation showed a competitive performance for the robust regularizers, close to the performance of the baseline diffeomorphic registration methods.

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.

A survey on locally uniformly A-convex algebras

International Nuclear Information System (INIS)

Oudadess, M.

1984-12-01

Using a bornological technic of M. Akkar, we reduce the study of classical questions (spectrum, boundedness of characters, functional calculus, etc.) in locally uniformly A-convex algebras to the Banach case. (author)

On the complexity of a combined homotopy interior method for convex programming

Science.gov (United States)

Yu, Bo; Xu, Qing; Feng, Guochen

2007-03-01

In [G.C. Feng, Z.H. Lin, B. Yu, Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem, Nonlinear Anal. 32 (1998) 761-768; G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics, Proceedings of the Second Japan-China Seminar on Numerical Mathematics, Lecture Notes in Numerical and Applied Analysis, vol. 14, Kinokuniya, Tokyo, 1995, pp. 9-16; Z.H. Lin, B. Yu, G.C. Feng, A combined homotopy interior point method for convex programming problem, Appl. Math. Comput. 84 (1997) 193-211.], a combined homotopy was constructed for solving non-convex programming and convex programming with weaker conditions, without assuming the logarithmic barrier function to be strictly convex and the solution set to be bounded. It was proven that a smooth interior path from an interior point of the feasible set to a K-K-T point of the problem exists. This shows that combined homotopy interior point methods can solve the problem that commonly used interior point methods cannot solveE However, so far, there is no result on its complexity, even for linear programming. The main difficulty is that the objective function is not monotonically decreasing on the combined homotopy path. In this paper, by taking a piecewise technique, under commonly used conditions, polynomiality of a combined homotopy interior point method is given for convex nonlinear programming.

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.

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 ...

Measurement system for diffraction efficiency of convex gratings

Science.gov (United States)

Liu, Peng; Chen, Xin-hua; Zhou, Jian-kang; Zhao, Zhi-cheng; Liu, Quan; Luo, Chao; Wang, Xiao-feng; Tang, Min-xue; Shen, Wei-min

2017-08-01

A measurement system for diffraction efficiency of convex gratings is designed. The measurement system mainly includes four components as a light source, a front system, a dispersing system that contains a convex grating, and a detector. Based on the definition and measuring principle of diffraction efficiency, the optical scheme of the measurement system is analyzed and the design result is given. Then, in order to validate the feasibility of the designed system, the measurement system is set up and the diffraction efficiency of a convex grating with the aperture of 35 mm, the curvature-radius of 72mm, the blazed angle of 6.4°, the grating period of 2.5μm and the working waveband of 400nm-900nm is tested. Based on GUM (Guide to the Expression of Uncertainty in Measurement), the uncertainties in the measuring results are evaluated. The measured diffraction efficiency data are compared to the theoretical ones, which are calculated based on the grating groove parameters got by an atomic force microscope and Rigorous Couple Wave Analysis, and the reliability of the measurement system is illustrated. Finally, the measurement performance of the system is analyzed and tested. The results show that, the testing accuracy, the testing stability and the testing repeatability are 2.5%, 0.085% and 3.5% , respectively.

A generalization of the convex Kakeya problem

KAUST Repository

Ahn, Heekap; Bae, Sangwon; Cheong, Otfried; Gudmundsson, Joachim; Tokuyama, Takeshi; Vigneron, Antoine E.

2013-01-01

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

Localized Multiple Kernel Learning A Convex Approach

Science.gov (United States)

2016-11-22

data. All the aforementioned approaches to localized MKL are formulated in terms of non-convex optimization problems, and deep the- oretical...learning. IEEE Transactions on Neural Networks, 22(3):433–446, 2011. Jingjing Yang, Yuanning Li, Yonghong Tian, Lingyu Duan, and Wen Gao. Group-sensitive

Pattern Discovery in Brain Imaging Genetics via SCCA Modeling with a Generic Non-convex Penalty.

Science.gov (United States)

Du, Lei; Liu, Kefei; Yao, Xiaohui; Yan, Jingwen; Risacher, Shannon L; Han, Junwei; Guo, Lei; Saykin, Andrew J; Shen, Li

2017-10-25

Brain imaging genetics intends to uncover associations between genetic markers and neuroimaging quantitative traits. Sparse canonical correlation analysis (SCCA) can discover bi-multivariate associations and select relevant features, and is becoming popular in imaging genetic studies. The L1-norm function is not only convex, but also singular at the origin, which is a necessary condition for sparsity. Thus most SCCA methods impose [Formula: see text]-norm onto the individual feature or the structure level of features to pursuit corresponding sparsity. However, the [Formula: see text]-norm penalty over-penalizes large coefficients and may incurs estimation bias. A number of non-convex penalties are proposed to reduce the estimation bias in regression tasks. But using them in SCCA remains largely unexplored. In this paper, we design a unified non-convex SCCA model, based on seven non-convex functions, for unbiased estimation and stable feature selection simultaneously. We also propose an efficient optimization algorithm. The proposed method obtains both higher correlation coefficients and better canonical loading patterns. Specifically, these SCCA methods with non-convex penalties discover a strong association between the APOE e4 rs429358 SNP and the hippocampus region of the brain. They both are Alzheimer's disease related biomarkers, indicating the potential and power of the non-convex methods in brain imaging genetics.

Convex nonnegative matrix factorization with manifold regularization.

Science.gov (United States)

Hu, Wenjun; Choi, Kup-Sze; Wang, Peiliang; Jiang, Yunliang; Wang, Shitong

2015-03-01

Nonnegative Matrix Factorization (NMF) has been extensively applied in many areas, including computer vision, pattern recognition, text mining, and signal processing. However, nonnegative entries are usually required for the data matrix in NMF, which limits its application. Besides, while the basis and encoding vectors obtained by NMF can represent the original data in low dimension, the representations do not always reflect the intrinsic geometric structure embedded in the data. Motivated by manifold learning and Convex NMF (CNMF), we propose a novel matrix factorization method called Graph Regularized and Convex Nonnegative Matrix Factorization (GCNMF) by introducing a graph regularized term into CNMF. The proposed matrix factorization technique not only inherits the intrinsic low-dimensional manifold structure, but also allows the processing of mixed-sign data matrix. Clustering experiments on nonnegative and mixed-sign real-world data sets are conducted to demonstrate the effectiveness of the proposed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks

DEFF Research Database (Denmark)

Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui

2016-01-01

This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed...... solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....... sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal...

Headache as a crucial symptom in the etiology of convexal subarachnoid hemorrhage.

Science.gov (United States)

Rico, María; Benavente, Lorena; Para, Marta; Santamarta, Elena; Pascual, Julio; Calleja, Sergio

2014-03-01

Convexal subarachnoid hemorrhage has been associated with different diseases, reversible cerebral vasoconstriction syndrome and cerebral amyloid angiopathy being the 2 main causes. To investigate whether headache at onset is determinant in identifying the underlying etiology for convexal subarachnoid hemorrhage. After searching in the database of our hospital, 24 patients were found with convexal subarachnoid hemorrhage in the last 10 years. The mean age of the sample was 69.5 years. We recorded data referring to demographics, symptoms and neuroimaging. Cerebral amyloid angiopathy patients accounted for 46% of the sample, 13% were diagnosed with reversible cerebral vasoconstriction syndrome, 16% with several other etiologies, and in 25%, the cause remained unknown. Mild headache was present only in 1 (9%) of the 11 cerebral amyloid angiopathy patients, while severe headache was the dominant feature in 86% of cases of the remaining etiologies. Headache is a key symptom allowing a presumptive etiological diagnosis of convexal subarachnoid hemorrhage. While the absence of headache suggests cerebral amyloid angiopathy as the more probable cause, severe headache obliges us to rule out other etiologies, such as reversible cerebral vasoconstriction syndrome. © 2013 American Headache Society.

Effective potential for non-convex potentials

International Nuclear Information System (INIS)

Fujimoto, Y.; O'Raifeartaigh, L.; Parravicini, G.

1983-01-01

It is shown that the well-known relationship between the effective potential GAMMA and the vacuum graphs μ of scalar QFT follows directly from the translational invariance of the measure, and that it holds for all values of the fields phi if, and only if, the classical potential is convex. In the non-convex case μ appears to become complex for some values of phi, but it is shown that the complexity is only apparent and is due to the failure of the loop expansion. The effective potential actually remains real and well-defined for all phi, and reduces to μ in the neighbourhood of the classical minima. A number of examples are considered, notably potentials which are spontaneously broken. In particular the mechanism by which a spontaneous breakdown may be generated by radiative corrections is re-investigated and some new insights obtained. Finally, it is shown that the renormalization group equations for the parameters may be obtained by inspection from the effective potential, and among the examples considered are SU(n) fields and supermultiplets. In particular, it is shown that for supermultiplets the effective potential is not only real but positive. (orig.)

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.

Cohesive granular media modelization with non-convex particles shape: Application to UO2 powder compaction

International Nuclear Information System (INIS)

Saint-Cyr, B.

2011-01-01

We model in this work granular materials composed of non-convex and cohesive aggregates, in view of application to the rheology of UO 2 powders. The effect of non convexity is analyzed in terms of bulk quantities (Coulomb internal friction and cohesion) and micromechanical parameters such as texture anisotropy and force transmission. In particular, we find that the packing fraction evolves in a complex manner with the shape non convexity and the shear strength increases but saturates due to interlocking between the aggregates. We introduce simple models to describe these features in terms of micro-mechanical parameters. Furthermore, a systematic investigation of shearing, uniaxial compaction and simple compression of cohesive packings show that bulk cohesion increases with non-convexity but is strongly influenced by the boundary conditions and shear bands or stress concentration. (author) [fr

The spectral positioning algorithm of new spectrum vehicle based on convex programming in wireless sensor network

Science.gov (United States)

Zhang, Yongjun; Lu, Zhixin

2017-10-01

Spectrum resources are very precious, so it is increasingly important to locate interference signals rapidly. Convex programming algorithms in wireless sensor networks are often used as localization algorithms. But in view of the traditional convex programming algorithm is too much overlap of wireless sensor nodes that bring low positioning accuracy, the paper proposed a new algorithm. Which is mainly based on the traditional convex programming algorithm, the spectrum car sends unmanned aerial vehicles (uses) that can be used to record data periodically along different trajectories. According to the probability density distribution, the positioning area is segmented to further reduce the location area. Because the algorithm only increases the communication process of the power value of the unknown node and the sensor node, the advantages of the convex programming algorithm are basically preserved to realize the simple and real-time performance. The experimental results show that the improved algorithm has a better positioning accuracy than the original convex programming algorithm.

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.

Robust Utility Maximization Under Convex Portfolio Constraints

International Nuclear Information System (INIS)

Matoussi, Anis; Mezghani, Hanen; Mnif, Mohamed

2015-01-01

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

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.

Numerical modeling of isothermal compositional grading by convex splitting methods

KAUST Repository

Li, Yiteng

2017-04-09

In this paper, an isothermal compositional grading process is simulated based on convex splitting methods with the Peng-Robinson equation of state. We first present a new form of gravity/chemical equilibrium condition by minimizing the total energy which consists of Helmholtz free energy and gravitational potential energy, and incorporating Lagrange multipliers for mass conservation. The time-independent equilibrium equations are transformed into a system of transient equations as our solution strategy. It is proved our time-marching scheme is unconditionally energy stable by the semi-implicit convex splitting method in which the convex part of Helmholtz free energy and its derivative are treated implicitly and the concave parts are treated explicitly. With relaxation factor controlling Newton iteration, our method is able to converge to a solution with satisfactory accuracy if a good initial estimate of mole compositions is provided. More importantly, it helps us automatically split the unstable single phase into two phases, determine the existence of gas-oil contact (GOC) and locate its position if GOC does exist. A number of numerical examples are presented to show the performance of our method.

Speech Enhancement by Modified Convex Combination of Fractional Adaptive Filtering

Directory of Open Access Journals (Sweden)

M. Geravanchizadeh

2014-12-01

Full Text Available This paper presents new adaptive filtering techniques used in speech enhancement system. Adaptive filtering schemes are subjected to different trade-offs regarding their steady-state misadjustment, speed of convergence, and tracking performance. Fractional Least-Mean-Square (FLMS is a new adaptive algorithm which has better performance than the conventional LMS algorithm. Normalization of LMS leads to better performance of adaptive filter. Furthermore, convex combination of two adaptive filters improves its performance. In this paper, new convex combinational adaptive filtering methods in the framework of speech enhancement system are proposed. The proposed methods utilize the idea of normalization and fractional derivative, both in the design of different convex mixing strategies and their related component filters. To assess our proposed methods, simulation results of different LMS-based algorithms based on their convergence behavior (i.e., MSE plots and different objective and subjective criteria are compared. The objective and subjective evaluations include examining the results of SNR improvement, PESQ test, and listening tests for dual-channel speech enhancement. The powerful aspects of proposed methods are their low complexity, as expected with all LMS-based methods, along with a high convergence rate.

TH-EF-BRB-05: 4pi Non-Coplanar IMRT Beam Angle Selection by Convex Optimization with Group Sparsity Penalty

International Nuclear Information System (INIS)

O’Connor, D; Nguyen, D; Voronenko, Y; Yin, W; Sheng, K

2016-01-01

Purpose: Integrated beam orientation and fluence map optimization is expected to be the foundation of robust automated planning but existing heuristic methods do not promise global optimality. We aim to develop a new method for beam angle selection in 4π non-coplanar IMRT systems based on solving (globally) a single convex optimization problem, and to demonstrate the effectiveness of the method by comparison with a state of the art column generation method for 4π beam angle selection. Methods: The beam angle selection problem is formulated as a large scale convex fluence map optimization problem with an additional group sparsity term that encourages most candidate beams to be inactive. The optimization problem is solved using an accelerated first-order method, the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The beam angle selection and fluence map optimization algorithm is used to create non-coplanar 4π treatment plans for several cases (including head and neck, lung, and prostate cases) and the resulting treatment plans are compared with 4π treatment plans created using the column generation algorithm. Results: In our experiments the treatment plans created using the group sparsity method meet or exceed the dosimetric quality of plans created using the column generation algorithm, which was shown superior to clinical plans. Moreover, the group sparsity approach converges in about 3 minutes in these cases, as compared with runtimes of a few hours for the column generation method. Conclusion: This work demonstrates the first non-greedy approach to non-coplanar beam angle selection, based on convex optimization, for 4π IMRT systems. The method given here improves both treatment plan quality and runtime as compared with a state of the art column generation algorithm. When the group sparsity term is set to zero, we obtain an excellent method for fluence map optimization, useful when beam angles have already been selected. NIH R43CA183390, NIH R01CA

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.

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.

The canonical partial metric and the uniform convexity on normed spaces

Directory of Open Access Journals (Sweden)

S. Oltra

2005-10-01

Full Text Available In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm. We prove that these geometric properties can be considered, in this sense, as topological properties that appear when we compare the natural metric topology of the space with the non translation invariant topology induced by the canonical partial metric in the normed space.

On the convexity of relativistic hydrodynamics

International Nuclear Information System (INIS)

Ibáñez, José M; Martí, José M; Cordero-Carrión, Isabel; Miralles, Juan A

2013-01-01

The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 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 Plohr1989 Rev. Mod. Phys. 61 75). The classical limit is recovered. Communicated by L Rezzolla (note)

A two-layer recurrent neural network for nonsmooth convex optimization problems.

Science.gov (United States)

Qin, Sitian; Xue, Xiaoping

2015-06-01

In this paper, a two-layer recurrent neural network is proposed to solve the nonsmooth convex optimization problem subject to convex inequality and linear equality constraints. Compared with existing neural network models, the proposed neural network has a low model complexity and avoids penalty parameters. It is proved that from any initial point, the state of the proposed neural network reaches the equality feasible region in finite time and stays there thereafter. Moreover, the state is unique if the initial point lies in the equality feasible region. The equilibrium point set of the proposed neural network is proved to be equivalent to the Karush-Kuhn-Tucker optimality set of the original optimization problem. It is further proved that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov. Moreover, from any initial point, the state is proved to be convergent to an equilibrium point of the proposed neural network. Finally, as applications, the proposed neural network is used to solve nonlinear convex programming with linear constraints and L1 -norm minimization problems.

Global Convergence of a Modified LS Method

Directory of Open Access Journals (Sweden)

Liu JinKui

2012-01-01

Full Text Available The LS method is one of the effective conjugate gradient methods in solving the unconstrained optimization problems. The paper presents a modified LS method on the basis of the famous LS method and proves the strong global convergence for the uniformly convex functions and the global convergence for general functions under the strong Wolfe line search. The numerical experiments show that the modified LS method is very effective in practice.

Convex polyhedral abstractions, specialisation and property-based predicate splitting in Horn clause verification

DEFF Research Database (Denmark)

Kafle, Bishoksan; Gallagher, John Patrick

2014-01-01

We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of query-answer transformed clauses, and refinement by splitting...... in conjunction with specialisation for propagating constraints it can frequently solve challenging verification problems. This is a contribution in itself, but refinement is needed when it fails, and the question of how to refine convex polyhedral analyses has not been studied much. We present a refinement...... technique based on interpolants derived from a counterexample trace; these are used to drive a property-based specialisation that splits predicates, leading in turn to more precise convex polyhedral analyses. The process of specialisation, analysis and splitting can be repeated, in a manner similar...

Uniform estimate of a compact convex set by a ball in an arbitrary norm

International Nuclear Information System (INIS)

Dudov, S I; Zlatorunskaya, I V

2000-01-01

The problem of the best uniform approximation of a compact convex set by a ball with respect to an arbitrary norm in the Hausdorff metric corresponding to that norm is considered. The question is reduced to a convex programming problem, which can be studied by means of convex analysis. Necessary and sufficient conditions for the solubility of this problem are obtained and several properties of its solution are described. It is proved, in particular, that the centre of at least one ball of best approximation lies in the compact set under consideration; in addition, conditions ensuring that the centres of all balls of best approximation lie in this compact set and a condition for unique solubility are obtained

Efficiency measurement with a non-convex free disposal hull technology

DEFF Research Database (Denmark)

Fukuyama, Hirofumi; Hougaard, Jens Leth; Sekitani, Kazuyuki

2016-01-01

We investigate the basic monotonicity properties of least-distance (in)efficiency measures on the class of non-convex FDH (free disposable hull) technologies. We show that any known FDH least-distance measure violates strong monotonicity over the strongly (Pareto-Koopmans) efficient frontier. Tak....... Taking this result into account, we develop a new class of FDH least-distance measures that satisfy strong monotonicity and show that the developed (in)efficiency measurement framework has a natural profit interpretation.......We investigate the basic monotonicity properties of least-distance (in)efficiency measures on the class of non-convex FDH (free disposable hull) technologies. We show that any known FDH least-distance measure violates strong monotonicity over the strongly (Pareto-Koopmans) efficient frontier...

Convex variational problems linear, nearly linear and anisotropic growth conditions

CERN Document Server

Bildhauer, Michael

2003-01-01

The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions. This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems.

A Survey on Operator Monotonicity, Operator Convexity, and Operator Means

Directory of Open Access Journals (Sweden)

Pattrawut Chansangiam

2015-01-01

Full Text Available This paper is an expository devoted to an important class of real-valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations for such functions are given from the viewpoint of differential analysis in terms of matrix of divided differences. From the viewpoint of operator inequalities, various characterizations and the relationship between operator monotonicity and operator convexity are given by Hansen and Pedersen. In the viewpoint of measure theory, operator monotone functions on the nonnegative reals admit meaningful integral representations with respect to Borel measures on the unit interval. Furthermore, Kubo-Ando theory asserts the correspondence between operator monotone functions and operator means.

Towards reproducible experimental studies for non-convex polyhedral shaped particles

Directory of Open Access Journals (Sweden)

Wilke Daniel N.

2017-01-01

Full Text Available The packing density and flat bottomed hopper discharge of non-convex polyhedral particles are investigated in a systematic experimental study. The motivation for this study is two-fold. Firstly, to establish an approach to deliver quality experimental particle packing data for non-convex polyhedral particles that can be used for characterization and validation purposes of discrete element codes. Secondly, to make the reproducibility of experimental setups as convenient and readily available as possible using affordable and accessible technology. The primary technology for this study is fused deposition modeling used to 3D print polylactic acid (PLA particles using readily available 3D printer technology. A total of 8000 biodegradable particles were printed, 1000 white particles and 1000 black particles for each of the four particle types considered in this study. Reproducibility is one benefit of using fused deposition modeling to print particles, but an extremely important additional benefit is that specific particle properties can be explicitly controlled. As an example in this study the volume fraction of each particle can be controlled i.e. the effective particle density can be adjusted. In this study the particle volumes reduces drastically as the non-convexity is increased, however all printed white particles in this study have the same mass within 2% of each other.

Towards reproducible experimental studies for non-convex polyhedral shaped particles

Science.gov (United States)

Wilke, Daniel N.; Pizette, Patrick; Govender, Nicolin; Abriak, Nor-Edine

2017-06-01

The packing density and flat bottomed hopper discharge of non-convex polyhedral particles are investigated in a systematic experimental study. The motivation for this study is two-fold. Firstly, to establish an approach to deliver quality experimental particle packing data for non-convex polyhedral particles that can be used for characterization and validation purposes of discrete element codes. Secondly, to make the reproducibility of experimental setups as convenient and readily available as possible using affordable and accessible technology. The primary technology for this study is fused deposition modeling used to 3D print polylactic acid (PLA) particles using readily available 3D printer technology. A total of 8000 biodegradable particles were printed, 1000 white particles and 1000 black particles for each of the four particle types considered in this study. Reproducibility is one benefit of using fused deposition modeling to print particles, but an extremely important additional benefit is that specific particle properties can be explicitly controlled. As an example in this study the volume fraction of each particle can be controlled i.e. the effective particle density can be adjusted. In this study the particle volumes reduces drastically as the non-convexity is increased, however all printed white particles in this study have the same mass within 2% of each other.

Intracranial Convexity Lipoma with Massive Calcification: Case Report

Energy Technology Data Exchange (ETDEWEB)

Kim, Eung Tae; Park, Dong Woo; Ryu, Jeong Ah; Park, Choong Ki; Lee, Young Jun; Lee, Seung Ro [Dept. of Radiology, Hanyang University College of Medicine, Seoul (Korea, Republic of)

2011-12-15

Intracranial lipoma is a rare entity, accounting for less than 0.5% of intracranial tumors, which usually develops in the callosal cisterns. We report a case of lipoma with an unusual location; in the high parietal convexity combined with massive calcification, and no underlying vascular malformation or congenital anomaly.

A duality recipe for non-convex variational problems

Science.gov (United States)

Bouchitté, Guy; Phan, Minh

2018-03-01

The aim of this paper is to present a general convexification recipe that can be useful for studying non-convex variational problems. In particular, this allows us to treat such problems by using a powerful primal-dual scheme. Possible further developments and open issues are given. xml:lang="fr"

On conditional independence and log-convexity

Czech Academy of Sciences Publication Activity Database

Matúš, František

2012-01-01

Roč. 48, č. 4 (2012), s. 1137-1147 ISSN 0246-0203 R&D Projects: GA AV ČR IAA100750603; GA ČR GA201/08/0539 Institutional support: RVO:67985556 Keywords : Conditional independence * Markov properties * factorizable distributions * graphical Markov models * log-convexity * Gibbs- Markov equivalence * Markov fields * Gaussian distributions * positive definite matrices * covariance selection model Subject RIV: BA - General Mathematics Impact factor: 0.933, year: 2012 http://library.utia.cas.cz/separaty/2013/MTR/matus-0386229.pdf

Distributed Topological Convex Hull Estimation of Event Region in Wireless Sensor Networks without Location Information

NARCIS (Netherlands)

Guo, Peng; Cao, Jiannong; Zhang, Kui

2015-01-01

In critical event (e.g., fire or gas) monitoring applications of wireless sensor networks (WSNs), convex hull of the event region is an efficient tool in handling the usual tasks like event report, routes reconstruction and human motion planning. Existing works on estimating convex hull of event

On the convex closed set-valued operators in Banach spaces and their applications in control problems

International Nuclear Information System (INIS)

Vu Ngoc Phat; Jong Yeoul Park

1995-10-01

The paper studies a class of set-values operators with emphasis on properties of their adjoints and existence of eigenvalues and eigenvectors of infinite-dimensional convex closed set-valued operators. Sufficient conditions for existence of eigenvalues and eigenvectors of set-valued convex closed operators are derived. These conditions specify possible features of control problems. The results are applied to some constrained control problems of infinite-dimensional systems described by discrete-time inclusions whose right-hand-sides are convex closed set- valued functions. (author). 8 refs

A note on supercyclic operators in locally convex spaces

OpenAIRE

Albanese, Angela A.; Jornet, David

2018-01-01

We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some examples are given.

Anomalous dynamics triggered by a non-convex equation of state in relativistic flows

Science.gov (United States)

Ibáñez, J. M.; Marquina, A.; Serna, S.; Aloy, M. A.

2018-05-01

The non-monotonicity of the local speed of sound in dense matter at baryon number densities much higher than the nuclear saturation density (n0 ≈ 0.16 fm-3) suggests the possible existence of a non-convex thermodynamics which will lead to a non-convex dynamics. Here, we explore the rich and complex dynamics that an equation of state (EoS) with non-convex regions in the pressure-density plane may develop as a result of genuinely relativistic effects, without a classical counterpart. To this end, we have introduced a phenomenological EoS, the parameters of which can be restricted owing to causality and thermodynamic stability constraints. This EoS can be regarded as a toy model with which we may mimic realistic (and far more complex) EoSs of practical use in the realm of relativistic hydrodynamics.

Generalization of the fejer-hadamard type inequalities for p-convex functions via k-fractional integrals

Directory of Open Access Journals (Sweden)

Ghulam Farid

2017-10-01

Full Text Available The aim of this paper is to obtain some more general fractional integral inequalities of Fejer Hadamard type for p-convex functions via Riemann-Liouville k-fractional integrals. Also in particular fractional inequalities for p-convex functions via Riemann-Liouville fractional integrals have been deduced.

Convex solutions of systems arising from Monge-Ampere equations

Directory of Open Access Journals (Sweden)

Haiyan Wang

2009-10-01

Full Text Available We establish two criteria for the existence of convex solutions to a boundary value problem for weakly coupled systems arising from the Monge-Ampère equations. We shall use fixed point theorems in a cone.

Gap filling strategies and error in estimating annual soil respiration

Science.gov (United States)

Soil respiration (Rsoil) is one of the largest CO2 fluxes in the global carbon (C) cycle. Estimation of annual Rsoil requires extrapolation of survey measurements or gap-filling of automated records to produce a complete time series. While many gap-filling methodologies have been employed, there is ...

Neural network for nonsmooth pseudoconvex optimization with general convex constraints.

Science.gov (United States)

Bian, Wei; Ma, Litao; Qin, Sitian; Xue, Xiaoping

2018-05-01

In this paper, a one-layer recurrent neural network is proposed for solving a class of nonsmooth, pseudoconvex optimization problems with general convex constraints. Based on the smoothing method, we construct a new regularization function, which does not depend on any information of the feasible region. Thanks to the special structure of the regularization function, we prove the global existence, uniqueness and "slow solution" character of the state of the proposed neural network. Moreover, the state solution of the proposed network is proved to be convergent to the feasible region in finite time and to the optimal solution set of the related optimization problem subsequently. In particular, the convergence of the state to an exact optimal solution is also considered in this paper. Numerical examples with simulation results are given to show the efficiency and good characteristics of the proposed network. In addition, some preliminary theoretical analysis and application of the proposed network for a wider class of dynamic portfolio optimization are included. Copyright © 2018 Elsevier Ltd. All rights reserved.

Link Prediction via Convex Nonnegative Matrix Factorization on Multiscale Blocks

Directory of Open Access Journals (Sweden)

Enming Dong

2014-01-01

Full Text Available Low rank matrices approximations have been used in link prediction for networks, which are usually global optimal methods and lack of using the local information. The block structure is a significant local feature of matrices: entities in the same block have similar values, which implies that links are more likely to be found within dense blocks. We use this insight to give a probabilistic latent variable model for finding missing links by convex nonnegative matrix factorization with block detection. The experiments show that this method gives better prediction accuracy than original method alone. Different from the original low rank matrices approximations methods for link prediction, the sparseness of solutions is in accord with the sparse property for most real complex networks. Scaling to massive size network, we use the block information mapping matrices onto distributed architectures and give a divide-and-conquer prediction method. The experiments show that it gives better results than common neighbors method when the networks have a large number of missing links.

WE-AB-209-07: Explicit and Convex Optimization of Plan Quality Metrics in Intensity-Modulated Radiation Therapy Treatment Planning

International Nuclear Information System (INIS)

Engberg, L; Eriksson, K; Hardemark, B; Forsgren, A

2016-01-01

Purpose: To formulate objective functions of a multicriteria fluence map optimization model that correlate well with plan quality metrics, and to solve this multicriteria model by convex approximation. Methods: In this study, objectives of a multicriteria model are formulated to explicitly either minimize or maximize a dose-at-volume measure. Given the widespread agreement that dose-at-volume levels play important roles in plan quality assessment, these objectives correlate well with plan quality metrics. This is in contrast to the conventional objectives, which are to maximize clinical goal achievement by relating to deviations from given dose-at-volume thresholds: while balancing the new objectives means explicitly balancing dose-at-volume levels, balancing the conventional objectives effectively means balancing deviations. Constituted by the inherently non-convex dose-at-volume measure, the new objectives are approximated by the convex mean-tail-dose measure (CVaR measure), yielding a convex approximation of the multicriteria model. Results: Advantages of using the convex approximation are investigated through juxtaposition with the conventional objectives in a computational study of two patient cases. Clinical goals of each case respectively point out three ROI dose-at-volume measures to be considered for plan quality assessment. This is translated in the convex approximation into minimizing three mean-tail-dose measures. Evaluations of the three ROI dose-at-volume measures on Pareto optimal plans are used to represent plan quality of the Pareto sets. Besides providing increased accuracy in terms of feasibility of solutions, the convex approximation generates Pareto sets with overall improved plan quality. In one case, the Pareto set generated by the convex approximation entirely dominates that generated with the conventional objectives. Conclusion: The initial computational study indicates that the convex approximation outperforms the conventional objectives

A one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion

International Nuclear Information System (INIS)

Suidan, T M

2001-01-01

The surprising connection between a one-dimensional gravitationally interacting gas of sticky particles and the convex minorant process generated by Brownian motion on [0,1] is studied. A study is made of the dynamics of this 1-D gas system by identifying three distinct clustering regimes and the time scales at which they occur. At the critical moment of time the mass distribution of the gas can be computed in terms of functionals of the convex minorant process

A canonical process for estimation of convex functions : The "invelope" of integrated Brownian motion +t4

NARCIS (Netherlands)

Groeneboom, P.; Jongbloed, G.; Wellner, J.A.

2001-01-01

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely

Sequential Change-Point Detection via Online Convex Optimization

Directory of Open Access Journals (Sweden)

Yang Cao

2018-02-01

Full Text Available Sequential change-point detection when the distribution parameters are unknown is a fundamental problem in statistics and machine learning. When the post-change parameters are unknown, we consider a set of detection procedures based on sequential likelihood ratios with non-anticipating estimators constructed using online convex optimization algorithms such as online mirror descent, which provides a more versatile approach to tackling complex situations where recursive maximum likelihood estimators cannot be found. When the underlying distributions belong to a exponential family and the estimators satisfy the logarithm regret property, we show that this approach is nearly second-order asymptotically optimal. This means that the upper bound for the false alarm rate of the algorithm (measured by the average-run-length meets the lower bound asymptotically up to a log-log factor when the threshold tends to infinity. Our proof is achieved by making a connection between sequential change-point and online convex optimization and leveraging the logarithmic regret bound property of online mirror descent algorithm. Numerical and real data examples validate our theory.

Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization.

Science.gov (United States)

Craft, David

2010-10-01

A discrete set of points and their convex combinations can serve as a sparse representation of the Pareto surface in multiple objective convex optimization. We develop a method to evaluate the quality of such a representation, and show by example that in multiple objective radiotherapy planning, the number of Pareto optimal solutions needed to represent Pareto surfaces of up to five dimensions grows at most linearly with the number of objectives. The method described is also applicable to the representation of convex sets. Copyright © 2009 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

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].

Optimal skill distribution under convex skill costs

Directory of Open Access Journals (Sweden)

Tin Cheuk Leung

2018-03-01

Full Text Available This paper studies optimal distribution of skills in an optimal income tax framework with convex skill constraints. The problem is cast as a social planning problem where a redistributive planner chooses how to distribute a given amount of aggregate skills across people. We find that optimal skill distribution is either perfectly equal or perfectly unequal, but an interior level of skill inequality is never optimal.

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.

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.

On the areas of various bodies in the Euclidean space: The case of irregular convex polygons

International Nuclear Information System (INIS)

Ozoemena, P.C.

1988-11-01

A theorem is proposed for the areas of n-sided irregular convex polygons, of given length of sides. The theorem is illustrated as a simple but powerful one in estimating the areas of irregular polygons, being dependent only on the number of sides n (and not on any of the explicit angles) of the irregular polygon. Finally, because of the global symmetry shown by equilateral triangles, squares and circles under group (gauge) theory, the relationships governing their areas, when they are inscribed or escribed in one another are discussed as riders, and some areas of their applications in graph theory, ratios and maxima and minima problems of differential calculus briefly mentioned. (author). 11 refs, 6 figs, 1 tab

On the polarizability dyadics of electrically small, convex objects

Science.gov (United States)

Lakhtakia, Akhlesh

1993-11-01

This communication on the polarizability dyadics of electrically small objects of convex shapes has been prompted by a recent paper published by Sihvola and Lindell on the polarizability dyadic of an electrically gyrotropic sphere. A mini-review of recent work on polarizability dyadics is appended.

Perturbation of convex risk minimization and its application in differential private learning algorithms

Directory of Open Access Journals (Sweden)

Weilin Nie

2017-01-01

Full Text Available Abstract Convex risk minimization is a commonly used setting in learning theory. In this paper, we firstly give a perturbation analysis for such algorithms, and then we apply this result to differential private learning algorithms. Our analysis needs the objective functions to be strongly convex. This leads to an extension of our previous analysis to the non-differentiable loss functions, when constructing differential private algorithms. Finally, an error analysis is then provided to show the selection for the parameters.

License or entry decision for innovator in international duopoly with convex cost functions

OpenAIRE

Hattori, Masahiko; Tanaka, Yasuhito

2017-01-01

We consider a choice of options for a foreign innovating firm to license its new cost-reducing technology to a domestic incumbent firm or to enter the domestic market with or without license under convex cost functions. With convex cost functions the domestic market and the foreign market are not separated, and the results depend on the relative size of those markets. In a specific case with linear demand and quadratic cost, entry without license strategy is never the optimal strategy for the...

The steady-state of the (Normalized) LMS is schur convex

KAUST Repository

Al-Hujaili, Khaled A.

2016-06-24

In this work, we demonstrate how the theory of majorization and schur-convexity can be used to assess the impact of input-spread on the Mean Squares Error (MSE) performance of adaptive filters. First, we show that the concept of majorization can be utilized to measure the spread in input-regressors and subsequently order the input-regressors according to their spread. Second, we prove that the MSE of the Least Mean Squares Error (LMS) and Normalized LMS (NLMS) algorithms are schur-convex, that is, the MSE of the LMS and the NLMS algorithms preserve the majorization order of the inputs which provide an analytical justification to why and how much the MSE performance of the LMS and the NLMS algorithms deteriorate as the spread in input increases. © 2016 IEEE.

Convex lattice polygons of fixed area with perimeter-dependent weights.

Science.gov (United States)

Rajesh, R; Dhar, Deepak

2005-01-01

We study fully convex polygons with a given area, and variable perimeter length on square and hexagonal lattices. We attach a weight tm to a convex polygon of perimeter m and show that the sum of weights of all polygons with a fixed area s varies as s(-theta(conv))eK(t)square root(s) for large s and t less than a critical threshold tc, where K(t) is a t-dependent constant, and theta(conv) is a critical exponent which does not change with t. Using heuristic arguments, we find that theta(conv) is 1/4 for the square lattice, but -1/4 for the hexagonal lattice. The reason for this unexpected nonuniversality of theta(conv) is traced to existence of sharp corners in the asymptotic shape of these polygons.

The steady-state of the (Normalized) LMS is schur convex

KAUST Repository

Al-Hujaili, Khaled A.; Al-Naffouri, Tareq Y.; Moinuddin, Muhammad

2016-01-01

In this work, we demonstrate how the theory of majorization and schur-convexity can be used to assess the impact of input-spread on the Mean Squares Error (MSE) performance of adaptive filters. First, we show that the concept of majorization can be utilized to measure the spread in input-regressors and subsequently order the input-regressors according to their spread. Second, we prove that the MSE of the Least Mean Squares Error (LMS) and Normalized LMS (NLMS) algorithms are schur-convex, that is, the MSE of the LMS and the NLMS algorithms preserve the majorization order of the inputs which provide an analytical justification to why and how much the MSE performance of the LMS and the NLMS algorithms deteriorate as the spread in input increases. © 2016 IEEE.

Reconstruction of Undersampled Big Dynamic MRI Data Using Non-Convex Low-Rank and Sparsity Constraints

Directory of Open Access Journals (Sweden)

Ryan Wen Liu

2017-03-01

Full Text Available Dynamic magnetic resonance imaging (MRI has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments.

Optimization of Transverse Oscillating Fields for Vector Velocity Estimation with Convex Arrays

DEFF Research Database (Denmark)

Jensen, Jørgen Arendt

2013-01-01

A method for making Vector Flow Images using the transverse oscillation (TO) approach on a convex array is presented. The paper presents optimization schemes for TO fields for convex probes and evaluates their performance using Field II simulations and measurements using the SARUS experimental...... from 90 to 45 degrees in steps of 15 degrees. The optimization routine changes the lateral oscillation period lx to yield the best possible estimates based on the energy ratio between positive and negative spatial frequencies in the ultrasound field. The basic equation for lx gives 1.14 mm at 40 mm...

A New Interpolation Approach for Linearly Constrained Convex Optimization

KAUST Repository

Espinoza, Francisco

2012-08-01

In this thesis we propose a new class of Linearly Constrained Convex Optimization methods based on the use of a generalization of Shepard\\'s interpolation formula. We prove the properties of the surface such as the interpolation property at the boundary of the feasible region and the convergence of the gradient to the null space of the constraints at the boundary. We explore several descent techniques such as steepest descent, two quasi-Newton methods and the Newton\\'s method. Moreover, we implement in the Matlab language several versions of the method, particularly for the case of Quadratic Programming with bounded variables. Finally, we carry out performance tests against Matab Optimization Toolbox methods for convex optimization and implementations of the standard log-barrier and active-set methods. We conclude that the steepest descent technique seems to be the best choice so far for our method and that it is competitive with other standard methods both in performance and empirical growth order.

Free locally convex spaces with a small base

Czech Academy of Sciences Publication Activity Database

Gabriyelyan, S.; Kąkol, Jerzy

2017-01-01

Roč. 111, č. 2 (2017), s. 575-585 ISSN 1578-7303 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : compact resolution * free locally convex space * G-base Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.690, year: 2016 http://link.springer.com/article/10.1007%2Fs13398-016-0315-1

Some fixed point theorems on non-convex sets

Directory of Open Access Journals (Sweden)

Mohanasundaram Radhakrishnan

2017-10-01

Full Text Available In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\\to K$ is a nonexpansive map satisfying $\\frac{x+Tx}{2}\\in K$ for all $x\\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$

Electron-pair logarithmic convexity and interelectronic moments in atoms: Application to heliumlike ions

International Nuclear Information System (INIS)

Koga, T.; Kasai, Y.; Dehesa, J.S.; Angulo, J.C.

1993-01-01

The electron-pair function h(u) of a finite many-electron system is not monotonic, but the related quantity h(u)/u α , α>0, is not only monotonically decreasing from the origin but also convex for the values α 1 and α 2 , respectively, as has been recently found. Here, it is first argued that this quantity is also logarithmically convex for any α≥α' with α'=max{-u 2 d2[lnh(u)]/du 2 }. Then this property is used to obtain a general inequality which involves three interelectronic moments left-angle u t right-angle. Particular cases of this inequality involve relevant characteristics of the system such as the number of electrons and the total electron-electron repulsion energy. Second, the logarithmic-convexity property of h(u) as well as the accuracy of this inequality are investigated by the optimum 20-term Hylleraas-type wave functions for two-electron atoms with nuclear charge Z=1, 2, 3, 5, and 10. It is found that (i) 14 2 much-gt α 1 ) and (ii) the accuracy of the inequality which involves moments of contiguous orders oscillates between 62.4% and 96.7% according to the specific He-like atom and the moments involved. Finally, the importance of the logarithmic-convexity effects on the interelectronic moments relative to those coming from other monotonicity properties of h(u)/u α are analyzed in the same numerical Hylleraas framework

Dynamic Convex Duality in Constrained Utility Maximization

OpenAIRE

Li, Yusong; Zheng, Harry

2016-01-01

In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual problems in terms of FBSDEs plus additional conditions. Such formulation then allows us to explicitly characterize the primal optimal control as a function of the adjoint process coming from the dual FBSDEs in a dynamic fashion and vice versa. Moreover, we also...

On evolving deformation microstructures in non-convex partially damaged solids

KAUST Repository

Gurses, Ercan; Miehe, Christian

2011-01-01

. 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

Moduli spaces of convex projective structures on surfaces

DEFF Research Database (Denmark)

Fock, V. V.; Goncharov, A. B.

2007-01-01

We introduce explicit parametrisations of the moduli space of convex projective structures on surfaces, and show that the latter moduli space is identified with the higher Teichmüller space for defined in [V.V. Fock, A.B. Goncharov, Moduli spaces of local systems and higher Teichmüller theory, math.......AG/0311149]. We investigate the cluster structure of this moduli space, and define its quantum version....

Convex blind image deconvolution with inverse filtering

Science.gov (United States)

Lv, Xiao-Guang; Li, Fang; Zeng, Tieyong

2018-03-01

Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption.

Computing Convex Coverage Sets for Faster Multi-Objective Coordination

NARCIS (Netherlands)

Roijers, D.M.; Whiteson, S.; Oliehoek, F.A.

2015-01-01

In this article, we propose new algorithms for multi-objective coordination graphs (MO-CoGs). Key to the efficiency of these algorithms is that they compute a convex coverage set (CCS) instead of a Pareto coverage set (PCS). Not only is a CCS a sufficient solution set for a large class of problems,

Positive definite functions and dual pairs of locally convex spaces

Directory of Open Access Journals (Sweden)

Daniel Alpay

2018-01-01

Full Text Available Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions.

Convex relationships in ecosystems containing mixtures of trees and grass

CSIR Research Space (South Africa)

Scholes, RJ

2003-12-01

Full Text Available The relationship between grass production and the quantity of trees in mixed tree-grass ecosystems (savannas) is convex for all or most of its range. In other words, the grass production declines more steeply per unit increase in tree quantity...

Pluripotential theory and convex bodies

Science.gov (United States)

Bayraktar, T.; Bloom, T.; Levenberg, N.

2018-03-01

A seminal paper by Berman and Boucksom exploited ideas from complex geometry to analyze the asymptotics of spaces of holomorphic sections of tensor powers of certain line bundles L over compact, complex manifolds as the power grows. This yielded results on weighted polynomial spaces in weighted pluripotential theory in {C}^d. Here, motivated by a recent paper by the first author on random sparse polynomials, we work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body in ({R}^+)^d. These classes of polynomials need not occur as sections of tensor powers of a line bundle L over a compact, complex manifold. We follow the approach of Berman and Boucksom to obtain analogous results. Bibliography: 16 titles.

Constrained convex minimization via model-based excessive gap

OpenAIRE

Tran Dinh, Quoc; Cevher, Volkan

2014-01-01

We introduce a model-based excessive gap technique to analyze first-order primal- dual methods for constrained convex minimization. As a result, we construct new primal-dual methods with optimal convergence rates on the objective residual and the primal feasibility gap of their iterates separately. Through a dual smoothing and prox-function selection strategy, our framework subsumes the augmented Lagrangian, and alternating methods as special cases, where our rates apply.

A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions

KAUST Repository

Fowkes, Jaroslav M.; Gould, Nicholas I. M.; Farmer, Chris L.

2012-01-01

We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation

PENNON: A code for convex nonlinear and semidefinite programming

Czech Academy of Sciences Publication Activity Database

Kočvara, Michal; Stingl, M.

2003-01-01

Roč. 18, č. 3 (2003), s. 317-333 ISSN 1055-6788 R&D Projects: GA ČR GA201/00/0080 Grant - others:BMBF(DE) 03ZOM3ER Institutional research plan: CEZ:AV0Z1075907 Keywords : convex programming * semidefinite programming * large-scale problems Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.306, year: 2003

Modeling IrisCode and its variants as convex polyhedral cones and its security implications.

Science.gov (United States)

Kong, Adams Wai-Kin

2013-03-01

IrisCode, developed by Daugman, in 1993, is the most influential iris recognition algorithm. A thorough understanding of IrisCode is essential, because over 100 million persons have been enrolled by this algorithm and many biometric personal identification and template protection methods have been developed based on IrisCode. This paper indicates that a template produced by IrisCode or its variants is a convex polyhedral cone in a hyperspace. Its central ray, being a rough representation of the original biometric signal, can be computed by a simple algorithm, which can often be implemented in one Matlab command line. The central ray is an expected ray and also an optimal ray of an objective function on a group of distributions. This algorithm is derived from geometric properties of a convex polyhedral cone but does not rely on any prior knowledge (e.g., iris images). The experimental results show that biometric templates, including iris and palmprint templates, produced by different recognition methods can be matched through the central rays in their convex polyhedral cones and that templates protected by a method extended from IrisCode can be broken into. These experimental results indicate that, without a thorough security analysis, convex polyhedral cone templates cannot be assumed secure. Additionally, the simplicity of the algorithm implies that even junior hackers without knowledge of advanced image processing and biometric databases can still break into protected templates and reveal relationships among templates produced by different recognition methods.

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

2006-12-01

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.

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

International Nuclear Information System (INIS)

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

2006-01-01

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

A note on the nucleolus for 2-convex TU games

NARCIS (Netherlands)

Driessen, Theo; Hou, D.

For 2-convex n-person cooperative TU games, the nucleolus is determined as some type of constrained equal award rule. Its proof is based on Maschler, Peleg, and Shapley’s geometrical characterization for the intersection of the prekernel with the core. Pairwise bargaining ranges within the core are

Tensor completion and low-n-rank tensor recovery via convex optimization

International Nuclear Information System (INIS)

Gandy, Silvia; Yamada, Isao; Recht, Benjamin

2011-01-01

In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers

Global smooth solutions of 3-D null-form wave equations in exterior domains with Neumann boundary conditions

Science.gov (United States)

Jun, Li; Huicheng, Yin

2018-05-01

The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions. Concretely speaking, when the surface of a 3-D compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition, we prove that the smooth small data solution exists globally provided that the Neumann boundary condition on the exterior domain is given. One of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself. As an application of the main result, the global stability to 3-D static compressible Chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude.

Blaschke- and Minkowski-endomorphisms of convex bodies

DEFF Research Database (Denmark)

Kiderlen, Markus

2006-01-01

We consider maps of the family of convex bodies in Euclidean d-dimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d>2, a representation theorem for such maps......-endomorphisms, where additivity is now understood with respect to Blaschke-addition. Using a special mixed volume, an adjoining operator can be introduced. This operator allows one to identify the class of Blaschke-endomorphisms with the class of weakly monotonic, non-degenerate and translation-covariant Minkowski...

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.

Dynamic Planar Convex Hull with Optimal Query Time and O(log n · log log n ) Update Time

DEFF Research Database (Denmark)

Brodal, Gerth Stølting; Jakob, Riko

2000-01-01

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log log n) time, point deletions in amortized O(log n · log log n) time......, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requires O(n) space. Applications of the new dynamic convex hull data structure are improved deterministic algorithms for the k-level problem and the red-blue segment intersection problem where all red and all...

On the Convexity of Step out - Step in Sequencing Games

NARCIS (Netherlands)

Musegaas, Marieke; Borm, Peter; Quant, Marieke

2016-01-01

The main result of this paper is the convexity of Step out - Step in (SoSi) sequencing games, a class of relaxed sequencing games first analyzed by Musegaas, Borm, and Quant (2015). The proof makes use of a polynomial time algorithm determining the value and an optimal processing order for an

Transonic shock wave. Boundary layer interaction at a convex wall

NARCIS (Netherlands)

Koren, B.; Bannink, W.J.

1984-01-01

A standard finite element procedure has been applied to the problem of transonic shock wave – boundary layer interaction at a convex wall. The method is based on the analytical Bohning-Zierep model, where the boundary layer is perturbed by a weak normal shock wave which shows a singular pressure

Integration of polystyrene microlenses with both convex and concave profiles in a polymer-based microfluidic system

KAUST Repository

Fan, Yiqiang

2013-12-20

This paper reports a new technique of fabricating polystyrene microlenses with both convex and concave profiles that are integrated in polymer-based microfluidic system. The polystyrene microlenses, or microlens array, are fabricated using the free-surface thermal compression molding method. The laser fabricated poly(methyl methacrylate) (PMMA) sheet is used as the mold for the thermal compression molding process. With different surface treatment methods of the PMMA mold, microlenses with either convex or concave profiles could be achieved during the thermal molding process. By integrating the microlenses in the microfluidic systems, observing the flow inside the microchannels is easier. This new technique is rapid, low cost, and it does not require cleanroom facilities. Microlenses with both convex and concave profiles can be easily fabricated and integrated in microfluidic system with this technique. © 2013 Springer-Verlag Berlin Heidelberg.

Usefulness of the convexity apparent hyperperfusion sign in 123I-iodoamphetamine brain perfusion SPECT for the diagnosis of idiopathic normal pressure hydrocephalus.

Science.gov (United States)

Ohmichi, Takuma; Kondo, Masaki; Itsukage, Masahiro; Koizumi, Hidetaka; Matsushima, Shigenori; Kuriyama, Nagato; Ishii, Kazunari; Mori, Etsuro; Yamada, Kei; Mizuno, Toshiki; Tokuda, Takahiko

2018-03-16

OBJECTIVE The gold standard for the diagnosis of idiopathic normal pressure hydrocephalus (iNPH) is the CSF removal test. For elderly patients, however, a less invasive diagnostic method is required. On MRI, high-convexity tightness was reported to be an important finding for the diagnosis of iNPH. On SPECT, patients with iNPH often show hyperperfusion of the high-convexity area. The authors tested 2 hypotheses regarding the SPECT finding: 1) it is relative hyperperfusion reflecting the increased gray matter density of the convexity, and 2) it is useful for the diagnosis of iNPH. The authors termed the SPECT finding the convexity apparent hyperperfusion (CAPPAH) sign. METHODS Two clinical studies were conducted. In study 1, SPECT was performed for 20 patients suspected of having iNPH, and regional cerebral blood flow (rCBF) of the high-convexity area was examined using quantitative analysis. Clinical differences between patients with the CAPPAH sign (CAP) and those without it (NCAP) were also compared. In study 2, the CAPPAH sign was retrospectively assessed in 30 patients with iNPH and 19 healthy controls using SPECT images and 3D stereotactic surface projection. RESULTS In study 1, rCBF of the high-convexity area of the CAP group was calculated as 35.2-43.7 ml/min/100 g, which is not higher than normal values of rCBF determined by SPECT. The NCAP group showed lower cognitive function and weaker responses to the removal of CSF than the CAP group. In study 2, the CAPPAH sign was positive only in patients with iNPH (24/30) and not in controls (sensitivity 80%, specificity 100%). The coincidence rate between tight high convexity on MRI and the CAPPAH sign was very high (28/30). CONCLUSIONS Patients with iNPH showed hyperperfusion of the high-convexity area on SPECT; however, the presence of the CAPPAH sign did not indicate real hyperperfusion of rCBF in the high-convexity area. The authors speculated that patients with iNPH without the CAPPAH sign, despite showing

Uniqueness of a pre-generator for $C_0$-semigroup on a general locally convex vector space

OpenAIRE

Lemle, Ludovic Dan; Wu, Liming

2007-01-01

The main purpose is to generalize a theorem of Arendt about uniqueness of $C_0$-semigroups from Banach space setting to the general locally convex vector spaces, more precisely, we show that cores are the only domains of uniqueness for $C_0$-semigroups on locally convex spaces. As an application, we find a necessary and sufficient condition for that the mass transport equation has one unique $L^1(\\R^d,dx)$ weak solution.

Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization

NARCIS (Netherlands)

Simonetto, A.; Jamali-Rad, H.

2015-01-01

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled, the dual decomposition scheme involves local parallel

Mean-square performance of a convex combination of two adaptive filters

DEFF Research Database (Denmark)

Garcia, Jeronimo; Figueiras-Vidal, A.R.; Sayed, A.H.

2006-01-01

Combination approaches provide an interesting way to improve adaptive filter performance. In this paper, we study the mean-square performance of a convex combination of two transversal filters. The individual filters are independently adapted using their own error signals, while the combination i...

3rd World Congress on Global Optimization in Engineering & Science

CERN Document Server

Ruan, Ning; Xing, Wenxun; WCGO-III; Advances in Global Optimization

2015-01-01

This proceedings volume addresses advances in global optimization—a multidisciplinary research field that deals with the analysis, characterization, and computation of global minima and/or maxima of nonlinear, non-convex, and nonsmooth functions in continuous or discrete forms. The volume contains selected papers from the third biannual World Congress on Global Optimization in Engineering & Science (WCGO), held in the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation; and complex simulation and supply chain analysis.

Three-Dimensional Synthetic Aperture Focusing Using a Rocking Convex Array Transducer

DEFF Research Database (Denmark)

Andresen, Henrik; Nikolov, Svetoslav; Pedersen, Mads Møller

2010-01-01

Volumetric imaging can be performed using 1-D arrays in combination with mechanical motion. Outside the elevation focus of the array, the resolution and contrast quickly degrade compared with the lateral plane, because of the fixed transducer focus. This paper shows the feasibility of using...... synthetic aperture focusing for enhancing the elevation focus for a convex rocking array. The method uses a virtual source (VS) for defocused multi-element transmit, and another VS in the elevation focus point. This allows a direct time-of-flight to be calculated for a given 3-D point. To avoid artifacts...... and increase SNR at the elevation VS, a plane-wave VS approach has been implemented. Simulations and measurements using an experimental scanner with a convex rocking array show an average improvement in resolution of 26% and 33%, respectively. This improvement is also seen in in vivo measurements...

SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints

Energy Technology Data Exchange (ETDEWEB)

Ungun, B [Stanford University, Stanford, CA (United States); Stanford University School of Medicine, Stanford, CA (United States); Fu, A; Xing, L [Stanford University School of Medicine, Stanford, CA (United States); Boyd, S [Stanford University, Stanford, CA (United States)

2016-06-15

Purpose: To develop a procedure for including dose constraints in convex programming-based approaches to treatment planning, and to support dynamic modification of such constraints during planning. Methods: We present a mathematical approach that allows mean dose, maximum dose, minimum dose and dose volume (i.e., percentile) constraints to be appended to any convex formulation of an inverse planning problem. The first three constraint types are convex and readily incorporated. Dose volume constraints are not convex, however, so we introduce a convex restriction that is related to CVaR-based approaches previously proposed in the literature. To compensate for the conservatism of this restriction, we propose a new two-pass algorithm that solves the restricted problem on a first pass and uses this solution to form exact constraints on a second pass. In another variant, we introduce slack variables for each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints. We implement the proposed methods in Python using the convex programming package cvxpy in conjunction with the open source convex solvers SCS and ECOS. Results: We show, for several cases taken from the clinic, that our proposed method meets specified constraints (often with margin) when they are feasible. Constraints are met exactly when we use the two-pass method, and infeasible constraints are replaced with the nearest feasible constraint when slacks are used. Finally, we introduce ConRad, a Python-embedded free software package for convex radiation therapy planning. ConRad implements the methods described above and offers a simple interface for specifying prescriptions and dose constraints. Conclusion: This work demonstrates the feasibility of using modifiable dose constraints in a convex formulation, making it practical to guide the treatment planning process with interactively specified dose constraints. This work was supported by the

SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints

International Nuclear Information System (INIS)

Ungun, B; Fu, A; Xing, L; Boyd, S

2016-01-01

Purpose: To develop a procedure for including dose constraints in convex programming-based approaches to treatment planning, and to support dynamic modification of such constraints during planning. Methods: We present a mathematical approach that allows mean dose, maximum dose, minimum dose and dose volume (i.e., percentile) constraints to be appended to any convex formulation of an inverse planning problem. The first three constraint types are convex and readily incorporated. Dose volume constraints are not convex, however, so we introduce a convex restriction that is related to CVaR-based approaches previously proposed in the literature. To compensate for the conservatism of this restriction, we propose a new two-pass algorithm that solves the restricted problem on a first pass and uses this solution to form exact constraints on a second pass. In another variant, we introduce slack variables for each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints. We implement the proposed methods in Python using the convex programming package cvxpy in conjunction with the open source convex solvers SCS and ECOS. Results: We show, for several cases taken from the clinic, that our proposed method meets specified constraints (often with margin) when they are feasible. Constraints are met exactly when we use the two-pass method, and infeasible constraints are replaced with the nearest feasible constraint when slacks are used. Finally, we introduce ConRad, a Python-embedded free software package for convex radiation therapy planning. ConRad implements the methods described above and offers a simple interface for specifying prescriptions and dose constraints. Conclusion: This work demonstrates the feasibility of using modifiable dose constraints in a convex formulation, making it practical to guide the treatment planning process with interactively specified dose constraints. This work was supported by the

Image restoration by the method of convex projections: part 1 theory.

Science.gov (United States)

Youla, D C; Webb, H

1982-01-01

A projection operator onto a closed convex set in Hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms. Moreover, it minimizes distance and is nonexpansive, and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds. In this paper, we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically. Their common conceptual basis is as follows. Every known property of an original image f is envisaged as restricting it to lie in a well-defined closed convex set. Thus, m such properties place f in the intersection E(0) = E(i) of the corresponding closed convex sets E(1),E(2),...EE(m). Given only the projection operators PE(i) onto the individual E(i)'s, i = 1 --> m, we restore f by recursive means. Clearly, in this approach, the realization of the P(i)'s in a Hilbert space setting is one of the major synthesis problems. Section I describes the geometrical significance of the three main theorems in considerable detail, and most of the underlying ideas are illustrated with the aid of simple diagrams. Section II presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal-processing applications, and the Appendix contains proofs of all the major results.

CudaPre3D: An Alternative Preprocessing Algorithm for Accelerating 3D Convex Hull Computation on the GPU

Directory of Open Access Journals (Sweden)

MEI, G.

2015-05-01

Full Text Available In the calculating of convex hulls for point sets, a preprocessing procedure that is to filter the input points by discarding non-extreme points is commonly used to improve the computational efficiency. We previously proposed a quite straightforward preprocessing approach for accelerating 2D convex hull computation on the GPU. In this paper, we extend that algorithm to being used in 3D cases. The basic ideas behind these two preprocessing algorithms are similar: first, several groups of extreme points are found according to the original set of input points and several rotated versions of the input set; then, a convex polyhedron is created using the found extreme points; and finally those interior points locating inside the formed convex polyhedron are discarded. Experimental results show that: when employing the proposed preprocessing algorithm, it achieves the speedups of about 4x on average and 5x to 6x in the best cases over the cases where the proposed approach is not used. In addition, more than 95 percent of the input points can be discarded in most experimental tests.

The role of convexity in perceptual completion: beyond good continuation.

Science.gov (United States)

Liu, Z; Jacobs, D W; Basri, R

1999-01-01

Since the seminal work of the Gestalt psychologists, there has been great interest in understanding what factors determine the perceptual organization of images. While the Gestaltists demonstrated the significance of grouping cues such as similarity, proximity and good continuation, it has not been well understood whether their catalog of grouping cues is complete--in part due to the paucity of effective methodologies for examining the significance of various grouping cues. We describe a novel, objective method to study perceptual grouping of planar regions separated by an occluder. We demonstrate that the stronger the grouping between two such regions, the harder it will be to resolve their relative stereoscopic depth. We use this new method to call into question many existing theories of perceptual completion (Ullman, S. (1976). Biological Cybernetics, 25, 1-6; Shashua, A., & Ullman, S. (1988). 2nd International Conference on Computer Vision (pp. 321-327); Parent, P., & Zucker, S. (1989). IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 823-839; Kellman, P. J., & Shipley, T. F. (1991). Cognitive psychology, Liveright, New York; Heitger, R., & von der Heydt, R. (1993). A computational model of neural contour processing, figure-ground segregation and illusory contours. In Internal Conference Computer Vision (pp. 32-40); Mumford, D. (1994). Algebraic geometry and its applications, Springer, New York; Williams, L. R., & Jacobs, D. W. (1997). Neural Computation, 9, 837-858) that are based on Gestalt grouping cues by demonstrating that convexity plays a strong role in perceptual completion. In some cases convexity dominates the effects of the well known Gestalt cue of good continuation. While convexity has been known to play a role in figure/ground segmentation (Rubin, 1927; Kanizsa & Gerbino, 1976), this is the first demonstration of its importance in perceptual completion.

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...

A deep cut ellipsoid algorithm for convex programming : Theory and applications

NARCIS (Netherlands)

J.B.G. Frenk (Hans); J.A.S. Gromicho (Joaquim); S. Zhang (Shuzhong)

1994-01-01

textabstractThis paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules

Sequential and Parallel Algorithms for Finding a Maximum Convex Polygon

DEFF Research Database (Denmark)

Fischer, Paul

1997-01-01

This paper investigates the problem where one is given a finite set of n points in the plane each of which is labeled either ?positive? or ?negative?. We consider bounded convex polygons, the vertices of which are positive points and which do not contain any negative point. It is shown how...... such a polygon which is maximal with respect to area can be found in time O(n³ log n). With the same running time one can also find such a polygon which contains a maximum number of positive points. If, in addition, the number of vertices of the polygon is restricted to be at most M, then the running time...... becomes O(M n³ log n). It is also shown how to find a maximum convex polygon which contains a given point in time O(n³ log n). Two parallel algorithms for the basic problem are also presented. The first one runs in time O(n log n) using O(n²) processors, the second one has polylogarithmic time but needs O...

A one-layer recurrent neural network for non-smooth convex optimization subject to linear inequality constraints

International Nuclear Information System (INIS)

Liu, Xiaolan; Zhou, Mi

2016-01-01

In this paper, a one-layer recurrent network is proposed for solving a non-smooth convex optimization subject to linear inequality constraints. Compared with the existing neural networks for optimization, the proposed neural network is capable of solving more general convex optimization with linear inequality constraints. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed as long as the designed parameters in the model are larger than the derived lower bounds.

Global Convergence of Arbitrary-Block Gradient Methods for Generalized Polyak-{\\L} ojasiewicz Functions

KAUST Repository

Csiba, Dominik

2017-09-09

In this paper we introduce two novel generalizations of the theory for gradient descent type methods in the proximal setting. First, we introduce the proportion function, which we further use to analyze all known (and many new) block-selection rules for block coordinate descent methods under a single framework. This framework includes randomized methods with uniform, non-uniform or even adaptive sampling strategies, as well as deterministic methods with batch, greedy or cyclic selection rules. Second, the theory of strongly-convex optimization was recently generalized to a specific class of non-convex functions satisfying the so-called Polyak-{\\\\L}ojasiewicz condition. To mirror this generalization in the weakly convex case, we introduce the Weak Polyak-{\\\\L}ojasiewicz condition, using which we give global convergence guarantees for a class of non-convex functions previously not considered in theory. Additionally, we establish (necessarily somewhat weaker) convergence guarantees for an even larger class of non-convex functions satisfying a certain smoothness assumption only. By combining the two abovementioned generalizations we recover the state-of-the-art convergence guarantees for a large class of previously known methods and setups as special cases of our general framework. Moreover, our frameworks allows for the derivation of new guarantees for many new combinations of methods and setups, as well as a large class of novel non-convex objectives. The flexibility of our approach offers a lot of potential for future research, as a new block selection procedure will have a convergence guarantee for all objectives considered in our framework, while a new objective analyzed under our approach will have a whole fleet of block selection rules with convergence guarantees readily available.

Global Convergence of Arbitrary-Block Gradient Methods for Generalized Polyak-{\\L} ojasiewicz Functions

KAUST Repository

Csiba, Dominik; Richtarik, Peter

2017-01-01

In this paper we introduce two novel generalizations of the theory for gradient descent type methods in the proximal setting. First, we introduce the proportion function, which we further use to analyze all known (and many new) block-selection rules for block coordinate descent methods under a single framework. This framework includes randomized methods with uniform, non-uniform or even adaptive sampling strategies, as well as deterministic methods with batch, greedy or cyclic selection rules. Second, the theory of strongly-convex optimization was recently generalized to a specific class of non-convex functions satisfying the so-called Polyak-{\\L}ojasiewicz condition. To mirror this generalization in the weakly convex case, we introduce the Weak Polyak-{\\L}ojasiewicz condition, using which we give global convergence guarantees for a class of non-convex functions previously not considered in theory. Additionally, we establish (necessarily somewhat weaker) convergence guarantees for an even larger class of non-convex functions satisfying a certain smoothness assumption only. By combining the two abovementioned generalizations we recover the state-of-the-art convergence guarantees for a large class of previously known methods and setups as special cases of our general framework. Moreover, our frameworks allows for the derivation of new guarantees for many new combinations of methods and setups, as well as a large class of novel non-convex objectives. The flexibility of our approach offers a lot of potential for future research, as a new block selection procedure will have a convergence guarantee for all objectives considered in our framework, while a new objective analyzed under our approach will have a whole fleet of block selection rules with convergence guarantees readily available.

Report on the observation of IAEA international emergency response exercise ConvEx-3(2008)

International Nuclear Information System (INIS)

Yamamoto, Kazuya; Sumiya, Akihiro

2009-02-01

The International Atomic Energy Agency IAEA carried out a large-scale international emergency response exercise under the designated name of ConvEx-3(2008), accompanying the national exercise of Mexico in July 2008. This review report summarizes two simultaneous observations of the exercises in Mexico and the IAEA headquarter during ConvEx-3(2008). Mexico has established a very steady nuclear emergency response system based on that of US, while only two BWR nuclear power units have been operated yet. The Mexican nuclear emergency response system and the emergency response activities of the Incident and Emergency Centre of the IAEA headquarter impressed important knowledge on observers that is helpful for enhancement of Japanese nuclear emergency response system in the future, e.g. establishment of Emergency Action Level and of implementation of long time exercise and enhancement of prompt protective actions. Japan had established the Act on Special Measures Concerning Nuclear Emergency Preparedness and has developed the nuclear disaster prevention system since the JCO Criticality Accident in Tokai-mura. Now is the new stage to enhance the system on the view point of prevention of a nuclear disaster affecting the neighboring countries' or prevention of a nuclear disaster which arise from the neighboring countries'. The ConvEx-3(2008) suggested key issues about nuclear disaster prevention related to the neighboring countries, e.g. establishment of much wider environmental monitoring and of international assistance system against a foreign nuclear disaster. The observations of the IAEA ConvEx-3(2008) exercise described in this review report were funded by the MEXT (Ministry of Education, Culture, Sports, Science and Technology). (author)

A DEEP CUT ELLIPSOID ALGORITHM FOR CONVEX-PROGRAMMING - THEORY AND APPLICATIONS

NARCIS (Netherlands)

FRENK, JBG; GROMICHO, J; ZHANG, S

1994-01-01

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent

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 Deep Cut Ellipsoid Algorithm for convex Programming: theory and Applications

NARCIS (Netherlands)

Frenk, J.B.G.; Gromicho Dos Santos, J.A.; Zhang, S.

1994-01-01

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent

Novel method of finding extreme edges in a convex set of N-dimension vectors

Science.gov (United States)

Hu, Chia-Lun J.

2001-11-01

As we published in the last few years, for a binary neural network pattern recognition system to learn a given mapping {Um mapped to Vm, m=1 to M} where um is an N- dimension analog (pattern) vector, Vm is a P-bit binary (classification) vector, the if-and-only-if (IFF) condition that this network can learn this mapping is that each i-set in {Ymi, m=1 to M} (where Ymithere existsVmiUm and Vmi=+1 or -1, is the i-th bit of VR-m).)(i=1 to P and there are P sets included here.) Is POSITIVELY, LINEARLY, INDEPENDENT or PLI. We have shown that this PLI condition is MORE GENERAL than the convexity condition applied to a set of N-vectors. In the design of old learning machines, we know that if a set of N-dimension analog vectors form a convex set, and if the machine can learn the boundary vectors (or extreme edges) of this set, then it can definitely learn the inside vectors contained in this POLYHEDRON CONE. This paper reports a new method and new algorithm to find the boundary vectors of a convex set of ND analog vectors.

Lift-and-fill face lift: integrating the fat compartments.

Science.gov (United States)

Rohrich, Rod J; Ghavami, Ashkan; Constantine, Fadi C; Unger, Jacob; Mojallal, Ali

2014-06-01

Recent discovery of the numerous fat compartments of the face has improved our ability to more precisely restore facial volume while rejuvenating it through differential superficial musculoaponeurotic system treatment. Incorporation of selective fat compartment volume restoration along with superficial musculoaponeurotic system manipulation allows for improved control in recontouring while addressing one of the key problems in facial aging, namely, volume deflation. This theory was evaluated by assessing the contour changes from simultaneous face "lifting" and "filling" through fat compartment-guided facial fat transfer. A review of 100 face-lift patients was performed. All patients had an individualized component face lift with fat grafting to the nasolabial fold, deep malar, and high/lateral malar fat compartment locations. Photographic analysis using a computer program was conducted on oblique facial views preoperatively and postoperatively, to obtain the most projected malar contour point. Two independent observers visually evaluated the malar prominence and nasolabial fold improvements based on standardized photographs. Nasolabial fold improved by at least one grade in 81 percent and by over one grade in 11 percent. Malar prominence average projection increase was 13.47 percent and the average amount of lift was 12.24 percent. The malar prominence score improved by at least one grade in 62 percent of the patients postoperatively, and 9 percent had a greater than one grade improvement. Twenty-eight percent of the patients had a convex malar prominence postoperatively compared with 6 percent preoperatively. Malar prominence improved by at least one grade in 63 percent and by over one grade in 10 percent. The lift-and-fill face lift merges two key concepts in facial rejuvenation: (1) effective tissue manipulation by means of lifting and tightening in differential vectors according to original facial asymmetry and shape; and (2) selective fat compartment filling

Framework to model neutral particle flux in convex high aspect ratio structures using one-dimensional radiosity

Science.gov (United States)

Manstetten, Paul; Filipovic, Lado; Hössinger, Andreas; Weinbub, Josef; Selberherr, Siegfried

2017-02-01

We present a computationally efficient framework to compute the neutral flux in high aspect ratio structures during three-dimensional plasma etching simulations. The framework is based on a one-dimensional radiosity approach and is applicable to simulations of convex rotationally symmetric holes and convex symmetric trenches with a constant cross-section. The framework is intended to replace the full three-dimensional simulation step required to calculate the neutral flux during plasma etching simulations. Especially for high aspect ratio structures, the computational effort, required to perform the full three-dimensional simulation of the neutral flux at the desired spatial resolution, conflicts with practical simulation time constraints. Our results are in agreement with those obtained by three-dimensional Monte Carlo based ray tracing simulations for various aspect ratios and convex geometries. With this framework we present a comprehensive analysis of the influence of the geometrical properties of high aspect ratio structures as well as of the particle sticking probability on the neutral particle flux.

Convex order approximations in case of cash flows of mixed signs

NARCIS (Netherlands)

Dhaene, J.; Goovaerts, M.J.; Vanmaele, M.; van Weert, K.

2012-01-01

In Van Weert et al. (2010), results are obtained showing that, when allowing some of the cash flows to be negative, convex order lower bound approximations can still be used to solve general investment problems in a context of provisioning or terminal wealth. In this paper, a correction and further

Gröbner bases and convex polytopes

CERN Document Server

Sturmfels, Bernd

1995-01-01

This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gröbner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.

The role of concavo-convex walls of a nanopore on the density profile, adsorption, solvation force, and capillary condensation of confined fluids: A DFT study

International Nuclear Information System (INIS)

Helmi, Abbas; Keshavarzi, Ezat

2014-01-01

Highlights: • The effect of concavo-convex walls of nanopores on the density profile was studied. • For HS fluids the contact density at concave wall is greater than for convex wall. • For Yukawa fluid the contact density at concave wall can be less than convex wall. • Capillary condensation was observed for Yukawa fluids in the homocentric pores. - Abstract: We investigate the effects of concavo-convex walls of a nanopore on the structure and certain thermodynamic properties of confined fluids. Adsorption, solvation force, and capillary condensation in a nanopore formed between two homocentric spheres will be determined using the MFMT. For hard sphere fluids, contact density is greater at the concave wall than it is at the convex wall. In Yukawa fluids, for the thermodynamic state in which the energy effect is the dominant factor, contact density at a concave wall is less than that at a convex wall; this will be reversed for the thermodynamic state in which the entropy effect is the dominant factor. It is possible to find thermodynamic states in which contact densities at concave and convex walls become identical. The adsorption and solvation force of hard sphere fluid show an oscillatory behavior versus H. Capillary condensation is in certain cases observed for Yukawa fluids

Convex Bodies With Minimal Volume Product in R^2 --- A New Proof

OpenAIRE

Lin, Youjiang

2010-01-01

In this paper, a new proof of the following result is given: The product of the volumes of an origin symmetric convex bodies $K$ in R^2 and of its polar body is minimal if and only if $K$ is a parallelogram.

Selection and specification criteria for fills for cut-and-fill mining

Energy Technology Data Exchange (ETDEWEB)

Thomas, E. G.

1980-05-15

Because of significant differences in placement and loading conditions, the ideal fill material for a cut-and-fill operation has different characteristics to those for a fill for a filled open stoping operation. The differing requirements of the two mining operations must be understood and accounted for in establishing fill selection and specification criteria. Within the paper, aspects of the particular requirements of cut-and-fill mining are analyzed and related to the specific fill tests and properties required. Emphasis is placed upon the role of fill in ground support, though this cannot be isolated from overall fill performance. Where appropriate, test data are introduced and areas requiring continuing research highlighted.

Equilibrium prices supported by dual price functions in markets with non-convexities

International Nuclear Information System (INIS)

Bjoerndal, Mette; Joernsten, Kurt

2004-06-01

The issue of finding market clearing prices in markets with non-convexities has had a renewed interest due to the deregulation of the electricity sector. In the day-ahead electricity market, equilibrium prices are calculated based on bids from generators and consumers. In most of the existing markets, several generation technologies are present, some of which have considerable non-convexities, such as capacity limitations and large start up costs. In this paper we present equilibrium prices composed of a commodity price and an uplift charge. The prices are based on the generation of a separating valid inequality that supports the optimal resource allocation. In the case when the sub-problem generated as the integer variables are held fixed to their optimal values possess the integrality property, the generated prices are also supported by non-linear price-functions that are the basis for integer programming duality. (Author)

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.

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.

Determining Representative Elementary Volume For Multiple Petrophysical Parameters using a Convex Hull Analysis of Digital Rock Data

Science.gov (United States)

Shah, S.; Gray, F.; Yang, J.; Crawshaw, J.; Boek, E.

2016-12-01

Advances in 3D pore-scale imaging and computational methods have allowed an exceptionally detailed quantitative and qualitative analysis of the fluid flow in complex porous media. A fundamental problem in pore-scale imaging and modelling is how to represent and model the range of scales encountered in porous media, starting from the smallest pore spaces. In this study, a novel method is presented for determining the representative elementary volume (REV) of a rock for several parameters simultaneously. We calculate the two main macroscopic petrophysical parameters, porosity and single-phase permeability, using micro CT imaging and Lattice Boltzmann (LB) simulations for 14 different porous media, including sandpacks, sandstones and carbonates. The concept of the `Convex Hull' is then applied to calculate the REV for both parameters simultaneously using a plot of the area of the convex hull as a function of the sub-volume, capturing the different scales of heterogeneity from the pore-scale imaging. The results also show that the area of the convex hull (for well-chosen parameters such as the log of the permeability and the porosity) decays exponentially with sub-sample size suggesting a computationally efficient way to determine the system size needed to calculate the parameters to high accuracy (small convex hull area). Finally we propose using a characteristic length such as the pore size to choose an efficient absolute voxel size for the numerical rock.

Extreme points of the convex set of joint probability distributions with ...

Indian Academy of Sciences (India)

Here we address the following problem: If G is a standard ... convex set of all joint probability distributions on the product Borel space (X1 ×X2, F1 ⊗. F2) which .... cannot be identically zero when X and Y vary in A1 and u and v vary in H2. Thus.

Environmental protection stability of river bed and banks using convex, concave, and linear bed sills.

Science.gov (United States)

Keshavarzi, Alireza; Noori, Lila Khaje

2010-12-01

River bed scourings are a major environmental problem for fish and aquatic habitat resources. In this study, to prevent river bed and banks from scouring, different types of bed sills including convex, concave and linear patterns were installed in a movable channel bed in a laboratory flume. The bed sills were tested with nine different arrangements and under different flow conditions. To find the most effective bed sill pattern, the scouring depth was measured downstream of the bed sill for a long experimental duration. The scour depth was measured at the middle and at the end of each experimental test for different ratios of the arch radius to the channel width [r/w]. The experimental results indicated that the convex pattern with r/w=0.35 produced minimum bed scouring depth at the center line whereas the concave pattern with r/w=0.23 produced the minimum scour depth at the wall banks. Therefore, the convex pattern was the most effective configuration for prevention of scouring at the center line of the river while the concave pattern was very effective to prevent scouring at the river banks. These findings can be suggested to be used in practical applications.

Method of convex rigid frames and applications in studies of multipartite quNit pure states

International Nuclear Information System (INIS)

Zhong Zaizhe

2005-01-01

In this letter, we suggest a method of convex rigid frames in the studies of multipartite quNit pure states. We illustrate what the convex rigid frames are, and what is their method. As applications, we use this method to solve some basic problems and give some new results (three theorems): the problem of the partial separability of the multipartite quNit pure states and its geometric explanation; the problem of the classification of multipartite quNit pure states, giving a perfect explanation of the local unitary transformations; thirdly, we discuss the invariants of classes and give a possible physical explanation. (letter to the editor)

Parthood and Convexity as the Basic Notions of a Theory of Space

DEFF Research Database (Denmark)

Robering, Klaus

A deductive system of geometry is presented which is based on atomistic mereology ("mereology with points'') and the notion of convexity. The system is formulated in a liberal many-sorted logic which makes use of class-theoretic notions without however adopting any comprehension axioms. The geome...

On the Monotonicity and Log-Convexity of a Four-Parameter Homogeneous Mean

Directory of Open Access Journals (Sweden)

Yang Zhen-Hang

2008-01-01

Full Text Available Abstract A four-parameter homogeneous mean is defined by another approach. The criterion of its monotonicity and logarithmically convexity is presented, and three refined chains of inequalities for two-parameter mean values are deduced which contain many new and classical inequalities for means.

Hermite-Hadamard Type Integral Inequalities for Functions Whose Second-Order Mixed Derivatives Are Coordinated (s,m-P-Convex

Directory of Open Access Journals (Sweden)

Yu-Mei Bai

2018-01-01

Full Text Available We establish some new Hermite-Hadamard type integral inequalities for functions whose second-order mixed derivatives are coordinated (s,m-P-convex. An expression form of Hermite-Hadamard type integral inequalities via the beta function and the hypergeometric function is also presented. Our results provide a significant complement to the work of Wu et al. involving the Hermite-Hadamard type inequalities for coordinated (s,m-P-convex functions in an earlier article.

From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation

International Nuclear Information System (INIS)

Egozcue, J.; Meziat, R.; Pedregal, P.

2002-01-01

We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature

Structural Health Monitoring of Tall Buildings with Numerical Integrator and Convex-Concave Hull Classification

Directory of Open Access Journals (Sweden)

Suresh Thenozhi

2012-01-01

Full Text Available An important objective of health monitoring systems for tall buildings is to diagnose the state of the building and to evaluate its possible damage. In this paper, we use our prototype to evaluate our data-mining approach for the fault monitoring. The offset cancellation and high-pass filtering techniques are combined effectively to solve common problems in numerical integration of acceleration signals in real-time applications. The integration accuracy is improved compared with other numerical integrators. Then we introduce a novel method for support vector machine (SVM classification, called convex-concave hull. We use the Jarvis march method to decide the concave (nonconvex hull for the inseparable points. Finally the vertices of the convex-concave hull are applied for SVM training.

Convex relaxation of Optimal Power Flow in Distribution Feeders with embedded solar power

DEFF Research Database (Denmark)

Hermann, Alexander Niels August; Wu, Qiuwei; Huang, Shaojun

2016-01-01

There is an increasing interest in using Distributed Energy Resources (DER) directly coupled to end user distribution feeders. This poses an array of challenges because most of today’s distribution feeders are designed for unidirectional power flow. Therefore when installing DERs such as solar...... panels with uncontrolled inverters, the upper limit of installable capacity is quickly reached in many of today’s distribution feeders. This problem can often be mitigated by optimally controlling the voltage angles of inverters. However, the optimal power flow problem in its standard form is a large...... scale non-convex optimization problem, and thus can’t be solved precisely and also is computationally heavy and intractable for large systems. This paper examines the use of a convex relaxation using Semi-definite programming to optimally control solar power inverters in a distribution grid in order...

Global robust exponential stability analysis for interval recurrent neural networks

International Nuclear Information System (INIS)

Xu Shengyuan; Lam, James; Ho, Daniel W.C.; Zou Yun

2004-01-01

This Letter investigates the problem of robust global exponential stability analysis for interval recurrent neural networks (RNNs) via the linear matrix inequality (LMI) approach. The values of the time-invariant uncertain parameters are assumed to be bounded within given compact sets. An improved condition for the existence of a unique equilibrium point and its global exponential stability of RNNs with known parameters is proposed. Based on this, a sufficient condition for the global robust exponential stability for interval RNNs is obtained. Both of the conditions are expressed in terms of LMIs, which can be checked easily by various recently developed convex optimization algorithms. Examples are provided to demonstrate the reduced conservatism of the proposed exponential stability condition

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.

On the structure of self-affine convex bodies

Energy Technology Data Exchange (ETDEWEB)

Voynov, A S [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2013-08-31

We study the structure of convex bodies in R{sup d} that can be represented as a union of their affine images with no common interior points. Such bodies are called self-affine. Vallet's conjecture on the structure of self-affine bodies was proved for d = 2 by Richter in 2011. In the present paper we disprove the conjecture for all d≥3 and derive a detailed description of self-affine bodies in R{sup 3}. Also we consider the relation between properties of self-affine bodies and functional equations with a contraction of an argument. Bibliography: 10 titles.

Stability of the Minimizers of Least Squares with a Non-Convex Regularization. Part I: Local Behavior

International Nuclear Information System (INIS)

Durand, S.; Nikolova, M.

2006-01-01

Many estimation problems amount to minimizing a piecewise C m objective function, with m ≥ 2, composed of a quadratic data-fidelity term and a general regularization term. It is widely accepted that the minimizers obtained using non-convex and possibly non-smooth regularization terms are frequently good estimates. However, few facts are known on the ways to control properties of these minimizers. This work is dedicated to the stability of the minimizers of such objective functions with respect to variations of the data. It consists of two parts: first we consider all local minimizers, whereas in a second part we derive results on global minimizers. In this part we focus on data points such that every local minimizer is isolated and results from a C m-1 local minimizer function, defined on some neighborhood. We demonstrate that all data points for which this fails form a set whose closure is negligible

Geometry of Moishezon and 1-convex spaces II: Projectivity of Moishezon spaces and its non-compact version

International Nuclear Information System (INIS)

Sitaramayya, M.

1993-11-01

After a brief review of the geometry of Moishezon spaces, their relation with l-convex spaces and a reasonable and up to date understanding of the obstructions for projectivity of Moishezon objects both in singular and non-singular case is given. The geometry of l-convex manifolds and with l-dimensional exceptional set is studied and some problems and conjectures are stated. The tools of cohomology vanishing theorems important for the subject are briefly sketched. Compactifications of C 3 and Stein spaces are finally outlined. given. 111 refs, 2 figs

Geometry of power flows and convex-relaxed power flows in distribution networks with high penetration of renewables

DEFF Research Database (Denmark)

Huang, Shaojun; Wu, Qiuwei; Zhao, Haoran

2016-01-01

Renewable energies are increasingly integrated in electric distribution networks and will cause severe overvoltage issues. Smart grid technologies make it possible to use coordinated control to mitigate the overvoltage issues and the optimal power flow (OPF) method is proven to be efficient...... in the applications such as curtailment management and reactive power control. Nonconvex nature of the OPF makes it difficult to solve and convex relaxation is a promising method to solve the OPF very efficiently. This paper investigates the geometry of the power flows and the convex-relaxed power flows when high...

First-order convex feasibility algorithms for x-ray CT

DEFF Research Database (Denmark)

Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan

2013-01-01

Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times...... problems. Conclusions: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited...

Safety Distances for hydrogen filling stations

Energy Technology Data Exchange (ETDEWEB)

Matthijsen, A. J. C. M.; Kooi, E. S.

2005-07-01

In the Netherlands there is a growing interest in using natural gas as a transport fuel. The most important drivers behind this development are formed by poor inner city air quality and the decision to close several LPG filling stations. Dwellings are not allowed within the safety distances of 45 or 110 meters from the tanker filling point of these LPG stations, depending on the capacity of the station. Another driver is global warming. We are carrying out a study on station supply, compression, storage and filling for natural gas stations, and a similar, simultaneous study on hydrogen as a followup to our risk analysis for the hydrogen filling station in Amsterdam. Here, three buses drive on hydrogen as part of the European CUTE project. Driving on natural gas is an important step in the transition to cars on hydrogen. This study was commissioned by the Dutch Ministry of Spatial Planning, Housing and the Environment to advise on external safety aspects of future hydrogen filling stations. According to Dutch law homes may not be built within an individual risk contour of 10-6 per year of a dangerous object, such as a plant with hazardous materials or a filling station. An individual risk contour of 10-6 is represented by a line around a dangerous object that connects locations with an individual risk level of 10-6 per year. An individual 'located' within this contour line has a chance of one per million per year or more to be killed as a result of an accident caused by this object. The longest distance between the object and such a contour is called a 'safety distance'. A study on safety distances is now in progress for different kinds of hydrogen filling stations (e. g. gaseous and liquid hydrogen) and for different capacities, such as big, medium and small stations. The focus is on different kinds of hydrogen production and the hydrogen supply of the filling station. To decide on the design and supply of the hydrogen station, we examined the

Coarse-convex-compactification approach to numerical solution of nonconvex variational problems

Czech Academy of Sciences Publication Activity Database

Meziat, R.; Roubíček, Tomáš; Patino, D.

2010-01-01

Roč. 31, č. 4 (2010), s. 460-488 ISSN 0163-0563 Grant - others:GA MŠk(CZ) LC06052 Program:LC Institutional research plan: CEZ:AV0Z20760514 Keywords : convex approximations * method of moments * relaxed variational problems Subject RIV: BA - General Mathematics Impact factor: 0.687, year: 2010 http://www.informaworld.com/smpp/content~db=all~content=a922886514~frm=titlelink

Global optimization methods for engineering design

Science.gov (United States)

Arora, Jasbir S.

1990-01-01

The problem is to find a global minimum for the Problem P. Necessary and sufficient conditions are available for local optimality. However, global solution can be assured only under the assumption of convexity of the problem. If the constraint set S is compact and the cost function is continuous on it, existence of a global minimum is guaranteed. However, in view of the fact that no global optimality conditions are available, a global solution can be found only by an exhaustive search to satisfy Inequality. The exhaustive search can be organized in such a way that the entire design space need not be searched for the solution. This way the computational burden is reduced somewhat. It is concluded that zooming algorithm for global optimizations appears to be a good alternative to stochastic methods. More testing is needed; a general, robust, and efficient local minimizer is required. IDESIGN was used in all numerical calculations which is based on a sequential quadratic programming algorithm, and since feasible set keeps on shrinking, a good algorithm to find an initial feasible point is required. Such algorithms need to be developed and evaluated.

Convex Hypersurfaces and $L^p$ Estimates for Schr\\"odinger Equations

OpenAIRE

Zheng, Quan; Yao, Xiaohua; Fan, Da

2004-01-01

This paper is concerned with Schr\\"odinger equations whose principal operators are homogeneous elliptic. When the corresponding level hypersurface is convex, we show the $L^p$-$L^q$ estimate of solution operator in free case. This estimate, combining with the results of fractionally integrated groups, allows us to further obtain the $L^p$ estimate of solutions for the initial data belonging to a dense subset of $L^p$ in the case of integrable potentials.

Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities

Czech Academy of Sciences Publication Activity Database

Imre, C.; Matúš, František

2012-01-01

Roč. 48, č. 4 (2012), s. 637-689 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539; GA ČR GAP202/10/0618 Institutional support: RVO:67985556 Keywords : maximum entropy * moment constraint * generalized primal/dual solutions * normal integrand * convex duality * Bregman projection * inference principles Subject RIV: BA - General Mathematics Impact factor: 0.619, year: 2012 http://library.utia.cas.cz/separaty/2012/MTR/matus-0381750.pdf

DEVELOPMENTS OF POLYHEDRA USING OBLIQUE COORDINATES

Directory of Open Access Journals (Sweden)

J. Akiyama

2007-04-01

Full Text Available This paper is an exposition of the results in the paper entitled "Convex Development of a Regular Tetrahedron" by J. Akiyama, et. al. [1]. We fill in the detail which have been omitted in the paper. We determine all convex developments of a regular tetrahedron V using a tiling generated by V and we arrive at conditions for convex polygons to be convex develpments of V . Moreover, we identify all convex polyhedra whose convex developments can be determined by the method used for V .

Full correspondence between asymmetric filling of slits and first-order phase transition lines

Directory of Open Access Journals (Sweden)

Leszek Szybisz

2011-12-01

Full Text Available Adsorption on single planar walls and filling of slits with identical planar walls are investigated in the frame of the density functional theory. In this sort of slits the external potential is symmetric with respect to its central plane. Calculations were carried out by applying both the canonical and grand canonical ensembles (CE and GCE, respectively. The behavior is analyzed by varying the strength of the adsorbate-substrate attraction, the temperature T, and the coverage Γℓ. Results obtained for physisorption of Xe on alkaline surfaces are reported in the present work. Prewetting (PW lines and wetting temperatures, Tw, are determined from the analysis of adsorption on single walls. The filling of slits is analyzed for temperatures T > Tw. It is found that whenever for a given Xe-substrate combination the adsorption on a single wall exhibits a first-order wetting transition then asymmetric profiles that break the left-right symmetry of the external potential appear in the filling of an equivalent slit. These spontaneously symmetry breaking (SSB solutions occur in a restricted range of Γℓ with a T-dependent width. In the case of closed slits analyzed in the CE scheme, the obtained asymmetric profiles exhibit lower Helmholtz free energies than the symmetric species and, therefore, could be stabilized in this geometry. For open slits, the GCE scheme yields all the symmetric and SSB states in the corresponding convex regimes of the free energy. It is shown that both the CE and the GCE frames yield three coexistent states, two symmetric and one asymmetric twofold degenerate. Both a PW line and the related SSB effect terminate at the same temperature. For rather strongly attractive surfaces reentrant SSB states are found at a fixed value of T.

Global existence for a quasi-linear evolution equation with a non-convex energy

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Petzeltová, Hana

2002-01-01

Roč. 354, č. 4 (2002), s. 1421-1437 ISSN 0002-9947 R&D Projects: GA AV ČR IAA1019002 Keywords : existence of global %initial-boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.664, year: 2002

Computation of complexity measures of morphologically significant zones decomposed from binary fractal sets via multiscale convexity analysis

International Nuclear Information System (INIS)

Lim, Sin Liang; Koo, Voon Chet; Daya Sagar, B.S.

2009-01-01

Multiscale convexity analysis of certain fractal binary objects-like 8-segment Koch quadric, Koch triadic, and random Koch quadric and triadic islands-is performed via (i) morphologic openings with respect to recursively changing the size of a template, and (ii) construction of convex hulls through half-plane closings. Based on scale vs convexity measure relationship, transition levels between the morphologic regimes are determined as crossover scales. These crossover scales are taken as the basis to segment binary fractal objects into various morphologically prominent zones. Each segmented zone is characterized through normalized morphologic complexity measures. Despite the fact that there is no notably significant relationship between the zone-wise complexity measures and fractal dimensions computed by conventional box counting method, fractal objects-whether they are generated deterministically or by introducing randomness-possess morphologically significant sub-zones with varied degrees of spatial complexities. Classification of realistic fractal sets and/or fields according to sub-zones possessing varied degrees of spatial complexities provides insight to explore links with the physical processes involved in the formation of fractal-like phenomena.

Convex models and probabilistic approach of nonlinear fatigue failure

International Nuclear Information System (INIS)

Qiu Zhiping; Lin Qiang; Wang Xiaojun

2008-01-01

This paper is concerned with the nonlinear fatigue failure problem with uncertainties in the structural systems. In the present study, in order to solve the nonlinear problem by convex models, the theory of ellipsoidal algebra with the help of the thought of interval analysis is applied. In terms of the inclusion monotonic property of ellipsoidal functions, the nonlinear fatigue failure problem with uncertainties can be solved. A numerical example of 25-bar truss structures is given to illustrate the efficiency of the presented method in comparison with the probabilistic approach

Elastic energy of liquid crystals in convex polyhedra

International Nuclear Information System (INIS)

Majumdar, A; Robbins, J M; Zyskin, M

2004-01-01

We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants. For a right rectangular prism and a large class of topologies, we derive upper bounds by introducing test configurations constructed from local conformal solutions of the Euler-Lagrange equation. The ratio of the upper and lower bounds depends only on the aspect ratios of the prism. As the aspect ratios are varied, the minimum-energy conformal state undergoes a sharp transition from being smooth to having singularities on the edges. (letter to the editor)

On the Fermat-Lagrange principle for mixed smooth convex extremal problems

International Nuclear Information System (INIS)

Brinkhuis, Ya

2001-01-01

A simple geometric condition that can be attached to an extremal problem of a fairly general form included in a family of problems is indicated. This is used to demonstrate that the task of formulating a uniform condition for smooth convex problems can be satisfactorily accomplished. On the other hand, the necessity of this new condition of optimality is proved under certain technical assumptions

Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses.

Science.gov (United States)

Schein, Stan; Gayed, James Maurice

2014-02-25

The three known classes of convex polyhedron with equal edge lengths and polyhedral symmetry--tetrahedral, octahedral, and icosahedral--are the 5 Platonic polyhedra, the 13 Archimedean polyhedra--including the truncated icosahedron or soccer ball--and the 2 rhombic polyhedra reported by Johannes Kepler in 1611. (Some carbon fullerenes, inorganic cages, icosahedral viruses, geodesic structures, and protein complexes resemble these fundamental shapes.) Here we add a fourth class, "Goldberg polyhedra," which are also convex and equilateral. We begin by decorating each of the triangular facets of a tetrahedron, an octahedron, or an icosahedron with the T vertices and connecting edges of a "Goldberg triangle." We obtain the unique set of internal angles in each planar face of each polyhedron by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, and the variables are a subset of the internal angles in 6gons. Like the faces in Kepler's rhombic polyhedra, the 6gon faces in Goldberg polyhedra are equilateral and planar but not equiangular. We show that there is just a single tetrahedral Goldberg polyhedron, a single octahedral one, and a systematic, countable infinity of icosahedral ones, one for each Goldberg triangle. Unlike carbon fullerenes and faceted viruses, the icosahedral Goldberg polyhedra are nearly spherical. The reasoning and techniques presented here will enable discovery of still more classes of convex equilateral polyhedra with polyhedral symmetry.

Measurement of laser welding pool geometry using a closed convex active contour model

International Nuclear Information System (INIS)

Zheng, Rui; Zhang, Pu; Duan, Aiqing; Xiao, Peng

2014-01-01

The purpose of this study was to develop a computer vision method to measure geometric parameters of the weld pool in a deep penetration CO 2 laser welding system. Accurate measurement was achieved by removing a huge amount of interference caused by spatter, arc light and plasma to extract the true weld pool contour. This paper introduces a closed convex active contour (CCAC) model derived from the active contour model (snake model), which is a more robust high-level vision method than the traditional low-level vision methods. We made an improvement by integrating an active contour with the information that the weld pool contour is almost a closed convex curve. An effective thresholding method and an improved greedy algorithm are also given to complement the CCAC model. These influences can be effectively removed by using the CCAC model to acquire and measure the weld pool contour accurately and relatively fast. (paper)

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.

A Sequential Convex Semidefinite Programming Algorithm for Multiple-Load Free Material Optimization

Czech Academy of Sciences Publication Activity Database

Stingl, M.; Kočvara, Michal; Leugering, G.

2009-01-01

Roč. 20, č. 1 (2009), s. 130-155 ISSN 1052-6234 R&D Projects: GA AV ČR IAA1075402 Grant - others:commision EU(XE) EU-FP6-30717 Institutional research plan: CEZ:AV0Z10750506 Keywords : structural optimization * material optimization * semidefinite programming * sequential convex programming Subject RIV: BA - General Mathematics Impact factor: 1.429, year: 2009

Multiobjective optimization of classifiers by means of 3D convex-hull-based evolutionary algorithms

NARCIS (Netherlands)

Zhao, J.; Basto, Fernandes V.; Jiao, L.; Yevseyeva, I.; Asep, Maulana A.; Li, R.; Bäck, T.H.W.; Tang, T.; Michael, Emmerich T. M.

2016-01-01

The receiver operating characteristic (ROC) and detection error tradeoff(DET) curves are frequently used in the machine learning community to analyze the performance of binary classifiers. Recently, the convex-hull-based multiobjective genetic programming algorithm was proposed and successfully

Perimeter generating functions for the mean-squared radius of gyration of convex polygons

International Nuclear Information System (INIS)

Jensen, Iwan

2005-01-01

We have derived long series expansions for the perimeter generating functions of the radius of gyration of various polygons with a convexity constraint. Using the series we numerically find simple (algebraic) exact solutions for the generating functions. In all cases the size exponent ν 1. (letter to the editor)

The Lp Lp Lp-curvature images of convex bodies and Lp Lp Lp ...

Indian Academy of Sciences (India)

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 ...

Annuity factors, duration and convexity : insights from a financial engineering perspective

OpenAIRE

Ekern, Steinar

1998-01-01

This paper applies a unified and integrative financial engineering perspective to key derived concepts in traditional fixed income analysis, with the purpose of enhancing conceptual insights and motivating computational applications. The emphasis on annuity factors and their impact on duration and convexity differs from the focus prevailing in related discussions. By decomposing the cashflow streams of a coupon bond into different, specific, and clearly defined portfolios of component bonds w...

Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms

OpenAIRE

Chen, Pin-Yu; Hero, Alfred O.

2017-01-01

Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. Non-standard multilayer graph clustering methods are needed for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a multilayer spectral graph clustering (SGC) framework that performs convex layer aggregation. Under a multilayer signal plus noise model, we provide a phase transition analys...

Narrow CSF space at high convexity and high midline areas in idiopathic normal pressure hydrocephalus detected by axial and coronal MRI

International Nuclear Information System (INIS)

Sasaki, Makoto; Honda, Satoshi; Yuasa, Tatsuhiko; Iwamura, Akihide; Shibata, Eri; Ohba, Hideki

2008-01-01

The aim of this study was to determine the performance of axial and coronal magnetic resonance imaging (MRI) in detecting the narrowing of the cerebrospinal fluid (CSF) space at the high convexity and high midline areas, which is speculated to be one of the clinical characteristics of idiopathic normal pressure hydrocephalus (iNPH). We retrospectively examined axial and coronal T1-weighted images of 14 iNPH patients and 12 age-matched controls. The narrowness of the CSF space at the high convexity/midline was blindly evaluated by five raters using a continuous confidence rating scale for receiver operating characteristic (ROC) analysis. Axial and coronal imaging accurately determined the presence of the narrow cisterns/sulci at the high convexity/midline and was capable of predicting probable/definite iNPH with a high degree of accuracy. there were also no significant differences in the detection of this finding between the axial and coronal images. Both axial and coronal T1-weighted MRI can detect the narrow CSF space at the high convexity/midline accurately and may therefore facilitate clinicians in choosing a management strategy for iNPH patients. (orig.)

Narrow CSF space at high convexity and high midline areas in idiopathic normal pressure hydrocephalus detected by axial and coronal MRI

Energy Technology Data Exchange (ETDEWEB)

Sasaki, Makoto [Iwate Medical University, Department of Radiology, Morioka (Japan); Honda, Satoshi [St. Luke' s International Hospital, Department of Radiology, Tokyo (Japan); Yuasa, Tatsuhiko; Iwamura, Akihide [Kohnodai Hospital, National Center of Neurology and Psychiatry, Department of Neurology, Ichikawa (Japan); Shibata, Eri [Iwate Medical University, Department of Neuropsychiatry, Morioka (Japan); Ohba, Hideki [Iwate Medical University, Department of Neurology, Morioka (Japan)

2008-02-15

The aim of this study was to determine the performance of axial and coronal magnetic resonance imaging (MRI) in detecting the narrowing of the cerebrospinal fluid (CSF) space at the high convexity and high midline areas, which is speculated to be one of the clinical characteristics of idiopathic normal pressure hydrocephalus (iNPH). We retrospectively examined axial and coronal T1-weighted images of 14 iNPH patients and 12 age-matched controls. The narrowness of the CSF space at the high convexity/midline was blindly evaluated by five raters using a continuous confidence rating scale for receiver operating characteristic (ROC) analysis. Axial and coronal imaging accurately determined the presence of the narrow cisterns/sulci at the high convexity/midline and was capable of predicting probable/definite iNPH with a high degree of accuracy. there were also no significant differences in the detection of this finding between the axial and coronal images. Both axial and coronal T1-weighted MRI can detect the narrow CSF space at the high convexity/midline accurately and may therefore facilitate clinicians in choosing a management strategy for iNPH patients. (orig.)

Multi-Period Trading via Convex Optimization

DEFF Research Database (Denmark)

Boyd, Stephen; Busseti, Enzo; Diamond, Steve

2017-01-01

We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk......, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the first one executed, using estimates of future quantities that are unknown when the trades....... In this paper, we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software...

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

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...... is a quantitative calibrated model for a complete ultrasound system. This includes a sensitivity study aspresented here.Statement of Contribution/MethodsThe study alters 35 different model parameters which describe a 128 element convex transducer from BK Medical Aps. The changes are within ±20 % of the values...

Surface tension-induced high aspect-ratio PDMS micropillars with concave and convex lens tips

KAUST Repository

Li, Huawei; Fan, Yiqiang; Yi, Ying; Foulds, Ian G.

2013-01-01

This paper reports a novel method for the fabrication of 3-dimensional (3D) Polydimethylsiloxane (PDMS) micropillars with concave and convex lens tips in a one-step molding process, using a CO2 laser-machined Poly(methyl methacrylate) (PMMA) mold with through holes. The PDMS micropillars are 4 mm high and have an aspect ratio of 251. The micropillars are formed by capillary force drawing up PDMS into the through hole mold. The concave and convex lens tips of the PDMS cylindrical micropillars are induced by surface tension and are controllable by changing the surface wetting properties of the through holes in the PMMA mold. This technique eliminates the requirements of expensive and complicated facilities to prepare a 3D mold, and it provides a simple and rapid method to fabricate 3D PDMS micropillars with controllable dimensions and tip shapes. © 2013 IEEE.

Surface tension-induced high aspect-ratio PDMS micropillars with concave and convex lens tips

KAUST Repository

Li, Huawei

2013-04-01

This paper reports a novel method for the fabrication of 3-dimensional (3D) Polydimethylsiloxane (PDMS) micropillars with concave and convex lens tips in a one-step molding process, using a CO2 laser-machined Poly(methyl methacrylate) (PMMA) mold with through holes. The PDMS micropillars are 4 mm high and have an aspect ratio of 251. The micropillars are formed by capillary force drawing up PDMS into the through hole mold. The concave and convex lens tips of the PDMS cylindrical micropillars are induced by surface tension and are controllable by changing the surface wetting properties of the through holes in the PMMA mold. This technique eliminates the requirements of expensive and complicated facilities to prepare a 3D mold, and it provides a simple and rapid method to fabricate 3D PDMS micropillars with controllable dimensions and tip shapes. © 2013 IEEE.

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.

Global structure of curves from generalized unitarity cut of three-loop diagrams

International Nuclear Information System (INIS)

Hauenstein, Jonathan D.; Huang, Rijun; Mehta, Dhagash; Zhang, Yang

2015-01-01

This paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structure is a topological invariant that is characterized by the geometric genus of the algebraic curve. We use the Riemann-Hurwitz formula to compute the geometric genus of algebraic curves with the help of techniques involving convex hull polytopes and numerical algebraic geometry. Some interesting properties of genus for arbitrary loop orders are also explored where computing the genus serves as an initial step for integral or integrand reduction of three-loop amplitudes via an algebraic geometric approach.

Unifying kinetic approach to phoretic forces and torques onto moving and rotating convex particles

NARCIS (Netherlands)

Kröger, M.; Hütter, M.

2006-01-01

We derive general expressions and present several examples for the phoretic forces and torques acting on a translationally moving and rotating convex tracer particle, usually a submicrosized aerosol particle, assumed to be small compared to the mean free path of the surrounding nonequilibrium gas.

Graph Design via Convex Optimization: Online and Distributed Perspectives

Science.gov (United States)

Meng, De

Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation

Comparisons of Energy Management Methods for a Parallel Plug-In Hybrid Electric Vehicle between the Convex Optimization and Dynamic Programming

Directory of Open Access Journals (Sweden)

Renxin Xiao

2018-01-01

Full Text Available This paper proposes a comparison study of energy management methods for a parallel plug-in hybrid electric vehicle (PHEV. Based on detailed analysis of the vehicle driveline, quadratic convex functions are presented to describe the nonlinear relationship between engine fuel-rate and battery charging power at different vehicle speed and driveline power demand. The engine-on power threshold is estimated by the simulated annealing (SA algorithm, and the battery power command is achieved by convex optimization with target of improving fuel economy, compared with the dynamic programming (DP based method and the charging depleting–charging sustaining (CD/CS method. In addition, the proposed control methods are discussed at different initial battery state of charge (SOC values to extend the application. Simulation results validate that the proposed strategy based on convex optimization can save the fuel consumption and reduce the computation burden obviously.

Global solutions to the equation of thermoelasticity with fading memory

Science.gov (United States)

Okada, Mari; Kawashima, Shuichi

2017-07-01

We consider the initial-history value problem for the one-dimensional equation of thermoelasticity with fading memory. It is proved that if the data are smooth and small, then a unique smooth solution exists globally in time and converges to the constant equilibrium state as time goes to infinity. Our proof is based on a technical energy method which makes use of the strict convexity of the entropy function and the properties of strongly positive definite kernels.

Well-Posedness and Primal-Dual Analysis of Some Convex Separable Optimization Problems

Directory of Open Access Journals (Sweden)

Stefan M. Stefanov

2013-01-01

Full Text Available We focus on some convex separable optimization problems, considered by the author in previous papers, for which problems, necessary and sufficient conditions or sufficient conditions have been proved, and convergent algorithms of polynomial computational complexity have been proposed for solving these problems. The concepts of well-posedness of optimization problems in the sense of Tychonov, Hadamard, and in a generalized sense, as well as calmness in the sense of Clarke, are discussed. It is shown that the convex separable optimization problems under consideration are calm in the sense of Clarke. The concept of stability of the set of saddle points of the Lagrangian in the sense of Gol'shtein is also discussed, and it is shown that this set is not stable for the “classical” Lagrangian. However, it turns out that despite this instability, due to the specificity of the approach, suggested by the author for solving problems under consideration, it is not necessary to use modified Lagrangians but only the “classical” Lagrangians. Also, a primal-dual analysis for problems under consideration in view of methods for solving them is presented.

Fréchet derivative with respect to the shape of a strongly convex nonscattering region in optical tomography

Science.gov (United States)

Hyvönen, Nuutti

2007-10-01

The aim of optical tomography is to reconstruct the optical properties inside a physical body, e.g. a neonatal head, by illuminating it with near-infrared light and measuring the outward flux of photons on the object boundary. Because a brain consists of strongly scattering tissue with imbedded cavities filled by weakly scattering cerebrospinal fluid, propagation of near-infrared photons in the human head can be treated by combining the diffusion approximation of the radiative transfer equation with geometrical optics to obtain the radiosity-diffusion forward model of optical tomography. At the moment, a disadvantage with the radiosity-diffusion model is that the locations of the transparent cavities must be known in advance in order to be able to reconstruct the physiologically interesting quantities, i.e., the absorption and the scatter in the strongly scattering brain tissue. In this work we show that the boundary measurement map of optical tomography is Fréchet differentiable with respect to the shape of a strongly convex nonscattering region. Using this result, we introduce a numerical algorithm for approximating an unknown nonscattering cavity by a ball if the background diffuse optical properties of the object are known. The functionality of the method is demonstrated through two-dimensional numerical experiments.

On global stability criterion for neural networks with discrete and distributed delays

International Nuclear Information System (INIS)

Park, Ju H.

2006-01-01

Based on the Lyapunov functional stability analysis for differential equations and the linear matrix inequality (LMI) optimization approach, a new delay-dependent criterion for neural networks with discrete and distributed delays is derived to guarantee global asymptotic stability. The criterion is expressed in terms of LMIs, which can be solved easily by various convex optimization algorithms. Some numerical examples are given to show the effectiveness of proposed method

Classification of cerebrospinal fluid dynamics in hydrocephalus by computed tomographic cisternography

International Nuclear Information System (INIS)

Tamaki, Norihiko; Kanazawa, Yasuhisa; Asada, Masahiro; Nogaki, Hidekazu; Kusunoki, Tadaki

1980-01-01

Nine patients with normal CSF circulation and 49 patients with hydrocephalus of various etiologies were used to analyse the CSF dynamics by metrizamide CT cisternography. This investigation resulted in a new classification of CSF dynamics in both normal and hydrocephalic patients. We classified the patterns of CSF dynamics into seven types. Types I and II showed normal CSF kinetics, the former having no ventricular reflux, but the latter showing a transient ventricular reflux by 6 hours. The CSF dynamics in cases with communicating hydrocephalus was divided into types III, IV and V, according to the extent of ventricular filling and the convexity flow of the metrizamide. These types seen in communicating hydrocephalus were characterized by the presence of ventricular dilatation and persistent ventricular filling on 24 hours after the intrathecal injection of metrizamide. Type III showed more prominent flow into the convexity subarachnoid space than into the ventricular system. In Type IV the ventricular filling was almost the same extent as the convexity flow. Type V demonstrated a more prominent ventricular filling than convexity flow. Type VI had no intracranial entry of the metrizamide. Type VII, which represents the CSF kinetics in obstructive hydrocephalus, showed either a normal or delayed convexity flow. However no ventricular filling was present in spite of the marked ventricular enlargement. There was a close correlation between this new system of classification and the pathogenesis of hydrocephalus, as well as the various factors associated with the pathology of hydrocephalus. Our CT cisternographic classification of CSF dynamics seems to be of use in evaluating the grade of CSF circulation disturbance and in deciding the method of treatment of hydrocephalus. (author)

An Efficient Algorithm to Calculate the Minkowski Sum of Convex 3D Polyhedra

NARCIS (Netherlands)

Bekker, Henk; Roerdink, Jos B.T.M.

2001-01-01

A new method is presented to calculate the Minkowski sum of two convex polyhedra A and B in 3D. These graphs are given edge attributes. From these attributed graphs the attributed graph of the Minkowski sum is constructed. This graph is then transformed into the Minkowski sum of A and B. The running

WE-G-207-02: Full Sequential Projection Onto Convex Sets (FS-POCS) for X-Ray CT Reconstruction

International Nuclear Information System (INIS)

Liu, L; Han, Y; Jin, M

2015-01-01

Purpose: To develop an iterative reconstruction method for X-ray CT, in which the reconstruction can quickly converge to the desired solution with much reduced projection views. Methods: The reconstruction is formulated as a convex feasibility problem, i.e. the solution is an intersection of three convex sets: 1) data fidelity (DF) set – the L2 norm of the difference of observed projections and those from the reconstructed image is no greater than an error bound; 2) non-negativity of image voxels (NN) set; and 3) piecewise constant (PC) set - the total variation (TV) of the reconstructed image is no greater than an upper bound. The solution can be found by applying projection onto convex sets (POCS) sequentially for these three convex sets. Specifically, the algebraic reconstruction technique and setting negative voxels as zero are used for projection onto the DF and NN sets, respectively, while the projection onto the PC set is achieved by solving a standard Rudin, Osher, and Fatemi (ROF) model. The proposed method is named as full sequential POCS (FS-POCS), which is tested using the Shepp-Logan phantom and the Catphan600 phantom and compared with two similar algorithms, TV-POCS and CP-TV. Results: Using the Shepp-Logan phantom, the root mean square error (RMSE) of reconstructed images changing along with the number of iterations is used as the convergence measurement. In general, FS- POCS converges faster than TV-POCS and CP-TV, especially with fewer projection views. FS-POCS can also achieve accurate reconstruction of cone-beam CT of the Catphan600 phantom using only 54 views, comparable to that of FDK using 364 views. Conclusion: We developed an efficient iterative reconstruction for sparse-view CT using full sequential POCS. The simulation and physical phantom data demonstrated the computational efficiency and effectiveness of FS-POCS

Fast Gaussian kernel learning for classification tasks based on specially structured global optimization.

Science.gov (United States)

Zhong, Shangping; Chen, Tianshun; He, Fengying; Niu, Yuzhen

2014-09-01

For a practical pattern classification task solved by kernel methods, the computing time is mainly spent on kernel learning (or training). However, the current kernel learning approaches are based on local optimization techniques, and hard to have good time performances, especially for large datasets. Thus the existing algorithms cannot be easily extended to large-scale tasks. In this paper, we present a fast Gaussian kernel learning method by solving a specially structured global optimization (SSGO) problem. We optimize the Gaussian kernel function by using the formulated kernel target alignment criterion, which is a difference of increasing (d.i.) functions. Through using a power-transformation based convexification method, the objective criterion can be represented as a difference of convex (d.c.) functions with a fixed power-transformation parameter. And the objective programming problem can then be converted to a SSGO problem: globally minimizing a concave function over a convex set. The SSGO problem is classical and has good solvability. Thus, to find the global optimal solution efficiently, we can adopt the improved Hoffman's outer approximation method, which need not repeat the searching procedure with different starting points to locate the best local minimum. Also, the proposed method can be proven to converge to the global solution for any classification task. We evaluate the proposed method on twenty benchmark datasets, and compare it with four other Gaussian kernel learning methods. Experimental results show that the proposed method stably achieves both good time-efficiency performance and good classification performance. Copyright © 2014 Elsevier Ltd. All rights reserved.

Convexity and Weighted Integral Inequalities for Energy Decay Rates of Nonlinear Dissipative Hyperbolic Systems

International Nuclear Information System (INIS)

Alabau-Boussouira, Fatiha

2005-01-01

This work is concerned with the stabilization of hyperbolic systems by a nonlinear feedback which can be localized on a part of the boundary or locally distributed. We show that general weighted integral inequalities together with convexity arguments allow us to produce a general semi-explicit formula which leads to decay rates of the energy in terms of the behavior of the nonlinear feedback close to the origin. This formula allows us to unify for instance the cases where the feedback has a polynomial growth at the origin, with the cases where it goes exponentially fast to zero at the origin. We also give three other significant examples of nonpolynomial growth at the origin. We also prove the optimality of our results for the one-dimensional wave equation with nonlinear boundary dissipation. The key property for obtaining our general energy decay formula is the understanding between convexity properties of an explicit function connected to the feedback and the dissipation of energy

On the stretch factor of convex polyhedra whose vertices are (almost on a sphere

Directory of Open Access Journals (Sweden)

Michiel Smid

2016-10-01

Full Text Available Let $P$ be a convex polyhedron in $\\mathbb{R}^3$. The skeleton of $P$ is the graph whose vertices and edges are the vertices and edges of $P$, respectively. We prove that, if these vertices are on the unit-sphere, the skeleton is a $(0.999 \\cdot \\pi$-spanner. If the vertices are very close to this sphere, then the skeleton is not necessarily a spanner. For the case when the boundary of $P$ is between two concentric spheres of radii $1$ and $R>1$, and the angles in all faces are at least $\\theta$, we prove that the skeleton is a $t$-spanner, where $t$ depends only on $R$ and $\\theta$. One of the ingredients in the proof is a tight upper bound on the geometric dilation of a convex cycle that is contained in an annulus.  

Six-month-old infants' perception of the hollow face illusion: evidence for a general convexity bias.

Science.gov (United States)

Corrow, Sherryse L; Mathison, Jordan; Granrud, Carl E; Yonas, Albert

2014-01-01

Corrow, Granrud, Mathison, and Yonas (2011, Perception, 40, 1376-1383) found evidence that 6-month-old infants perceive the hollow face illusion. In the present study we asked whether 6-month-old infants perceive illusory depth reversal for a nonface object and whether infants' perception of the hollow face illusion is affected by mask orientation inversion. In experiment 1 infants viewed a concave bowl, and their reaches were recorded under monocular and binocular viewing conditions. Infants reached to the bowl as if it were convex significantly more often in the monocular than in the binocular viewing condition. These results suggest that infants perceive illusory depth reversal with a nonface stimulus and that the infant visual system has a bias to perceive objects as convex. Infants in experiment 2 viewed a concave face-like mask in upright and inverted orientations. Infants reached to the display as if it were convex more in the monocular than in the binocular condition; however, mask orientation had no effect on reaching. Previous findings that adults' perception of the hollow face illusion is affected by mask orientation inversion have been interpreted as evidence of stored-knowledge influences on perception. However, we found no evidence of such influences in infants, suggesting that their perception of this illusion may not be affected by stored knowledge, and that perceived depth reversal is not face-specific in infants.

Renorming c0 and closed, bounded, convex sets with fixed point property for affine nonexpansive mappings

Science.gov (United States)

Nezir, Veysel; Mustafa, Nizami

2017-04-01

In 2008, P.K. Lin provided the first example of a nonreflexive space that can be renormed to have fixed point property for nonexpansive mappings. This space was the Banach space of absolutely summable sequences l1 and researchers aim to generalize this to c0, Banach space of null sequences. Before P.K. Lin's intriguing result, in 1979, Goebel and Kuczumow showed that there is a large class of non-weak* compact closed, bounded, convex subsets of l1 with fixed point property for nonexpansive mappings. Then, P.K. Lin inspired by Goebel and Kuczumow's ideas to give his result. Similarly to P.K. Lin's study, Hernández-Linares worked on L1 and in his Ph.D. thesis, supervisored under Maria Japón, showed that L1 can be renormed to have fixed point property for affine nonexpansive mappings. Then, related questions for c0 have been considered by researchers. Recently, Nezir constructed several equivalent norms on c0 and showed that there are non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings. In this study, we construct a family of equivalent norms containing those developed by Nezir as well and show that there exists a large class of non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings.

The European Union's Role in the Development of Global Environmental Law

DEFF Research Database (Denmark)

Basse, Ellen Margrethe

2017-01-01

This article is focused on the role that the European Union (EU) is playing as a global actor when it is using its 'internal' regulatory power as well as its parallel market power 'externally' to strengthen and to fill out gaps in the global environmental law.......This article is focused on the role that the European Union (EU) is playing as a global actor when it is using its 'internal' regulatory power as well as its parallel market power 'externally' to strengthen and to fill out gaps in the global environmental law....

Kinetic and electron-electron energies for convex sums of ground state densities with degeneracies and fractional electron number

Energy Technology Data Exchange (ETDEWEB)

Levy, Mel, E-mail: ayers@mcmaster.ca, E-mail: mlevy@tulane.edu [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Department of Physics, North Carolina A and T State University, Greensboro, North Carolina 27411 (United States); Department of Chemistry, Tulane University, New Orleans, Louisiana 70118 (United States); Anderson, James S. M.; Zadeh, Farnaz Heidar; Ayers, Paul W., E-mail: ayers@mcmaster.ca, E-mail: mlevy@tulane.edu [Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario (Canada)

2014-05-14

Properties of exact density functionals provide useful constraints for the development of new approximate functionals. This paper focuses on convex sums of ground-level densities. It is observed that the electronic kinetic energy of a convex sum of degenerate ground-level densities is equal to the convex sum of the kinetic energies of the individual degenerate densities. (The same type of relationship holds also for the electron-electron repulsion energy.) This extends a known property of the Levy-Valone Ensemble Constrained-Search and the Lieb Legendre-Transform refomulations of the Hohenberg-Kohn functional to the individual components of the functional. Moreover, we observe that the kinetic and electron-repulsion results also apply to densities with fractional electron number (even if there are no degeneracies), and we close with an analogous point-wise property involving the external potential. Examples where different degenerate states have different kinetic energy and electron-nuclear attraction energy are given; consequently, individual components of the ground state electronic energy can change abruptly when the molecular geometry changes. These discontinuities are predicted to be ubiquitous at conical intersections, complicating the development of universally applicable density-functional approximations.

Recurrent neural network for non-smooth convex optimization problems with application to the identification of genetic regulatory networks.

Science.gov (United States)

Cheng, Long; Hou, Zeng-Guang; Lin, Yingzi; Tan, Min; Zhang, Wenjun Chris; Wu, Fang-Xiang

2011-05-01

A recurrent neural network is proposed for solving the non-smooth convex optimization problem with the convex inequality and linear equality constraints. Since the objective function and inequality constraints may not be smooth, the Clarke's generalized gradients of the objective function and inequality constraints are employed to describe the dynamics of the proposed neural network. It is proved that the equilibrium point set of the proposed neural network is equivalent to the optimal solution of the original optimization problem by using the Lagrangian saddle-point theorem. Under weak conditions, the proposed neural network is proved to be stable, and the state of the neural network is convergent to one of its equilibrium points. Compared with the existing neural network models for non-smooth optimization problems, the proposed neural network can deal with a larger class of constraints and is not based on the penalty method. Finally, the proposed neural network is used to solve the identification problem of genetic regulatory networks, which can be transformed into a non-smooth convex optimization problem. The simulation results show the satisfactory identification accuracy, which demonstrates the effectiveness and efficiency of the proposed approach.

Bulk-Fill Resin Composites

DEFF Research Database (Denmark)

Benetti, Ana Raquel; Havndrup-Pedersen, Cæcilie; Honoré, Daniel

2015-01-01

the restorative procedure. The aim of this study, therefore, was to compare the depth of cure, polymerization contraction, and gap formation in bulk-fill resin composites with those of a conventional resin composite. To achieve this, the depth of cure was assessed in accordance with the International Organization...... for Standardization 4049 standard, and the polymerization contraction was determined using the bonded-disc method. The gap formation was measured at the dentin margin of Class II cavities. Five bulk-fill resin composites were investigated: two high-viscosity (Tetric EvoCeram Bulk Fill, SonicFill) and three low......-viscosity (x-tra base, Venus Bulk Fill, SDR) materials. Compared with the conventional resin composite, the high-viscosity bulk-fill materials exhibited only a small increase (but significant for Tetric EvoCeram Bulk Fill) in depth of cure and polymerization contraction, whereas the low-viscosity bulk...

Using Fisher Information Criteria for Chemical Sensor Selection via Convex Optimization Methods

Science.gov (United States)

2016-11-16

burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis...10 3.4 Defining the Mean Response Vector, ECD Scale Matrix, Slack Variables and their Con- straints for Convex Optimization...parametrized for optimization and the objective function thus becomes, ln(det(C(θ )))≥ ln(det(F−1(θ ;s))) =− ln(det(F (θ ;s))) (29) where s are the slack

30 CFR 817.72 - Disposal of excess spoil: Valley fill/head-of-hollow fills.

Science.gov (United States)

2010-07-01

... STANDARDS-UNDERGROUND MINING ACTIVITIES § 817.72 Disposal of excess spoil: Valley fill/head-of-hollow fills.... Uncontrolled surface drainage may not be directed over the outslope of the fill. (2) Runoff from areas above the fill and runoff from the surface of the fill shall be diverted into stabilized diversion channels...

Integration of polystyrene microlenses with both convex and concave profiles in a polymer-based microfluidic system

KAUST Repository

Fan, Yiqiang; Li, Huawei; Foulds, Ian G.

2013-01-01

This paper reports a new technique of fabricating polystyrene microlenses with both convex and concave profiles that are integrated in polymer-based microfluidic system. The polystyrene microlenses, or microlens array, are fabricated using the free

On the rank 1 convexity of stored energy functions of physically linear stress-strain relations

Czech Academy of Sciences Publication Activity Database

Šilhavý, Miroslav; Bertram, A.; Böhlke, T.

2007-01-01

Roč. 86, č. 3 (2007), s. 235-243 ISSN 0374-3535 Institutional research plan: CEZ:AV0Z10190503 Keywords : generalized linear elastic law s * generalized strain measures * rank 1 convexity Subject RIV: BA - General Mathematics Impact factor: 0.743, year: 2007

Nonparametric instrumental regression with non-convex constraints

International Nuclear Information System (INIS)

Grasmair, M; Scherzer, O; Vanhems, A

2013-01-01

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. (paper)

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.

Sodium fill of FFTF

International Nuclear Information System (INIS)

Waldo, J.B.; Greenwell, R.K.; Keasling, T.A.; Collins, J.R.; Klos, D.B.

1980-02-01

With construction of the Fast Flux Test Facility (FFTF) completed, the first major objective in the startup program was to fill the sodium systems. A sodium fill sequence was developed to match construction completion, and as systems became available, they were inerted, preheated, and filled with sodium. The secondary sodium systems were filled first while dry refueling system testing was in progress in the reactor vessel. The reactor vessel and the primary loops were filled last. This paper describes the methods used and some of the key results achieved for this major FFTF objective

About Dental Amalgam Fillings

Science.gov (United States)

... and Medical Procedures Dental Devices Dental Amalgam About Dental Amalgam Fillings Share Tweet Linkedin Pin it More ... should I have my fillings removed? What is dental amalgam? Dental amalgam is a dental filling material ...

Preliminary In-Vivo Evaluation of Convex Array Synthetic Aperture Imaging

DEFF Research Database (Denmark)

Pedersen, Morten Høgholm; Gammelmark, Kim; Jensen, Jørgen Arendt

2004-01-01

of STA imaging in comparison to conventional imaging. The purpose is to evaluate whether STA imaging is feasible in-vivo. and whether the image quality obtained is comparable to traditional scanned imaging in terms of penetration depth, spatial resolution, contrast resolution, and artifacts. Acquisition...... was done using our RASMUS research scanner and a 5.5 MHz convex array transducer. STA imaging applies spherical wave emulation using multi-element subapertures and a 20 mus linear FM signal as excitation pulse. For conventional imaging a 64 element aperture was used in transmit and receive with a 1.5 cycle...

Oracle Inequalities for Convex Loss Functions with Non-Linear Targets

DEFF Research Database (Denmark)

Caner, Mehmet; Kock, Anders Bredahl

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target...... 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...

Downscaling drivers of global environmental change: Enabling use of global SRES scenarios at the national and grid levels

NARCIS (Netherlands)

van Vuuren, D.P.; Lucas, P.L.; Hilderink, H.

2007-01-01

Global environmental change scenarios typically distinguish between about 10–20 global regions. However, various studies need scenario information at a higher level of spatial detail. This paper presents a set of algorithms that aim to fill this gap by providing downscaled scenario data for

Static and high frequency magnetic properties of FeGa thin films deposited on convex flexible substrates

International Nuclear Information System (INIS)

Yu, Ying; Zhan, Qingfeng; Dai, Guohong; Zuo, Zhenghu; Zhang, Xiaoshan; Liu, Yiwei; Yang, Huali; Zhang, Yao; Wang, Baomin; Li, Run-Wei; Wei, Jinwu; Wang, Jianbo; Xie, Shuhong

2015-01-01

Magnetostrictive FeGa thin films were deposited on the bowed flexible polyethylene terephthalate (PET) substrates, which were fixed on the convex mold. A compressive stress was induced in FeGa films when the PET substrates were shaped from convex to flat. Due to the effect of magnetostriction, FeGa films exhibit an obvious in-plane uniaxial magnetic anisotropy which could be enhanced by increasing the applied pre-strains on the substrates during growth. Consequently, the ferromagnetic resonance frequency of the films was significantly increased, but the corresponding initial permeability was decreased. Moreover, the films with pre-strains less than 0.78% exhibit a working bandwidth of microwave absorption about 2 GHz. Our investigations demonstrated a convenient method via the pre-strained substrates to tune the high frequency properties of magnetic thin films which could be applied in flexible microwave devices

Static and high frequency magnetic properties of FeGa thin films deposited on convex flexible substrates

Science.gov (United States)

Yu, Ying; Zhan, Qingfeng; Wei, Jinwu; Wang, Jianbo; Dai, Guohong; Zuo, Zhenghu; Zhang, Xiaoshan; Liu, Yiwei; Yang, Huali; Zhang, Yao; Xie, Shuhong; Wang, Baomin; Li, Run-Wei

2015-04-01

Magnetostrictive FeGa thin films were deposited on the bowed flexible polyethylene terephthalate (PET) substrates, which were fixed on the convex mold. A compressive stress was induced in FeGa films when the PET substrates were shaped from convex to flat. Due to the effect of magnetostriction, FeGa films exhibit an obvious in-plane uniaxial magnetic anisotropy which could be enhanced by increasing the applied pre-strains on the substrates during growth. Consequently, the ferromagnetic resonance frequency of the films was significantly increased, but the corresponding initial permeability was decreased. Moreover, the films with pre-strains less than 0.78% exhibit a working bandwidth of microwave absorption about 2 GHz. Our investigations demonstrated a convenient method via the pre-strained substrates to tune the high frequency properties of magnetic thin films which could be applied in flexible microwave devices.

Neural network for solving convex quadratic bilevel programming problems.

Science.gov (United States)

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

2014-03-01

In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.

Hearing preservation in retrosigmoid approach of small vestibular schwannomas: prognostic value of the degree of internal auditory canal filling.

Science.gov (United States)

Tringali, Stéphane; Ferber-Viart, Chantal; Fuchsmann, Carine; Buiret, Guillaume; Zaouche, Sandra; Dubreuil, Christian

2010-12-01

To assess the contribution of preoperative radiologic appearance of vestibular schwannoma (VS) on the magnetic resonance imaging in constructive interference in steady-state sequences and demonstrate if the degree of the internal auditory canal (IAC) filling is correlated with hearing and facial preservation. A group of 278 patients who underwent VS surgery in a tertiary referral center. Retrosigmoid approach surgery. Patients were classified in 4 groups according to the percentage of IAC filling on the preoperative magnetic resonance imaging as Group IAC 1(IAC empty or filled filled from 25% to 50% with free fundus), Group IAC 3 (IAC filled from 50% to 75% with free fundus), and Group IAC 4 (complete filling of the IAC without fundus obliteration). A good correlation was observed between the IAC classification and the rate of hearing and facial preservation. The global rate of postoperative facial palsy was 10.4%. The global rate of hearing preservation in 213 patients with preoperative hearing class A and B was 40.8%. Regression analysis showed that the degree of lateral extension of the VS in the IAC was a strong predictor of hearing preservation ( p facial outcomes in selected patients with possible hearing preservation. In case of patient with small tumor and IAC empty or filled less than 75% and with free fundus, surgery is the treatment of choice for patients with serviceable hearing and the desire to retain it.

Restoration of the analytically reconstructed OpenPET images by the method of convex projections

Energy Technology Data Exchange (ETDEWEB)

Tashima, Hideaki; Murayama, Hideo; Yamaya, Taiga [National Institute of Radiological Sciences, Chiba (Japan); Katsunuma, Takayuki; Suga, Mikio [Chiba Univ. (Japan). Graduate School of Engineering; Kinouchi, Shoko [National Institute of Radiological Sciences, Chiba (Japan); Chiba Univ. (Japan). Graduate School of Engineering; Obi, Takashi [Tokyo Institute of Technology (Japan). Interdisciplinary Graduate School of Science and Engineering; Kudo, Hiroyuki [Tsukuba Univ. (Japan). Graduate School of Systems and Information Engineering

2011-07-01

We have proposed the OpenPET geometry which has gaps between detector rings and physically opened field-of-view. The image reconstruction of the OpenPET is classified into an incomplete problem because it does not satisfy the Orlov's condition. Even so, the simulation and experimental studies have shown that applying iterative methods such as the maximum likelihood expectation maximization (ML-EM) algorithm successfully reconstruct images in the gap area. However, the imaging process of the iterative methods in the OpenPET imaging is not clear. Therefore, the aim of this study is to analytically analyze the OpenPET imaging and estimate implicit constraints involved in the iterative methods. To apply explicit constraints in the OpenPET imaging, we used the method of convex projections for restoration of the images reconstructed by the analytical way in which low-frequency components are lost. Numerical simulations showed that the similar restoration effects are involved both in the ML-EM and the method of convex projections. Therefore, the iterative methods have advantageous effect of restoring lost frequency components of the OpenPET imaging. (orig.)

Numerical Simulation of Recycled Concrete Using Convex Aggregate Model and Base Force Element Method

Directory of Open Access Journals (Sweden)

Yijiang Peng

2016-01-01

Full Text Available By using the Base Force Element Method (BFEM on potential energy principle, a new numerical concrete model, random convex aggregate model, is presented in this paper to simulate the experiment under uniaxial compression for recycled aggregate concrete (RAC which can also be referred to as recycled concrete. This model is considered as a heterogeneous composite which is composed of five mediums, including natural coarse aggregate, old mortar, new mortar, new interfacial transition zone (ITZ, and old ITZ. In order to simulate the damage processes of RAC, a curve damage model was adopted as the damage constitutive model and the strength theory of maximum tensile strain was used as the failure criterion in the BFEM on mesomechanics. The numerical results obtained in this paper which contained the uniaxial compressive strengths, size effects on strength, and damage processes of RAC are in agreement with experimental observations. The research works show that the random convex aggregate model and the BFEM with the curve damage model can be used for simulating the relationship between microstructure and mechanical properties of RAC.

T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory

CERN Document Server

Takahashi, Wataru

1995-01-01

The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.) , and supported by Nihon Keizai Shimbun Inc .. A lot of economic problems can be formulated as constrained optimiza­ tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the­ ories. Although our special emphasis was laid upon "nonlinearity" and "con­ vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark­ able rapid growth of this dis...

An Alternating Direction Method for Convex Quadratic Second-Order Cone Programming with Bounded Constraints

Directory of Open Access Journals (Sweden)

Xuewen Mu

2015-01-01

quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is efficient for the convex quadratic second-order cone programming problems with bounded constraints.

F-SVM: Combination of Feature Transformation and SVM Learning via Convex Relaxation

OpenAIRE

Wu, Xiaohe; Zuo, Wangmeng; Zhu, Yuanyuan; Lin, Liang

2015-01-01

The generalization error bound of support vector machine (SVM) depends on the ratio of radius and margin, while standard SVM only considers the maximization of the margin but ignores the minimization of the radius. Several approaches have been proposed to integrate radius and margin for joint learning of feature transformation and SVM classifier. However, most of them either require the form of the transformation matrix to be diagonal, or are non-convex and computationally expensive. In this ...

Regular growth of systems of functions and systems of non-homogeneous convolution equations in convex domains of the complex plane

International Nuclear Information System (INIS)

Krivosheev, A S

2000-01-01

In this paper we introduce the notion of regular growth for a system of entire functions of finite order and type. This is a direct and natural generalization of the classical completely regular growth of an entire function. We obtain sufficient and necessary conditions for the solubility of a system of non-homogeneous convolution equations in convex domains of the complex plane. These conditions depend on whether the system of Laplace transforms of the analytic functionals that generate the convolution equations has regular growth. In the case of smooth convex domains, these solubility conditions form a criterion

An Implementable First-Order Primal-Dual Algorithm for Structured Convex Optimization

Directory of Open Access Journals (Sweden)

Feng Ma

2014-01-01

Full Text Available Many application problems of practical interest can be posed as structured convex optimization models. In this paper, we study a new first-order primaldual algorithm. The method can be easily implementable, provided that the resolvent operators of the component objective functions are simple to evaluate. We show that the proposed method can be interpreted as a proximal point algorithm with a customized metric proximal parameter. Convergence property is established under the analytic contraction framework. Finally, we verify the efficiency of the algorithm by solving the stable principal component pursuit problem.

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

Supermarket refrigeration consumes substantial amounts of energy. However, due to the thermal capacity of the refrigerated goods, parts of the cooling capacity delivered can be shifted in time without deteriorating the food quality. In this study, we develop a realistic model for the energy...... consumption in super market refrigeration systems. This model is used in a Nonlinear Model Predictive Controller (NMPC) to minimise the energy used by operation of a supermarket refrigeration system. The model is non-convex and we develop a computational efficient algorithm tailored to this problem...

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.

Approximating convex Pareto surfaces in multiobjective radiotherapy planning

International Nuclear Information System (INIS)

Craft, David L.; Halabi, Tarek F.; Shih, Helen A.; Bortfeld, Thomas R.

2006-01-01

Radiotherapy planning involves inherent tradeoffs: the primary mission, to treat the tumor with a high, uniform dose, is in conflict with normal tissue sparing. We seek to understand these tradeoffs on a case-to-case basis, by computing for each patient a database of Pareto optimal plans. A treatment plan is Pareto optimal if there does not exist another plan which is better in every measurable dimension. The set of all such plans is called the Pareto optimal surface. This article presents an algorithm for computing well distributed points on the (convex) Pareto optimal surface of a multiobjective programming problem. The algorithm is applied to intensity-modulated radiation therapy inverse planning problems, and results of a prostate case and a skull base case are presented, in three and four dimensions, investigating tradeoffs between tumor coverage and critical organ sparing

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.

Impact of diastolic dysfunction severity on global left ventricular volumetric filling - assessment by automated segmentation of routine cine cardiovascular magnetic resonance

Directory of Open Access Journals (Sweden)

Mendoza Dorinna D

2010-07-01

Full Text Available Abstract Objectives To examine relationships between severity of echocardiography (echo -evidenced diastolic dysfunction (DD and volumetric filling by automated processing of routine cine cardiovascular magnetic resonance (CMR. Background Cine-CMR provides high-resolution assessment of left ventricular (LV chamber volumes. Automated segmentation (LV-METRIC yields LV filling curves by segmenting all short-axis images across all temporal phases. This study used cine-CMR to assess filling changes that occur with progressive DD. Methods 115 post-MI patients underwent CMR and echo within 1 day. LV-METRIC yielded multiple diastolic indices - E:A ratio, peak filling rate (PFR, time to peak filling rate (TPFR, and diastolic volume recovery (DVR80 - proportion of diastole required to recover 80% stroke volume. Echo was the reference for DD. Results LV-METRIC successfully generated LV filling curves in all patients. CMR indices were reproducible (≤ 1% inter-reader differences and required minimal processing time (175 ± 34 images/exam, 2:09 ± 0:51 minutes. CMR E:A ratio decreased with grade 1 and increased with grades 2-3 DD. Diastolic filling intervals, measured by DVR80 or TPFR, prolonged with grade 1 and shortened with grade 3 DD, paralleling echo deceleration time (p 80 identified 71% of patients with echo-evidenced grade 1 but no patients with grade 3 DD, and stroke-volume adjusted PFR identified 67% with grade 3 but none with grade 1 DD (matched specificity = 83%. The combination of DVR80 and PFR identified 53% of patients with grade 2 DD. Prolonged DVR80 was associated with grade 1 (OR 2.79, CI 1.65-4.05, p = 0.001 with a similar trend for grade 2 (OR 1.35, CI 0.98-1.74, p = 0.06, whereas high PFR was associated with grade 3 (OR 1.14, CI 1.02-1.25, p = 0.02 DD. Conclusions Automated cine-CMR segmentation can discern LV filling changes that occur with increasing severity of echo-evidenced DD. Impaired relaxation is associated with prolonged

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.

An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays

International Nuclear Information System (INIS)

Park, Ju H.

2007-01-01

This paper considers the robust stability analysis of cellular neural networks with discrete and distributed delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, a novel stability criterion guaranteeing the global robust convergence of the equilibrium point is derived. The criterion can be solved easily by various convex optimization algorithms. An example is given to illustrate the usefulness of our results

Free-Energy Barrier of Filling a Spherical Cavity in the Presence of Line Tension: Implication to the Energy Barrier between the Cassie and Wenzel States on a Superhydrophobic Surface with Spherical Cavities.

Science.gov (United States)

Iwamatsu, Masao

2016-09-20

The free-energy barrier of filling a spherical cavity having an inner wall of various wettabilities is studied. The morphology and free energy of a lens-shaped droplet are determined from the minimum of the free energy. The effect of line tension on the free energy is also studied. Then, the equilibrium contact angle of the droplet is determined from the generalized Young's equation. By increasing the droplet volume within the spherical cavity, the droplet morphology changes from spherical with an equilibrium contact angle of 180° to a lens with a convex meniscus, where the morphological complete drying transition occurs. By further increasing the droplet volume, the meniscus changes from convex to concave. Then, the lens-shaped droplet with concave meniscus spreads over the whole inner wall, resulting in an equilibrium contact angle of 0° to leave a spherical bubble, where the morphological complete wetting transition occurs. Finally, the whole cavity is filled with liquid. The free energy shows a barrier from complete drying to complete wetting as a function of droplet volume, which corresponds to the energy barrier between the Cassie and Wenzel states of the superhydrophobic surface with spherical cavities. The free-energy maximum occurs when the meniscus of the droplet becomes flat, and it is given by an analytic formula. The effect of line tension is expressed by the scaled line tension, and this effect is largest at the free-energy maximum. The positive line tension increases the free-energy maximum, which thus increases the stability of the Cassie superhydrophobic state, whereas the negative line tension destabilizes the superhydrophobic state.

A Novel Method Using Abstract Convex Underestimation in Ab-Initio Protein Structure Prediction for Guiding Search in Conformational Feature Space.

Science.gov (United States)

Hao, Xiao-Hu; Zhang, Gui-Jun; Zhou, Xiao-Gen; Yu, Xu-Feng

2016-01-01

To address the searching problem of protein conformational space in ab-initio protein structure prediction, a novel method using abstract convex underestimation (ACUE) based on the framework of evolutionary algorithm was proposed. Computing such conformations, essential to associate structural and functional information with gene sequences, is challenging due to the high-dimensionality and rugged energy surface of the protein conformational space. As a consequence, the dimension of protein conformational space should be reduced to a proper level. In this paper, the high-dimensionality original conformational space was converted into feature space whose dimension is considerably reduced by feature extraction technique. And, the underestimate space could be constructed according to abstract convex theory. Thus, the entropy effect caused by searching in the high-dimensionality conformational space could be avoided through such conversion. The tight lower bound estimate information was obtained to guide the searching direction, and the invalid searching area in which the global optimal solution is not located could be eliminated in advance. Moreover, instead of expensively calculating the energy of conformations in the original conformational space, the estimate value is employed to judge if the conformation is worth exploring to reduce the evaluation time, thereby making computational cost lower and the searching process more efficient. Additionally, fragment assembly and the Monte Carlo method are combined to generate a series of metastable conformations by sampling in the conformational space. The proposed method provides a novel technique to solve the searching problem of protein conformational space. Twenty small-to-medium structurally diverse proteins were tested, and the proposed ACUE method was compared with It Fix, HEA, Rosetta and the developed method LEDE without underestimate information. Test results show that the ACUE method can more rapidly and more

Log-Log Convexity of Type-Token Growth in Zipf's Systems

Science.gov (United States)

Font-Clos, Francesc; Corral, Álvaro

2015-06-01

It is traditionally assumed that Zipf's law implies the power-law growth of the number of different elements with the total number of elements in a system—the so-called Heaps' law. We show that a careful definition of Zipf's law leads to the violation of Heaps' law in random systems, with growth curves that have a convex shape in log-log scale. These curves fulfill universal data collapse that only depends on the value of Zipf's exponent. We observe that real books behave very much in the same way as random systems, despite the presence of burstiness in word occurrence. We advance an explanation for this unexpected correspondence.

Convex hull and tour crossings in the Euclidean traveling salesperson problem : implications for human performance studies

NARCIS (Netherlands)

Rooij, van I.; Stege, U.; Schactman, A.

2003-01-01

Recently there has been growing interest among psychologists in human performance on the Euclidean traveling salesperson problem (E-TSP). A debate has been initiated on what strategy people use in solving visually presented E-TSP instances. The most prominent hypothesis is the convex-hull

Neural Network in Fixed Time for Collision Detection between Two Convex Polyhedra

OpenAIRE

M. Khouil; N. Saber; M. Mestari

2014-01-01

In this paper, a different architecture of a collision detection neural network (DCNN) is developed. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons, linear and threshold logic, which simplified the actual implementation of all the networks proposed. The study of the collision detection is divided into two sections, the coll...

A Depth-Adjustment Deployment Algorithm Based on Two-Dimensional Convex Hull and Spanning Tree for Underwater Wireless Sensor Networks

Directory of Open Access Journals (Sweden)

Peng Jiang

2016-07-01

Full Text Available Most of the existing node depth-adjustment deployment algorithms for underwater wireless sensor networks (UWSNs just consider how to optimize network coverage and connectivity rate. However, these literatures don’t discuss full network connectivity, while optimization of network energy efficiency and network reliability are vital topics for UWSN deployment. Therefore, in this study, a depth-adjustment deployment algorithm based on two-dimensional (2D convex hull and spanning tree (NDACS for UWSNs is proposed. First, the proposed algorithm uses the geometric characteristics of a 2D convex hull and empty circle to find the optimal location of a sleep node and activate it, minimizes the network coverage overlaps of the 2D plane, and then increases the coverage rate until the first layer coverage threshold is reached. Second, the sink node acts as a root node of all active nodes on the 2D convex hull and then forms a small spanning tree gradually. Finally, the depth-adjustment strategy based on time marker is used to achieve the three-dimensional overall network deployment. Compared with existing depth-adjustment deployment algorithms, the simulation results show that the NDACS algorithm can maintain full network connectivity with high network coverage rate, as well as improved network average node degree, thus increasing network reliability.

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.

Decomposability and convex structure of thermal processes

Science.gov (United States)

Mazurek, Paweł; Horodecki, Michał

2018-05-01

We present an example of a thermal process (TP) for a system of d energy levels, which cannot be performed without an instant access to the whole energy space. This TP is uniquely connected with a transition between some states of the system, that cannot be performed without access to the whole energy space even when approximate transitions are allowed. Pursuing the question about the decomposability of TPs into convex combinations of compositions of processes acting non-trivially on smaller subspaces, we investigate transitions within the subspace of states diagonal in the energy basis. For three level systems, we determine the set of extremal points of these operations, as well as the minimal set of operations needed to perform an arbitrary TP, and connect the set of TPs with thermomajorization criterion. We show that the structure of the set depends on temperature, which is associated with the fact that TPs cannot increase deterministically extractable work from a state—the conclusion that holds for arbitrary d level system. We also connect the decomposability problem with detailed balance symmetry of an extremal TPs.

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.

Silicon microneedle formation using modified mask designs based on convex corner undercut

Science.gov (United States)

Wilke, N.; Morrissey, A.

2007-02-01

In this work, we present microneedle fabrication using the mechanism of silicon convex corner undercutting for modified etch masks in aqueous KOH solution (29% KOH, 79 °C). The presented modified mask designs include three different shapes, as well as different compensation structures applied to a square mask shape. We have found that square mask shapes present an optimum needle structure in contrast to circular or diamond shapes. The use of compensation structures facilitates an increase in needle density of 33-50% over that otherwise achieved.

High-Dimensional Analysis of Convex Optimization-Based Massive MIMO Decoders

KAUST Repository

Ben Atitallah, Ismail

2017-04-01

A wide range of modern large-scale systems relies on recovering a signal from noisy linear measurements. In many applications, the useful signal has inherent properties, such as sparsity, low-rankness, or boundedness, and making use of these properties and structures allow a more efficient recovery. Hence, a significant amount of work has been dedicated to developing and analyzing algorithms that can take advantage of the signal structure. Especially, since the advent of Compressed Sensing (CS) there has been significant progress towards this direction. Generally speaking, the signal structure can be harnessed by solving an appropriate regularized or constrained M-estimator. In modern Multi-input Multi-output (MIMO) communication systems, all transmitted signals are drawn from finite constellations and are thus bounded. Besides, most recent modulation schemes such as Generalized Space Shift Keying (GSSK) or Generalized Spatial Modulation (GSM) yield signals that are inherently sparse. In the recovery procedure, boundedness and sparsity can be promoted by using the ℓ1 norm regularization and by imposing an ℓ∞ norm constraint respectively. In this thesis, we propose novel optimization algorithms to recover certain classes of structured signals with emphasis on MIMO communication systems. The exact analysis permits a clear characterization of how well these systems perform. Also, it allows an automatic tuning of the parameters. In each context, we define the appropriate performance metrics and we analyze them exactly in the High Dimentional Regime (HDR). The framework we use for the analysis is based on Gaussian process inequalities; in particular, on a new strong and tight version of a classical comparison inequality (due to Gordon, 1988) in the presence of additional convexity assumptions. The new framework that emerged from this inequality is coined as Convex Gaussian Min-max Theorem (CGMT).

Image restoration by the method of convex projections: part 2 applications and numerical results.

Science.gov (United States)

Sezan, M I; Stark, H

1982-01-01

The image restoration theory discussed in a previous paper by Youla and Webb [1] is applied to a simulated image and the results compared with the well-known method known as the Gerchberg-Papoulis algorithm. The results show that the method of image restoration by projection onto convex sets, by providing a convenient technique for utilizing a priori information, performs significantly better than the Gerchberg-Papoulis method.

High speed global shutter image sensors for professional applications

Science.gov (United States)

Wu, Xu; Meynants, Guy

2015-04-01

Global shutter imagers expand the use to miscellaneous applications, such as machine vision, 3D imaging, medical imaging, space etc. to eliminate motion artifacts in rolling shutter imagers. A low noise global shutter pixel requires more than one non-light sensitive memory to reduce the read noise. But larger memory area reduces the fill-factor of the pixels. Modern micro-lenses technology can compensate this fill-factor loss. Backside illumination (BSI) is another popular technique to improve the pixel fill-factor. But some pixel architecture may not reach sufficient shutter efficiency with backside illumination. Non-light sensitive memory elements make the fabrication with BSI possible. Machine vision like fast inspection system, medical imaging like 3D medical or scientific applications always ask for high frame rate global shutter image sensors. Thanks to the CMOS technology, fast Analog-to-digital converters (ADCs) can be integrated on chip. Dual correlated double sampling (CDS) on chip ADC with high interface digital data rate reduces the read noise and makes more on-chip operation control. As a result, a global shutter imager with digital interface is a very popular solution for applications with high performance and high frame rate requirements. In this paper we will review the global shutter architectures developed in CMOSIS, discuss their optimization process and compare their performances after fabrication.

Modeling global mangrove soil carbon stocks: filling the gaps in coastal environments

Science.gov (United States)

Rovai, A.; Twilley, R.

2017-12-01

We provide an overview of contemporaneous global mangrove soil organic carbon (SOC) estimates, focusing on a framework to explain disproportionate differences among observed data as a way to improve global estimates. This framework is based on a former conceptual model, the coastal environmental setting, in contrast to the more popular latitude-based hypotheses largely believed to explain hemispheric variation in mangrove ecosystem properties. To demonstrate how local and regional estimates of SOC linked to coastal environmental settings can render more realistic global mangrove SOC extrapolations we combined published and unpublished data, yielding a total of 106 studies, reporting on 552 sites from 43 countries. These sites were classified into distinct coastal environmental setting types according to two concurrent worldwide typology of nearshore coastal systems classifications. Mangrove SOC density varied substantially across coastal environmental settings, ranging from 14.9 ± 0.8 in river dominated (deltaic) soils to 53.9 ± 1.6 mg cm-3 (mean ± SE) in karstic coastlines. Our findings reveal striking differences between published values and contemporary global mangrove SOC extrapolation based on country-level mean reference values, particularly for karstic-dominated coastlines where mangrove SOC stocks have been underestimated by up to 50%. Correspondingly, climate-based global estimates predicted lower mangrove SOC density values (32-41 mg C cm-3) for mangroves in karstic environments, differing from published (21-126 mg C cm-3) and unpublished (47-58 mg C cm-3) values. Moreover, climate-based projections yielded higher SOC density values (27-70 mg C cm-3) for river-dominated mangroves compared to lower ranges reported in the literature (11-24 mg C cm-3). We argue that this inconsistent reporting of SOC stock estimates between river-dominated and karstic coastal environmental settings is likely due to the omission of geomorphological and geophysical

Reachability by paths of bounded curvature in a convex polygon

KAUST Repository

Ahn, Heekap; Cheong, Otfried; Matoušek, Jiřǐ; Vigneron, Antoine E.

2012-01-01

Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n2) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment. © 2011 Elsevier B.V.

Globalization of consumer confidence

Directory of Open Access Journals (Sweden)

Çelik Sadullah

2017-01-01

Full Text Available The globalization of world economies and the importance of nowcasting analysis have been at the core of the recent literature. Nevertheless, these two strands of research are hardly coupled. This study aims to fill this gap through examining the globalization of the consumer confidence index (CCI by applying conventional and unconventional econometric methods. The US CCI is used as the benchmark in tests of comovement among the CCIs of several developing and developed countries, with the data sets divided into three sub-periods: global liquidity abundance, the Great Recession, and postcrisis. The existence and/or degree of globalization of the CCIs vary according to the period, whereas globalization in the form of coherence and similar paths is observed only during the Great Recession and, surprisingly, stronger in developing/emerging countries.

The structure of filled skutterudites and the local vibration behavior of the filling atom

Energy Technology Data Exchange (ETDEWEB)

Zhou, Xiaojuan [Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China); Dongguan Institute of Neutron Science, Dongguan 523808 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Zong, Peng-an [State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China); Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050 (China); Chen, Xihong [Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050 (China); Tao, Juzhou, E-mail: taoj@ihep.ac.cn [Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China); Dongguan Institute of Neutron Science, Dongguan 523808 (China); Lin, He, E-mail: linhe@sinap.ac.cn [Shanghai Institute of Applied Physics, Chinese Academy of Science, Shanghai 201204 (China)

2017-02-15

Both of atomic pair distribution function (PDF) and extended x-ray absorption fine structure (EXAFS) experiments have been carried out on unfilled and Yb-filled skutterudites Yb{sub x}Co{sub 4}Sb{sub 12} (x=0, 0.15, 0.2 and 0.25) samples. The structure refinements on PDF data confirm the large amplitude vibration of Yb atom and the dependence of Yb vibration amplitude on the filling content. Temperature dependent EXAFS experiment on filled skutterudites have been carried out at Yb L{sub Ⅲ}-edge in order to explore the local vibration behavior of filled atom. EXAFS experiments show that the Einstein temperature of the filled atom is very low (70.9 K) which agrees with the rattling behavior.

Geometry of convex polygons and locally minimal binary trees spanning these polygons

International Nuclear Information System (INIS)

Ivanov, A O; Tuzhilin, A A

1999-01-01

In previous works the authors have obtained an effective classification of planar locally minimal binary trees with convex boundaries. The main aim of the present paper is to find more subtle restrictions on the possible structure of such trees in terms of the geometry of the given boundary set. Special attention is given to the case of quasiregular boundaries (that is, boundaries that are sufficiently close to regular ones in a certain sense). In particular, a series of quasiregular boundaries that cannot be spanned by a locally minimal binary tree is constructed

Weighted mining of massive collections of [Formula: see text]-values by convex optimization.

Science.gov (United States)

Dobriban, Edgar

2018-06-01

Researchers in data-rich disciplines-think of computational genomics and observational cosmology-often wish to mine large bodies of [Formula: see text]-values looking for significant effects, while controlling the false discovery rate or family-wise error rate. Increasingly, researchers also wish to prioritize certain hypotheses, for example, those thought to have larger effect sizes, by upweighting, and to impose constraints on the underlying mining, such as monotonicity along a certain sequence. We introduce Princessp , a principled method for performing weighted multiple testing by constrained convex optimization. Our method elegantly allows one to prioritize certain hypotheses through upweighting and to discount others through downweighting, while constraining the underlying weights involved in the mining process. When the [Formula: see text]-values derive from monotone likelihood ratio families such as the Gaussian means model, the new method allows exact solution of an important optimal weighting problem previously thought to be non-convex and computationally infeasible. Our method scales to massive data set sizes. We illustrate the applications of Princessp on a series of standard genomics data sets and offer comparisons with several previous 'standard' methods. Princessp offers both ease of operation and the ability to scale to extremely large problem sizes. The method is available as open-source software from github.com/dobriban/pvalue_weighting_matlab (accessed 11 October 2017).

Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms With Directed Gossip Communication

Science.gov (United States)

Jakovetic, Dusan; Xavier, João; Moura, José M. F.

2011-08-01

We study distributed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x=x^\\star. The objective function of the corresponding optimization problem is the sum of private (known only by a node,) convex, nodes' objectives and each node imposes a private convex constraint on the allowed values of x. We solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed, decentralized algorithm. We refer to this algorithm as AL-G (augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual function. Dual variables are updated by the standard method of multipliers, at a slow time scale. To update the primal variables, we propose a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses unidirectional gossip communication, only between immediate neighbors in the network and is resilient to random link failures. For networks with reliable communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian broadcast gossiping) algorithm reduces communication, computation and data storage cost. We prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications: l_1-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.

Study on feed forward neural network convex optimization for LiFePO4 battery parameters

Science.gov (United States)

Liu, Xuepeng; Zhao, Dongmei

2017-08-01

Based on the modern facility agriculture automatic walking equipment LiFePO4 Battery, the parameter identification of LiFePO4 Battery is analyzed. An improved method for the process model of li battery is proposed, and the on-line estimation algorithm is presented. The parameters of the battery are identified using feed forward network neural convex optimization algorithm.

Formation of Sheeting Joints as a Result of Compression Parallel to Convex Surfaces, With Examples from Yosemite National Park, California

Science.gov (United States)

Martel, S. J.

2008-12-01

The formation of sheeting joints has been an outstanding problem in geology. New observations and analyses indicate that sheeting joints develop in response to a near-surface tension induced by compressive stresses parallel to a convex slope (hypothesis 1) rather than by removal of overburden by erosion, as conventionally assumed (hypothesis 2). Opening mode displacements across the joints together with the absence of mineral precipitates within the joints mean that sheeting joints open in response to a near-surface tension normal to the surface rather than a pressurized fluid. Consideration of a plot of this tensile stress as a function of depth normal to the surface reveals that a true tension must arise in the shallow subsurface if the rate of that tensile stress change with depth is positive at the surface. Static equilibrium requires this rate (derivative) to equal P22 k2 + P33 k3 - ρ g cosβ, where k2 and k3 are the principal curvatures of the surface, P22 and P33 are the respective surface- parallel normal stresses along the principal curvatures, ρ is the material density, g is gravitational acceleration, and β is the slope. This derivative will be positive and sheeting joints can open if at least one principal curvature is sufficiently convex (negative) and the surface-parallel stresses are sufficiently compressive (negative). At several sites with sheeting joints (e.g., Yosemite National Park in California), the measured topographic curvatures and the measured surface-parallel stresses of about -10 MPa combine to meet this condition. In apparent violation of hypothesis 1, sheeting joints occur locally at the bottom of Tenaya Canyon, one of the deepest glaciated, U-shaped (concave) canyons in the park. The canyon-bottom sheeting joints only occur, however, where the canyon is convex downstream, a direction that nearly coincides with direction of the most compressive stress measured in the vicinity. The most compressive stress acting along the convex

Operation feedback of hydrogen filling station

International Nuclear Information System (INIS)

Pregassame, S.; Barral, K.; Allidieres, L.; Charbonneau, T.; Lacombe, Y.

2004-01-01

One of the technical challenges of hydrogen technology is the development of hydrogen infrastructures which satisfy either safety requirements and reliability of filling processes. AIR LIQUIDE realized an hydrogen filling station in Sassenage (France) operational since September 2003. This station is able to fill 3 buses a day up to 350bar by equilibrium with high pressure buffers. In parallel with commercial stations, the group wanted to create a testing ground in real conditions running with several objectives: validate on a full scale bench a simulation tool able to predict the temperature of both gas and cylinder's materials during filling processes; define the best filling procedures in order to reach mass, temperature and filling time targets; analyse the temperature distribution and evolution inside the cylinder; get a general knowledge about hydrogen stations from safety and reliability point of view; operate the first full scale refuelling station in France. The station is also up-graded for 700bar filling from either a liquid hydrogen source or a gas booster, with cold filling possibility. This paper presents the results concerning 350bar filling : thermal effects, optimal filling procedures and influence of parameters such as climatic conditions are discussed. (author)

Droplet Measurement below Single-Layer Grid Fill

Directory of Open Access Journals (Sweden)

Vitkovic Pavol

2016-01-01

Full Text Available The main part of the heat transfer in a cooling tower is in a fill zone. This one is consist of a cooling fill. For the cooling tower is used a film fill or grid fill or splash fill in the generally. The grid fill has lower heat transfer performance like film fill usually. But their advantage is high resistance to blockage of the fill. The grid fill is consisted with independent layers made from plastic usually. The layers consist of several bars connected to the different shapes. For experiment was used the rhombus shape. The drops diameter was measured above and below the Grid fill.

Theoretical study of the influence of decentring on longitudinal stability of a flat-convex lenticular lighted wing

Energy Technology Data Exchange (ETDEWEB)

Bouquet, R [Univ. de Poitiers, ENSMA, Poitiers (France)

1985-07-01

The flat-convex lenticular wings have a very interesting polar-diagram, with a big relative thickness, good for partial static lifting force by introduction of light gas. But the longitudinal balance can be easily realized only with a notable decentring for the load. The theoretical study of stability conditions, in horizontal propulsed flight, as in gliding without engine power, gives the localization of a balance center, different of the gravity center, and the calculation of an optimal centring, function of a diagram-family c{sub m}(i) established on computer. In this new calculation, described in this paper, the relative of static lifting force is one of the principal parameters. A 16 mm coloured movie in annex shows the flight tests with a motorized wireless-controlled scale-model, realized according to the theory. This experiments give proof of aeronautical possibilities of this flat-convex lenticular lighted air-ship, with the name of: 'flying turtle' project. (author)

Filling a Conical Cavity

Science.gov (United States)

Nye, Kyle; Eslam-Panah, Azar

2016-11-01

Root canal treatment involves the removal of infected tissue inside the tooth's canal system and filling the space with a dense sealing agent to prevent further infection. A good root canal treatment happens when the canals are filled homogeneously and tightly down to the root apex. Such a tooth is able to provide valuable service for an entire lifetime. However, there are some examples of poorly performed root canals where the anterior and posterior routes are not filled completely. Small packets of air can be trapped in narrow access cavities when restoring with resin composites. Such teeth can cause trouble even after many years and lead the conditions like acute bone infection or abscesses. In this study, the filling of dead-end conical cavities with various liquids is reported. The first case studies included conical cavity models with different angles and lengths to visualize the filling process. In this investigation, the rate and completeness at which a variety of liquids fill the cavity were observed to find ideal conditions for the process. Then, a 3D printed model of the scaled representation of a molar with prepared post spaces was used to simulate the root canal treatment. The results of this study can be used to gain a better understanding of the restoration for endodontically treated teeth.

Determination of left and right ventricular ejection and filling by fast cine MR imaging in the breath-hold technique in healthy subjects

International Nuclear Information System (INIS)

Rominger, M.B.; Bachmann, G.F.; Geuer, M.; Puzik, M.; Rau, W.S.; Pabst, W.

1999-01-01

Purpose: Evaluation and comparison of localized and global left and right ventricular ejection and filling with fast cine MR imaging in the breath-hold technique. Materials and Methods: 10 healthy volunteers were examined with a 1.5 Tesla unit and phased-array-coil using a segmented FLASH-2D sequence in breath-hold technique. Peak ejection and peak filling rates [PER, PFR enddiastolic volume (EDV)/s], time to PER and PFR [TPER, TPFR ms] and time of endsystole [TSYS in % RR-intervall] of all slices (complete-slice-evaluation) were evaluated and compared to three left ventricular and one right ventricular slices (reduced three-slice-evaluation). Results: There were significant regional left ventricular differences of PER (p=0.002) and PFR (p=0.007), but not of TPER and TPFR. Ejection and filling indices of the left ventricular middle slice were closest to the overall evaluation of all sections. In the left-/right-side comparison the right ventricular PFR was higher than the left ventricular (5.1 and 4.2 EDV/s) and the right ventricular TPFR was earlier than the left (92.2 and 123.5 ms). Conclusions: With fast cine techniques, regional and global left and right ventricular ejection and filling indices can be evaluated in addition to the global heart volume indices. The three-slice-evaluation represents a comprehensive, clear and time-saving method for daily routine. (orig.) [de

Geometry intuitive, discrete, and convex : a tribute to László Fejes Tóth

CERN Document Server

Böröczky, Károly; Tóth, Gábor; Pach, János

2013-01-01

The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth.

A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds

OpenAIRE

Baker, Mark; Cooper, Daryl

2005-01-01

We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generate a subgroup that is an amalgamated free product. Constructions of infinite volume hyperbolic n-manifolds are described by gluing lo...

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). ​

Filling some black holes: modeling the connection between urbanization, infrastructure, and global service intensity

OpenAIRE

Van De Vijver, Elien; Derudder, Ben; Bassens, David; Witlox, Frank

2014-01-01

This empirical article combines insights from previous research on the level of knowledge-intensive service in metropolitan areas with the aim to develop an understanding of the spatial structure of the global service economy. We use a stepwise regression model with the Globalization and World Cities research network's measure of globalized service provisioning as the dependent variable and a range of variables focusing on population, infrastructure, urban primacy, and national regulation as ...

Comparison of anatomic vs. straight femoral stem design in total hip replacement - femoral canal fill in vivo.

Science.gov (United States)

de Boer, Friso A; Sariali, Elhadi

2017-05-12

The femoral canal fill between an anatomic and a straight prosthesis design in cementless total hip arthroplasty (THA) was compared. We hypothesised that the anatomic SPS stem has higher proximal fill and lesser distal fill than the straight stem. The femoral canal fill was measured on 3 months routine postoperative x-rays at 5 levels of the stem in 50 consecutive patients, aged 35-83 years, who underwent 56 THA procedures by a single surgeon in this hospital. 22 patients received a straight design Ceramconcept Global stem, 34 patients received an anatomic design Symbios SPS stem. Both anteroposterior (AP) and lateral x-rays were combined to suggest a 3-D measurement. On the AP x-rays, the canal fill was significantly higher using the anatomic design stem at the proximal measurement levels, and was significantly higher at the distal levels using the straight stem. With the AP and lateral x-rays combined, the canal fill at the proximal levels was also significantly higher in the anatomic groups, nonsignificantly lower at the central level and significantly lower at the distal levels. In THA surgery, achieving high fill at the metaphysis of the femur and less fill at the diaphysis has been suggested to result in satisfactory outcome and high stability of the prosthesis. This study demonstrated that, compared to straight stem design, an anatomically designed stem has a significantly higher metaphyseal femoral canal fill.

An Iterative Procedure for Obtaining I-Projections onto the Intersection of Convex Sets.

Science.gov (United States)

1984-06-01

Dykstra Department of Statistics and Actuarial Science The University of Iowa Iowa City, Iowa 52242 Technical Report #106 June 1984D I e ELECTE lSEP...t Theorem ~ ~ 2.. Asm i where the 4 are closed, convex sets of PD’s and R d 0 is a nonnegative vector such that there exists a T E 4 where I(TIR) < M...PERFOMING ORGANIZATION NAME AND ADDRESS 1. PROGIRA ILEMNT. PROJECT. TAK Department of Statistics and Actuarial Science AEAS a WORK UNIT Numaa The

Horn clause verification with convex polyhedral abstraction and tree automata-based refinement

DEFF Research Database (Denmark)

Kafle, Bishoksan; Gallagher, John Patrick

2017-01-01

In this paper we apply tree-automata techniques to refinement of abstract interpretation in Horn clause verification. We go beyond previous work on refining trace abstractions; firstly we handle tree automata rather than string automata and thereby can capture traces in any Horn clause derivations...... underlying the Horn clauses. Experiments using linear constraint problems and the abstract domain of convex polyhedra show that the refinement technique is practical and that iteration of abstract interpretation with tree automata-based refinement solves many challenging Horn clause verification problems. We...... compare the results with other state-of-the-art Horn clause verification tools....

Microhardness of bulk-fill composite materials

OpenAIRE

Kelić, Katarina; Matić, Sanja; Marović, Danijela; Klarić, Eva; Tarle, Zrinka

2016-01-01

The aim of the study was to determine microhardness of high- and low-viscosity bulk-fill composite resins and compare it with conventional composite materials. Four materials of high-viscosity were tested, including three bulk-fills: QuiXfi l (QF), x-tra fil (XTF) and Tetric EvoCeram Bulk Fill (TEBCF), while nanohybrid composite GrandioSO (GSO) served as control. The other four were low-viscosity composites, three bulk-fill materials: Smart Dentin Replacement (SDR), Venus Bulk Fill (VBF) and ...

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.

Radiopacity of root filling materials

International Nuclear Information System (INIS)

Beyer-Olsen, E.M.

1983-01-01

A method for measuring the radiopacity of root filling materials is described. Direct measurements were made of the optic density values of the materials in comparison with a standard curve relating optic density to the thickness of an aluminium step wedge exposed simultaneously. By proper selection of film and conditions for exposure and development, it was possible to obtain a near-linear standard curve which added to the safety and reproducibility of the method. The technique of radiographic assessment was modified from clinical procedures in evaluating the obturation in radiographs, and it was aimed at detecting slits or voids between the dental wall and the filling material. This radiographic assessment of potensial leakage was compared with actual in vitro lekage of dye (basic fuchsin) into the roots of filled teeth. The result of the investigation show that root filling materials display a very wide range of radiopacity, from less than 3 mm to more than 12 mm of aluminium. It also seem that tooth roots that appear to be well obturated by radiographic evaluation, stand a good chance of beeing resistant to leakage in vitro, and that the type of filling material rather than its radiographic appearance, determines the susceptibility of the filled tooth to leakage in vitro. As an appendix the report contains a survey of radiopaque additives in root filling materials

Globally inconsistent figure/ground relations induced by a negative part.

Science.gov (United States)

Kim, Sung-Ho; Feldman, Jacob

2009-09-10

Figure/ground interpretation is a dynamic and complex process involving the cooperation and competition of a number of perceptual factors. Most research has assumed that figure/ground assignment is globally consistent along the entire contour of a single figure, meaning that the one side of each boundary is interpreted as figure along the entire length of the boundary, and the other side interpreted as ground. We investigated a situation that challenges this assumption, because local cues to figure/ground conflict with global cues: a "negative part," a contour region that appears locally convex but that the global form requires be concave. To measure figure/ground assignment, we use a new task based on local contour motion attribution that allows us to measure border ownership locally at points along the contour. The results from two experiments showed that the more salient a negative part is, the more border ownership tended to locally reverse within it, creating an inconsistency in figure/ground assignments along the contour. This suggests that border ownership assignment is not an all-or-none process, but rather a locally autonomous process that is not strictly constrained by global cues.

Highly efficient absorption of visible and near infrared light in convex gold and nickel grooves

DEFF Research Database (Denmark)

Eriksen, René Lynge; Beermann, Jonas; Søndergaard, Thomas

The realization of nonresonant light absorption with nanostructured metal surfaces by making practical use of nanofocusing optical energy in tapered plasmonic waveguides, is of one of the most fascinating and fundamental phenomena in plasmonics [1,2]. We recently realized broadband light absorption...... in gold via adiabatic nanofocusing of gap surface plasmon modes in well-defined geometries of ultra-sharp convex grooves and being excited by scattering off subwavelength-sized wedges [3]....

Estimation of water-filled and air-filled porosity in the unsaturated zone, Yucca Mountain, Nevada

International Nuclear Information System (INIS)

Nelson, P.H.

1993-01-01

Water content and porosity vary considerably within the unsaturated zone at Yucca Mountain. Measurement of these quantities has been based on core samples. A log-based approach offers the advantage of in-situ measurements, continuous throughout the borehole. This paper describes an algorithm which determines the air-filled and water-filled porosities from density and dielectric logs. The responses of density and dielectric logs are formulated in terms of the matrix properties, air-filled porosity and water-filled porosity. Porosity values obtained from logs from borehole USW G-2 are in reasonable agreement with estimates from core determinations

The effect of tube filling on the electronic properties of Fe filled carbon nanotubes

International Nuclear Information System (INIS)

Linganiso, Ella C.; Chimowa, George; Franklyn, Paul J.; Bhattacharyya, Somnath; Coville, Neil J.

2012-01-01

Graphical abstract: HRTEM image of a twisted CNT filled with a bent single crystal of Fe. Insets from top to bottom show the power spectra of the corresponding regions, indicating the twisting of the Fe lattice. Inset in the top right shows the relative angling of the lattice fringes to accommodate the twisting of the Fe. Highlights: ► Synthesis of Fe filled CNTs with Fe content varying from 3 to 35%. ► TEM analysis indicates that Fe in the tubes is in contact with the CNTs. ► TEM analysis reveals that α-Fe crystallizes after CNT formation. ► Temperature dependent electronic transport measurements performed. ► Conductivity varies with the % Fe filling in the CNTs. - Abstract: Carbon nanotubes filled with Fe nanostructures (Fe-CNTs) were synthesized using an injection method in a 1-stage horizontal CVD furnace and a bubbling method in a 2-stage horizontal CVD reactor. Fe-CNTs were obtained through the pyrolysis of a mixture of dichlorobenzene and ferrocene in 5%H 2 /Ar. Metal impurities from the Fe-CNTs were removed using 1 M HCl solution. CNTs filled with crystalline Fe nanoparticles, nanorods and nanowires were obtained using these procedures. An intimate interaction between the Fe and the CNT was established by HRTEM studies. The α-Fe phase was observed to be the most dominant fraction found in the synthesized Fe-CNTs. The Fe 2 O 3 residue obtained from the TGA analysis revealed the amount of Fe filled inside the CNTs and this ranged between 3 and 31% by mass after purification. The temperature dependence of the conductivity in the temperature range between 2.5 and 100 K for an entangled network of Fe-CNTs was measured. An increase in conductivity due to the increased Fe filling inside the CNTs with increased temperature was observed. The observed temperature dependence was explained in terms of variable range hopping (VRH) conduction mechanisms. A transition from Efros–Shklovskii behavior at low % Fe filling of the CNTs to Mott 3D VRH behavior at

Mechanics of filled carbon nanotubes

KAUST Repository

Monteiro, A.O.; Cachim, P.B.; Da Costa, Pedro M. F. J.

2014-01-01

The benefits of filling carbon nanotubes (CNTs) with assorted molecular and crystalline substances have been investigated for the past two decades. Amongst the study of new structural phases, defects, chemical reactions and varied types of host-guest interactions, there is one fundamental characterisation aspect of these systems that continues to be overlooked: the mechanical behaviour of filled CNTs. In contrast to their empty counterparts, the mechanics of filled CNTs is a subject where reports appear far and apart, this despite being key to the application of these materials in technological devices. In the following paragraphs, we review the work that has been carried out up to the present on the mechanics of filled CNTs. The studies discussed range from experimental resonant frequency essays performed within electron microscopes to modelling, via molecular dynamics, of three-point bending of nanotubes filled with gases. (C) 2014 Elsevier B.V. All rights reserved.

Mechanics of filled carbon nanotubes

KAUST Repository

Monteiro, A.O.

2014-04-01

The benefits of filling carbon nanotubes (CNTs) with assorted molecular and crystalline substances have been investigated for the past two decades. Amongst the study of new structural phases, defects, chemical reactions and varied types of host-guest interactions, there is one fundamental characterisation aspect of these systems that continues to be overlooked: the mechanical behaviour of filled CNTs. In contrast to their empty counterparts, the mechanics of filled CNTs is a subject where reports appear far and apart, this despite being key to the application of these materials in technological devices. In the following paragraphs, we review the work that has been carried out up to the present on the mechanics of filled CNTs. The studies discussed range from experimental resonant frequency essays performed within electron microscopes to modelling, via molecular dynamics, of three-point bending of nanotubes filled with gases. (C) 2014 Elsevier B.V. All rights reserved.

Investigations into the tensile failure of doubly-convex cylindrical tablets under diametral loading using finite element methodology.

Science.gov (United States)

Podczeck, Fridrun; Drake, Kevin R; Newton, J Michael

2013-09-15

In the literature various solutions exist for the calculation of the diametral compression tensile strength of doubly-convex tablets and each approach is based on experimental data obtained from single materials (gypsum, microcrystalline cellulose) only. The solutions are represented by complex equations and further differ for elastic and elasto-plastic behaviour of the compacts. The aim of this work was to develop a general equation that is applicable independently of deformation behaviour and which is based on simple tablet dimensions such as diameter and total tablet thickness only. With the help of 3D-FEM analysis the tensile failure stress of doubly-convex tables with central cylinder to total tablet thickness ratios W/D between 0.06 and 0.50 and face-curvature ratios D/R between 0.25 and 1.85 were evaluated. Both elastic and elasto-plastic deformation behaviour were considered. The results of 80 individual simulations were combined and showed that the tensile failure stress σt of doubly-convex tablets can be calculated from σt=(2P/πDW)(W/T)=2P/πDT with P being the failure load, D the diameter, W the central cylinder thickness, and T the total thickness of the tablet. This equation converts into the standard Brazilian equation (σt=2P/πDW) when W equals T, i.e. is equally valid for flat cylindrical tablets. In practice, the use of this new equation removes the need for complex measurements of tablet dimensions, because it only requires values for diameter and total tablet thickness. It also allows setting of standards for the mechanical strength of doubly-convex tablets. The new equation holds both for elastic and elasto-plastic deformation behaviour of the tablets under load. It is valid for all combinations of W/D-ratios between 0.06 and 0.50 with D/R-ratios between 0.00 and 1.85 except for W/D=0.50 in combination with D/R-ratios of 1.85 and 1.43 and for W/D-ratios of 0.40 and 0.30 in combination with D/R=1.85. FEM-analysis indicated a tendency to

Systolic ventricular filling.

Science.gov (United States)

Torrent-Guasp, Francisco; Kocica, Mladen J; Corno, Antonio; Komeda, Masashi; Cox, James; Flotats, A; Ballester-Rodes, Manel; Carreras-Costa, Francesc

2004-03-01

The evidence of the ventricular myocardial band (VMB) has revealed unavoidable coherence and mutual coupling of form and function in the ventricular myocardium, making it possible to understand the principles governing electrical, mechanical and energetical events within the human heart. From the earliest Erasistratus' observations, principal mechanisms responsible for the ventricular filling have still remained obscured. Contemporary experimental and clinical investigations unequivocally support the attitude that only powerful suction force, developed by the normal ventricles, would be able to produce an efficient filling of the ventricular cavities. The true origin and the precise time frame for generating such force are still controversial. Elastic recoil and muscular contraction were the most commonly mentioned, but yet, still not clearly explained mechanisms involved in the ventricular suction. Classical concepts about timing of successive mechanical events during the cardiac cycle, also do not offer understandable insight into the mechanism of the ventricular filling. The net result is the current state of insufficient knowledge of systolic and particularly diastolic function of normal and diseased heart. Here we summarize experimental evidence and theoretical backgrounds, which could be useful in understanding the phenomenon of the ventricular filling. Anatomy of the VMB, and recent proofs for its segmental electrical and mechanical activation, undoubtedly indicates that ventricular filling is the consequence of an active muscular contraction. Contraction of the ascendent segment of the VMB, with simultaneous shortening and rectifying of its fibers, produces the paradoxical increase of the ventricular volume and lengthening of its long axis. Specific spatial arrangement of the ascendent segment fibers, their interaction with adjacent descendent segment fibers, elastic elements and intra-cavitary blood volume (hemoskeleton), explain the physical principles

Fast globally optimal segmentation of cells in fluorescence microscopy images.

Science.gov (United States)

Bergeest, Jan-Philip; Rohr, Karl

2011-01-01

Accurate and efficient segmentation of cells in fluorescence microscopy images is of central importance for the quantification of protein expression in high-throughput screening applications. We propose a new approach for segmenting cell nuclei which is based on active contours and convex energy functionals. Compared to previous work, our approach determines the global solution. Thus, the approach does not suffer from local minima and the segmentation result does not depend on the initialization. We also suggest a numeric approach for efficiently computing the solution. The performance of our approach has been evaluated using fluorescence microscopy images of different cell types. We have also performed a quantitative comparison with previous segmentation approaches.

Insurance-markets Equilibrium with Sequential Non-convex Straight-time and Over-time Labor Supply

OpenAIRE

Vasilev, Aleksandar

2016-01-01

This note describes the lottery- and insurance-market equilibrium in an economy with non-convex straight-time and overtime employment. In contrast to Hansen and Sargent (1988), the overtime-decision is a sequential one. This requires two separate insurance market to operate, one for straight-time work, and one for overtime. In addi- tion, given that the labor choice for regular and overtime hours is made in succession, the insurance market for overtime needs to open once the insurance market ...

Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations

Science.gov (United States)

Dey, C.; Dey, S. K.

1983-01-01

An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

Vertical Scan-Conversion for Filling Purposes

OpenAIRE

Hersch, R. D.

1988-01-01

Conventional scan-conversion algorithms were developed independently of filling algorithms. They cause many problems, when used for filling purposes. However, today's raster printers and plotters require extended use of filling, especially for the generation of typographic characters and graphic line art. A new scan-conversion algorithm, called vertical scan-conversion has been specifically designed to meet the requirements of parity scan line fill algorithms. Vertical scan-conversion ensures...

Globalization of food and agriculture and the poor:

OpenAIRE

von Braun, Joachim; Díaz-Bonilla, Eugenio

2008-01-01

The economic impact of globalization, particularly on poverty, and the changes in agri-food markets have received much attention in recent years. However, the intersection of these two trends has been neglected. The present volume fills this gap by focusing on the way globalization of agri-food systems affects the world's poor and its impact on food and nutrition security in developing countries. Rather than offering a single policy prescription or simplistic messages about globalization bein...

Removal of root filling materials.

LENUS (Irish Health Repository)

Duncan, H.F. Chong, B.S.

2011-05-01

Safe, successful and effective removal of root filling materials is an integral component of non-surgical root canal re-treatment. Access to the root canal system must be achieved in order to negotiate to the canal terminus so that deficiencies in the original treatment can be rectified. Since a range of materials have been advocated for filling root canals, different techniques are required for their removal. The management of commonly encountered root filling materials during non-surgical re-treatment, including the clinical procedures necessary for removal and the associated risks, are reviewed. As gutta-percha is the most widely used and accepted root filling material, there is a greater emphasis on its removal in this review.

A Duality Theory for Non-convex Problems in the Calculus of Variations

Science.gov (United States)

Bouchitté, Guy; Fragalà, Ilaria

2018-02-01

We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375-379, 2015).

On asphericity of convex bodies in linear normed spaces.

Science.gov (United States)

Faried, Nashat; Morsy, Ahmed; Hussein, Aya M

2018-01-01

In 1960, Dvoretzky proved that in any infinite dimensional Banach space X and for any [Formula: see text] there exists a subspace L of X of arbitrary large dimension ϵ -iometric to Euclidean space. A main tool in proving this deep result was some results concerning asphericity of convex bodies. In this work, we introduce a simple technique and rigorous formulas to facilitate calculating the asphericity for each set that has a nonempty boundary set with respect to the flat space generated by it. We also give a formula to determine the center and the radius of the smallest ball containing a nonempty nonsingleton set K in a linear normed space, and the center and the radius of the largest ball contained in it provided that K has a nonempty boundary set with respect to the flat space generated by it. As an application we give lower and upper estimations for the asphericity of infinite and finite cross products of these sets in certain spaces, respectively.

Convex analysis and monotone operator theory in Hilbert spaces

CERN Document Server

Bauschke, Heinz H

2017-01-01

This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...

Global optimization of discrete truss topology design problems using a parallel cut-and-branch method

DEFF Research Database (Denmark)

Rasmussen, Marie-Louise Højlund; Stolpe, Mathias

2008-01-01

the physics, and the cuts (Combinatorial Benders’ and projected Chvátal–Gomory) come from an understanding of the particular mathematical structure of the reformulation. The impact of a stronger representation is investigated on several truss topology optimization problems in two and three dimensions.......The subject of this article is solving discrete truss topology optimization problems with local stress and displacement constraints to global optimum. We consider a formulation based on the Simultaneous ANalysis and Design (SAND) approach. This intrinsically non-convex problem is reformulated...

Results on an integral inequality of the opial- type | Rauf | Global ...

African Journals Online (AJOL)

Abstract. We obtain integral inequalities which are Opial-type inequalities, mainly by using Jensen's inequality for the case of convex function. Keywords: Integral inequalities, Opial's inequality, Jensen's inequality and convex functions ...

Technology of hardening fills for mined spaces

International Nuclear Information System (INIS)

Simek, P.; Holas, M.; Chyla, A.; Pech, P.

1985-01-01

The technology is described of hardening fills for mined spaces of uranium deposits in North Bohemian chalk. A special equipment was developed for the controlled preparation of a hardening mixture. The composition of the fill is determined by the strength of the filled rock, expecially by the standard strength, i.e., the minimal strength of the filling under uniaxial pressure. The said parameter determines the consumption of binding materials and thereby the total costs of the filling. A description is presented of the filling technology, including rabbit tube transport of the mixture and quality control. (Pu)

Gas-filled hohlraum fabrication

International Nuclear Information System (INIS)

Salazar, M.A.; Gobby, P.L.; Foreman, L.R.; Bush, H. Jr.; Gomez, V.M.; Moore, J.E.; Stone, G.F.

1995-01-01

Los Alamos National Laboratory (LANL) researchers have fabricated and fielded gas-filled hohlraums at the Lawrence Livermore National Laboratory (LLNL) Nova laser. Fill pressures of 1--5 atmospheres have been typical. We describe the production of the parts, their assembly and fielding. Emphasis is placed on the production of gas-tight polyimide windows and the fielding apparatus and procedure

NSLS-II filling pattern measurement

International Nuclear Information System (INIS)

Yong Hu; Dalesio, L.B.; Kiman Ha; Pinayev, I.

2012-01-01

Multi-bunch injection will be deployed at NSLS-II. High bandwidth diagnostic beam monitors with high speed digitizers are used to measure bunch-by-bunch charge variation. In order to minimize intensity-correlated orbit oscillations due to uneven bunch patterns, we need to measure the filling pattern (also named bunch pattern or bunch structure). This paper focuses on filling pattern measurements: how to measure bunch structure and make this information available in EPICS-based control system. This measurement requires combination of 3 types of beam monitors (Wall Current Monitor, Fast Current Transformer and Beam Position Monitor), data acquisition and controls (fast digitizer, EPICS software, etc.) and Event Timing system. High-bandwidth filling pattern monitor requires high-speed digitizer to sample its analog output signal. The evaluation results of commercial fast digitizer Agilent Acqiris and high bandwidth detector Bergoz FCT are presented. We have also tested the algorithm software for filling pattern measurement as well as the interface to event timing system. It appears that filling pattern measurement system is well understood and the tests for control hardware and software have given good results

Research Synthesis Methods in an Age of Globalized Risks: Lessons from the Global Burden of Foodborne Disease Expert Elicitation

DEFF Research Database (Denmark)

Hald, Tine; Angulo, Fred; Bin Hamzah, Wan Mansor

2016-01-01

We live in an age that increasingly calls for national or regional management of global risks. This article discusses the contributions that expert elicitation can bring to efforts to manage global risks and identifies challenges faced in conducting expert elicitation at this scale. In doing so...... it draws on lessons learned from conducting an expert elicitation as part of the World Health Organizations (WHO) initiative to estimate the global burden of foodborne disease; a study commissioned by the Foodborne Disease Epidemiology Reference Group (FERG). Expert elicitation is designed to fill gaps...

Convex relaxations of spectral sparsity for robust super-resolution and line spectrum estimation

Science.gov (United States)

Chi, Yuejie

2017-08-01

We consider recovering the amplitudes and locations of spikes in a point source signal from its low-pass spectrum that may suffer from missing data and arbitrary outliers. We first review and provide a unified view of several recently proposed convex relaxations that characterize and capitalize the spectral sparsity of the point source signal without discretization under the framework of atomic norms. Next we propose a new algorithm when the spikes are known a priori to be positive, motivated by applications such as neural spike sorting and fluorescence microscopy imaging. Numerical experiments are provided to demonstrate the effectiveness of the proposed approach.

The monotonicity and convexity of a function involving digamma one and their applications

OpenAIRE

Yang, Zhen-Hang

2014-01-01

Let $\\mathcal{L}(x,a)$ be defined on $\\left( -1,\\infty \\right) \\times \\left( 4/15,\\infty \\right) $ or $\\left( 0,\\infty \\right) \\times \\left( 1/15,\\infty \\right) $ by the formula% \\begin{equation*} \\mathcal{L}(x,a)=\\tfrac{1}{90a^{2}+2}\\ln \\left( x^{2}+x+\\tfrac{3a+1}{3}% \\right) +\\tfrac{45a^{2}}{90a^{2}+2}\\ln \\left( x^{2}+x+\\allowbreak \\tfrac{% 15a-1}{45a}\\right) . \\end{equation*} We investigate the monotonicity and convexity of the function $x\\rightarrow F_{a}\\left( x\\right) =\\psi \\left( x+1\\r...

Review of fill mining technology in Canada

Energy Technology Data Exchange (ETDEWEB)

Singh, K. H.; Hedley, D. G.F.

1980-05-15

The Canadian mining industry has a long history of being in the fore-front in developing new technology in underground hardrock mines. Examples include the development of hydraulic and cemented fills, undercut-and-fill, mechanized cut-and-fill, post pillar, vertical retreat and blasthole mining methods. The evolution of this technology is briefly described in an historical review. Backfill serves many functions, although it is generally considered in terms of its support capabilities. These functions, mainly related to the mining method used, are evaluated in regard to regional support, pillar support, fill roof, working floor, dilution control and waste disposal. With the advent of blasthole and vertical retreat methods for pillar recovery operations, the freestanding height of backfill walls has assumed greater importance. Consequently, more attention is being given to what fill properties are required to achieve fill wall exposures up to 25 m wide by 90 m high. With the large increases in energy costs, alternatives to partially replace Portland cement in fill are being examined. The validation of mining concepts and the interaction of backfill is perhaps best evaluated by in-situ measurements. Examples are given of stress, deformation and fill pressure measurements in longitudinal cut-and-fill, post pillar mining and blasthole stoping with delayed fill which were taken in several mines in Canada. Finally, the overall design procedure used in deciding mining method, stope and pillar dimensions, sequence of extraction, fill properties and support systems at a new mine is described.

3D prostate TRUS segmentation using globally optimized volume-preserving prior.

Science.gov (United States)

Qiu, Wu; Rajchl, Martin; Guo, Fumin; Sun, Yue; Ukwatta, Eranga; Fenster, Aaron; Yuan, Jing

2014-01-01

An efficient and accurate segmentation of 3D transrectal ultrasound (TRUS) images plays an important role in the planning and treatment of the practical 3D TRUS guided prostate biopsy. However, a meaningful segmentation of 3D TRUS images tends to suffer from US speckles, shadowing and missing edges etc, which make it a challenging task to delineate the correct prostate boundaries. In this paper, we propose a novel convex optimization based approach to extracting the prostate surface from the given 3D TRUS image, while preserving a new global volume-size prior. We, especially, study the proposed combinatorial optimization problem by convex relaxation and introduce its dual continuous max-flow formulation with the new bounded flow conservation constraint, which results in an efficient numerical solver implemented on GPUs. Experimental results using 12 patient 3D TRUS images show that the proposed approach while preserving the volume-size prior yielded a mean DSC of 89.5% +/- 2.4%, a MAD of 1.4 +/- 0.6 mm, a MAXD of 5.2 +/- 3.2 mm, and a VD of 7.5% +/- 6.2% in - 1 minute, deomonstrating the advantages of both accuracy and efficiency. In addition, the low standard deviation of the segmentation accuracy shows a good reliability of the proposed approach.

Improved methods for dewarping images in convex mirrors in fine art: applications to van Eyck and Parmigianino

Science.gov (United States)

Usami, Yumi; Stork, David G.; Fujiki, Jun; Hino, Hideitsu; Akaho, Shotaro; Murata, Noboru

2011-03-01

We derive and demonstrate new methods for dewarping images depicted in convex mirrors in artwork and for estimating the three-dimensional shapes of the mirrors themselves. Previous methods were based on the assumption that mirrors were spherical or paraboloidal, an assumption unlikely to hold for hand-blown glass spheres used in early Renaissance art, such as Johannes van Eyck's Portrait of Giovanni (?) Arnolfini and his wife (1434) and Robert Campin's Portrait of St. John the Baptist and Heinrich von Werl (1438). Our methods are more general than such previous methods in that we assume merely that the mirror is radially symmetric and that there are straight lines (or colinear points) in the actual source scene. We express the mirror's shape as a mathematical series and pose the image dewarping task as that of estimating the coefficients in the series expansion. Central to our method is the plumbline principle: that the optimal coefficients are those that dewarp the mirror image so as to straighten lines that correspond to straight lines in the source scene. We solve for these coefficients algebraically through principal component analysis, PCA. Our method relies on a global figure of merit to balance warping errors throughout the image and it thereby reduces a reliance on the somewhat subjective criterion used in earlier methods. Our estimation can be applied to separate image annuli, which is appropriate if the mirror shape is irregular. Once we have found the optimal image dewarping, we compute the mirror shape by solving a differential equation based on the estimated dewarping function. We demonstrate our methods on the Arnolfini mirror and reveal a dewarped image superior to those found in prior work|an image noticeably more rectilinear throughout and having a more coherent geometrical perspective and vanishing points. Moreover, we find the mirror deviated from spherical and paraboloidal shape; this implies that it would have been useless as a concave

Text-Filled Stacked Area Graphs

DEFF Research Database (Denmark)

Kraus, Martin

2011-01-01

-filled stacked area graphs; i.e., graphs that feature stacked areas that are filled with small-typed text. Since these graphs allow for computing the text layout automatically, it is possible to include large amounts of textual detail with very little effort. We discuss the most important challenges and some...... solutions for the design of text-filled stacked area graphs with the help of an exemplary visualization of the genres, publication years, and titles of a database of several thousand PC games....

Global supply chain: The consolidators’ role

Directory of Open Access Journals (Sweden)

Rosa Caiazza

2016-01-01

Full Text Available Challenges and opportunities of the global market lead agro-food small and medium firms (SMEs to focus their source of value on production of high quality goods and implementation of flexible and robust supply chains. Despite the relevance of consolidators in the supply chain, few articles demonstrate their role in internationalization strategies of SMEs. In order to fill this literature gap, this article shows factors that affect global success of SMEs and offers some advice to decision makers.

Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process

Directory of Open Access Journals (Sweden)

Chuancun Yin

2015-01-01

Full Text Available We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy.

Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process

Science.gov (United States)

Yuen, Kam Chuen; Shen, Ying

2015-01-01

We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy. PMID:26351655

7 CFR 58.923 - Filling containers.

Science.gov (United States)

2010-01-01

... 7 Agriculture 3 2010-01-01 2010-01-01 false Filling containers. 58.923 Section 58.923 Agriculture... Procedures § 58.923 Filling containers. (a) The filling of small containers with product shall be done in a sanitary manner. The containers shall not contaminate or detract from the quality of the product in any way...

Contact point generation for convex polytopes in interactive rigid body dynamics

DEFF Research Database (Denmark)

Silcowitz-Hansen, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny

When computing contact forces in rigid body dynamics systems, most state-of-the-art solutions use iterative methods such as the projected Gauss–Seidel (PGS) method. Methods such as the PGS method are preferred for their robustness. However, the time-critical nature of interactive applications...... combined with the linear convergence rates of such methods, will often result in visual artifacts in the final simulation. With this paper, we address an issue which is of major impact on the animation quality, when using methods such as the PGS method. The issue is robust generation of contact points...... for convex polytopes. A novel contact point generation method is presented, which is based on growth distances and Gauss maps. We demonstrate improvements when using our method in the context of interactive rigid body simulation...

Raman spectra of filled carbon nanotubes

International Nuclear Information System (INIS)

Bose, S.M.; Behera, S.N.; Sarangi, S.N.; Entel, P.

2004-01-01

The Raman spectra of a metallic carbon nanotube filled with atoms or molecules have been investigated theoretically. It is found that there will be a three way splitting of the main Raman lines due to the interaction of the nanotube phonon with the collective excitations (plasmons) of the conduction electrons of the nanotube as well as its coupling with the phonon of the filling material. The positions and relative strengths of these Raman peaks depend on the strength of the electron-phonon interaction, phonon frequency of the filling atom and the strength of interaction of the nanotube phonon and the phonon of the filling atoms. Careful experimental studies of the Raman spectra of filled nanotubes should show these three peaks. It is also shown that in a semiconducting nanotube the Raman line will split into two and should be observed experimentally

Managing CSR Globally and Locally

DEFF Research Database (Denmark)

L. Brown, Dana; Knudsen, Jette Steen

Corporate Responsibility (CR) is today an essential component of corporate global strategy. CR can bolster the institutional context for market expansion (Porter and Kramer 2006); fill institutional voids (Tarun, et.al. 2005); or facilitate market entry as a component of non-market strategy (Baron...... 2006). Yet, in fulfilling these functions, CR may need to be highly sensitive to local contexts. How can transnational firms organize CR so as to maximize efficiencies from globalization and to minimize the fragmentation of corporate organizational cultures? Bartlett and Ghoshal (1989) provide...... a framework for analyzing the way that corporations coordinate global and local functions. We build on this framework in a case study of Novo Nordisk and its approach to determining global and local CR policies and procedures with regard to its China and United States subsidiaries. Our findings suggest...

Deriving Global Convection Maps From SuperDARN Measurements

Science.gov (United States)

Gjerloev, J. W.; Waters, C. L.; Barnes, R. J.

2018-04-01

A new statistical modeling technique for determining the global ionospheric convection is described. The principal component regression (PCR)-based technique is based on Super Dual Auroral Radar Network (SuperDARN) observations and is an advanced version of the PCR technique that Waters et al. (https//:doi.org.10.1002/2015JA021596) used for the SuperMAG data. While SuperMAG ground magnetic field perturbations are vector measurements, SuperDARN provides line-of-sight measurements of the ionospheric convection flow. Each line-of-sight flow has a known azimuth (or direction), which must be converted into the actual vector flow. However, the component perpendicular to the azimuth direction is unknown. Our method uses historical data from the SuperDARN database and PCR to determine a fill-in model convection distribution for any given universal time. The fill-in data process is driven by a list of state descriptors (magnetic indices and the solar zenith angle). The final solution is then derived from a spherical cap harmonic fit to the SuperDARN measurements and the fill-in model. When compared with the standard SuperDARN fill-in model, we find that our fill-in model provides improved solutions, and the final solutions are in better agreement with the SuperDARN measurements. Our solutions are far less dynamic than the standard SuperDARN solutions, which we interpret as being due to a lack of magnetosphere-ionosphere inertia and communication delays in the standard SuperDARN technique while it is inherently included in our approach. Rather, we argue that the magnetosphere-ionosphere system has inertia that prevents the global convection from changing abruptly in response to an interplanetary magnetic field change.

A New Ultrasound-Guided Puncture Device with Augmented Degrees of Performance Freedom and Ability to Attach to Most Convex Probes

International Nuclear Information System (INIS)

Jung, Sung Il; Son, Kyu Ri; Kim, Young Jun; Jeon, Hae Jeong; Park, Sang Woo; Cho, Jeong Yeon; Kim, Seung Hyup

2008-01-01

To evaluate the performance of a newly-designed ultrasound (US)-guided puncture device. A newly-designed US-guided puncture device was composed of a guide segment and an attachable segment. The guide segment allowed the needle to be placed in the plane of US view with a maximal degree of freedom, and the attachable segment was designed to attach to most convex US probes. Six operators punctured 144 targets in phantoms using either the new device (n = 72) or free-hand technique (n = 72). The number of required needle passages and the necessary procedure times were compared between the two groups. The number of required needle passages and the necessary procedure time were significantly reduced in five operators when the newly-designed US-guided puncture device was used (p < 0.05). A newly-designed US-guided puncture device, which allows for a maximal degree of freedom in needle placement and can attach to most convex US probes, showed good performance in our study

Plasmonic black metals via radiation absorption by two-dimensional arrays of ultra-sharp convex grooves

DEFF Research Database (Denmark)

Beermann, Jonas; Eriksen, René L.; Stær, Tobias Holmgaard

2014-01-01

Plasmonic black surfaces formed by two-dimensional arrays of ultra-sharp convex metal grooves, in which the incident radiation is converted into gap surface plasmon polaritons (GSPPs) and subsequently absorbed (via adiabatic nanofocusing), are fabricated and investigated experimentally for gold......%, averaged over the investigated wavelength range of 400-985 nm. The highest averaged absorption level (similar to 97%) is achieved with 250-nm-period arrays in palladium that also has the highest melting temperature(similar to 15526 degrees C), promising thereby potential applications for broadband...

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...

A Convex Formulation for Magnetic Particle Imaging X-Space Reconstruction.

Science.gov (United States)

Konkle, Justin J; Goodwill, Patrick W; Hensley, Daniel W; Orendorff, Ryan D; Lustig, Michael; Conolly, Steven M

2015-01-01

Magnetic Particle Imaging (mpi) is an emerging imaging modality with exceptional promise for clinical applications in rapid angiography, cell therapy tracking, cancer imaging, and inflammation imaging. Recent publications have demonstrated quantitative mpi across rat sized fields of view with x-space reconstruction methods. Critical to any medical imaging technology is the reliability and accuracy of image reconstruction. Because the average value of the mpi signal is lost during direct-feedthrough signal filtering, mpi reconstruction algorithms must recover this zero-frequency value. Prior x-space mpi recovery techniques were limited to 1d approaches which could introduce artifacts when reconstructing a 3d image. In this paper, we formulate x-space reconstruction as a 3d convex optimization problem and apply robust a priori knowledge of image smoothness and non-negativity to reduce non-physical banding and haze artifacts. We conclude with a discussion of the powerful extensibility of the presented formulation for future applications.

Existence theorem and optimality conditions for a class of convex semi-infinite problems with noncompact index sets

Directory of Open Access Journals (Sweden)

Olga Kostyukova

2017-11-01

Full Text Available The paper is devoted to study of a special class of semi-infinite problems arising in nonlinear parametric Semi-infinite Programming, when the differential properties of the solutions are being studied. These problems are convex and possess noncompact index sets. In the paper, we present conditions guaranteeing the existence of optimal solutions, and prove new optimality criterion. An example illustrating the obtained results is presented.

Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in -Uniformly Smooth and Strictly Convex Banach Spaces

Directory of Open Access Journals (Sweden)

Meng Wen

2012-01-01

Full Text Available We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in -uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.

Surgical treatment of convexity focal epilepsy

International Nuclear Information System (INIS)

Shimizu, Hiroyuki; Ishijima, Buichi; Iio, Masaaki.

1987-01-01

We have hitherto applied PET study in 72 epileptic patients. The main contents of their seizures consists of complex partial in 32, elementary partial in 32, generalized in 6, and others in 3 cases. We administered perorally 10 mCi glucose labeled with C11 produced in the JSW Baby Cyclotron for the study of CMRG(cerebral metabolic rate of glucose). The continuous inhalation method of CO 2 and O 2 labeled with O15 produced in the same cyclotron was also employed for measurement of rCBE(cerebral blood flow) and CMRO 2 (cerebral metabolic rate of oxygen). In both studies, epileptic foci were shown as well demarcated hypometabolic zones with decreased CMRG, rCBF or CMRO 2 . The locations of PET diagnosed foci were not contradictory with the clinical symptoms, scalp EEGs or X-ray CT findings. Of the 32 patients with the convexity epileptic foci, 8 patients underwent surgical treatment. Prior to the surgical intervention, subdural strip electrodes were inserted in the four cases for further assessment of focus locations. Subdural EEG disclosed very active brain activity with high amplitude 4 to 5 times scalp EEG and revealed epileptiform discharges most of which were not detected by scalp recording. PET scans did not characterize epileptogenic nature of a lesion. Subdural recording therefore was useful for detecting the foci responsible for habitual seizures in the cases with multiple PET foci. Ambiguous hypometabolic zones on PECT images also could be confirmed by the subdural technique. Of the 8 operated cases, five patients are seizure free, one is signigicantly improved and two are not improved although the postoperative follow-up is too short for precise evaluation. (J.P.N.)

100 kyr fluvial cut-and-fill terrace cycles since the Middle Pleistocene in the southern Central Andes, NW Argentina

Science.gov (United States)

Tofelde, Stefanie; Schildgen, Taylor F.; Savi, Sara; Pingel, Heiko; Wickert, Andrew D.; Bookhagen, Bodo; Wittmann, Hella; Alonso, Ricardo N.; Cottle, John; Strecker, Manfred R.

2017-09-01

Fluvial fill terraces in intermontane basins are valuable geomorphic archives that can record tectonically and/or climatically driven changes of the Earth-surface process system. However, often the preservation of fill terrace sequences is incomplete and/or they may form far away from their source areas, complicating the identification of causal links between forcing mechanisms and landscape response, especially over multi-millennial timescales. The intermontane Toro Basin in the southern Central Andes exhibits at least five generations of fluvial terraces that have been sculpted into several-hundred-meter-thick Quaternary valley-fill conglomerates. New surface-exposure dating using nine cosmogenic 10Be depth profiles reveals the successive abandonment of these terraces with a 100 kyr cyclicity between 75 ± 7 and 487 ± 34 ka. Depositional ages of the conglomerates, determined by four 26Al/10Be burial samples and U-Pb zircon ages of three intercalated volcanic ash beds, range from 18 ± 141 to 936 ± 170 ka, indicating that there were multiple cut-and-fill episodes. Although the initial onset of aggradation at ∼1 Ma and the overall net incision since ca. 500 ka can be linked to tectonic processes at the narrow basin outlet, the superimposed 100 kyr cycles of aggradation and incision are best explained by eccentricity-driven climate change. Within these cycles, the onset of river incision can be correlated with global cold periods and enhanced humid phases recorded in paleoclimate archives on the adjacent Bolivian Altiplano, whereas deposition occurred mainly during more arid phases on the Altiplano and global interglacial periods. We suggest that enhanced runoff during global cold phases - due to increased regional precipitation rates, reduced evapotranspiration, or both - resulted in an increased sediment-transport capacity in the Toro Basin, which outweighed any possible increases in upstream sediment supply and thus triggered incision. Compared with two

Precision platform for convex lens-induced confinement microscopy

Science.gov (United States)

Berard, Daniel; McFaul, Christopher M. J.; Leith, Jason S.; Arsenault, Adriel K. J.; Michaud, François; Leslie, Sabrina R.

2013-10-01

We present the conception, fabrication, and demonstration of a versatile, computer-controlled microscopy device which transforms a standard inverted fluorescence microscope into a precision single-molecule imaging station. The device uses the principle of convex lens-induced confinement [S. R. Leslie, A. P. Fields, and A. E. Cohen, Anal. Chem. 82, 6224 (2010)], which employs a tunable imaging chamber to enhance background rejection and extend diffusion-limited observation periods. Using nanopositioning stages, this device achieves repeatable and dynamic control over the geometry of the sample chamber on scales as small as the size of individual molecules, enabling regulation of their configurations and dynamics. Using microfluidics, this device enables serial insertion as well as sample recovery, facilitating temporally controlled, high-throughput measurements of multiple reagents. We report on the simulation and experimental characterization of this tunable chamber geometry, and its influence upon the diffusion and conformations of DNA molecules over extended observation periods. This new microscopy platform has the potential to capture, probe, and influence the configurations of single molecules, with dramatically improved imaging conditions in comparison to existing technologies. These capabilities are of immediate interest to a wide range of research and industry sectors in biotechnology, biophysics, materials, and chemistry.

Adaptive terminal sliding mode control for hypersonic flight vehicles with strictly lower convex function based nonlinear disturbance observer.

Science.gov (United States)

Wu, Yun-Jie; Zuo, Jing-Xing; Sun, Liang-Hua

2017-11-01

In this paper, the altitude and velocity tracking control of a generic hypersonic flight vehicle (HFV) is considered. A novel adaptive terminal sliding mode controller (ATSMC) with strictly lower convex function based nonlinear disturbance observer (SDOB) is proposed for the longitudinal dynamics of HFV in presence of both parametric uncertainties and external disturbances. First, for the sake of enhancing the anti-interference capability, SDOB is presented to estimate and compensate the equivalent disturbances by introducing a strictly lower convex function. Next, the SDOB based ATSMC (SDOB-ATSMC) is proposed to guarantee the system outputs track the reference trajectory. Then, stability of the proposed control scheme is analyzed by the Lyapunov function method. Compared with other HFV control approaches, key novelties of SDOB-ATSMC are that a novel SDOB is proposed and drawn into the (virtual) control laws to compensate the disturbances and that several adaptive laws are used to deal with the differential explosion problem. Finally, it is illustrated by the simulation results that the new method exhibits an excellent robustness and a better disturbance rejection performance than the convention approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

Directory of Open Access Journals (Sweden)

Gurucharan Singh Saluja

2010-01-01

Full Text Available In this paper, we give some necessary and sufficient conditions for an implicit iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converging to a common fixed of the mappings in convex metric spaces. Our results extend and improve some recent results of Sun, Wittmann, Xu and Ori, and Zhou and Chang.

Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle–Pock algorithm

DEFF Research Database (Denmark)

Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan

2012-01-01

The primal–dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1–26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems...... for the purpose of designing iterative image reconstruction algorithms for CT. The primal–dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application...

Fabrication of complex free-standing nanostructures with concave and convex curvature via the layer-by-layer approach.

Science.gov (United States)

Raoufi, Mohammad; Schönherr, Holger

2014-02-18

We report on the fabrication of unprecedented free-standing complex polymeric nanoobjects, which possess both concave and convex curvatures, by exploiting the layer-by-layer (LBL) deposition of polyelectrolytes. In a combined top-down/bottom-up replication approach pore diameter-modulated anodic aluminum oxide (AAO) templates, fabricated by temperature modulation hard anodization (TMHA), were replicated with multilayers of poly(styrene sulfonate) (PSS) and poly(allylamine hydrochloride) (PAH) to yield open nanotubes with diameters in the wide and narrow segments of 210 and 150 nm, respectively. To obtain stable pore diameter-modulated nanopores, which possess segment lengths between 1 and 5 μm and 5 and 10 μm in the narrow and wide pore portion, respectively, conventional hard anodization of aluminum was followed by a subsequent temperature-modulated anodization. After removing the backside aluminum electrode, silanizing the aluminum oxide, and passivating the exposed membrane surface with a thin layer of gold, PSS and PAH were deposited alternatingly to yield LBL multilayers. For optimized LBL multilayer thicknesses and compactness, established in separate experiments on silicon substrates and nanoporous AAO with straight pores, free-standing polymeric nanoobjects with concave and convex curvatures, were obtained. These were stable for wall thickness to pore diameter ratios of ≥0.08.

Clinical significance of cerebrospinal fluid tap test and magnetic resonance imaging/computed tomography findings of tight high convexity in patients with possible idiopathic normal pressure hydrocephalus

International Nuclear Information System (INIS)

Ishikawa, Masatsune; Furuse, Motomasa; Nishida, Namiko; Oowaki, Hisayuki; Matsumoto, Atsuhito; Suzuki, Takayuki

2010-01-01

Idiopathic normal pressure hydrocephalus (iNPH) is a treatable syndrome with a classical triad of symptoms. The Japanese iNPH guidelines indicate that the cerebrospinal fluid (CSF) tap test and tight high-convexity on magnetic resonance (MR) imaging are important for the diagnosis. The relationships between the effectiveness of CSF shunt surgery in possible iNPH patients, the tap test result, and the MR imaging/computed tomography (CT) findings of tight high-convexity were evaluated in 88 possible iNPH patients (mean age 75 years) with one or more of the classical triad of symptoms, and mild to moderate ventricular dilation. All patients underwent the tap test in the outpatient clinic, and patients and caregivers assessed the clinical changes during one week. The tap test was positive in 47 patients and negative in 41 patients. Surgery was performed in 19 patients with positive tap test, and was effective in 17 patients. Although the findings were inconsistent in some patients, the result of the tap test was found to be highly correlated with the MR imaging/CT finding of tight high-convexity (p<0.0001), confirming that both these diagnostic tests are promising predictors of shunt effectiveness. (author)

Characterization of vegetative and grain filling periods of winter wheat by stepwise regression procedure. II. Grain filling period

Directory of Open Access Journals (Sweden)

Pržulj Novo

2011-01-01

Full Text Available In wheat, rate and duration of dry matter accumulation and remobilization depend on genotype and growing conditions. The objective of this study was to determine the most appropriate polynomial regression of stepwise regression procedure for describing grain filling period in three winter wheat cultivars. The stepwise regression procedure showed that grain filling is a complex biological process and that it is difficult to offer a simple and appropriate polynomial equation that fits the pattern of changes in dry matter accumulation during the grain filling period, i.e., from anthesis to maximum grain weight, in winter wheat. If grain filling is to be represented with a high power polynomial, quartic and quintic equations showed to be most appropriate. In spite of certain disadvantages, a cubic equation of stepwise regression could be used for describing the pattern of winter wheat grain filling.

Ensuring dynamic strategic fit of firms that compete globally in alliances and networks: proposing the Global SNA - Strategic Network Analysis - framework

Directory of Open Access Journals (Sweden)

T. Diana L. Van Aduard de Macedo-Soares

2011-02-01

Full Text Available In order to sustain their competitive advantage in the current increasingly globalized and turbulent context, more and more firms are competing globally in alliances and networks that oblige them to adopt new managerial paradigms and tools. However, their strategic analyses rarely take into account the strategic implications of these alliances and networks, considering their global relational characteristics, admittedly because of a lack of adequate tools to do so. This paper contributes to research that seeks to fill this gap by proposing the Global Strategic Network Analysis - SNA - framework. Its purpose is to help firms that compete globally in alliances and networks to carry out their strategic assessments and decision-making with a view to ensuring dynamic strategic fit from both a global and relational perspective.

An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State

Energy Technology Data Exchange (ETDEWEB)

Kamm, James Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-03-05

This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.

A Block Coordinate Descent Method for Multi-Convex Optimization with Applications to Nonnegative Tensor Factorization and Completion

Science.gov (United States)

2012-08-01

Sciandrone, On the convergence of the block nonlinear Gauss - Seidel method under convex constraints , Oper. Res. Lett., 26 (2000), pp. 127–136. [23] S.P...include nonsmooth functions. Our main interest is the block coordinate descent (BCD) method of the Gauss - Seidel type, which mini- mizes F cyclically over...original objective around the current iterate . They do not use extrapolation either and only have subsequence convergence . There are examples of ri

Iron filled carbon nanostructures from different precursors

International Nuclear Information System (INIS)

Costa, S.; Borowiak-Palen, E.; Bachmatiuk, A.; Ruemmeli, M.H.; Gemming, T.; Kalenczuk, R.J.

2008-01-01

Here, we present a study on the synthesis of different nanostructures with one single-step in situ filling (encapsulation) via carbon vapor deposition (CVD). Ferrocene, acetylferrocene and iron (II) nitrate as iron precursors were explored. The application of each of these compounds resulted in different carbon nanomaterials such as: iron filled multiwalled carbon nanotubes with a low filling ratio (Fe-MWCNT), iron filled nanocapsules and unfilled MWCNT. The as-produced samples were purified by high temperature annealing and acid treatment. The purified materials were characterised using transmission electron microscopy (TEM) and Raman spectroscopy

Iterating the Number of Intersection Points of the Diagonals of Irregular Convex Polygons, or C (n, 4) the Hard Way!

Science.gov (United States)

Hathout, Leith

2007-01-01

Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…