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...

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

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...

Notions of convexity

CERN Document Server

Hörmander, Lars

1994-01-01

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

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.

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)

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.

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:...

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

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

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.

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

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

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.

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...

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)

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

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

Conference on Convex Analysis and Global Optimization

CERN Document Server

Pardalos, Panos

2001-01-01

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

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

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.

Globally convergent optimization algorithm using conservative convex separable diagonal quadratic approximations

NARCIS (Netherlands)

Groenwold, A.A.; Wood, D.W.; Etman, L.F.P.; Tosserams, S.

2009-01-01

We implement and test a globally convergent sequential approximate optimization algorithm based on (convexified) diagonal quadratic approximations. The algorithm resides in the class of globally convergent optimization methods based on conservative convex separable approximations developed by

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.

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.

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]....

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.

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.

Convexities move because they contain matter.

Science.gov (United States)

Barenholtz, Elan

2010-09-22

Figure-ground assignment to a contour is a fundamental stage in visual processing. The current paper introduces a novel, highly general dynamic cue to figure-ground assignment: "Convex Motion." Across six experiments, subjects showed a strong preference to assign figure and ground to a dynamically deforming contour such that the moving contour segment was convex rather than concave. Experiments 1 and 2 established the preference across two different kinds of deformational motion. Additional experiments determined that this preference was not due to fixation (Experiment 3) or attentional mechanisms (Experiment 4). Experiment 5 found a similar, but reduced bias for rigid-as opposed to deformational-motion, and Experiment 6 demonstrated that the phenomenon depends on the global motion of the effected contour. An explanation of this phenomenon is presented on the basis of typical natural deformational motion, which tends to involve convex contour projections that contain regions consisting of physical "matter," as opposed to concave contour indentations that contain empty space. These results highlight the fundamental relationship between figure and ground, perceived shape, and the inferred physical properties of an object.

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.

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.

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.

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

Fabricating small-scale, curved, polymeric structures with convex and concave menisci through interfacial free energy equilibrium.

Science.gov (United States)

Cheng, Chao-Min; Matsuura, Koji; Wang, I-Jan; Kuroda, Yuka; LeDuc, Philip R; Naruse, Keiji

2009-11-21

Polymeric curved structures are widely used in imaging systems including optical fibers and microfluidic channels. Here, we demonstrate that small-scale, poly(dimethylsiloxane) (PDMS)-based, curved structures can be fabricated through controlling interfacial free energy equilibrium. Resultant structures have a smooth, symmetric, curved surface, and may be convex or concave in form based on surface tension balance. Their curvatures are controlled by surface characteristics (i.e., hydrophobicity and hydrophilicity) of the molds and semi-liquid PDMS. In addition, these structures are shown to be biocompatible for cell culture. Our system provides a simple, efficient and economical method for generating integrateable optical components without costly fabrication facilities.

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.

Visualizing Data as Objects by DC (Difference of Convex) Optimization

DEFF Research Database (Denmark)

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

2018-01-01

In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value, as convex objects. 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 Difference of Convex Algorithm (DCA) in a very efficient way. Our algorithmic approach is used to visualize two real-world datasets....

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.

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.

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.

Glass molding of 3mm diameter aspheric plano-convex lens

Science.gov (United States)

Sung, Hayeong; Hue, Myung sang; Lee, Giljae; Ryu, Geunman; Kim, Dongguk; Yang, Suncheol

2017-10-01

The many industries and research fields have demands for small scale optical systems. To satisfy the demands, many studies are conducted and the miniaturization technologies have been developed. The optical lens is directly related to the optical systems and a key component for the miniaturization. So the aspheric surface which can replace multispherical lenses is applied to the optical lens. And fabrication methods to reduce the diameter of the lens have been developed. The glass molding pressing (GMP) process is an attractive method to fabricate aspheric lens among the lens manufacturing processes. Because the GMP process has advantages of productivity, repeatability and so on. In this study, a 3 mm diameter aspheric plano-convex lens was fabricated using the GMP process. The GMP process was divided into heating, pressing, annealing and cooling. And the process was conducted using a commercial glass molding machine. Mold tools consist of an upper and a lower mold insert, an inner and an outer guide. The aspheric and the flat surfaces of the mold inserts were coated with ta-C to prevent the sticking of the glass to the mold. The surfaces of molded lens were measured by white interferometry and surface profilometer. The height and the diameter were measured using optical microscopy. As results, the aspheric surface of the lens was 5.1187 nm in Ra and 0.242 um in Pt. And the flat surface was 2.6697 nm in Ra and 0.13 um in Pt. The height and the diameter were 1.935 mm and 3.002 mm respectively.

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.

A convex optimization approach for solving large scale linear systems

Directory of Open Access Journals (Sweden)

Debora Cores

2017-01-01

Full Text Available The well-known Conjugate Gradient (CG method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.

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

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.

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.

Convex-based void filling method for CAD-based Monte Carlo geometry modeling

International Nuclear Information System (INIS)

Yu, Shengpeng; Cheng, Mengyun; Song, Jing; Long, Pengcheng; Hu, Liqin

2015-01-01

Highlights: • We present a new void filling method named CVF for CAD based MC geometry modeling. • We describe convex based void description based and quality-based space subdivision. • The results showed improvements provided by CVF for both modeling and MC calculation efficiency. - Abstract: CAD based automatic geometry modeling tools have been widely applied to generate Monte Carlo (MC) calculation geometry for complex systems according to CAD models. Automatic void filling is one of the main functions in the CAD based MC geometry modeling tools, because the void space between parts in CAD models is traditionally not modeled while MC codes such as MCNP need all the problem space to be described. A dedicated void filling method, named Convex-based Void Filling (CVF), is proposed in this study for efficient void filling and concise void descriptions. The method subdivides all the problem space into disjointed regions using Quality based Subdivision (QS) and describes the void space in each region with complementary descriptions of the convex volumes intersecting with that region. It has been implemented in SuperMC/MCAM, the Multiple-Physics Coupling Analysis Modeling Program, and tested on International Thermonuclear Experimental Reactor (ITER) Alite model. The results showed that the new method reduced both automatic modeling time and MC calculation time

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)

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.

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...

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.

Optical design and testing: introduction.

Science.gov (United States)

Liang, Chao-Wen; Koshel, John; Sasian, Jose; Breault, Robert; Wang, Yongtian; Fang, Yi Chin

2014-10-10

Optical design and testing has numerous applications in industrial, military, consumer, and medical settings. Assembling a complete imaging or nonimage optical system may require the integration of optics, mechatronics, lighting technology, optimization, ray tracing, aberration analysis, image processing, tolerance compensation, and display rendering. This issue features original research ranging from the optical design of image and nonimage optical stimuli for human perception, optics applications, bio-optics applications, 3D display, solar energy system, opto-mechatronics to novel imaging or nonimage modalities in visible and infrared spectral imaging, modulation transfer function measurement, and innovative interferometry.

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.

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

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.

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.

Optical design of a LED searchlight system

Science.gov (United States)

Gong, Chen; Xu, Haiping; Liang, Jinhua; Liu, Yunfei; Yuan, Zengquan

2018-01-01

A 1200m visible searchlight system is designed based on photometry and application of geometric optics. To generate intensity distribution of this relatively powerful light beam we propose to use a high power LED and several refractive optical elements, which are composed of two plane-convex lenses and a conventional Fresnel lens. Two plane-convex lenses enable refraction of the side rays from the LED to the front direction which incident on the Fresnel lens. Fresnel lens, in its turn, concentrate the light flux and provide a nearly collimated beam to meet the requirement of forming a well-illuminated area across the road in the far field. Simulation data shows that this searchlight allow generating an appropriate illumination distribution for the long range requirements. A proof-of-concept prototype producing acceptable illuminance is developed.

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

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 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.)

Nanoantennas for enhancing and confining the magnetic optical field

Science.gov (United States)

Grosjean, Thierry; Mivelle, Mathieu; Baida, Fadi I.; Burr, Geoffrey W.; Fischer, Ulrich C.

2011-05-01

We propose different optical antenna structures for enhancing and confining the magnetic optical field. A common feature of these structures are concave corners in thin metal films as locations of the enhanced magnetic field. This proposal is inspired by Babinet's principle as the concave edges are the complementary structures to convex metal corners, which are known to be locations of a strongly enhanced electric field. Bowtie antennas and the bowtie apertures of appropriate size were shown to exhibit resonances in the infrared frequency range with an especially strong enhancement of the electrical field in the gap between 2 convex metal corners. We show by numerical calculations, that the complementary structures, the complementary bowtie aperture - the diabolo antenna - and the complementary bow tie antenna - two closely spaced triangular apertures in a metal film with a narrow gap between two opposing concave corners - exhibit resonances with a strongly enhanced magnetic field at the narrow metal constriction between the concave corners. We suggest sub-wavelength circuits of concave and convex corners as building blocks of planar metamaterials.

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

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....

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.

Test Port for Fiber-Optic-Coupled Laser Altimeter

Science.gov (United States)

Ramos Izquierdo, Luis; Scott, V. Stanley; Rinis, Haris; Cavanaugh, John

2011-01-01

A test port designed as part of a fiber optic coupled laser altimeter receiver optical system allows for the back-illumination of the optical system for alignment verification, as well as illumination of the detector(s) for testing the receiver electronics and signal-processing algorithms. Measuring the optical alignment of a laser altimeter instrument is difficult after the instrument is fully assembled. The addition of a test port in the receiver aft-optics allows for the back-illumination of the receiver system such that its focal setting and boresight alignment can be easily verified. For a multiple-detector receiver system, the addition of the aft-optics test port offers the added advantage of being able to simultaneously test all the detectors with different signals that simulate the expected operational conditions. On a laser altimeter instrument (see figure), the aft-optics couple the light from the receiver telescope to the receiver detector(s). Incorporating a beam splitter in the aft-optics design allows for the addition of a test port to back-illuminate the receiver telescope and/or detectors. The aft-optics layout resembles a T with the detector on one leg, the receiver telescope input port on the second leg, and the test port on the third leg. The use of a custom beam splitter with 99-percent reflection, 1-percent transmission, and a mirrored roof can send the test port light to the receiver telescope leg as well as the detector leg, without unduly sacrificing the signal from the receiver telescope to the detector. The ability to test the receiver system alignment, as well as multiple detectors with different signals without the need to disassemble the instrument or connect and reconnect components, is a great advantage to the aft-optics test port. Another benefit is that the receiver telescope aperture is fully back-illuminated by the test port so the receiver telescope focal setting vs. pressure and or temperature can be accurately measured (as

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)

Test facility for astronomical x-ray optics

DEFF Research Database (Denmark)

Christensen, Finn Erland; Lewis, Robert A.; Bordas, J.

1990-01-01

Grazing incidence x-ray optics for x-ray astronomical applications are used outside the earth's atmosphere. These devices require a large collection aperture and the imaging of an x-ray source that is essentially placed at infinity. The ideal testing system for these optical elements has to appro......Grazing incidence x-ray optics for x-ray astronomical applications are used outside the earth's atmosphere. These devices require a large collection aperture and the imaging of an x-ray source that is essentially placed at infinity. The ideal testing system for these optical elements has...... to approximate that encountered under working conditions; however, the testing of these optical elements is notoriously difficult with conventional x-ray generators. Synchrotron radiation (SR) sources are sufficiently brilliant to produce a nearly perfect parallel beam over a large area while still retaining...... a flux considerably higher than that available from conventional x-ray generators. A facility designed for the testing of x-ray optics, particularly in connection with x-ray telescopes, is described. It is proposed that this facility will be accommodated at the Synchrotron Radiation Source...

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...

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.

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.)

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 ...

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...

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)

A 'range test' for determining scatterers with unknown physical properties

Science.gov (United States)

Potthast, Roland; Sylvester, John; Kusiak, Steven

2003-06-01

We describe a new scheme for determining the convex scattering support of an unknown scatterer when the physical properties of the scatterers are not known. The convex scattering support is a subset of the scatterer and provides information about its location and estimates for its shape. For convex polygonal scatterers the scattering support coincides with the scatterer and we obtain full shape reconstructions. The method will be formulated for the reconstruction of the scatterers from the far field pattern for one or a few incident waves. The method is non-iterative in nature and belongs to the type of recently derived generalized sampling schemes such as the 'no response test' of Luke-Potthast. The range test operates by testing whether it is possible to analytically continue a far field to the exterior of any test domain Omegatest. By intersecting the convex hulls of various test domains we can produce a minimal convex set, the convex scattering support of which must be contained in the convex hull of the support of any scatterer which produces that far field. The convex scattering support is calculated by testing the range of special integral operators for a sampling set of test domains. The numerical results can be used as an approximation for the support of the unknown scatterer. We prove convergence and regularity of the scheme and show numerical examples for sound-soft, sound-hard and medium scatterers. We can apply the range test to non-convex scatterers as well. We can conclude that an Omegatest which passes the range test has a non-empty intersection with the infinity-support (the complement of the unbounded component of the complement of the support) of the true scatterer, but cannot find a minimal set which must be contained therein.

Specification and testing of optics for LIS system

International Nuclear Information System (INIS)

Singh, Sunita; Sridhar, G.; Rawat, V.S.; Gantayet, L.M.

2005-01-01

Optical component specification for the high average power lasers and laser beam transport system used in the laser isotope separation demonstration facility must address demanding system performance requirements. In a typical demonstration facility a few thousand of commercial and custom optical components are required. The optical system is expected to perform at a high level of optical efficiency and reliability. Evaluation and testing of optical components used in LIS plant is critical for qualification of suppliers and assurance of performance in the actual process. The stringent specifications require specialized test equipment and techniques, which are not routine. Careful planning with the optics manufacturer, detailed quality assurance plan, comprehensive procedures for testing and evaluation, and a plan for corrective action are required. The specifications are given on material characteristics, surface quality and flatness, reflectance or transmittance and high average power laser damage. Our approach to specifying, testing the performance characteristics and assuring quality of optical components required for the technology demonstration of laser based isotopic clean-up of 233 U project is presented. (author)

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.

Laboratory testing & measurement on optical imaging systems

CSIR Research Space (South Africa)

Theron, B

2013-04-01

Full Text Available on Optical Imaging Systems Bertus Theron 27 April 2013 presented at SIECPC 2013, Riyadh, Saudi Arabia Overview of Workshop Part 1. Introduction & Context  Some history of Arabic Optics  Context: Global vs Local optical testing... of Arabic Optics 1 See [4]  Arabic records of study of geometrical optics  Traced to Hellenistic (Greek) optics  Translated to Arabic  9th century  Arabic contribution to geometric optics  Not just translation to Arabic  Innovative research...

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.

MD Test of a Ballistic Optics

CERN Document Server

Garcia-Tabares Valdivieso, Ana; Salvachua Ferrando, Belen Maria; Skowronski, Piotr Krzysztof; Solfaroli Camillocci, Matteo; Tomas Garcia, Rogelio; Wenninger, Jorg; Coello De Portugal - Martinez Vazquez, Jaime Maria; CERN. Geneva. ATS Department

2016-01-01

The ballistic optics is designed to improve the understanding of optical errors and BPM systematic effects in the critical triplet region. The particularity of that optics is that the triplet is switched off, effectively transforming the triplets on both sides of IR1 and IR5 into drift spaces. Advantage can be taken from that fact to localize better errors in the Q4-Q5-triplet region. During this MD this new optics was tested for the first time at injection with beam 2.

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.

New Cryogenic Optical Test Capability at Marshall Space Flight Center's Space Optics Manufacturing Technology Center

Science.gov (United States)

Kegley, Jeff; Burdine, Robert V. (Technical Monitor)

2002-01-01

A new cryogenic optical testing capability exists at Marshall Space Flight Center's Space Optics Manufacturing Technology Center (SOMTC). SOMTC has been performing optical wavefront testing at cryogenic temperatures since 1999 in the X-ray Cryogenic Test Facility's (XRCF's) large vacuum chamber. Recently the cryogenic optical testing capability has been extended to a smaller vacuum chamber. This smaller horizontal cylindrical vacuum chamber has been outfitted with a helium-cooled liner that can be connected to the facility's helium refrigeration system bringing the existing kilowatt of refrigeration capacity to bear on a 1 meter diameter x 2 meter long test envelope. Cryogenic environments to less than 20 Kelvin are now possible in only a few hours. SOMTC's existing instruments (the Instantaneous Phase-shifting Interferometer (IPI) from ADE Phase-Shift Technologies and the PhaseCam from 4D Vision Technologies) view the optic under test through a 150 mm clear aperture BK-7 window. Since activation and chamber characterization tests in September 2001, the new chamber has been used to perform a cryogenic (less than 30 Kelvin) optical test of a 22.5 cm diameter x 127 cm radius of curvature Si02 mirror, a cryogenic survival (less than 30 Kelvin) test of an adhesive, and a cryogenic cycle (less than 20 Kelvin) test of a ULE mirror. A vibration survey has also been performed on the test chamber. Chamber specifications and performance data, vibration environment data, and limited test results will be presented.

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.

Testing methodologies and systems for semiconductor optical amplifiers

Science.gov (United States)

Wieckowski, Michael

Semiconductor optical amplifiers (SOA's) are gaining increased prominence in both optical communication systems and high-speed optical processing systems, due primarily to their unique nonlinear characteristics. This in turn, has raised questions regarding their lifetime performance reliability and has generated a demand for effective testing techniques. This is especially critical for industries utilizing SOA's as components for system-in-package products. It is important to note that very little research to date has been conducted in this area, even though production volume and market demand has continued to increase. In this thesis, the reliability of dilute-mode InP semiconductor optical amplifiers is studied experimentally and theoretically. The aging characteristics of the production level devices are demonstrated and the necessary techniques to accurately characterize them are presented. In addition, this work proposes a new methodology for characterizing the optical performance of these devices using measurements in the electrical domain. It is shown that optical performance degradation, specifically with respect to gain, can be directly qualified through measurements of electrical subthreshold differential resistance. This metric exhibits a linear proportionality to the defect concentration in the active region, and as such, can be used for prescreening devices before employing traditional optical testing methods. A complete theoretical analysis is developed in this work to explain this relationship based upon the device's current-voltage curve and its associated leakage and recombination currents. These results are then extended to realize new techniques for testing semiconductor optical amplifiers and other similarly structured devices. These techniques can be employed after fabrication and during packaged operation through the use of a proposed stand-alone testing system, or using a proposed integrated CMOS self-testing circuit. Both methods are capable

NIF small optics laser damage test specifications

International Nuclear Information System (INIS)

Sheehan, L

1999-01-01

The Laser Damage Group is currently conducting tests on small optics samples supplied for initial evaluation of potential NIF suppliers. This document is meant to define the specification of laser-induced damage for small optics and the test methods used to collect the data. A rating system which will be applied for vendor selection is presented

ACIGA's high optical power test facility

International Nuclear Information System (INIS)

Ju, L; Aoun, M; Barriga, P

2004-01-01

Advanced laser interferometer detectors utilizing more than 100 W of laser power and with ∼10 6 W circulating laser power present many technological problems. The Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) is developing a high power research facility in Gingin, north of Perth, Western Australia, which will test techniques for the next generation interferometers. In particular it will test thermal lensing compensation and control strategies for optical cavities in which optical spring effects and parametric instabilities may present major difficulties

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.

Optical performance of random anti-reflection structured surfaces (rARSS) on spherical lenses

Science.gov (United States)

Taylor, Courtney D.

Random anti-reflection structured surfaces (rARSS) have been reported to improve transmittance of optical-grade fused silica planar substrates to values greater than 99%. These textures are fabricated directly on the substrates using reactive-ion/inductively-coupled plasma etching (RIE/ICP) techniques, and often result in transmitted spectra with no measurable interference effects (fringes) for a wide range of wavelengths. The RIE/ICP processes used in the fabrication process to etch the rARSS is anisotropic and thus well suited for planar components. The improvement in spectral transmission has been found to be independent of optical incidence angles for values from 0° to +/-30°. Qualifying and quantifying the rARSS performance on curved substrates, such as convex lenses, is required to optimize the fabrication of the desired AR effect on optical-power elements. In this work, rARSS was fabricated on fused silica plano-convex (PCX) and plano-concave (PCV) lenses using a planar-substrate optimized RIE process to maximize optical transmission in the range from 500 to 1100 nm. An additional set of lenses were etched in a non-optimized ICP process to provide additional comparisons. Results are presented from optical transmission and beam propagation tests (optimized lenses only) of rARSS lenses for both TE and TM incident polarizations at a wavelength of 633 nm and over a 70° full field of view in both singlet and doublet configurations. These results suggest optimization of the fabrication process is not required, mainly due to the wide angle-of-incidence AR tolerance performance of the rARSS lenses. Non-optimized recipe lenses showed low transmission enhancement, and confirmed the need to optimized etch recipes prior to process transfer of PCX/PCV lenses. Beam propagation tests indicated no major beam degradation through the optimized lens elements. Scanning electron microscopy (SEM) images confirmed different structure between optimized and non-optimized samples

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.

Optical Automatic Car Identification (OACI) Field Test Program

Science.gov (United States)

1976-05-01

The results of the Optical Automatic Car Identification (OACI) tests at Chicago conducted from August 16 to September 4, 1975 are presented. The main purpose of this test was to determine the suitability of optics as a principle of operation for an a...

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...

Retinal Nerve Fiber Layer Converges More Convexly on Normal Smaller Optic Nerve Head.

Science.gov (United States)

Jung, Kyoung In; Shin, Jeong Ah; Park, Hae-Young Lopilly; Park, Chan Kee

2015-08-01

To investigate retinal nerve fiber layer (RNFL) configuration in the optic nerve head (ONH) and peripapillary area according to disc size and to determine whether it explains cup discrepancy among eyes with different disc sizes. Horizontal and vertical RNFL curvature and mean thickness were measured using confocal scanning laser ophthalmoscopy (Heidelberg Retina Tomograph) in 63 normal subjects grouped by disc size. Average and quadrant RNFL thickness, disc size, average cup-to-disc ratio (CDR), and convergence angle at the optic disc were also measured using Cirrus HD-optical coherence tomography. The relationships between disc size and RNFL curvature, thickness, angle at optic disc, and CDR were evaluated. RNFL curvature and convergence angle reflects convexity "on" and "into" the optic disc, respectively. CDR was smaller for small discs and was positively correlated with disc size (Poptic disc were positively correlated with disc size (POptic disc area was negatively correlated with mean RNFL thickness at the optic disc margin measured by HRT (P=0.002), but not in the peripapillary area by optical coherence tomography. Using imaging techniques, we demonstrated that the shape of the RNFLs converging "on" and entering "into" the optic disc was more convex for small optic discs compared with large discs. A low CDR for small discs could be mediated by these RNFL profiles at the ONH, which may guide the clinical evaluation of glaucomatous ONH damage.

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.

A Test Facility For Astronomical X-Ray Optics

DEFF Research Database (Denmark)

Lewis, R. A.; Bordas, J.; Christensen, Finn Erland

1989-01-01

Grazing incidence x-ray optics for x-ray astronomical applications are used outside the earths atmosphere. These devices require a large collection aperture and the imaging of an x-ray source which is essentially placed at infinity. The ideal testing system for these optical elements has...... to approximate that encountered under working conditions, however the testing of these optical elements is notoriously difficult with conventional x-ray generators. Synchrotron Radiation (SR) sources are sufficiently brilliant to produce a nearly perfect parallel beam over a large area whilst still retaining...... a flux considerably higher than that available from conventional x-ray generators. A facility designed for the testing of x-ray optics, particularly in connection with x-ray telescopes is described below. It is proposed that this facility will be accommodated at the Synchrotron Radiation Source...

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

Large area damage testing of optics

International Nuclear Information System (INIS)

Sheehan, L.; Kozlowski, M.; Stolz, C.

1996-01-01

The damage threshold specifications for the National Ignition Facility will include a mixture of standard small-area tests and new large-area tests. During our studies of laser damage and conditioning processes of various materials we have found that some damage morphologies are fairly small and this damage does not grow with further illumination. This type of damage might not be detrimental to the laser performance. We should therefore assume that some damage can be allowed on the optics, but decide on a maximum damage allowance of damage. A new specification of damage threshold termed open-quotes functional damage thresholdclose quotes was derived. Further correlation of damage size and type to system performance must be determined in order to use this measurement, but it is clear that it will be a large factor in the optics performance specifications. Large-area tests have verified that small-area testing is not always sufficient when the optic in question has defect-initiated damage. This was evident for example on sputtered polarizer and mirror coatings where the defect density was low enough that the features could be missed by standard small- area testing. For some materials, the scale-length at which damage non-uniformities occur will effect the comparison of small-area and large-area tests. An example of this was the sub-aperture tests on KD*P crystals on the Beamlet test station. The tests verified the large-area damage threshold to be similar to that found when testing a small-area. Implying that for this KD*P material, the dominate damage mechanism is of sufficiently small scale-length that small-area testing is capable of determining the threshold. The Beamlet test station experiments also demonstrated the use of on-line laser conditioning to increase the crystals damage threshold

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.

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.

Ultra-high accuracy optical testing: creating diffraction-limitedshort-wavelength optical systems

Energy Technology Data Exchange (ETDEWEB)

Goldberg, Kenneth A.; Naulleau, Patrick P.; Rekawa, Senajith B.; Denham, Paul E.; Liddle, J. Alexander; Gullikson, Eric M.; Jackson, KeithH.; Anderson, Erik H.; Taylor, John S.; Sommargren, Gary E.; Chapman,Henry N.; Phillion, Donald W.; Johnson, Michael; Barty, Anton; Soufli,Regina; Spiller, Eberhard A.; Walton, Christopher C.; Bajt, Sasa

2005-08-03

Since 1993, research in the fabrication of extreme ultraviolet (EUV) optical imaging systems, conducted at Lawrence Berkeley National Laboratory (LBNL) and Lawrence Livermore National Laboratory (LLNL), has produced the highest resolution optical systems ever made. We have pioneered the development of ultra-high-accuracy optical testing and alignment methods, working at extreme ultraviolet wavelengths, and pushing wavefront-measuring interferometry into the 2-20-nm wavelength range (60-600 eV). These coherent measurement techniques, including lateral shearing interferometry and phase-shifting point-diffraction interferometry (PS/PDI) have achieved RMS wavefront measurement accuracies of 0.5-1-{angstrom} and better for primary aberration terms, enabling the creation of diffraction-limited EUV optics. The measurement accuracy is established using careful null-testing procedures, and has been verified repeatedly through high-resolution imaging. We believe these methods are broadly applicable to the advancement of short-wavelength optical systems including space telescopes, microscope objectives, projection lenses, synchrotron beamline optics, diffractive and holographic optics, and more. Measurements have been performed on a tunable undulator beamline at LBNL's Advanced Light Source (ALS), optimized for high coherent flux; although many of these techniques should be adaptable to alternative ultraviolet, EUV, and soft x-ray light sources. To date, we have measured nine prototype all-reflective EUV optical systems with NA values between 0.08 and 0.30 (f/6.25 to f/1.67). These projection-imaging lenses were created for the semiconductor industry's advanced research in EUV photolithography, a technology slated for introduction in 2009-13. This paper reviews the methods used and our program's accomplishments to date.

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.

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

Fiber optic utilization at the Nevada Test Site

International Nuclear Information System (INIS)

Lyons, P.B.; Golob, J.E.; Looney, L.D.; Robichaud, R.E.; Nelson, M.A.; Davies, T.J.

1978-11-01

Optical fiber cables have been successfully used for 100-MHz analog data transmission during an underground nuclear test at the Nevada Test Site. Two 700-m Corning Corguide cables were used to provide thirteen single fiber data channels from the vicinity of the underground detonation, 350 meters below ground level, to recording instrumentation, 350 meters from the downhole shaft. No fiber performance degradation was observed during the extensive procedures used to seal the shaft. These procedures included backfilling the shaft with layers of sand and gravel, as well as poured epoxy plugs. Techniques were developed for internal sealing of the Corguide cable to prevent any possible radioactive gas flow through voids within the cable. The effects on optical fibers of intense, pulsed neutron and gamma irradiation were studied. Specialized tools, including a system for location of faults or breaks in the optical fibers, were developed. The success of this first test will allow consideration of fiber optic cables for future nuclear tests as well as for other applications involving extremely rough handling in field environments

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

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.

Ultra-high accuracy optical testing: creating diffraction-limited short-wavelength optical systems

International Nuclear Information System (INIS)

Goldberg, Kenneth A.; Naulleau, Patrick P.; Rekawa, Senajith B.; Denham, Paul E.; Liddle, J. Alexander; Gullikson, Eric M.; Jackson, KeithH.; Anderson, Erik H.; Taylor, John S.; Sommargren, Gary E.; Chapman, Henry N.; Phillion, Donald W.; Johnson, Michael; Barty, Anton; Soufli, Regina; Spiller, Eberhard A.; Walton, Christopher C.; Bajt, Sasa

2005-01-01

Since 1993, research in the fabrication of extreme ultraviolet (EUV) optical imaging systems, conducted at Lawrence Berkeley National Laboratory (LBNL) and Lawrence Livermore National Laboratory (LLNL), has produced the highest resolution optical systems ever made. We have pioneered the development of ultra-high-accuracy optical testing and alignment methods, working at extreme ultraviolet wavelengths, and pushing wavefront-measuring interferometry into the 2-20-nm wavelength range (60-600 eV). These coherent measurement techniques, including lateral shearing interferometry and phase-shifting point-diffraction interferometry (PS/PDI) have achieved RMS wavefront measurement accuracies of 0.5-1-(angstrom) and better for primary aberration terms, enabling the creation of diffraction-limited EUV optics. The measurement accuracy is established using careful null-testing procedures, and has been verified repeatedly through high-resolution imaging. We believe these methods are broadly applicable to the advancement of short-wavelength optical systems including space telescopes, microscope objectives, projection lenses, synchrotron beamline optics, diffractive and holographic optics, and more. Measurements have been performed on a tunable undulator beamline at LBNL's Advanced Light Source (ALS), optimized for high coherent flux; although many of these techniques should be adaptable to alternative ultraviolet, EUV, and soft x-ray light sources. To date, we have measured nine prototype all-reflective EUV optical systems with NA values between 0.08 and 0.30 (f/6.25 to f/1.67). These projection-imaging lenses were created for the semiconductor industry's advanced research in EUV photolithography, a technology slated for introduction in 2009-13. This paper reviews the methods used and our program's accomplishments to date

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...

Geometrical optics modeling of the grating-slit test.

Science.gov (United States)

Liang, Chao-Wen; Sasian, Jose

2007-02-19

A novel optical testing method termed the grating-slit test is discussed. This test uses a grating and a slit, as in the Ronchi test, but the grating-slit test is different in that the grating is used as the incoherent illuminating object instead of the spatial filter. The slit is located at the plane of the image of a sinusoidal intensity grating. An insightful geometrical-optics model for the grating-slit test is presented and the fringe contrast ratio with respect to the slit width and object-grating period is obtained. The concept of spatial bucket integration is used to obtain the fringe contrast ratio.

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...

Cryogenic test facility instrumentation with fiber optic and fiber optic sensors for testing superconducting accelerator magnets

Science.gov (United States)

Chiuchiolo, A.; Bajas, H.; Bajko, M.; Castaldo, B.; Consales, M.; Cusano, A.; Giordano, M.; Giloux, C.; Perez, J. C.; Sansone, L.; Viret, P.

2017-12-01

The magnets for the next steps in accelerator physics, such as the High Luminosity upgrade of the LHC (HL- LHC) and the Future Circular Collider (FCC), require the development of new technologies for manufacturing and monitoring. To meet the HL-LHC new requirements, a large upgrade of the CERN SM18 cryogenic test facilities is ongoing with the implementation of new cryostats and cryogenic instrumentation. The paper deals with the advances in the development and the calibration of fiber optic sensors in the range 300 - 4 K using a dedicated closed-cycle refrigerator system composed of a pulse tube and a cryogen-free cryostat. The calibrated fiber optic sensors (FOS) have been installed in three vertical cryostats used for testing superconducting magnets down to 1.9 K or 4.2 K and in the variable temperature test bench (100 - 4.2 K). Some examples of FOS measurements of cryostat temperature evolution are presented as well as measurements of strain performed on a subscale of High Temperature Superconducting magnet during its powering tests.

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

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)

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

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...

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.

Effect of pH on the morphology, mechanical and optical properties of ...

Indian Academy of Sciences (India)

Administrator

Indian Academy of Sciences. 1419. Effect of pH on the morphology, mechanical and optical properties of .... 1 mm and the focal length ( f ) of the convex lens used to focus the laser beam was 300 mm. In the present work,. 20 laser shots ...

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,

Small Optics Laser Damage Test Procedure

Energy Technology Data Exchange (ETDEWEB)

Wolfe, Justin [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2017-10-19

This specification defines the requirements and procedure for laser damage testing of coatings and bare surfaces designated for small optics in the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory (LLNL).

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...

An Optical Receiver Post Processing System for the Integrated Radio and Optical Communications Software Defined Radio Test Bed

Science.gov (United States)

Nappier, Jennifer M.; Tokars, Roger P.; Wroblewski, Adam C.

2016-01-01

The Integrated Radio and Optical Communications (iROC) project at the National Aeronautics and Space Administrations (NASA) Glenn Research Center is investigating the feasibility of a hybrid radio frequency (RF) and optical communication system for future deep space missions. As a part of this investigation, a test bed for a radio frequency (RF) and optical software defined radio (SDR) has been built. Receivers and modems for the NASA deep space optical waveform are not commercially available so a custom ground optical receiver system has been built. This paper documents the ground optical receiver, which is used in order to test the RF and optical SDR in a free space optical communications link.

An Optical Receiver Post-Processing System for the Integrated Radio and Optical Communications Software Defined Radio Test Bed

Science.gov (United States)

Nappier, Jennifer M.; Tokars, Roger P.; Wroblewski, Adam C.

2016-01-01

The Integrated Radio and Optical Communications (iROC) project at the National Aeronautics and Space Administration's (NASA) Glenn Research Center is investigating the feasibility of a hybrid radio frequency (RF) and optical communication system for future deep space missions. As a part of this investigation, a test bed for a radio frequency (RF) and optical software defined radio (SDR) has been built. Receivers and modems for the NASA deep space optical waveform are not commercially available so a custom ground optical receiver system has been built. This paper documents the ground optical receiver, which is used in order to test the RF and optical SDR in a free space optical communications link.

Stress Optical Coefficient, Test Methodology, and Glass Standard Evaluation

Science.gov (United States)

2016-05-01

ARL-TN-0756 ● MAY 2016 US Army Research Laboratory Stress Optical Coefficient, Test Methodology , and Glass Standard Evaluation...Stress Optical Coefficient, Test Methodology , and Glass Standard Evaluation by Clayton M Weiss Oak Ridge Institute for Science and Education...ORISE), Belcamp, MD Parimal J Patel Weapons and Materials Research Directorate, ARL Approved for public release; distribution is

Diffractive optics: design, fabrication, and test

National Research Council Canada - National Science Library

O'Shea, Donald C

2004-01-01

This book provides the reader with the broad range of materials that were discussed in a series of short courses presented at Georgia Tech on the design, fabrication, and testing of diffractive optical elements (DOEs...

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.

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

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).

ACIGA's high optical power test facility

Energy Technology Data Exchange (ETDEWEB)

Ju, L [School of Physics, University of Western Australia, Perth (Australia); Aoun, M [Computer and Information Science, Edith Cowan University, Perth (Australia); Barriga, P [School of Physics, University of Western Australia, Perth (Australia)] [and others

2004-03-07

Advanced laser interferometer detectors utilizing more than 100 W of laser power and with {approx}10{sup 6} W circulating laser power present many technological problems. The Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) is developing a high power research facility in Gingin, north of Perth, Western Australia, which will test techniques for the next generation interferometers. In particular it will test thermal lensing compensation and control strategies for optical cavities in which optical spring effects and parametric instabilities may present major difficulties.

Construction of an optical test-bed for eLISA

International Nuclear Information System (INIS)

Lieser, Maike; Isleif, K-S; Schuster, S; Tröbs, M; Veith, S; Heinzel, G; Danzmann, K; Fitzsimons, E; Killow, C; Perreur-Lloyd, M; Robertson, D; Ward, H

2016-01-01

In the planned eLISA mission a key part of the system is the optical bench that holds the interferometers for reading out the inter-spacecraft distance and the test mass position. We report on ongoing technology development for the eLISA optical system like the back-link between the optical benches and the science interferometer where the local beam is interfered with the received beam from the distant spacecraft. The focus will be on a setup to investigate the tilt-to-pathlength coupling in the science interferometer. To test the science interferometer in the lab a second bench providing a laser beam and a reference interferometer is needed. We present a setup with two ultra-stable low expansion glass benches and bonded optics. To suppress the tilt-to-pathlength coupling to the required level (few μm/rad) imaging optics are placed in front of the interferometer photo diodes. (paper)

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.

Irradiation tests of radiation resistance optical fibers for fusion diagnostic application

Science.gov (United States)

Kakuta, Tsunemi; Shikama, Tatsuo; Nishitani, Takeo; Yamamoto, Shin; Nagata, Shinji; Tsuchiya, Bun; Toh, Kentaro; Hori, Junichi

2002-11-01

To promote development of radiation-resistant core optical fibers, the ITER-EDA (International Thermonuclear Experimental Reactor-Engineering Design Activity) recommended carrying out international round-robin irradiation tests of optical fibers to establish a reliable database for their applications in the ITER plasma diagnostics. Ten developed optical fibers were irradiation-tested in a Co-60 gamma cell, a Japan Materials Testing Reactor (JMTR). Also, some of them were irradiation tested in a fast neutron irradiation facility of FNS (Fast Neutron Source), especially to study temperature dependence of neutron-associated irradiation effects. Included were several Japanese fluorine doped fibers and one Japanese standard fiber (purified and undoped silica core), as well as seven Russian fibers. Some of Russian fibers were drawn by Japanese manufactures from Russian made pre-form rods to study effects of manufacturing processes to radiation resistant properties. The present paper will describe behaviors of growth of radiation-induced optical transmission loss in the wavelength range of 350-1750nm. Results indicate that role of displacement damages by fast neutrons are very important in introducing permanent optical transmission loss. Spectra of optical transmission loss in visible range will depend on irradiation temperatures and material parameters of optical fibers.

Perspective and potential of smart optical materials

Science.gov (United States)

Choi, Sang H.; Duzik, Adam J.; Kim, Hyun-Jung; Park, Yeonjoon; Kim, Jaehwan; Ko, Hyun-U.; Kim, Hyun-Chan; Yun, Sungryul; Kyung, Ki-Uk

2017-09-01

The increasing requirements of hyperspectral imaging optics, electro/photo-chromic materials, negative refractive index metamaterial optics, and miniaturized optical components from micro-scale to quantum-scale optics have all contributed to new features and advancements in optics technology. Development of multifunctional capable optics has pushed the boundaries of optics into new fields that require new disciplines and materials to maximize the potential benefits. The purpose of this study is to understand and show the fundamental materials and fabrication technology for field-controlled spectrally active optics (referred to as smart optics) that are essential for future industrial, scientific, military, and space applications, such as membrane optics, filters, windows for sensors and probes, telescopes, spectroscopes, cameras, light valves, light switches, and flat-panel displays. The proposed smart optics are based on the Stark and Zeeman effects in materials tailored with quantum dot arrays and thin films made from readily polarizable materials via ferroelectricity or ferromagnetism. Bound excitonic states of organic crystals are also capable of optical adaptability, tunability, and reconfigurability. To show the benefits of smart optics, this paper reviews spectral characteristics of smart optical materials and device technology. Experiments testing the quantum-confined Stark effect, arising from rare earth element doping effects in semiconductors, and applied electric field effects on spectral and refractive index are discussed. Other bulk and dopant materials were also discovered to have the same aspect of shifts in spectrum and refractive index. Other efforts focus on materials for creating field-controlled spectrally smart active optics on a selected spectral range. Surface plasmon polariton transmission of light through apertures is also discussed, along with potential applications. New breakthroughs in micro scale multiple zone plate optics as a micro

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

Use of thermal sieve to allow optical testing of cryogenic optical systems.

Science.gov (United States)

Kim, Dae Wook; Cai, Wenrui; Burge, James H

2012-05-21

Full aperture testing of large cryogenic optical systems has been impractical due to the difficulty of operating a large collimator at cryogenic temperatures. The Thermal Sieve solves this problem by acting as a thermal barrier between an ambient temperature collimator and the cryogenic system under test. The Thermal Sieve uses a set of thermally controlled baffles with array of holes that are lined up to pass the light from the collimator without degrading the wavefront, while attenuating the thermal background by nearly 4 orders of magnitude. This paper provides the theory behind the Thermal Sieve system, evaluates the optimization for its optical and thermal performance, and presents the design and analysis for a specific system.

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

Experimental method for testing diffraction properties of reflection waveguide holograms.

Science.gov (United States)

Xie, Yi; Kang, Ming-Wu; Wang, Bao-Ping

2014-07-01

Waveguide holograms' diffraction properties include peak wavelength and diffraction efficiency, which play an important role in determining their display performance. Based on the record and reconstruction theory of reflection waveguide holograms, a novel experimental method for testing diffraction properties is introduced and analyzed in this paper, which uses a plano-convex lens optically contacted to the surface of the substrate plate of the waveguide hologram, so that the diffracted light beam can be easily detected. Then an experiment is implemented. The designed reconstruction wavelength of the test sample is 530 nm, and its diffraction efficiency is 100%. The experimental results are a peak wavelength of 527.7 nm and a diffraction efficiency of 94.1%. It is shown that the tested value corresponds well with the designed value.

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...

Optical verification tests of the NISP/Euclid grism qualification model

Science.gov (United States)

Caillat, Amandine; Costille, Anne; Pascal, Sandrine; Vives, Sébastien; Rossin, Christelle; Sanchez, Patrice; Foulon, Benjamin

2016-07-01

The Euclid space mission aims at elucidating dark matter and dark energy mysteries thanks to two scientific instruments: VIS, the visible camera and NISP, the Near Infrared Spectro-Photometer. Millions of galaxies spectra will be recorded thanks to its spectroscopic mode using four grisms developed under LAM (Laboratoire d'Astrophysique de Marseille) responsibility. These dispersive optical components are made of a grating on a prism and include also, specifically for NISP, three other optical functions: spectral filtering, focus adjustment and spectral wavefront correction. Therefore, these optical elements are very challenging to manufacture (four industrial partners work on a single optical component) and to test before integration into NISP. In this paper, first we describe the optical specifications and the manufacturing process. Second, we explain the optical validation tests campaign: optical setups, measurements and data processing procedures used to validate these complex optical components, particularly for transmitted efficiency and wavefront error for which specifications are very stringent. Finally, we present the first results obtained on the grism EQM which manufacturing is on-going and almost finished.

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.

Fiber-optic dipping liquid analyzer: theoretical and experimental study of light transmission

International Nuclear Information System (INIS)

Zhou Ai; Liu Zhihai; Yuan Libo

2009-01-01

A fiber-optic dipping liquid analyzer (FDLA) is developed for measuring liquid properties such as concentration, refractive index, surface tension, and viscosity. An important feature of the FDLA is that a liquid drop is introduced on the end face of a fiber probe, and the drop can be regarded as a planar-convex lens. The light transmitting path and receiving power are affected by the refractive index of the liquid drop. We present a theoretical and experimental analysis of the light transmission. A mathematical model of receiving power is established based on paraxial refraction imaging and fiber reflective intensity modulation methods. Sucrose-water solutions were tested with the FDLA. The experimental results agree well with the theoretical analysis.

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...

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...

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.

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.

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.

Fiber optic sensor applications in field testing

International Nuclear Information System (INIS)

Perea, J.A.

1984-01-01

Fiber optic sensors (F.O.S.) are defined, and the application of this technology to measuring various phenomonon in diverse and hostile environments are discussed. F.O.S. advantages and disavantages both technically and operationally are summarized. Three sensor techniques - intensity, interferometric, and polarization - are then discussed in some detail. General environmental instrumentation and controls that support the Nuclear Weapons Test Program at the Nevada Test Site are discussed next to provide the reader with a basic understanding of the programmatic task. This will aid in recognizing the various difficulties of the traditional measurement techniques at the NTS and the potential advantages that fiber optic measurement systems can provide. An F.O.S. development program is then outlined, depicting a plan to design and fabricate a prototype sensor to be available for field testing by the end of FY84. We conclude with future plans for further development of F.O.S. to measure more of the desired physical parameters for the Test Program, and to eventually become an integral part of an overall measurement and control system

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...

Fabrication and evaluation of variable focus and large deformation plano-convex microlens based on non-ionic poly(vinyl chloride)/dibutyl adipate gels

International Nuclear Information System (INIS)

Kim, Sang-Youn; Yeo, Myoung; Shin, Eun-Jae; Park, Won-Hyeong; Jang, Jong-Seok; Nam, Byeong-Uk; Bae, Jin Woo

2015-01-01

In this paper, we propose a variable focus microlens module based on a transparent, electroactive, and non-ionic PVC/DBA gel. A non-ionic PVC/DBA (nPVC) gel on an ITO glass was confined beneath a rigid annular electrode, and applied pressure squeezed a bulge of the nPVC gel into the annular electrode, resulting in a hemispherical plano-convex nPVC gel microlens. The proposed nPVC gel microlens was analyzed and optimized. When voltage is applied to the circular perimeter (the annular electrode) of this fabricated microlens, electrically induced creep deformation of the nPVC gel occurs, changing its optical focal length. The focal length remarkably increases from 3.8 mm up to 14.3 mm with increasing applied voltages from 300 V to 800 V. Due to its compact, transparent, and electroactive characteristics, the proposed nPVC gel microlens can be easily inserted into small consumer electronic devices, such as digital cameras, camcorders, cell phones, and other portable optical devices. (paper)

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.

Tests of optical glues for the PANDA electromagnetic calorimeter

NARCIS (Netherlands)

Dbeyssi, A.; Tomasi-Gustafsson, E.; Hennino, T.; Imre, M.; Kunne, R.; Le Galliard, C.; Marchand, D.; Maroni, A.; Ramstein, B.; Rosier, P.; Bremer, D.; Dormenev, V.; Eissner, T.; Kuske, T.; Novotny, R.; Moeini, H.; Bondarenko, O.; Kavatsyuk, M.; Loehner, H.; Messchendorp, G.; Tambave, G.

2013-01-01

This paper reports on the results of tests for low temperature applications of two commercial optical glues in the electromagnetic calorimeter of PANDA at FAIR. Mechanical, thermal and optical properties are presented, as well as radiation hardness to photon and proton radiation. (C) 2013 Elsevier

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

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

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.

Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens

International Nuclear Information System (INIS)

Ke, Yougang; Liu, Yachao; Zhou, Junxiao; Liu, Yuanyuan; Luo, Hailu; Wen, Shuangchun

2016-01-01

In the optical system, most elements such as lens, prism, and optical fiber are made of silica glass. Therefore, integrating Pancharatnam-Berry phase elements into silica glass has potential applications in the optical system. In this paper, we take a lens, for example, which integrates a Pancharatnam-Berry phase lens into a conventional plano-convex lens. The spin states and positions of focal points can be modulated by controlling the polarization states of the incident beam. The proposed lens has a high transmission efficiency, and thereby acts as a simple and powerful tool to manipulate spin photons. Furthermore, the method can be conveniently extended to the optical fiber and laser cavity, and may provide a route to the design of the spin-photonic devices.

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 analysis and global optimization

CERN Document Server

Tuy, Hoang

2016-01-01

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

Application of identifying transmission spheres for spherical surface testing

Science.gov (United States)

Han, Christopher B.; Ye, Xin; Li, Xueyuan; Wang, Quanzhao; Tang, Shouhong; Han, Sen

2017-06-01

We developed a new application on Microsoft Foundation Classes (MFC) to identify correct transmission spheres (TS) for Spherical Surface Testing (SST). Spherical surfaces are important optical surfaces, and the wide application and high production rate of spherical surfaces necessitates an accurate and highly reliable measuring device. A Fizeau Interferometer is an appropriate tool for SST due to its subnanometer accuracy. It measures the contour of a spherical surface using a common path, which is insensitive to the surrounding circumstances. The Fizeau Interferometer transmits a wide laser beam, creating interference fringes from re-converging light from the transmission sphere and the test surface. To make a successful measurement, the application calculates and determines the appropriate transmission sphere for the test surface. There are 3 main inputs from the test surfaces that are utilized to determine the optimal sizes and F-numbers of the transmission spheres: (1) the curvatures (concave or convex), (2) the Radii of Curvature (ROC), and (3) the aperture sizes. The application will firstly calculate the F-numbers (i.e. ROC divided by aperture) of the test surface, secondly determine the correct aperture size of a convex surface, thirdly verify that the ROC of the test surface must be shorter than the reference surface's ROC of the transmission sphere, and lastly calculate the percentage of area that the test surface will be measured. However, the amount of interferometers and transmission spheres should be optimized when measuring large spherical surfaces to avoid requiring a large amount of interferometers and transmission spheres for each test surface. Current measuring practices involve tedious and potentially inaccurate calculations. This smart application eliminates human calculation errors, optimizes the selection of transmission spheres (including the least number required) and interferometer sizes, and increases efficiency.

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

A modified artificial bee colony based on chaos theory for solving non-convex emission/economic dispatch

International Nuclear Information System (INIS)

Shayeghi, H.; Ghasemi, A.

2014-01-01

Highlights: • This paper presents a developed multi objective CIABC based on CLS theory for solving EED problem. • The EED problem is formulated as a non-convex multi objective optimization problem. • Considered three test systems to demonstrate its efficiency including practical constrains. • The significant improvement in the results comparing the reported literature. - Abstract: In this paper, a modified ABC based on chaos theory namely CIABC is comprehensively enhanced and effectively applied for solving a multi-objective EED problem to minimize three conflicting objective functions with non-smooth and non-convex generator fuel cost characteristics while satisfying the operation constraints. The proposed method uses a Chaotic Local Search (CLS) to enhance the self searching ability of the original ABC algorithm for finding feasible optimal solutions of the EED problem. Also, many linear and nonlinear constraints, such as generation limits, transmission line loss, security constraints and non-smooth cost functions are considered as dynamic operational constraints. Moreover, a method based on fuzzy set theory is employed to extract one of the Pareto-optimal solutions as the best compromise one. The proposed multi objective evolutionary method has been applied to the standard IEEE 30 bus six generators, fourteen generators and 40 thermal generating units, respectively, as small, medium and large test power system. The numerical results obtained with the proposed method based on tables and figures compared with other evolutionary algorithm of scientific literatures. The results regards that the proposed CIABC algorithm surpasses the other available methods in terms of computational efficiency and solution quality

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.

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.

Design of a Test Bench for Intraocular Lens Optical Characterization

Energy Technology Data Exchange (ETDEWEB)

Alba-Bueno, Francisco; Vega, Fidel; Millan, Maria S, E-mail: francisco.alba-bueno@upc.edu, E-mail: fvega@oo.upc.edu, E-mail: millan@oo.upc.edu [Departamento de Optica y Optometria, Universidad Politecnica de Cataluna, C/ Violinista Vellsola 37, 08222 Terrassa (Spain)

2011-01-01

The crystalline lens is the responsible for focusing at different distances (accommodation) in the human eye. This organ grows throughout life increasing in size and rigidity. Moreover, due this growth it loses transparency through life, and becomes gradually opacified causing what is known as cataracts. Cataract is the most common cause of visual loss in the world. At present, this visual loss is recoverable by surgery in which the opacified lens is destroyed (phacoemulsification) and replaced by the implantation of an intraocular lens (IOL). If the IOL implanted is mono-focal the patient loses its natural capacity of accommodation, and as a consequence they would depend on an external optic correction to focus at different distances. In order to avoid this dependency, multifocal IOLs designs have been developed. The multi-focality can be achieved by using either, a refractive surface with different radii of curvature (refractive IOLs) or incorporating a diffractive surface (diffractive IOLs). To analyze the optical quality of IOLs it is necessary to test them in an optical bench that agrees with the ISO119679-2 1999 standard (Ophthalmic implants. Intraocular lenses. Part 2. Optical Properties and Test Methods). In addition to analyze the IOLs according to the ISO standard, we have designed an optical bench that allows us to simulate the conditions of a real human eye. To do that, we will use artificial corneas with different amounts of optical aberrations and several illumination sources with different spectral distributions. Moreover, the design of the test bench includes the possibility of testing the IOLs under off-axis conditions as well as in the presence of decentration and/or tilt. Finally, the optical imaging quality of the IOLs is assessed by using common metrics like the Modulation Transfer Function (MTF), the Point Spread Function (PSF) and/or the Strehl ratio (SR), or via registration of the IOL's wavefront with a Hartmann-Shack sensor and its

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.

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)

Inverting Image Data For Optical Testing And Alignment

Science.gov (United States)

Shao, Michael; Redding, David; Yu, Jeffrey W.; Dumont, Philip J.

1993-01-01

Data from images produced by slightly incorrectly figured concave primary mirror in telescope processed into estimate of spherical aberration of mirror, by use of algorithm finding nonlinear least-squares best fit between actual images and synthetic images produced by multiparameter mathematical model of telescope optical system. Estimated spherical aberration, in turn, converted into estimate of deviation of reflector surface from nominal precise shape. Algorithm devised as part of effort to determine error in surface figure of primary mirror of Hubble space telescope, so corrective lens designed. Modified versions of algorithm also used to find optical errors in other components of telescope or of other optical systems, for purposes of testing, alignment, and/or correction.

Optical oscillator-amplifier laser configuration

International Nuclear Information System (INIS)

McAllister, G.L.

1975-01-01

A laser is described that has incorporated therein an oscillator formed by a pair of mirrors, at least one of the mirrors being positioned outside of the envelope. The mirrors are dimensioned and spaced from each other so that the resonator has a relatively low Fresnel number and is operated unstably. The entire surface of one of these mirrors is convex and diffracts a portion of the energy outside of the oscillator region. Also incorporated into the laser is an amplifier region defined by a separate pair of mirrors which receive the energy diffracted from the oscillator region. The second pair of mirrors form an optical system with a high Fresnel number. A filter, modulator or other control for the laser signal may be placed outside the laser envelope in the optical path of the oscillator

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...

Concentrator optical characterization using computer mathematical modelling and point source testing

Science.gov (United States)

Dennison, E. W.; John, S. L.; Trentelman, G. F.

1984-01-01

The optical characteristics of a paraboloidal solar concentrator are analyzed using the intercept factor curve (a format for image data) to describe the results of a mathematical model and to represent reduced data from experimental testing. This procedure makes it possible not only to test an assembled concentrator, but also to evaluate single optical panels or to conduct non-solar tests of an assembled concentrator. The use of three-dimensional ray tracing computer programs to calculate the mathematical model is described. These ray tracing programs can include any type of optical configuration from simple paraboloids to array of spherical facets and can be adapted to microcomputers or larger computers, which can graphically display real-time comparison of calculated and measured data.

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.

High-Resolution Adaptive Optics Test-Bed for Vision Science

International Nuclear Information System (INIS)

Wilks, S.C.; Thomspon, C.A.; Olivier, S.S.; Bauman, B.J.; Barnes, T.; Werner, J.S.

2001-01-01

We discuss the design and implementation of a low-cost, high-resolution adaptive optics test-bed for vision research. It is well known that high-order aberrations in the human eye reduce optical resolution and limit visual acuity. However, the effects of aberration-free eyesight on vision are only now beginning to be studied using adaptive optics to sense and correct the aberrations in the eye. We are developing a high-resolution adaptive optics system for this purpose using a Hamamatsu Parallel Aligned Nematic Liquid Crystal Spatial Light Modulator. Phase-wrapping is used to extend the effective stroke of the device, and the wavefront sensing and wavefront correction are done at different wavelengths. Issues associated with these techniques will be discussed

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...

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

Novel fabrication method for three-dimensional nanostructuring: an application to micro-optics

International Nuclear Information System (INIS)

Tormen, Massimo; Carpentiero, Alessandro; Ferrari, Enrico; Cojoc, Dan; Fabrizio, Enzo Di

2007-01-01

We propose a 3D micro and nanofabrication method with potential applications to several nanotechnology-related fields. Our approach is based on the combination of lithographic steps and isotropic wet etchings performed on a quartz or glass substrate to form 3D structures with very accurate shape control and nanometer scale surface roughness. The resulting concavities at the quartz surface are converted into convex plastic elements by hot embossing or casting techniques. Complex all-polymer refractive optical elements have been realized by this method. Upon illumination, such micro-optics focus the light into predetermined 3D distributions of focal lines and spots. The general fabrication scheme explored here is illustrated through a series of examples in optics, but is expected to offer new solutions to other fields such as medicine, microfluidics and nano-optics

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

Experimental study on performance verification tests for coordinate measuring systems with optical distance sensors

Science.gov (United States)

Carmignato, Simone

2009-01-01

Optical sensors are increasingly used for dimensional and geometrical metrology. However, the lack of international standards for testing optical coordinate measuring systems is currently limiting the traceability of measurements and the easy comparison of different optical systems. This paper presents an experimental investigation on artefacts and procedures for testing coordinate measuring systems equipped with optical distance sensors. The work is aimed at contributing to the standardization of testing methods. The VDI/VDE 2617-6.2:2005 guideline, which is probably the most complete document available at the state of the art for testing systems with optical distance sensors, is examined with specific experiments. Results from the experiments are discussed, with particular reference to the tests used for determining the following characteristics: error of indication for size measurement, probing error and structural resolution. Particular attention is given to the use of artefacts alternative to gauge blocks for determining the error of indication for size measurement.

TOCUSO: Test of Conceptual Understanding on High School Optics Topics

Science.gov (United States)

Akarsu, Bayram

2012-01-01

Physics educators around the world often need reliable diagnostic materials to measure students' understanding of physics concept in high school. The purpose of this study is to evaluate a new diagnostic tool on High School Optics concept. Test of Conceptual Understanding on High School Optics (TOCUSO) consists of 25 conceptual items that measures…

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.

Implementation of Fiber Optic Sensing System on Sandwich Composite Cylinder Buckling Test

Science.gov (United States)

Pena, Francisco; Richards, W. Lance; Parker, Allen R.; Piazza, Anthony; Schultz, Marc R.; Rudd, Michelle T.; Gardner, Nathaniel W.; Hilburger, Mark W.

2018-01-01

The National Aeronautics and Space Administration (NASA) Engineering and Safety Center Shell Buckling Knockdown Factor Project is a multicenter project tasked with developing new analysis-based shell buckling design guidelines and design factors (i.e., knockdown factors) through high-fidelity buckling simulations and advanced test technologies. To validate these new buckling knockdown factors for future launch vehicles, the Shell Buckling Knockdown Factor Project is carrying out structural testing on a series of large-scale metallic and composite cylindrical shells at the NASA Marshall Space Flight Center (Marshall Space Flight Center, Alabama). A fiber optic sensor system was used to measure strain on a large-scale sandwich composite cylinder that was tested under multiple axial compressive loads up to more than 850,000 lb, and equivalent bending loads over 22 million in-lb. During the structural testing of the composite cylinder, strain data were collected from optical cables containing distributed fiber Bragg gratings using a custom fiber optic sensor system interrogator developed at the NASA Armstrong Flight Research Center. A total of 16 fiber-optic strands, each containing nearly 1,000 fiber Bragg gratings, measuring strain, were installed on the inner and outer cylinder surfaces to monitor the test article global structural response through high-density real-time and post test strain measurements. The distributed sensing system provided evidence of local epoxy failure at the attachment-ring-to-barrel interface that would not have been detected with conventional instrumentation. Results from the fiber optic sensor system were used to further refine and validate structural models for buckling of the large-scale composite structures. This paper discusses the techniques employed for real-time structural monitoring of the composite cylinder for structural load introduction and distributed bending-strain measurements over a large section of the cylinder by

Assembly, alignment and test of the Transiting Exoplanet Survey Satellite (TESS) optical assemblies

Science.gov (United States)

Balonek, Gregory; Brown, Joshua J.; Andre, James E.; Chesbrough, Christian D.; Chrisp, Michael P.; Dalpiaz, Michael; Lennon, Joseph; Richards, B. C.; Clark, Kristin E.

2017-08-01

The Transiting Exoplanet Survey Satellite (TESS) will carry four visible waveband, seven-element, refractive F/1.4 lenses, each with a 34 degree diagonal field of view. This paper describes the methods used for the assembly, alignment and test of the four flight optical assemblies. Prior to commencing the build of the four flight optical assemblies, a Risk Reduction Unit (RRU) was successfully assembled and tested [1]. The lessons learned from the RRU were applied to the build of the flight assemblies. The main modifications to the flight assemblies include the inking of the third lens element stray light mitigation, tighter alignment tolerances, and diamond turning for critical mechanical surfaces. Each of the optical assemblies was tested interferometrically and measured with a low coherence distance measuring interferometer (DMI) to predict the optimal shim thickness between the lens assembly and detector before -75°C environmental testing. In addition to individual test data, environmental test results from prior assemblies allow for the exploration of marginal performance differences between each of the optical assemblies.

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

The TMS-1 corneal topography measurement applied to calibrated ellipsoidal convex surfaces.

Science.gov (United States)

Douthwaite, W A; Matilla, M T

1996-03-01

The purpose of this report is to assess the accuracy of the TMS-1 videokeratoscope (Computed Anatomy Inc.) by using convex ellipsoidal surfaces. The ellipsoids were calibrated using Form Talysurf analysis, which allowed for subsequent calculation of the vertex radius and p value. The videokeratoscope was used to examine the same ellipsoids. The data provided by the instrument software were used to plot a graph of r2 verses y2, where r is the measured radius at y, the distance from the corneal point being measured to the optical axis of the instrument. The intercept on the ordinate of this graph gives the vertex radius, and the slope give the p value. The results arising from the Talysurf and the TMS-1 techniques were compared. The TMS-1 videokeratoscope gave readings for the vertex radius that were generally higher than those of the Talysurf analysis. The vertex radius was up to 0.09 mm greater. The p value results were similar by the two methods for p values of approximately 0.8; however, the TMS-1 results were higher, and the discrepancy increased as the p value approached that of a paraboloid. Although the videokeratoscope may be useful in comparative studies of the cornea, there must be some doubt about the absolute values displayed as the surface becomes increasingly aspheric.

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

Towards Loophole-Free Optical Bell Test of CHSH Inequality

Science.gov (United States)

Tan, Yong-gang; Li, Hong-wei

2016-09-01

Bell test had been suggested to end the long-standing debate on the EPR paradox, while the imperfections of experimental devices induce some loopholes in Bell test experiments and hence the assumption of local reality by EPR cannot be excluded with current experimental results. In optical Bell test experiments, the locality loophole can be closed easily, while the attempt of closing detection loophole requires very high efficiency of single photon detectors. Previous studies showed that the violation of Clauser-Horne-Shimony-Holt (CHSH) inequality with maximally entangled states requires the detection efficiency to be higher than 82.8 %. In this paper, we raise a modified CHSH inequality that covers all measurement events including the efficient and inefficient detections in the Bell test and prove that all local hidden models can be excluded when the inequality is violated. We find that, when non-maximally entangled states are applied to the Bell test, the lowest detection efficiency for violation of the present inequality is 66.7 %. This makes it feasible to close the detection loophole and the locality loophole simultaneously in optical Bell test of CHSH inequality.

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.

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

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.

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.

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 ...

Lattice design of the integrable optics test accelerator and optical stochastic cooling experiment at Fermilab

Energy Technology Data Exchange (ETDEWEB)

Kafka, Gene [Illinois Inst. of Technology, Chicago, IL (United States)

2015-05-01

The Integrable Optics Test Accelerator (IOTA) storage ring at Fermilab will serve as the backbone for a broad spectrum of Advanced Accelerator R&D (AARD) experiments, and as such, must be designed with signi cant exibility in mind, but without compromising cost e ciency. The nonlinear experiments at IOTA will include: achievement of a large nonlinear tune shift/spread without degradation of dynamic aperture; suppression of strong lattice resonances; study of stability of nonlinear systems to perturbations; and studies of di erent variants of nonlinear magnet design. The ring optics control has challenging requirements that reach or exceed the present state of the art. The development of a complete self-consistent design of the IOTA ring optics, meeting the demands of all planned AARD experiments, is presented. Of particular interest are the precise control for nonlinear integrable optics experiments and the transverse-to-longitudinal coupling and phase stability for the Optical Stochastic Cooling Experiment (OSC). Since the beam time-of- ight must be tightly controlled in the OSC section, studies of second order corrections in this section are presented.

Cryogenic Fiber Optic Assemblies for Spaceflight Environments: Design, Manufacturing, Testing, and Integration

Science.gov (United States)

Thomes, W. Joe; Ott, Melanie N.; Chuska, Richard; Switzer, Robert; Onuma, Eleanya; Blair, Diana; Frese, Erich; Matyseck, Marc

2016-01-01

Fiber optic assemblies have been used on spaceflight missions for many years as an enabling technology for routing, transmitting, and detecting optical signals. Due to the overwhelming success of NASA in implementing fiber optic assemblies on spaceflight science-based instruments, system scientists increasingly request fibers that perform in extreme environments while still maintaining very high optical transmission, stability, and reliability. Many new applications require fiber optic assemblies that will operate down to cryogenic temperatures as low as 20 Kelvin. In order for the fiber assemblies to operate with little loss in optical throughput at these extreme temperatures requires a system level approach all the way from how the fiber assembly is manufactured to how it is held, routed, and integrated. The NASA Goddard Code 562 Photonics Group has been designing, manufacturing, testing, and integrating fiber optics for spaceflight and other high reliability applications for nearly 20 years. Design techniques and lessons learned over the years are consistently applied to developing new fiber optic assemblies that meet these demanding environments. System level trades, fiber assembly design methods, manufacturing, testing, and integration will be discussed. Specific recent examples of ground support equipment for the James Webb Space Telescope (JWST); the Ice, Cloud and Land Elevation Satellite-2 (ICESat-2); and others will be included.

Post-Test Inspection of Nasa's Evolutionary Xenon Thruster Long Duration Test Hardware: Ion Optics

Science.gov (United States)

Soulas, George C.; Shastry, Rohit

2016-01-01

A Long Duration Test (LDT) was initiated in June 2005 as a part of NASAs Evolutionary Xenon Thruster (NEXT) service life validation approach. Testing was voluntarily terminated in February 2014, with the thruster accumulating 51,184 hours of operation, processing 918 kg of xenon propellant, and delivering 35.5 MN-s of total impulse. This presentation will present the post-test inspection results to date for the thrusters ion optics.

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.)

The effect of optical system design for laser micro-hole drilling process

Science.gov (United States)

Ding, Chien-Fang; Lan, Yin-Te; Chien, Yu-Lun; Young, Hong-Tsu

2017-08-01

Lasers are a promising high accuracy tool to make small holes in composite or hard material. They offer advantages over the conventional machining process, which is time consuming and has scaling limitations. However, the major downfall in laser material processing is the relatively large heat affect zone or number of molten burrs it generates, even when using nanosecond lasers over high-cost ultrafast lasers. In this paper, we constructed a nanosecond laser processing system with a 532 nm wavelength laser source. In order to enhance precision and minimize the effect of heat generation with the laser drilling process, we investigated the geometric shape of optical elements and analyzed the images using the modulation transfer function (MTF) and encircled energy (EE) by using optical software Zemax. We discuss commercial spherical lenses, including plano-convex lenses, bi-convex lenses, plano-concave lenses, bi-concave lenses, best-form lenses, and meniscus lenses. Furthermore, we determined the best lens configuration by image evaluation, and then verified the results experimentally by carrying out the laser drilling process on multilayer flexible copper clad laminate (FCCL). The paper presents the drilling results obtained with different lens configurations and found the best configuration had a small heat affect zone and a clean edge along laser-drilled holes.

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...

[Dome-shaped macula: appearance on ultrasound and optical coherence tomography].

Science.gov (United States)

Chéour, M; Ben Aleya, N; Brour, J; Falfoul, Y; Agrebi, S; Skhiri, M; Kraïem, A

2013-10-01

The purpose of our work is to demonstrate the role of optical coherence tomography and ocular ultrasound in the diagnosis of the dome-shaped macula in high myopia. We report the case of a patient with high myopia who presented with a decrease in visual acuity and metamorphopsia in the left eye. She underwent visual acuity measurement, biomicroscopic examination and measurement of axial length. B-mode ultrasound and optical coherence tomography showed a projection of the macula in the convexity of the myopic staphyloma confirming the diagnosis of dome-shaped macula. Dome-shaped macula is a recently discovered entity, which may be responsible for a decrease in visual acuity in patients with high myopic posterior staphyloma. Ultrasound and optical coherence tomography are very helpful in making the diagnosis. Copyright © 2013. Published by Elsevier Masson SAS.

Testing of a Fiber Optic Wear, Erosion and Regression Sensor

Science.gov (United States)

Korman, Valentin; Polzin, Kurt A.

2011-01-01

The nature of the physical processes and harsh environments associated with erosion and wear in propulsion environments makes their measurement and real-time rate quantification difficult. A fiber optic sensor capable of determining the wear (regression, erosion, ablation) associated with these environments has been developed and tested in a number of different applications to validate the technique. The sensor consists of two fiber optics that have differing attenuation coefficients and transmit light to detectors. The ratio of the two measured intensities can be correlated to the lengths of the fiber optic lines, and if the fibers and the host parent material in which they are embedded wear at the same rate the remaining length of fiber provides a real-time measure of the wear process. Testing in several disparate situations has been performed, with the data exhibiting excellent qualitative agreement with the theoretical description of the process and when a separate calibrated regression measurement is available good quantitative agreement is obtained as well. The light collected by the fibers can also be used to optically obtain the spectra and measure the internal temperature of the wear layer.

Hartmann test of the COMPASS RICH-1 optical telescopes

CERN Document Server

Polak, J; Alekseev, M; Angerer, H; Apollonio, M; Birsa, R; Bordalo, P; Bradamante, F; Bressan, A; Busso, L; Chiosso, V M; Ciliberti, P; Colantoni, M L; Costa, S; Dibiase, N; Dafni, T; Dalla Torre, S; Diaz, V; Duic, V; Delagnes, E; Deschamps, H; Eyrich, W; Faso, D; Ferrero, A; Finger, M; Finger, M Jr; Fischer, H; Gerassimov, S; Giorgi, M; Gobbo, B; Hagemann, R; von Harrach, D; Heinsius, F H; Joosten, R; Ketzer, B; Königsmann, K; Kolosov, V N; Konorov, I; Kramer, D; Kunne, F; Levorato, S; Maggiora, A; Magnon, A; Mann, A; Martin, A; Rebourgeard, P; Mutter, A; Nähle, O; Neyret, D; Nerling, F; Pagano, P; Paul, S; Panebianco, S; Panzieri, D; Pesaro, G; Pizzolotto, C; Menon, G; Rocco, E; Robinet, F; Schiavon, P; Schill, C; Schoenmeier, P; Silva, L; Slunecka, M; Steiger, L; Sozzi, F; Sulc, M; Svec, M; Tessarotto, F; Teufel, A; Wollny, H

2008-01-01

The central region of COMPASS RICH-1 has been equipped with a new photon detection system based on MultiAnode PhotoMultiplier Tubes (MAPMT). The Cherenkov photons are focused by an array of 576 fused silica telescopes onto 576 MAPMTs. The quality and positioning of all optical components have been tested by Hartmann method. The validation procedures are described. The quality of the optical concentrators was checked and alignment corrections were made. The upgraded detector showed excellent performances during 2006 data taking.

Test of Special Relativity Using a Fiber Network of Optical Clocks.

Science.gov (United States)

Delva, P; Lodewyck, J; Bilicki, S; Bookjans, E; Vallet, G; Le Targat, R; Pottie, P-E; Guerlin, C; Meynadier, F; Le Poncin-Lafitte, C; Lopez, O; Amy-Klein, A; Lee, W-K; Quintin, N; Lisdat, C; Al-Masoudi, A; Dörscher, S; Grebing, C; Grosche, G; Kuhl, A; Raupach, S; Sterr, U; Hill, I R; Hobson, R; Bowden, W; Kronjäger, J; Marra, G; Rolland, A; Baynes, F N; Margolis, H S; Gill, P

2017-06-02

Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution. By searching for a daily variation of the frequency difference between four strontium optical lattice clocks in different locations throughout Europe connected by such links, we improve upon previous tests of time dilation predicted by special relativity. We obtain a constraint on the Robertson-Mansouri-Sexl parameter |α|≲1.1×10^{-8}, quantifying a violation of time dilation, thus improving by a factor of around 2 the best known constraint obtained with Ives-Stilwell type experiments, and by 2 orders of magnitude the best constraint obtained by comparing atomic clocks. This work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links. As clocks improve, and as fiber links are routinely operated, we expect that the tests initiated in this Letter will improve by orders of magnitude in the near future.

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.

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.

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.

The new null testing method for the special optical window

Science.gov (United States)

Huang, Changchun

2009-07-01

The high speed, high precision and wide range specifications are requirement for the modern aircraft, which the traditional hemispherical dome can't achieve now, and the novel conformal window instead can enhance the aerodynamic performance of the aircraft obviously. To reduce the aerodynamic drag and radar cross-section, the window geometry is generally aspheric in shape. As a result, the involved fabrication and testing processes are much more challenging than that of conventional optics and must be mastered before these windows and systems can be implemented at an acceptable cost and risk. Metrology is one of the critical areas required to advance the conformal window technology. But as the surface of these conformal windows is not the traditional sphere lens, the measurement method for it is infeasible with the conventional optics measurement processes. This paper we express the development of testing technology for the special conformal windows in brief, and emphatically introduces one available novel testing method- a new null testing, and here based on the theory of compensation methods, The principle of Offner's refractive null lens has been extended to test the transmission wavefront through conformal window optics and provide feedback during surface fabrication. a compensator system for the was designed for the conformal window is given which parameters are 100mm for its aperture and two parabolic surface as conformal window, the final residual wavefront error(RMS) of which is less than 1/20λ(λ=632.8nm).

Real-Time Optical Antimicrobial Susceptibility Testing

DEFF Research Database (Denmark)

Fredborg, Marlene; Andersen, Klaus R; Jørgensen, Erik

2013-01-01

Rapid antibiotic susceptibility testing is in highly demand in health-care fields as antimicrobial resistant bacterial strains emerge and spread. Here we describe an optical screening system (oCelloScope), which based on time-lapse imaging of 96 bacteria-antibiotic combinations at a time......, introduces real-time detection of bacterial growth and antimicrobial susceptibility, with imaging material to support the automatically generated graphs. Automated antibiotic susceptibility tests of a monoculture showed statistically significant antibiotic effect within 6 minutes and within 30 minutes...... from multidrug-resistant pathogenic bacteria. The oCelloScope system can be employed for a broad range of applications within bacteriology and may present new vistas as a point-of-care instrument in both clinical and veterinarian settings....

Quantitative cognitive-test characterization of reconnectable implantable fiber-optic neurointerfaces for optogenetic neurostimulation.

Science.gov (United States)

Fedotov, I V; Ivashkina, O I; Pochechuev, M S; Roshchina, M A; Toropova, K A; Fedotov, A B; Anokhin, K V; Zheltikov, A M

2017-11-01

Cognitive tests on representative groups of freely behaving transgenic mice are shown to enable a quantitative characterization of reconnectable implantable fiber-optic neurointerfaces for optogenetic neurostimulation. A systematic analysis of such tests provides a robust quantitative measure for the cognitive effects induced by fiber-optic neurostimulation, validating the performance of fiber-optic neurointerfaces for long-term optogenetic brain stimulations and showing no statistically significant artifacts in the behavior of transgenic mice due to interface implantation. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

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.

Field test investigation of high sensitivity fiber optic seismic geophone

Science.gov (United States)

Wang, Meng; Min, Li; Zhang, Xiaolei; Zhang, Faxiang; Sun, Zhihui; Li, Shujuan; Wang, Chang; Zhao, Zhong; Hao, Guanghu

2017-10-01

Seismic reflection, whose measured signal is the artificial seismic waves ,is the most effective method and widely used in the geophysical prospecting. And this method can be used for exploration of oil, gas and coal. When a seismic wave travelling through the Earth encounters an interface between two materials with different acoustic impedances, some of the wave energy will reflect off the interface and some will refract through the interface. At its most basic, the seismic reflection technique consists of generating seismic waves and measuring the time taken for the waves to travel from the source, reflect off an interface and be detected by an array of geophones at the surface. Compared to traditional geophones such as electric, magnetic, mechanical and gas geophone, optical fiber geophones have many advantages. Optical fiber geophones can achieve sensing and signal transmission simultaneously. With the development of fiber grating sensor technology, fiber bragg grating (FBG) is being applied in seismic exploration and draws more and more attention to its advantage of anti-electromagnetic interference, high sensitivity and insensitivity to meteorological conditions. In this paper, we designed a high sensitivity geophone and tested its sensitivity, based on the theory of FBG sensing. The frequency response range is from 10 Hz to 100 Hz and the acceleration of the fiber optic seismic geophone is over 1000pm/g. sixteen-element fiber optic seismic geophone array system is presented and the field test is performed in Shengli oilfield of China. The field test shows that: (1) the fiber optic seismic geophone has a higher sensitivity than the traditional geophone between 1-100 Hz;(2) The low frequency reflection wave continuity of fiber Bragg grating geophone is better.

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.

Optical tests for using smartphones inside medical devices

Science.gov (United States)

Bernat, Amir S.; Acobas, Jennifer K.; Phang, Ye Shang; Hassan, David; Bolton, Frank J.; Levitz, David

2018-02-01

Smartphones are currently used in many medical applications and are more frequently being integrated into medical imaging devices. The regulatory requirements in existence today however, particularly the standardization of smartphone imaging through validation and verification testing, only partially cover imaging characteristics with a smartphone. Specifically, it has been shown that smartphone camera specifications are of sufficient quality for medical imaging, and there are devices which comply with the FDA's regulatory requirements for a medical device such as a device's field of view, direction of viewing and optical resolution and optical distortion. However, these regulatory requirements do not call specifically for color testing. Images of the same object using automatic settings or different light sources can show different color composition. Experimental results showing such differences are presented. Under some circumstances, such differences in color composition could potentially lead to incorrect diagnoses. It is therefore critical to control the smartphone camera and illumination parameters properly. This paper examines different smartphone camera settings that affect image quality and color composition. To test and select the correct settings, a test methodology is proposed. It aims at evaluating and testing image color correctness and white balance settings for mobile phones and LED light sources. Emphasis is placed on color consistency and deviation from gray values, specifically by evaluating the ΔC values based on the CIEL*a*b* color space. Results show that such standardization minimizes differences in color composition and thus could reduce the risk of a wrong diagnosis.

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

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.

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.  

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....

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.

Comprehensive validation scheme for in situ fiber optics dissolution method for pharmaceutical drug product testing.

Science.gov (United States)

Mirza, Tahseen; Liu, Qian Julie; Vivilecchia, Richard; Joshi, Yatindra

2009-03-01

There has been a growing interest during the past decade in the use of fiber optics dissolution testing. Use of this novel technology is mainly confined to research and development laboratories. It has not yet emerged as a tool for end product release testing despite its ability to generate in situ results and efficiency improvement. One potential reason may be the lack of clear validation guidelines that can be applied for the assessment of suitability of fiber optics. This article describes a comprehensive validation scheme and development of a reliable, robust, reproducible and cost-effective dissolution test using fiber optics technology. The test was successfully applied for characterizing the dissolution behavior of a 40-mg immediate-release tablet dosage form that is under development at Novartis Pharmaceuticals, East Hanover, New Jersey. The method was validated for the following parameters: linearity, precision, accuracy, specificity, and robustness. In particular, robustness was evaluated in terms of probe sampling depth and probe orientation. The in situ fiber optic method was found to be comparable to the existing manual sampling dissolution method. Finally, the fiber optic dissolution test was successfully performed by different operators on different days, to further enhance the validity of the method. The results demonstrate that the fiber optics technology can be successfully validated for end product dissolution/release testing. (c) 2008 Wiley-Liss, Inc. and the American Pharmacists Association

[Measuring contrast sensitivity using visual acuity tests in retinal and optic nerve diseases].

Science.gov (United States)

Sommer, E; Marré, E; Mierdel, P

1990-01-01

The luminance contrast needed to discern various test types was measured with monochromatic and achromatic light to detect discrete functional deficiencies of the retina and optic nerve in cases of normal visual acuity. Landolt rings corresponding to visual acuity levels from 0.04 to 1.0 were used as test types. A significant increase in the necessary minimum contrast was detectable with blue test light on large Landolt rings in patients with diabetic retinopathy, ocular hypertension and glaucoma and with green or yellow test light on medium-sized and small Landolt rings in patients with central serous chorioidopathy and optic atrophy. The additional contrast needed to reach the maximum visual acuity amounts to 14-100% compared with normal visual acuity, depending on the color of the test light and the diagnosis. The amount of contrast needed is greatest in retinal diseases, and it is therefore possible to a certain extent to distinguish these from diseases of the optic nerve.

Integrating optical, mechanical, and test software (with applications to freeform optics)

Science.gov (United States)

Genberg, Victor; Michels, Gregory; Myer, Brian

2017-10-01

Optical systems must perform under environmental conditions including thermal and mechanical loading. To predict the performance in the field, integrated analysis combining optical and mechanical software is required. Freeform and conformal optics offer many new opportunities for optical design. The unconventional geometries can lead to unconventional, and therefore unintuitive, mechanical behavior. Finite element (FE) analysis offers the ability to predict the deformations of freeform optics under various environments and load conditions. To understand the impact on optical performance, the deformations must be brought into optical analysis codes. This paper discusses several issues related to the integrated optomechanical analysis of freeform optics.

Testing the Foundations of Relativity Using Cryogenic Optical Resonators

Science.gov (United States)

Müller, H.; Braxmaier, C.; Herrmann, S.; Pradl, O.; Lämmerzahl, C.; Mlynek, J.; Schiller, S.; Peters, A.

We present a new generation of experiments using cryogenic optical resonators(COREs) to test the foundations of relativity. The experiments test the isotropy of the speed of light (Michelson-Morley experiment), the independece of the speed of light from the velocity of the laboratory (Kennedy-Thorndike experiments), and the gravitational redshift for clocks based on an electronic transition. Compared with the best previous results, our tests have already yielded improvements up to a factor of three. Future versions promise significant improvements.

A Convex Model of Risk-Based Unit Commitment for Day-Ahead Market Clearing Considering Wind Power Uncertainty

DEFF Research Database (Denmark)

Zhang, Ning; Kang, Chongqing; Xia, Qing

2015-01-01

The integration of wind power requires the power system to be sufficiently flexible to accommodate its forecast errors. In the market clearing process, the scheduling of flexibility relies on the manner in which the wind power uncertainty is addressed in the unit commitment (UC) model. This paper...... and are considered in both the objective functions and the constraints. The RUC model is shown to be convex and is transformed into a mixed integer linear programming (MILP) problem using relaxation and piecewise linearization. The proposed RUC model is tested using a three-bus system and an IEEE RTS79 system...... that the risk modeling facilitates a strategic market clearing procedure with a reasonable computational expense....

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.

Discovery Channel Telescope active optics system early integration and test

Science.gov (United States)

Venetiou, Alexander J.; Bida, Thomas A.

2012-09-01

The Discovery Channel Telescope (DCT) is a 4.3-meter telescope with a thin meniscus primary mirror (M1) and a honeycomb secondary mirror (M2). The optical design is an f/6.1 Ritchey-Chrétien (RC) with an unvignetted 0.5° Field of View (FoV) at the Cassegrain focus. We describe the design, implementation and performance of the DCT active optics system (AOS). The DCT AOS maintains collimation and controls the figure of the mirror to provide seeing-limited images across the focal plane. To minimize observing overhead, rapid settling times are achieved using a combination of feed-forward and low-bandwidth feedback control using a wavefront sensing system. In 2011, we mounted a Shack-Hartmann wavefront sensor at the prime focus of M1, the Prime Focus Test Assembly (PFTA), to test the AOS with the wavefront sensor, and the feedback loop. The incoming wavefront is decomposed using Zernike polynomials, and the mirror figure is corrected with a set of bending modes. Components of the system that we tested and tuned included the Zernike to Bending Mode transformations. We also started open-loop feed-forward coefficients determination. In early 2012, the PFTA was replaced by M2, and the wavefront sensor moved to its normal location on the Cassegrain instrument assembly. We present early open loop wavefront test results with the full optical system and instrument cube, along with refinements to the overall control loop operating at RC Cassegrain focus.

TESTING THE APODIZED PUPIL LYOT CORONAGRAPH ON THE LABORATORY FOR ADAPTIVE OPTICS EXTREME ADAPTIVE OPTICS TESTBED

International Nuclear Information System (INIS)

Thomas, Sandrine J.; Dillon, Daren; Gavel, Donald; Soummer, Remi; Macintosh, Bruce; Sivaramakrishnan, Anand

2011-01-01

We present testbed results of the Apodized Pupil Lyot Coronagraph (APLC) at the Laboratory for Adaptive Optics (LAO). These results are part of the validation and tests of the coronagraph and of the Extreme Adaptive Optics (ExAO) for the Gemini Planet Imager (GPI). The apodizer component is manufactured with a halftone technique using black chrome microdots on glass. Testing this APLC (like any other coronagraph) requires extremely good wavefront correction, which is obtained to the 1 nm rms level using the microelectricalmechanical systems (MEMS) technology, on the ExAO visible testbed of the LAO at the University of Santa Cruz. We used an APLC coronagraph without central obstruction, both with a reference super-polished flat mirror and with the MEMS to obtain one of the first images of a dark zone in a coronagraphic image with classical adaptive optics using a MEMS deformable mirror (without involving dark hole algorithms). This was done as a complementary test to the GPI coronagraph testbed at American Museum of Natural History, which studied the coronagraph itself without wavefront correction. Because we needed a full aperture, the coronagraph design is very different from the GPI design. We also tested a coronagraph with central obstruction similar to that of GPI. We investigated the performance of the APLC coronagraph and more particularly the effect of the apodizer profile accuracy on the contrast. Finally, we compared the resulting contrast to predictions made with a wavefront propagation model of the testbed to understand the effects of phase and amplitude errors on the final contrast.

Turbulent boundary layer heat transfer experiments: Convex curvature effects including introduction and recovery

Science.gov (United States)

Simon, T. W.; Moffat, R. J.; Johnston, J. P.; Kays, W. M.

1982-01-01

Measurements were made of the heat transfer rate through turbulent and transitional boundary layers on an isothermal, convexly curved wall and downstream flat plate. The effect of convex curvature on the fully turbulent boundary layer was a reduction of the local Stanton numbers 20% to 50% below those predicted for a flat wall under the same circumstances. The recovery of the heat transfer rates on the downstream flat wall was extremely slow. After 60 cm of recovery length, the Stanton number was still typically 15% to 20% below the flat wall predicted value. Various effects important in the modeling of curved flows were studied separately. These are: the effect of initial boundary layer thickness, the effect of freestream velocity, the effect of freestream acceleration, the effect of unheated starting length, and the effect of the maturity of the boundary layer. An existing curvature prediction model was tested against this broad heat transfer data base to determine where it could appropriately be used for heat transfer predictions.

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

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.

Corneal topographer based on the Hartmann test.

Science.gov (United States)

Mejía, Yobani; Galeano, Janneth C

2009-04-01

The purpose of this article is to show the performance of a topographer based on the Hartmann test for convex surfaces of F/# approximately 1. This topographer, called "Hartmann Test topographer (HT topographer)," is a prototype developed in the Physics Department of the Universidad Nacional de Colombia. From the Hartmann pattern generated by the surface under test, and by the Fourier analysis and the optical aberration theory we obtain the sagitta (elevation map) of the surface. Then, taking the first and the second derivatives of the sagitta in the radial direction we obtain the meridional curvature map. The method is illustrated with an example. To check the performance of the HT topographer a toric surface, a revolution aspherical surface, and two human corneas were measured. Our results are compared with those obtained with a Placido ring topographer (Tomey TMS-4 videokeratoscope), and we show that our curvature maps are similar to those obtained with the Placido ring topographer. The HT topographer is able to reconstruct the corneal topography potentially eradicating the skew ray problem, therefore, corneal defects can be visualized more. The results are presented by elevation and meridional curvature maps.

Post delivery test report for light duty utility arm optical alignment system (OAS)

International Nuclear Information System (INIS)

Pardini, A.F.

1996-01-01

This report documents the post delivery testing of the Optical Alignment System (OAS) LDUA system, designed for use by the Light Duty Utility Arm (LDUA) project. The post delivery test shows by demonstration that the optical alignment system is fully operational to perform the task of aligning the LDUA arm and mast with the entry riser during deployment operations within a Hanford Site waste tank

Post delivery test report for light duty utility arm optical alignment system (OAS)

Energy Technology Data Exchange (ETDEWEB)

Pardini, A.F.

1996-04-18

This report documents the post delivery testing of the Optical Alignment System (OAS) LDUA system, designed for use by the Light Duty Utility Arm (LDUA) project. The post delivery test shows by demonstration that the optical alignment system is fully operational to perform the task of aligning the LDUA arm and mast with the entry riser during deployment operations within a Hanford Site waste tank.

Automated damage test facilities for materials development and production optic quality assurance at Lawrence Livermore National Laboratory

International Nuclear Information System (INIS)

Battersby, C.; Dickson, R.; Jennings, R.; Kimmons, J.; Kozlowski, M. R.; Maricle, S.; Mouser, R.; Runkel, M.; Schwartz, S.; Sheehan, L. M.; Weinzapfel, C.

1998-01-01

The Laser Program at LLNL has developed automated facilities for damage testing optics up to 1 meter in diameter. The systems were developed to characterize the statistical distribution of localized damage performance across large-aperture National Ignition Facility optics. Full aperture testing is a key component of the quality assurance program for several of the optical components. The primary damage testing methods used are R:1 mapping and raster scanning. Automation of these test methods was required to meet the optics manufacturing schedule. The automated activities include control and diagnosis of the damage-test laser beam as well as detection and characterization of damage events

System for testing optical fibers

Science.gov (United States)

Golob, John E. [Olathe, KS; Looney, Larry D. [Los Alamos, NM; Lyons, Peter B. [Los Alamos, NM; Nelson, Melvin A. [Santa Barbara, CA; Davies, Terence J. [Santa Barbara, CA

1980-07-15

A system for measuring a combination of optical transmission properties of fiber optic waveguides. A polarized light pulse probe is injected into one end of the optical fiber. Reflections from discontinuities within the fiber are unpolarized whereas reflections of the probe pulse incident to its injection remain polarized. The polarized reflections are prevented from reaching a light detector whereas reflections from the discontinuities reaches the detector.

Testing the precision optical calibration module for PINGU

Energy Technology Data Exchange (ETDEWEB)

Jurkovic, Martin; Holzapfel, Kilian [TU Muenchen, Physik-Department, Excellence Cluster Universe, Boltzmannstr. 2, 85748 Garching (Germany); Collaboration: IceCube-Collaboration

2015-07-01

The Precision IceCube Next Generation Upgrade (PINGU) is primarily designed to determine the neutrino mass hierarchy. This measurement requires an accurate calibration of the detector in order to reduce systematic uncertainties. The Precision Optical Calibration Modules (POCAM) will be placed in the detector as a well calibrated artificial light source in the ice. The POCAM will be enclosed in a glass sphere identical to those used for the detector modules. To construct and simulate a prototype of the POCAM, every component needs to be analyzed by their optical characteristics and by the behavior in temperatures down to -50 C. Therefore a highly shielded an isolated environment has to be build up. We report the status of the testing environment and the hardware selected.

Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics

Science.gov (United States)

Hahne, G. E.

1993-01-01

The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.

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...

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.

Applications of optical fibers in nuclear test diagnostics

International Nuclear Information System (INIS)

Lyons, P.B.; Hodson, E.K.; Looney, L.D.

1980-01-01

Two new plasma diagnostic experiments have been successfully fielded on nuclear device tests at NTS. Both systems rely on the unique advantages provided by optical fiber technology and both systems provide new diagnostic capabilities that previously were beyond the state-of-the-art in coaxial cable systems. One system addresses the need to record e wide bandwidth data on gamma-ray sources. Over the long (< 1 km) distances that characterize NTS testing, the bandwidth of coaxial cable systems is usually limited to < 200 to 400 MHz even with extensive equalization. The new system uses the Cerenkov process to generate light in a converter material. High bandwidth fibers and detectors are used to approach a 1-GHz bandwidth. In this case fibers provided the bandwidth capability. The second system provides time and space resolution of a neutron source on a fast (ns) time scale. Previous systems have utilized either an array of neutron detectors with individual coaxial cables or a fast scintillator viewed by a gated image intensifier. For a large number of channels, the coaxial system becomes very costly and is subject to potentially severe EMI concerns. The gated intensifier system requires complex electronics and accurate timing and can be affected by EMI. An alternative system is described which provides continuous time coverage with limited spatial resolution. Complete freedom from EMI is achieved through the use of optical data collection and transmission. The optical fibers offered a major (2 to 3 times) cost savings and a large weight savings relative to the coax system. Each system is discussed

INTRODUCING NOVEL GENERATION OF HIGH ACCURACY CAMERA OPTICAL-TESTING AND CALIBRATION TEST-STANDS FEASIBLE FOR SERIES PRODUCTION OF CAMERAS

Directory of Open Access Journals (Sweden)

M. Nekouei Shahraki

2015-12-01

Full Text Available The recent advances in the field of computer-vision have opened the doors of many opportunities for taking advantage of these techniques and technologies in many fields and applications. Having a high demand for these systems in today and future vehicles implies a high production volume of video cameras. The above criterions imply that it is critical to design test systems which deliver fast and accurate calibration and optical-testing capabilities. In this paper we introduce new generation of test-stands delivering high calibration quality in single-shot calibration of fisheye surround-view cameras. This incorporates important geometric features from bundle-block calibration, delivers very high (sub-pixel calibration accuracy, makes possible a very fast calibration procedure (few seconds, and realizes autonomous calibration via machines. We have used the geometrical shape of a Spherical Helix (Type: 3D Spherical Spiral with special geometrical characteristics, having a uniform radius which corresponds to the uniform motion. This geometrical feature was mechanically realized using three dimensional truncated icosahedrons which practically allow the implementation of a spherical helix on multiple surfaces. Furthermore the test-stand enables us to perform many other important optical tests such as stray-light testing, enabling us to evaluate the certain qualities of the camera optical module.

Fiber Optic Telemetry System for LLL High-Voltage Test Stand

International Nuclear Information System (INIS)

Richter, J.P.

1977-01-01

This paper describes the Fiber Optic Telemetry System designed to operate in the hostile particle and electromagnetic radiation environment of the High Voltage Test Stand. It discusses system criteria, components, packaging, and performance. In all tests to date, the system exceeds its design goals with very comfortable margins. It is well advanced into the fabrication stages with all crucial components tested and only straightforward TTL (Transistor Transistor Logic) circuitry to be completed

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...

Wafer-level micro-optics: trends in manufacturing, testing, packaging, and applications

Science.gov (United States)

Voelkel, Reinhard; Gong, Li; Rieck, Juergen; Zheng, Alan

2012-11-01

Micro-optics is an indispensable key enabling technology (KET) for many products and applications today. Probably the most prestigious examples are the diffractive light shaping elements used in high-end DUV lithography steppers. Highly efficient refractive and diffractive micro-optical elements are used for precise beam and pupil shaping. Micro-optics had a major impact on the reduction of aberrations and diffraction effects in projection lithography, allowing a resolution enhancement from 250 nm to 45 nm within the last decade. Micro-optics also plays a decisive role in medical devices (endoscopes, ophthalmology), in all laser-based devices and fiber communication networks (supercomputer, ROADM), bringing high-speed internet to our homes (FTTH). Even our modern smart phones contain a variety of micro-optical elements. For example, LED flashlight shaping elements, the secondary camera, and ambient light and proximity sensors. Wherever light is involved, micro-optics offers the chance to further miniaturize a device, to improve its performance, or to reduce manufacturing and packaging costs. Wafer-scale micro-optics fabrication is based on technology established by semiconductor industry. Thousands of components are fabricated in parallel on a wafer. We report on the state of the art in wafer-based manufacturing, testing, packaging and present examples and applications for micro-optical components and systems.

Bit-error-rate testing of fiber optic data links for MMIC-based phased array antennas

Science.gov (United States)

Shalkhauser, K. A.; Kunath, R. R.; Daryoush, A. S.

1990-01-01

The measured bit-error-rate (BER) performance of a fiber optic data link to be used in satellite communications systems is presented and discussed. In the testing, the link was measured for its ability to carry high burst rate, serial-minimum shift keyed (SMSK) digital data similar to those used in actual space communications systems. The fiber optic data link, as part of a dual-segment injection-locked RF fiber optic link system, offers a means to distribute these signals to the many radiating elements of a phased array antenna. Test procedures, experimental arrangements, and test results are presented.

Bit error rate testing of fiber optic data links for MMIC-based phased array antennas

Science.gov (United States)

Shalkhauser, K. A.; Kunath, R. R.; Daryoush, A. S.

1990-01-01

The measured bit-error-rate (BER) performance of a fiber optic data link to be used in satellite communications systems is presented and discussed. In the testing, the link was measured for its ability to carry high burst rate, serial-minimum shift keyed (SMSK) digital data similar to those used in actual space communications systems. The fiber optic data link, as part of a dual-segment injection-locked RF fiber optic link system, offers a means to distribute these signals to the many radiating elements of a phased array antenna. Test procedures, experimental arrangements, and test results are presented.

Double-Arched LD Array Stagger Pumped Electro-Optic Q-Switched Nd:YAG Laser without Water Cooling

International Nuclear Information System (INIS)

Xin-Yu, Chen; Guang-Yong, Jin; Yong-Ji, Yu; Chao, Wang; Da-Wei, Hao; Yi-Bo, Wang

2010-01-01

We report an experimental study on a double-arched LD array stagger pumped electro-optic Q-switched Nd:YAG laser without water cooling by using a convex-concave compensate resonator. Perfect matching of the gain field inside the rod and the fundamental mode of the cavity is made by this structure. When the repetition rate is 20 Hz, A maximum output energy at 1064 nm wavelength of 176 mJ (M 2 = 1.55) and 9.6 ns FWHM pulse width in fundamental mode Q-switch operation is obtained with LD injection current 120 A. The optical-optical conversion efficiency is 14.7%, the divergence angle of the output beam is about 1.8 mrad. (fundamental areas of phenomenology(including applications))

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.

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.

Automated bone segmentation from dental CBCT images using patch-based sparse representation and convex optimization

Energy Technology Data Exchange (ETDEWEB)

Wang, Li; Gao, Yaozong; Shi, Feng; Liao, Shu; Li, Gang [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 (United States); Chen, Ken Chung [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Stomatology, National Cheng Kung University Medical College and Hospital, Tainan, Taiwan 70403 (China); Shen, Steve G. F.; Yan, Jin [Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People' s Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Lee, Philip K. M.; Chow, Ben [Hong Kong Dental Implant and Maxillofacial Centre, Hong Kong, China 999077 (China); Liu, Nancy X. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Oral and Maxillofacial Surgery, Peking University School and Hospital of Stomatology, Beijing, China 100050 (China); Xia, James J. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 (United States); Department of Surgery (Oral and Maxillofacial Surgery), Weill Medical College, Cornell University, New York, New York 10065 (United States); Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People' s Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Shen, Dinggang, E-mail: dgshen@med.unc.edu [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 and Department of Brain and Cognitive Engineering, Korea University, Seoul, 136701 (Korea, Republic of)

2014-04-15

Purpose: Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. Accurate segmentation of CBCT image is an essential step to generate three-dimensional (3D) models for the diagnosis and treatment planning of the patients with CMF deformities. However, due to the poor image quality, including very low signal-to-noise ratio and the widespread image artifacts such as noise, beam hardening, and inhomogeneity, it is challenging to segment the CBCT images. In this paper, the authors present a new automatic segmentation method to address these problems. Methods: To segment CBCT images, the authors propose a new method for fully automated CBCT segmentation by using patch-based sparse representation to (1) segment bony structures from the soft tissues and (2) further separate the mandible from the maxilla. Specifically, a region-specific registration strategy is first proposed to warp all the atlases to the current testing subject and then a sparse-based label propagation strategy is employed to estimate a patient-specific atlas from all aligned atlases. Finally, the patient-specific atlas is integrated into amaximum a posteriori probability-based convex segmentation framework for accurate segmentation. Results: The proposed method has been evaluated on a dataset with 15 CBCT images. The effectiveness of the proposed region-specific registration strategy and patient-specific atlas has been validated by comparing with the traditional registration strategy and population-based atlas. The experimental results show that the proposed method achieves the best segmentation accuracy by comparison with other state-of-the-art segmentation methods. Conclusions: The authors have proposed a new CBCT segmentation method by using patch-based sparse representation and convex optimization, which can achieve considerably accurate segmentation results in CBCT

Automated bone segmentation from dental CBCT images using patch-based sparse representation and convex optimization

International Nuclear Information System (INIS)

Wang, Li; Gao, Yaozong; Shi, Feng; Liao, Shu; Li, Gang; Chen, Ken Chung; Shen, Steve G. F.; Yan, Jin; Lee, Philip K. M.; Chow, Ben; Liu, Nancy X.; Xia, James J.; Shen, Dinggang

2014-01-01

Purpose: Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. Accurate segmentation of CBCT image is an essential step to generate three-dimensional (3D) models for the diagnosis and treatment planning of the patients with CMF deformities. However, due to the poor image quality, including very low signal-to-noise ratio and the widespread image artifacts such as noise, beam hardening, and inhomogeneity, it is challenging to segment the CBCT images. In this paper, the authors present a new automatic segmentation method to address these problems. Methods: To segment CBCT images, the authors propose a new method for fully automated CBCT segmentation by using patch-based sparse representation to (1) segment bony structures from the soft tissues and (2) further separate the mandible from the maxilla. Specifically, a region-specific registration strategy is first proposed to warp all the atlases to the current testing subject and then a sparse-based label propagation strategy is employed to estimate a patient-specific atlas from all aligned atlases. Finally, the patient-specific atlas is integrated into amaximum a posteriori probability-based convex segmentation framework for accurate segmentation. Results: The proposed method has been evaluated on a dataset with 15 CBCT images. The effectiveness of the proposed region-specific registration strategy and patient-specific atlas has been validated by comparing with the traditional registration strategy and population-based atlas. The experimental results show that the proposed method achieves the best segmentation accuracy by comparison with other state-of-the-art segmentation methods. Conclusions: The authors have proposed a new CBCT segmentation method by using patch-based sparse representation and convex optimization, which can achieve considerably accurate segmentation results in CBCT

Development of a synchrotron radiation beam monitor for the Integrable Optics Test Accelerator

Energy Technology Data Exchange (ETDEWEB)

Scarpelli, Andrea [Univ. of Ferrara (Italy)

2016-01-01

Nonlinear integrable optics applied to beam dynamics may mitigate multi-particle instabilities, but proof of principle experiments have never been carried out. The Integrable Optics Test Accelerator (IOTA) is an electron and proton storage ring currently being built at Fermilab, which addresses tests of nonlinear lattice elements in a real machine in addition to experiments on optical stochastic cooling and on the single-electron wave function. These experiments require an outstanding control over the lattice parameters, achievable with fast and precise beam monitoring systems. This work describes the steps for designing and building a beam monitor for IOTA based on synchrotron radiation, able to measure intensity, position and transverse cross-section beam.

Tracking integration in concentrating photovoltaics using laterally moving optics.

Science.gov (United States)

Duerr, Fabian; Meuret, Youri; Thienpont, Hugo

2011-05-09

In this work the concept of tracking-integrated concentrating photovoltaics is studied and its capabilities are quantitatively analyzed. The design strategy desists from ideal concentration performance to reduce the external mechanical solar tracking effort in favor of a compact installation, possibly resulting in lower overall cost. The proposed optical design is based on an extended Simultaneous Multiple Surface (SMS) algorithm and uses two laterally moving plano-convex lenses to achieve high concentration over a wide angular range of ±24°. It achieves 500× concentration, outperforming its conventional concentrating photovoltaic counterparts on a polar aligned single axis tracker.

Error Analysis in a Device to Test Optical Systems by Using Ronchi Test and Phase Shifting

International Nuclear Information System (INIS)

Cabrera-Perez, Brasilia; Castro-Ramos, Jorge; Gordiano-Alvarado, Gabriel; Vazquez y Montiel, Sergio

2008-01-01

In optical workshops, Ronchi test is used to determine the optical quality of any concave surface, while it is in the polishing process its quality is verified. The Ronchi test is one of the simplest and most effective methods used for evaluating and measuring aberrations. In this work, we describe a device to test converging mirrors and lenses either with small F/numbers or large F/numbers, using LED (Light-Emitting Diode) that has been adapted in the Ronchi testing as source of illumination. With LED used the radiation angle is bigger than common LED. It uses external power supplies to have well stability intensity to avoid error during the phase shift. The setup also has the advantage to receive automatic input and output data, this is possible because phase shifting interferometry and a square Ronchi ruling with a variable intensity LED were used. Error analysis of the different parameters involved in the test of Ronchi was made. For example, we analyze the error in the shifting of phase, the error introduced by the movement of the motor, misalignments of x-axis, y-axis and z-axis of the surface under test, error in the period of the grid used

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

Analytical Model of Doppler Spectra of Light Backscattered from Rotating Convex Bodies of Revolution in the Global Cartesian Coordinate System

International Nuclear Information System (INIS)

Yan-Jun, Gong; Zhen-Sen, Wu; Jia-Ji, Wu

2009-01-01

We present an analytical model of Doppler spectra in backscattering from arbitrary rough convex bodies of revolution rotating around their axes in the global Cartesian coordinate system. This analytical model is applied to analyse Doppler spectra in backscatter from two cones and two cylinders, as well as two ellipsoids of revolution. We numerically analyse the influences of attitude and geometry size of objects on Doppler spectra. The analytical model can give contribution of the surface roughness, attitude and geometry size of convex bodies of revolution to Doppler spectra and may contribute to laser Doppler velocimetry as well as ladar applications

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.

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.

Quantitative assessment of slit Mura defect in a thin film transistor-liquid crystal display based on chromaticity and optical density

International Nuclear Information System (INIS)

Tzu, Fu-Ming; Chou, Jung-Hua

2010-01-01

An innovative non-contact optical inspection method is developed to quantify slit Mura defects for thin film transistor–liquid crystal displays (TFT-LCDs). From the measurements of both chromaticity and optical densities across the slit Mura, the results indicate that the optical density profile is a concave shape and the chromaticity distribution is a convex shape. A linear relation with a negative slope exists between the chromaticity and optical density. A larger colour difference has a steeper slope, and vice versa. All of the measurements with uncertainties of a 99.7% confidence interval satisfy the requirements of the flat panel display industry. The proposed method can accurately quantify the pattern of blue slit Mura of TFT-LCDs; even the perceptibility is below the just noticeable difference

Optical Production and Detection of Ultrasonic Waves in Metals for Nondestructive Testing

Science.gov (United States)

Morrison, R. A.

1972-01-01

Ultrasonic waves were produced by striking the surface of a metal with the focused one-joule pulse of a Q-switched ruby laser. Rayleigh (surface) waves and longitudinal waves were detected with conventional transducers. Optical methods of detection were tested and developed. Rayleigh waves were produced with an oscillator and transducer. They were optically detected on curved polished surfaces, and on unpolished surfaces. The technique uses a knife edge to detect small angle changes of the surface as the wave pulse passes the illuminated spot. Optical flaw detection using pulse echo and attenuation is demonstrated.

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.

Rapid Process to Generate Beam Envelopes for Optical System Analysis

Science.gov (United States)

Howard, Joseph; Seals, Lenward

2012-01-01

The task of evaluating obstructions in the optical throughput of an optical system requires the use of two disciplines, and hence, two models: optical models for the details of optical propagation, and mechanical models for determining the actual structure that exists in the optical system. Previous analysis methods for creating beam envelopes (or cones of light) for use in this obstruction analysis were found to be cumbersome to calculate and take significant time and resources to complete. A new process was developed that takes less time to complete beam envelope analysis, is more accurate and less dependent upon manual node tracking to create the beam envelopes, and eases the burden on the mechanical CAD (computer-aided design) designers to form the beam solids. This algorithm allows rapid generation of beam envelopes for optical system obstruction analysis. Ray trace information is taken from optical design software and used to generate CAD objects that represent the boundary of the beam envelopes for detailed analysis in mechanical CAD software. Matlab is used to call ray trace data from the optical model for all fields and entrance pupil points of interest. These are chosen to be the edge of each space, so that these rays produce the bounding volume for the beam. The x and y global coordinate data is collected on the surface planes of interest, typically an image of the field and entrance pupil internal of the optical system. This x and y coordinate data is then evaluated using a convex hull algorithm, which removes any internal points, which are unnecessary to produce the bounding volume of interest. At this point, tolerances can be applied to expand the size of either the field or aperture, depending on the allocations. Once this minimum set of coordinates on the pupil and field is obtained, a new set of rays is generated between the field plane and aperture plane (or vice-versa). These rays are then evaluated at planes between the aperture and field, at a

The scintillating optical fiber isotope experiment: Bevalac calibrations of test models

International Nuclear Information System (INIS)

Connell, J.J.; Binns, W.R.; Dowkontt, P.F.; Epstein, J.W.; Israel, M.H.; Klarmann, J.; Washington Univ., St. Louis, MO; Webber, W.R.; Kish, J.C.

1990-01-01

The Scintillating Optical Fiber Isotope Experiment (SOFIE) is a Cherenkov dE/dx-range experiment being developed to study the isotopic composition of cosmic rays in the iron region with sufficient resolution to resolve isotopes separated by one mass unit at iron. This instrument images stopping particles with a block of scintillating optical fibers coupled to an image intensified video camera. From the digitized video data the trajectory and range of particles stopping in the fiber bundle can be determined; this information, together with a Cherenkov measurement, is used to determine mass. To facilitate this determination, a new Cherenkov response equation was derived for heavy ions at energies near threshold in thick Cherenkov radiators. Test models of SOFIE were calibrated at the Lawrence Berkeley Laboratory's Bevalac heavy ion accelerator in 1985 and 1986 using beams of iron nuclei with energies of 465 to 515 MeV/nucleon. This paper presents the results of these calibrations and discusses the design of the SOFIE Bevalac test models in the context of the scientific objectives of the eventual balloon experiment. The test models show a mass resolution of σ A ≅0.30 amu and a range resolution of σ R ≅250 μm. These results are sufficient for a successful cosmic ray isotope experiment, thus demonstrating the feasibility of the detector system. The SOFIE test models represent the first successful application in the field of cosmic ray astrophysics of the emerging technology of scintillating optical fibers. (orig.)

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

Development and Testing of a Post-Installable Deepwater Monitoring System Using Fiber-Optic Sensors

Science.gov (United States)

Seaman, Calvin H.; Brower, David V.; Le, Suy Q.; Tang, Henry H.

2015-01-01

This paper addresses the design and development of a fiber-optic monitoring system that can be deployed on existing deepwater risers and flowlines; and provides a summary of test article fabrication and the subsequent laboratory testing performed at the National Aeronautics and Space Administration-Johnson Space Center (NASA-JSC). A major challenge of a post-installed instrumentation system is to ensure adequate coupling between the instruments and the riser or flowline of interest. This work investigates the sensor coupling for pipelines that are suspended in a water column (from topside platform to seabed) using a fiber-optic sensor clamp and subsea bonding adhesive. The study involved the design, fabrication, and test of several prototype clamps that contained fiber-optic sensors. A mold was produced by NASA using 3-D printing methods that allowed the casting of polyurethane clamp test articles to accommodate 4-inch and 8-inch diameter pipes. The prototype clamps were installed with a subsea adhesive in a "wet" environment and then tested in the NASA Structures Test Laboratory (STL). The tension, compression, and bending test data showed that the prototype sensor clamps achieved good structural coupling, and could provide high quality strain measurement for active monitoring.

Method used to test the imaging consistency of binocular camera's left-right optical system

Science.gov (United States)

Liu, Meiying; Wang, Hu; Liu, Jie; Xue, Yaoke; Yang, Shaodong; Zhao, Hui

2016-09-01

To binocular camera, the consistency of optical parameters of the left and the right optical system is an important factor that will influence the overall imaging consistency. In conventional testing procedure of optical system, there lacks specifications suitable for evaluating imaging consistency. In this paper, considering the special requirements of binocular optical imaging system, a method used to measure the imaging consistency of binocular camera is presented. Based on this method, a measurement system which is composed of an integrating sphere, a rotary table and a CMOS camera has been established. First, let the left and the right optical system capture images in normal exposure time under the same condition. Second, a contour image is obtained based on the multiple threshold segmentation result and the boundary is determined using the slope of contour lines near the pseudo-contour line. Third, the constraint of gray level based on the corresponding coordinates of left-right images is established and the imaging consistency could be evaluated through standard deviation σ of the imaging grayscale difference D (x, y) between the left and right optical system. The experiments demonstrate that the method is suitable for carrying out the imaging consistency testing for binocular camera. When the standard deviation 3σ distribution of imaging gray difference D (x, y) between the left and right optical system of the binocular camera does not exceed 5%, it is believed that the design requirements have been achieved. This method could be used effectively and paves the way for the imaging consistency testing of the binocular camera.

Tests, measurements, and characterization of electro-optic devices and systems

International Nuclear Information System (INIS)

Wadekar, S.G.

1989-01-01

This book contains the proceedings on tests, measurements and characterization of electro-optic devices and systems. Topics covered include: Measurement of spectral dynamics in single-quantum-well lasers, High power computer controlled laser diode characterization tester, and Laser diode characterization instrumentation

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...

Spectral Filtering Criteria for U-Band Test Light for In-Service Line Monitoring in Optical Fiber Networks

Science.gov (United States)

Honda, Nazuki; Izumita, Hisashi; Nakamura, Minoru

2006-06-01

In the fiber-to-the-home era, thousands of optical fibers will have to be accommodated in the central offices of optical access networks. To reduce maintenance costs and improve the service reliability of optical fiber networks, the authors must develop an optical fiber line testing system with a function for in-service line monitoring that uses a test light with a wavelength different from the communication light wavelength. To monitor an in-service line in an optical network, the effective rejection ratio of the test light must be taken into account. This ratio depends on the spectrum of the test light from the optical time-domain reflectometer and the rejection band of the filter in front of the optical network unit. The dependence of the effective rejection ratio as a function of the sideband suppression ratio (SBSR) and of the ratio of the rejection band to the bandwidth of the sideband noise d/D is clarified. When d/D =0.1 and the target effective rejection ratio of the filter is -40 dB, the SBSR and the filter loss of the termination cable must be -70 and -43 dB, respectively, or the SBSR must be -80 dB. When d/D service line monitoring for a 10-Gb/s transmission using a 1650-nm test light with an SBSR of -80 dB is also demonstrated.

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.

The optics of the Final Focus Test Beam

International Nuclear Information System (INIS)

Irwin, J.; Brown, K.; Bulos, F.; Burke, D.; Helm, R.; Roy, G.; Ruth, R.; Yamamoto, N.; Oide, K.

1991-05-01

The Final Focus Test Beam (FFTB), currently under construction at the end of the SLAC Linac, is being built by an international collaboration as a test bed for ideas and methods required in the design and construction of final focus systems for next generation e + e - linear colliders. The FFTB lattice is based on the previously developed principle of using sextupole pairs in a dispersive region to compensate chromaticity. The linear lattice was optimized for length, and implementation of diagnostic procedures. The transformations between sextupole pairs (CCX and CCY) are exactly -I, the matrix for the intermediate transformer (BX) is exactly diagonal, and the dispersion function has zero slope at the sextupoles and is thus zero at the minimum of the β x function in the intermediate transformer. The introduction of sextupoles in final focus systems leads to the presence of additional optical aberrations, and synchrotron radiation in the dipoles also enlarges the final spot size. The important fourth-order optical aberrations which determine the main features of the design have been identified. Additional lower order aberrations arise in the implementation of these designs, since the real system is not the ideal design. We concentrate on these aberrations and describe strategies for their diagnosis and correction

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.

Poster Presentation: Optical Test of NGST Developmental Mirrors

Science.gov (United States)

Hadaway, James B.; Geary, Joseph; Reardon, Patrick; Peters, Bruce; Keidel, John; Chavers, Greg

2000-01-01

An Optical Testing System (OTS) has been developed to measure the figure and radius of curvature of NGST developmental mirrors in the vacuum, cryogenic environment of the X-Ray Calibration Facility (XRCF) at Marshall Space Flight Center (MSFC). The OTS consists of a WaveScope Shack-Hartmann sensor from Adaptive Optics Associates as the main instrument, a Point Diffraction Interferometer (PDI), a Point Spread Function (PSF) imager, an alignment system, a Leica Disto Pro distance measurement instrument, and a laser source palette (632.8 nm wavelength) that is fiber-coupled to the sensor instruments. All of the instruments except the laser source palette are located on a single breadboard known as the Wavefront Sensor Pallet (WSP). The WSP is located on top of a 5-DOF motion system located at the center of curvature of the test mirror. Two PC's are used to control the OTS. The error in the figure measurement is dominated by the WaveScope's measurement error. An analysis using the absolute wavefront gradient error of 1/50 wave P-V (at 0.6328 microns) provided by the manufacturer leads to a total surface figure measurement error of approximately 1/100 wave rms. This easily meets the requirement of 1/10 wave P-V. The error in radius of curvature is dominated by the Leica's absolute measurement error of VI.5 mm and the focus setting error of Vi.4 mm, giving an overall error of V2 mm. The OTS is currently being used to test the NGST Mirror System Demonstrators (NMSD's) and the Subscale Beryllium Mirror Demonstrator (SBNM).

IOTA (Integrable Optics Test Accelerator): facility and experimental beam physics program

Science.gov (United States)

Antipov, S.; Broemmelsiek, D.; Bruhwiler, D.; Edstrom, D.; Harms, E.; Lebedev, V.; Leibfritz, J.; Nagaitsev, S.; Park, C. S.; Piekarz, H.; Piot, P.; Prebys, E.; Romanov, A.; Ruan, J.; Sen, T.; Stancari, G.; Thangaraj, C.; Thurman-Keup, R.; Valishev, A.; Shiltsev, V.

2017-03-01

The Integrable Optics Test Accelerator (IOTA) is a storage ring for advanced beam physics research currently being built and commissioned at Fermilab. It will operate with protons and electrons using injectors with momenta of 70 and 150 MeV/c, respectively. The research program includes the study of nonlinear focusing integrable optical beam lattices based on special magnets and electron lenses, beam dynamics of space-charge effects and their compensation, optical stochastic cooling, and several other experiments. In this article, we present the design and main parameters of the facility, outline progress to date and provide the timeline of the construction, commissioning and research. The physical principles, design, and hardware implementation plans for the major IOTA experiments are also discussed.

IOTA (Integrable Optics Test Accelerator): Facility and experimental beam physics program

International Nuclear Information System (INIS)

Antipov, Sergei; Broemmelsiek, Daniel; Bruhwiler, David; Edstrom, Dean; Harms, Elvin

2017-01-01

The Integrable Optics Test Accelerator (IOTA) is a storage ring for advanced beam physics research currently being built and commissioned at Fermilab. It will operate with protons and electrons using injectors with momenta of 70 and 150 MeV/c, respectively. The research program includes the study of nonlinear focusing integrable optical beam lattices based on special magnets and electron lenses, beam dynamics of space-charge effects and their compensation, optical stochastic cooling, and several other experiments. In this article, we present the design and main parameters of the facility, outline progress to date and provide the timeline of the construction, commissioning and research. Finally, the physical principles, design, and hardware implementation plans for the major IOTA experiments are also discussed.

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.

Efficient globally optimal segmentation of cells in fluorescence microscopy images using level sets and convex energy functionals.

Science.gov (United States)

Bergeest, Jan-Philip; Rohr, Karl

2012-10-01

In high-throughput applications, accurate and efficient segmentation of cells in fluorescence microscopy images is of central importance for the quantification of protein expression and the understanding of cell function. We propose an approach for segmenting cell nuclei which is based on active contours using level sets 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 consider three different well-known energy functionals for active contour-based segmentation and introduce convex formulations of these functionals. We also suggest a numeric approach for efficiently computing the solution. The performance of our approach has been evaluated using fluorescence microscopy images from different experiments comprising different cell types. We have also performed a quantitative comparison with previous segmentation approaches. Copyright © 2012 Elsevier B.V. All rights reserved.

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

Multilevel microvibration test for performance predictions of a space optical load platform

Science.gov (United States)

Li, Shiqi; Zhang, Heng; Liu, Shiping; Wang, Yue

2018-05-01

This paper presents a framework for the multilevel microvibration analysis and test of a space optical load platform. The test framework is conducted on three levels, including instrument, subsystem, and system level. Disturbance source experimental investigations are performed to evaluate the vibration amplitude and study vibration mechanism. Transfer characteristics of space camera are validated by a subsystem test, which allows the calculation of transfer functions from various disturbance sources to optical performance outputs. In order to identify the influence of the source on the spacecraft performance, a system level microvibration measurement test has been performed on the ground. From the time domain analysis and spectrum analysis of multilevel microvibration tests, we concluded that the disturbance source has a significant effect on its installation position. After transmitted through mechanical links, the residual vibration reduces to a background noise level. In addition, the angular microvibration of the platform jitter is mainly concentrated in the rotation of y-axes. This work is applied to a real practical application involving the high resolution satellite camera system.

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

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.

[The eye, the optic system and its anomalies].

Science.gov (United States)

Cohen, S Y

1993-09-15

The eye is a perceptive system with extremely complex physiology, although its optical properties can be assimilated to those of spherical diopters. Various approximations make it possible to reduce the eyeball to a single convex diopter. With a normal eye the image of an object situated ad infinitum focuses on the retina. The normal eye is called emmetropic. Otherwise, the eye is called ametropic. Several types of ametropy exist. When the image focuses in front of the retina the eye is said to be myopic. When the image focuses behind the retina the eye is called hypermetropic (or hyperopic). When the image of an object differs according to various focusing axes, the eye is said to be astigmatic.

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

Optical readout in a multi-module system test for the ATLAS pixel detector

International Nuclear Information System (INIS)

Flick, Tobias; Becks, Karl-Heinz; Gerlach, Peter; Kersten, Susanne; Maettig, Peter; Nderitu Kirichu, Simon; Reeves, Kendall; Richter, Jennifer; Schultes, Joachim

2006-01-01

The innermost part of the ATLAS experiment at the LHC, CERN, will be a pixel detector, which is presently under construction. The command messages and the readout data of the detector are transmitted over an optical data path. The readout chain consists of many components which are produced at several locations around the world, and must work together in the pixel detector. To verify that these parts are working together as expected a system test has been built up. It consists of detector modules, optoboards, optical fibres, Back of Crate cards, Readout Drivers, and control computers. In this paper, the system test setup and the operation of the readout chain are described. Also, some results of tests using the final pixel detector readout chain are given

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.

Quality Assurance Programme for the Environmental Testing of the CMS Tracker Optical Links

CERN Document Server

Gill, K; Troska, Jan K; Vasey, F; Zanet, A

2001-01-01

The QA programme is reviewed for the environmental compliance tests of commercial off-the-shelf (COTS) components for the CMS Tracker Optical link system. These environmental tests will take place in the pre-production and final production phases of the project and will measure radiation resistance, component lifetime, and sensitivity to magnetic fields. The evolution of the programme from small-scale prototype tests to the final pre-production manufacturing tests is outlined and the main environmental effects expected for optical links operating within the Tracker are summarised. A special feature of the environmental QA programme is the plan for Advance Validation Tests (AVT's) developed in close collaboration with the various industrial partners. AVT procedures involve validation of a relatively small set of basic samples in advance of the full production of the corresponding batch of devices. Only those lots that have been confirmed as sufficiently rad-tolerant will be purchased and used in the final prod...

Lessons Learned During Cryogenic Optical Testing of the Advanced Mirror System Demonstrators (AMSDs)

Science.gov (United States)

Hadaway, James; Reardon, Patrick; Geary, Joseph; Robinson, Brian; Stahl, Philip; Eng, Ron; Kegley, Jeff

2004-01-01

Optical testing in a cryogenic environment presents a host of challenges above and beyond those encountered during room temperature testing. The Advanced Mirror System Demonstrators (AMSDs) are 1.4 m diameter, ultra light-weight (mA2), off-axis parabolic segments. They are required to have 250 nm PV & 50 nm RMS surface figure error or less at 35 K. An optical testing system, consisting of an Instantaneous Phase Interferometer (PI), a diffractive null corrector (DNC), and an Absolute Distance Meter (ADM), was used to measure the surface figure & radius-of-curvature of these mirrors at the operational temperature within the X-Ray Calibration Facility (XRCF) at Marshall Space Flight Center (MSFC). The Ah4SD program was designed to improve the technology related to the design, fabrication, & testing of such mirrors in support of NASA s James Webb Space Telescope (JWST). This paper will describe the lessons learned during preparation & cryogenic testing of the AMSDs.

Optical vortex metrology for non-destructive testing

DEFF Research Database (Denmark)

Wang, W.; Hanson, Steen Grüner

2009-01-01

Based on the phase singularities in optical fields, we introduce a new technique, referred to as Optical Vortex Metrology, and demonstrate its application to nano- displacement, flow measurements and biological kinematic analysis.......Based on the phase singularities in optical fields, we introduce a new technique, referred to as Optical Vortex Metrology, and demonstrate its application to nano- displacement, flow measurements and biological kinematic analysis....