Convex analysis and global optimization
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;
Conference on Convex Analysis and Global Optimization
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-based void filling method for CAD-based Monte Carlo geometry modeling
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
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
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
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.
M. Gaspar, Raquel; Murgoci, Agatha
2010-01-01
A convexity adjustment (or convexity correction) in fixed income markets arises when one uses prices of standard (plain vanilla) products plus an adjustment to price nonstandard products. We explain the basic and appealing idea behind the use of convexity adjustments and focus on the situations...
Lauritzen, Niels
-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point......Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier...
Lauritzen, Niels
Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier-Motzkin elimin......Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier......-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point...... algorithm....
A Genealogy of Convex Solids Via Local and Global Bifurcations of Gradient Vector Fields
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.
Rockafellar, Ralph Tyrell
2015-01-01
Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and
Lauritzen, Niels
Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier-Motzkin elimin...
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.
Global existence for a quasi-linear evolution equation with a non-convex energy
Feireisl, Eduard; Petzeltová, Hana
2002-01-01
Roč. 354, č. 4 (2002), s. 1421-1437 ISSN 0002-9947 R&D Projects: GA AV ČR IAA1019002 Keywords : existence of global %initial-boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.664, year: 2002
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...
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...
A New Filled Function Method with One Parameter for Global Optimization
Fei Wei
2013-01-01
Full Text Available The filled function method is an effective approach to find the global minimizer of multidimensional multimodal functions. The conventional filled functions are numerically unstable due to exponential or logarithmic term and sensitive to parameters. In this paper, a new filled function with only one parameter is proposed, which is continuously differentiable and proved to satisfy all conditions of the filled function definition. Moreover, this filled function is not sensitive to parameter, and the overflow can not happen for this function. Based on these, a new filled function method is proposed, and it is numerically stable to the initial point and the parameter variable. The computer simulations indicate that the proposed filled function method is efficient and effective.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Scott, Paul
2006-01-01
A "convex" polygon is one with no re-entrant angles. Alternatively one can use the standard convexity definition, asserting that for any two points of the convex polygon, the line segment joining them is contained completely within the polygon. In this article, the author provides a solution to a problem involving convex lattice polygons.
Aichholzer, Oswin; Aurenhammer, Franz; Hurtado Díaz, Fernando Alfredo; Ramos, Pedro A.; Urrutia, J.
2009-01-01
We introduce a notion of k-convexity and explore some properties of polygons that have this property. In particular, 2-convex polygons can be recognized in O(n log n) time, and k-convex polygons can be triangulated in O(kn) time.
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.
van de Vel, MLJ
1993-01-01
Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear si
Parekh, Ankit
Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the ℓ1 norm is used to induce sparsity, so much so that ℓ1 regularization is considered to be `modern least-squares'. The use of ℓ1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the ℓ1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal
Convexity and Marginal Vectors
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
Alparslan-Gok, S.Z.; Brânzei, R.; Tijs, S.H.
2008-01-01
In this paper, convex interval games are introduced and some characterizations are given. Some economic situations leading to convex interval games are discussed. The Weber set and the Shapley value are defined for a suitable class of interval games and their relations with the interval core for
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....
Stereotype locally convex spaces
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
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
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.
Generalized Convexity and Inequalities
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...
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....
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.
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.
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
Subordination by convex functions
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.
Visualizing Data as Objects by DC (Difference of Convex) Optimization
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....
Convex games versus clan games
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
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
Convexity Adjustments for ATS Models
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...
Nested convex bodies are chaseable
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
Van De Vijver, Elien; Derudder, Ben; Bassens, David; Witlox, Frank
2014-01-01
This empirical article combines insights from previous research on the level of knowledge-intensive service in metropolitan areas with the aim to develop an understanding of the spatial structure of the global service economy. We use a stepwise regression model with the Globalization and World Cities research network's measure of globalized service provisioning as the dependent variable and a range of variables focusing on population, infrastructure, urban primacy, and national regulation as ...
Filiberti, A.W.; Bianco, J.A.; Baker, S.P.; Doherty; Nalivaika, L.A.; King, M.A.; Alpert, J.S.
1984-01-01
Early peak diastolic filling rate (PFR) of the left ventricle (LV) is said to be a sensitive index of LV dysfunction in patients with coronary disease, hypertension and hypertrophic cardiomyopathy. Radionuclide (RN0 multigated PFR was measured in 20 normal volunteers (13 males, 7 females, mean age 31 yrs., range 20-43) at rest and during supine bicycle exercise conducted to a symptomatic end-point. At rest, RN PFR was 3.4 +- SD 0.4 end-diastolic vols./sec (range 3.1 - 3.6). During exercise all normal volunteers had a progressive and numerically and statistically significant increase in PFR. Stepwise multiple linear regression (BMPD2R) was applied to the rest and exercise PFR data to develop a linear model describing the main determinants of the RN PFR. The potential independent variables which were included in the model were heart rate (HR), ejection fraction (EF), systolic arterial pressure, systolic ejection rate and exercise stage. Ranking of variables for prediction of RN PFR, and exclusion of less important variables, was done by F value criteria. The final multivariate equation was: LVPFR = -3.84437 + 0.03834 HR + 0.07537 LVEF. The model fit was highly significant (p<0.001), and accounted for 89 per cent of variability in the PFR. The authors conclude that the left ventricular peak filling rate is critically determined by heart rate and by ejection fraction at rest and during exercise
Convexities move because they contain matter.
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.
Modeling global mangrove soil carbon stocks: filling the gaps in coastal environments
Rovai, A.; Twilley, R.
2017-12-01
We provide an overview of contemporaneous global mangrove soil organic carbon (SOC) estimates, focusing on a framework to explain disproportionate differences among observed data as a way to improve global estimates. This framework is based on a former conceptual model, the coastal environmental setting, in contrast to the more popular latitude-based hypotheses largely believed to explain hemispheric variation in mangrove ecosystem properties. To demonstrate how local and regional estimates of SOC linked to coastal environmental settings can render more realistic global mangrove SOC extrapolations we combined published and unpublished data, yielding a total of 106 studies, reporting on 552 sites from 43 countries. These sites were classified into distinct coastal environmental setting types according to two concurrent worldwide typology of nearshore coastal systems classifications. Mangrove SOC density varied substantially across coastal environmental settings, ranging from 14.9 ± 0.8 in river dominated (deltaic) soils to 53.9 ± 1.6 mg cm-3 (mean ± SE) in karstic coastlines. Our findings reveal striking differences between published values and contemporary global mangrove SOC extrapolation based on country-level mean reference values, particularly for karstic-dominated coastlines where mangrove SOC stocks have been underestimated by up to 50%. Correspondingly, climate-based global estimates predicted lower mangrove SOC density values (32-41 mg C cm-3) for mangroves in karstic environments, differing from published (21-126 mg C cm-3) and unpublished (47-58 mg C cm-3) values. Moreover, climate-based projections yielded higher SOC density values (27-70 mg C cm-3) for river-dominated mangroves compared to lower ranges reported in the literature (11-24 mg C cm-3). We argue that this inconsistent reporting of SOC stock estimates between river-dominated and karstic coastal environmental settings is likely due to the omission of geomorphological and geophysical
θ-convex nonlinear programming problems
Emam, T.
2008-01-01
A class of sets and a class of functions called θ-convex sets and θ-convex functions are introduced by relaxing the definitions of convex sets and operator θ on the sets and domain of definition of the functions. The optimally results for θ-convex programming problems are established.
Raspaldo, Hervé; Aziza, Richard; Belhaouari, Lakhdar; Berros, Philippe; Body, Sylvie; Galatoire, Olivier; Le Louarn, Claude; Michaud, Thierry; Niforos, François; Rousseaux, Isabelle; Runge, Marc; Taieb, Maryna
2011-04-01
The objective of this paper is to provide an expert consensus regarding facial rejuvenation using a combination of volume replacement (Juvéderm(®) VOLUMA(®)), filling products (Juvéderm(®) Ultra product line) and botulinum toxin. The Juvéderm product line exploits innovative 3-D technology, producing a range of cohesive, homogenous gels that produce predictable, long-lasting and natural results. The products are easy to use by practitioners and are well-tolerated by patients, and used in combination can provide additional benefits not achieved with one product alone. An assessment of facial anatomy and consideration of the aging process, as well as available treatment options, are also addressed in determining the best combination of products to use. Outcomes from a questionnaire and workshop sessions focusing on specific aspects of use of the Juvéderm product line and botulinum toxin in daily clinical practice are discussed, and recommendations for product use following debate amongst the experts are provided.
A class of free locally convex spaces
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
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...
A new convexity measure for polygons.
Zunic, Jovisa; Rosin, Paul L
2004-07-01
Abstract-Convexity estimators are commonly used in the analysis of shape. In this paper, we define and evaluate a new convexity measure for planar regions bounded by polygons. The new convexity measure can be understood as a "boundary-based" measure and in accordance with this it is more sensitive to measured boundary defects than the so called "area-based" convexity measures. When compared with the convexity measure defined as the ratio between the Euclidean perimeter of the convex hull of the measured shape and the Euclidean perimeter of the measured shape then the new convexity measure also shows some advantages-particularly for shapes with holes. The new convexity measure has the following desirable properties: 1) the estimated convexity is always a number from (0, 1], 2) the estimated convexity is 1 if and only if the measured shape is convex, 3) there are shapes whose estimated convexity is arbitrarily close to 0, 4) the new convexity measure is invariant under similarity transformations, and 5) there is a simple and fast procedure for computing the new convexity measure.
NP-completeness of weakly convex and convex dominating set decision problems
Joanna Raczek
2004-01-01
Full Text Available The convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are \\(NP\\-complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can verify in polynomial time whether a given subset of vertices of a graph is convex or weakly convex.
Nonsmooth Mechanics and Convex Optimization
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
Quantum information and convex optimization
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.)
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
Quantum information and convex optimization
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.)
Convexity of the effective potential
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
A working-set framework for sequential convex approximation methods
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....
Relaxation Methods for Strictly Convex Regularizations of Piecewise Linear Programs
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)
Computing farthest neighbors on a convex polytope
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
A noncommutative convexity in C*-bimodules
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.
Quantum logics and convex geometry
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.)
Learning Convex Inference of Marginals
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 ...
Diameter 2 properties and convexity
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 convex optimization approach for solving large scale linear systems
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.
Finite dimensional convexity and optimization
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.
Use of Convexity in Ostomy Care
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
Reconstruction of convex bodies from moments
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...
Entropy coherent and entropy convex measures of risk
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
Pluripotential theory and convex bodies
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.
Characterizing Convexity of Games using Marginal Vectors
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
Convex trace functions of several variables
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 ...
Differential analysis of matrix convex functions II
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...
Strictly convex functions on complete Finsler manifolds
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 ...
Introduction to Convex and Quasiconvex Analysis
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
Convexity of oligopoly games without transferable technologies
Driessen, Theo; Meinhardt, Holger I.
2005-01-01
We present sufficient conditions involving the inverse demand function and the cost functions to establish the convexity of oligopoly TU-games without transferable technologies. For convex TU-games it is well known that the core is relatively large and that it is generically nonempty. The former
Convex bodies with many elliptic sections
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.
Generalized convexity, generalized monotonicity recent results
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...
Two generalizations of column-convex polygons
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.
Alpha-Concave Hull, a Generalization of Convex Hull
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...
Duality and calculus of convex objects (theory and applications)
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.
Convex sets in probabilistic normed spaces
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
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao
2015-01-01
be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution
ON THE GENERALIZED CONVEXITY AND CONCAVITY
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].
On convexity and Schoenberg's variation diminishing splines
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
Recent characterizations of generalized convexity in convexity in cooperative game thoery
Driessen, T.
1994-12-31
The notion of convexity for a real-valued function on the power set of the finite set N (the so-called cooperative game with player set N) is defined as in other mathematical fields. The study of convexity plays an important role within the field of cooperative game theory because the application of the solution part of game theory to convex games provides elegant results for the solution concepts involved. Especially, the well known solution concept called core is, for convex games, very well characterized. The current paper focuses on a notion of generalized convexity, called k- convexity, for cooperative n-person games. Due to very recent characterizations of convexity for cooperative games, the goal is to provide similar new characterizations of k-convexity. The main characterization states that for the k-convexity of an n-person game it is both necessary and sufficient that half of all the so-called marginal worth vectors belong to the core of the game. Here it is taken into account whether a marginal worth vector corresponds to an even or odd ordering of k elements of the n-person player set N. Another characterization of k-convexity is presented in terms of a so-called finite min-modular decomposition. That is, some specific cover game of a k-convex game can be decomposed as the minimum of a finite number of modular (or additive) games. Finally it is established that the k-convexity of a game can be characterized in terms of the second order partial derivates of the so-called multilinear extension of the game.
Hermitian harmonic maps into convex balls
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)
Counting convex polygons in planar point sets
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
Entropy Coherent and Entropy Convex Measures of Risk
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,
On Hadamard-Type Inequalities Involving Several Kinds of Convexity
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.
Terando, A. J.; Collazo, J.
2017-12-01
Boundary organizations, entities that facilitate the co-production and translation of scientific research in decision making processes, have been promoted as a means to assist global change adaptation, particularly in the areas of landscape conservation and natural resource management. However, scientists can and often still must perform a similar role and act as anchoring agents within wicked adaptation problems that involve a myriad of actors, values, scientific uncertainties, governance structures, and multidisciplinary research needs. We illustrate one such case study in Puerto Rico's Bosque Modelo (Model Forest) where we discuss an ongoing scientific effort to undertake a multi-objective landscape conservation design project that intersects with the Bosque Modelo geography and goals. Perspectives are provided from two research ecologists, one with a background in terrestrial ecology who has worked at the intersection of science, conservation, and government for over 30 years, and the other with a multi-disciplinary background in earth sciences, climatology, and terrestrial ecology. We frame our discussion around the learning process that accompanies the development of global change scenarios that are both useful and useable for a wide spectrum of scientists, and the likelihood that scientifically informed adaptive management actions will ultimately be implemented in this complex and changing landscape.
Convex Banding of the Covariance Matrix.
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.
Reconstruction of convex bodies from surface tensors
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....
Non-convex multi-objective optimization
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...
A generalization of the convex Kakeya problem
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.
Reconstruction of convex bodies from surface tensors
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...
Probing convex polygons with X-rays
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
Recovering convexity in non-associated plasticity
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.
Posewitz, Matthew C
2011-06-30
The green alga Chlamydomonas reinhardtii (Chlamydomonas) has numerous genes encoding enzymes that function in fermentative pathways. Among these genes, are the [FeFe]-hydrogenases, pyruvate formate lyase, pyruvate ferredoxin oxidoreductase, acetate kinase, and phosphotransacetylase. We have systematically undertaken a series of targeted mutagenesis approaches to disrupt each of these key genes and omics techniques to characterize alterations in metabolic flux. Funds from DE-FG02-07ER64423 were specifically leveraged to generate mutants with disruptions in the genes encoding the [FeFe]-hydrogenases HYDA1 and HYDA2, pyruvate formate lyase (PFL1), and in bifunctional alcohol/aldehyde alcohol dehydrogenase (ADH1). Additionally funds were used to conduct global transcript profiling experiments of wildtype Chlamydomonas cells, as well as of the hydEF-1 mutant, which is unable to make H2 due to a lesion in the [FeFe]-hydrogenase biosynthetic pathway. In the wildtype cells, formate, acetate and ethanol are the dominant fermentation products with traces of CO2 and H2 also being produced. In the hydEF-1 mutant, succinate production is increased to offset the loss of protons as a terminal electron acceptor. In the pfl-1 mutant, lactate offsets the loss of formate production, and in the adh1-1 mutant glycerol is made instead of ethanol. To further probe the system, we generated a double mutant (pfl1-1 adh1) that is unable to synthesize both formate and ethanol. This strain, like the pfl1 mutants, secreted lactate, but also exhibited a significant increase in the levels of extracellular glycerol, acetate, and intracellular reduced sugars, and a decline in dark, fermentative H2 production. Whereas wild-type Chlamydomonas fermentation primarily produces formate and ethanol, the double mutant performs a complete rerouting of the glycolytic carbon to lactate and glycerol. Lastly, transcriptome data have been analysed for both the wildtype and hydEF-1, that correlate with our
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
Differential analysis of matrix convex functions
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...
Robust Utility Maximization Under Convex Portfolio Constraints
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
Localized Multiple Kernel Learning A Convex Approach
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
A generalization of the convex Kakeya problem
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
Minimizing convex functions by continuous descent methods
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.
Directional Convexity and Finite Optimality Conditions.
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
Convexity properties of Hamiltonian group actions
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...
Some Characterizations of Convex Interval Games
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.
A generalization of the convex Kakeya problem
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
A generalization of the convex Kakeya problem
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.
Dynamic Matchings in Convex Bipartite Graphs
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...
Cost Allocation and Convex Data Envelopment
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...
Tropicalized Lambda Lengths, Measured Laminations and Convexity
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 ...
Deformation patterning driven by rate dependent non-convex strain gradient plasticity
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
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.
Fast approximate convex decomposition using relative concavity
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
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.
Schur Convexity of Generalized Heronian Means Involving Two Parameters
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.
A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES
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.
Displacement Convexity for First-Order Mean-Field Games
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.
Convex stoma appliances: an audit of stoma care nurses.
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.
Convexity, gauge-dependence and tunneling rates
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.
Reconstruction of convex bodies from surface tensors
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...
Exact generating function for 2-convex polygons
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
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.
Convex nonnegative matrix factorization with manifold regularization.
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.
Convexity, gauge-dependence and tunneling rates
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.
An easy path to convex analysis and applications
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
Convex geometry of quantum resource quantification
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 \
On the convexity of relativistic hydrodynamics
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)
Dynamic Convex Duality in Constrained Utility Maximization
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...
Optimal skill distribution under convex skill costs
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.
The occipital lobe convexity sulci and gyri.
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.
Convex Hull Aided Registration Method (CHARM).
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.
Generalized vector calculus on convex domain
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.
Neuro-genetic hybrid approach for the solution of non-convex economic dispatch problem
Malik, T.N.; Asar, A.U.
2009-01-01
ED (Economic Dispatch) is non-convex constrained optimization problem, and is used for both on line and offline studies in power system operation. Conventionally, it is solved as convex problem using optimization techniques by approximating generator input/output characteristic. Curves of monotonically increasing nature thus resulting in an inaccurate dispatch. The GA (Genetic Algorithm) has been used for the solution of this problem owing to its inherent ability to address the convex and non-convex problems equally. This approach brings the solution to the global minimum region of search space in a short time and then takes longer time to converge to near optimal results. GA based hybrid approaches are used to fine tune the near optimal results produced by GA. This paper proposes NGH (Neuro Genetic Hybrid) approach to solve the economic dispatch with valve point effect. The proposed approach combines the GA with the ANN (Artificial Neural Network) using SI (Swarm Intelligence) learning rule. The GA acts as a global optimizer and the neural network fine tunes the GA results to the desired targets. Three machines standard test system has been tested for validation of the approach. Comparing the results with GA and NGH model based on back-propagation learning, the proposed approach gives contrast improvements showing the promise of the approach. (author)
A new corrective technique for adolescent idiopathic scoliosis (Ucar′s convex rod rotation
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.
Convex and Radially Concave Contoured Distributions
Wolf-Dieter Richter
2015-01-01
Full Text Available Integral representations of the locally defined star-generalized surface content measures on star spheres are derived for boundary spheres of balls being convex or radially concave with respect to a fan in Rn. As a result, the general geometric measure representation of star-shaped probability distributions and the general stochastic representation of the corresponding random vectors allow additional specific interpretations in the two mentioned cases. Applications to estimating and testing hypotheses on scaling parameters are presented, and two-dimensional sample clouds are simulated.
On conditional independence and log-convexity
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
Convex functions and optimization methods on Riemannian manifolds
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...
Chance-Constrained Guidance With Non-Convex Constraints
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
CVXPY: A Python-Embedded Modeling Language for Convex Optimization
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.
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.
Mendoza Dorinna D
2010-07-01
Full Text Available Abstract Objectives To examine relationships between severity of echocardiography (echo -evidenced diastolic dysfunction (DD and volumetric filling by automated processing of routine cine cardiovascular magnetic resonance (CMR. Background Cine-CMR provides high-resolution assessment of left ventricular (LV chamber volumes. Automated segmentation (LV-METRIC yields LV filling curves by segmenting all short-axis images across all temporal phases. This study used cine-CMR to assess filling changes that occur with progressive DD. Methods 115 post-MI patients underwent CMR and echo within 1 day. LV-METRIC yielded multiple diastolic indices - E:A ratio, peak filling rate (PFR, time to peak filling rate (TPFR, and diastolic volume recovery (DVR80 - proportion of diastole required to recover 80% stroke volume. Echo was the reference for DD. Results LV-METRIC successfully generated LV filling curves in all patients. CMR indices were reproducible (≤ 1% inter-reader differences and required minimal processing time (175 ± 34 images/exam, 2:09 ± 0:51 minutes. CMR E:A ratio decreased with grade 1 and increased with grades 2-3 DD. Diastolic filling intervals, measured by DVR80 or TPFR, prolonged with grade 1 and shortened with grade 3 DD, paralleling echo deceleration time (p 80 identified 71% of patients with echo-evidenced grade 1 but no patients with grade 3 DD, and stroke-volume adjusted PFR identified 67% with grade 3 but none with grade 1 DD (matched specificity = 83%. The combination of DVR80 and PFR identified 53% of patients with grade 2 DD. Prolonged DVR80 was associated with grade 1 (OR 2.79, CI 1.65-4.05, p = 0.001 with a similar trend for grade 2 (OR 1.35, CI 0.98-1.74, p = 0.06, whereas high PFR was associated with grade 3 (OR 1.14, CI 1.02-1.25, p = 0.02 DD. Conclusions Automated cine-CMR segmentation can discern LV filling changes that occur with increasing severity of echo-evidenced DD. Impaired relaxation is associated with prolonged
Convex blind image deconvolution with inverse filtering
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.
Effective potential for non-convex potentials
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.)
INdAM Workshop on Analytic Aspects of Convexity
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.
On Difference of Convex Optimization to Visualize Statistical Data and Dissimilarities
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....
Multi-Period Trading via Convex Optimization
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...
Conditionally exponential convex functions on locally compact groups
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
Approximate convex hull of affine iterated function system attractors
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.
Entropy coherent and entropy convex measures of risk
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
Convexity-preserving Bernstein–Bézier quartic scheme
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.
Convergence of Algorithms for Reconstructing Convex Bodies and Directional Measures
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...
On approximation and energy estimates for delta 6-convex functions.
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.
On approximation and energy estimates for delta 6-convex functions
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.
STRICT CONVEXITY THROUGH EQUIVALENT NORMS IN SEPARABLES BANACH SPACES
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.
Fundamentals of convex analysis duality, separation, representation, and resolution
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...
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.
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.
Decomposability and convex structure of thermal processes
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.
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard
2015-05-04
In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport).
... and Medical Procedures Dental Devices Dental Amalgam About Dental Amalgam Fillings Share Tweet Linkedin Pin it More ... should I have my fillings removed? What is dental amalgam? Dental amalgam is a dental filling material ...
Neural network for nonsmooth pseudoconvex optimization with general convex constraints.
Bian, Wei; Ma, Litao; Qin, Sitian; Xue, Xiaoping
2018-05-01
In this paper, a one-layer recurrent neural network is proposed for solving a class of nonsmooth, pseudoconvex optimization problems with general convex constraints. Based on the smoothing method, we construct a new regularization function, which does not depend on any information of the feasible region. Thanks to the special structure of the regularization function, we prove the global existence, uniqueness and "slow solution" character of the state of the proposed neural network. Moreover, the state solution of the proposed network is proved to be convergent to the feasible region in finite time and to the optimal solution set of the related optimization problem subsequently. In particular, the convergence of the state to an exact optimal solution is also considered in this paper. Numerical examples with simulation results are given to show the efficiency and good characteristics of the proposed network. In addition, some preliminary theoretical analysis and application of the proposed network for a wider class of dynamic portfolio optimization are included. Copyright © 2018 Elsevier Ltd. All rights reserved.
Link Prediction via Convex Nonnegative Matrix Factorization on Multiscale Blocks
Enming Dong
2014-01-01
Full Text Available Low rank matrices approximations have been used in link prediction for networks, which are usually global optimal methods and lack of using the local information. The block structure is a significant local feature of matrices: entities in the same block have similar values, which implies that links are more likely to be found within dense blocks. We use this insight to give a probabilistic latent variable model for finding missing links by convex nonnegative matrix factorization with block detection. The experiments show that this method gives better prediction accuracy than original method alone. Different from the original low rank matrices approximations methods for link prediction, the sparseness of solutions is in accord with the sparse property for most real complex networks. Scaling to massive size network, we use the block information mapping matrices onto distributed architectures and give a divide-and-conquer prediction method. The experiments show that it gives better results than common neighbors method when the networks have a large number of missing links.
Van De Vijver, Elien; Derudder, Ben; Bassens, David; Witlox, Frank
2012-01-01
This empirical article combines insights from previous research on the level of knowledge-intensive service in metropolitan areas with the aim to develop an understanding of the spatial structure of the global service economy. We use a stepwise regression model with GaWC’s measure of globalized service provisioning as the dependent variable and a range of variables focusing on population, infrastructure, urban primacy, and national regulation as independent variables. The discussion of the re...
A survey on locally uniformly A-convex algebras
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)
Lipschitz estimates for convex functions with respect to vector fields
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].
A note on supercyclic operators in locally convex spaces
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.
Convex solutions of systems arising from Monge-Ampere equations
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.
Entropy and convexity for nonlinear partial differential equations.
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.
Displacement Convexity for First-Order Mean-Field Games
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.
Multi-objective convex programming problem arising in multivariate ...
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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.
Surgical treatment of convexity focal epilepsy
Shimizu, Hiroyuki; Ishijima, Buichi; Iio, Masaaki.
1987-01-01
We have hitherto applied PET study in 72 epileptic patients. The main contents of their seizures consists of complex partial in 32, elementary partial in 32, generalized in 6, and others in 3 cases. We administered perorally 10 mCi glucose labeled with C11 produced in the JSW Baby Cyclotron for the study of CMRG(cerebral metabolic rate of glucose). The continuous inhalation method of CO 2 and O 2 labeled with O15 produced in the same cyclotron was also employed for measurement of rCBE(cerebral blood flow) and CMRO 2 (cerebral metabolic rate of oxygen). In both studies, epileptic foci were shown as well demarcated hypometabolic zones with decreased CMRG, rCBF or CMRO 2 . The locations of PET diagnosed foci were not contradictory with the clinical symptoms, scalp EEGs or X-ray CT findings. Of the 32 patients with the convexity epileptic foci, 8 patients underwent surgical treatment. Prior to the surgical intervention, subdural strip electrodes were inserted in the four cases for further assessment of focus locations. Subdural EEG disclosed very active brain activity with high amplitude 4 to 5 times scalp EEG and revealed epileptiform discharges most of which were not detected by scalp recording. PET scans did not characterize epileptogenic nature of a lesion. Subdural recording therefore was useful for detecting the foci responsible for habitual seizures in the cases with multiple PET foci. Ambiguous hypometabolic zones on PECT images also could be confirmed by the subdural technique. Of the 8 operated cases, five patients are seizure free, one is signigicantly improved and two are not improved although the postoperative follow-up is too short for precise evaluation. (J.P.N.)
Efficiency and Generalized Convex Duality for Nondifferentiable Multiobjective Programs
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.
Two examples of non strictly convex large deviations
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.
Decompositions, partitions, and coverings with convex polygons and pseudo-triangles
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
Surgery for convexity/parasagittal/falx meningiomas
Ochi, Takashi; Saito, Nobuhito
2013-01-01
Incidence of the complication related with the surgical treatment of meningiomas in the title was reviewed together with consideration of data about progress observation and stereotactic radiosurgery. MEDLINE papers in English were on line searched with keywords contained in above using PubMed System. For the convexity meningioma, 50-141 cases (mean age, 48-58.9 y) with 1.9-3.6 cm or 146.3 mL of the tumor size or volume were reported in 6 literatures (2006-2011), presenting 0% of surgery related death, 1-5.9% of internal medical or 5.5-37.4% of surgical complication, 0-2% of postoperative hemorrhage, 0-15.4% of neurological and 0-15.4% of prolonged/permanent deficits. For the parasagittal/falx meningioma, 46-108 cases (age, 55-58 y) with 1.9-4 cm tumor were reported in 8 literatures (2004-2011), presenting 0-5.7% death, 2-7.4% medical or 5.4-31% surgical complication, 0-3% hemorrhage, 0-15.4 neurologic and 0-15.4% prolonged deficits. For complications after the radiosurgery of the all 3 meningiomas, 41-832 cases (50-60 y) with tumors of 24.7-28 mm or 4.7-7.4 mL were reported in 8 literatures (2003-2012), presenting the incidence of 6.8-26.8% of radiation-related complications like headache, seizures and paralysis necessary for steroid treatment, and 1.20 or 4.80% of permanent morbidity. For the natural history of incidental meningiomas involving tentorium one, 16-144 cases in 6 literatures (2000-2012) revealed the growth rate/y of 1.9-3.9 mm or 0.54-1.15 mL. The outcome of surgical treatment of the meningiomas, a representative benign tumor, was concluded to be rather good as surgery was generally needed only when the disease became symptomatic due to the tumor growth. (T.T.)
Tobias Nüesch
2014-02-01
Full Text Available This paper presents a novel method to solve the energy management problem for hybrid electric vehicles (HEVs with engine start and gearshift costs. The method is based on a combination of deterministic dynamic programming (DP and convex optimization. As demonstrated in a case study, the method yields globally optimal results while returning the solution in much less time than the conventional DP method. In addition, the proposed method handles state constraints, which allows for the application to scenarios where the battery state of charge (SOC reaches its boundaries.
Convex unwraps its first grown-up supercomputer
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.
Inhibitory competition in figure-ground perception: context and convexity.
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.
Tulio Rosembuj
2006-12-01
Full Text Available There is no singular globalization, nor is the result of an individual agent. We could start by saying that global action has different angles and subjects who perform it are different, as well as its objectives. The global is an invisible invasion of materials and immediate effects.
Tulio Rosembuj
2006-01-01
There is no singular globalization, nor is the result of an individual agent. We could start by saying that global action has different angles and subjects who perform it are different, as well as its objectives. The global is an invisible invasion of materials and immediate effects.
Dose evaluation from multiple detector outputs using convex optimisation
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)
Convexity and concavity constants in Lorentz and Marcinkiewicz spaces
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].
Transient disturbance growth in flows over convex surfaces
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.
Graph Design via Convex Optimization: Online and Distributed Perspectives
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
Convex Hull Abstraction in Specialisation of CLP Programs
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...
Closedness type regularity conditions in convex optimization and beyond
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.
Distribution functions of sections and projections of convex bodies
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 ...
Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons.
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.
Waldo, J.B.; Greenwell, R.K.; Keasling, T.A.; Collins, J.R.; Klos, D.B.
1980-02-01
With construction of the Fast Flux Test Facility (FFTF) completed, the first major objective in the startup program was to fill the sodium systems. A sodium fill sequence was developed to match construction completion, and as systems became available, they were inerted, preheated, and filled with sodium. The secondary sodium systems were filled first while dry refueling system testing was in progress in the reactor vessel. The reactor vessel and the primary loops were filled last. This paper describes the methods used and some of the key results achieved for this major FFTF objective
Andru?cã Maria Carmen
2013-01-01
The field of globalization has highlighted an interdependence implied by a more harmonious understanding determined by the daily interaction between nations through the inducement of peace and the management of streamlining and the effectiveness of the global economy. For the functioning of the globalization, the developing countries that can be helped by the developed ones must be involved. The international community can contribute to the institution of the development environment of the gl...
The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases
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
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.
Subset Selection by Local Convex Approximation
Øjelund, Henrik; Sadegh, Payman; Madsen, Henrik
1999-01-01
This paper concerns selection of the optimal subset of variables in a lenear regression setting. The posed problem is combinatiorial and the globally best subset can only be found in exponential time. We define a cost function for the subset selection problem by adding the penalty term to the usual...... of the subset selection problem so as to guarantee positive definiteness of the Hessian term, hence avoiding numerical instability. The backward Elemination type algorithm attempts to improve the results upon termination of the modified Newton-Raphson search by sing the current solution as an initial guess...
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.
On the polarizability dyadics of electrically small, convex objects
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.
Riemann solvers and undercompressive shocks of convex FPU chains
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
On the Convexity of Step out - Step in Sequencing Games
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
Preconditioning 2D Integer Data for Fast Convex Hull Computations.
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.
Convex relationships in ecosystems containing mixtures of trees and grass
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...
Positive definite functions and dual pairs of locally convex spaces
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.
Intracranial Convexity Lipoma with Massive Calcification: Case Report
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
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"
A note on the nucleolus for 2-convex TU games
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
Transonic shock wave. Boundary layer interaction at a convex wall
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
Computing Convex Coverage Sets for Faster Multi-Objective Coordination
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,
Flat tori in three-dimensional space and convex integration.
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.
Short Run Profit Maximization in a Convex Analysis Framework
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.
Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes
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.
Plum, Maja
Globalization is often referred to as external to education - a state of affair facing the modern curriculum with numerous challenges. In this paper it is examined as internal to curriculum; analysed as a problematization in a Foucaultian sense. That is, as a complex of attentions, worries, ways...... of reasoning, producing curricular variables. The analysis is made through an example of early childhood curriculum in Danish Pre-school, and the way the curricular variable of the pre-school child comes into being through globalization as a problematization, carried forth by the comparative practices of PISA...
F. Gerard Adams
2008-01-01
The rapid globalization of the world economy is causing fundamental changes in patterns of trade and finance. Some economists have argued that globalization has arrived and that the world is â€œflatâ€ . While the geographic scope of markets has increased, the author argues that new patterns of trade and finance are a result of the discrepancies between â€œoldâ€ countries and â€œnewâ€ . As the differences are gradually wiped out, particularly if knowledge and technology spread worldwide, the t...
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.
A Convex Optimization Model and Algorithm for Retinex
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.
Convexity and the Euclidean Metric of Space-Time
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.
On the stretch factor of convex Delaunay graphs
Prosenjit Bose
2010-06-01
Full Text Available Let C be a compact and convex set in the plane that contains the origin in its interior, and let S be a finite set of points in the plane. The Delaunay graph DGC(S of S is defined to be the dual of the Voronoi diagram of S with respect to the convex distance function defined by C. We prove that DGC(S is a t-spanner for S, for some constant t that depends only on the shape of the set C. Thus, for any two points p and q in S, the graph DGC(S contains a path between p and q whose Euclidean length is at most t times the Euclidean distance between p and q.
A Survey on Operator Monotonicity, Operator Convexity, and Operator Means
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.
Convex variational problems linear, nearly linear and anisotropic growth conditions
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.
Moduli spaces of convex projective structures on surfaces
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....
Constrained convex minimization via model-based excessive gap
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.
Free locally convex spaces with a small base
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
A formulation of combinatorial auction via reverse convex programming
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.
Some fixed point theorems on non-convex sets
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 $K.$
PENNON: A code for convex nonlinear and semidefinite programming
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
Convex Clustering: An Attractive Alternative to Hierarchical Clustering
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
Numerical modeling of isothermal compositional grading by convex splitting methods
Li, Yiteng
2017-04-09
In this paper, an isothermal compositional grading process is simulated based on convex splitting methods with the Peng-Robinson equation of state. We first present a new form of gravity/chemical equilibrium condition by minimizing the total energy which consists of Helmholtz free energy and gravitational potential energy, and incorporating Lagrange multipliers for mass conservation. The time-independent equilibrium equations are transformed into a system of transient equations as our solution strategy. It is proved our time-marching scheme is unconditionally energy stable by the semi-implicit convex splitting method in which the convex part of Helmholtz free energy and its derivative are treated implicitly and the concave parts are treated explicitly. With relaxation factor controlling Newton iteration, our method is able to converge to a solution with satisfactory accuracy if a good initial estimate of mole compositions is provided. More importantly, it helps us automatically split the unstable single phase into two phases, determine the existence of gas-oil contact (GOC) and locate its position if GOC does exist. A number of numerical examples are presented to show the performance of our method.
Speech Enhancement by Modified Convex Combination of Fractional Adaptive Filtering
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.
Measures of symmetry for convex sets and stability
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:...
Measurement system for diffraction efficiency of convex gratings
Liu, Peng; Chen, Xin-hua; Zhou, Jian-kang; Zhao, Zhi-cheng; Liu, Quan; Luo, Chao; Wang, Xiao-feng; Tang, Min-xue; Shen, Wei-min
2017-08-01
A measurement system for diffraction efficiency of convex gratings is designed. The measurement system mainly includes four components as a light source, a front system, a dispersing system that contains a convex grating, and a detector. Based on the definition and measuring principle of diffraction efficiency, the optical scheme of the measurement system is analyzed and the design result is given. Then, in order to validate the feasibility of the designed system, the measurement system is set up and the diffraction efficiency of a convex grating with the aperture of 35 mm, the curvature-radius of 72mm, the blazed angle of 6.4°, the grating period of 2.5μm and the working waveband of 400nm-900nm is tested. Based on GUM (Guide to the Expression of Uncertainty in Measurement), the uncertainties in the measuring results are evaluated. The measured diffraction efficiency data are compared to the theoretical ones, which are calculated based on the grating groove parameters got by an atomic force microscope and Rigorous Couple Wave Analysis, and the reliability of the measurement system is illustrated. Finally, the measurement performance of the system is analyzed and tested. The results show that, the testing accuracy, the testing stability and the testing repeatability are 2.5%, 0.085% and 3.5% , respectively.
Nye, Kyle; Eslam-Panah, Azar
2016-11-01
Root canal treatment involves the removal of infected tissue inside the tooth's canal system and filling the space with a dense sealing agent to prevent further infection. A good root canal treatment happens when the canals are filled homogeneously and tightly down to the root apex. Such a tooth is able to provide valuable service for an entire lifetime. However, there are some examples of poorly performed root canals where the anterior and posterior routes are not filled completely. Small packets of air can be trapped in narrow access cavities when restoring with resin composites. Such teeth can cause trouble even after many years and lead the conditions like acute bone infection or abscesses. In this study, the filling of dead-end conical cavities with various liquids is reported. The first case studies included conical cavity models with different angles and lengths to visualize the filling process. In this investigation, the rate and completeness at which a variety of liquids fill the cavity were observed to find ideal conditions for the process. Then, a 3D printed model of the scaled representation of a molar with prepared post spaces was used to simulate the root canal treatment. The results of this study can be used to gain a better understanding of the restoration for endodontically treated teeth.
On the areas of various bodies in the Euclidean space: The case of irregular convex polygons
Ozoemena, P.C.
1988-11-01
A theorem is proposed for the areas of n-sided irregular convex polygons, of given length of sides. The theorem is illustrated as a simple but powerful one in estimating the areas of irregular polygons, being dependent only on the number of sides n (and not on any of the explicit angles) of the irregular polygon. Finally, because of the global symmetry shown by equilateral triangles, squares and circles under group (gauge) theory, the relationships governing their areas, when they are inscribed or escribed in one another are discussed as riders, and some areas of their applications in graph theory, ratios and maxima and minima problems of differential calculus briefly mentioned. (author). 11 refs, 6 figs, 1 tab
The role of convexity in perceptual completion: beyond good continuation.
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.
Blaschke- and Minkowski-endomorphisms of convex bodies
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...
Convex models and probabilistic approach of nonlinear fatigue failure
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
Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities
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
Iterative Schemes for Convex Minimization Problems with Constraints
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.
Gröbner bases and convex polytopes
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.
On the structure of self-affine convex bodies
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.
Use of Convexity in Ostomy Care: Results of an International Consensus Meeting.
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.
Celik, Tim Holst
on the statesituated tension-filled functional relationship between legitimation and accumulation, the study both historically and theoretically reworks this approach and reapplies it for the post-1970s/1990s governance period. It asks whether and to what extent governance has served as a distinctive post- 1970s/1990s...
Boron trifluoride (BF3) proportional counters are used as detectors for thermal neutrons. They are characterized by high neutron sensitivity and good gamma discriminating properties. Most practical BF3 counters are filled with pure boron trifluoride gas enriched up to 96% 10B. But BF3 is not an ideal proportional counter ...
Stephan, C.
1993-01-01
The main types of gas filled nuclear detectors: ionization chambers, proportional counters, parallel-plate avalanche counters (PPAC) and microstrip detectors are described. New devices are shown. A description of the processes involved in such detectors is also given. (K.A.) 123 refs.; 25 figs.; 3 tabs
Canonical Primal-Dual Method for Solving Non-convex Minimization Problems
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...
Sequential Change-Point Detection via Online Convex Optimization
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.
A New Interpolation Approach for Linearly Constrained Convex Optimization
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.
Sequential and Parallel Algorithms for Finding a Maximum Convex Polygon
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...
Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and -convexity
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.
Generalized Bregman distances and convergence rates for non-convex regularization methods
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
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.
First-order Convex Optimization Methods for Signal and Image Processing
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...
Torrent-Guasp, Francisco; Kocica, Mladen J; Corno, Antonio; Komeda, Masashi; Cox, James; Flotats, A; Ballester-Rodes, Manel; Carreras-Costa, Francesc
2004-03-01
The evidence of the ventricular myocardial band (VMB) has revealed unavoidable coherence and mutual coupling of form and function in the ventricular myocardium, making it possible to understand the principles governing electrical, mechanical and energetical events within the human heart. From the earliest Erasistratus' observations, principal mechanisms responsible for the ventricular filling have still remained obscured. Contemporary experimental and clinical investigations unequivocally support the attitude that only powerful suction force, developed by the normal ventricles, would be able to produce an efficient filling of the ventricular cavities. The true origin and the precise time frame for generating such force are still controversial. Elastic recoil and muscular contraction were the most commonly mentioned, but yet, still not clearly explained mechanisms involved in the ventricular suction. Classical concepts about timing of successive mechanical events during the cardiac cycle, also do not offer understandable insight into the mechanism of the ventricular filling. The net result is the current state of insufficient knowledge of systolic and particularly diastolic function of normal and diseased heart. Here we summarize experimental evidence and theoretical backgrounds, which could be useful in understanding the phenomenon of the ventricular filling. Anatomy of the VMB, and recent proofs for its segmental electrical and mechanical activation, undoubtedly indicates that ventricular filling is the consequence of an active muscular contraction. Contraction of the ascendent segment of the VMB, with simultaneous shortening and rectifying of its fibers, produces the paradoxical increase of the ventricular volume and lengthening of its long axis. Specific spatial arrangement of the ascendent segment fibers, their interaction with adjacent descendent segment fibers, elastic elements and intra-cavitary blood volume (hemoskeleton), explain the physical principles
Tota, Pasqua Marina
2014-01-01
) with the main aim to achieve basic education for all children, youth and adults. A participant in this process since 2000 is the Global Campaign for Education (GCE), an advocacy network of INGOs, established jointly by Oxfam, ActionAid International, Education International and Global March Against Child Labour...
Gap filling strategies and error in estimating annual soil respiration
Soil respiration (Rsoil) is one of the largest CO2 fluxes in the global carbon (C) cycle. Estimation of annual Rsoil requires extrapolation of survey measurements or gap-filling of automated records to produce a complete time series. While many gap-filling methodologies have been employed, there is ...
Nonparametric instrumental regression with non-convex constraints
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
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.
Elastic energy of liquid crystals in convex polyhedra
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)
Convex analysis and monotone operator theory in Hilbert spaces
Bauschke, Heinz H
2017-01-01
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...
Reachability by paths of bounded curvature in a convex polygon
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.
Rocking convex array used for 3D synthetic aperture focusing
Andresen, Henrik; Nikolov, Svetoslav; Pedersen, M M
2008-01-01
Volumetric imaging can be performed using 1D arrays in combination with mechanical motion. Outside the elevation focus of the array, the resolution and contrast quickly degrade compared to the azimuth plane, because of the fixed transducer focus. The purpose of this paper is to use synthetic...... aperture focusing (SAF) for enhancing the elevation focusing for a convex rocking array, to obtain a more isotropic point spread function. This paper presents further development of the SAF method, which can be used with curved array combined with a rocking motion. The method uses a virtual source (VS...... Kretztechnik, Zipf, Austria). The array has an elevation focus at 60 mm of depth, and the angular rocking velocity is up to 140deg/s. The scan sequence uses an fprf of 4500 - 7000 Hz allowing up to 15 cm of penetration. The full width at half max (FWHM) and main-lobe to side-lobe ratio (MLSL) is used...
Approximating convex Pareto surfaces in multiobjective radiotherapy planning
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
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.
Neural network for solving convex quadratic bilevel programming problems.
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.
Entropies from Coarse-graining: Convex Polytopes vs. Ellipsoids
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.
Path Following in the Exact Penalty Method of Convex Programming.
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.
Hermite-Hadamard type inequalities for GA-s-convex functions
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.
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
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
The Concept of Convexity in Fuzzy Set Theory | Rauf | Journal of the ...
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 ...
Effect of dental arch convexity and type of archwire on frictional forces
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
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
Wilson, D.C.
1982-01-01
A security seal for providing an indication of unauthorized access to a sealed object includes an elongate member to be entwined in the object such that access is denied unless the member is removed. The elongate member has a hollow, pressurizable chamber extending throughout its length that is filled with a permanent dye under greater than atmospheric pressure. Attempts to cut the member and weld it together are revealed when dye flows through a rupture in the chamber wall and stains the outside surface of the member
Oh, K. K.; Lee, Y. H.; Cho, O. K.; Park, C. Y.
1979-01-01
The gastric lesion is a common source of complaints to Orientals, however, evaluation of gastric symptoms and laboratory examination offer little specific aid in the diagnosis of gastric diseases. Thus roentgenography of gastrointestinal tract is one of the most reliable method for detail diagnosis. On double contract study of stomach, gastric filling defect is mostly caused by malignant gastric cancer, however, other benign lesions can cause similar pictures which can be successfully treated by surgery. 66 cases of benign causes of gastric filling defect were analyzed at this point of view, which was verified pathologically by endoscope or surgery during recent 7 years in Yensei University College of Medicine, Severance Hospital. The characteristic radiological picture of each disease was discussed for precise radiologic diagnosis. 1. Of total 66 cases, there were 52 cases of benign gastric tumor 10 cases of gastric varices, 5 cases of gastric bezoar, 5 cases of corrosive gastritis, 3 cases of granulomatous disease and one case of gastric hematoma. 2. The most frequent causes of benign tumors were adenomatous polyp (35/42) and the next was leiomyoma (4/42). Others were one of case of carcinoid, neurofibroma and cyst. 3. Characteristic of benign adenomatous polyp were relatively small in size, smooth surface and were observed that large size, benign polyp was frequently type IV lesion with a stalk. 4. Submucosal tumors such as leiomyoma needed differential diagnosis with polypoid malignant cancer. However, the characteristic points of differentiation was well circumscribed smooth margined filling defect without definite mucosal destruction on surface. 5. Gastric varices showed multiple lobulated filling defected especially on gastric fundus that changed its size and shape by respiration and posture of patients. Same varices lesions on esophagus and history of liver disease were helpful for easier diagnosis. 6. Gastric bezoar showed well defined movable mass
Oh, K. K.; Lee, Y. H.; Cho, O. K.; Park, C. Y. [Yonsei University College of Medicine, Seoul (Korea, Republic of)
1979-06-15
The gastric lesion is a common source of complaints to Orientals, however, evaluation of gastric symptoms and laboratory examination offer little specific aid in the diagnosis of gastric diseases. Thus roentgenography of gastrointestinal tract is one of the most reliable method for detail diagnosis. On double contract study of stomach, gastric filling defect is mostly caused by malignant gastric cancer, however, other benign lesions can cause similar pictures which can be successfully treated by surgery. 66 cases of benign causes of gastric filling defect were analyzed at this point of view, which was verified pathologically by endoscope or surgery during recent 7 years in Yensei University College of Medicine, Severance Hospital. The characteristic radiological picture of each disease was discussed for precise radiologic diagnosis. 1. Of total 66 cases, there were 52 cases of benign gastric tumor 10 cases of gastric varices, 5 cases of gastric bezoar, 5 cases of corrosive gastritis, 3 cases of granulomatous disease and one case of gastric hematoma. 2. The most frequent causes of benign tumors were adenomatous polyp (35/42) and the next was leiomyoma (4/42). Others were one of case of carcinoid, neurofibroma and cyst. 3. Characteristic of benign adenomatous polyp were relatively small in size, smooth surface and were observed that large size, benign polyp was frequently type IV lesion with a stalk. 4. Submucosal tumors such as leiomyoma needed differential diagnosis with polypoid malignant cancer. However, the characteristic points of differentiation was well circumscribed smooth margined filling defect without definite mucosal destruction on surface. 5. Gastric varices showed multiple lobulated filling defected especially on gastric fundus that changed its size and shape by respiration and posture of patients. Same varices lesions on esophagus and history of liver disease were helpful for easier diagnosis. 6. Gastric bezoar showed well defined movable mass
Oh, K K; Lee, Y H; Cho, O K; Park, C Y [Yonsei University College of Medicine, Seoul (Korea, Republic of)
1979-06-15
The gastric lesion is a common source of complaints to Orientals, however, evaluation of gastric symptoms and laboratory examination offer little specific aid in the diagnosis of gastric diseases. Thus roentgenography of gastrointestinal tract is one of the most reliable method for detail diagnosis. On double contract study of stomach, gastric filling defect is mostly caused by malignant gastric cancer, however, other benign lesions can cause similar pictures which can be successfully treated by surgery. 66 cases of benign causes of gastric filling defect were analyzed at this point of view, which was verified pathologically by endoscope or surgery during recent 7 years in Yensei University College of Medicine, Severance Hospital. The characteristic radiological picture of each disease was discussed for precise radiologic diagnosis. 1. Of total 66 cases, there were 52 cases of benign gastric tumor 10 cases of gastric varices, 5 cases of gastric bezoar, 5 cases of corrosive gastritis, 3 cases of granulomatous disease and one case of gastric hematoma. 2. The most frequent causes of benign tumors were adenomatous polyp (35/42) and the next was leiomyoma (4/42). Others were one of case of carcinoid, neurofibroma and cyst. 3. Characteristic of benign adenomatous polyp were relatively small in size, smooth surface and were observed that large size, benign polyp was frequently type IV lesion with a stalk. 4. Submucosal tumors such as leiomyoma needed differential diagnosis with polypoid malignant cancer. However, the characteristic points of differentiation was well circumscribed smooth margined filling defect without definite mucosal destruction on surface. 5. Gastric varices showed multiple lobulated filling defected especially on gastric fundus that changed its size and shape by respiration and posture of patients. Same varices lesions on esophagus and history of liver disease were helpful for easier diagnosis. 6. Gastric bezoar showed well defined movable mass
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.
Boehm, Robert F; Sabacky, Bruce; Anderson II, Everett B; Haberman, David; Al-Hassin, Mowafak; He, Xiaoming; Morriseau, Brian
2010-02-24
future. Project partners also conducted a workshop on hydrogen safety and permitting. This provided an opportunity for the various permitting agencies and end users to gather to share experiences and knowledge. As a result of this workshop, the permitting process for the hydrogen filling station on the Las Vegas Valley Water District’s land was done more efficiently and those who would be responsible for the operation were better educated on the safety and reliability of hydrogen production and storage. The lessons learned in permitting the filling station and conducting this workshop provided a basis for future hydrogen projects in the region. Continuing efforts to increase the working pressure of electrolysis and efficiency have been pursued. Research was also performed on improving the cost, efficiency and durability of Proton Exchange Membrane (PEM) hydrogen technology. Research elements focused upon PEM membranes, electrodes/catalysts, membrane-electrode assemblies, seals, bipolar plates, utilization of renewable power, reliability issues, scale, and advanced conversion topics. Additionally, direct solar-to-hydrogen conversion research to demonstrate stable and efficient photoelectrochemistry (PEC) hydrogen production systems based on a number of optional concepts was performed. Candidate PEC concepts included technical obstacles such as inefficient photocatalysis, inadequate photocurrent due to non-optimal material band gap energies, rapid electron-hole recombination, reduced hole mobility and diminished operational lifetimes of surface materials exposed to electrolytes. Project Objective 1: Design, build, operate hydrogen filling station Project Objective 2: Perform research and development for utilizing solar technologies on the hydrogen filling station and convert two utility vehicles for use by the station operators Project Objective 3: Increase capacity of hydrogen filling station; add additional vehicle; conduct safety workshop; develop a roadmap for
Global affine differential geometry of hypersurfaces
Li, An-Min; Zhao, Guosong; Hu, Zejun
2015-01-01
This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.
CERN Bulletin
2010-01-01
Following the programmed technical stop last week, operators focussed on preparing the machine for faster filling, which includes multibunch injection and a faster pre-cycle phase. The LHC1 screen shot during the first multibunch injection operation. The LHC operational schedule incorporates a technical stop for preventive maintenance roughly every six weeks of stable operation, during which several interventions on the various machines are carried out. Last week these included the replacement of a faulty magnet in the SPS pre-accelerator, which required the subsequent re-setting of the system of particle extraction and transfer to the LHC. At the end of last week, all the machines were handed back for operation and work could start on accommodating all the changes made into the complex systems in order for normal operation to be resumed. These ‘recovery’ operations continued through the weekend and into this week. At the beginning of this week, operators succeeded in pro...
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.
Benetti, Ana Raquel; Havndrup-Pedersen, Cæcilie; Honoré, Daniel
2015-01-01
the restorative procedure. The aim of this study, therefore, was to compare the depth of cure, polymerization contraction, and gap formation in bulk-fill resin composites with those of a conventional resin composite. To achieve this, the depth of cure was assessed in accordance with the International Organization...... for Standardization 4049 standard, and the polymerization contraction was determined using the bonded-disc method. The gap formation was measured at the dentin margin of Class II cavities. Five bulk-fill resin composites were investigated: two high-viscosity (Tetric EvoCeram Bulk Fill, SonicFill) and three low......-viscosity (x-tra base, Venus Bulk Fill, SDR) materials. Compared with the conventional resin composite, the high-viscosity bulk-fill materials exhibited only a small increase (but significant for Tetric EvoCeram Bulk Fill) in depth of cure and polymerization contraction, whereas the low-viscosity bulk...
Precision platform for convex lens-induced confinement microscopy
Berard, Daniel; McFaul, Christopher M. J.; Leith, Jason S.; Arsenault, Adriel K. J.; Michaud, François; Leslie, Sabrina R.
2013-10-01
We present the conception, fabrication, and demonstration of a versatile, computer-controlled microscopy device which transforms a standard inverted fluorescence microscope into a precision single-molecule imaging station. The device uses the principle of convex lens-induced confinement [S. R. Leslie, A. P. Fields, and A. E. Cohen, Anal. Chem. 82, 6224 (2010)], which employs a tunable imaging chamber to enhance background rejection and extend diffusion-limited observation periods. Using nanopositioning stages, this device achieves repeatable and dynamic control over the geometry of the sample chamber on scales as small as the size of individual molecules, enabling regulation of their configurations and dynamics. Using microfluidics, this device enables serial insertion as well as sample recovery, facilitating temporally controlled, high-throughput measurements of multiple reagents. We report on the simulation and experimental characterization of this tunable chamber geometry, and its influence upon the diffusion and conformations of DNA molecules over extended observation periods. This new microscopy platform has the potential to capture, probe, and influence the configurations of single molecules, with dramatically improved imaging conditions in comparison to existing technologies. These capabilities are of immediate interest to a wide range of research and industry sectors in biotechnology, biophysics, materials, and chemistry.
On asphericity of convex bodies in linear normed spaces.
Faried, Nashat; Morsy, Ahmed; Hussein, Aya M
2018-01-01
In 1960, Dvoretzky proved that in any infinite dimensional Banach space X and for any [Formula: see text] there exists a subspace L of X of arbitrary large dimension ϵ -iometric to Euclidean space. A main tool in proving this deep result was some results concerning asphericity of convex bodies. In this work, we introduce a simple technique and rigorous formulas to facilitate calculating the asphericity for each set that has a nonempty boundary set with respect to the flat space generated by it. We also give a formula to determine the center and the radius of the smallest ball containing a nonempty nonsingleton set K in a linear normed space, and the center and the radius of the largest ball contained in it provided that K has a nonempty boundary set with respect to the flat space generated by it. As an application we give lower and upper estimations for the asphericity of infinite and finite cross products of these sets in certain spaces, respectively.
JPEG2000-coded image error concealment exploiting convex sets projections.
Atzori, Luigi; Ginesu, Giaime; Raccis, Alessio
2005-04-01
Transmission errors in JPEG2000 can be grouped into three main classes, depending on the affected area: LL, high frequencies at the lower decomposition levels, and high frequencies at the higher decomposition levels. The first type of errors are the most annoying but can be concealed exploiting the signal spatial correlation like in a number of techniques proposed in the past; the second are less annoying but more difficult to address; the latter are often imperceptible. In this paper, we address the problem of concealing the second class or errors when high bit-planes are damaged by proposing a new approach based on the theory of projections onto convex sets. Accordingly, the error effects are masked by iteratively applying two procedures: low-pass (LP) filtering in the spatial domain and restoration of the uncorrupted wavelet coefficients in the transform domain. It has been observed that a uniform LP filtering brought to some undesired side effects that negatively compensated the advantages. This problem has been overcome by applying an adaptive solution, which exploits an edge map to choose the optimal filter mask size. Simulation results demonstrated the efficiency of the proposed approach.
Convergence theorems for quasi-contractive maps in uniformly convex spaces
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 One-Layer Recurrent Neural Network for Constrained Complex-Variable Convex Optimization.
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.
Yamagishi, Takashi; Ozaki, Masaharu; Furutani, Yuhji; Yamamoto, Kouzo; Saeki, Atsushi; Satoh, Shinichi; Kusukawa, Reizo
1990-01-01
Contributions of rapid filling, slow filling and atrial systole to the left ventricular(LV) filling volume were analyzed with the use of radionuclide ventriculography at rest, both globally and regionally, in 34 patients with isolated disease of the left anterior descending coronary artery. The patients included 17 with a normal ejection fraction (EF≥50%; group 1) and 17 with a depressed EF (<50%; group 2), and the data were compared with those obtained from 13 normal subjects. A computer program subdivided the LV image into 4 regions, and time-activity curves were constructed globally and regionally by reverse-gating from the R wave. In both groups the contribution of rapid filling to the LV filling volume was decreased significantly in the affected septal and apical regions, and in the global left ventricle compared with that in normal subjects. In group 1, the contribution of atrial systole showed an increase in these affected regions and in the global left ventricle. In contrast, in group 2, the atrial contribution was not increased globally or regionally as much as was expected. However, the contribution of slow filling was either increased significantly or tended to increase in the affected regions and in the global left ventricle. There were negative correlations between the contribution of rapid filling and that of slow filling in the global left ventricle (r=-0.73, p<0.001) and in each of the septal, apical and lateral regions (r≥-0.60, p<0.001), which suggested that the contribution of slow filling as well as of atrial systole undergoes an increase as rapid filling is impaired. Thus, in patients with coronary artery disease, the left ventricle relies on slow filling as well as atrial systole to affect diastolic LV filling in the affected regions and in the global left ventricle in the presence of LV systolic dysfunction. (author)
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
Convex integration theory solutions to the h-principle in geometry and topology
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...
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks
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...
A one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion
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
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.
A Fast Algorithm of Convex Hull Vertices Selection for Online Classification.
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.
Pattern Discovery in Brain Imaging Genetics via SCCA Modeling with a Generic Non-convex Penalty.
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.
Study on IAEA international emergency response exercise convEx-3
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)
Durand, S.; Nikolova, M.
2006-01-01
Many estimation problems amount to minimizing a piecewise C m objective function, with m ≥ 2, composed of a quadratic data-fidelity term and a general regularization term. It is widely accepted that the minimizers obtained using non-convex and possibly non-smooth regularization terms are frequently good estimates. However, few facts are known on the ways to control properties of these minimizers. This work is dedicated to the stability of the minimizers of such objective functions with respect to variations of the data. It consists of two parts: first we consider all local minimizers, whereas in a second part we derive results on global minimizers. In this part we focus on data points such that every local minimizer is isolated and results from a C m-1 local minimizer function, defined on some neighborhood. We demonstrate that all data points for which this fails form a set whose closure is negligible
Gas-filled hohlraum fabrication
Salazar, M.A.; Gobby, P.L.; Foreman, L.R.; Bush, H. Jr.; Gomez, V.M.; Moore, J.E.; Stone, G.F.
1995-01-01
Los Alamos National Laboratory (LANL) researchers have fabricated and fielded gas-filled hohlraums at the Lawrence Livermore National Laboratory (LLNL) Nova laser. Fill pressures of 1--5 atmospheres have been typical. We describe the production of the parts, their assembly and fielding. Emphasis is placed on the production of gas-tight polyimide windows and the fielding apparatus and procedure
Mechanics of filled carbon nanotubes
Monteiro, A.O.; Cachim, P.B.; Da Costa, Pedro M. F. J.
2014-01-01
The benefits of filling carbon nanotubes (CNTs) with assorted molecular and crystalline substances have been investigated for the past two decades. Amongst the study of new structural phases, defects, chemical reactions and varied types of host-guest interactions, there is one fundamental characterisation aspect of these systems that continues to be overlooked: the mechanical behaviour of filled CNTs. In contrast to their empty counterparts, the mechanics of filled CNTs is a subject where reports appear far and apart, this despite being key to the application of these materials in technological devices. In the following paragraphs, we review the work that has been carried out up to the present on the mechanics of filled CNTs. The studies discussed range from experimental resonant frequency essays performed within electron microscopes to modelling, via molecular dynamics, of three-point bending of nanotubes filled with gases. (C) 2014 Elsevier B.V. All rights reserved.
Mechanics of filled carbon nanotubes
Monteiro, A.O.
2014-04-01
The benefits of filling carbon nanotubes (CNTs) with assorted molecular and crystalline substances have been investigated for the past two decades. Amongst the study of new structural phases, defects, chemical reactions and varied types of host-guest interactions, there is one fundamental characterisation aspect of these systems that continues to be overlooked: the mechanical behaviour of filled CNTs. In contrast to their empty counterparts, the mechanics of filled CNTs is a subject where reports appear far and apart, this despite being key to the application of these materials in technological devices. In the following paragraphs, we review the work that has been carried out up to the present on the mechanics of filled CNTs. The studies discussed range from experimental resonant frequency essays performed within electron microscopes to modelling, via molecular dynamics, of three-point bending of nanotubes filled with gases. (C) 2014 Elsevier B.V. All rights reserved.
A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions
Fowkes, Jaroslav M.; Gould, Nicholas I. M.; Farmer, Chris L.
2012-01-01
We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation
Radiopacity of root filling materials
Beyer-Olsen, E.M.
1983-01-01
A method for measuring the radiopacity of root filling materials is described. Direct measurements were made of the optic density values of the materials in comparison with a standard curve relating optic density to the thickness of an aluminium step wedge exposed simultaneously. By proper selection of film and conditions for exposure and development, it was possible to obtain a near-linear standard curve which added to the safety and reproducibility of the method. The technique of radiographic assessment was modified from clinical procedures in evaluating the obturation in radiographs, and it was aimed at detecting slits or voids between the dental wall and the filling material. This radiographic assessment of potensial leakage was compared with actual in vitro lekage of dye (basic fuchsin) into the roots of filled teeth. The result of the investigation show that root filling materials display a very wide range of radiopacity, from less than 3 mm to more than 12 mm of aluminium. It also seem that tooth roots that appear to be well obturated by radiographic evaluation, stand a good chance of beeing resistant to leakage in vitro, and that the type of filling material rather than its radiographic appearance, determines the susceptibility of the filled tooth to leakage in vitro. As an appendix the report contains a survey of radiopaque additives in root filling materials
Safety Distances for hydrogen filling stations
Matthijsen, A. J. C. M.; Kooi, E. S.
2005-07-01
In the Netherlands there is a growing interest in using natural gas as a transport fuel. The most important drivers behind this development are formed by poor inner city air quality and the decision to close several LPG filling stations. Dwellings are not allowed within the safety distances of 45 or 110 meters from the tanker filling point of these LPG stations, depending on the capacity of the station. Another driver is global warming. We are carrying out a study on station supply, compression, storage and filling for natural gas stations, and a similar, simultaneous study on hydrogen as a followup to our risk analysis for the hydrogen filling station in Amsterdam. Here, three buses drive on hydrogen as part of the European CUTE project. Driving on natural gas is an important step in the transition to cars on hydrogen. This study was commissioned by the Dutch Ministry of Spatial Planning, Housing and the Environment to advise on external safety aspects of future hydrogen filling stations. According to Dutch law homes may not be built within an individual risk contour of 10-6 per year of a dangerous object, such as a plant with hazardous materials or a filling station. An individual risk contour of 10-6 is represented by a line around a dangerous object that connects locations with an individual risk level of 10-6 per year. An individual 'located' within this contour line has a chance of one per million per year or more to be killed as a result of an accident caused by this object. The longest distance between the object and such a contour is called a 'safety distance'. A study on safety distances is now in progress for different kinds of hydrogen filling stations (e. g. gaseous and liquid hydrogen) and for different capacities, such as big, medium and small stations. The focus is on different kinds of hydrogen production and the hydrogen supply of the filling station. To decide on the design and supply of the hydrogen station, we examined the
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)
Removal of root filling materials.
Duncan, H.F. Chong, B.S.
2011-05-01
Safe, successful and effective removal of root filling materials is an integral component of non-surgical root canal re-treatment. Access to the root canal system must be achieved in order to negotiate to the canal terminus so that deficiencies in the original treatment can be rectified. Since a range of materials have been advocated for filling root canals, different techniques are required for their removal. The management of commonly encountered root filling materials during non-surgical re-treatment, including the clinical procedures necessary for removal and the associated risks, are reviewed. As gutta-percha is the most widely used and accepted root filling material, there is a greater emphasis on its removal in this review.
On the complexity of a combined homotopy interior method for convex programming
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.
Better building of valley fills
Chironis, N.P.
1980-03-01
Current US regulations for building valley fills or head of hollow fills to hold excess spoil resulting from contour mining are meeting with considerable opposition, particularly from operators in steep-slope areas. An alternative method has been submitted to the Office of Surface Mining by Virgina. Known as the zoned concept method, it has already been used successfully in building water-holding dams and coal refuse embankments on sloping terrain. The ways in which drainage and seepage are managed are described.
Visualizing Data as Objects by DC (Difference of Convex) Optimization
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
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. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective...
Hyvönen, Nuutti
2007-10-01
The aim of optical tomography is to reconstruct the optical properties inside a physical body, e.g. a neonatal head, by illuminating it with near-infrared light and measuring the outward flux of photons on the object boundary. Because a brain consists of strongly scattering tissue with imbedded cavities filled by weakly scattering cerebrospinal fluid, propagation of near-infrared photons in the human head can be treated by combining the diffusion approximation of the radiative transfer equation with geometrical optics to obtain the radiosity-diffusion forward model of optical tomography. At the moment, a disadvantage with the radiosity-diffusion model is that the locations of the transparent cavities must be known in advance in order to be able to reconstruct the physiologically interesting quantities, i.e., the absorption and the scatter in the strongly scattering brain tissue. In this work we show that the boundary measurement map of optical tomography is Fréchet differentiable with respect to the shape of a strongly convex nonscattering region. Using this result, we introduce a numerical algorithm for approximating an unknown nonscattering cavity by a ball if the background diffuse optical properties of the object are known. The functionality of the method is demonstrated through two-dimensional numerical experiments.
Anomalous dynamics triggered by a non-convex equation of state in relativistic flows
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.
Kafle, Bishoksan; Gallagher, John Patrick
2014-01-01
We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of query-answer transformed clauses, and refinement by splitting...... in conjunction with specialisation for propagating constraints it can frequently solve challenging verification problems. This is a contribution in itself, but refinement is needed when it fails, and the question of how to refine convex polyhedral analyses has not been studied much. We present a refinement...... technique based on interpolants derived from a counterexample trace; these are used to drive a property-based specialisation that splits predicates, leading in turn to more precise convex polyhedral analyses. The process of specialisation, analysis and splitting can be repeated, in a manner similar...
Uniform estimate of a compact convex set by a ball in an arbitrary norm
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
Schur-Convexity for a Class of Symmetric Functions and Its Applications
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≤i1
A parallel Discrete Element Method to model collisions between non-convex particles
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.
Lift-and-fill face lift: integrating the fat compartments.
Rohrich, Rod J; Ghavami, Ashkan; Constantine, Fadi C; Unger, Jacob; Mojallal, Ali
2014-06-01
Recent discovery of the numerous fat compartments of the face has improved our ability to more precisely restore facial volume while rejuvenating it through differential superficial musculoaponeurotic system treatment. Incorporation of selective fat compartment volume restoration along with superficial musculoaponeurotic system manipulation allows for improved control in recontouring while addressing one of the key problems in facial aging, namely, volume deflation. This theory was evaluated by assessing the contour changes from simultaneous face "lifting" and "filling" through fat compartment-guided facial fat transfer. A review of 100 face-lift patients was performed. All patients had an individualized component face lift with fat grafting to the nasolabial fold, deep malar, and high/lateral malar fat compartment locations. Photographic analysis using a computer program was conducted on oblique facial views preoperatively and postoperatively, to obtain the most projected malar contour point. Two independent observers visually evaluated the malar prominence and nasolabial fold improvements based on standardized photographs. Nasolabial fold improved by at least one grade in 81 percent and by over one grade in 11 percent. Malar prominence average projection increase was 13.47 percent and the average amount of lift was 12.24 percent. The malar prominence score improved by at least one grade in 62 percent of the patients postoperatively, and 9 percent had a greater than one grade improvement. Twenty-eight percent of the patients had a convex malar prominence postoperatively compared with 6 percent preoperatively. Malar prominence improved by at least one grade in 63 percent and by over one grade in 10 percent. The lift-and-fill face lift merges two key concepts in facial rejuvenation: (1) effective tissue manipulation by means of lifting and tightening in differential vectors according to original facial asymmetry and shape; and (2) selective fat compartment filling
Method of convex rigid frames and applications in studies of multipartite quNit pure states
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)
Optimization of Transverse Oscillating Fields for Vector Velocity Estimation with Convex Arrays
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...
The canonical partial metric and the uniform convexity on normed spaces
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.
License or entry decision for innovator in international duopoly with convex cost functions
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...
QENS investigation of filled rubbers
Triolo, A; Desmedt, A; Pieper, J K; Lo Celso, F; Triolo, R; Negroni, F; Arrighi, V; Qian, H; Frick, B
2002-01-01
The polymer segmental dynamics is investigated in a series of silica-filled rubbers. The presence of inert fillers in polymers greatly affects the mechanical and physical performance of the final materials. For example, silica has been proposed as a reinforcing agent of elastomers in tire production. Results from quasielastic neutron scattering and Dynamic Mechanical Thermal Analysis (DMTA) measurements are presented on styrene-ran-butadiene rubber filled with silica. A clear indication is obtained of the existence of a bimodal dynamics, which can be rationalized in terms of the relaxation of bulk rubber and the much slower relaxation of the rubber adsorbed on the filler surface. (orig.)
Steinhauer, L. C.; Kimura, W. D.
2006-01-01
We have developed a 1-D, quasi-steady-state numerical model for a gas-filled capillary discharge that is designed to aid in selecting the optimum capillary radius in order to guide a laser beam with the required intensity through the capillary. The model also includes the option for an external solenoid B-field around the capillary, which increases the depth of the parabolic density channel in the capillary, thereby allowing for propagation of smaller laser beam waists. The model has been used to select the parameters for gas-filled capillaries to be utilized during the Staged Electron Laser Acceleration -- Laser Wakefield (STELLA-LW) experiment
Behavior of Hollow Thin Welded Tubes Filled with Sand Slag Concrete
Noureddine Ferhoune
2016-01-01
Full Text Available This paper presents the axial bearing capacity of thin welded rectangular steel stubs filled with concrete sand. A series of tests was conducted to study the behavior of short composite columns under axial compressive load; the cross section dimensions were 100 × 70 × 2 mm. A total of 20 stubs have been tested, as follows: 4 hollow thin welded tubes were tested to axial and eccentric load compression, 4 were filled with ordinary concrete appointed by BO columns, 6 were filled with concrete whose natural sand was completely substituted by a crystallized sand slag designated in this paper by BSI, and 6 were tucked in concrete whose natural sand was partially replaced by a crystallized sand slag called BSII. The main parameters studied are the height of the specimen (300 mm–500 mm, eccentricity of load and type of filling concrete. Based on test results obtained, it is confirmed that the length of the tubes has a considerable effect on the bearing capacity and the failure mode. In all test tubes, fracture occurred by the convex local buckling of steel section due to the outward thrust of the concrete; it was observed that the sand concrete improves the bearing capacity of tubes compounds compared to those filled with ordinary concrete.
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.
Global Convergence of a Modified LS Method
Liu JinKui
2012-01-01
Full Text Available The LS method is one of the effective conjugate gradient methods in solving the unconstrained optimization problems. The paper presents a modified LS method on the basis of the famous LS method and proves the strong global convergence for the uniformly convex functions and the global convergence for general functions under the strong Wolfe line search. The numerical experiments show that the modified LS method is very effective in practice.
Convexity of Energy-Like Functions: Theoretical Results and Applications to Power System Operations
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.
Perimeter generating functions for the mean-squared radius of gyration of convex polygons
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)
A Convex Variational Model for Restoring Blurred Images with Multiplicative Noise
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...
Modeling IrisCode and its variants as convex polyhedral cones and its security implications.
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.
Unifying kinetic approach to phoretic forces and torques onto moving and rotating convex particles
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.
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
On the convex hull of the simple integer recourse objective function
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
On evolving deformation microstructures in non-convex partially damaged solids
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
Convex Bodies With Minimal Volume Product in R^2 --- A New Proof
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.
Multiobjective optimization of classifiers by means of 3D convex-hull-based evolutionary algorithms
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
Parthood and Convexity as the Basic Notions of a Theory of Space
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...
Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization
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
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.
A DEEP CUT ELLIPSOID ALGORITHM FOR CONVEX-PROGRAMMING - THEORY AND APPLICATIONS
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 rank 1 convexity of stored energy functions of physically linear stress-strain relations
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
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.
On the Monotonicity and Log-Convexity of a Four-Parameter Homogeneous Mean
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.
Convex order approximations in case of cash flows of mixed signs
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
From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation
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
Headache as a crucial symptom in the etiology of convexal subarachnoid hemorrhage.
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.
Extreme points of the convex set of joint probability distributions with ...
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.
Mean-square performance of a convex combination of two adaptive filters
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...
Robust Nearfield Wideband Beamforming Design Based on Adaptive-Weighted Convex Optimization
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 Deep Cut Ellipsoid Algorithm for convex Programming: theory and Applications
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
A deep cut ellipsoid algorithm for convex programming : Theory and applications
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
Study on feed forward neural network convex optimization for LiFePO4 battery parameters
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.
An Efficient Algorithm to Calculate the Minkowski Sum of Convex 3D Polyhedra
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
The Lp Lp Lp-curvature images of convex bodies and Lp Lp Lp ...
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 ...
On the Fermat-Lagrange principle for mixed smooth convex extremal problems
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
Filling of charged cylindrical capillaries
Das, Siddhartha; Chanda, Sourayon; Eijkel, J.C.T.; Tas, N.R.; Chakraborty, Suman; Mitra, Sushanta K.
2014-01-01
We provide an analytical model to describe the filling dynamics of horizontal cylindrical capillaries having charged walls. The presence of surface charge leads to two distinct effects: It leads to a retarding electrical force on the liquid column and also causes a reduced viscous drag force because
Space-filling polyhedral sorbents
Haaland, Peter
2016-06-21
Solid sorbents, systems, and methods for pumping, storage, and purification of gases are disclosed. They derive from the dynamics of porous and free convection for specific gas/sorbent combinations and use space filling polyhedral microliths with facial aplanarities to produce sorbent arrays with interpenetrating interstitial manifolds of voids.
Global Asymptotic Stability of Switched Neural Networks with Delays
Zhenyu Lu
2015-01-01
Full Text Available This paper investigates the global asymptotic stability of a class of switched neural networks with delays. Several new criteria ensuring global asymptotic stability in terms of linear matrix inequalities (LMIs are obtained via Lyapunov-Krasovskii functional. And here, we adopt the quadratic convex approach, which is different from the linear and reciprocal convex combinations that are extensively used in recent literature. In addition, the proposed results here are very easy to be verified and complemented. Finally, a numerical example is provided to illustrate the effectiveness of the results.
Williams, Ruth
2010-09-29
Skills for Health has launched a set of resources to help healthcare employers tackle hard-to-fill entry-level vacancies and provide sustainable employment for local unemployed people. The Sector Employability Toolkit aims to reduce recruitment and retention costs for entry-level posts and repare people for employment through pre-job training programmes, and support employers to develop local partnerships to gain access to wider pools of candidates and funding streams.
Selection and specification criteria for fills for cut-and-fill mining
Thomas, E. G.
1980-05-15
Because of significant differences in placement and loading conditions, the ideal fill material for a cut-and-fill operation has different characteristics to those for a fill for a filled open stoping operation. The differing requirements of the two mining operations must be understood and accounted for in establishing fill selection and specification criteria. Within the paper, aspects of the particular requirements of cut-and-fill mining are analyzed and related to the specific fill tests and properties required. Emphasis is placed upon the role of fill in ground support, though this cannot be isolated from overall fill performance. Where appropriate, test data are introduced and areas requiring continuing research highlighted.
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
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.
30 CFR 817.72 - Disposal of excess spoil: Valley fill/head-of-hollow fills.
2010-07-01
... STANDARDS-UNDERGROUND MINING ACTIVITIES § 817.72 Disposal of excess spoil: Valley fill/head-of-hollow fills.... Uncontrolled surface drainage may not be directed over the outslope of the fill. (2) Runoff from areas above the fill and runoff from the surface of the fill shall be diverted into stabilized diversion channels...
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
Measurement of laser welding pool geometry using a closed convex active contour model
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)
Parameter sensitivity study of a Field II multilayer transducer model on a convex transducer
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...
Convex relaxation of Optimal Power Flow in Distribution Feeders with embedded solar power
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...
Efficiency measurement with a non-convex free disposal hull technology
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...
Three-Dimensional Synthetic Aperture Focusing Using a Rocking Convex Array Transducer
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...
Equilibrium prices supported by dual price functions in markets with non-convexities
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)
Surface tension-induced high aspect-ratio PDMS micropillars with concave and convex lens tips
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.
The steady-state of the (Normalized) LMS is schur convex
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.
Surface tension-induced high aspect-ratio PDMS micropillars with concave and convex lens tips
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.
Tensor completion and low-n-rank tensor recovery via convex optimization
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
Convex lattice polygons of fixed area with perimeter-dependent weights.
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.
Reduction of shock induced noise in imperfectly expanded supersonic jets using convex optimization
Adhikari, Sam
2007-11-01
Imperfectly expanded jets generate screech noise. The imbalance between the backpressure and the exit pressure of the imperfectly expanded jets produce shock cells and expansion or compression waves from the nozzle. The instability waves and the shock cells interact to generate the screech sound. The mathematical model consists of cylindrical coordinate based full Navier-Stokes equations and large-eddy-simulation turbulence modeling. Analytical and computational analysis of the three-dimensional helical effects provide a model that relates several parameters with shock cell patterns, screech frequency and distribution of shock generation locations. Convex optimization techniques minimize the shock cell patterns and the instability waves. The objective functions are (convex) quadratic and the constraint functions are affine. In the quadratic optimization programs, minimization of the quadratic functions over a set of polyhedrons provides the optimal result. Various industry standard methods like regression analysis, distance between polyhedra, bounding variance, Markowitz optimization, and second order cone programming is used for Quadratic Optimization.
A Total Variation Model Based on the Strictly Convex Modification for Image Denoising
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.
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.
The steady-state of the (Normalized) LMS is schur convex
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.
Usami, Yumi; Stork, David G.; Fujiki, Jun; Hino, Hideitsu; Akaho, Shotaro; Murata, Noboru
2011-03-01
We derive and demonstrate new methods for dewarping images depicted in convex mirrors in artwork and for estimating the three-dimensional shapes of the mirrors themselves. Previous methods were based on the assumption that mirrors were spherical or paraboloidal, an assumption unlikely to hold for hand-blown glass spheres used in early Renaissance art, such as Johannes van Eyck's Portrait of Giovanni (?) Arnolfini and his wife (1434) and Robert Campin's Portrait of St. John the Baptist and Heinrich von Werl (1438). Our methods are more general than such previous methods in that we assume merely that the mirror is radially symmetric and that there are straight lines (or colinear points) in the actual source scene. We express the mirror's shape as a mathematical series and pose the image dewarping task as that of estimating the coefficients in the series expansion. Central to our method is the plumbline principle: that the optimal coefficients are those that dewarp the mirror image so as to straighten lines that correspond to straight lines in the source scene. We solve for these coefficients algebraically through principal component analysis, PCA. Our method relies on a global figure of merit to balance warping errors throughout the image and it thereby reduces a reliance on the somewhat subjective criterion used in earlier methods. Our estimation can be applied to separate image annuli, which is appropriate if the mirror shape is irregular. Once we have found the optimal image dewarping, we compute the mirror shape by solving a differential equation based on the estimated dewarping function. We demonstrate our methods on the Arnolfini mirror and reveal a dewarped image superior to those found in prior work|an image noticeably more rectilinear throughout and having a more coherent geometrical perspective and vanishing points. Moreover, we find the mirror deviated from spherical and paraboloidal shape; this implies that it would have been useless as a concave
Technology of hardening fills for mined spaces
Simek, P.; Holas, M.; Chyla, A.; Pech, P.
1985-01-01
The technology is described of hardening fills for mined spaces of uranium deposits in North Bohemian chalk. A special equipment was developed for the controlled preparation of a hardening mixture. The composition of the fill is determined by the strength of the filled rock, expecially by the standard strength, i.e., the minimal strength of the filling under uniaxial pressure. The said parameter determines the consumption of binding materials and thereby the total costs of the filling. A description is presented of the filling technology, including rabbit tube transport of the mixture and quality control. (Pu)
Neural Network in Fixed Time for Collision Detection between Two Convex Polyhedra
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...
Annuity factors, duration and convexity : insights from a financial engineering perspective
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...
Report on the observation of IAEA international emergency response exercise ConvEx-3(2008)
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)
F-SVM: Combination of Feature Transformation and SVM Learning via Convex Relaxation
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 ...
Convex Hypersurfaces and $L^p$ Estimates for Schr\\"odinger Equations
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.
Highly efficient absorption of visible and near infrared light in convex gold and nickel grooves
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]....
Geometry intuitive, discrete, and convex : a tribute to László Fejes Tóth
Böröczky, Károly; Tóth, Gábor; Pach, János
2013-01-01
The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth.
Image restoration by the method of convex projections: part 2 applications and numerical results.
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.
On evolving deformation microstructures in non-convex partially damaged solids
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.
A Sequential Convex Semidefinite Programming Algorithm for Multiple-Load Free Material Optimization
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
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
A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds
Baker, Mark; Cooper, Daryl
2005-01-01
We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generate a subgroup that is an amalgamated free product. Constructions of infinite volume hyperbolic n-manifolds are described by gluing lo...
Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms
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...
Dey, C.; Dey, S. K.
1983-01-01
An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.
Using Fisher Information Criteria for Chemical Sensor Selection via Convex Optimization Methods
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
Coarse-convex-compactification approach to numerical solution of nonconvex variational problems
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
Charge balancing fill rate monitor
Rothman, J.L.; Blum, E.B.
1995-01-01
A fill rate monitor has been developed for the NSLS storage rings to allow machine tuning over a very large dynamic range of beam current. Synchrotron light, focused on a photodiode, produces a signal proportional to the beam current. A charge balancing circuit processes the diode current, creating an output signal proportional to the current injected into the ring. The unit operates linearly over a dynamic range of 120 dB and can resolve pulses of injected beam as small as 1 μA
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.
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.
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.
Towards reproducible experimental studies for non-convex polyhedral shaped particles
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.
A two-layer recurrent neural network for nonsmooth convex optimization problems.
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.
Derivative-free generation and interpolation of convex Pareto optimal IMRT plans
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
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
Towards reproducible experimental studies for non-convex polyhedral shaped particles
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.
Novel method of finding extreme edges in a convex set of N-dimension vectors
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.
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.
Deyhle, Hans; Bunk, Oliver; Buser, Stefan; Krastl, Gabriel; Zitzmann, Nicola U.; Ilgenstein, Bernd; Beckmann, Felix; Pfeiffer, Franz; Weiger, Roland; Müller, Bert
2009-08-01
Human teeth are anisotropic composites. Dentin as the core material of the tooth consists of nanometer-sized calcium phosphate crystallites embedded in collagen fiber networks. It shows its anisotropy on the micrometer scale by its well-oriented microtubules. The detailed three-dimensional nanostructure of the hard tissues namely dentin and enamel, however, is not understood, although numerous studies on the anisotropic mechanical properties have been performed and evaluated to explain the tooth function including the enamel-dentin junction acting as effective crack barrier. Small angle X-ray scattering (SAXS) with a spatial resolution in the 10 μm range allows determining the size and orientation of the constituents on the nanometer scale with reasonable precision. So far, only some dental materials, i.e. the fiber reinforced posts exhibit anisotropic properties related to the micrometer-size glass fibers. Dental fillings, composed of nanostructures oriented similar to the natural hard tissues of teeth, however, do not exist at all. The current X-ray-based investigations of extracted human teeth provide evidence for oriented micro- and nanostructures in dentin and enamel. These fundamental quantitative findings result in profound knowledge to develop biologically inspired dental fillings with superior resistance to thermal and mechanical shocks.
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
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.
Uniqueness of a pre-generator for $C_0$-semigroup on a general locally convex vector space
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.
Vertical Scan-Conversion for Filling Purposes
Hersch, R. D.
1988-01-01
Conventional scan-conversion algorithms were developed independently of filling algorithms. They cause many problems, when used for filling purposes. However, today's raster printers and plotters require extended use of filling, especially for the generation of typographic characters and graphic line art. A new scan-conversion algorithm, called vertical scan-conversion has been specifically designed to meet the requirements of parity scan line fill algorithms. Vertical scan-conversion ensures...
7 CFR 58.923 - Filling containers.
2010-01-01
... 7 Agriculture 3 2010-01-01 2010-01-01 false Filling containers. 58.923 Section 58.923 Agriculture... Procedures § 58.923 Filling containers. (a) The filling of small containers with product shall be done in a sanitary manner. The containers shall not contaminate or detract from the quality of the product in any way...
O’Connor, D; Nguyen, D; Voronenko, Y; Yin, W; Sheng, K
2016-01-01
Purpose: Integrated beam orientation and fluence map optimization is expected to be the foundation of robust automated planning but existing heuristic methods do not promise global optimality. We aim to develop a new method for beam angle selection in 4π non-coplanar IMRT systems based on solving (globally) a single convex optimization problem, and to demonstrate the effectiveness of the method by comparison with a state of the art column generation method for 4π beam angle selection. Methods: The beam angle selection problem is formulated as a large scale convex fluence map optimization problem with an additional group sparsity term that encourages most candidate beams to be inactive. The optimization problem is solved using an accelerated first-order method, the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The beam angle selection and fluence map optimization algorithm is used to create non-coplanar 4π treatment plans for several cases (including head and neck, lung, and prostate cases) and the resulting treatment plans are compared with 4π treatment plans created using the column generation algorithm. Results: In our experiments the treatment plans created using the group sparsity method meet or exceed the dosimetric quality of plans created using the column generation algorithm, which was shown superior to clinical plans. Moreover, the group sparsity approach converges in about 3 minutes in these cases, as compared with runtimes of a few hours for the column generation method. Conclusion: This work demonstrates the first non-greedy approach to non-coplanar beam angle selection, based on convex optimization, for 4π IMRT systems. The method given here improves both treatment plan quality and runtime as compared with a state of the art column generation algorithm. When the group sparsity term is set to zero, we obtain an excellent method for fluence map optimization, useful when beam angles have already been selected. NIH R43CA183390, NIH R01CA
Microhardness of bulk-fill composite materials
Kelić, Katarina; Matić, Sanja; Marović, Danijela; Klarić, Eva; Tarle, Zrinka
2016-01-01
The aim of the study was to determine microhardness of high- and low-viscosity bulk-fill composite resins and compare it with conventional composite materials. Four materials of high-viscosity were tested, including three bulk-fills: QuiXfi l (QF), x-tra fil (XTF) and Tetric EvoCeram Bulk Fill (TEBCF), while nanohybrid composite GrandioSO (GSO) served as control. The other four were low-viscosity composites, three bulk-fill materials: Smart Dentin Replacement (SDR), Venus Bulk Fill (VBF) and ...
Review of fill mining technology in Canada
Singh, K. H.; Hedley, D. G.F.
1980-05-15
The Canadian mining industry has a long history of being in the fore-front in developing new technology in underground hardrock mines. Examples include the development of hydraulic and cemented fills, undercut-and-fill, mechanized cut-and-fill, post pillar, vertical retreat and blasthole mining methods. The evolution of this technology is briefly described in an historical review. Backfill serves many functions, although it is generally considered in terms of its support capabilities. These functions, mainly related to the mining method used, are evaluated in regard to regional support, pillar support, fill roof, working floor, dilution control and waste disposal. With the advent of blasthole and vertical retreat methods for pillar recovery operations, the freestanding height of backfill walls has assumed greater importance. Consequently, more attention is being given to what fill properties are required to achieve fill wall exposures up to 25 m wide by 90 m high. With the large increases in energy costs, alternatives to partially replace Portland cement in fill are being examined. The validation of mining concepts and the interaction of backfill is perhaps best evaluated by in-situ measurements. Examples are given of stress, deformation and fill pressure measurements in longitudinal cut-and-fill, post pillar mining and blasthole stoping with delayed fill which were taken in several mines in Canada. Finally, the overall design procedure used in deciding mining method, stope and pillar dimensions, sequence of extraction, fill properties and support systems at a new mine is described.
Filling in biodiversity threat gaps
Joppa, L. N.; O'Connor, Brian; Visconti, Piero
2016-01-01
increase to 10,000 times the background rate should species threatened with extinction succumb to pressures they face (4). Reversing these trends is a focus of the Convention on Biological Diversity's 2020 Strategic Plan for Biodiversity and its 20 Aichi Targets and is explicitly incorporated...... into the United Nations' 2030 Agenda for Sustainable Development and its 17 Sustainable Development Goals (SDGs). We identify major gaps in data available for assessing global biodiversity threats and suggest mechanisms for closing them....
Image restoration by the method of convex projections: part 1 theory.
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.
Sørensen, Søren N.; Stolpe, Mathias
2015-01-01
rate. The capabilities of the method and the effect of active versus inactive manufacturing constraints are demonstrated on several numerical examples of limited size, involving at most 320 binary variables. Most examples are solved to guaranteed global optimality and may constitute benchmark examples...... but is, however, convex in the original mixed binary nested form. Convexity is the foremost important property of optimization problems, and the proposed method can guarantee the global or near-global optimal solution; unlike most topology optimization methods. The material selection is limited...... for popular topology optimization methods and heuristics based on solving sequences of non-convex problems. The results will among others demonstrate that the difficulty of the posed problem is highly dependent upon the composition of the constitutive properties of the material candidates....
Fast globally optimal segmentation of 3D prostate MRI with axial symmetry prior.
Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Sun, Yue; Rajchl, Martin; Fenster, Aaron
2013-01-01
We propose a novel global optimization approach to segmenting a given 3D prostate T2w magnetic resonance (MR) image, which enforces the inherent axial symmetry of the prostate shape and simultaneously performs a sequence of 2D axial slice-wise segmentations with a global 3D coherence prior. We show that the proposed challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. With this regard, we introduce a novel coupled continuous max-flow model, which is dual to the studied convex relaxed optimization formulation and leads to an efficient multiplier augmented algorithm based on the modern convex optimization theory. Moreover, the new continuous max-flow based algorithm was implemented on GPUs to achieve a substantial improvement in computation. Experimental results using public and in-house datasets demonstrate great advantages of the proposed method in terms of both accuracy and efficiency.
Operation feedback of hydrogen filling station
Pregassame, S.; Barral, K.; Allidieres, L.; Charbonneau, T.; Lacombe, Y.
2004-01-01
One of the technical challenges of hydrogen technology is the development of hydrogen infrastructures which satisfy either safety requirements and reliability of filling processes. AIR LIQUIDE realized an hydrogen filling station in Sassenage (France) operational since September 2003. This station is able to fill 3 buses a day up to 350bar by equilibrium with high pressure buffers. In parallel with commercial stations, the group wanted to create a testing ground in real conditions running with several objectives: validate on a full scale bench a simulation tool able to predict the temperature of both gas and cylinder's materials during filling processes; define the best filling procedures in order to reach mass, temperature and filling time targets; analyse the temperature distribution and evolution inside the cylinder; get a general knowledge about hydrogen stations from safety and reliability point of view; operate the first full scale refuelling station in France. The station is also up-graded for 700bar filling from either a liquid hydrogen source or a gas booster, with cold filling possibility. This paper presents the results concerning 350bar filling : thermal effects, optimal filling procedures and influence of parameters such as climatic conditions are discussed. (author)
Dielectric-filled radiofrequency linacs
Faehl, R J; Keinigs, R K; Pogue, E W [Los Alamos National Lab., NM (United States)
1997-12-31
High current, high brightness electron beam accelerators promise to open up dramatic new applications. Linear induction accelerators are currently viewed as the appropriate technology for these applications. A concept by Humphries and Hwang may permit radiofrequency accelerators to fulfill the same functions with greater simplicity and enhanced flexibility. This concept involves the replacement of vacuum rf cavities with dielectric filled ones. Simple analysis indicates that the resonant frequencies are reduced by a factor of ({epsilon}{sub 0}/{epsilon}){sup 1/2} while the stored energy is increased by {epsilon}/{epsilon}{sub 0}. For a high dielectric constant like water, this factor can approach 80. A series of numerical calculations of simple pill-box cavities was performed. Eigenfunctions and resonant frequencies for a full system configuration, including dielectric material, vacuum beamline, and a ceramic window separating the two have been computed. These calculations are compared with the results of a small experimental cavity which have been constructed and operated. Low power tests show excellent agreement. (author). 4 figs., 8 refs.
An inequality for convex functionals and its application to a maxwellian gas
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.
An Iterative Procedure for Obtaining I-Projections onto the Intersection of Convex Sets.
1984-06-01
Dykstra Department of Statistics and Actuarial Science The University of Iowa Iowa City, Iowa 52242 Technical Report #106 June 1984D I e ELECTE lSEP...t Theorem ~ ~ 2.. Asm i where the 4 are closed, convex sets of PD’s and R d 0 is a nonnegative vector such that there exists a T E 4 where I(TIR) < M...PERFOMING ORGANIZATION NAME AND ADDRESS 1. PROGIRA ILEMNT. PROJECT. TAK Department of Statistics and Actuarial Science AEAS a WORK UNIT Numaa The
Horn clause verification with convex polyhedral abstraction and tree automata-based refinement
Kafle, Bishoksan; Gallagher, John Patrick
2017-01-01
In this paper we apply tree-automata techniques to refinement of abstract interpretation in Horn clause verification. We go beyond previous work on refining trace abstractions; firstly we handle tree automata rather than string automata and thereby can capture traces in any Horn clause derivations...... underlying the Horn clauses. Experiments using linear constraint problems and the abstract domain of convex polyhedra show that the refinement technique is practical and that iteration of abstract interpretation with tree automata-based refinement solves many challenging Horn clause verification problems. We...... compare the results with other state-of-the-art Horn clause verification tools....
Preliminary In-Vivo Evaluation of Convex Array Synthetic Aperture Imaging
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...
Geometry of convex polygons and locally minimal binary trees spanning these polygons
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
Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan
2012-01-01
The primal–dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1–26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems...... for the purpose of designing iterative image reconstruction algorithms for CT. The primal–dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application...
An Implementable First-Order Primal-Dual Algorithm for Structured Convex Optimization
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.
Convex relaxations of spectral sparsity for robust super-resolution and line spectrum estimation
Chi, Yuejie
2017-08-01
We consider recovering the amplitudes and locations of spikes in a point source signal from its low-pass spectrum that may suffer from missing data and arbitrary outliers. We first review and provide a unified view of several recently proposed convex relaxations that characterize and capitalize the spectral sparsity of the point source signal without discretization under the framework of atomic norms. Next we propose a new algorithm when the spikes are known a priori to be positive, motivated by applications such as neural spike sorting and fluorescence microscopy imaging. Numerical experiments are provided to demonstrate the effectiveness of the proposed approach.
Hamid A. Jalab
2014-01-01
Full Text Available The interest in using fractional mask operators based on fractional calculus operators has grown for image denoising. Denoising is one of the most fundamental image restoration problems in computer vision and image processing. This paper proposes an image denoising algorithm based on convex solution of fractional heat equation with regularized fractional power parameters. The performances of the proposed algorithms were evaluated by computing the PSNR, using different types of images. Experiments according to visual perception and the peak signal to noise ratio values show that the improvements in the denoising process are competent with the standard Gaussian filter and Wiener filter.
First-order convex feasibility algorithms for x-ray CT
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...
Log-Log Convexity of Type-Token Growth in Zipf's Systems
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.
Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process
Chuancun Yin
2015-01-01
Full Text Available We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy.
Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process
Yuen, Kam Chuen; Shen, Ying
2015-01-01
We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy. PMID:26351655
A Duality Theory for Non-convex Problems in the Calculus of Variations
Bouchitté, Guy; Fragalà, Ilaria
2018-02-01
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375-379, 2015).
Silicon microneedle formation using modified mask designs based on convex corner undercut
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.
Oracle Inequalities for Convex Loss Functions with Non-Linear Targets
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...
Optimal Energy Consumption in Refrigeration Systems - Modelling and Non-Convex Optimisation
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...
Chen, Yunjie; Zhao, Bo; Zhang, Jianwei; Zheng, Yuhui
2014-09-01
Accurate segmentation of magnetic resonance (MR) images remains challenging mainly due to the intensity inhomogeneity, which is also commonly known as bias field. Recently active contour models with geometric information constraint have been applied, however, most of them deal with the bias field by using a necessary pre-processing step before segmentation of MR data. This paper presents a novel automatic variational method, which can segment brain MR images meanwhile correcting the bias field when segmenting images with high intensity inhomogeneities. We first define a function for clustering the image pixels in a smaller neighborhood. The cluster centers in this objective function have a multiplicative factor that estimates the bias within the neighborhood. In order to reduce the effect of the noise, the local intensity variations are described by the Gaussian distributions with different means and variances. Then, the objective functions are integrated over the entire domain. In order to obtain the global optimal and make the results independent of the initialization of the algorithm, we reconstructed the energy function to be convex and calculated it by using the Split Bregman theory. A salient advantage of our method is that its result is independent of initialization, which allows robust and fully automated application. Our method is able to estimate the bias of quite general profiles, even in 7T MR images. Moreover, our model can also distinguish regions with similar intensity distribution with different variances. The proposed method has been rigorously validated with images acquired on variety of imaging modalities with promising results. Copyright © 2014 Elsevier Inc. All rights reserved.
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.
Iron filled carbon nanostructures from different precursors
Costa, S.; Borowiak-Palen, E.; Bachmatiuk, A.; Ruemmeli, M.H.; Gemming, T.; Kalenczuk, R.J.
2008-01-01
Here, we present a study on the synthesis of different nanostructures with one single-step in situ filling (encapsulation) via carbon vapor deposition (CVD). Ferrocene, acetylferrocene and iron (II) nitrate as iron precursors were explored. The application of each of these compounds resulted in different carbon nanomaterials such as: iron filled multiwalled carbon nanotubes with a low filling ratio (Fe-MWCNT), iron filled nanocapsules and unfilled MWCNT. The as-produced samples were purified by high temperature annealing and acid treatment. The purified materials were characterised using transmission electron microscopy (TEM) and Raman spectroscopy
Characterization of Low Density Glass Filled Epoxies
Quesenberry, Matthew
2003-01-01
This report discusses the experimental determination and modeling of several thermophysical and mechanical properties of glass filled epoxy composite systems for potential use as electronic potting compounds...
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.
On the stretch factor of convex polyhedra whose vertices are (almost on a sphere
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.
Restoration of the analytically reconstructed OpenPET images by the method of convex projections
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
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.
Well-Posedness and Primal-Dual Analysis of Some Convex Separable Optimization Problems
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.
Weighted mining of massive collections of [Formula: see text]-values by convex optimization.
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).
T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory
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...
A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions
Fowkes, Jaroslav M.
2012-06-21
We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. Unlike other branch and bound algorithms, lower bounds are obtained via nonconvex underestimators of the function. For a numerical example, we apply the proposed branch and bound algorithm to radial basis function approximations. © 2012 Springer Science+Business Media, LLC.
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
Dynamic Planar Convex Hull with Optimal Query Time and O(log n · log log n ) Update Time
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...
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.
7 CFR 58.730 - Filling containers.
2010-01-01
... 7 Agriculture 3 2010-01-01 2010-01-01 false Filling containers. 58.730 Section 58.730 Agriculture... Procedures § 58.730 Filling containers. Hot fluid cheese from the cookers may be held in hotwells or hoppers... shall effectively measure the desired amount of product into the pouch or container in a sanitary manner...
Selective filling of Photonic Crystal Fibres
Nielsen, Kristian; Noordegraaf, Danny; Sørensen, Thorkild
2005-01-01
A model for calculating the time necessary for filling one or more specific holes in a photonic crystal fibre is made. This model is verified for water, and its enabling potential is illustrated by a polymer application. Selective filling of the core in an air-guide photonic crystal fibre...
Raman spectra of filled carbon nanotubes
Bose, S.M.; Behera, S.N.; Sarangi, S.N.; Entel, P.
2004-01-01
The Raman spectra of a metallic carbon nanotube filled with atoms or molecules have been investigated theoretically. It is found that there will be a three way splitting of the main Raman lines due to the interaction of the nanotube phonon with the collective excitations (plasmons) of the conduction electrons of the nanotube as well as its coupling with the phonon of the filling material. The positions and relative strengths of these Raman peaks depend on the strength of the electron-phonon interaction, phonon frequency of the filling atom and the strength of interaction of the nanotube phonon and the phonon of the filling atoms. Careful experimental studies of the Raman spectra of filled nanotubes should show these three peaks. It is also shown that in a semiconducting nanotube the Raman line will split into two and should be observed experimentally
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
Fixed point theorems in locally convex spacesÃ¢Â€Â”the Schauder mapping method
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.
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...
Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities
Romero, Ignacio; Segurado, Javier; LLorca, Javier
2008-04-01
The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.
Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities
Romero, Ignacio; Segurado, Javier; LLorca, Javier
2008-01-01
The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix
An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State
Kamm, James Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-03-05
This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.
Massioni, Paolo; Massari, Mauro
2018-05-01
This paper describes an interesting and powerful approach to the constrained fuel-optimal control of spacecraft in close relative motion. The proposed approach is well suited for problems under linear dynamic equations, therefore perfectly fitting to the case of spacecraft flying in close relative motion. If the solution of the optimisation is approximated as a polynomial with respect to the time variable, then the problem can be approached with a technique developed in the control engineering community, known as "Sum Of Squares" (SOS), and the constraints can be reduced to bounds on the polynomials. Such a technique allows rewriting polynomial bounding problems in the form of convex optimisation problems, at the cost of a certain amount of conservatism. The principles of the techniques are explained and some application related to spacecraft flying in close relative motion are shown.
Contact point generation for convex polytopes in interactive rigid body dynamics
Silcowitz-Hansen, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny
When computing contact forces in rigid body dynamics systems, most state-of-the-art solutions use iterative methods such as the projected Gauss–Seidel (PGS) method. Methods such as the PGS method are preferred for their robustness. However, the time-critical nature of interactive applications...... combined with the linear convergence rates of such methods, will often result in visual artifacts in the final simulation. With this paper, we address an issue which is of major impact on the animation quality, when using methods such as the PGS method. The issue is robust generation of contact points...... for convex polytopes. A novel contact point generation method is presented, which is based on growth distances and Gauss maps. We demonstrate improvements when using our method in the context of interactive rigid body simulation...
Evaluation and Treatment of the Acute Cerebral Infarction with Convexal Subarachnoid Hemorrhage.
Lee, Min Hyung; Kim, Sang Uk; Lee, Dong Hoon; Kim, Young Il; Cho, Chul Bum; Yang, Seung Ho; Kim, Il Sup; Hong, Jae Taek; Sung, Jae Hoon; Lee, Sang Won
2016-09-01
Non-traumatic convexal subarachnoid hemorrhage (CSAH) is a comparatively infrequent with various vascular and nonvascular causes, it rarely occurs concomitant to acute ischemic stroke. We report a case of a 59-year-old woman, visited emergency room with right side subjective weakness spontaneously. Magnetic resonance diffusion-weighted images revealed an acute infarction of anterior cerebral arterial territory. Computed tomographic angiography showed a left frontal CSAH without any vascular lesions. And other laboratory studies were non-specific. We treated with dual antiplatelet drugs (cilostazole [Otsuka Pharmaceutical Co., Ltd. tokyo, Japan] and Aspirin [Bayer Pharma AG., Leverkusen, Germany]). She has done well for a follow-up period. (5 months) This case demonstrates the CSAH with acute infarction is rare but need to work up to identify the etiology and antiplatelet dugs are taken into account for treatments.
A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization
AUTHOR|(CDS)2092751; Martino, Michele
The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate physical models for these plants using first principles may be impossible. Albeit a model may be available; however, such a model may be too complex to consider for an appropriate controller design. With the increased developments in the computing world, large amounts of measured data can be easily collected and stored for processing purposes. Data can also be collected and used in an on-line fashion. Thus it would be very sensible to make full use of this data for controller design, performance evaluation, and stability analysis. The design methods imposed in this work ensure that the dynamics of a system are captured in an experiment and avoids the problem of unmodeled dynamics associated with parametric models. The devised methods consider robust designs...
A Convex Formulation for Magnetic Particle Imaging X-Space Reconstruction.
Konkle, Justin J; Goodwill, Patrick W; Hensley, Daniel W; Orendorff, Ryan D; Lustig, Michael; Conolly, Steven M
2015-01-01
Magnetic Particle Imaging (mpi) is an emerging imaging modality with exceptional promise for clinical applications in rapid angiography, cell therapy tracking, cancer imaging, and inflammation imaging. Recent publications have demonstrated quantitative mpi across rat sized fields of view with x-space reconstruction methods. Critical to any medical imaging technology is the reliability and accuracy of image reconstruction. Because the average value of the mpi signal is lost during direct-feedthrough signal filtering, mpi reconstruction algorithms must recover this zero-frequency value. Prior x-space mpi recovery techniques were limited to 1d approaches which could introduce artifacts when reconstructing a 3d image. In this paper, we formulate x-space reconstruction as a 3d convex optimization problem and apply robust a priori knowledge of image smoothness and non-negativity to reduce non-physical banding and haze artifacts. We conclude with a discussion of the powerful extensibility of the presented formulation for future applications.
The monotonicity and convexity of a function involving digamma one and their applications
Yang, Zhen-Hang
2014-01-01
Let $\\mathcal{L}(x,a)$ be defined on $\\left( -1,\\infty \\right) \\times \\left( 4/15,\\infty \\right) $ or $\\left( 0,\\infty \\right) \\times \\left( 1/15,\\infty \\right) $ by the formula% \\begin{equation*} \\mathcal{L}(x,a)=\\tfrac{1}{90a^{2}+2}\\ln \\left( x^{2}+x+\\tfrac{3a+1}{3}% \\right) +\\tfrac{45a^{2}}{90a^{2}+2}\\ln \\left( x^{2}+x+\\allowbreak \\tfrac{% 15a-1}{45a}\\right) . \\end{equation*} We investigate the monotonicity and convexity of the function $x\\rightarrow F_{a}\\left( x\\right) =\\psi \\left( x+1\\r...
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
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
High-Dimensional Analysis of Convex Optimization-Based Massive MIMO Decoders
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).
Text-Filled Stacked Area Graphs
Kraus, Martin
2011-01-01
-filled stacked area graphs; i.e., graphs that feature stacked areas that are filled with small-typed text. Since these graphs allow for computing the text layout automatically, it is possible to include large amounts of textual detail with very little effort. We discuss the most important challenges and some...... solutions for the design of text-filled stacked area graphs with the help of an exemplary visualization of the genres, publication years, and titles of a database of several thousand PC games....
Droplet Measurement below Single-Layer Grid Fill
Vitkovic Pavol
2016-01-01
Full Text Available The main part of the heat transfer in a cooling tower is in a fill zone. This one is consist of a cooling fill. For the cooling tower is used a film fill or grid fill or splash fill in the generally. The grid fill has lower heat transfer performance like film fill usually. But their advantage is high resistance to blockage of the fill. The grid fill is consisted with independent layers made from plastic usually. The layers consist of several bars connected to the different shapes. For experiment was used the rhombus shape. The drops diameter was measured above and below the Grid fill.
Meng Wen
2012-01-01
Full Text Available We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in -uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.
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.
Gurucharan Singh Saluja
2010-01-01
Full Text Available In this paper, we give some necessary and sufficient conditions for an implicit iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converging to a common fixed of the mappings in convex metric spaces. Our results extend and improve some recent results of Sun, Wittmann, Xu and Ori, and Zhou and Chang.
Hathout, Leith
2007-01-01
Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…
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.
PERVAPORATION USING ADSORBENT-FILLED MEMBRANES
Membranes containing selective fillers, such as zeolites and activated carbon, can improve the separation by pervaporation. Applications of adsorbent-filled membranes in pervaporation have been demonstrated by a number of studies. These applications include removal of organic co...
Dural sinus filling defect: intrasigmoid encephalocele
Karatag, Ozan; Cosar, Murat; Kizildag, Betul; Sen, Halil Murat
2013-01-01
Filling defects of dural venous sinuses are considered to be a challenging problem especially in case of symptomatic patients. Many lesions have to be ruled out such as sinus thrombosis, arachnoid granulations and tumours. Encephalocele into dural sinus is also a rare cause of these filling defects of dural sinuses. Here, we report an extremely rare case with spontaneous occult invagination of temporal brain tissue into the left sigmoid sinus and accompanying cerebellar ectopia. PMID:24311424
Assessment of periapical health, quality of root canal filling, and ...
Sixty three teeth were found to have short root canal fillings, whereas 74 teeth had adequate root canal fillings, and the remaining 10 teeth had over extended root canal filling. A significant correlation was observed between the length of root filling and apical periodontitis (P = 0,023). Inadequately dense root canal filling was ...
Globalization of consumer confidence
Çelik Sadullah
2017-01-01
Full Text Available The globalization of world economies and the importance of nowcasting analysis have been at the core of the recent literature. Nevertheless, these two strands of research are hardly coupled. This study aims to fill this gap through examining the globalization of the consumer confidence index (CCI by applying conventional and unconventional econometric methods. The US CCI is used as the benchmark in tests of comovement among the CCIs of several developing and developed countries, with the data sets divided into three sub-periods: global liquidity abundance, the Great Recession, and postcrisis. The existence and/or degree of globalization of the CCIs vary according to the period, whereas globalization in the form of coherence and similar paths is observed only during the Great Recession and, surprisingly, stronger in developing/emerging countries.
Full correspondence between asymmetric filling of slits and first-order phase transition lines
Leszek Szybisz
2011-12-01
Full Text Available Adsorption on single planar walls and filling of slits with identical planar walls are investigated in the frame of the density functional theory. In this sort of slits the external potential is symmetric with respect to its central plane. Calculations were carried out by applying both the canonical and grand canonical ensembles (CE and GCE, respectively. The behavior is analyzed by varying the strength of the adsorbate-substrate attraction, the temperature T, and the coverage Γℓ. Results obtained for physisorption of Xe on alkaline surfaces are reported in the present work. Prewetting (PW lines and wetting temperatures, Tw, are determined from the analysis of adsorption on single walls. The filling of slits is analyzed for temperatures T > Tw. It is found that whenever for a given Xe-substrate combination the adsorption on a single wall exhibits a first-order wetting transition then asymmetric profiles that break the left-right symmetry of the external potential appear in the filling of an equivalent slit. These spontaneously symmetry breaking (SSB solutions occur in a restricted range of Γℓ with a T-dependent width. In the case of closed slits analyzed in the CE scheme, the obtained asymmetric profiles exhibit lower Helmholtz free energies than the symmetric species and, therefore, could be stabilized in this geometry. For open slits, the GCE scheme yields all the symmetric and SSB states in the corresponding convex regimes of the free energy. It is shown that both the CE and the GCE frames yield three coexistent states, two symmetric and one asymmetric twofold degenerate. Both a PW line and the related SSB effect terminate at the same temperature. For rather strongly attractive surfaces reentrant SSB states are found at a fixed value of T.
Topological materials discovery using electron filling constraints
Chen, Ru; Po, Hoi Chun; Neaton, Jeffrey B.; Vishwanath, Ashvin
2018-01-01
Nodal semimetals are classes of topological materials that have nodal-point or nodal-line Fermi surfaces, which give them novel transport and topological properties. Despite being highly sought after, there are currently very few experimental realizations, and identifying new materials candidates has mainly relied on exhaustive database searches. Here we show how recent studies on the interplay between electron filling and nonsymmorphic space-group symmetries can guide the search for filling-enforced nodal semimetals. We recast the previously derived constraints on the allowed band-insulator fillings in any space group into a new form, which enables effective screening of materials candidates based solely on their space group, electron count in the formula unit, and multiplicity of the formula unit. This criterion greatly reduces the computation load for discovering topological materials in a database of previously synthesized compounds. As a demonstration, we focus on a few selected nonsymmorphic space groups which are predicted to host filling-enforced Dirac semimetals. Of the more than 30,000 entires listed, our filling criterion alone eliminates 96% of the entries before they are passed on for further analysis. We discover a handful of candidates from this guided search; among them, the monoclinic crystal Ca2Pt2Ga is particularly promising.
NSLS-II filling pattern measurement
Yong Hu; Dalesio, L.B.; Kiman Ha; Pinayev, I.
2012-01-01
Multi-bunch injection will be deployed at NSLS-II. High bandwidth diagnostic beam monitors with high speed digitizers are used to measure bunch-by-bunch charge variation. In order to minimize intensity-correlated orbit oscillations due to uneven bunch patterns, we need to measure the filling pattern (also named bunch pattern or bunch structure). This paper focuses on filling pattern measurements: how to measure bunch structure and make this information available in EPICS-based control system. This measurement requires combination of 3 types of beam monitors (Wall Current Monitor, Fast Current Transformer and Beam Position Monitor), data acquisition and controls (fast digitizer, EPICS software, etc.) and Event Timing system. High-bandwidth filling pattern monitor requires high-speed digitizer to sample its analog output signal. The evaluation results of commercial fast digitizer Agilent Acqiris and high bandwidth detector Bergoz FCT are presented. We have also tested the algorithm software for filling pattern measurement as well as the interface to event timing system. It appears that filling pattern measurement system is well understood and the tests for control hardware and software have given good results
Improving the support characteristics of hydraulic fill
Corson, D. R.; Dorman, K. R.; Sprute, R. H.
1980-05-15
Extensive laboratory and field testing has defined the physical properties of hydraulic fill. Effect of void ratio on percolation rate has been quantified, and tests were developed to estimate waterflow through fill material in a given state underground. Beneficial effect on fill's support capability through addition of cement alone or in conjunction with vibratory compaction has been investigated. Two separate field studies in operating cut-and-fill mines measured vein-wall deformation and loads imposed on backfilled stopes. Technology has been developed that will effectively and efficiently dewater and densify ultra-fine-grained slurries typical of metal mine hydraulic backfill. At least two operators are using this electrokinetic technique to dewater slimes collected in underground sumps or impoundments. This technique opens up the possibility of using the total unclassified tailings product as a hydraulic backfill. Theoretical enhancement of ground support and rock-burst control through improved support capability will be tested in a full-scale mine stope installation. Both a horizontal layer and a vertical column of high modulus fill will be placed in an attempt to reduce stope wall closure, support more ground pressure, and lessen rock-burst occurrence.
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
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
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
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
Fissure fillings from Finnsjoen and Studsvik Sweden
Tullborg, E.-L.; Larsson, S.Aa.
1982-12-01
Samples were taken from cores and collected at different levels. The bedrock at Finnsjoen is a Svecokarelian granite-granodiorite, the most frequent mineral in the fissures being calcite. The water from boreholes have a mean S 18 O value of -12 per thousand and saturated by calcite. Isotopically three different groups of calcite have been distinguished. Ages of 29+-13x10 3 years to 79+-25x10 3 years were estimated. Two generations of quartz were recognized the minerals prehnite and lanmontite were found Most fissure filling materials have cation exchange capacities. The bedrock at Studsvik is a Svecokarelian gneiss of sedimentary type which is migmatized with calcite and chlorite as fissure filling minerals. Most fissure fillings are thin and simple Claby minerals of smectite type are also frequent. (G.B.)
One-dimensional Gromov minimal filling problem
Ivanov, Alexandr O; Tuzhilin, Alexey A
2012-01-01
The paper is devoted to a new branch in the theory of one-dimensional variational problems with branching extremals, the investigation of one-dimensional minimal fillings introduced by the authors. On the one hand, this problem is a one-dimensional version of a generalization of Gromov's minimal fillings problem to the case of stratified manifolds. On the other hand, this problem is interesting in itself and also can be considered as a generalization of another classical problem, the Steiner problem on the construction of a shortest network connecting a given set of terminals. Besides the statement of the problem, we discuss several properties of the minimal fillings and state several conjectures. Bibliography: 38 titles.
Global solutions to the equation of thermoelasticity with fading memory
Okada, Mari; Kawashima, Shuichi
2017-07-01
We consider the initial-history value problem for the one-dimensional equation of thermoelasticity with fading memory. It is proved that if the data are smooth and small, then a unique smooth solution exists globally in time and converges to the constant equilibrium state as time goes to infinity. Our proof is based on a technical energy method which makes use of the strict convexity of the entropy function and the properties of strongly positive definite kernels.
3rd World Congress on Global Optimization in Engineering & Science
Ruan, Ning; Xing, Wenxun; WCGO-III; Advances in Global Optimization
2015-01-01
This proceedings volume addresses advances in global optimization—a multidisciplinary research field that deals with the analysis, characterization, and computation of global minima and/or maxima of nonlinear, non-convex, and nonsmooth functions in continuous or discrete forms. The volume contains selected papers from the third biannual World Congress on Global Optimization in Engineering & Science (WCGO), held in the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation; and complex simulation and supply chain analysis.
Physics and life-business: Participation of IFIN-HH in ConvEX-3 Exercise
Vamanu, D.; Slavnicu, D.; Gheorghiu, Dorina; Acasandrei, V.; Vamanu, B.
2005-01-01
The paper illustrates a less popular yet by no means less consequential task within IFIN-HH's public mission, namely - to provide scientific advice and technical support in the management of nuclear accidents and radiological emergencies. The case in point is ConvEX-3, a 36-hour, 41-actor-countries international alert exercise conducted, May 2005, by the International Atomic Energy Agency in Vienna and targeting a virtual accident at Cernavoda Nuclear Power Plant, Romania. A comprehensive Technical Report compiled in the aftermath of the exercise covers the results, as well as the ways and means at work, highlighting the productive complementarities of the two chief tools employed as assessment and decision support: RODOS (Real Time On-line Decision Support) - a 'major league' expert system based on fixed workstations, in development under an EC project and vying for a position of comprehensive, reference European tool 160 in nuclear emergency crises - for which IFIN-HH is the sole licensed operator in Romania; and RAT (Radiological Assessment Toolkit), a 'minor league' domestic counterpart operating at PC level, assembling a vademecum of, mainly U.S.-originated, reference models dwelling in radioactive inventories, source terms, environmental dispersion, dose and derived response levels, cadastral evaluation of impacts, and countermeasure assessment. (authors)
Position-based coding and convex splitting for private communication over quantum channels
Wilde, Mark M.
2017-10-01
The classical-input quantum-output (cq) wiretap channel is a communication model involving a classical sender X, a legitimate quantum receiver B, and a quantum eavesdropper E. The goal of a private communication protocol that uses such a channel is for the sender X to transmit a message in such a way that the legitimate receiver B can decode it reliably, while the eavesdropper E learns essentially nothing about which message was transmitted. The ɛ -one-shot private capacity of a cq wiretap channel is equal to the maximum number of bits that can be transmitted over the channel, such that the privacy error is no larger than ɛ \\in (0,1). The present paper provides a lower bound on the ɛ -one-shot private classical capacity, by exploiting the recently developed techniques of Anshu, Devabathini, Jain, and Warsi, called position-based coding and convex splitting. The lower bound is equal to a difference of the hypothesis testing mutual information between X and B and the "alternate" smooth max-information between X and E. The one-shot lower bound then leads to a non-trivial lower bound on the second-order coding rate for private classical communication over a memoryless cq wiretap channel.
Avis, David [School of Computer Science, McGill University, 3480 University, Montreal, Quebec, H3A 2A7 (Canada); Imai, Hiroshi [Department of Computer Science, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Ito, Tsuyoshi [Department of Computer Science, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)
2006-09-08
In this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization, especially cut polyhedra. Such a relationship was established in Avis et al (2005 J. Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show that several well-known bodies related to cut polyhedra are equivalent to bodies such as those defined by Tsirelson (1993 Hadronic J. Suppl. 8 329-45) to represent hidden deterministic behaviours, quantum behaviours and no-signalling behaviours. Among other things, our results allow a unique representation of these bodies, give a necessary condition for vertices of the no-signalling polytope, and give a method for bounding the quantum violation of Bell inequalities by means of a body that contains the set of quantum behaviours. Optimization over this latter body may be performed efficiently by semidefinite programming. In the second part of the paper we apply these results to the study of classical correlation functions. We provide a complete list of tight inequalities for the two party case with (m, n) dichotomic observables when m = 4, n = 4 and when min{l_brace}m, n{r_brace} {<=} 3, and give a new general family of correlation inequalities.
Study on mechanics of driving drum with superelastic convexity surface covering-layer structure
Xiao, L.J.; Sui, X.H.; Miao, D.J. [Shandong University of Science & Technology, Qingdao (China)
2008-09-15
Belt conveyor is one of the main transport equipment in coal mine and the driving drum is its key part. With the method of bionic design, the mushroom morphological structure is applied to the design of covering-layer structure of driving drum surface of belt conveyor. Superelastic rubber with large deformation is adopted as the covering-layer material. Nonlinear constitutive model of rubber, which is of superelasticity and large deformation, is established. The stress states and deformation principles of driving drums including both bionic covering-layer and common covering-layer are obtained by static intensity analysis with Finite Element Analysis (FEA) software ANSYS. The values of the stress and strain on the driving drum surface are gotten and the dangerous area is determined. FEA results show that the superelastic convexity surface structure can enlarge the contact area between the driving drum and viscoelastic belt. The results also show that in comparison with common driving drum, the bionic surface driving drum can not only increase the friction coefficient between drum and belt but also prolong its service life.
The TMS-1 corneal topography measurement applied to calibrated ellipsoidal convex surfaces.
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.
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.
A Class of Prediction-Correction Methods for Time-Varying Convex Optimization
Simonetto, Andrea; Mokhtari, Aryan; Koppel, Alec; Leus, Geert; Ribeiro, Alejandro
2016-09-01
This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate of $1/h$, where $h$ is the length of the sampling interval. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions. The correction step adjusts for the distance between the current prediction and the optimizer at each time step, and consists either of one or multiple gradient steps or Newton steps, which respectively correspond to the gradient trajectory tracking (GTT) or Newton trajectory tracking (NTT) algorithms. Under suitable conditions, we establish that the asymptotic error incurred by both proposed methods behaves as $O(h^2)$, and in some cases as $O(h^4)$, which outperforms the state-of-the-art error bound of $O(h)$ for correction-only methods in the gradient-correction step. Moreover, when the characteristics of the objective function variation are not available, we propose approximate gradient and Newton tracking algorithms (AGT and ANT, respectively) that still attain these asymptotical error bounds. Numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude.
Convex optimization of MRI exposure for mitigation of RF-heating from active medical implants
Córcoles, Juan; Zastrow, Earl; Kuster, Niels
2015-09-01
Local RF-heating of elongated medical implants during magnetic resonance imaging (MRI) may pose a significant health risk to patients. The actual patient risk depends on various parameters including RF magnetic field strength and frequency, MR coil design, patient’s anatomy, posture, and imaging position, implant location, RF coupling efficiency of the implant, and the bio-physiological responses associated with the induced local heating. We present three constrained convex optimization strategies that incorporate the implant’s RF-heating characteristics, for the reduction of local heating of medical implants during MRI. The study emphasizes the complementary performances of the different formulations. The analysis demonstrates that RF-induced heating of elongated metallic medical implants can be carefully controlled and balanced against MRI quality. A reduction of heating of up to 25 dB can be achieved at the cost of reduced uniformity in the magnitude of the B1+ field of less than 5%. The current formulations incorporate a priori knowledge of clinically-specific parameters, which is assumed to be available. Before these techniques can be applied practically in the broader clinical context, further investigations are needed to determine whether reduced access to a priori knowledge regarding, e.g. the patient’s anatomy, implant routing, RF-transmitter, and RF-implant coupling, can be accepted within reasonable levels of uncertainty.
Kibar, Ali, E-mail: alikibar@kocaeli.edu.tr [Department of Mechanical and Material Technologies, Kocaeli University, Arslanbey Campus, 41285, Kocaeli (Turkey)
2017-02-15
Experiments and numerical simulations were carried out to examine the vertical impingement a round liquid jet on the edges of horizontal convex surfaces that were either superhydrophobic or hydrophobic. The experiments examine the effects on the flow behaviour of curvature, wettability, inertia of the jet, and the impingement rate. Three copper pipes with outer diameters of 15, 22, and 35 mm were investigated. The pipes were wrapped with a piece of a Brassica oleracea leaf or a smooth Teflon sheet, which have apparent contact angles of 160° and 113°. The Reynolds number ranged from 1000 to 4500, and the impingement rates of the liquid jets were varied. Numerical results show good agreement with the experimental results for explaining flow and provide detailed information about the impingement on the surfaces. The liquid jet reflected off the superhydrophobic surfaces for all conditions. However, the jet reflected or deflected off the hydrophobic surface, depending on the inertia of the jet, the curvature of the surface, and the impingement rate. The results suggest that pressure is not the main reason for the bending of the jet around the curved hydrophobic surface. (paper)