STRICT CONVEXITY THROUGH EQUIVALENT NORMS IN SEPARABLES BANACH SPACES
Directory of Open Access Journals (Sweden)
Willy Zubiaga Vera
2016-12-01
Full Text Available Let E be a separable Banach space with norm || . ||. In the present work, the objective is to construct a norm || . ||1 that is equivalent to || . || in E, such that || . ||1 is strictly convex. In addition it is shown that its dual conjugate norm is also strictly convex.
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss ... map expp at some point p ∈ M (and hence at every point on M) is defined on the whole tangent space Mp to M at ... The influence of the existence of convex functions on the metric and topology of under- lying manifolds has ...
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.
Relaxation Methods for Strictly Convex Regularizations of Piecewise Linear Programs
International Nuclear Information System (INIS)
Kiwiel, K. C.
1998-01-01
We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that occur in entropy maximization, quadratic programming, and network flows. In particular, it may solve exact penalty versions of such (possibly inconsistent) problems, and subproblems of bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity, and in certain cases is highly parallelizable. Its global convergence is established in the recent framework of B -functions (generalized Bregman functions)
A Total Variation Model Based on the Strictly Convex Modification for Image Denoising
Directory of Open Access Journals (Sweden)
Boying Wu
2014-01-01
Full Text Available We propose a strictly convex functional in which the regular term consists of the total variation term and an adaptive logarithm based convex modification term. We prove the existence and uniqueness of the minimizer for the proposed variational problem. The existence, uniqueness, and long-time behavior of the solution of the associated evolution system is also established. Finally, we present experimental results to illustrate the effectiveness of the model in noise reduction, and a comparison is made in relation to the more classical methods of the traditional total variation (TV, the Perona-Malik (PM, and the more recent D-α-PM method. Additional distinction from the other methods is that the parameters, for manual manipulation, in the proposed algorithm are reduced to basically only one.
Directory of Open Access Journals (Sweden)
Meng Wen
2012-01-01
Full Text Available We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in -uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.
Wu, Yun-Jie; Zuo, Jing-Xing; Sun, Liang-Hua
2017-11-01
In this paper, the altitude and velocity tracking control of a generic hypersonic flight vehicle (HFV) is considered. A novel adaptive terminal sliding mode controller (ATSMC) with strictly lower convex function based nonlinear disturbance observer (SDOB) is proposed for the longitudinal dynamics of HFV in presence of both parametric uncertainties and external disturbances. First, for the sake of enhancing the anti-interference capability, SDOB is presented to estimate and compensate the equivalent disturbances by introducing a strictly lower convex function. Next, the SDOB based ATSMC (SDOB-ATSMC) is proposed to guarantee the system outputs track the reference trajectory. Then, stability of the proposed control scheme is analyzed by the Lyapunov function method. Compared with other HFV control approaches, key novelties of SDOB-ATSMC are that a novel SDOB is proposed and drawn into the (virtual) control laws to compensate the disturbances and that several adaptive laws are used to deal with the differential explosion problem. Finally, it is illustrated by the simulation results that the new method exhibits an excellent robustness and a better disturbance rejection performance than the convention approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Managing Hanford Site solid waste through strict acceptance criteria
International Nuclear Information System (INIS)
Jasen, W.G.; Pierce, R.D.; Willis, N.P.
1993-02-01
Various types of waste have been generated during the 50-year history of the Hanford Site. Regulatory changes in the last 20 years have provided the emphasis for better management of these wastes. Interpretations of the Atomic Energy Act of 1954 (AEA) and the Resource Conservation and Recovery Act of 1976 (RCRA) have led to the definition of a group of wastes called radioactive mixed wastes (RMW). As a result of the radioactive and hazardous properties of these wastes, strict management programs have been implemented for the management of these wastes. Solid waste management is accomplished through a systems performance approach to waste management that used best-demonstrated available technology (BDAT) and best management practices. The solid waste program at the Hanford Site strives to integrate all aspects of management relative to the treatment, storage and disposal (TSD) of solid waste. Often there are many competing and important needs. It is a difficult task to balance these needs in a manner that is both equitable and productive. Management science is used to help the process of making decisions. Tools used to support the decision making process include five-year planning, cost estimating, resource allocation, performance assessment, waste volume forecasts, input/output models, and waste acceptance criteria. The purpose of this document is to describe how one of these tools, waste acceptance criteria, has helped the Hanford Site manage solid wastes
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
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 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.
DEFF Research Database (Denmark)
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...
DEFF Research Database (Denmark)
Lauritzen, Niels
-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point......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...
DEFF Research Database (Denmark)
Lauritzen, Niels
Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier-Motzkin elimin......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....
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
DEFF Research Database (Denmark)
Lauritzen, Niels
Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier-Motzkin elimin...
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.
Zhang, Xuefeng; Chen, YangQuan
2017-11-01
The paper considers the stabilization issue of linear continuous singular systems by dealing with strict linear matrix inequalities (LMIs) without invoking equality constraint and proposes a complete and effective solved LMIs formulation. The criterion is necessary and sufficient condition and can be directly solved the feasible solutions with LMI toolbox and is much more tractable and reliable in numerical simulation than existing results, which involve positive semi-definite LMIs with equality constraints. The most important property of the criterion proposed in the paper is that it can overcome the drawbacks of the invalidity caused by the singularity of Ω=PE T +SQ for stabilization of singular systems. Two counterexamples are presented to avoid the disadvantages of the existing condition of stabilization of continuous singular systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
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...
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.
Convexity of the effective potential
International Nuclear Information System (INIS)
Haymaker, R.W.; Perez-Mercader, J.
1978-01-01
The effective potential V(phi) in field theories is a convex function of phi. V(lambda phi 1 + (1 - lambda)phi 2 ) less than or equal to lambdaV(phi 1 ) + (1 - lambda)V(phi 2 ), 0 less than or equal to lambda less than or equal to 1, all phi 1 , phi 2 . A linear interpolation of V(phi) is always larger than or equal to V(phi). There are numerous examples in the tree approximation and in perturbation theory for which this is not the case, the most notorious example being the double dip potential. More complete solutions may or may not show this property automatically. However, a non-convex V(phi) simply indicates that an unstable vacuum state was used in implementing the definition of V(phi). A strict definition will instruct one to replace V(phi) with its linear interpolation in such a way as to make it convex. (Alternatively one can just as well take the view that V(phi) is undefined in these domains.) In this note, attention is called to a very simple argument for convexity based on a construction described by H. Callen in his classic book Thermodynamics
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.
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
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.
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
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
Eppstein, D.; Holten, D.H.R.; Löffler, M.; Nöllenburg, M.; Speckmann, B.; Verbeek, K.A.B.
2013-01-01
We define strict confluent drawing, a form of confluent drawing in which the existence of an edge is indicated by the presence of a smooth path through a system of arcs and junctions (without crossings), and in which such a path, if it exists, must be unique. We prove that it is NP-complete to
Eppstein, D.; Holten, D.; Löffler, M.; Nöllenburg, M.; Speckmann, B.; Verbeek, K.A.B.
2016-01-01
We define strict confluent drawing, a form of confluent drawing in which the existence of an edge is indicated by the presence of a smooth path through a system of arcs and junctions (without crossings), and in which such a path, if it exists, must be unique. We prove that it is NP-complete to
Quine's "Strictly Vegetarian" Analyticity
Decock, L.B.
2017-01-01
I analyze Quine’s later writings on analyticity from a linguistic point of view. In Word and Object Quine made room for a “strictly vegetarian” notion of analyticity. In later years, he developed this notion into two more precise notions, which I have coined “stimulus analyticity” and “behaviorist
DEFF Research Database (Denmark)
Jacob, Riko
We determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage of the data structure...... is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects the convex hull......, and the tangent queries to determine whether a given point is inside the convex hull. The space usage of the data structure is O(n). We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure....
Stereotype locally convex spaces
International Nuclear Information System (INIS)
Akbarov, S S
2000-01-01
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis
Stereotype locally convex spaces
Energy Technology Data Exchange (ETDEWEB)
Akbarov, S S
2000-08-31
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.
Stereotype locally convex spaces
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...
DEFF Research Database (Denmark)
Brodal, Gerth Stølfting; Jacob, Rico
2002-01-01
In this paper we determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage of the d......In this paper we determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage...... of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects...... the convex hull, and the tangent queries to determine whether a given point is inside the convex hull. We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure....
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...
Indian Academy of Sciences (India)
for all t E [0,1] and all x, y (in the domain of definition of f). ... Proof: (a) is a consequence of the definition. (b) Define conv(S) ... More generally, a set F is said to be a face of the convex .... and bounded, and assume the validity (for a proof, see.
Directory of Open Access Journals (Sweden)
Roger Koenker
2014-09-01
Full Text Available Convex optimization now plays an essential role in many facets of statistics. We briefly survey some recent developments and describe some implementations of these methods in R . Applications of linear and quadratic programming are introduced including quantile regression, the Huber M-estimator and various penalized regression methods. Applications to additively separable convex problems subject to linear equality and inequality constraints such as nonparametric density estimation and maximum likelihood estimation of general nonparametric mixture models are described, as are several cone programming problems. We focus throughout primarily on implementations in the R environment that rely on solution methods linked to R, like MOSEK by the package Rmosek. Code is provided in R to illustrate several of these problems. Other applications are available in the R package REBayes, dealing with empirical Bayes estimation of nonparametric mixture models.
Czech Academy of Sciences Publication Activity Database
Hrubeš, P.; Jukna, S.; Kulikov, A.; Pudlák, Pavel
2010-01-01
Roč. 411, 16-18 (2010), s. 1842-1854 ISSN 0304-3975 R&D Projects: GA AV ČR IAA1019401 Institutional research plan: CEZ:AV0Z10190503 Keywords : boolean formula * complexity measure * combinatorial rectangle * convexity Subject RIV: BA - General Mathematics Impact factor: 0.838, year: 2010 http://www.sciencedirect.com/science/article/pii/S0304397510000885
Liu, Jianmin; Wang, Baoyu; Tai, Chao; Wu, Li; Zhao, Han; Guan, Jiadong; Chen, Linyong
2016-01-01
Bioconversion of coal to methane has gained increased attention in recent decades because of its economic and environmental advantages. However, the mechanism of this process is difficult to study in depth, partly because of difficulties associated with the analysis of intermediates generated in coal bioconversion. In this investigation, we report on an effective method to analyze volatile intermediates generated in the bioconversion of coal under strict anaerobic conditions. We conduct in-situ extraction of intermediates using headspace solid-phase micro-extraction followed by detection by gas chromatography-mass spectrometry. Bioconversion simulation equipment was modified and combined with a solid-phase micro-extraction device. In-situ extraction could be achieved by using the combined units, to avoid a breakdown in anaerobic conditions and to maintain the experiment continuity. More than 30 intermediates were identified qualitatively in the conversion process, and the variation in trends of some typical intermediates has been discussed. Volatile organic acids (C2-C7) were chosen for a quantitative study of the intermediates because of their importance during coal bioconversion to methane. Fiber coating, extraction time, and solution acidity were optimized in the solid-phase micro-extraction procedure. The pressure was enhanced during the bioconversion process to investigate the influence of headspace pressure on analyte extraction. The detection limits of the method ranged from 0.0006 to 0.02 mmol/L for the volatile organic acids and the relative standard deviations were between 4.6% and 11.5%. The volatile organic acids (C2-C7) generated in the bioconversion process were 0.01-1.15 mmol/L with a recovery range from 80% to 105%. The developed method is useful for further in-depth research on the bioconversion of coal to methane.
Subordination by convex functions
Directory of Open Access Journals (Sweden)
Rosihan M. Ali
2006-01-01
Full Text Available For a fixed analytic function g(z=z+∑n=2∞gnzn defined on the open unit disk and γ<1, let Tg(γ denote the class of all analytic functions f(z=z+∑n=2∞anzn satisfying ∑n=2∞|angn|≤1−γ. For functions in Tg(γ, a subordination result is derived involving the convolution with a normalized convex function. Our result includes as special cases several earlier works.
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
DEFF Research Database (Denmark)
Murgoci, Agatha; Gaspar, Raquel M.
. As a result we classify convexity adjustments into forward adjustments and swaps adjustments. We, then, focus on affine term structure (ATS) models and, in this context, conjecture convexity adjustments should be related of affine functionals. In the case of forward adjustments, we show how to obtain exact...
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
Species Protection in the European Union : How Strict is Strict?
Schoukens, Hendrik; Bastmeijer, Kees; Born et al., Charles-Hubert
2015-01-01
European Union law to protect wild species of plants and animals is generally considered as ‘strict’. Opponents of nature conservation law often pick the species protection components of the EU Bird Directive and Habitat Directive as a prime example of an unnecessary strict regulatory scheme that
Efficient Strictness Analysis of Haskell
DEFF Research Database (Denmark)
Jensen, Kristian Damm; Hjæresen, Peter; Rosendahl, Mads
1994-01-01
Strictness analysis has been a living field of investigation since Mycroft's original work in 1980, and is getting increasingly significant with the still wider use of lazy functional programming languages. This paper focuses on an actual implementation of a strictness analyser for Haskell....... The analyser uses abstract interpretation with chaotic fixpoint iteration. The demand-driven nature of this iteration technique allows us to use large domains including function domains in the style of Burn et al. 1986 and Wadler 87 and retain reasonable efficiency. The implementation, furthermore, allows us...
Flexible or Strict Taxonomic Organization?
DEFF Research Database (Denmark)
Glückstad, Fumiko Kano; Mørup, Morten
2012-01-01
This work compares methods for constructing feature-based ontologies that are supposed to be used for culturally-specific knowledge transfer. The methods to be compared are the Terminological Ontology (TO) [1], a method of constructing ontology based on strict principles and rules, and the Infinite...
θ-convex nonlinear programming problems
International Nuclear Information System (INIS)
Emam, T.
2008-01-01
A class of sets and a class of functions called θ-convex sets and θ-convex functions are introduced by relaxing the definitions of convex sets and operator θ on the sets and domain of definition of the functions. The optimally results for θ-convex programming problems are established.
A class of free locally convex spaces
International Nuclear Information System (INIS)
Sipacheva, O V
2003-01-01
Stratifiable spaces are a natural generalization of metrizable spaces for which Dugundji's theorem holds. It is proved that the free locally convex space of a stratifiable space is stratifiable. This means, in particular, that the space of finitely supported probability measures on a stratifiable space is a retract of a locally convex space, and that each stratifiable convex subset of a locally convex space is a retract of a locally convex space
Strictness Analysis for Attribute Grammars
DEFF Research Database (Denmark)
Rosendahl, Mads
1992-01-01
interpretation of attribute grammars. The framework is used to construct a strictness analysis for attribute grammars. Results of the analysis enable us to transform an attribute grammar such that attributes are evaluated during parsing, if possible. The analysis is proved correct by relating it to a fixpoint...... semantics for attribute grammars. An implementation of the analysis is discussed and some extensions to the analysis are mentioned....
International Nuclear Information System (INIS)
Clarke, Chris.
1997-01-01
Most policy makers in the USA and Europe are committed to strict environmental liability. The polluter pays principle is seen as popular with voters and easy to defend. For the energy sector, encompassing everything from disused gas works and coal mines to refineries, tank farms and filling stations, the cost of cleaning up old sites can be huge. Within the policy commitment to strict liability there are some issues up for negotiation, however. These include such things as: available defences; the burden of proof; mechanisms for sharing liability at multi-party sites; funding of orphan shares; the protection afforded to lenders. Most governments have shown some flexibility on these issues and some examples from the USA are given. Nevertheless, in Europe the momentum towards comprehensive strict liability regimes seems unrelenting. In the Member states of the European Union, liability laws are either already in place or new laws are in preparation. The European Commission is working on proposals for an EU-wide environmental liability regime but there are formidable obstacles to overcome if it is to become EU law. In the meanwhile, the process of trying to reach agreement at an EU level is likely to strengthen the legislative drive at national level. (UK)
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 convex optimization approach for solving large scale linear systems
Directory of Open Access Journals (Sweden)
Debora Cores
2017-01-01
Full Text Available The well-known Conjugate Gradient (CG method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.
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
Directory of Open Access Journals (Sweden)
Joanna Raczek
2004-01-01
Full Text Available The convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are \\(NP\\-complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can verify in polynomial time whether a given subset of vertices of a graph is convex or weakly convex.
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
A Convex Variational Model for Restoring Blurred Images with Multiplicative Noise
DEFF Research Database (Denmark)
Dong, Yiqiu; Tieyong Zeng
2013-01-01
In this paper, a new variational model for restoring blurred images with multiplicative noise is proposed. Based on the statistical property of the noise, a quadratic penalty function technique is utilized in order to obtain a strictly convex model under a mild condition, which guarantees...
Quantum information and convex optimization
International Nuclear Information System (INIS)
Reimpell, Michael
2008-01-01
This thesis is concerned with convex optimization problems in quantum information theory. It features an iterative algorithm for optimal quantum error correcting codes, a postprocessing method for incomplete tomography data, a method to estimate the amount of entanglement in witness experiments, and it gives necessary and sufficient criteria for the existence of retrodiction strategies for a generalized mean king problem. (orig.)
Czech Academy of Sciences Publication Activity Database
Guirao, A. J.; Hájek, Petr Pavel
2007-01-01
Roč. 135, č. 10 (2007), s. 3233-3240 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190502 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach spaces * moduli of convexity * uniformly rotund norms Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007
Quantum information and convex optimization
Energy Technology Data Exchange (ETDEWEB)
Reimpell, Michael
2008-07-01
This thesis is concerned with convex optimization problems in quantum information theory. It features an iterative algorithm for optimal quantum error correcting codes, a postprocessing method for incomplete tomography data, a method to estimate the amount of entanglement in witness experiments, and it gives necessary and sufficient criteria for the existence of retrodiction strategies for a generalized mean king problem. (orig.)
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.
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
Directory of Open Access Journals (Sweden)
Mohsen Kian
2017-02-01
Full Text Available Let A and B be C*-algebras. We consider a noncommutative convexity in Hilbert A-B-bimodules, called A-B-convexity, as a generalization of C*-convexity in C*-algebras. We show that if X is a Hilbert A-B-bimodule, then Mn(X is a Hilbert Mn(A-Mn(B-bimodule and apply it to show that the closed unit ball of every Hilbert A-B-bimodule is A-B-convex. Some properties of this kind of convexity and various examples have been given.
Quantum logics and convex geometry
International Nuclear Information System (INIS)
Bunce, L.J.; Wright, J.D.M.
1985-01-01
The main result is a representation theorem which shows that, for a large class of quantum logics, a quantum logic, Q, is isomorphic to the lattice of projective faces in a suitable convex set K. As an application we extend our earlier results, which, subject to countability conditions, gave a geometric characterization of those quantum logics which are isomorphic to the projection lattice of a von Neumann algebra or a JBW-algebra. (orig.)
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
Czech Academy of Sciences Publication Activity Database
Abrahamsen, T. A.; Hájek, Petr Pavel; Nygaard, O.; Talponen, J.; Troyanski, S.
2016-01-01
Roč. 232, č. 3 (2016), s. 227-242 ISSN 0039-3223 R&D Projects: GA ČR GA16-07378S Institutional support: RVO:67985840 Keywords : diameter 2 property * midpoint locally uniformly rotund * Daugavet property Subject RIV: BA - General Mathematics Impact factor: 0.535, year: 2016 https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia- mathematica /all/232/3/91534/diameter-2-properties-and-convexity
The canonical partial metric and the uniform convexity on normed spaces
Directory of Open Access Journals (Sweden)
S. Oltra
2005-10-01
Full Text Available In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm. We prove that these geometric properties can be considered, in this sense, as topological properties that appear when we compare the natural metric topology of the space with the non translation invariant topology induced by the canonical partial metric in the normed space.
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
DEFF Research Database (Denmark)
Hörrmann, Julia; Kousholt, Astrid
We investigate how much information about a convex body can be retrieved from a finite number of its geometric moments. We give a sufficient condition for a convex body to be uniquely determined by a finite number of its geometric moments, and we show that among all convex bodies, those which......- rithm that approximates a convex body using a finite number of its Legendre moments. The consistency of the algorithm is established using the stabil- ity result for Legendre moments. When only noisy measurements of Legendre moments are available, the consistency of the algorithm is established under...
Finite Metric Spaces of Strictly Negative Type
DEFF Research Database (Denmark)
Hjorth, Poul; Lisonek, P.; Markvorsen, Steen
1998-01-01
of Euclidean spaces. We prove that, if the distance matrix is both hypermetric and regular, then it is of strictly negative type. We show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points. In connection with an open problem raised...
Extremely strict ideals in Banach spaces
Indian Academy of Sciences (India)
Abstract. Motivated by the notion of an ideal introduced by Godefroy et al. (Stu- dia Math. 104 (1993) 13–59), in this article, we introduce and study the notion of an extremely strict ideal. For a Poulsen simplex K, we show that the space of affine contin- uous functions on K is an extremely strict ideal in the space of continuous ...
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.
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;
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
DEFF Research Database (Denmark)
Hansen, Frank
2002-01-01
We prove that the function (x1,...,xk)¿Tr(f(x1,...,xk)), defined on k-tuples of symmetric matrices of order (n1,...,nk) in the domain of f, is convex for any convex function f of k variables. The matrix f(x1,...,xk) is defined by the functional calculus for functions of several variables, and it ...
Differential analysis of matrix convex functions II
DEFF Research Database (Denmark)
Hansen, Frank; Tomiyama, Jun
2009-01-01
We continue the analysis in [F. Hansen, and J. Tomiyama, Differential analysis of matrix convex functions. Linear Algebra Appl., 420:102--116, 2007] of matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided...
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
International Nuclear Information System (INIS)
Feretic, Svjetlan; Guttmann, Anthony J
2009-01-01
Column-convex polygons were first counted by area several decades ago, and the result was found to be a simple, rational, generating function. In this work we generalize that result. Let a p-column polyomino be a polyomino whose columns can have 1, 2, ..., p connected components. Then column-convex polygons are equivalent to 1-convex polyominoes. The area generating function of even the simplest generalization, namely 2-column polyominoes, is unlikely to be solvable. We therefore define two classes of polyominoes which interpolate between column-convex polygons and 2-column polyominoes. We derive the area generating functions of those two classes, using extensions of existing algorithms. The growth constants of both classes are greater than the growth constant of column-convex polyominoes. Rather tight lower bounds on the growth constants complement a comprehensive asymptotic analysis.
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...
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.
Hyperbolic spaces are of strictly negative type
DEFF Research Database (Denmark)
Hjorth, Poul G.; Kokkendorff, Simon L.; Markvorsen, Steen
2002-01-01
We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative....... The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type....
Strictly diagonal holomorphic functions on Banach spaces
Directory of Open Access Journals (Sweden)
O. I. Fedak
2016-01-01
Full Text Available In this paper we investigate the boundedness of holomorphic functionals on a Banach space with a normalized basis $\\{e_n\\}$ which have a very special form $f(x=f(0+\\sum_{n=1}^\\infty c_nx_n^n$ and which we call strictly diagonal. We consider under which conditions strictly diagonal functions are entire and uniformly continuous on every ball of a fixed radius.
Duality and calculus of convex objects (theory and applications)
International Nuclear Information System (INIS)
Brinkhuis, Ya; Tikhomirov, V M
2007-01-01
A new approach to convex calculus is presented, which allows one to treat from a single point of view duality and calculus for various convex objects. This approach is based on the possibility of associating with each convex object (a convex set or a convex function) a certain convex cone without loss of information about the object. From the duality theorem for cones duality theorems for other convex objects are deduced as consequences. The theme 'Duality formulae and the calculus of convex objects' is exhausted (from a certain precisely formulated point of view). Bibliography: 5 titles.
Convex sets in probabilistic normed spaces
International Nuclear Information System (INIS)
Aghajani, Asadollah; Nourouzi, Kourosh
2008-01-01
In this paper we obtain some results on convexity in a probabilistic normed space. We also investigate the concept of CSN-closedness and CSN-compactness in a probabilistic normed space and generalize the corresponding results of normed spaces
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
Directory of Open Access Journals (Sweden)
Bhayo B.
2015-11-01
Full Text Available A function ƒ : R+ → R+ is (m1, m2-convex (concave if ƒ(m1(x,y ≤ (≥ m2(ƒ(x, ƒ(y for all x,y Є R+ = (0,∞ and m1 and m2 are two mean functions. Anderson et al. [1] studies the dependence of (m1, m2-convexity (concavity on m1 and m2 and gave the sufficient conditions of (m1, m2-convexity and concavity of a function defined by Maclaurin series. In this paper, we make a contribution to the topic and study the (m1, m2-convexity and concavity of a function where m1 and m2 are identric mean, Alzer mean mean. As well, we prove a conjecture posed by Bruce Ebanks in [2].
On convexity and Schoenberg's variation diminishing splines
International Nuclear Information System (INIS)
Feng, Yuyu; Kozak, J.
1992-11-01
In the paper we characterize a convex function by the monotonicity of a particular variation diminishing spline sequence. The result extends the property known for the Bernstein polynomial sequence. (author). 4 refs
Recent characterizations of generalized convexity in convexity in cooperative game thoery
Energy Technology Data Exchange (ETDEWEB)
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
International Nuclear Information System (INIS)
Li Zhenyang; Xi Zhang
2004-07-01
In this paper, we consider Hermitian harmonic maps from Hermitian manifolds into convex balls. We prove that there exist no non-trivial Hermitian harmonic maps from closed Hermitian manifolds into convex balls, and we use the heat flow method to solve the Dirichlet problem for Hermitian harmonic maps when the domain is compact Hermitian manifold with non-empty boundary. The case where the domain manifold is complete(noncompact) is also studied. (author)
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
Electronuclear Park, Privatization and Civil Strict Liability
International Nuclear Information System (INIS)
Mondello, Gerard Camille
2008-01-01
The civil strict liability regime of the electronuclear industry is a fundamental variable for preventing risk. Because prices of other energies as oil or gas are becoming higher and unpredictable, nuclear power becomes cost-effective and may favour the partial privatization of nuclear parks. By considering theoretical traditional liability models, we study the conditions that ensure the most efficient safety level when comparing natural monopoly situation and Bertrand duopoly. Our results are that natural monopoly is safer than duopoly only when strict liability is fully applied. We define conditions that neutralize risk for applying some privatization plan to nuclear park
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
Directory of Open Access Journals (Sweden)
Dragomir SeverS
2010-01-01
Full Text Available We do not only give the extensions of the results given by Gill et al. (1997 for log-convex functions but also obtain some new Hadamard-type inequalities for log-convex -convex, and -convex functions.
Finite Metric Spaces of Strictly negative Type
DEFF Research Database (Denmark)
Hjorth, Poul G.
If a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by an infinite extent (“load vector''). Finite metric spaces that have this property include all trees, and all finite subspaces of Euclidean and Hyperbolic spaces. We prove that if the distance...
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.
Dynamic Enforcement of the Strict Integrity Policy
Institute of Scientific and Technical Information of China (English)
ZHANGXiangfeng; LIANGHongliang; SUNYufang
2005-01-01
The Strict integrity policy (SIP) in Biba's integrity model is widely used in protecting information integrity, but the static integrity labels of both subjects and objects increase compatibility cost of applications and might prevent some operations that are indeed harmless.In order to improve compatibility, Dynamic enforcement of the Strict integrity policy (DESIP) is put forward. The current integrity label attribute of a subject in SIP is replaced with two attributes in DESIP, which are used to confine dynamically the range of objects a subject could be allowed to access. The new rules of access control in DESIP are given for each kind of access mode (observe,modify and invoke) together with the proofs of their valid-ity. Comparison between SIP and DESIP shows that after a sequence of operations, a subject controlled by DESIP tends to behave in a similar way as it is controlled by SIP and DESIP is more compatible than SIP.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
. The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available...... tensors up to rank s. This is used to establish consistency of the developed reconstruction algorithm....
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.
A strictly hyperbolic equilibrium phase transition model
International Nuclear Information System (INIS)
Allaire, G; Faccanoni, G; Kokh, S.
2007-01-01
This Note is concerned with the strict hyperbolicity of the compressible Euler equations equipped with an equation of state that describes the thermodynamical equilibrium between the liquid phase and the vapor phase of a fluid. The proof is valid for a very wide class of fluids. The argument only relies on smoothness assumptions and on the classical thermodynamical stability assumptions, that requires a definite negative Hessian matrix for each phase entropy as a function of the specific volume and internal energy. (authors)
On Fixed Points of Strictly Causal Functions
2013-04-08
were defined to be the functions that are strictly contracting with respect to the Cantor metric (also called the Baire distance) on signals over non...in Computer Science, pages 447–484. Springer Berlin / Heidelberg, 1992. [36] George Markowsky. Chain-complete posets and directed sets with...Journal of Logic Programming, 42(2):59–70, 2000. [53] George M. Reed and A. William Roscoe. A timed model for communicating sequential processes. In
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based...
Probing convex polygons with X-rays
International Nuclear Information System (INIS)
Edelsbrunner, H.; Skiena, S.S.
1988-01-01
An X-ray probe through a polygon measures the length of intersection between a line and the polygon. This paper considers the properties of various classes of X-ray probes, and shows how they interact to give finite strategies for completely describing convex n-gons. It is shown that (3n/2)+6 probes are sufficient to verify a specified n-gon, while for determining convex polygons (3n-1)/2 X-ray probes are necessary and 5n+O(1) sufficient, with 3n+O(1) sufficient given that a lower bound on the size of the smallest edge of P is known
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.
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
Strict topoligies in non-Archimedean function spaces
Directory of Open Access Journals (Sweden)
A. K. Katsaras
1984-01-01
Full Text Available Let F be a non-trivial complete non-Archimedean valued field. Some locally F-convex topologies, on the space Cb(X,E of all bounded continuous functions from a zero-dimensional topological space X to a non-Archimedean locally F-convex space E, are studied. The corresponding dual spaces are also investigated.
Differential analysis of matrix convex functions
DEFF Research Database (Denmark)
Hansen, Frank; Tomiyama, Jun
2007-01-01
We analyze matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus [F. Kraus, Über konvekse Matrixfunktionen, Math. Z. 41 (1936) 18-42]. We obtain for each order conditions for ma...
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...
Robust Utility Maximization Under Convex Portfolio Constraints
International Nuclear Information System (INIS)
Matoussi, Anis; Mezghani, Hanen; Mnif, Mohamed
2015-01-01
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption–investment strategy by studying the associated quadratic backward stochastic differential equation. We characterize the optimal control by using the duality method and deriving a dynamic maximum principle
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
Directory of Open Access Journals (Sweden)
Sergiu Aizicovici
2010-01-01
Full Text Available We study continuous descent methods for minimizing convex functions, defined on general Banach spaces, which are associated with an appropriate complete metric space of vector fields. We show that there exists an everywhere dense open set in this space of vector fields such that each of its elements generates strongly convergent trajectories.
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
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Georgiadis, Loukas; Hansen, Kristoffer Arnsfelt
2007-01-01
We consider the problem of maintaining a maximum matching in a convex bipartite graph G = (V,E) under a set of update operations which includes insertions and deletions of vertices and edges. It is not hard to show that it is impossible to maintain an explicit representation of a maximum matching...
Cost Allocation and Convex Data Envelopment
DEFF Research Database (Denmark)
Hougaard, Jens Leth; Tind, Jørgen
such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output...
Tropicalized Lambda Lengths, Measured Laminations and Convexity
DEFF Research Database (Denmark)
C. Penner, R.
This work uncovers the tropical analogue for measured laminations of the convex hull construction of decorated Teichmueller theory, namely, it is a study in coordinates of geometric degeneration to a point of Thurston's boundary for Teichmueller space. This may offer a paradigm for the extension ...
7 CFR 28.441 - Strict Middling Yellow Stained Color.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Middling Yellow Stained Color. 28.441 Section... Strict Middling Yellow Stained Color. Strict Middling Yellow Stained Color is color which is deeper than that of Strict Middling Tinged Color. [57 FR 34498, Aug. 5, 1992] ...
7 CFR 28.412 - Strict Middling Light Spotted Color.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Middling Light Spotted Color. 28.412 Section 28... Light Spotted Color. Strict Middling Light Spotted Color is color which in spot or color, or both, is between Strict Middling Color and Strict Middling Spotted Color. ...
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
Directory of Open Access Journals (Sweden)
Bencze Mihály
2008-01-01
Full Text Available Abstract The Schur convexity and Schur-geometric convexity of generalized Heronian means involving two parameters are studied, the main result is then used to obtain several interesting and significantly inequalities for generalized Heronian means.
A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
程立新; 腾岩梅
2003-01-01
This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.
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
Energy Technology Data Exchange (ETDEWEB)
Plascencia, Alexis D.; Tamarit, Carlos [Institute for Particle Physics Phenomenology, Durham University,South Road, DH1 3LE (United Kingdom)
2016-10-19
We clarify issues of convexity, gauge-dependence and radiative corrections in relation to tunneling rates. Despite the gauge dependence of the effective action at zero and finite temperature, it is shown that tunneling and nucleation rates remain independent of the choice of gauge-fixing. Taking as a starting point the functional that defines the transition amplitude from a false vacuum onto itself, it is shown that decay rates are exactly determined by a non-convex, false vacuum effective action evaluated at an extremum. The latter can be viewed as a generalized bounce configuration, and gauge-independence follows from the appropriate Nielsen identities. This holds for any election of gauge-fixing that leads to an invertible Faddeev-Popov matrix.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
2016-01-01
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy...... measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise...
Exact generating function for 2-convex polygons
International Nuclear Information System (INIS)
James, W R G; Jensen, I; Guttmann, A J
2008-01-01
Polygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their 'concavity index', m. Such polygons are called m-convex polygons and are characterized by having up to m indentations in their perimeter. We first describe how we conjectured the (isotropic) generating function for the case m = 2 using a numerical procedure based on series expansions. We then proceed to prove this result for the more general case of the full anisotropic generating function, in which steps in the x and y directions are distinguished. In doing so, we develop tools that would allow for the case m > 2 to be studied
Solving ptychography with a convex relaxation
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
International Nuclear Information System (INIS)
Plascencia, Alexis D.; Tamarit, Carlos
2016-01-01
We clarify issues of convexity, gauge-dependence and radiative corrections in relation to tunneling rates. Despite the gauge dependence of the effective action at zero and finite temperature, it is shown that tunneling and nucleation rates remain independent of the choice of gauge-fixing. Taking as a starting point the functional that defines the transition amplitude from a false vacuum onto itself, it is shown that decay rates are exactly determined by a non-convex, false vacuum effective action evaluated at an extremum. The latter can be viewed as a generalized bounce configuration, and gauge-independence follows from the appropriate Nielsen identities. This holds for any election of gauge-fixing that leads to an invertible Faddeev-Popov matrix.
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
International Nuclear Information System (INIS)
Ibáñez, José M; Martí, José M; Cordero-Carrión, Isabel; Miralles, Juan A
2013-01-01
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 Relativistic Fluids and Magneto-Fluids (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr1989 Rev. Mod. Phys. 61 75). The classical limit is recovered. Communicated by L Rezzolla (note)
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
Directory of Open Access Journals (Sweden)
Tin Cheuk Leung
2018-03-01
Full Text Available This paper studies optimal distribution of skills in an optimal income tax framework with convex skill constraints. The problem is cast as a social planning problem where a redistributive planner chooses how to distribute a given amount of aggregate skills across people. We find that optimal skill distribution is either perfectly equal or perfectly unequal, but an interior level of skill inequality is never optimal.
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.
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.
On The Integral Representation of Strictly Continuous Set-Valued Maps
Directory of Open Access Journals (Sweden)
Anaté K. Lakmon
2015-11-01
Full Text Available Let T be a completely regular topological space and C(T be the space of bounded, continuous real-valued functions on T. C(T is endowed with the strict topology (the topology generated by seminorms determined by continuous functions vanishing at in_nity. R. Giles ([13], p. 472, Theorem 4.6 proved in 1971 that the dual of C(T can be identi_ed with the space of regular Borel measures on T. We prove this result for positive, additive set-valued maps with values in the space of convex weakly compact non-empty subsets of a Banach space and we deduce from this result the theorem of R. Giles ([13], theorem 4.6, p.473.
STRICT STABILITY OF IMPULSIVE SET VALUED DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper, we develop strict stability concepts of ODE to impulsive hybrid set valued differential equations. By Lyapunov’s original method, we get some basic strict stability criteria of impulsive hybrid set valued equations.
Some results on a general iterative method for
Jung Jong Soo
2011-01-01
Abstract Let H be a Hilbert space, C be a closed convex subset of H such that C ± C ⊂ C, and T : C → H be a k-strictly pseudo-contractive mapping with F(T) ≠ ∅ for some 0 ≤ k < 1. Let F : C → C be a κ-Lipschitzian and η-strongly monotone operator with κ > 0 and η > 0 and f : C → C be a contraction with the contractive constant α ∈ (0, 1). Let , and τ < 1. Let {αn } and {βn } be sequen...
Public healthcare interests require strict competition enforcement.
Loozen, Edith M H
2015-07-01
Several countries have introduced competition in their health systems in order to maintain the supply of high quality health care in a cost-effective manner. The introduction of competition triggers competition enforcement. Since healthcare is characterized by specific market failures, many favor healthcare-specific competition enforcement in order not only to account for the competition interest, but also for the healthcare interests. The question is whether healthcare systems based on competition can succeed when competition enforcement deviates from standard practice. This paper analyzes whether healthcare-specific competition enforcement is theoretically sound and practically effective. This is exemplified by the Dutch system that is based on regulated competition and thus crucially depends on getting competition enforcement right. Governments are responsible for correcting market failures. Markets are responsible for maximizing the public healthcare interests. By securing sufficient competitive pressure, competition enforcement makes sure they do. When interpreted according to welfare-economics, competition law takes into account both costs and benefits specific market behavior may have for healthcare. Competition agencies and judiciary are not legitimized to deviate from standard evidentiary requirements. Dutch case law shows that healthcare-specific enforcement favors the healthcare undertakings concerned, but to the detriment of public health care. Healthcare-specific competition enforcement is conceptually flawed and counterproductive. In order for healthcare systems based on competition to succeed, competition enforcement should be strict. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.
7 CFR 28.406 - Strict Good Ordinary Color.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Good Ordinary Color. 28.406 Section 28.406... for the Color Grade of American Upland Cotton § 28.406 Strict Good Ordinary Color. Strict Good Ordinary Color is color which is within the range represented by a set of samples in the custody of the...
7 CFR 28.404 - Strict Low Middling Color.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Low Middling Color. 28.404 Section 28.404... for the Color Grade of American Upland Cotton § 28.404 Strict Low Middling Color. Strict Low Middling Color is color which is within the range represented by a set of samples in the custody of the United...
7 CFR 28.402 - Strict Middling Color.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Middling Color. 28.402 Section 28.402... for the Color Grade of American Upland Cotton § 28.402 Strict Middling Color. Strict Middling Color is color which is within the range represented by a set of samples in the custody of the United States...
Synchronizing strict-feedback and general strict-feedback chaotic systems via a single controller
International Nuclear Information System (INIS)
Chen Shihua; Wang Feng; Wang Changping
2004-01-01
We present a systematic design procedure to synchronize a class of chaotic systems in a so-called strict-feedback form based on back-stepping procedure. This approach needs only a single controller to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, we point out that the method does not work for general strict-feedback chaotic systems, for instance, Lorenz system. Therefore, we propose three kinds of synchronization schemes for Lorenz system using the Lyapunov function method. All the three schemes avoid including divergence factor as in Ref. [Chaos, Solitons and Fractals 16 (2003) 37]. Especially in the last two schemes, we need only one state variable in controller, which has important significance in chaos synchronization used for communication purposes. Finally numerical simulations are provided to show the effectiveness and feasibility of the developed methods
Convex and Radially Concave Contoured Distributions
Directory of Open Access Journals (Sweden)
Wolf-Dieter Richter
2015-01-01
Full Text Available Integral representations of the locally defined star-generalized surface content measures on star spheres are derived for boundary spheres of balls being convex or radially concave with respect to a fan in Rn. As a result, the general geometric measure representation of star-shaped probability distributions and the general stochastic representation of the corresponding random vectors allow additional specific interpretations in the two mentioned cases. Applications to estimating and testing hypotheses on scaling parameters are presented, and two-dimensional sample clouds are simulated.
On conditional independence and log-convexity
Czech Academy of Sciences Publication Activity Database
Matúš, František
2012-01-01
Roč. 48, č. 4 (2012), s. 1137-1147 ISSN 0246-0203 R&D Projects: GA AV ČR IAA100750603; GA ČR GA201/08/0539 Institutional support: RVO:67985556 Keywords : Conditional independence * Markov properties * factorizable distributions * graphical Markov models * log-convexity * Gibbs- Markov equivalence * Markov fields * Gaussian distributions * positive definite matrices * covariance selection model Subject RIV: BA - General Mathematics Impact factor: 0.933, year: 2012 http://library.utia.cas.cz/separaty/2013/MTR/matus-0386229.pdf
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...
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.
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
International Nuclear Information System (INIS)
Fujimoto, Y.; O'Raifeartaigh, L.; Parravicini, G.
1983-01-01
It is shown that the well-known relationship between the effective potential GAMMA and the vacuum graphs μ of scalar QFT follows directly from the translational invariance of the measure, and that it holds for all values of the fields phi if, and only if, the classical potential is convex. In the non-convex case μ appears to become complex for some values of phi, but it is shown that the complexity is only apparent and is due to the failure of the loop expansion. The effective potential actually remains real and well-defined for all phi, and reduces to μ in the neighbourhood of the classical minima. A number of examples are considered, notably potentials which are spontaneously broken. In particular the mechanism by which a spontaneous breakdown may be generated by radiative corrections is re-investigated and some new insights obtained. Finally, it is shown that the renormalization group equations for the parameters may be obtained by inspection from the effective potential, and among the examples considered are SU(n) fields and supermultiplets. In particular, it is shown that for supermultiplets the effective potential is not only real but positive. (orig.)
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.
Multi-Period Trading via Convex Optimization
DEFF Research Database (Denmark)
Boyd, Stephen; Busseti, Enzo; Diamond, Steve
2017-01-01
We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades oﬀ expected return, risk......, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the ﬁrst one executed, using estimates of future quantities that are unknown when the trades....... In this paper, we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software...
Conditionally exponential convex functions on locally compact groups
International Nuclear Information System (INIS)
Okb El-Bab, A.S.
1992-09-01
The main results of the thesis are: 1) The construction of a compact base for the convex cone of all conditionally exponential convex functions. 2) The determination of the extreme parts of this cone. Some supplementary lemmas are proved for this purpose. (author). 8 refs
Approximate convex hull of affine iterated function system attractors
International Nuclear Information System (INIS)
Mishkinis, Anton; Gentil, Christian; Lanquetin, Sandrine; Sokolov, Dmitry
2012-01-01
Highlights: ► We present an iterative algorithm to approximate affine IFS attractor convex hull. ► Elimination of the interior points significantly reduces the complexity. ► To optimize calculations, we merge the convex hull images at each iteration. ► Approximation by ellipses increases speed of convergence to the exact convex hull. ► We present a method of the output convex hull simplification. - Abstract: In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy.
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
Directory of Open Access Journals (Sweden)
Maria Hussain
2014-07-01
Full Text Available A C1 convex surface data interpolation scheme is presented to preserve the shape of scattered data arranged over a triangular grid. Bernstein–Bézier quartic function is used for interpolation. Lower bound of the boundary and inner Bézier ordinates is determined to guarantee convexity of surface. The developed scheme is flexible and involves more relaxed constraints.
Convergence of Algorithms for Reconstructing Convex Bodies and Directional Measures
DEFF Research Database (Denmark)
Gardner, Richard; Kiderlen, Markus; Milanfar, Peyman
2006-01-01
We investigate algorithms for reconstructing a convex body K in Rn from noisy measurements of its support function or its brightness function in k directions u1, . . . , uk. The key idea of these algorithms is to construct a convex polytope Pk whose support function (or brightness function) best...
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
Directory of Open Access Journals (Sweden)
Muhammad Shoaib Saleem
2018-02-01
Full Text Available Abstract The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted L2 $L^{2}$-norm.
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...
Modal Inclusion Logic: Being Lax is Simpler than Being Strict
DEFF Research Database (Denmark)
Hella, Lauri; Kuusisto, Antti Johannes; Meier, Arne
2015-01-01
We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for strict and another one for lax semantics. The complexity of the lax version turns out to be complete for EXPTIME, whereas with strict semantics...
7 CFR 28.426 - Strict Good Ordinary Spotted Color.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Good Ordinary Spotted Color. 28.426 Section 28.426 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards... Spotted Color. Strict Good Ordinary Spotted Color is color which is within the range represented by a set...
7 CFR 28.433 - Strict Low Middling Tinged Color.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Low Middling Tinged Color. 28.433 Section 28.433 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards... Tinged Color. Strict Low Middling Tinged Color is color which is within the range represented by a set of...
7 CFR 28.422 - Strict Middling Spotted Color.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Middling Spotted Color. 28.422 Section 28.422 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards... Color. Strict Middling Spotted Color is color which is within the range represented by a set of samples...
7 CFR 28.424 - Strict Low Middling Spotted Color.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Low Middling Spotted Color. 28.424 Section 28.424 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards... Spotted Color. Strict Low Middling Spotted Color is color which is within the range represented by a set...
7 CFR 28.431 - Strict Middling Tinged Color.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Middling Tinged Color. 28.431 Section 28.431 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards... Color. Strict Middling Tinged Color is color which is better than Middling Tinged Color. ...
43 CFR 29.7 - Imposition of strict liability.
2010-10-01
... LIABILITY FUND § 29.7 Imposition of strict liability. (a) Notwithstanding the provisions of any other law... prove that the damages were caused by an act of war or by the negligence of the United States or other... negligence of such damaged party. (c)(1) Strict liability for all claims arising out of any one incident...
Strictly-regular number system and data structures
DEFF Research Database (Denmark)
Elmasry, Amr Ahmed Abd Elmoneim; Jensen, Claus; Katajainen, Jyrki
2010-01-01
We introduce a new number system that we call the strictly-regular system, which efficiently supports the operations: digit-increment, digit-decrement, cut, concatenate, and add. Compared to other number systems, the strictly-regular system has distinguishable properties. It is superior to the re...
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).
Visualizing Data as Objects by DC (Difference of Convex) Optimization
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
2018-01-01
In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value, as convex objects. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization...... problem whose objective is the difference of two convex functions (DC). Suitable DC decompositions allow us to use the Difference of Convex Algorithm (DCA) in a very efficient way. Our algorithmic approach is used to visualize two real-world datasets....
Strategy and Aspects of Monitoring / Control Strictly in Coordinated Subsystems
Directory of Open Access Journals (Sweden)
William José Borges
2012-06-01
Full Text Available This paper aims to discuss the approach structures of the strictly coordinated theoretical framework developed by Zylbersztajn and Farina (1999 as an expanded perspective of the firm, taking into account the food supply chains as an extension of the nexus of contracts proposed by Coase (1937 and taken up by Williamson (1985. The structures stand out as strictly coordinated. Zylbersztajn and Farina (1999 turn to identifying points of common interests that encourage firms to promote contracts between themselves in a strictly coordinated way, considering the degree of asset specificity involved in the transaction and the competitive forces that determine the search for strategic positioning organizations to achieve sustainable superior results.
Normal form and synchronization of strict-feedback chaotic systems
International Nuclear Information System (INIS)
Wang, Feng; Chen, Shihua; Yu Minghai; Wang Changping
2004-01-01
This study concerns the normal form and synchronization of strict-feedback chaotic systems. We prove that, any strict-feedback chaotic system can be rendered into a normal form with a invertible transform and then a design procedure to synchronize the normal form of a non-autonomous strict-feedback chaotic system is presented. This approach needs only a scalar driving signal to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, the Roessler chaotic system is taken as a concrete example to illustrate the procedure of designing without transforming a strict-feedback chaotic system into its normal form. Numerical simulations are also provided to show the effectiveness and feasibility of the developed methods
Strict finitism and the logic of mathematical applications
Ye, Feng
2011-01-01
Exploring the logic behind applied mathematics to the physical world, this volume illustrates how radical naturalism, nominalism and strict finitism can account for the applications of classical mathematics in current theories about natural phenomena.
A survey on locally uniformly A-convex algebras
International Nuclear Information System (INIS)
Oudadess, M.
1984-12-01
Using a bornological technic of M. Akkar, we reduce the study of classical questions (spectrum, boundedness of characters, functional calculus, etc.) in locally uniformly A-convex algebras to the Banach case. (author)
Lipschitz estimates for convex functions with respect to vector fields
Directory of Open Access Journals (Sweden)
Valentino Magnani
2012-12-01
Full Text Available We present Lipschitz continuity estimates for a class of convex functions with respect to Hörmander vector fields. These results have been recently obtained in collaboration with M. Scienza, [22].
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
Directory of Open Access Journals (Sweden)
Haiyan Wang
2009-10-01
Full Text Available We establish two criteria for the existence of convex solutions to a boundary value problem for weakly coupled systems arising from the Monge-Ampère equations. We shall use fixed point theorems in a cone.
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 ...
African Journals Online (AJOL)
user
Multi-objective convex programming problem arising in ... However, although the consideration of multiple objectives may seem a novel concept, virtually any nontrivial ..... Solving multiobjective programming problems by discrete optimization.
Strictly contractive quantum channels and physically realizable quantum computers
International Nuclear Information System (INIS)
Raginsky, Maxim
2002-01-01
We study the robustness of quantum computers under the influence of errors modeled by strictly contractive channels. A channel T is defined to be strictly contractive if, for any pair of density operators ρ, σ in its domain, parallel Tρ-Tσ parallel 1 ≤k parallel ρ-σ parallel 1 for some 0≤k 1 denotes the trace norm). In other words, strictly contractive channels render the states of the computer less distinguishable in the sense of quantum detection theory. Starting from the premise that all experimental procedures can be carried out with finite precision, we argue that there exists a physically meaningful connection between strictly contractive channels and errors in physically realizable quantum computers. We show that, in the absence of error correction, sensitivity of quantum memories and computers to strictly contractive errors grows exponentially with storage time and computation time, respectively, and depends only on the constant k and the measurement precision. We prove that strict contractivity rules out the possibility of perfect error correction, and give an argument that approximate error correction, which covers previous work on fault-tolerant quantum computation as a special case, is possible
Surgical treatment of convexity focal epilepsy
International Nuclear Information System (INIS)
Shimizu, Hiroyuki; Ishijima, Buichi; Iio, Masaaki.
1987-01-01
We have hitherto applied PET study in 72 epileptic patients. The main contents of their seizures consists of complex partial in 32, elementary partial in 32, generalized in 6, and others in 3 cases. We administered perorally 10 mCi glucose labeled with C11 produced in the JSW Baby Cyclotron for the study of CMRG(cerebral metabolic rate of glucose). The continuous inhalation method of CO 2 and O 2 labeled with O15 produced in the same cyclotron was also employed for measurement of rCBE(cerebral blood flow) and CMRO 2 (cerebral metabolic rate of oxygen). In both studies, epileptic foci were shown as well demarcated hypometabolic zones with decreased CMRG, rCBF or CMRO 2 . The locations of PET diagnosed foci were not contradictory with the clinical symptoms, scalp EEGs or X-ray CT findings. Of the 32 patients with the convexity epileptic foci, 8 patients underwent surgical treatment. Prior to the surgical intervention, subdural strip electrodes were inserted in the four cases for further assessment of focus locations. Subdural EEG disclosed very active brain activity with high amplitude 4 to 5 times scalp EEG and revealed epileptiform discharges most of which were not detected by scalp recording. PET scans did not characterize epileptogenic nature of a lesion. Subdural recording therefore was useful for detecting the foci responsible for habitual seizures in the cases with multiple PET foci. Ambiguous hypometabolic zones on PECT images also could be confirmed by the subdural technique. Of the 8 operated cases, five patients are seizure free, one is signigicantly improved and two are not improved although the postoperative follow-up is too short for precise evaluation. (J.P.N.)
Efficiency and Generalized Convex Duality for Nondifferentiable Multiobjective Programs
Directory of Open Access Journals (Sweden)
Bae KwanDeok
2010-01-01
Full Text Available We introduce nondifferentiable multiobjective programming problems involving the support function of a compact convex set and linear functions. The concept of (properly efficient solutions are presented. We formulate Mond-Weir-type and Wolfe-type dual problems and establish weak and strong duality theorems for efficient solutions by using suitable generalized convexity conditions. Some special cases of our duality results are given.
DEFF Research Database (Denmark)
Karakashev, Dimitar Borisov; Kotay, Shireen Meher; Trably, Eric
2009-01-01
The aim of this study was to enrich, characterize and identify strict anaerobic extreme thermophilic hydrogen (H-2) producers from digested household solid wastes. A strict anaerobic extreme thermophilic H-2 producing bacterial culture was enriched from a lab-scale digester treating household...... wastes at 70 degrees C. The enriched mixed culture consisted of two rod-shaped bacterial members growing at an optimal temperature of 80 degrees C and an optimal pH 8.1. The culture was able to utilize glucose, galactose, mannose, xylose, arabinose, maltose, sucrose, pyruvate and glycerol as carbon...... sources. Growth on glucose produced acetate, H-2 and carbon dioxide. Maximal H-2 production rate on glucose was 1.1 mmol l(-1) h(-1) with a maximum H-2 yield of 1.9 mole H-2 per mole glucose. 16S ribosomal DNA clone library analyses showed that the culture members were phylogenetically affiliated...
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
International Nuclear Information System (INIS)
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.)
Convergence theorems for strictly hemi-contractive maps
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1992-04-01
It is proved that each of two well-known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly to the fixed point of strictly hemi-contractive map in real Banach spaces with property (U, λ, m+1,m), λ is an element of R, m is an element of IN. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets; and Banach spaces with property (U, λ, m+1, m), λ is an element of R, m is an element of IN include the L p (or l p ) spaces, p≥2. Our theorems generalize important known results. (author). 22 refs
Convex unwraps its first grown-up supercomputer
Energy Technology Data Exchange (ETDEWEB)
Manuel, T.
1988-03-03
Convex Computer Corp.'s new supercomputer family is even more of an industry blockbuster than its first system. At a tenfold jump in performance, it's far from just an incremental upgrade over its first minisupercomputer, the C-1. The heart of the new family, the new C-2 processor, churning at 50 million floating-point operations/s, spawns a group of systems whose performance could pass for some fancy supercomputers-namely those of the Cray Research Inc. family. When added to the C-1, Convex's five new supercomputers create the C series, a six-member product group offering a performance range from 20 to 200 Mflops. They mark an important transition for Convex from a one-product high-tech startup to a multinational company with a wide-ranging product line. It's a tough transition but the Richardson, Texas, company seems to be doing it. The extended product line propels Convex into the upper end of the minisupercomputer class and nudges it into the low end of the big supercomputers. It positions Convex in an uncrowded segment of the market in the $500,000 to $1 million range offering 50 to 200 Mflops of performance. The company is making this move because the minisuper area, which it pioneered, quickly became crowded with new vendors, causing prices and gross margins to drop drastically.
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.
Analytic properties of form factors in strictly confining models
International Nuclear Information System (INIS)
Csikor, F.
1979-12-01
An argument is presented showing that strict confinement implies the possible existence of an (unwanted) branch point at q 2 =0 in the form factors. In case of a bag extended to infinity in the relative time, the branch point is certainly there (provided that the form factor is non zero at q 2 =0). (author)
Dominance on Strict Triangular Norms and Mulholland Inequality
Czech Academy of Sciences Publication Activity Database
Petrík, Milan
2018-01-01
Roč. 335, 15 March (2018), s. 3-17 ISSN 0165-0114 R&D Projects: GA ČR GJ15-07724Y Institutional support: RVO:67985807 Keywords : dominance relation * Mulholland inequality * strict triangular norm * transitivity Subject RIV: BA - General Mathematics Impact factor: 2.718, year: 2016
Effects of strict prolonged bed rest on cardiorespiratory fitness
DEFF Research Database (Denmark)
Ried-Larsen, Mathias; Aarts, Hugo M; Joyner, Michael J
2017-01-01
The aim of this systematic review and meta-analysis [International Prospective Register of Systematic Reviews (PROSPERO) CRD42017055619] was to assess the effects of strict prolonged bed rest (without countermeasures) on maximal oxygen uptake (V̇o2max) and to explore sources of variation therein....
Dose evaluation from multiple detector outputs using convex optimisation
International Nuclear Information System (INIS)
Hashimoto, M.; Iimoto, T.; Kosako, T.
2011-01-01
A dose evaluation using multiple radiation detectors can be improved by the convex optimisation method. It enables flexible dose evaluation corresponding to the actual radiation energy spectrum. An application to the neutron ambient dose equivalent evaluation is investigated using a mixed-gas proportional counter. The convex derives the certain neutron ambient dose with certain width corresponding to the true neutron energy spectrum. The range of the evaluated dose is comparable to the error of conventional neutron dose measurement equipments. An application to the neutron individual dose equivalent measurement is also investigated. Convexes of particular dosemeter combinations evaluate the individual dose equivalent better than the dose evaluation of a single dosemeter. The combinations of dosemeters with high orthogonality of their response characteristics tend to provide a good suitability for dose evaluation. (authors)
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.
A working-set framework for sequential convex approximation methods
DEFF Research Database (Denmark)
Stolpe, Mathias
2008-01-01
We present an active-set algorithmic framework intended as an extension to existing implementations of sequential convex approximation methods for solving nonlinear inequality constrained programs. The framework is independent of the choice of approximations and the stabilization technique used...... to guarantee global convergence of the method. The algorithm works directly on the nonlinear constraints in the convex sub-problems and solves a sequence of relaxations of the current sub-problem. The algorithm terminates with the optimal solution to the sub-problem after solving a finite number of relaxations....
Convex Hull Abstraction in Specialisation of CLP Programs
DEFF Research Database (Denmark)
Peralta, J.C.; Gallagher, John Patrick
2003-01-01
We introduce an abstract domain consisting of atomic formulas constrained by linear arithmetic constraints (or convex hulls). This domain is used in an algorithm for specialization of constraint logic programs. The algorithm incorporates in a single phase both top-down goal directed propagation...... and bottom-up answer propagation, and uses a widening on the convex hull domain to ensure termination. We give examples to show the precision gained by this approach over other methods in the literature for specializing constraint logic programs. The specialization method can also be used for ordinary logic...
Closedness type regularity conditions in convex optimization and beyond
Directory of Open Access Journals (Sweden)
Sorin-Mihai Grad
2016-09-01
Full Text Available The closedness type regularity conditions have proven during the last decade to be viable alternatives to their more restrictive interiority type counterparts, in both convex optimization and different areas where it was successfully applied. In this review article we de- and reconstruct some closedness type regularity conditions formulated by means of epigraphs and subdifferentials, respectively, for general optimization problems in order to stress that they arise naturally when dealing with such problems. The results are then specialized for constrained and unconstrained convex optimization problems. We also hint towards other classes of optimization problems where closedness type regularity conditions were successfully employed and discuss other possible applications of them.
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.
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We consider the problem of minimizing a convex separable logarithmic function over a region defined by a convex inequality constraint or linear equality constraint, and two-sided bounds on the variables (box constraints. Such problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems as well as in various practical problems such as problems of production planning and scheduling, allocation of resources, decision making, facility location problems, and so forth. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.
Strong Convergence Theorems for a Pair of Strictly Pseudononspreading Mappings
Directory of Open Access Journals (Sweden)
Bin-Chao Deng
2013-01-01
Full Text Available Let H be a real Hilbert space. Let T1,T2:H→H be k1-, k2-strictly pseudononspreading mappings; let αn and βn be two real sequences in (0,1. For given x0∈H, the sequence xn is generated iteratively by xn+1=βnxn+1-βnTw1αnγfxn+I-μαnBTw2xn, ∀n∈N, where Twi=1−wiI+wiTi with i=1,2 and B:H→H is strongly monotone and Lipschitzian. Under some mild conditions on parameters αn and βn, we prove that the sequence xn converges strongly to the set FixT1∩FixT2 of fixed points of a pair of strictly pseudononspreading mappings T1 and T2.
Growth of a Strictly Anaerobic Bacterium on Furfural (2-Furaldehyde)
Brune, Gerhard; Schoberth, Siegfried M.; Sahm, Hermann
1983-01-01
A strictly anaerobic bacterium was isolated from a continuous fermentor culture which converted the organic constituents of sulfite evaporator condensate to methane and carbon dioxide. Furfural is one of the major components of this condensate. This furfural isolate could degrade furfural as the sole source of carbon and energy in a defined mineral-vitamin-sulfate medium. Acetic acid was the major fermentation product. This organism could also use ethanol, lactate, pyruvate, or fumarate and c...
The Fixed-Point Theory of Strictly Causal Functions
2013-06-09
functions were defined to be the functions that are strictly contracting with respect to the Cantor metric (also called the Baire distance) on signals...of Lecture Notes in Computer Science, pages 447–484. Springer Berlin / Heidelberg, 1992. [36] George Markowsky. Chain-complete posets and directed...Journal of Logic Programming, 42(2):59–70, 2000. [52] George M. Reed and A. William Roscoe. A timed model for communicating sequential processes. In Laurent
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
International Nuclear Information System (INIS)
Herrmann, Michael; Rademacher, Jens D M
2010-01-01
We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space–time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax shocks are replaced by so-called dispersive shocks. For convex–concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave–convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions
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
CSIR Research Space (South Africa)
Scholes, RJ
2003-12-01
Full Text Available The relationship between grass production and the quantity of trees in mixed tree-grass ecosystems (savannas) is convex for all or most of its range. In other words, the grass production declines more steeply per unit increase in tree quantity...
Positive definite functions and dual pairs of locally convex spaces
Directory of Open Access Journals (Sweden)
Daniel Alpay
2018-01-01
Full Text Available Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions.
Intracranial Convexity Lipoma with Massive Calcification: Case Report
Energy Technology Data Exchange (ETDEWEB)
Kim, Eung Tae; Park, Dong Woo; Ryu, Jeong Ah; Park, Choong Ki; Lee, Young Jun; Lee, Seung Ro [Dept. of Radiology, Hanyang University College of Medicine, Seoul (Korea, Republic of)
2011-12-15
Intracranial lipoma is a rare entity, accounting for less than 0.5% of intracranial tumors, which usually develops in the callosal cisterns. We report a case of lipoma with an unusual location; in the high parietal convexity combined with massive calcification, and no underlying vascular malformation or congenital anomaly.
A duality recipe for non-convex variational problems
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
Directory of Open Access Journals (Sweden)
Ilko Vrankic
2017-03-01
Full Text Available In this article we analyse the short run profit maximization problem in a convex analysis framework. The goal is to apply the results of convex analysis due to unique structure of microeconomic phenomena on the known short run profit maximization problem where the results from convex analysis are deductively applied. In the primal optimization model the technology in the short run is represented by the short run production function and the normalized profit function, which expresses profit in the output units, is derived. In this approach the choice variable is the labour quantity. Alternatively, technology is represented by the real variable cost function, where costs are expressed in the labour units, and the normalized profit function is derived, this time expressing profit in the labour units. The choice variable in this approach is the quantity of production. The emphasis in these two perspectives of the primal approach is given to the first order necessary conditions of both models which are the consequence of enveloping the closed convex set describing technology with its tangents. The dual model includes starting from the normalized profit function and recovering the production function, and alternatively the real variable cost function. In the first perspective of the dual approach the choice variable is the real wage, and in the second it is the real product price expressed in the labour units. It is shown that the change of variables into parameters and parameters into variables leads to both optimization models which give the same system of labour demand and product supply functions and their inverses. By deductively applying the results of convex analysis the comparative statics results are derived describing the firm's behaviour in the short run.
Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes
Energy Technology Data Exchange (ETDEWEB)
Sarıkaya, Mehmet Zeki, E-mail: sarikayamz@gmail.com [Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce (Turkey); Kiriş, Mehmet Eyüp, E-mail: kiris@aku.edu.tr [Department of Mathematics, Institute of Science and Arts, Afyon Kocatepe University, Afyonkarahisar (Turkey); Çelik, Nuri, E-mail: ncelik@bartin.edu.tr [Department of Statistics, Faculty of Science, Bartın University, Bartın-Turkey (Turkey)
2016-04-18
The main aim of the present paper is to introduce φ{sub h}-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φ{sub h}-convex stochastic processes. We also give some new general inequalities for φ{sub h}-convex stochastic processes.
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2014-01-01
Full Text Available We introduce and analyze one iterative algorithm by hybrid shrinking projection method for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: finitely many generalized mixed equilibrium problems, finitely many variational inequalities, the general system of variational inequalities and the fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense 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 iterative algorithm by hybrid shrinking projection method for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.
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
International Nuclear Information System (INIS)
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
Modular PNML revisited: Some ideas for strict typing
DEFF Research Database (Denmark)
Kindler, Ekkart
2007-01-01
The Petri Net Markup Language (PNML) is currently standardised by ISO/IEC JTC1/SC7 WG 19 as Part 2 of ISO/IEC 15909. But, there is not yet a mechanism for structuring large Petri nets and for constructing Petri nets from modules. To this end, modular PNML has been proposed some time ago. But, mod...... of Petri net, but still has a strict type system. This paper focuses on the ideas and concepts; the technical details still need to be worked out. To this end, this paper also raises some issues and questions that need to be discussed before standardising modular PNML....
A Convex Optimization Model and Algorithm for Retinex
Directory of Open Access Journals (Sweden)
Qing-Nan Zhao
2017-01-01
Full Text Available Retinex is a theory on simulating and explaining how human visual system perceives colors under different illumination conditions. The main contribution of this paper is to put forward a new convex optimization model for Retinex. Different from existing methods, the main idea is to rewrite a multiplicative form such that the illumination variable and the reflection variable are decoupled in spatial domain. The resulting objective function involves three terms including the Tikhonov regularization of the illumination component, the total variation regularization of the reciprocal of the reflection component, and the data-fitting term among the input image, the illumination component, and the reciprocal of the reflection component. We develop an alternating direction method of multipliers (ADMM to solve the convex optimization model. Numerical experiments demonstrate the advantages of the proposed model which can decompose an image into the illumination and the reflection components.
Convexity and the Euclidean Metric of Space-Time
Directory of Open Access Journals (Sweden)
Nikolaos Kalogeropoulos
2017-02-01
Full Text Available We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.
On the stretch factor of convex Delaunay graphs
Directory of Open Access Journals (Sweden)
Prosenjit Bose
2010-06-01
Full Text Available Let C be a compact and convex set in the plane that contains the origin in its interior, and let S be a finite set of points in the plane. The Delaunay graph DGC(S of S is defined to be the dual of the Voronoi diagram of S with respect to the convex distance function defined by C. We prove that DGC(S is a t-spanner for S, for some constant t that depends only on the shape of the set C. Thus, for any two points p and q in S, the graph DGC(S contains a path between p and q whose Euclidean length is at most t times the Euclidean distance between p and q.
A Survey on Operator Monotonicity, Operator Convexity, and Operator Means
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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.
Non-strictly black body spectrum from the tunnelling mechanism
International Nuclear Information System (INIS)
Corda, Christian
2013-01-01
The tunnelling mechanism is widely used to explain Hawking radiation. However, in many cases the analysis used to obtain the Hawking temperature only involves comparing the emission probability for an outgoing particle with the Boltzmann factor. Banerjee and Majhi improved this approach by explicitly finding a black body spectrum associated with black holes. Their result, obtained using a reformulation of the tunnelling mechanism, is in contrast to that of Parikh and Wilczek, who found an emission probability that is compatible with a non-strictly thermal spectrum. Using the recently identified effective state for a black hole, we solve this contradiction via a slight modification of the analysis by Banerjee and Majhi. The final result is a non-strictly black body spectrum from the tunnelling mechanism. We also show that for an effective temperature, we can express the corresponding effective metric using Hawking’s periodicity arguments. Potential important implications for the black hole information puzzle are discussed. -- Highlights: •We review an important result by Banerjee and Majhi on the tunnelling mechanism in the framework of Hawking radiation. •This result is in contrast to another result reported by Parikh and Wilczek. •We introduce the effective state of a black hole. •We explain the contrast via a slight modification of the analysis by Banerjee and Majhi. •We discuss potential important implications for the black hole information puzzle
Moduli spaces of convex projective structures on surfaces
DEFF Research Database (Denmark)
Fock, V. V.; Goncharov, A. B.
2007-01-01
We introduce explicit parametrisations of the moduli space of convex projective structures on surfaces, and show that the latter moduli space is identified with the higher Teichmüller space for defined in [V.V. Fock, A.B. Goncharov, Moduli spaces of local systems and higher Teichmüller theory, math.......AG/0311149]. We investigate the cluster structure of this moduli space, and define its quantum version....
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
Czech Academy of Sciences Publication Activity Database
Gabriyelyan, S.; Kąkol, Jerzy
2017-01-01
Roč. 111, č. 2 (2017), s. 575-585 ISSN 1578-7303 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : compact resolution * free locally convex space * G-base Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.690, year: 2016 http://link.springer.com/article/10.1007%2Fs13398-016-0315-1
A formulation of combinatorial auction via reverse convex programming
Directory of Open Access Journals (Sweden)
Henry Schellhorn
2005-01-01
of this problem, where orders are aggregated and integrality constraints are relaxed. It was proved that this problem could be solved efficiently in two steps by calculating two fixed points, first the fixed point of a contraction mapping, and then of a set-valued function. In this paper, we generalize the problem to incorporate constraints on maximum price changes between two auction rounds. This generalized problem cannot be solved by the aforementioned methods and necessitates reverse convex programming techniques.
Some fixed point theorems on non-convex sets
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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
Czech Academy of Sciences Publication Activity Database
Kočvara, Michal; Stingl, M.
2003-01-01
Roč. 18, č. 3 (2003), s. 317-333 ISSN 1055-6788 R&D Projects: GA ČR GA201/00/0080 Grant - others:BMBF(DE) 03ZOM3ER Institutional research plan: CEZ:AV0Z1075907 Keywords : convex programming * semidefinite programming * large-scale problems Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.306, year: 2003
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
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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.
Strict calculation of electron energy distribution functions in inhomogeneous plasmas
International Nuclear Information System (INIS)
Winkler, R.
1996-01-01
It is objective of the paper to report on strict calculations of the velocity or energy distribution function function and related macroscopic properties of the electrons from appropriate electron kinetic equations under various plasma conditions and to contribute to a better understanding of the electron behaviour in inhomogeneous plasma regions. In particular, the spatial relaxation of plasma electrons acted upon by uniform electric fields, the response of plasma electrons on spatial disturbances of the electric field, the electron kinetics under the impact of space charge field confinement in the dc column plasma and the electron velocity distribution is stronger field as occurring in the electrode regions of a dc glow discharge is considered. (author)
Asymptotic state discrimination and a strict hierarchy in distinguishability norms
Energy Technology Data Exchange (ETDEWEB)
Chitambar, Eric [Department of Physics and Astronomy, Southern Illinois University, Carbondale, Illinois 62901 (United States); Hsieh, Min-Hsiu [Centre for Quantum Computation and Intelligent Systems (QCIS), Faculty of Engineering and Information Technology (FEIT), University of Technology Sydney - UTS, NSW 2007 (Australia)
2014-11-15
In this paper, we consider the problem of discriminating quantum states by local operations and classical communication (LOCC) when an arbitrarily small amount of error is permitted. This paradigm is known as asymptotic state discrimination, and we derive necessary conditions for when two multipartite states of any size can be discriminated perfectly by asymptotic LOCC. We use this new criterion to prove a gap in the LOCC and separable distinguishability norms. We then turn to the operational advantage of using two-way classical communication over one-way communication in LOCC processing. With a simple two-qubit product state ensemble, we demonstrate a strict majorization of the two-way LOCC norm over the one-way norm.
Growth of a Strictly Anaerobic Bacterium on Furfural (2-Furaldehyde)
Brune, Gerhard; Schoberth, Siegfried M.; Sahm, Hermann
1983-01-01
A strictly anaerobic bacterium was isolated from a continuous fermentor culture which converted the organic constituents of sulfite evaporator condensate to methane and carbon dioxide. Furfural is one of the major components of this condensate. This furfural isolate could degrade furfural as the sole source of carbon and energy in a defined mineral-vitamin-sulfate medium. Acetic acid was the major fermentation product. This organism could also use ethanol, lactate, pyruvate, or fumarate and contained cytochrome c3 and desulfoviridin. Except for furfural degradation, the characteristics of the furfural isolate were remarkably similar to those of the sulfate reducer Desulfovibrio gigas. The furfural isolate has been tentatively identified as Desulfovibrio sp. strain F-1. Images PMID:16346423
Effects of a strict cutoff on Quantum Field Theory
International Nuclear Information System (INIS)
Sturnfield, J.F.
1987-01-01
Standard Quantum Field Theory has a number of integrals which are infinite. Although these are eliminated for some cases by renormalization, this aspect of the theory is not fully satisfactory. A number of theories with fundamental lengths have been introduced as alternatives and it would be useful to be able to distinguish between them. In particular, the effects that a strict cutoff would have on Quantum Field Theory is studied. It is noted that care must be taken in the method used to apply a strict cutoff. This lead to considering a theory where the cutoffs are defined by restricting each internal line. This theory is only piece-wise analytic. The resulting scattering matrix is frame dependent, yet the theory still satisfies the special relativity view that all frames are subjectively identical. The renormalization of this theory is finite. The change in mass from the electron self-energy will be a spinor operator. The main distinctions of this theory from standard theory will occur at super high energies. New poles and resonances which arise from new endpoint singularities will be found. The locations of these singularities will be frame dependent. Some of these singularities will correspond to creations or interactions of the normal particles with tachyons. It will be shown that for the one loop diagram, the form of the cutoff singularities are closely related to the standard singularities. When there is more than one loop, there can appear some new type of behavior. In particular, a cube root type of behavior in the two loop self-energy diagram will be found. Also the asymptotic behavior of the ladder diagram is studied
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
DEFF Research Database (Denmark)
Kiderlen, Markus
2006-01-01
We consider maps of the family of convex bodies in Euclidean d-dimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d>2, a representation theorem for such maps......-endomorphisms, where additivity is now understood with respect to Blaschke-addition. Using a special mixed volume, an adjoining operator can be introduced. This operator allows one to identify the class of Blaschke-endomorphisms with the class of weakly monotonic, non-degenerate and translation-covariant Minkowski...
Convex models and probabilistic approach of nonlinear fatigue failure
International Nuclear Information System (INIS)
Qiu Zhiping; Lin Qiang; Wang Xiaojun
2008-01-01
This paper is concerned with the nonlinear fatigue failure problem with uncertainties in the structural systems. In the present study, in order to solve the nonlinear problem by convex models, the theory of ellipsoidal algebra with the help of the thought of interval analysis is applied. In terms of the inclusion monotonic property of ellipsoidal functions, the nonlinear fatigue failure problem with uncertainties can be solved. A numerical example of 25-bar truss structures is given to illustrate the efficiency of the presented method in comparison with the probabilistic approach
Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities
Czech Academy of Sciences Publication Activity Database
Imre, C.; Matúš, František
2012-01-01
Roč. 48, č. 4 (2012), s. 637-689 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539; GA ČR GAP202/10/0618 Institutional support: RVO:67985556 Keywords : maximum entropy * moment constraint * generalized primal/dual solutions * normal integrand * convex duality * Bregman projection * inference principles Subject RIV: BA - General Mathematics Impact factor: 0.619, year: 2012 http://library.utia.cas.cz/separaty/2012/MTR/matus-0381750.pdf
Iterative Schemes for Convex Minimization Problems with Constraints
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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
Energy Technology Data Exchange (ETDEWEB)
Voynov, A S [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2013-08-31
We study the structure of convex bodies in R{sup d} that can be represented as a union of their affine images with no common interior points. Such bodies are called self-affine. Vallet's conjecture on the structure of self-affine bodies was proved for d = 2 by Richter in 2011. In the present paper we disprove the conjecture for all d≥3 and derive a detailed description of self-affine bodies in R{sup 3}. Also we consider the relation between properties of self-affine bodies and functional equations with a contraction of an argument. Bibliography: 10 titles.
Efficient FPT Algorithms for (Strict) Compatibility of Unrooted Phylogenetic Trees.
Baste, Julien; Paul, Christophe; Sau, Ignasi; Scornavacca, Celine
2017-04-01
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species X; these relationships are often depicted via a phylogenetic tree-a tree having its leaves labeled bijectively by elements of X and without degree-2 nodes-called the "species tree." One common approach for reconstructing a species tree consists in first constructing several phylogenetic trees from primary data (e.g., DNA sequences originating from some species in X), and then constructing a single phylogenetic tree maximizing the "concordance" with the input trees. The obtained tree is our estimation of the species tree and, when the input trees are defined on overlapping-but not identical-sets of labels, is called "supertree." In this paper, we focus on two problems that are central when combining phylogenetic trees into a supertree: the compatibility and the strict compatibility problems for unrooted phylogenetic trees. These problems are strongly related, respectively, to the notions of "containing as a minor" and "containing as a topological minor" in the graph community. Both problems are known to be fixed parameter tractable in the number of input trees k, by using their expressibility in monadic second-order logic and a reduction to graphs of bounded treewidth. Motivated by the fact that the dependency on k of these algorithms is prohibitively large, we give the first explicit dynamic programming algorithms for solving these problems, both running in time [Formula: see text], where n is the total size of the input.
Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1993-05-01
It is proved that the Mann iteration process converges strongly to the fixed point of a strictly hemi-contractive map in real uniformly smooth Banach spaces. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets. A related result deals with the Ishikawa iteration scheme when the mapping is Lipschitzian and strictly hemi-contractive. Our theorems generalize important known results. (author). 29 refs
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.
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
Directory of Open Access Journals (Sweden)
Yang Cao
2018-02-01
Full Text Available Sequential change-point detection when the distribution parameters are unknown is a fundamental problem in statistics and machine learning. When the post-change parameters are unknown, we consider a set of detection procedures based on sequential likelihood ratios with non-anticipating estimators constructed using online convex optimization algorithms such as online mirror descent, which provides a more versatile approach to tackling complex situations where recursive maximum likelihood estimators cannot be found. When the underlying distributions belong to a exponential family and the estimators satisfy the logarithm regret property, we show that this approach is nearly second-order asymptotically optimal. This means that the upper bound for the false alarm rate of the algorithm (measured by the average-run-length meets the lower bound asymptotically up to a log-log factor when the threshold tends to infinity. Our proof is achieved by making a connection between sequential change-point and online convex optimization and leveraging the logarithmic regret bound property of online mirror descent algorithm. Numerical and real data examples validate our theory.
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
DEFF Research Database (Denmark)
Fischer, Paul
1997-01-01
This paper investigates the problem where one is given a finite set of n points in the plane each of which is labeled either ?positive? or ?negative?. We consider bounded convex polygons, the vertices of which are positive points and which do not contain any negative point. It is shown how...... such a polygon which is maximal with respect to area can be found in time O(n³ log n). With the same running time one can also find such a polygon which contains a maximum number of positive points. If, in addition, the number of vertices of the polygon is restricted to be at most M, then the running time...... becomes O(M n³ log n). It is also shown how to find a maximum convex polygon which contains a given point in time O(n³ log n). Two parallel algorithms for the basic problem are also presented. The first one runs in time O(n log n) using O(n²) processors, the second one has polylogarithmic time but needs O...
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
International Nuclear Information System (INIS)
Grasmair, Markus
2010-01-01
We generalize the notion of Bregman distance using concepts from abstract convexity in order to derive convergence rates for Tikhonov regularization with non-convex regularization terms. In particular, we study the non-convex regularization of linear operator equations on Hilbert spaces, showing that the conditions required for the application of the convergence rates results are strongly related to the standard range conditions from the convex case. Moreover, we consider the setting of sparse regularization, where we show that a rate of order δ 1/p holds, if the regularization term has a slightly faster growth at zero than |t| p
First-order Convex Optimization Methods for Signal and Image Processing
DEFF Research Database (Denmark)
Jensen, Tobias Lindstrøm
2012-01-01
In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can...... be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple...
Disordered strictly jammed binary sphere packings attain an anomalously large range of densities
Hopkins, Adam B.; Stillinger, Frank H.; Torquato, Salvatore
2013-08-01
Previous attempts to simulate disordered binary sphere packings have been limited in producing mechanically stable, isostatic packings across a broad spectrum of packing fractions. Here we report that disordered strictly jammed binary packings (packings that remain mechanically stable under general shear deformations and compressions) can be produced with an anomalously large range of average packing fractions 0.634≤ϕ≤0.829 for small to large sphere radius ratios α restricted to α≥0.100. Surprisingly, this range of average packing fractions is obtained for packings containing a subset of spheres (called the backbone) that are exactly strictly jammed, exactly isostatic, and also generated from random initial conditions. Additionally, the average packing fractions of these packings at certain α and small sphere relative number concentrations x approach those of the corresponding densest known ordered packings. These findings suggest for entropic reasons that these high-density disordered packings should be good glass formers and that they may be easy to prepare experimentally. We also identify an unusual feature of the packing fraction of jammed backbones (packings with rattlers excluded). The backbone packing fraction is about 0.624 over the majority of the α-x plane, even when large numbers of small spheres are present in the backbone. Over the (relatively small) area of the α-x plane where the backbone is not roughly constant, we find that backbone packing fractions range from about 0.606 to 0.829, with the volume of rattler spheres comprising between 1.6% and 26.9% of total sphere volume. To generate isostatic strictly jammed packings, we use an implementation of the Torquato-Jiao sequential linear programming algorithm [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.82.061302 82, 061302 (2010)], which is an efficient producer of inherent structures (mechanically stable configurations at the local maxima in the density landscape). The identification and
Shimao, Hajime; Nakamaru, Mayuko
2013-01-01
Whether costly punishment encourages cooperation is one of the principal questions in studies on the evolution of cooperation and social sciences. In society, punishment helps deter people from flouting rules in institutions. Specifically, graduated punishment is a design principle for long-enduring common-pool resource institutions. In this study, we investigate whether graduated punishment can promote a higher cooperation level when each individual plays the public goods game and has the opportunity to punish others whose cooperation levels fall below the punisher’s threshold. We then examine how spatial structure affects evolutionary dynamics when each individual dies inversely proportional to the game score resulting from the social interaction and another player is randomly chosen from the population to produce offspring to fill the empty site created after a player’s death. Our evolutionary simulation outcomes demonstrate that stricter punishment promotes increased cooperation more than graduated punishment in a spatially structured population, whereas graduated punishment increases cooperation more than strict punishment when players interact with randomly chosen opponents from the population. The mathematical analysis also supports the results. PMID:23555826
Directory of Open Access Journals (Sweden)
Hajime Shimao
Full Text Available Whether costly punishment encourages cooperation is one of the principal questions in studies on the evolution of cooperation and social sciences. In society, punishment helps deter people from flouting rules in institutions. Specifically, graduated punishment is a design principle for long-enduring common-pool resource institutions. In this study, we investigate whether graduated punishment can promote a higher cooperation level when each individual plays the public goods game and has the opportunity to punish others whose cooperation levels fall below the punisher's threshold. We then examine how spatial structure affects evolutionary dynamics when each individual dies inversely proportional to the game score resulting from the social interaction and another player is randomly chosen from the population to produce offspring to fill the empty site created after a player's death. Our evolutionary simulation outcomes demonstrate that stricter punishment promotes increased cooperation more than graduated punishment in a spatially structured population, whereas graduated punishment increases cooperation more than strict punishment when players interact with randomly chosen opponents from the population. The mathematical analysis also supports the results.
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
Nonparametric instrumental regression with non-convex constraints
International Nuclear Information System (INIS)
Grasmair, M; Scherzer, O; Vanhems, A
2013-01-01
This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, such as integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition. (paper)
Nonparametric instrumental regression with non-convex constraints
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
International Nuclear Information System (INIS)
Majumdar, A; Robbins, J M; Zyskin, M
2004-01-01
We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants. For a right rectangular prism and a large class of topologies, we derive upper bounds by introducing test configurations constructed from local conformal solutions of the Euler-Lagrange equation. The ratio of the upper and lower bounds depends only on the aspect ratios of the prism. As the aspect ratios are varied, the minimum-energy conformal state undergoes a sharp transition from being smooth to having singularities on the edges. (letter to the editor)
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
DEFF Research Database (Denmark)
Andresen, Henrik; Nikolov, Svetoslav; Pedersen, M M
2008-01-01
Volumetric imaging can be performed using 1D arrays in combination with mechanical motion. Outside the elevation focus of the array, the resolution and contrast quickly degrade compared to the azimuth plane, because of the fixed transducer focus. The purpose of this paper is to use synthetic...... aperture focusing (SAF) for enhancing the elevation focusing for a convex rocking array, to obtain a more isotropic point spread function. This paper presents further development of the SAF method, which can be used with curved array combined with a rocking motion. The method uses a virtual source (VS...... Kretztechnik, Zipf, Austria). The array has an elevation focus at 60 mm of depth, and the angular rocking velocity is up to 140deg/s. The scan sequence uses an fprf of 4500 - 7000 Hz allowing up to 15 cm of penetration. The full width at half max (FWHM) and main-lobe to side-lobe ratio (MLSL) is used...
Approximating convex Pareto surfaces in multiobjective radiotherapy planning
International Nuclear Information System (INIS)
Craft, David L.; Halabi, Tarek F.; Shih, Helen A.; Bortfeld, Thomas R.
2006-01-01
Radiotherapy planning involves inherent tradeoffs: the primary mission, to treat the tumor with a high, uniform dose, is in conflict with normal tissue sparing. We seek to understand these tradeoffs on a case-to-case basis, by computing for each patient a database of Pareto optimal plans. A treatment plan is Pareto optimal if there does not exist another plan which is better in every measurable dimension. The set of all such plans is called the Pareto optimal surface. This article presents an algorithm for computing well distributed points on the (convex) Pareto optimal surface of a multiobjective programming problem. The algorithm is applied to intensity-modulated radiation therapy inverse planning problems, and results of a prostate case and a skull base case are presented, in three and four dimensions, investigating tradeoffs between tumor coverage and critical organ sparing
Convex Relaxations for a Generalized Chan-Vese Model
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
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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
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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 ...
African Journals Online (AJOL)
The notions of convex analysis are indispensable in theoretical and applied Mathematics especially in the study of Calculus where it has a natural generalization for the several variables case. This paper investigates the concept of Fuzzy set theory in relation to the idea of convexity. Some fundamental theorems were ...
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
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.
Energy Technology Data Exchange (ETDEWEB)
Yoo, Ik Dong; Kim, Sung Hoon; Seo, Ye Young; Oh, Jin Kyoung; O, Joo Hyun; Chung, Soo Kyo [The Catholic Univ. of Korea, Seoul (Korea, Republic of)
2012-03-15
To decrease the risk of recurrence or metastasis in differentiated thyroid cancer (DTC), selected patients receive radioactive iodine ablation of remnant thyroid tissue or tumor. A low iodine diet can enhance uptake of radioactive iodine. We compared the success rates of radioactive iodine ablation therapy in patients who followed two different low iodine diets (LIDs). The success rates of postsurgical radioactive iodine ablation in DTC patients receiving empiric doses of 150 mCi were retrospectively reviewed. First-time radioactive iodine ablation therapy was done in 71 patients following less strict LID. Less strict LID restricted seafood, iodized salt, egg yolk, dairy products, processed meat, instant prepared meals, and multivitamins. Very strict LID additionally restricted rice, freshwater fish, spinach, and soybean products. Radioactive iodine ablation therapy was considered successful when follow up {sup 123I} whole body scan was negative and stimulated serum thyroglobulin level was less than 2.0 ng/mL. The success rate of patients following less strict LID was 80.3% and for very strict LID 75.6%. There was no statistically significant difference in the success rates between the two LID groups (P=0.48). Very strict LID may not contribute to improving the success rate of initial radioactive iodine ablation therapy at the cost of great inconvenience to the patient.
DEFF Research Database (Denmark)
Xia, Xiaojuan; Ruwald, Anne-Christine; Ruwald, Martin H
2017-01-01
AIMS: Strict left bundle branch block (LBBB) criteria were recently proposed to identify LBBB patients to benefit most from cardiac resynchronization therapy (CRT). The aim of our study was to automate identification of strict LBBB in order to facilitate its broader application. METHODS: We devel...
The Effect of the Strictness of Consultation Requirements on Fraud Consultation
Gold, A.H.; Knechel, W.R.; Wallage, P.
2012-01-01
We investigate how the strictness of a requirement to consult on potential client fraud affects auditors' propensity to consult with firm experts. We consider two specific forms of guidance about fraud consultations: (1) strict, i.e., mandatory and binding; and (2) lenient, i.e., advisory and
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.
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.
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.
Link Prediction via Convex Nonnegative Matrix Factorization on Multiscale Blocks
Directory of Open Access Journals (Sweden)
Enming Dong
2014-01-01
Full Text Available Low rank matrices approximations have been used in link prediction for networks, which are usually global optimal methods and lack of using the local information. The block structure is a significant local feature of matrices: entities in the same block have similar values, which implies that links are more likely to be found within dense blocks. We use this insight to give a probabilistic latent variable model for finding missing links by convex nonnegative matrix factorization with block detection. The experiments show that this method gives better prediction accuracy than original method alone. Different from the original low rank matrices approximations methods for link prediction, the sparseness of solutions is in accord with the sparse property for most real complex networks. Scaling to massive size network, we use the block information mapping matrices onto distributed architectures and give a divide-and-conquer prediction method. The experiments show that it gives better results than common neighbors method when the networks have a large number of missing links.
Convergence theorems for quasi-contractive maps in uniformly convex spaces
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1992-04-01
Let K be a nonempty closed convex and bounded subset of a real uniformly convex Banach space E of modulus of convexity of power type q≥2. Let T by a quasi-contractive mapping of K into itself. It is proved that each of two well known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of T in K. Our theorems generalize important known results. (author). 22 refs
A 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.
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
International Nuclear Information System (INIS)
Saint-Cyr, B.
2011-01-01
We model in this work granular materials composed of non-convex and cohesive aggregates, in view of application to the rheology of UO 2 powders. The effect of non convexity is analyzed in terms of bulk quantities (Coulomb internal friction and cohesion) and micromechanical parameters such as texture anisotropy and force transmission. In particular, we find that the packing fraction evolves in a complex manner with the shape non convexity and the shear strength increases but saturates due to interlocking between the aggregates. We introduce simple models to describe these features in terms of micro-mechanical parameters. Furthermore, a systematic investigation of shearing, uniaxial compaction and simple compression of cohesive packings show that bulk cohesion increases with non-convexity but is strongly influenced by the boundary conditions and shear bands or stress concentration. (author) [fr
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
DEFF Research Database (Denmark)
Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui
2016-01-01
This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed...... solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....... sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal...
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
A one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion
International Nuclear Information System (INIS)
Suidan, T M
2001-01-01
The surprising connection between a one-dimensional gravitationally interacting gas of sticky particles and the convex minorant process generated by Brownian motion on [0,1] is studied. A study is made of the dynamics of this 1-D gas system by identifying three distinct clustering regimes and the time scales at which they occur. At the critical moment of time the mass distribution of the gas can be computed in terms of functionals of the convex minorant process
Directory of Open Access Journals (Sweden)
Weilin Nie
2017-01-01
Full Text Available Abstract Convex risk minimization is a commonly used setting in learning theory. In this paper, we firstly give a perturbation analysis for such algorithms, and then we apply this result to differential private learning algorithms. Our analysis needs the objective functions to be strongly convex. This leads to an extension of our previous analysis to the non-differentiable loss functions, when constructing differential private algorithms. Finally, an error analysis is then provided to show the selection for the parameters.
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
International Nuclear Information System (INIS)
Yamamoto, Kazuya
2007-05-01
The International Atomic Energy Agency (IAEA) carried out a large-scale international emergency response exercise in 2005 under the designated name of ConvEx-3(2005), at Romania. This review report summarizes a study about ConvEx-3(2005) based on several related open literature. The ConvEx-3 was conducted in accordance with Agency's safety standard series and requirements in the field of Emergency Preparedness and Response. The study on the preparation, conduct and evaluation of ConvEx-3(2005) exercise is expected to provide very useful knowledge for development of drills and educational programs conducted by Nuclear Emergency Assistance and Training Center (NEAT). Especially, study on the exercise evaluations is instrumental in improving evaluations of drills planned by the national government and local governments. As international cooperation among Asian countries in the field of nuclear emergency preparedness and response is going to realize, it is very useful to survey and consider scheme and methodology about international emergency preparedness, response and exercise referring the knowledge of this ConvEx-3 study. The lessons learned from this study of ConvEx-3(2005) are summarized in four chapters; methodology of exercises and educational programs, exercise evaluation process, amendments/verification of the emergency response plan of NEAT, and technical issues of systems for emergency response and assistance of NEAT relevant to interface for international emergency communication. (author)
Reactive solid surface morphology variation via ionic diffusion.
Sun, Zhenchao; Zhou, Qiang; Fan, Liang-Shih
2012-08-14
In gas-solid reactions, one of the most important factors that determine the overall reaction rate is the solid morphology, which can be characterized by a combination of smooth, convex and concave structures. Generally, the solid surface structure varies in the course of reactions, which is classically noted as being attributed to one or more of the following three mechanisms: mechanical interaction, molar volume change, and sintering. Here we show that if a gas-solid reaction involves the outward ionic diffusion of a solid-phase reactant then this outward ionic diffusion could eventually smooth the surface with an initial concave and/or convex structure. Specifically, the concave surface is filled via a larger outward diffusing surface pointing to the concave valley, whereas the height of the convex surface decreases via a lower outward diffusion flux in the vertical direction. A quantitative 2-D continuum diffusion model is established to analyze these two morphological variation processes, which shows consistent results with the experiments. This surface morphology variation by solid-phase ionic diffusion serves to provide a fourth mechanism that supplements the traditionally acknowledged solid morphology variation or, in general, porosity variation mechanisms in gas-solid reactions.
International Nuclear Information System (INIS)
Wang Jing; Gao Jinfeng; Ma Xikui
2007-01-01
This Letter presents a novel cross active backstepping design method for synchronization control of cross-strict feedback hyperchaotic system, in which the ordinary backstepping design is unavailable. The proposed control method, combining backstepping design and active control approach, extends the application of backstepping technique in chaos control. Based on this method, different combinations of controllers can be designed to meet the needs of different applications. The proposed method is applied to achieve chaos synchronization of two identical cross-strict feedback hyperchaotic systems. Also it is used to implement synchronization between cross-strict feedback hyperchaotic system and Roessler hyperchaotic system. Numerical examples illustrate the validity of the control method
International Nuclear Information System (INIS)
Nyagu, A.I.; Yukhimuk, L.N.; Egorova, D.M.; Pogontseva, I.M.
1992-01-01
The blood of 118 people permanently working within the area of strict radiation control has been investigated. Erythrocyte morphofunctional value has been estimated taking into consideration the erythrocyte morphological index as well as mechanical and osmotic resistivity of erythrocytes. For people permanently working within the area of strict radiation control intensity of signals of EPR for blood paramagnetic centres essentially changes. It proves profound changes in functioning of blood plasma antioxidant system for people working in the area of strict radiation control. For the people permanently working within the area of strict radiation control in peripheric blood growth of echynocytes and spherocytes as well as lowering of mechanical resistivity of erythrocytes is observed. 4 refs.; 1 fig.; 1 tab
Strict deformation quantization for actions of a class of symplectic lie groups
International Nuclear Information System (INIS)
Bieliavsky, Pierre; Massar, Marc
2002-01-01
We present explicit universal strict deformation quantization formulae for actions of Iwasawa subgroups AN of SN(1, n). This answers a question raised by Rieffel in [Contemp. Math. 228 (1998), 315]. (author)
Do strict rules and moving images increase the reliability of sequential identification procedures?.
Valentine, Tim; Darling, Stephen; Memon, Amina
2007-01-01
Live identification procedures in England and Wales have been replaced by use of video, which provides a sequential presentation of facial images. Sequential presentation of photographs provides some protection to innocent suspects from mistaken identification when used with strict instructions designed to prevent relative judgements (Lindsay, Lea & Fulford, 1991). However, the current procedure in England and Wales is incompatible with these strict instructions. The reported research investi...
Strict optical orthogonal codes for purely asynchronous code-division multiple-access applications
Zhang, Jian-Guo
1996-12-01
Strict optical orthogonal codes are presented for purely asynchronous optical code-division multiple-access (CDMA) applications. The proposed code can strictly guarantee the peaks of its cross-correlation functions and the sidelobes of any of its autocorrelation functions to have a value of 1 in purely asynchronous data communications. The basic theory of the proposed codes is given. An experiment on optical CDMA systems is also demonstrated to verify the characteristics of the proposed code.
International Nuclear Information System (INIS)
Phan Thanh An
2008-06-01
The convex rope problem, posed by Peshkin and Sanderson in IEEE J. Robotics Automat, 2 (1986) pp. 53-58, is to find the counterclockwise and clockwise convex ropes starting at the vertex a and ending at the vertex b of a simple polygon, where a is on the boundary of the convex hull of the polygon and b is visible from infinity. In this paper, we present a linear time algorithm for solving this problem without resorting to a linear-time triangulation algorithm and without resorting to a convex hull algorithm for the polygon. The counterclockwise (clockwise, respectively) convex rope consists of two polylines obtained in a basic incremental strategy described in convex hull algorithms for the polylines forming the polygon from a to b. (author)
Einstein and solid-state physics
International Nuclear Information System (INIS)
Aut, I.
1982-01-01
A connection between the development of solid-state physics and the works and activity of Albert Einstein is traced. A tremendous Einstein contribution to solid state physics is marked. A strict establishment of particle-wave dualism; a conclusion about the applicability of the Plank radiation law not only to black body radiation; finding out particles indistinguishability - all three discoveries have a principle significance for solid state physics too
Isolated abnormal strict morphology is not a contraindication for intrauterine insemination.
Lockwood, G M; Deveneau, N E; Shridharani, A N; Strawn, E Y; Sandlow, J I
2015-11-01
This study sought to investigate whether isolated abnormal strict morphology (<5% normal forms) and very low strict morphology (0-1% normal forms) affects pregnancy rates in intrauterine insemination (IUI). This was a retrospective study performed at an Academic Medical Center/Reproductive Medicine Center. Four hundred and eight couples were included for 856 IUI cycles. 70 IUI cycles were performed in couples with abnormal strict morphology and otherwise normal semen parameters. Outcomes were measured as clinical pregnancy rate per IUI cycle as documented by fetal heart activity on maternal ultrasound. Clinical pregnancy rate did not significantly differ between the group with abnormal strict morphology [11/70 (15.7%)] and the normal morphology group [39/281 (13.9%)]. Additionally, there was no significant difference between the pregnancy rate in the abnormal morphology group compared to that of our overall institutional IUI pregnancy rate [145/856 (16.9%)]. Furthermore, there was no significant difference between pregnancy rate in the very low morphology group [3/14 (21.4%)] compared to those with normal morphology or the overall IUI pregnancy rate. Patients with isolated abnormal strict morphology have clinical pregnancy rates similar to those with normal morphology for IUI. Even in those with very low normal forms, consideration of IUI for assisted reproduction should not be excluded. © 2015 American Society of Andrology and European Academy of Andrology.
A European map regarding the strictness of the transfer pricing regulations
Directory of Open Access Journals (Sweden)
Ioana Ignat
2017-12-01
Full Text Available In the context in which transfer pricing may represent a mechanism through which multinationals have the possibility to move funds internationally, in order to prevent the base erosion and profit shifting between multinationals, countries over the world have adopted various transfer pricing regulations. Furthermore, some of the countries adopted stricter regulations than others. The objective of our research was to identify the level of strictness for the transfer pricing regulations from the European countries. To achieve this objective, we analyzed the transfer pricing regulations of all European countries and we built a transfer pricing strictness index, based on which we defined 4 categories of countries (where category 1 includes the countries with the least strict transfer pricing regulations and category 4 countries with the strictest regulations. After that, we illustrated how these categories are distributed on the European map. In order to collect the information, we used the transfer pricing guides issued by the Big Four companies for the year 2015. The study`s results show that the strictness of the transfer pricing regulations decreases from the west of Europe to east. Moreover, most of the countries were included in category 2, respectively category 3, meaning that the transfer pricing regulations from the European continent are not so flexible, but in the same time are not so strict.
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.
DEFF Research Database (Denmark)
Kafle, Bishoksan; Gallagher, John Patrick
2014-01-01
We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of query-answer transformed clauses, and refinement by splitting...... in conjunction with specialisation for propagating constraints it can frequently solve challenging verification problems. This is a contribution in itself, but refinement is needed when it fails, and the question of how to refine convex polyhedral analyses has not been studied much. We present a refinement...... technique based on interpolants derived from a counterexample trace; these are used to drive a property-based specialisation that splits predicates, leading in turn to more precise convex polyhedral analyses. The process of specialisation, analysis and splitting can be repeated, in a manner similar...
Uniform estimate of a compact convex set by a ball in an arbitrary norm
International Nuclear Information System (INIS)
Dudov, S I; Zlatorunskaya, I V
2000-01-01
The problem of the best uniform approximation of a compact convex set by a ball with respect to an arbitrary norm in the Hausdorff metric corresponding to that norm is considered. The question is reduced to a convex programming problem, which can be studied by means of convex analysis. Necessary and sufficient conditions for the solubility of this problem are obtained and several properties of its solution are described. It is proved, in particular, that the centre of at least one ball of best approximation lies in the compact set under consideration; in addition, conditions ensuring that the centres of all balls of best approximation lie in this compact set and a condition for unique solubility are obtained
Schur-Convexity for a Class of Symmetric Functions and Its Applications
Directory of Open Access Journals (Sweden)
Wei-Feng Xia
2009-01-01
Full Text Available For x=(x1,x2,…,xn∈R+n, the symmetric function ϕn(x,r is defined by ϕn(x,r=ϕn(x1,x2,…,xn;r=∏1≤i1
A parallel Discrete Element Method to model collisions between non-convex particles
Directory of Open Access Journals (Sweden)
Rakotonirina Andriarimina Daniel
2017-01-01
Full Text Available In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called “glued-convex method” (in the sense clumping convex bodies together, as an extension of the popular “glued-spheres” method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i the collapse of a granular column made of convex particles and (i the microstructure of a heap of non-convex particles in a cylindrical reactor.
New strict left bundle branch block criteria reflect left ventricular activation differences
DEFF Research Database (Denmark)
Emerek, Kasper Janus Grønn; Risum, Niels; Hjortshøj, Søren Pihlkjær
2015-01-01
AIMS: Pacing lead electrical delays and strict left bundle branch block (LBBB) criteria were assessed against cardiac resynchronization therapy (CRT) outcome. METHODS: Forty-nine patients with LBBB and QRS duration >130 milliseconds underwent CRT-implantation. Sensed right ventricular to left ven....... CONCLUSION: Interventricular electrical delay predicts left ventricular remodeling after CRT and new, strict ECG criteria of LBBB are superior in predicting remodeling.......AIMS: Pacing lead electrical delays and strict left bundle branch block (LBBB) criteria were assessed against cardiac resynchronization therapy (CRT) outcome. METHODS: Forty-nine patients with LBBB and QRS duration >130 milliseconds underwent CRT-implantation. Sensed right ventricular to left...... ventricular electrical delay (RV-LV-IED) was measured. Response to CRT was defined as ≥15% decrease in left ventricular end-systolic volume. RESULTS: Eighteen of 20 (90%) patients with non-ischemic dilated cardiomyopathy (DCM) and 18 of 29 (62%) with ischemic heart disease (IHD) responded to CRT, p
Actions of a separately strict cpo-monoid on pointed directed complete posets
Directory of Open Access Journals (Sweden)
Halimeh Moghbeli Damaneh
2015-07-01
Full Text Available In the present article, we study some categorical properties of the category {$bf Cpo_{Sep}$-$S$} of all {separately strict $S$-cpo's}; cpo's equipped with a compatible right action of a separately strict cpo-monoid $S$ which is strict continuous in each component. In particular, we show that this category is reflective and coreflective in the category of $S$-cpo's, find the free and cofree functors, characterize products and coproducts. Furthermore, epimorphisms and monomorphisms in {$bf Cpo_{Sep}$-$S$} are studied, and show that {$bf Cpo_{Sep}$-$S$} is not cartesian closed.
Method of convex rigid frames and applications in studies of multipartite quNit pure states
International Nuclear Information System (INIS)
Zhong Zaizhe
2005-01-01
In this letter, we suggest a method of convex rigid frames in the studies of multipartite quNit pure states. We illustrate what the convex rigid frames are, and what is their method. As applications, we use this method to solve some basic problems and give some new results (three theorems): the problem of the partial separability of the multipartite quNit pure states and its geometric explanation; the problem of the classification of multipartite quNit pure states, giving a perfect explanation of the local unitary transformations; thirdly, we discuss the invariants of classes and give a possible physical explanation. (letter to the editor)
Optimization of Transverse Oscillating Fields for Vector Velocity Estimation with Convex Arrays
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt
2013-01-01
A method for making Vector Flow Images using the transverse oscillation (TO) approach on a convex array is presented. The paper presents optimization schemes for TO fields for convex probes and evaluates their performance using Field II simulations and measurements using the SARUS experimental...... from 90 to 45 degrees in steps of 15 degrees. The optimization routine changes the lateral oscillation period lx to yield the best possible estimates based on the energy ratio between positive and negative spatial frequencies in the ultrasound field. The basic equation for lx gives 1.14 mm at 40 mm...
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...
The photon is no strict particle and nonlocality is far from being proven
Energy Technology Data Exchange (ETDEWEB)
Greulich, Karl Otto [Fritz Lipmann Institut, Jena (Germany)
2010-07-01
Two aspects of philosophical discussions on physics are the wave particle dualism and non locality including entanglement. However the strict particle aspect of the photon, in the common sense view, has never been proven. The accumulation time argument, the only experimental verification of a strictly particle like photon, has so far not yet been satisfied. Also, experiments thought to prove nonlocality have loophole which have so far not yet been safely closed, and now an even more serious loophole emerges. Thus, also nonlocality cannot be seen as proven. This demands some fine tuning of philosophical discussions on critical experiments in physics.
The Fixed-Point Theory of Strictly Contracting Functions on Generalized Ultrametric Semilattices
Directory of Open Access Journals (Sweden)
Eleftherios Matsikoudis
2013-08-01
Full Text Available We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and in which the meet operation of the semilattice coexists with a generalized distance function in a tightly coordinated way. We prove a constructive fixed-point theorem for strictly contracting functions on directed-complete generalized ultrametric semilattices, and introduce a corresponding induction principle. We cite examples of application in the semantics of logic programming and timed computation, where, until now, the only tool available has been the non-constructive fixed-point theorem of Priess-Crampe and Ribenboim for strictly contracting functions on spherically complete generalized ultrametric semilattices.
International Nuclear Information System (INIS)
Ferraro, Paul J; Hanauer, Merlin M; Miteva, Daniela A; Pattanayak, Subhrendu K; Canavire-Bacarreza, Gustavo Javier; Sims, Katharine R E
2013-01-01
National parks and other protected areas are at the forefront of global efforts to protect biodiversity and ecosystem services. However, not all protection is equal. Some areas are assigned strict legal protection that permits few extractive human uses. Other protected area designations permit a wider range of uses. Whether strictly protected areas are more effective in achieving environmental objectives is an empirical question: although strictly protected areas legally permit less anthropogenic disturbance, the social conflicts associated with assigning strict protection may lead politicians to assign strict protection to less-threatened areas and may lead citizens or enforcement agents to ignore the strict legal restrictions. We contrast the impacts of strictly and less strictly protected areas in four countries using IUCN designations to measure de jure strictness, data on deforestation to measure outcomes, and a quasi-experimental design to estimate impacts. On average, stricter protection reduced deforestation rates more than less strict protection, but the additional impact was not always large and sometimes arose because of where stricter protection was assigned rather than regulatory strictness per se. We also show that, in protected area studies contrasting y management regimes, there are y 2 policy-relevant impacts, rather than only y, as earlier studies have implied. (letter)
Directory of Open Access Journals (Sweden)
Ghulam Farid
2017-10-01
Full Text Available The aim of this paper is to obtain some more general fractional integral inequalities of Fejer Hadamard type for p-convex functions via Riemann-Liouville k-fractional integrals. Also in particular fractional inequalities for p-convex functions via Riemann-Liouville fractional integrals have been deduced.
She's Strict for a Good Reason: Highly Effective Teachers in Low-Performing Urban Schools
Poplin, Mary; Rivera, John; Durish, Dena; Hoff, Linda; Kawell, Susan; Pawlak, Pat; Hinman, Ivannia Soto; Straus, Laura; Veney, Cloetta
2011-01-01
A study of 31 high-performing teachers in low-performing urban schools found that these teachers had certain traits in common. They were strict; they taught in traditional, explicit ways; there was little time in their classrooms when instruction was not occurring; and they moved around the room helping their students. They used very few…
Detection of low numbers of microplastics in North Sea fish using strict quality assurance criteria
Hermsen, E.; Pompe, R.; Besseling, E.; Koelmans, A.A.
2017-01-01
We investigated 400 individual fish of four North Sea species: Atlantic Herring, Sprat, Common Dab, and Whiting on ingestion of > 20 μm microplastic. Strict quality assurance criteria were followed in order to control contamination during the study. Two plastic particles were found in only 1 (a
Martin A. Spetich; Anna E. Kvashnina; Y.D. Nukhimovskya; Olin E. Jr. Rhodes
2009-01-01
One of the most comprehensive attempts at biodiversity conservation in Russia and the former Soviet Union has been the establishment of an extensive network of protected natural areas. Among all types of protected areas in Russia, zapovedniks (strictly protected scientific preserve) have been the most effective in protecting biodiversity at the ecosystem scale. Russia...
The Preventive Effect of Strict Gun Control Laws on Suicide and Homicide.
Lester, David; Murrell, Mary E.
1982-01-01
Examined state gun control laws and used a multidimensional scaling technique to study the relationship of strictness and death rates. Results showed states with stricter laws had lower suicide rates by firearms but higher rates by other means. No effect on homicide was found. (JAC)
Required sample size for monitoring stand dynamics in strict forest reserves: a case study
Diego Van Den Meersschaut; Bart De Cuyper; Kris Vandekerkhove; Noel Lust
2000-01-01
Stand dynamics in European strict forest reserves are commonly monitored using inventory densities of 5 to 15 percent of the total surface. The assumption that these densities guarantee a representative image of certain parameters is critically analyzed in a case study for the parameters basal area and stem number. The required sample sizes for different accuracy and...
ASHP therapeutic position statement on strict glycemic control in patients with diabetes.
2003-11-15
The deleterious effects of hyperglycemia have been documented from the biochemical to the pathophysiologic level. Given the research findings and the guidelines for glycemic control established by ADA and ACE, ASHP supports and encourages strict glycemic control in all appropriate patients with diabetes mellitus to reduce the progression of chronic complications.
Urbig, D.; Stauf, J.; Weitzel, U.|info:eu-repo/dai/nl/276323394
This study contributes to the ongoing discussion on the appropriate measurement of overconfidence, in particular, its strictly incentive compatible measurement in experiments. Despite a number of significant advances in recent research, several important issues remain to be solved. These relate to
Convexity of Energy-Like Functions: Theoretical Results and Applications to Power System Operations
Energy Technology Data Exchange (ETDEWEB)
Dvijotham, Krishnamurthy [California Inst. of Technology (CalTech), Pasadena, CA (United States); Low, Steven [California Inst. of Technology (CalTech), Pasadena, CA (United States); Chertkov, Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-01-12
Power systems are undergoing unprecedented transformations with increased adoption of renewables and distributed generation, as well as the adoption of demand response programs. All of these changes, while making the grid more responsive and potentially more efficient, pose significant challenges for power systems operators. Conventional operational paradigms are no longer sufficient as the power system may no longer have big dispatchable generators with sufficient positive and negative reserves. This increases the need for tools and algorithms that can efficiently predict safe regions of operation of the power system. In this paper, we study energy functions as a tool to design algorithms for various operational problems in power systems. These have a long history in power systems and have been primarily applied to transient stability problems. In this paper, we take a new look at power systems, focusing on an aspect that has previously received little attention: Convexity. We characterize the domain of voltage magnitudes and phases within which the energy function is convex in these variables. We show that this corresponds naturally with standard operational constraints imposed in power systems. We show that power of equations can be solved using this approach, as long as the solution lies within the convexity domain. We outline various desirable properties of solutions in the convexity domain and present simple numerical illustrations supporting our results.
Perimeter generating functions for the mean-squared radius of gyration of convex polygons
International Nuclear Information System (INIS)
Jensen, Iwan
2005-01-01
We have derived long series expansions for the perimeter generating functions of the radius of gyration of various polygons with a convexity constraint. Using the series we numerically find simple (algebraic) exact solutions for the generating functions. In all cases the size exponent ν 1. (letter to the editor)
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
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
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
Parthood and Convexity as the Basic Notions of a Theory of Space
DEFF Research Database (Denmark)
Robering, Klaus
A deductive system of geometry is presented which is based on atomistic mereology ("mereology with points'') and the notion of convexity. The system is formulated in a liberal many-sorted logic which makes use of class-theoretic notions without however adopting any comprehension axioms. The geome...
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
Directory of Open Access Journals (Sweden)
Xuewen Mu
2015-01-01
quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is efficient for the convex quadratic second-order cone programming problems with bounded constraints.
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
Czech Academy of Sciences Publication Activity Database
Šilhavý, Miroslav; Bertram, A.; Böhlke, T.
2007-01-01
Roč. 86, č. 3 (2007), s. 235-243 ISSN 0374-3535 Institutional research plan: CEZ:AV0Z10190503 Keywords : generalized linear elastic law s * generalized strain measures * rank 1 convexity Subject RIV: BA - General Mathematics Impact factor: 0.743, year: 2007
Directory of Open Access Journals (Sweden)
Mengkun Zhu
2015-01-01
Full Text Available Some sharp estimates of coefficients, distortion, and growth for harmonic mappings with analytic parts convex or starlike functions of order β are obtained. We also give area estimates and covering theorems. Our main results generalise those of Klimek and Michalski.
On the Monotonicity and Log-Convexity of a Four-Parameter Homogeneous Mean
Directory of Open Access Journals (Sweden)
Yang Zhen-Hang
2008-01-01
Full Text Available Abstract A four-parameter homogeneous mean is defined by another approach. The criterion of its monotonicity and logarithmically convexity is presented, and three refined chains of inequalities for two-parameter mean values are deduced which contain many new and classical inequalities for means.
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
International Nuclear Information System (INIS)
Egozcue, J.; Meziat, R.; Pedregal, P.
2002-01-01
We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature
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.
Neuro-genetic hybrid approach for the solution of non-convex economic dispatch problem
International Nuclear Information System (INIS)
Malik, T.N.; Asar, A.U.
2009-01-01
ED (Economic Dispatch) is non-convex constrained optimization problem, and is used for both on line and offline studies in power system operation. Conventionally, it is solved as convex problem using optimization techniques by approximating generator input/output characteristic. Curves of monotonically increasing nature thus resulting in an inaccurate dispatch. The GA (Genetic Algorithm) has been used for the solution of this problem owing to its inherent ability to address the convex and non-convex problems equally. This approach brings the solution to the global minimum region of search space in a short time and then takes longer time to converge to near optimal results. GA based hybrid approaches are used to fine tune the near optimal results produced by GA. This paper proposes NGH (Neuro Genetic Hybrid) approach to solve the economic dispatch with valve point effect. The proposed approach combines the GA with the ANN (Artificial Neural Network) using SI (Swarm Intelligence) learning rule. The GA acts as a global optimizer and the neural network fine tunes the GA results to the desired targets. Three machines standard test system has been tested for validation of the approach. Comparing the results with GA and NGH model based on back-propagation learning, the proposed approach gives contrast improvements showing the promise of the approach. (author)
Extreme points of the convex set of joint probability distributions with ...
Indian Academy of Sciences (India)
Here we address the following problem: If G is a standard ... convex set of all joint probability distributions on the product Borel space (X1 ×X2, F1 ⊗. F2) which .... cannot be identically zero when X and Y vary in A1 and u and v vary in H2. Thus.
Mean-square performance of a convex combination of two adaptive filters
DEFF Research Database (Denmark)
Garcia, Jeronimo; Figueiras-Vidal, A.R.; Sayed, A.H.
2006-01-01
Combination approaches provide an interesting way to improve adaptive filter performance. In this paper, we study the mean-square performance of a convex combination of two transversal filters. The individual filters are independently adapted using their own error signals, while the combination i...
Directory of Open Access Journals (Sweden)
San-Yang Liu
2014-01-01
Full Text Available Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large-scale nonsmooth equations.
Robust Nearfield Wideband Beamforming Design Based on Adaptive-Weighted Convex Optimization
Directory of Open Access Journals (Sweden)
Guo Ye-Cai
2017-01-01
Full Text Available Nearfield wideband beamformers for microphone arrays have wide applications in multichannel speech enhancement. The nearfield wideband beamformer design based on convex optimization is one of the typical representatives of robust approaches. However, in this approach, the coefficient of convex optimization is a constant, which has not used all the freedom provided by the weighting coefficient efficiently. Therefore, it is still necessary to further improve the performance. To solve this problem, we developed a robust nearfield wideband beamformer design approach based on adaptive-weighted convex optimization. The proposed approach defines an adaptive-weighted function by the adaptive array signal processing theory and adjusts its value flexibly, which has improved the beamforming performance. During each process of the adaptive updating of the weighting function, the convex optimization problem can be formulated as a SOCP (Second-Order Cone Program problem, which could be solved efficiently using the well-established interior-point methods. This method is suitable for the case where the sound source is in the nearfield range, can work well in the presence of microphone mismatches, and is applicable to arbitrary array geometries. Several design examples are presented to verify the effectiveness of the proposed approach and the correctness of the theoretical analysis.
A 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 ...
Indian Academy of Sciences (India)
Associated with the -curvature image defined by Lutwak, some inequalities for extended mixed -affine surface areas of convex bodies and the support functions of -projection bodies are established. As a natural extension of a result due to Lutwak, an -type affine isoperimetric inequality, whose special cases are ...
On the Fermat-Lagrange principle for mixed smooth convex extremal problems
International Nuclear Information System (INIS)
Brinkhuis, Ya
2001-01-01
A simple geometric condition that can be attached to an extremal problem of a fairly general form included in a family of problems is indicated. This is used to demonstrate that the task of formulating a uniform condition for smooth convex problems can be satisfactorily accomplished. On the other hand, the necessity of this new condition of optimality is proved under certain technical assumptions
A new corrective technique for adolescent idiopathic scoliosis (Ucar′s convex rod rotation
Directory of Open Access Journals (Sweden)
Bekir Yavuz Ucar
2014-01-01
Full Text Available Study Design: Prospective single-center study. Objective: To analyze the efficacy and safety of a new technique of global vertebral correction with convex rod rotation performed on the patients with adolescent idiopathic scoliosis. Summary of Background Data: Surgical goal is to obtain an optimal curve correction in scoliosis surgery. There are various correction techniques. This report describes a new technique of global vertebral correction with convex rod rotation. Materials and Methods: A total of 12 consecutive patients with Lenke type I adolescent idiopathic scoliosis and managed by convex rod rotation technique between years 2012 and 2013 having more than 1 year follow-up were included. Mean age was 14.5 (range = 13-17 years years at the time of operation. The hospital charts were reviewed for demographic data. Measurements of curve magnitude and balance were made on 36-inch standing anteroposterior and lateral radiographs taken before surgery and at most recent follow up to assess deformity correction, spinal balance, and complications related to the instrumentation. Results: Preoperative coronal plane major curve of 62° (range = 50°-72° with flexibility of less than 30% was corrected to 11.5°(range = 10°-14° showing a 81% scoliosis correction at the final follow-up. Coronal imbalance was improved 72% at the most recent follow-up assessment. No complications were found. Conclusion: The new technique of global vertebral correction with Ucar′s convex rod rotation is an effective technique. This method is a vertebral rotation procedure from convex side and it allows to put screws easily to the concave side.
A Hybrid P2P Overlay Network for Non-strictly Hierarchically Categorized Content
Wan, Yi; Asaka, Takuya; Takahashi, Tatsuro
In P2P content distribution systems, there are many cases in which the content can be classified into hierarchically organized categories. In this paper, we propose a hybrid overlay network design suitable for such content called Pastry/NSHCC (Pastry for Non-Strictly Hierarchically Categorized Content). The semantic information of classification hierarchies of the content can be utilized regardless of whether they are in a strict tree structure or not. By doing so, the search scope can be restrained to any granularity, and the number of query messages also decreases while maintaining keyword searching availability. Through simulation, we showed that the proposed method provides better performance and lower overhead than unstructured overlays exploiting the same semantic information.
Detection of low numbers of microplastics in North Sea fish using strict quality assurance criteria.
Hermsen, Enya; Pompe, Renske; Besseling, Ellen; Koelmans, Albert A
2017-09-15
We investigated 400 individual fish of four North Sea species: Atlantic Herring, Sprat, Common Dab, and Whiting on ingestion of >20μm microplastic. Strict quality assurance criteria were followed in order to control contamination during the study. Two plastic particles were found in only 1 (a Sprat) out of 400 individuals (0.25%, with a 95% confidence interval of 0.09-1.1%). The particles were identified to consist of polymethylmethacrylate (PMMA) through FTIR spectroscopy. No contamination occurred during the study, showing the method applied to be suitable for microplastic ingestion studies in biota. We discuss the low particle count for North Sea fish with those in other studies and suggest a relation between reported particle count and degree of quality assurance applied. Microplastic ingestion by fish may be less common than thought initially, with low incidence shown in this study, and other studies adhering to strict quality assurance criteria. Copyright © 2017 Elsevier Ltd. All rights reserved.
S2SA preconditioning for the Sn equations with strictly non negative spatial discretization
International Nuclear Information System (INIS)
Bruss, D. E.; Morel, J. E.; Ragusa, J. C.
2013-01-01
Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S n transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use a linear diffusion equation has important implications for preconditioning the S n equations with a strictly non negative spatial discretization in multiple dimensions. (authors)
Weak asymptotic solution for a non-strictly hyperbolic system of conservation laws-II
Directory of Open Access Journals (Sweden)
Manas Ranjan Sahoo
2016-04-01
Full Text Available In this article we introduce a concept of entropy weak asymptotic solution for a system of conservation laws and construct the same for a prolonged system of conservation laws which is highly non-strictly hyperbolic. This is first done for Riemann type initial data by introducing $\\delta,\\delta',\\delta''$ waves along a discontinuity curve and then for general initial data by piecing together the Riemann solutions.
Energy Technology Data Exchange (ETDEWEB)
Gruzdev, I.A.; Ekimova, M.M.; Truspekova, G.A.
1982-01-01
Expressions are derived for an idealized model of a complex electric power system; these expressions define the greatest level of stability of an electric power system and the optimum combination of stabilization factors with automatic excitation control in a single power system. The possibility of increasing the level of stability of an electric power system with simultaneous strict automatic excitation control of the synychronous generators in several power systems is analyzed.
Directory of Open Access Journals (Sweden)
Chang-ping Zhu
2011-03-01
Full Text Available The process of decomposing p-nitrophenol (PNP with power ultrasound requires strict control of acoustic and electric conditions. In this study, the conditions, including acoustic power and acoustic intensity, but not ultrasonic frequency, were controlled strictly at constant levels. The absorbency and the COD concentrations of the samples were measured in order to show the variation of the sample concentration. The results show significant differences in the trend of the solution degradation rate as acoustic power increases after the PNP solution (with a concentration of 114 mg/L and a pH value of 5.4 is irradiated for 60 min with ultrasonic frequencies of 530.8 kHz, 610.6 kHz, 855.0 kHz, and 1 130.0 kHz. The degradation rate of the solution increases with time and acoustic power (acoustic intensity. On the other hand, the degradation rate of the solution is distinctly dependent on frequency when the acoustic power and intensity are strictly controlled and maintained at constant levels. The degradation rate of the PNP solution declines with ultrasonic frequencies of 530.8 kHz, 610.6 kHz, 855.0 kHz, and 1 130.0 kHz; the COD concentration, on the contrary, increase.
International Nuclear Information System (INIS)
Berry, Ray A.; Martineau, Richard C.
2007-01-01
The conservative-form, pressure-based PCICE numerical method (Martineau and Berry, 2004) (Berry, 2006), recently developed for computing transient fluid flows of all speeds from very low to very high (with strong shocks), is simplified and generalized. Though the method automatically treats a continuous transition of compressibility, three distinct, limiting compressibility regimes are formally defined for purposes of discussion and comparison with traditional methods - the strictly incompressible limit, the nearly incompressible limit, and the fully compressible limit. The PCICE method's behavior is examined in each limiting regime. In the strictly incompressible limit the PCICE algorithm reduces to the traditional MAC-type method with velocity divergence driving the pressure Poisson equation. In the nearly incompressible limit the PCICE algorithm is found to reduce to a generalization of traditional incompressible methods, i.e. to one in which not only the velocity divergence effect, but also the density gradient effect is included as a driving function in the pressure Poisson equation. This nearly incompressible regime has received little attention, and it appears that in the past, strictly incompressible methods may have been conveniently applied to flows in this regime at the expense of ignoring a potentially important coupling mechanism. This could be significant in many important flows; for example, in natural convection flows resulting from high heat flux. In the fully compressible limit or regime, the algorithm is found to reduce to an expression equivalent to density-based methods for high-speed flow. (author)
TESTING STRICT HYDROSTATIC EQUILIBRIUM IN SIMULATED CLUSTERS OF GALAXIES: IMPLICATIONS FOR A1689
International Nuclear Information System (INIS)
Molnar, S. M.; Umetsu, K.; Chiu, I.-N.; Chen, P.; Hearn, N.; Broadhurst, T.; Bryan, G.; Shang, C.
2010-01-01
Accurate mass determination of clusters of galaxies is crucial if they are to be used as cosmological probes. However, there are some discrepancies between cluster masses determined based on gravitational lensing and X-ray observations assuming strict hydrostatic equilibrium (i.e., the equilibrium gas pressure is provided entirely by thermal pressure). Cosmological simulations suggest that turbulent gas motions remaining from hierarchical structure formation may provide a significant contribution to the equilibrium pressure in clusters. We analyze a sample of massive clusters of galaxies drawn from high-resolution cosmological simulations and find a significant contribution (20%-45%) from non-thermal pressure near the center of relaxed clusters, and, in accord with previous studies, a minimum contribution at about 0.1 R vir , growing to about 30%-45% at the virial radius, R vir . Our results strongly suggest that relaxed clusters should have significant non-thermal support in their core region. As an example, we test the validity of strict hydrostatic equilibrium in the well-studied massive galaxy cluster A1689 using the latest high-resolution gravitational lensing and X-ray observations. We find a contribution of about 40% from non-thermal pressure within the core region of A1689, suggesting an alternate explanation for the mass discrepancy: the strict hydrostatic equilibrium is not valid in this region.
Solid waste disposal in the Netherlands
Brasser, L.J.
1990-01-01
In The Netherlands, a small and densely populated country, the disposal of solid waste requires strict precautions. Because the landscape is flat and the watertable just under groundlevel, landfilling and dumping must be avoided as much as possible. Incineration of municipal and industrial waste are
International Nuclear Information System (INIS)
Vu Ngoc Phat; Jong Yeoul Park
1995-10-01
The paper studies a class of set-values operators with emphasis on properties of their adjoints and existence of eigenvalues and eigenvectors of infinite-dimensional convex closed set-valued operators. Sufficient conditions for existence of eigenvalues and eigenvectors of set-valued convex closed operators are derived. These conditions specify possible features of control problems. The results are applied to some constrained control problems of infinite-dimensional systems described by discrete-time inclusions whose right-hand-sides are convex closed set- valued functions. (author). 8 refs
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.
International Nuclear Information System (INIS)
Alabau-Boussouira, Fatiha
2005-01-01
This work is concerned with the stabilization of hyperbolic systems by a nonlinear feedback which can be localized on a part of the boundary or locally distributed. We show that general weighted integral inequalities together with convexity arguments allow us to produce a general semi-explicit formula which leads to decay rates of the energy in terms of the behavior of the nonlinear feedback close to the origin. This formula allows us to unify for instance the cases where the feedback has a polynomial growth at the origin, with the cases where it goes exponentially fast to zero at the origin. We also give three other significant examples of nonpolynomial growth at the origin. We also prove the optimality of our results for the one-dimensional wave equation with nonlinear boundary dissipation. The key property for obtaining our general energy decay formula is the understanding between convexity properties of an explicit function connected to the feedback and the dissipation of energy
Measurement of laser welding pool geometry using a closed convex active contour model
International Nuclear Information System (INIS)
Zheng, Rui; Zhang, Pu; Duan, Aiqing; Xiao, Peng
2014-01-01
The purpose of this study was to develop a computer vision method to measure geometric parameters of the weld pool in a deep penetration CO 2 laser welding system. Accurate measurement was achieved by removing a huge amount of interference caused by spatter, arc light and plasma to extract the true weld pool contour. This paper introduces a closed convex active contour (CCAC) model derived from the active contour model (snake model), which is a more robust high-level vision method than the traditional low-level vision methods. We made an improvement by integrating an active contour with the information that the weld pool contour is almost a closed convex curve. An effective thresholding method and an improved greedy algorithm are also given to complement the CCAC model. These influences can be effectively removed by using the CCAC model to acquire and measure the weld pool contour accurately and relatively fast. (paper)
Parameter sensitivity study of a Field II multilayer transducer model on a convex transducer
DEFF Research Database (Denmark)
Bæk, David; Jensen, Jørgen Arendt; Willatzen, Morten
2009-01-01
A multilayer transducer model for predicting a transducer impulse response has in earlier works been developed and combined with the Field II software. This development was tested on current, voltage, and intensity measurements on piezoceramics discs (Bæk et al. IUS 2008) and a convex 128 element...... ultrasound imaging transducer (Bæk et al. ICU 2009). The model benefits from its 1D simplicity and hasshown to give an amplitude error around 1.7‐2 dB. However, any prediction of amplitude, phase, and attenuation of pulses relies on the accuracy of manufacturer supplied material characteristics, which may...... is a quantitative calibrated model for a complete ultrasound system. This includes a sensitivity study aspresented here.Statement of Contribution/MethodsThe study alters 35 different model parameters which describe a 128 element convex transducer from BK Medical Aps. The changes are within ±20 % of the values...
Convex relaxation of Optimal Power Flow in Distribution Feeders with embedded solar power
DEFF Research Database (Denmark)
Hermann, Alexander Niels August; Wu, Qiuwei; Huang, Shaojun
2016-01-01
There is an increasing interest in using Distributed Energy Resources (DER) directly coupled to end user distribution feeders. This poses an array of challenges because most of today’s distribution feeders are designed for unidirectional power flow. Therefore when installing DERs such as solar...... panels with uncontrolled inverters, the upper limit of installable capacity is quickly reached in many of today’s distribution feeders. This problem can often be mitigated by optimally controlling the voltage angles of inverters. However, the optimal power flow problem in its standard form is a large...... scale non-convex optimization problem, and thus can’t be solved precisely and also is computationally heavy and intractable for large systems. This paper examines the use of a convex relaxation using Semi-definite programming to optimally control solar power inverters in a distribution grid in order...
Efficiency measurement with a non-convex free disposal hull technology
DEFF Research Database (Denmark)
Fukuyama, Hirofumi; Hougaard, Jens Leth; Sekitani, Kazuyuki
2016-01-01
We investigate the basic monotonicity properties of least-distance (in)efficiency measures on the class of non-convex FDH (free disposable hull) technologies. We show that any known FDH least-distance measure violates strong monotonicity over the strongly (Pareto-Koopmans) efficient frontier. Tak....... Taking this result into account, we develop a new class of FDH least-distance measures that satisfy strong monotonicity and show that the developed (in)efficiency measurement framework has a natural profit interpretation.......We investigate the basic monotonicity properties of least-distance (in)efficiency measures on the class of non-convex FDH (free disposable hull) technologies. We show that any known FDH least-distance measure violates strong monotonicity over the strongly (Pareto-Koopmans) efficient frontier...
Three-Dimensional Synthetic Aperture Focusing Using a Rocking Convex Array Transducer
DEFF Research Database (Denmark)
Andresen, Henrik; Nikolov, Svetoslav; Pedersen, Mads Møller
2010-01-01
Volumetric imaging can be performed using 1-D arrays in combination with mechanical motion. Outside the elevation focus of the array, the resolution and contrast quickly degrade compared with the lateral plane, because of the fixed transducer focus. This paper shows the feasibility of using...... synthetic aperture focusing for enhancing the elevation focus for a convex rocking array. The method uses a virtual source (VS) for defocused multi-element transmit, and another VS in the elevation focus point. This allows a direct time-of-flight to be calculated for a given 3-D point. To avoid artifacts...... and increase SNR at the elevation VS, a plane-wave VS approach has been implemented. Simulations and measurements using an experimental scanner with a convex rocking array show an average improvement in resolution of 26% and 33%, respectively. This improvement is also seen in in vivo measurements...
Equilibrium prices supported by dual price functions in markets with non-convexities
International Nuclear Information System (INIS)
Bjoerndal, Mette; Joernsten, Kurt
2004-06-01
The issue of finding market clearing prices in markets with non-convexities has had a renewed interest due to the deregulation of the electricity sector. In the day-ahead electricity market, equilibrium prices are calculated based on bids from generators and consumers. In most of the existing markets, several generation technologies are present, some of which have considerable non-convexities, such as capacity limitations and large start up costs. In this paper we present equilibrium prices composed of a commodity price and an uplift charge. The prices are based on the generation of a separating valid inequality that supports the optimal resource allocation. In the case when the sub-problem generated as the integer variables are held fixed to their optimal values possess the integrality property, the generated prices are also supported by non-linear price-functions that are the basis for integer programming duality. (Author)
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
International Nuclear Information System (INIS)
Gandy, Silvia; Yamada, Isao; Recht, Benjamin
2011-01-01
In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers
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.
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.
Directory of Open Access Journals (Sweden)
Suresh Thenozhi
2012-01-01
Full Text Available An important objective of health monitoring systems for tall buildings is to diagnose the state of the building and to evaluate its possible damage. In this paper, we use our prototype to evaluate our data-mining approach for the fault monitoring. The offset cancellation and high-pass filtering techniques are combined effectively to solve common problems in numerical integration of acceleration signals in real-time applications. The integration accuracy is improved compared with other numerical integrators. Then we introduce a novel method for support vector machine (SVM classification, called convex-concave hull. We use the Jarvis march method to decide the concave (nonconvex hull for the inseparable points. Finally the vertices of the convex-concave hull are applied for SVM training.
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.
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)
International Nuclear Information System (INIS)
Yamamoto, Kazuya; Sumiya, Akihiro
2009-02-01
The International Atomic Energy Agency IAEA carried out a large-scale international emergency response exercise under the designated name of ConvEx-3(2008), accompanying the national exercise of Mexico in July 2008. This review report summarizes two simultaneous observations of the exercises in Mexico and the IAEA headquarter during ConvEx-3(2008). Mexico has established a very steady nuclear emergency response system based on that of US, while only two BWR nuclear power units have been operated yet. The Mexican nuclear emergency response system and the emergency response activities of the Incident and Emergency Centre of the IAEA headquarter impressed important knowledge on observers that is helpful for enhancement of Japanese nuclear emergency response system in the future, e.g. establishment of Emergency Action Level and of implementation of long time exercise and enhancement of prompt protective actions. Japan had established the Act on Special Measures Concerning Nuclear Emergency Preparedness and has developed the nuclear disaster prevention system since the JCO Criticality Accident in Tokai-mura. Now is the new stage to enhance the system on the view point of prevention of a nuclear disaster affecting the neighboring countries' or prevention of a nuclear disaster which arise from the neighboring countries'. The ConvEx-3(2008) suggested key issues about nuclear disaster prevention related to the neighboring countries, e.g. establishment of much wider environmental monitoring and of international assistance system against a foreign nuclear disaster. The observations of the IAEA ConvEx-3(2008) exercise described in this review report were funded by the MEXT (Ministry of Education, Culture, Sports, Science and Technology). (author)
On Difference of Convex Optimization to Visualize Statistical Data and Dissimilarities
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
2016-01-01
In this talk we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective...... is the difference of two convex functions (DC). Suitable DC decompositions allow us to use the DCA algorithm in a very efficient way. Our algorithmic approach is used to visualize two real-world datasets....
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
DEFF Research Database (Denmark)
Eriksen, René Lynge; Beermann, Jonas; Søndergaard, Thomas
The realization of nonresonant light absorption with nanostructured metal surfaces by making practical use of nanofocusing optical energy in tapered plasmonic waveguides, is of one of the most fascinating and fundamental phenomena in plasmonics [1,2]. We recently realized broadband light absorption...... in gold via adiabatic nanofocusing of gap surface plasmon modes in well-defined geometries of ultra-sharp convex grooves and being excited by scattering off subwavelength-sized wedges [3]....
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.
A Sequential Convex Semidefinite Programming Algorithm for Multiple-Load Free Material Optimization
Czech Academy of Sciences Publication Activity Database
Stingl, M.; Kočvara, Michal; Leugering, G.
2009-01-01
Roč. 20, č. 1 (2009), s. 130-155 ISSN 1052-6234 R&D Projects: GA AV ČR IAA1075402 Grant - others:commision EU(XE) EU-FP6-30717 Institutional research plan: CEZ:AV0Z10750506 Keywords : structural optimization * material optimization * semidefinite programming * sequential convex programming Subject RIV: BA - General Mathematics Impact factor: 1.429, year: 2009
International Nuclear Information System (INIS)
Koga, T.; Kasai, Y.; Dehesa, J.S.; Angulo, J.C.
1993-01-01
The electron-pair function h(u) of a finite many-electron system is not monotonic, but the related quantity h(u)/u α , α>0, is not only monotonically decreasing from the origin but also convex for the values α 1 and α 2 , respectively, as has been recently found. Here, it is first argued that this quantity is also logarithmically convex for any α≥α' with α'=max{-u 2 d2[lnh(u)]/du 2 }. Then this property is used to obtain a general inequality which involves three interelectronic moments left-angle u t right-angle. Particular cases of this inequality involve relevant characteristics of the system such as the number of electrons and the total electron-electron repulsion energy. Second, the logarithmic-convexity property of h(u) as well as the accuracy of this inequality are investigated by the optimum 20-term Hylleraas-type wave functions for two-electron atoms with nuclear charge Z=1, 2, 3, 5, and 10. It is found that (i) 14 2 much-gt α 1 ) and (ii) the accuracy of the inequality which involves moments of contiguous orders oscillates between 62.4% and 96.7% according to the specific He-like atom and the moments involved. Finally, the importance of the logarithmic-convexity effects on the interelectronic moments relative to those coming from other monotonicity properties of h(u)/u α are analyzed in the same numerical Hylleraas framework
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
Czech Academy of Sciences Publication Activity Database
Meziat, R.; Roubíček, Tomáš; Patino, D.
2010-01-01
Roč. 31, č. 4 (2010), s. 460-488 ISSN 0163-0563 Grant - others:GA MŠk(CZ) LC06052 Program:LC Institutional research plan: CEZ:AV0Z20760514 Keywords : convex approximations * method of moments * relaxed variational problems Subject RIV: BA - General Mathematics Impact factor: 0.687, year: 2010 http://www.informaworld.com/smpp/content~db=all~content=a922886514~frm=titlelink
Directory of Open Access Journals (Sweden)
Kazuyuki Aihara
2011-04-01
Full Text Available The classical information-theoretic measures such as the entropy and the mutual information (MI are widely applicable to many areas in science and engineering. Csiszar generalized the entropy and the MI by using the convex functions. Recently, we proposed the grid occupancy (GO and the quasientropy (QE as measures of independence. The QE explicitly includes a convex function in its definition, while the expectation of GO is a subclass of QE. In this paper, we study the effect of different convex functions on GO, QE, and Csiszar’s generalized mutual information (GMI. A quality factor (QF is proposed to quantify the sharpness of their minima. Using the QF, it is shown that these measures can have sharper minima than the classical MI. Besides, a recursive algorithm for computing GMI, which is a generalization of Fraser and Swinney’s algorithm for computing MI, is proposed. Moreover, we apply GO, QE, and GMI to chaotic time series analysis. It is shown that these measures are good criteria for determining the optimum delay in strange attractor reconstruction.
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.
Convex-based void filling method for CAD-based Monte Carlo geometry modeling
International Nuclear Information System (INIS)
Yu, Shengpeng; Cheng, Mengyun; Song, Jing; Long, Pengcheng; Hu, Liqin
2015-01-01
Highlights: • We present a new void filling method named CVF for CAD based MC geometry modeling. • We describe convex based void description based and quality-based space subdivision. • The results showed improvements provided by CVF for both modeling and MC calculation efficiency. - Abstract: CAD based automatic geometry modeling tools have been widely applied to generate Monte Carlo (MC) calculation geometry for complex systems according to CAD models. Automatic void filling is one of the main functions in the CAD based MC geometry modeling tools, because the void space between parts in CAD models is traditionally not modeled while MC codes such as MCNP need all the problem space to be described. A dedicated void filling method, named Convex-based Void Filling (CVF), is proposed in this study for efficient void filling and concise void descriptions. The method subdivides all the problem space into disjointed regions using Quality based Subdivision (QS) and describes the void space in each region with complementary descriptions of the convex volumes intersecting with that region. It has been implemented in SuperMC/MCAM, the Multiple-Physics Coupling Analysis Modeling Program, and tested on International Thermonuclear Experimental Reactor (ITER) Alite model. The results showed that the new method reduced both automatic modeling time and MC calculation time
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
International Nuclear Information System (INIS)
Hoffmann, Aswin L; Siem, Alex Y D; Hertog, Dick den; Kaanders, Johannes H A M; Huizenga, Henk
2006-01-01
In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning
Towards reproducible experimental studies for non-convex polyhedral shaped particles
Directory of Open Access Journals (Sweden)
Wilke Daniel N.
2017-01-01
Full Text Available The packing density and flat bottomed hopper discharge of non-convex polyhedral particles are investigated in a systematic experimental study. The motivation for this study is two-fold. Firstly, to establish an approach to deliver quality experimental particle packing data for non-convex polyhedral particles that can be used for characterization and validation purposes of discrete element codes. Secondly, to make the reproducibility of experimental setups as convenient and readily available as possible using affordable and accessible technology. The primary technology for this study is fused deposition modeling used to 3D print polylactic acid (PLA particles using readily available 3D printer technology. A total of 8000 biodegradable particles were printed, 1000 white particles and 1000 black particles for each of the four particle types considered in this study. Reproducibility is one benefit of using fused deposition modeling to print particles, but an extremely important additional benefit is that specific particle properties can be explicitly controlled. As an example in this study the volume fraction of each particle can be controlled i.e. the effective particle density can be adjusted. In this study the particle volumes reduces drastically as the non-convexity is increased, however all printed white particles in this study have the same mass within 2% of each other.
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.
Groenveld, Hessel F.; Tijssen, Jan G. P.; Crijns, Harry J. G. M.; Van den Berg, Maarten P.; Hillege, Hans L.; Alings, Marco; Van Veldhuisen, Dirk J.; Van Gelder, Isabelle C.
2013-01-01
Objectives This study sought to investigate differences in outcome between patients treated with successful strict, failed strict, and lenient rate control. Background The RACE II (Rate Control Efficacy in Permanent Atrial Fibrillation) study showed no difference in outcome between lenient and
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
Bircher, Lea; Geirnaert, Annelies; Hammes, Frederik; Lacroix, Christophe; Schwab, Clarissa
2018-04-17
Strict anaerobic gut microbes have been suggested as 'next-generation probiotics' for treating several intestinal disorders. The development of preservation techniques is of major importance for therapeutic application. This study investigated cryopreservation (-80°C) and lyophilization survival and storage stability (4°C for 3 months) of the strict anaerobic gut microbes Bacteroides thetaiotaomicron, Faecalibacterium prausnitzii, Roseburia intestinalis, Anaerostipes caccae, Eubacterium hallii and Blautia obeum. To improve preservation survival, protectants sucrose and inulin (both 5% w/v) were added for lyophilization and were also combined with glycerol (15% v/v) for cryopreservation. Bacterial fitness, evaluated by maximum growth rate and lag phase, viability and membrane integrity were determined using a standardized growth assay and by flow cytometry as markers for preservation resistance. Lyophilization was more detrimental to viability and fitness than cryopreservation, but led to better storage stability. Adding sucrose and inulin enhanced viability and the proportion of intact cells during lyophilization of all strains. Viability of protectant-free B. thetaiotaomicron, A. caccae and F. prausnitzii was above 50% after cryopreservation and storage and increased to above 80% if protectants were present. The addition of glycerol, sucrose and inulin strongly enhanced the viability of B. obeum, E. hallii and R. intestinalis from 0.03-2% in protectant-free cultures to 11-37%. This is the first study that quantitatively compared the effect of cryopreservation and lyophilization and the addition of selected protectants on viability and fitness of six strict anaerobic gut microbes. Our results suggest that efficiency of protectants is process- and species-specific. © 2018 The Authors. Microbial Biotechnology published by John Wiley & Sons Ltd and Society for Applied Microbiology.
International Nuclear Information System (INIS)
Liu, Xiaolan; Zhou, Mi
2016-01-01
In this paper, a one-layer recurrent network is proposed for solving a non-smooth convex optimization subject to linear inequality constraints. Compared with the existing neural networks for optimization, the proposed neural network is capable of solving more general convex optimization with linear inequality constraints. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed as long as the designed parameters in the model are larger than the derived lower bounds.
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.
Directory of Open Access Journals (Sweden)
Nicolai Lang, Hans Peter Büchler
2018-01-01
Full Text Available Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the one-dimensional Majorana chain and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.
Single Molecule Experiments Challenge the Strict Wave-Particle Dualism of Light
Directory of Open Access Journals (Sweden)
Karl Otto Greulich
2010-01-01
Full Text Available Single molecule techniques improve our understanding of the photon and light. If the single photon double slit experiment is performed at the “single photon limit” of a multi-atom light source, faint light pulses with more than one photon hamper the interpretation. Single molecules, quantum dots or defect centres in crystals should be used as light source. “Single photon detectors” do not meet their promise―only “photon number resolving single photon detectors” do so. Particularly, the accumulation time argument, the only safe basis for the postulate of a strictly particle like photon, has so far not yet been verified.
Single molecule experiments challenge the strict wave-particle dualism of light.
Greulich, Karl Otto
2010-01-21
Single molecule techniques improve our understanding of the photon and light. If the single photon double slit experiment is performed at the "single photon limit" of a multi-atom light source, faint light pulses with more than one photon hamper the interpretation. Single molecules, quantum dots or defect centres in crystals should be used as light source. "Single photon detectors" do not meet their promise-only "photon number resolving single photon detectors" do so. Particularly, the accumulation time argument, the only safe basis for the postulate of a strictly particle like photon, has so far not yet been verified.
Strictly positive solutions for one-dimensional nonlinear problems involving the p-Laplacian
Kaufmann, Uriel; Medri, Ivan
2013-01-01
Let $\\Omega$ be a bounded open interval, and let $p>1$ and $q\\in\\left(0,p-1\\right) $. Let $m\\in L^{p^{\\prime}}\\left(\\Omega\\right) $ and $0\\leq c\\in L^{\\infty}\\left(\\Omega\\right) $. We study existence of strictly positive solutions for elliptic problems of the form $-\\left(\\left\\| u^{\\prime}\\right\\|^{p-2}u^{\\prime}\\right) ^{\\prime}+c\\left(x\\right) u^{p-1}=m\\left(x\\right) u^{q}$ in $\\Omega$, $u=0$ on $\\partial\\Omega$. We mention that our results are new even in the case $c\\equiv0$.
Directory of Open Access Journals (Sweden)
Xuefeng Wei
2016-12-01
Full Text Available This article concerns the wave interaction problem for a strictly hyperbolic system of conservation laws whose Riemann solutions involve delta shock waves. To cover all situations, the global solutions are constructed when the initial data are taken as three piecewise constant states. It is shown that the Riemann solutions are stable with respect to a specific small perturbation of the Riemann initial data. In addition, some interesting nonlinear phenomena are captured during the process of constructing the solutions, such as the generation and decomposition of delta shock waves.
The effect of 8 days of strict bed rest on the incretin effect in healthy volunteers.
Nielsen, Signe Tellerup; Harder-Lauridsen, Nina Majlund; Benatti, Fabiana Braga; Wedell-Neergaard, Anne-Sophie; Lyngbæk, Mark Preben; Møller, Kirsten; Pedersen, Bente Klarlund; Krogh-Madsen, Rikke
2016-03-15
Bed rest and physical inactivity are the consequences of hospital admission for many patients. Physical inactivity induces changes in glucose metabolism, but its effect on the incretin effect, which is reduced in, e.g., Type 2 diabetes, is unknown. To investigate how 8 days of strict bed rest affects the incretin effect, 10 healthy nonobese male volunteers underwent 8 days of strict bed rest. Before and after the intervention, all volunteers underwent an oral glucose tolerance test (OGTT) followed by an intravenous glucose infusion (IVGI) on the following day to mimic the blood glucose profile from the OGTT. Blood glucose, serum insulin, serum C-peptide, plasma incretin hormones [glucagon-like peptide (GLP-1) and glucose-dependent insulinotropic peptide (GIP)], and serum glucagon were measured serially during both the OGTT and the IVGI. The incretin effect is calculated as the relative difference between the area under the curve for the insulin response during the OGTT and that of the corresponding IVGI, respectively. Concentrations of glucose, insulin, C-peptide, and GIP measured during the OGTT were higher after the bed rest intervention (all P effect (P = 0.6). In conclusion, 8 days of bed rest induces insulin resistance, but we did not see evidence of an associated change in the incretin effect. Copyright © 2016 the American Physiological Society.
Optimal control of nonlinear continuous-time systems in strict-feedback form.
Zargarzadeh, Hassan; Dierks, Travis; Jagannathan, Sarangapani
2015-10-01
This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. The optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique. Subsequently, a neural network-based optimal control scheme is introduced to estimate the cost, or value function, over an infinite horizon for the resulting nonlinear continuous-time systems in affine form when the internal dynamics are unknown. The estimated cost function is then used to obtain the optimal feedback control input; therefore, the overall optimal control input for the nonlinear continuous-time system in strict-feedback form includes the feedforward plus the optimal feedback terms. It is shown that the estimated cost function minimizes the Hamilton-Jacobi-Bellman estimation error in a forward-in-time manner without using any value or policy iterations. Finally, optimal output feedback control is introduced through the design of a suitable observer. Lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller. Simulation examples are provided to validate the theoretical results.
International Nuclear Information System (INIS)
Mohapatra, P. K.; Deb, S.; Singh, B. P.; Vasa, P.; Dhar, S.
2016-01-01
Despite a tremendous interest on molybdenum disulfide as a thinnest direct band gap semiconductor, single step synthesis of a large area purely monolayer MoS 2 film has not yet been reported. Here, we report a CVD route to synthesize a continuous film of strictly monolayer MoS 2 covering an area as large as a few cm 2 on a variety of different substrates without using any seeding material or any elaborate pretreatment of the substrate. This is achieved by allowing the growth to take place in the naturally formed gap between a piece of SiO 2 coated Si wafer and the substrate, when the latter is placed on top of the former inside a CVD reactor. We propose a qualitative model to explain why the MoS 2 films are always strictly monolayer in this method. The photoluminescence study of these monolayers shows the characteristic excitonic and trionic features associated with monolayer MoS 2 . In addition, a broad defect related luminescence band appears at ∼1.7 eV. As temperature decreases, the intensity of this broad feature increases, while the band edge luminescence reduces
Directory of Open Access Journals (Sweden)
Ji Guo
2017-12-01
Full Text Available With the rapid economic growth and development, the problem of environmental pollution in China’s cities is becoming increasingly serious, and environmental pollution takes on a regional difference. There is, however, little comprehensive evaluation on the environmental performance and the regional difference of strictly-environmental-monitored cities in China. In this paper, the environmental performance of 109 strictly-environmental-monitored cities in China is evaluated in terms of natural performance, management performance, and scale performance by Data Envelopment Analysis (DEA, incorporating PM2.5 and PM10 as undesirable outputs. The empirical results show that: (1 At present, the natural performance is quite high, while the management performance is noticeably low for most cities. (2 The gap between the level of economic development and environmental protection among cities in China is large, and the scale efficiency of big cities is better than that of smaller cities. The efficiency value of large-scale cities such as Beijing, Shanghai, Guangzhou, Shenzhen, etc. is high, equaling 1; the value of smaller cities such as Sanmenxia, Baoding, Mudanjiang, and Pingdingshan is low, close to 0, indicating that big cities are characterized by high environmental efficiency. (3 From the perspective of region, the level of environmental performance in China is very uneven. For example, the environmental efficiency level of the Pan-Pearl River Delta region is superior to that of the Pan-Yangtze River region and the Bahia Rim region, whose values of environmental efficiency are 0.858, 0.658, and 0.622 respectively. The average efficiency of the Southern Coastal Economic Zone, Eastern Coastal Comprehensive Economic Zone, and the Comprehensive Economic Zone in the middle reaches of the Yangtze River is higher than that of other regions. Finally, corresponding countermeasures and suggestions are put forward. The method used in this paper is applicable
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.
An inequality for convex functionals and its application to a maxwellian gas
Directory of Open Access Journals (Sweden)
G. Toscani
1991-05-01
Full Text Available We study the trend towards equilibrium of the solution of the spatially homogeneous Boltzmann equation for a gas of Maxwellian molecules. The cases of axially symmetric and plane initial densities are investigated. In these situations, the strong L1 convergence to equilibrium follows by a suitable use of some convex and isotropic functionals, with monotonic behaviour in time along the solution. The initial density is required to have finite energy and entropy. It is shown that the functionals satisfy a common convolution inequality.
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
DEFF Research Database (Denmark)
Kafle, Bishoksan; Gallagher, John Patrick
2017-01-01
In this paper we apply tree-automata techniques to refinement of abstract interpretation in Horn clause verification. We go beyond previous work on refining trace abstractions; firstly we handle tree automata rather than string automata and thereby can capture traces in any Horn clause derivations...... underlying the Horn clauses. Experiments using linear constraint problems and the abstract domain of convex polyhedra show that the refinement technique is practical and that iteration of abstract interpretation with tree automata-based refinement solves many challenging Horn clause verification problems. We...... compare the results with other state-of-the-art Horn clause verification tools....
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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.
Preliminary In-Vivo Evaluation of Convex Array Synthetic Aperture Imaging
DEFF Research Database (Denmark)
Pedersen, Morten Høgholm; Gammelmark, Kim; Jensen, Jørgen Arendt
2004-01-01
of STA imaging in comparison to conventional imaging. The purpose is to evaluate whether STA imaging is feasible in-vivo. and whether the image quality obtained is comparable to traditional scanned imaging in terms of penetration depth, spatial resolution, contrast resolution, and artifacts. Acquisition...... was done using our RASMUS research scanner and a 5.5 MHz convex array transducer. STA imaging applies spherical wave emulation using multi-element subapertures and a 20 mus linear FM signal as excitation pulse. For conventional imaging a 64 element aperture was used in transmit and receive with a 1.5 cycle...
Geometry of convex polygons and locally minimal binary trees spanning these polygons
International Nuclear Information System (INIS)
Ivanov, A O; Tuzhilin, A A
1999-01-01
In previous works the authors have obtained an effective classification of planar locally minimal binary trees with convex boundaries. The main aim of the present paper is to find more subtle restrictions on the possible structure of such trees in terms of the geometry of the given boundary set. Special attention is given to the case of quasiregular boundaries (that is, boundaries that are sufficiently close to regular ones in a certain sense). In particular, a series of quasiregular boundaries that cannot be spanned by a locally minimal binary tree is constructed
DEFF Research Database (Denmark)
Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan
2012-01-01
The primal–dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1–26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems...... for the purpose of designing iterative image reconstruction algorithms for CT. The primal–dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application...
An Implementable First-Order Primal-Dual Algorithm for Structured Convex Optimization
Directory of Open Access Journals (Sweden)
Feng Ma
2014-01-01
Full Text Available Many application problems of practical interest can be posed as structured convex optimization models. In this paper, we study a new first-order primaldual algorithm. The method can be easily implementable, provided that the resolvent operators of the component objective functions are simple to evaluate. We show that the proposed method can be interpreted as a proximal point algorithm with a customized metric proximal parameter. Convergence property is established under the analytic contraction framework. Finally, we verify the efficiency of the algorithm by solving the stable principal component pursuit problem.
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.
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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
DEFF Research Database (Denmark)
Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan
2013-01-01
Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times...... problems. Conclusions: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited...
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
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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
DEFF Research Database (Denmark)
Caner, Mehmet; Kock, Anders Bredahl
This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target...... of the same order as that of the oracle. If the target is linear we give sufficient conditions for consistency of the estimated parameter vector. Next, we briefly discuss how a thresholded version of our estimator can be used to perform consistent variable selection. We give two examples of loss functions...
Optimal Energy Consumption in Refrigeration Systems - Modelling and Non-Convex Optimisation
DEFF Research Database (Denmark)
Hovgaard, Tobias Gybel; Larsen, Lars F. S.; Skovrup, Morten J.
2012-01-01
Supermarket refrigeration consumes substantial amounts of energy. However, due to the thermal capacity of the refrigerated goods, parts of the cooling capacity delivered can be shifted in time without deteriorating the food quality. In this study, we develop a realistic model for the energy...... consumption in super market refrigeration systems. This model is used in a Nonlinear Model Predictive Controller (NMPC) to minimise the energy used by operation of a supermarket refrigeration system. The model is non-convex and we develop a computational efficient algorithm tailored to this problem...
On a class of adjustable rate mortgage loans subject to a strict balance principle
DEFF Research Database (Denmark)
Astrup Jensen, Bjarne
We describe the background and the basic funding mechanisms for the type of adjustable rate mortgageloans that were introduced in the Danish market in 1996. Each loan is funded separately by tap issuingpass-through mortgage bonds (`strict balance principle'). The novelty is a funding mechanism...... that usesa roll-over strategy, where long term loans are funded by sequentially issuing short term pass-throughbonds, and the first issuer of these loans obtained a patent on the funding principles in 1999. Publiclyavailable descriptions of the principles leave an impression of very complicated numerical...... algorithms.The algorithms described here show that the essentials can be reduced to a `back of an envelope' complexity.Keywords: Adjustable rate mortgages, balance principle, patent, yield curve riding...
Control of Petri nets subject to strict temporal constraints using Max-Plus algebra
Tebani, K.; Amari, S.; Kara, R.
2018-04-01
In this paper, we treat the control problem of timed discrete event systems under temporal constraints. This type of constraint is very frequent in production systems, transportation network and in networked automation systems. Precisely, we are interested in the validation of strict temporal constraints imposed on the paths in a timed event graph (TEG) by using Max-Plus algebra. Not all the transitions of the considered TEG model are controllable, i.e. only the input transitions are controllable. An analytical approach for computing state feedback controllers is developed. Sufficient condition is given for the existence of causal control laws satisfying the temporal constraints. In the first, a TEG with observable transitions is considered. Then, the proposed approach is extended to the partially observable TEG. The synthesised feedback can be interpreted by places of control connected to the TEG to guarantee the respect of the time constraints. The proposed method is illustrated in the assembly system example.
Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.
Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping
2018-06-01
This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.
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David S. Younger
2010-01-01
Full Text Available Lyme neuroborreliosis or “neurological Lyme disease” was evidenced in 2 of 23 patients submitted to strict criteria for case selection of the Centers for Disease Control and Prevention employing a two-tier test to detect antibodies to Borrelia burgdorferi at a single institution. One patient had symptomatic polyradiculoneuritis, dysautonomia, and serological evidence of early infection; and another had symptomatic small fiber sensory neuropathy, distal polyneuropathy, dysautonomia, and serological evidence of late infection. In the remaining patients symptoms initially ascribed to Lyme disease were probably unrelated to B. burgdorferi infection. Our findings suggest early susceptibility and protracted involvement of the nervous system most likely due to the immunological effects of B. burgdorferi infection, although the exact mechanisms remain uncertain.
A semi-automatic method for positioning a femoral bone reconstruction for strict view generation.
Milano, Federico; Ritacco, Lucas; Gomez, Adrian; Gonzalez Bernaldo de Quiros, Fernan; Risk, Marcelo
2010-01-01
In this paper we present a semi-automatic method for femoral bone positioning after 3D image reconstruction from Computed Tomography images. This serves as grounding for the definition of strict axial, longitudinal and anterior-posterior views, overcoming the problem of patient positioning biases in 2D femoral bone measuring methods. After the bone reconstruction is aligned to a standard reference frame, new tomographic slices can be generated, on which unbiased measures may be taken. This could allow not only accurate inter-patient comparisons but also intra-patient comparisons, i.e., comparisons of images of the same patient taken at different times. This method could enable medical doctors to diagnose and follow up several bone deformities more easily.
Czech Academy of Sciences Publication Activity Database
Engliš, Miroslav; Hänninen, T.; Taskinen, J.
2006-01-01
Roč. 32, č. 2 (2006), s. 253-275 ISSN 0362-1588 R&D Projects: GA ČR(CZ) GA201/03/0041; GA AV ČR(CZ) IAA1019304 Institutional research plan: CEZ:AV0Z10190503 Keywords : Bergman projection * weighted supremum norms * locally convex space Subject RIV: BA - General Mathematics Impact factor: 0.354, year: 2006
Weight of fitness deviation governs strict physical chaos in replicator dynamics
Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar
2018-03-01
Replicator equation—a paradigm equation in evolutionary game dynamics—mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions—fixed points, periodic orbits, and chaotic trajectories—are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.
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Mohd Bakri Ishak
2010-01-01
Full Text Available Basically, strict liability is part of the mechanism for expressing judgment or sentence by using direct evidence. This principle is very useful in order to obtain remedies from any damage either directly or indirectly. The principle in Rylands v Fletcher is responsible on imposing strict liability where if something brought onto land or collected there escapes liability under this rule can include not only the owner of land but also those who control or occupation on it. However, as a matter of fact, policy and regulation are also important in taking any action against any party who are responsible for environmental pollution or damage, which may include mismanagement of waste or industrial waste or agricultural waste. There are certain policies and regulations on environmental protection such as the National Environmental Policy, certain Acts and several regulations under the Environmental Quality Act 1974 (Act 127, which are very useful for agricultural waste management inter alia: Waters Act 1920 (Act 418, Environmental Quality (Prescribed Premises (Crude Palm Oil Regulations 1977, Environmental Quality (Prescribed Premises (Raw Natural Rubber Regulations 1978, Environmental Quality (Sewage and Industrial Effluents Regulations 1979, and Environmental Quality (Compounding of Offences Rules 1978. As a matter of fact, we should realize that time is of an essence for any parties which are involved in court cases and especially in avoiding the element of externality, which is commonly suffered by the government. In making this paper, therefore, some element of comparison with certain developed jurisdiction such as in the United Kingdom and Japan could not be avoided in order to obtain better outcome and to be more practical for the purpose of environmental protection and agricultural waste management.
Cao, Xianhua; Liu, Xiaoli; Dong, Xiuzhu
2003-07-01
Two bacterial strains were isolated from methanogenic butyrate-oxidizing mixed cultures. The cells were straight to slightly curved, gram-positive rods that were motile by means of multiple flagella and formed endospores. Growth was observed in the temperature range 15-45 degrees C (optimum 37 degrees C) and pH range 5.5-9.0 (optimum pH 7.5). The novel isolates were strictly anaerobic chemo-organotrophs capable of utilizing yeast extract, peptone, tryptone and a variety of sugars and organic acids, but not glucose. None of the accessory electron acceptors tested (elemental sulfur, thiosulfate or fumarate) improved growth, except crotonate, which was dismutated to butyrate and acetate. The G + C content of the DNA of one of the isolates, strain B11-2T, was 30.6 mol%. Phylogenetic analysis based on 16S rDNA sequence similarity between strain B11-2T and some other strictly anaerobic, spore-forming bacteria indicated that the novel isolates represented a species in cluster XI within the low-GC gram-positive bacteria, being most closely related to Alkaliphilus transvaalensis JCM 10712T. DNA-DNA relatedness between strain B11-2T and A. transvaalensis JCM 10712T was 21%. On the basis of physiological and molecular properties, and cellular fatty acid and cell wall compositions, the novel isolates are proposed to represent a novel species of the genus Alkaliphilus, for which the name Alkaliphilus crotonatoxidans is proposed (type strain B11-2T=AS 1.2897T=JCM 11672T).
Weight of fitness deviation governs strict physical chaos in replicator dynamics.
Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar
2018-03-01
Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions-fixed points, periodic orbits, and chaotic trajectories-are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.
DEFF Research Database (Denmark)
Sørensen, N F; Jensen, A B; Wille-Jørgensen, P
2010-01-01
Aim The risk of local recurrence following curative surgery for colorectal cancer (CRC) is up to 50%. A rigorous follow-up program may increase survival. Guidelines on suitable methods for scheduled follow up examinations are needed. This study evaluates a strict follow-up program including...... supported a strict follow-up program following curative surgery for colorectal cancer. FDG-PET combined with CT should be included in control programs....
Directory of Open Access Journals (Sweden)
Ryan Wen Liu
2017-03-01
Full Text Available Dynamic magnetic resonance imaging (MRI has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments.
International Nuclear Information System (INIS)
Zhao Yunbin
2010-01-01
While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the condition number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.
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
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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
Energy Technology Data Exchange (ETDEWEB)
Tashima, Hideaki; Murayama, Hideo; Yamaya, Taiga [National Institute of Radiological Sciences, Chiba (Japan); Katsunuma, Takayuki; Suga, Mikio [Chiba Univ. (Japan). Graduate School of Engineering; Kinouchi, Shoko [National Institute of Radiological Sciences, Chiba (Japan); Chiba Univ. (Japan). Graduate School of Engineering; Obi, Takashi [Tokyo Institute of Technology (Japan). Interdisciplinary Graduate School of Science and Engineering; Kudo, Hiroyuki [Tsukuba Univ. (Japan). Graduate School of Systems and Information Engineering
2011-07-01
We have proposed the OpenPET geometry which has gaps between detector rings and physically opened field-of-view. The image reconstruction of the OpenPET is classified into an incomplete problem because it does not satisfy the Orlov's condition. Even so, the simulation and experimental studies have shown that applying iterative methods such as the maximum likelihood expectation maximization (ML-EM) algorithm successfully reconstruct images in the gap area. However, the imaging process of the iterative methods in the OpenPET imaging is not clear. Therefore, the aim of this study is to analytically analyze the OpenPET imaging and estimate implicit constraints involved in the iterative methods. To apply explicit constraints in the OpenPET imaging, we used the method of convex projections for restoration of the images reconstructed by the analytical way in which low-frequency components are lost. Numerical simulations showed that the similar restoration effects are involved both in the ML-EM and the method of convex projections. Therefore, the iterative methods have advantageous effect of restoring lost frequency components of the OpenPET imaging. (orig.)
Numerical Simulation of Recycled Concrete Using Convex Aggregate Model and Base Force Element Method
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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
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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...
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.
Dynamic Planar Convex Hull with Optimal Query Time and O(log n · log log n ) Update Time
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Jakob, Riko
2000-01-01
The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log log n) time, point deletions in amortized O(log n · log log n) time......, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requires O(n) space. Applications of the new dynamic convex hull data structure are improved deterministic algorithms for the k-level problem and the red-blue segment intersection problem where all red and all...
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.
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Manju Pathak
2012-10-01
Full Text Available Background: This study aimed to modify de Man Rogosa Sharpe culture medium (termed MRS for selective cultivation of probiotics strain for the consumption by the strictly vegetarian human population. Vegetarian probiotic foods by definition must be free from all animal-derived ingredients. This not only includes the product ingredients but the probiotic inoculum as well. Probiotic starter cultures are traditionally grown and stored in media containing milk or meatderived ingredients. The presence of these ingredients makes the probiotic cell concentrates unsuitable for use in vegetarian products and thus creates the need for a growth medium which isfree from animal-derived ingredients. Present study investigated the growth of a strain of Lactobacillus lactis in MRS. The present invention relates in general to a bacterial culture media,and more specifically a complex microbial culture media, based on plant seed powder extract in place of animal extract for probiotic bacterial growth.Methods: Lactobacillus lactis, a probiotic, was grown in standard MRS culture medium as well as in our various test media (TM containing various vegetal source in place of beef extract, yeast extract and peptone as in case of MRS. The inoculated culture mediums were incubated at 37C for 72 hours and growth of probiotic is recorded at regular intervals. The growth was recorded as Colony Forming Units (CFUs.Results: The best growth of probiotic is observed in TM 2. TM 2 is the leguminous seed extract. Starter culture mediums for probiotics or other bacteria primarily contain protein from animal source. The possibility of using vegetal protein from TM 2 extract in place of peptones and meat extract for the nitrogen supplementation of culture media for the growth of lactic acid bacteria has been demonstrated.Functional Foods in Health and Disease 2012, 2(10:369-378 Conclusion: The absolute vegetarian culture medium containing TM 2 is better than standard MRS for the
International Nuclear Information System (INIS)
Sitaramayya, M.
1993-11-01
After a brief review of the geometry of Moishezon spaces, their relation with l-convex spaces and a reasonable and up to date understanding of the obstructions for projectivity of Moishezon objects both in singular and non-singular case is given. The geometry of l-convex manifolds and with l-dimensional exceptional set is studied and some problems and conjectures are stated. The tools of cohomology vanishing theorems important for the subject are briefly sketched. Compactifications of C 3 and Stein spaces are finally outlined. given. 111 refs, 2 figs
Fixed point theorems in locally convex spacesÃ¢Â€Â”the Schauder mapping method
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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.
DEFF Research Database (Denmark)
Huang, Shaojun; Wu, Qiuwei; Zhao, Haoran
2016-01-01
Renewable energies are increasingly integrated in electric distribution networks and will cause severe overvoltage issues. Smart grid technologies make it possible to use coordinated control to mitigate the overvoltage issues and the optimal power flow (OPF) method is proven to be efficient...... in the applications such as curtailment management and reactive power control. Nonconvex nature of the OPF makes it difficult to solve and convex relaxation is a promising method to solve the OPF very efficiently. This paper investigates the geometry of the power flows and the convex-relaxed power flows when high...
International Nuclear Information System (INIS)
Yan-Jun, Gong; Zhen-Sen, Wu; Jia-Ji, Wu
2009-01-01
We present an analytical model of Doppler spectra in backscattering from arbitrary rough convex bodies of revolution rotating around their axes in the global Cartesian coordinate system. This analytical model is applied to analyse Doppler spectra in backscatter from two cones and two cylinders, as well as two ellipsoids of revolution. We numerically analyse the influences of attitude and geometry size of objects on Doppler spectra. The analytical model can give contribution of the surface roughness, attitude and geometry size of convex bodies of revolution to Doppler spectra and may contribute to laser Doppler velocimetry as well as ladar applications
Depauw, S; Bosch, G; Hesta, M; Whitehouse-Tedd, K; Hendriks, W H; Kaandorp, J; Janssens, G P J
2012-08-01
The natural diet of felids contains highly digestible animal tissues but also fractions resistant to small intestinal digestion, which enter the large intestine where they may be fermented by the resident microbial population. Little information exists on the microbial degradability of animal tissues in the large intestine of felids consuming a natural diet. This study aimed to rank animal substrates in their microbial degradability by means of an in vitro study using captive cheetahs fed a strict carnivorous diet as fecal donors. Fresh cheetah fecal samples were collected, pooled, and incubated with various raw animal substrates (chicken cartilage, collagen, glucosamine-chondroitin, glucosamine, rabbit bone, rabbit hair, and rabbit skin; 4 replicates per substrate) for cumulative gas production measurement in a batch culture technique. Negative (cellulose) and positive (casein and fructo-oligosaccharides; FOS) controls were incorporated in the study. Additionally, after 72 h of incubation, short-chain fatty acids (SCFA), including branched-chain fatty acids (BCFA), and ammonia concentrations were determined for each substrate. Glucosamine and glucosamine-chondroitin yielded the greatest organic matter cumulative gas volume (OMCV) among animal substrates (P carnivore, and indicates that animal tissues have potentially similar functions as soluble or insoluble plant fibers in vitro. Further research is warranted to assess the impact of fermentation of each type of animal tissue on gastro-intestinal function and health in the cheetah and other felid species.
Hunting the ghosts of a 'strictly quantum field': the Klein-Gordon equation
International Nuclear Information System (INIS)
Bertozzi, Eugenio
2010-01-01
This paper aims to identify and tackle some problems related to teaching quantum field theory (QFT) at university level. In particular, problems arising from the canonical quantization are addressed by focusing on the Klein-Gordon equation (KGE). After a brief description of the status of the KGE in teaching as it emerges from an analysis of a selected sample of university textbooks, an analysis of the applications of the KGE in contexts different from the QFT is presented. The results of the analysis show that, while in the real case the solutions of the equation can be easily interpreted from a physical point of view, in the complex case the coherence with relativistic quantum mechanics and the electrodynamics framework brings to light interpretative problems related to the classical complex KG field. The comparison between the classical cases investigated and the QFT framework, where the equation finds a coherent particle interpretation, leads to share Ryder's statement asserting that the KG field is a 'strictly quantum field'. Implications of the results in terms of remarks about the canonical procedure currently utilized for teaching are underlined.