Czech Academy of Sciences Publication Activity Database
Moltó, A.; Orihuela, J.; Troyanski, S.; Zizler, Václav
2007-01-01
Roč. 75, č. 3 (2007), s. 647-658 ISSN 0024-6107 R&D Projects: GA AV ČR IAA100190502 Institutional research plan: CEZ:AV0Z10190503 Keywords : strictly convex norms * lattice norm * quasi-diagonal sets Subject RIV: BA - General Mathematics Impact factor: 0.733, year: 2007
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
... Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 126; Issue 4. Strictly convex functions on complete Finsler manifolds. YOE ITOKAWA KATSUHIRO SHIOHAMA BANKTESHWAR TIWARI. Research Article Volume 126 Issue 4 October 2016 pp 623-627 ...
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 ...
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
minimum set of a super Busemann function contains a soul of M. Clearly, a complete simply connected Riemannian manifold H of non-positive sec- tional curvature, called Hadamard manifold, has the property that the distance function to an arbitrary fixed point is strongly convex exhaustion. Also, the exponential map expp :.
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)
The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex domains
Directory of Open Access Journals (Sweden)
David Hartenstine
2006-10-01
Full Text Available It is well-known that the Dirichlet problem for the Monge-Amp`ere equation $det D^2 u = mu$ in a bounded strictly convex domain $Omega$ in $mathbb{R}^n$ has a weak solution (in the sense of Aleksandrov for any finite Borel measure $mu$ on $Omega$ and for any continuous boundary data. We consider the Dirichlet problem when $Omega$ is only assumed to be convex, and give a necessary and sufficient condition on the boundary data for solvability.
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
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.
Unconditional bases and strictly convex dual renormings
Czech Academy of Sciences Publication Activity Database
Smith, Richard James; Troyanski, S.
2009-01-01
Roč. 41, č. 5 (2009), s. 831-840 ISSN 0024-6093 R&D Projects: GA AV ČR IAA100190801; GA ČR GA201/07/0394 Institutional research plan: CEZ:AV0Z10190503 Keywords : descroptive compact spaces * Banach spaces * norms Subject RIV: BA - General Mathematics Impact factor: 0.757, year: 2009 http://blms.oxfordjournals.org/content/41/5/831
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
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....
Krantz, Steven G
2014-01-01
Why Convexity?Basic IdeasIntroductionThe Classical TheorySeparation TheoremsApproximationFunctionsDefining FunctionAnalytic DefinitionConvex FunctionsExhaustion FunctionsMore on FunctionsOther CharacterizationsConvexity of Finite OrderExtreme PointsSupport FunctionsApproximation from BelowBumpingApplicationsThe Krein-Milman TheoremThe Minkowski SumBrunn-MinkowskiMore Sophisticated IdeasThe Polar of a SetOptimizationIntroductory
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.
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
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.
Bornological Locally Convex Cones
Directory of Open Access Journals (Sweden)
Davood Ayaseh
2014-10-01
Full Text Available In this paper we define bornological and b-bornological cones and investigate their properties. We give some characterization for these cones. In the special case of locally convex topological vector space both these concepts reduce to the known concept of bornological spaces. We introduce and investigate the convex quasiuniform structures U_{tau}, U_{sigma}(P,P* and \\U_{beta}(P,P* on locally convex cone (P,U.
Directory of Open Access Journals (Sweden)
David Eppstein
2016-01-01
Full Text Available 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 determine whether a given graph has a strict confluent drawing but polynomial to determine whether it has an outerplanar strict confluent drawing with a fixed vertex ordering (a drawing within a disk, with the vertices placed in a given order on the boundary.
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
Colesanti, Andrea; Gronchi, Paolo
2018-01-01
This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016. It offers a collection of selected articles, written by some of the world’s leading experts in the field of Convex Geometry, on recent developments in this area: theory of valuations; geometric inequalities; affine geometry; and curvature measures. The book will be of interest to a broad readership, from those involved in Convex Geometry, to those focusing on Functional Analysis, Harmonic Analysis, Differential Geometry, or PDEs. The book is a addressed to PhD students and researchers, interested in Convex Geometry and its links to analysis.
Convex Congestion Network Problems
Quant, M.; Reijnierse, J.H.
2004-01-01
This paper analyzes convex congestion network problems.It is shown that for network problems with convex congestion costs, an algorithm based on a shortest path algorithm, can be used to find an optimal network for any coalition. Furthermore an easy way of determining if a given network is optimal
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
Mann iteration with errors for strictly pseudo-contractive mappings ...
African Journals Online (AJOL)
It is well known that any fixed point of a Lipschitzian strictly pseudo-contractive self mapping of a nonempty closed convex and bounded subset K of a Banach space X is unique [6] and may be norm approximated by an iterative procedure. In this paper, we show that Mann iteration with errors can be used to approximate the ...
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
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.
Statistical properties of convex clustering
Tan, Kean Ming; Witten, Daniela
2015-01-01
In this manuscript, we study the statistical properties of convex clustering. We establish that convex clustering is closely related to single linkage hierarchical clustering and $k$-means clustering. In addition, we derive the range of the tuning parameter for convex clustering that yields a non-trivial solution. We also provide an unbiased estimator of the degrees of freedom, and provide a finite sample bound for the prediction error for convex clustering. We compare convex clustering to so...
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...
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.
Indian Academy of Sciences (India)
A subset C of an arbitrary vector space. V is called convex .... C c IR n is the set of those points X E IRn for which it is possible to find a sequence {Xk : k = 1, 2 } in C which converges to X (meaning that limk_oo Ilxk - xii = 0).) (3) Prove that if S ..... subject of linear programming which deals with extrema of linear forms subject to.
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
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
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.
Fuzzy efficiency without convexity
DEFF Research Database (Denmark)
Hougaard, Jens Leth; Balezentis, Tomas
2014-01-01
In this paper we develop a fuzzy version of the crisp Free Disposal Hull (FDH) method for measuring technical efficiency for samples of similar production units. The FDH-method is basically Data Envelopment Analysis (DEA) without the underlying assumption of convexity of the technology set. Our...... approach builds directly upon the definition of Farrell's indexes of technical efficiency used in crisp FDH. Therefore we do not require the use of fuzzy programming techniques but only utilize ranking probabilities of intervals as well as a related definition of dominance between pairs of intervals. We...
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...
Convex probe endobronchial ultrasound.
Bade, Brett; Furukawa, Brian; Tanner, Nichole T
2014-12-01
Convex probe endobronchial ultrasound (EBUS) is a minimally invasive diagnostic technique that allows real-time sampling of mediastinal and hilar lymph nodes and central pulmonary lesions. Its utility in diagnosing both malignant and nonmalignant diseases has led to an increased uptake and use by pulmonologists over the past decade. Because of the robust evidence supporting its safety and diagnostic yield, EBUS is now the first guideline recommended test for staging in non-small cell lung cancer (NSCLC). It has also a role in providing tissue for molecular analysis, thereby guiding in the selection of agents in the new era of personalized chemotherapies in the treatment of NSCLC. The following review highlights the evidence for EBUS in diagnosing mediastinal pathology and addresses technique, training, and competency and future directions for this technology. Thieme Medical Publishers 333 Seventh Avenue, New York, NY 10001, USA.
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
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
Analyse convexe et quasi-convexe ; applications en optimisation
DANIILIDIS, Aris
2002-01-01
Rapporteurs : R. Deville (Bordeaux) D.T. Luc (Avignon) J.-E. Martinez-Legaz (Barcelone, Espagne) Examinateurs : J.-P. Crouzeix (Clermont-Ferrand) (President du jury) S. Gautier (Pau) N. Hadjisavvas (Samos, Grece) J.-P. Penot (Pau) L. Thibault (Montpellier); This document is a research contribution on Convex Analysis, on Generalized Convexity and on their applications in Optimization Theory. The first part deals with several fundamental questions concerning continuity, differentiability and cr...
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
The Convex Coordinates of the Symmedian Point
Boyd, J. N.; Raychowdhury, P. N.
2006-01-01
In this note, we recall the convex (or barycentric) coordinates of the points of a closed triangular region. We relate the convex and trilinear coordinates of the interior points of the triangular region. We use the relationship between convex and trilinear coordinates to calculate the convex coordinates of the symmedian point of the triangular…
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....
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
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...... formulas. Concretely for LIBOR in arrears (LIA) contracts, we derive the system of Riccatti ODE-s one needs to compute to obtain the exact adjustment. Based upon the ideas of Schrager and Pelsser (2006) we are also able to derive general swap adjustments useful, in particular, when dealing with constant...
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...... Relational Model (IRM) [2], a novel unsupervised machine learning method that learns multi-dimensional relations among concepts and features from loosely structured datasets. These methods are combined with a novel cognitive model, the Bayesian Model of Generalization (BMG) [3] that maps culturally...
Quantum information and convex optimization
Energy Technology Data Exchange (ETDEWEB)
Reimpell, Michael
2008-07-01
This thesis is concerned with convex optimization problems in quantum information theory. It features an iterative algorithm for optimal quantum error correcting codes, a postprocessing method for incomplete tomography data, a method to estimate the amount of entanglement in witness experiments, and it gives necessary and sufficient criteria for the existence of retrodiction strategies for a generalized mean king problem. (orig.)
Quantum information and convex optimization
International Nuclear Information System (INIS)
Reimpell, Michael
2008-01-01
This thesis is concerned with convex optimization problems in quantum information theory. It features an iterative algorithm for optimal quantum error correcting codes, a postprocessing method for incomplete tomography data, a method to estimate the amount of entanglement in witness experiments, and it gives necessary and sufficient criteria for the existence of retrodiction strategies for a generalized mean king problem. (orig.)
CONVEX BODIES AND GAUSSIAN PROCESSES
Directory of Open Access Journals (Sweden)
Richard A Vitale
2011-05-01
Full Text Available For several decades, the topics of the title have had a fruitful interaction. This survey will describe some of these connections, including the GB/GC classification of convex bodies, Ito-Nisio singularities from a geometric viewpoint, Gaussian representation of intrinsic volumes, theWills functional in a Gaussian context, and inequalities.
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
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...
Fixed point theorems for paracompact convex sets
International Nuclear Information System (INIS)
Jiang Jiahe.
1986-08-01
In the present paper a few fixed point theorems are given for upper hemi-continuous mappings from a paracompact convex set to its embracing space, a real, locally convex, Hausdorff topological vector space. (author)
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
Revisiting separation properties of convex fuzzy sets
Separation of convex sets by hyperplanes has been extensively studied on crisp sets. In a seminal paper separability and convexity are investigated, however there is a flaw on the definition of degree of separation. We revisited separation on convex fuzzy sets that have level-wise (crisp) disjointne...
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
Scoliosis convexity and organ anatomy are related.
Schlösser, Tom P C; Semple, Tom; Carr, Siobhán B; Padley, Simon; Loebinger, Michael R; Hogg, Claire; Castelein, René M
2017-06-01
Primary ciliary dyskinesia (PCD) is a respiratory syndrome in which 'random' organ orientation can occur; with approximately 46% of patients developing situs inversus totalis at organogenesis. The aim of this study was to explore the relationship between organ anatomy and curve convexity by studying the prevalence and convexity of idiopathic scoliosis in PCD patients with and without situs inversus. Chest radiographs of PCD patients were systematically screened for existence of significant lateral spinal deviation using the Cobb angle. Positive values represented right-sided convexity. Curve convexity and Cobb angles were compared between PCD patients with situs inversus and normal anatomy. A total of 198 PCD patients were screened. The prevalence of scoliosis (Cobb >10°) and significant spinal asymmetry (Cobb 5-10°) was 8 and 23%, respectively. Curve convexity and Cobb angle were significantly different within both groups between situs inversus patients and patients with normal anatomy (P ≤ 0.009). Moreover, curve convexity correlated significantly with organ orientation (P scoliosis (8 situs inversus and 8 normal anatomy), except for one case, matching of curve convexity and orientation of organ anatomy was observed: convexity of the curve was opposite to organ orientation. This study supports our hypothesis on the correlation between organ anatomy and curve convexity in scoliosis: the convexity of the thoracic curve is predominantly to the right in PCD patients that were 'randomized' to normal organ anatomy and to the left in patients with situs inversus totalis.
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.
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...
Hadamard type inequalities for m-convex and (α, m)-convex functions via fractional integrals
Ardıç, Merve Avcı; Ekinci, Alper; Akdemir, Ahmet Ocak; Özdemir, M. Emin
2018-01-01
In this paper, we established some new Hadamard-type integral inequalities for functions whose derivatives of absolute values are m-convex and (α, m)-convex functions via Riemann-Liouville fractional integrals.
Extremely strict ideals in Banach spaces
Indian Academy of Sciences (India)
Motivated by the notion of an ideal introduced by Godefroy {\\it et al.} ({\\it Studia Math.} {\\bf 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 continuous functions on K is an extremely strict ideal in the space of continuous ...
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...
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
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;
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
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...
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...... matrix of a finite metric space 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....
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....
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.
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
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 ......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...
Convex analysis and optimization in Hadamard spaces
Bacak, Miroslav
2014-01-01
This book gives a first systematic account on the subject of convex analysis and optimization in Hadamard spaces. It is primarily aimed at both graduate students and researchers in analysis and optimization.
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.
Minimum convex partitions and maximum empty polytopes
Directory of Open Access Journals (Sweden)
Adrian Dumitrescu
2014-05-01
Full Text Available Let S be a set of n points in Rd. A Steiner convex partition is a tiling of conv(S with empty convex bodies. For every integer d, we show that S admits a Steiner convex partition with at most ⌈(n-1/d⌉ tiles. This bound is the best possible for points in general position in the plane, and it is the best possible apart from constant factors in every fixed dimension d≥3. We also give the first constant-factor approximation algorithm for computing a minimum Steiner convex partition of a planar point set in general position.Establishing a tight lower bound for the maximum volume of a tile in a Steiner convex partition of any n points in the unit cube is equivalent to a famous problem of Danzer and Rogers. It is conjectured that the volume of the largest tile is ω(1/n. Here we give a (1-\\epsilon-approximation algorithm for computing the maximum volume of an empty convex body amidst n given points in the d-dimensional unit box [0,1]d.
On the convexity of N-Chebyshev sets
International Nuclear Information System (INIS)
Borodin, Petr A
2011-01-01
We define N-Chebyshev sets in a Banach space X for every positive integer N (when N=1, these are ordinary Chebyshev sets) and study conditions that guarantee their convexity. In particular, we prove that all N-Chebyshev sets are convex when N is even and X is uniformly convex or N≥3 is odd and X is smooth uniformly convex.
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 superadditivity and convexity for cooperative games with random payoffs
Timmer, Judith B.
In this paper we study the relations between superadditivity and several types of convexity for cooperative games with random payoffs. The types of convexity considered are marginal convexity (all marginal vectors belong to the core), individual-merge convexity (any individual player is better off
Finite Metric Spaces of Strictly Negative Type
DEFF Research Database (Denmark)
Hjorth, Poul; Lisonek, P.; Markvorsen, Steen
1998-01-01
We prove that, if a finite metric space is of strictly negative type, then its transfinite diameter is uniquely realized by the infinite extender (load vector). Finite metric spaces that have this property include all spaces on two, three, or four points, all trees, and all finite subspaces of Eu...
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....
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.
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...
Extremely strict ideals in Banach spaces
Indian Academy of Sciences (India)
the space of regular Borel measures, it is easy to see that with respect to the projection μ → μ|(0, 1), M is an extremely strict ideal in C([0, 1]) but as the Lebesgue measure is non-atomic, M. ∗. 1 is not the norm closed ..... (Grenoble) 28 (1978) 35–65. [10] Rao T S S R K, On ideals in Banach spaces, Rocky Mountain J. Math.
Convex Regression with Interpretable Sharp Partitions.
Petersen, Ashley; Simon, Noah; Witten, Daniela
2016-06-01
We consider the problem of predicting an outcome variable on the basis of a small number of covariates, using an interpretable yet non-additive model. We propose convex regression with interpretable sharp partitions (CRISP) for this task. CRISP partitions the covariate space into blocks in a data-adaptive way, and fits a mean model within each block. Unlike other partitioning methods, CRISP is fit using a non-greedy approach by solving a convex optimization problem, resulting in low-variance fits. We explore the properties of CRISP, and evaluate its performance in a simulation study and on a housing price data set.
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...
Cost Allocation and Convex Data Envelopment
DEFF Research Database (Denmark)
Hougaard, Jens Leth; Tind, Jørgen
This paper considers allocation rules. First, we demonstrate that costs allocated by the Aumann-Shapley and the Friedman-Moulin cost allocation rules are easy to determine in practice using convex envelopment of registered cost data and parametric programming. Second, from the linear programming...... such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output...
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.
Directory of Open Access Journals (Sweden)
Upadhyay Balendu B.
2017-01-01
Full Text Available In this paper, we define some new generalizations of strongly convex functions of order m for locally Lipschitz functions using Clarke subdifferential. Suitable examples illustrating the non emptiness of the newly defined classes of functions and their relationships with classical notions of pseudoconvexity and quasiconvexity are provided. These generalizations are then employed to establish sufficient optimality conditions for a nonsmooth multiobjective optimization problem involving support functions of compact convex sets. Furthermore, we formulate a mixed type dual model for the primal problem and establish weak and strong duality theorems using the notion of strict efficiency of order m. The results presented in this paper extend and unify several known results from the literature to a more general class of functions as well as optimization problems.
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
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
Robust Utility Maximization Under Convex Portfolio Constraints
Energy Technology Data Exchange (ETDEWEB)
Matoussi, Anis, E-mail: anis.matoussi@univ-lemans.fr [Université du Maine, Risk and Insurance institut of Le Mans Laboratoire Manceau de Mathématiques (France); Mezghani, Hanen, E-mail: hanen.mezghani@lamsin.rnu.tn; Mnif, Mohamed, E-mail: mohamed.mnif@enit.rnu.tn [University of Tunis El Manar, Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT (Tunisia)
2015-04-15
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption–investment strategy by studying the associated quadratic backward stochastic differential equation. We characterize the optimal control by using the duality method and deriving a dynamic maximum principle.
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...
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.
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...
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...
Uniformly convex functions on Banach spaces
Czech Academy of Sciences Publication Activity Database
Borwein, J.; Guirao, A. J.; Hájek, Petr Pavel; Vanderwerff, J.
2009-01-01
Roč. 137, č. 3 (2009), s. 1081-1091 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190502; GA AV ČR IAA100190801 Institutional research plan: CEZ:AV0Z10190503 Keywords : power type 2 * uniform convexity Subject RIV: BA - General Mathematics Impact factor: 0.640, year: 2009
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
Convex Formulations of Learning from Crowds
Kajino, Hiroshi; Kashima, Hisashi
It has attracted considerable attention to use crowdsourcing services to collect a large amount of labeled data for machine learning, since crowdsourcing services allow one to ask the general public to label data at very low cost through the Internet. The use of crowdsourcing has introduced a new challenge in machine learning, that is, coping with low quality of crowd-generated data. There have been many recent attempts to address the quality problem of multiple labelers, however, there are two serious drawbacks in the existing approaches, that are, (i) non-convexity and (ii) task homogeneity. Most of the existing methods consider true labels as latent variables, which results in non-convex optimization problems. Also, the existing models assume only single homogeneous tasks, while in realistic situations, clients can offer multiple tasks to crowds and crowd workers can work on different tasks in parallel. In this paper, we propose a convex optimization formulation of learning from crowds by introducing personal models of individual crowds without estimating true labels. We further extend the proposed model to multi-task learning based on the resemblance between the proposed formulation and that for an existing multi-task learning model. We also devise efficient iterative methods for solving the convex optimization problems by exploiting conditional independence structures in multiple classifiers.
Toric Geometry of the Regular Convex Polyhedra
Directory of Open Access Journals (Sweden)
Fiammetta Battaglia
2017-01-01
Full Text Available We describe symplectic and complex toric spaces associated with the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the regular octahedron is not simple, the regular dodecahedron is not rational, and the regular icosahedron is neither simple nor rational. We remark that the last two cases cannot be treated via standard toric geometry.
Similarity measure computation of convex polyhedra revisited
Roerdink, Jos B.T.M.; Bekker, Henk
2001-01-01
We study the computation of rotation-invariant similarity measures of convex polyhedra, based on Minkowski’s theory of mixed volumes. To compute the similarity measure, a (mixed) volume functional has to be minimized over a number of critical orientations of these polyhedra. These critical
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.
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.
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.
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.
Strictness Analysis and Denotational Abstract Interpretation
DEFF Research Database (Denmark)
Nielson, Flemming
1988-01-01
there and this sufices to make the framework applicable to strictness analysis for the lambda-calculus. This shows the possibility of a general theory for the analysis of functional programs and it gives more insight into the relative precision of the various analyses. In particular it is shown that a collecting (static......A theory of abstract interpretation () is developed for a typed lambda-calculus. The typed lambda-calculus may be viewed as the ''static'' part of a two-level denotational metalanguage for which abstract interpretation was developed by ). The present development relaxes a condition imposed...
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. ...
Local Convexity-Preserving C 2 Rational Cubic Spline for Convex Data
Abd Majid, Ahmad; Ali, Jamaludin Md.
2014-01-01
We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data using C 2 rational cubic spline. It involves three families of shape parameters in its representation. Data dependent sufficient constraints are imposed on single shape parameter to conserve the inherited shape feature of data. Remaining two of these shape parameters are used for the modification of convex curve to get a visually pleasing curve according to industrial demand. The scheme is tested through several numerical examples, showing that the scheme is local, computationally economical, and visually pleasing. PMID:24757421
Xia, Youshen; Feng, Gang; Wang, Jun
2004-09-01
This paper presents a recurrent neural network for solving strict convex quadratic programming problems and related linear piecewise equations. Compared with the existing neural networks for quadratic program, the proposed neural network has a one-layer structure with a low model complexity. Moreover, the proposed neural network is shown to have a finite-time convergence and exponential convergence. Illustrative examples further show the good performance of the proposed neural network in real-time applications.
Multi-objective convex programming problem arising in multivariate ...
African Journals Online (AJOL)
objective convex programming problem. The objective functions are convex and there is a single linear constraint with some upper and lower bounds. We also consider a two dimensional multivariate problem when the cost is minimized. A numerical ...
Lyapunov convexity type theorems for non-atomic vector measures ...
African Journals Online (AJOL)
atomic, and σ-additive X-valued measure has a convex closure. We give a survey of Lyapunov convexity type theorems pertaining to this problem. We also give a necessary and sufficient condition that will insure the convexity of the closure of the ...
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.
Convex Modeling of Interactions with Strong Heredity.
Haris, Asad; Witten, Daniela; Simon, Noah
2016-01-01
We consider the task of fitting a regression model involving interactions among a potentially large set of covariates, in which we wish to enforce strong heredity. We propose FAMILY, a very general framework for this task. Our proposal is a generalization of several existing methods, such as VANISH [Radchenko and James, 2010], hierNet [Bien et al., 2013], the all-pairs lasso, and the lasso using only main effects. It can be formulated as the solution to a convex optimization problem, which we solve using an efficient alternating directions method of multipliers (ADMM) algorithm. This algorithm has guaranteed convergence to the global optimum, can be easily specialized to any convex penalty function of interest, and allows for a straightforward extension to the setting of generalized linear models. We derive an unbiased estimator of the degrees of freedom of FAMILY, and explore its performance in a simulation study and on an HIV sequence data set.
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...
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.
Regularity in mixed-integer convex representability
Lubin, Miles; Zadik, Ilias; Vielma, Juan Pablo
2017-01-01
Characterizations of the sets with mixed integer programming (MIP) formulations using only rational linear inequalities (rational MILP representable) and those with formulations that use arbitrary closed convex constraints (MICP representable) were given by Jeroslow and Lowe (1984), and Lubin, Zadik and Vielma (2017). The latter also showed that even MICP representable subsets of the natural numbers can be more irregular than rational MILP representable ones, unless certain rationality is imp...
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.
A Convex Framework for Fair Regression
Berk, Richard; Heidari, Hoda; Jabbari, Shahin; Joseph, Matthew; Kearns, Michael; Morgenstern, Jamie; Neel, Seth; Roth, Aaron
2017-01-01
We introduce a flexible family of fairness regularizers for (linear and logistic) regression problems. These regularizers all enjoy convexity, permitting fast optimization, and they span the rang from notions of group fairness to strong individual fairness. By varying the weight on the fairness regularizer, we can compute the efficient frontier of the accuracy-fairness trade-off on any given dataset, and we measure the severity of this trade-off via a numerical quantity we call the Price of F...
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 \
Stress-Strain diagrams for non-convex particles
Matuttis, Hans-Georg; Nawa, Masaki; Krengel, Dominik
2017-06-01
While most granular materials in nature and technology consist of non-convex particles, the majority of discrete element (DEM) codes are still only able to cope with convex particles, due to the complexity of the computational geometry and the occurrence of multiple contacts. We have reengineered a code for convex polygonal particles to model non-convex particles as rigidly connected clusters. Constricting non-convex particles along the symmetry axes by 30% leads to an increase of the materials strength of up to 50%.
Stress-Strain diagrams for non-convex particles
Directory of Open Access Journals (Sweden)
Matuttis Hans-Georg
2017-01-01
Full Text Available While most granular materials in nature and technology consist of non-convex particles, the majority of discrete element (DEM codes are still only able to cope with convex particles, due to the complexity of the computational geometry and the occurrence of multiple contacts. We have reengineered a code for convex polygonal particles to model non-convex particles as rigidly connected clusters. Constricting non-convex particles along the symmetry axes by 30% leads to an increase of the materials strength of up to 50%.
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
On convex relaxation of graph isomorphism
Aflalo, Yonathan; Bronstein, Alexander; Kimmel, Ron
2015-01-01
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving 2n equality and n2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic. PMID:25713342
Geometrical optimization for strictly localized structures
Mo, Yirong
2003-07-01
Recently we proposed the block localized wavefunction (BLW) approach which takes the advantages of valence bond theory and molecular orbital theory and defines the wavefunctions for resonance structures based on the assumption that all electrons and orbitals are partitioned into a few subgroups. In this work, we implement the geometrical optimization of the BLW method based on the algorithm proposed by Gianinetti and coworkers. Thus, we can study the conjugation effect on not only the molecular stability, but also the molecular geometry. With this capability, the π conjugation effect in trans-polyenes C2nH2n+2 (n=2-5) as well as in formamide and its analogs are studied by optimizing their delocalized and strictly localized forms with the 6-31G(d) and 6-311+G(d,p) basis sets. Although it has been well presumed that the π resonance shortens the single bonds and lengthens the double bonds with the delocalization of π electrons across the whole line in polyenes, our optimization of the strictly localized structures quantitatively shows that when the conjugation effect is "turned off," the double bond lengths will be identical to the CC bond length in ethylene and the single Csp2-Csp2 bond length will be about 1.513-1.517 Å. In agreement with the classical Hückel theory, the resonance energies in polyenes are approximately in proportion to the number of double bonds. Similarly, resonance is responsible not only for the planarity of formamide, thioformamide, and selenoformamide, but also for the lengthening of the CX (X=O,S,Se) double bond and the shortening of the CN bonds. Although it is assumed that the CX bond polarization decreases in the order of O>S>Se, the π electronic delocalization increases in the opposite order, i.e., formamide
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.
On the embedding of convex spaces in stratified L-convex spaces.
Jin, Qiu; Li, Lingqiang
2016-01-01
Consider L being a continuous lattice, two functors from the category of convex spaces (denoted by CS) to the category of stratified L-convex spaces (denoted by SL-CS) are defined. The first functor enables us to prove that the category CS can be embedded in the category SL-CS as a reflective subcategory. The second functor enables us to prove that the category CS can be embedded in the category SL-CS as a coreflective subcategory when L satisfying a multiplicative condition. By comparing the two functors and the well known Lowen functor (between topological spaces and stratified L-topological spaces), we exhibit the difference between (stratified L-)topological spaces and (stratified L-)convex spaces.
From Regular to Strictly Locally Testable Languages
Directory of Open Access Journals (Sweden)
Stefano Crespi Reghizzi
2011-08-01
Full Text Available A classical result (often credited to Y. Medvedev states that every language recognized by a finite automaton is the homomorphic image of a local language, over a much larger so-called local alphabet, namely the alphabet of the edges of the transition graph. Local languages are characterized by the value k=2 of the sliding window width in the McNaughton and Papert's infinite hierarchy of strictly locally testable languages (k-slt. We generalize Medvedev's result in a new direction, studying the relationship between the width and the alphabetic ratio telling how much larger the local alphabet is. We prove that every regular language is the image of a k-slt language on an alphabet of doubled size, where the width logarithmically depends on the automaton size, and we exhibit regular languages for which any smaller alphabetic ratio is insufficient. More generally, we express the trade-off between alphabetic ratio and width as a mathematical relation derived from a careful encoding of the states. At last we mention some directions for theoretical development and application.
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 28.406 - 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 28.402 - 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...
Mammalian evolution may not be strictly bifurcating.
Hallström, Björn M; Janke, Axel
2010-12-01
The massive amount of genomic sequence data that is now available for analyzing evolutionary relationships among 31 placental mammals reduces the stochastic error in phylogenetic analyses to virtually zero. One would expect that this would make it possible to finally resolve controversial branches in the placental mammalian tree. We analyzed a 2,863,797 nucleotide-long alignment (3,364 genes) from 31 placental mammals for reconstructing their evolution. Most placental mammalian relationships were resolved, and a consensus of their evolution is emerging. However, certain branches remain difficult or virtually impossible to resolve. These branches are characterized by short divergence times in the order of 1-4 million years. Computer simulations based on parameters from the real data show that as little as about 12,500 amino acid sites could be sufficient to confidently resolve short branches as old as about 90 million years ago (Ma). Thus, the amount of sequence data should no longer be a limiting factor in resolving the relationships among placental mammals. The timing of the early radiation of placental mammals coincides with a period of climate warming some 100-80 Ma and with continental fragmentation. These global processes may have triggered the rapid diversification of placental mammals. However, the rapid radiations of certain mammalian groups complicate phylogenetic analyses, possibly due to incomplete lineage sorting and introgression. These speciation-related processes led to a mosaic genome and conflicting phylogenetic signals. Split network methods are ideal for visualizing these problematic branches and can therefore depict data conflict and possibly the true evolutionary history better than strictly bifurcating trees. Given the timing of tectonics, of placental mammalian divergences, and the fossil record, a Laurasian rather than Gondwanan origin of placental mammals seems the most parsimonious explanation.
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.
Leadership games with convex strategy sets
Bernhard von Stengel; Shmuel Zamir
2010-01-01
A basic model of commitment is to convert a two-player game in strategic form to a “leadership game” with the same payoffs, where one player, the leader, commits to a strategy, to which the second player always chooses a best reply. This paper studies such leadership games for games with convex strategy sets. We apply them to mixed extensions of finite games, which we analyze completely, including nongeneric games. The main result is that leadership is advantageous in the sense that, as a set...
Localized Multiple Kernel Learning A Convex Approach
2016-11-22
1/2 . Theorem 9 (CLMKL Generalization Error Bounds) Assume that km(x, x) ≤ B, ∀m ∈ NM , x ∈ X . Suppose the loss function ℓ is L- Lipschitz and...mathematical foundation (e.g., Schölkopf and Smola, 2002). The performance of such algorithms, however, crucially depends on the involved kernel function ...approaches to localized MKL (reviewed in Section 1.1) optimize non-convex objective functions . This puts their generalization ability into doubt. Indeed
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
Directory of Open Access Journals (Sweden)
Satit Saejung
2005-01-01
Full Text Available We prove that the moduli of U-convexity, introduced by Gao (1995, of the ultrapower X˜ of a Banach space X and of X itself coincide whenever X is super-reflexive. As a consequence, some known results have been proved and improved. More precisely, we prove that uX(1>0 implies that both X and the dual space X∗ of X have uniform normal structure and hence the “worth” property in Corollary 7 of Mazcuñán-Navarro (2003 can be discarded.
Population monotonic solutions on convex games
Toru Hokari
2000-01-01
The Dutta-Ray solution and the Shapley value are two well-known examples of population-monotonic solutions on the domain of convex games. We provide a new formula for the Dutta-Ray solution from which population-monotonicity immediately follows. Then we define a new family of population-monotonic solutions, which we refer to as "sequential Dutta-Ray solutions." We also show that it is possible to construct several symmetric and population-monotonic solutions by using the solutions in this fam...
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...
Functions with bounded variation in locally convex space
Duchoň, Miloslav; Debiève, Camille
2011-01-01
The present paper is concerned with some properties of functions with values in locally convex vector space, namely functions having bounded variation and generalizations of some theorems for functions with values in locally convex vector spaces replacing Banach spaces, namely Theorem: If X is a sequentially complete locally convex vector space, then the function x(·): [a, b] → X having a bounded variation on the interval [a, b] defines a vector-valued measure m on borelian subsets of [a, b] ...
A Randomized Gossip Consenus Algorithm on Convex Metric Spaces
2012-01-01
Property (C) are not that rare. Indeed, by Smulian’s Theorem ([3], page 443), every weakly compact convex subset of a Banach space has Property (C...www.isr.umd.edu A randomized gossip consensus algorithm on convex metric spaces Ion Matei, Christoforos Somarakis, John S. Baras ISR TECHNICAL REPORT 2012-02...2. REPORT TYPE 3. DATES COVERED 00-00-2012 to 00-00-2012 4. TITLE AND SUBTITLE A randomized gossip consensus algorithm on convex metric spaces
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.
Optimality Certificates for Convex Minimization and Helly Numbers
2016-10-20
Optimality certificates for convex minimization and Helly numbers Amitabh Basu Michele Conforti Gérard Cornuéjols Robert Weismantel Stefan Weltge...October 20, 2016 Abstract We consider the problem of minimizing a convex function over a subset of Rn that is not necessarily convex ( minimization of a...problem. Moreover, the inner optimization problem (2) of minimizing on the boundary of C can be very hard if C has no structure other than being S-free
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.)
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.
Giant convexity chondroma with meningeal attachment.
Feierabend, Denise; Maksoud, Salah; Lawson McLean, Aaron; Koch, Arend; Kalff, Rolf; Walter, Jan
2018-03-27
Intracranial chondroma is a rare and benign tumor with usual onset in young adulthood. The skull base is the most common site of occurrence although, less often, the tumors can appear at the falx cerebri or at the dural convexity. The differentiation of these lesions from meningiomas through imaging is generally difficult. Clinical case presentation and review of the current literature. We report a case of a 25-year-old male patient with a giant convexity chondroma with meningeal attachment in the right frontal lobe that was detected after a first generalized seizure. Based on the putative diagnosis of meningioma, the tumor was completely resected via an osteoplastic parasagittal craniotomy. The postoperative MRI confirmed the complete tumor resection. Histopathological analysis revealed the presence of a chondroma. Intracranial chondromas are a rarity and their preoperative diagnosis based on neuroimaging is difficult. In young patients and those with skeletal disease, the differential diagnosis of a chondroma should be considered. In symptomatic patients, operative resection is sensible. In most cases total removal of the tumor is possible and leads to full recovery. When the finding is merely incidental in older patients, a watchful waiting approach is acceptable, given the benign and slow-growing nature of the lesion. Copyright © 2018 Elsevier B.V. All rights reserved.
Convex Optimization over Classes of Multiparticle Entanglement
Shang, Jiangwei; Gühne, Otfried
2018-02-01
A well-known strategy to characterize multiparticle entanglement utilizes the notion of stochastic local operations and classical communication (SLOCC), but characterizing the resulting entanglement classes is difficult. Given a multiparticle quantum state, we first show that Gilbert's algorithm can be adapted to prove separability or membership in a certain entanglement class. We then present two algorithms for convex optimization over SLOCC classes. The first algorithm uses a simple gradient approach, while the other one employs the accelerated projected-gradient method. For demonstration, the algorithms are applied to the likelihood-ratio test using experimental data on bound entanglement of a noisy four-photon Smolin state [Phys. Rev. Lett. 105, 130501 (2010), 10.1103/PhysRevLett.105.130501].
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...
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...
New type integral inequalities for convex functions with applications II
Mehrez, Khaled; Agarwal, Praveen
2017-01-01
We have recently established some integral inequalities for convex functions via the Hermite-Hadamard's inequalities. In continuation here, we also establish some interesting new integral inequalities for convex functions via the Hermite--Hadamard's inequalities and Jensen's integral inequality. Useful applications involving special means are also included.
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.
On some interpolation properties in locally convex spaces
Energy Technology Data Exchange (ETDEWEB)
Pater, Flavius [Department of Mathematics, Politehnica University of Timişoara, 300004 Timişoara (Romania)
2015-03-10
The aim of this paper is to introduce the notion of interpolation between locally convex spaces, the real method, and to present some elementary results in this setting. This represents a generalization from the Banach spaces framework to the locally convex spaces sequentially complete one, where the operators acting on them are locally bounded.
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 28.431 - 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. ...
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 28.424 - 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 28.426 - 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 28.422 - 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...
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...
Analytic convexity: some comments on an example of de Giorgi and Piccinini
International Nuclear Information System (INIS)
Andreotti, A.; Nacinovich, M.
1976-01-01
l. Introduction. 2. Csup(infinite) and analytical convexity for a complex of differential equations with constant coefficients. 3. Reduction of the analytic convexity to the Csup(infinite) convexity. 4. The example of de Giorgi-Piccinini. (author)
Gradient vs. approximation design optimization techniques in low-dimensional convex problems
Fedorik, Filip
2013-10-01
Design Optimization methods' application in structural designing represents a suitable manner for efficient designs of practical problems. The optimization techniques' implementation into multi-physical softwares permits designers to utilize them in a wide range of engineering problems. These methods are usually based on modified mathematical programming techniques and/or their combinations to improve universality and robustness for various human and technical problems. The presented paper deals with the analysis of optimization methods and tools within the frame of one to three-dimensional strictly convex optimization problems, which represent a component of the Design Optimization module in the Ansys program. The First Order method, based on combination of steepest descent and conjugate gradient method, and Supbproblem Approximation method, which uses approximation of dependent variables' functions, accompanying with facilitation of Random, Sweep, Factorial and Gradient Tools, are analyzed, where in different characteristics of the methods are observed.
Learning Convex Regularizers for Optimal Bayesian Denoising
Nguyen, Ha Q.; Bostan, Emrah; Unser, Michael
2018-02-01
We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative logarithm of the prior probability density function). Our alternating direction method of multipliers (ADMM)-based approach translates the estimation task into successive applications of the proximal mapping of the penalty function. Capitalizing on this direct link, we define the proximal operator as a parametric spline curve and optimize the spline coefficients by minimizing the average reconstruction error for a given training set. The key aspects of our learning method are that the associated penalty function is constrained to be convex and the convergence of the ADMM iterations is proven. As a result of these theoretical guarantees, adaptation of the proposed framework to different levels of measurement noise is extremely simple and does not require any retraining. We apply our method to estimation of both sparse and non-sparse models of L\\'{e}vy processes for which the minimum mean square error (MMSE) estimators are available. We carry out a single training session and perform comparisons at various signal-to-noise ratio (SNR) values. Simulations illustrate that the performance of our algorithm is practically identical to the one of the MMSE estimator irrespective of the noise power.
Almost convex metrics and Peano compactifications
Directory of Open Access Journals (Sweden)
R. F. Dickman
1982-01-01
Full Text Available Let (X,d denote a locally connected, connected separable metric space. We say the X is S-metrizable provided there is a topologically equivalent metric ρ on X such that (X,ρ has Property S, i.e., for any ϵ>0, X is the union of finitely many connected sets of ρ-diameter less than ϵ. It is well-known that S-metrizable spaces are locally connected and that if ρ is a Property S metric for X, then the usual metric completion (X˜,ρ˜ of (X,ρ is a compact, locally connected, connected metric space; i.e., (X˜,ρ˜ is a Peano compactification of (X,ρ. In an earlier paper, the author conjectured that if a space (X,d has a Peano compactification, then it must be S-metrizable. In this paper, that conjecture is shown to be false; however, the connected spaces which have Peano compactificatons are shown to be exactly those having a totally bounded, almost convex metric. Several related results are given.
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).
Shape preserving rational cubic spline for positive and convex data
Directory of Open Access Journals (Sweden)
Malik Zawwar Hussain
2011-11-01
Full Text Available In this paper, the problem of shape preserving C2 rational cubic spline has been proposed. The shapes of the positive and convex data are under discussion of the proposed spline solutions. A C2 rational cubic function with two families of free parameters has been introduced to attain the C2 positive curves from positive data and C2 convex curves from convex data. Simple data dependent constraints are derived on free parameters in the description of rational cubic function to obtain the desired shape of the data. The rational cubic schemes have unique representations.
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.
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.
Strict monotonicity and unique continuation of the biharmonic operator
Directory of Open Access Journals (Sweden)
Najib Tsouli
2012-01-01
Full Text Available In this paper, we will show that the strict monotonicity of the eigenvalues of the biharmonic operator holds if and only if some unique continuation property is satisfied by the corresponding eigenfunctions.
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)
Towards a Convex-Analytic View of Impossibility Results in ...
Indian Academy of Sciences (India)
Ankur A. Kulkarni
2016-11-05
Towards a Convex-Analytic View of Impossibility Results in. Stochastic Control and Information Theory. Ankur A. Kulkarni. Systems and Control Engineering. Indian Institute of Technology Bombay. November 5, 2016. 1 / 12 ...
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.
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.
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].
Subaperture Stitching Interferometry for Large Convex Aspheric Surfaces Project
National Aeronautics and Space Administration — The size and accuracy specifications of telescope mirrors are ever more demanding. This is particularly true for secondary mirrors, as they are convex and thus...
Subaperture Stitching Interferometry for Large Convex Aspheric Surfaces, Phase II
National Aeronautics and Space Administration — The size and accuracy specifications of telescope mirrors are ever more demanding. This is particularly true for secondary mirrors, as they are convex and thus...
A simple convex optimization problem with many applications
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1994-01-01
This paper presents an algorithm for the solution of a simple convex optimization problem. This problem is a generalization of several other optimization problems which have applications to resource allocation, optimal capacity expansion, and vehicle scheduling. The algorithm is based...
Celestial Walk: A Terminating Oblivious Walk for Convex Subdivisions
Kuijper, Wouter; Ermolaev, Victor; Devillers, Olivier
2017-01-01
We present a new oblivious walking strategy for convex subdivisions. Our walk is faster than the straight walk and more generally applicable than the visibility walk. To prove termination of our walk we use a novel monotonically decreasing distance measure.
Stochastic convex sparse principal component analysis.
Baytas, Inci M; Lin, Kaixiang; Wang, Fei; Jain, Anil K; Zhou, Jiayu
2016-12-01
Principal component analysis (PCA) is a dimensionality reduction and data analysis tool commonly used in many areas. The main idea of PCA is to represent high-dimensional data with a few representative components that capture most of the variance present in the data. However, there is an obvious disadvantage of traditional PCA when it is applied to analyze data where interpretability is important. In applications, where the features have some physical meanings, we lose the ability to interpret the principal components extracted by conventional PCA because each principal component is a linear combination of all the original features. For this reason, sparse PCA has been proposed to improve the interpretability of traditional PCA by introducing sparsity to the loading vectors of principal components. The sparse PCA can be formulated as an ℓ 1 regularized optimization problem, which can be solved by proximal gradient methods. However, these methods do not scale well because computation of the exact gradient is generally required at each iteration. Stochastic gradient framework addresses this challenge by computing an expected gradient at each iteration. Nevertheless, stochastic approaches typically have low convergence rates due to the high variance. In this paper, we propose a convex sparse principal component analysis (Cvx-SPCA), which leverages a proximal variance reduced stochastic scheme to achieve a geometric convergence rate. We further show that the convergence analysis can be significantly simplified by using a weak condition which allows a broader class of objectives to be applied. The efficiency and effectiveness of the proposed method are demonstrated on a large-scale electronic medical record cohort.
Multi-objective convex programming problem arising in multivariate ...
African Journals Online (AJOL)
user
C. XC to. Subject a p j. X a. V. Minimize i i. L i ii. L i i ij j. (5). The objective functions in (equation 5) are convex [see Kokan and Khan (1967)], the single constraint is linear and the bounds are also linear. The problem (5) is, therefore a multi-objective convex programming problem. If some tolerance limits, say j v are given on ...
Non-convex mixed-integer nonlinear programming: a survey
Burer, S; Letchford, Adam
2012-01-01
A wide range of problems arising in practical applications can be formulated as Mixed-Integer Nonlinear Programs (MINLPs). For the case in which the objective and constraint functions are convex, some quite effective exact and heuristic algorithms are available. When nonconvexities are present, however, things become much more difficult, since then even the continuous relaxation is a global optimisation problem. We survey the literature on non-convex MINLP, discussing applications, algorithms...
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
DEFF Research Database (Denmark)
Karakashev, Dimitar Borisov; Kotay, Shireen Meher; Trably, Eric
2009-01-01
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......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...
Directory of Open Access Journals (Sweden)
Horváth László
2011-01-01
Full Text Available Abstract In this paper, a new parameter-dependent refinement of the discrete Jensen's inequality is given for convex and mid-convex functions. The convergence of the introduced sequences is also studied. One of the proofs requires an interesting convergence theorem with probability theoretical background. We apply the results to define some new quasi-arithmetic and mixed symmetric means and study their monotonicity and convergence.
Directory of Open Access Journals (Sweden)
Rafa Espínola
2010-01-01
Full Text Available We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for set-valued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric which makes a big difference when studying the existence of fixed points for set-valued mappings.
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
Trace-Inequalities and Matrix-Convex Functions
Directory of Open Access Journals (Sweden)
Tsuyoshi Ando
2010-01-01
Full Text Available A real-valued continuous function f(t on an interval (α,β gives rise to a map X↦f(X via functional calculus from the convex set of n×n Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provided with the order structure induced by the cone of positive semidefinite matrices, one can consider convexity of this map. We will characterize its convexity by the following trace-inequalities: Tr(f(B−f(A(C−B≤Tr(f(C−f(B(B−A for A≤B≤C. A related topic will be also discussed.
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)
Stability results for convex bodies in geometric tomography
DEFF Research Database (Denmark)
Kiderlen, Markus
2008-01-01
improve the Holder exponents of known stability results for these transforms. The key idea for this improvement is to use the fact that support functions of convex bodies are elements of any spherical Sobolev space of derivative order less than 3/2. As the analytical representation Q(K,.) may......We consider the question in how far a convex body (non-empty compact convex set) K in n-dimensional space is determined by tomographic measurements (in a broad sense). Usually these measurements are derived from K by geometrical operations like sections, projections and certain averages of those....... We restrict to tomographic measurements F(K,.) that can be written as function on the unit sphere and depend additively on an analytical representation Q(K,.) of K. The first main result states that F(K,.) is a multiplier-rotation operator of Q(K,.) whenever the tomographic data depends...
Optimally Convex Controller and Model Reduction for a Dynamic System
Directory of Open Access Journals (Sweden)
P. S. KHUNTIA
2008-07-01
Full Text Available This paper presents analysis and design of a family of controllers based on numerical convex optimization for an aircraft pitch control system. A design method is proposed here to solve control system design problems in which a set of multiple closed loop performance specifications are simultaneously satisfied. The transfer matrix of the system is determined through the convex combination of the transfer matrices of the plant and the controllers. The present system with optimal convex controller has been tested for stability using Kharitonov’s Stability Criteria. The simulation deals here withthe problem of pitch control system of a BRAVO fighter aircraft which results in higher order close loop transfer function. So the order of the higher order transfer function is reduced to minimize the complexity of the system.
Dominated operators, absolutely summing operators and the strict ...
African Journals Online (AJOL)
b(X;E) be the space of all E-valued bounded continuous functions on X, equipped with the strict topology β. We study dominated and absolutely summing operators T : Cb(X;E) → F. We derive that if X is a locally compact Hausdorff space and E ...
Convergence of GAOR Iterative Method with Strictly Diagonally Dominant Matrices
Directory of Open Access Journals (Sweden)
Guangbin Wang
2011-01-01
Full Text Available We discuss the convergence of GAOR method for linear systems with strictly diagonally dominant matrices. Moreover, we show that our results are better than ones of Darvishi and Hessari (2006, Tian et al. (2008 by using three numerical examples.
Runaway selection for cooperation and strict-and-severe punishment.
Nakamaru, Mayuko; Dieckmann, Ulf
2009-03-07
Punishing defectors is an important means of stabilizing cooperation. When levels of cooperation and punishment are continuous, individuals must employ suitable social standards for defining defectors and for determining punishment levels. Here we investigate the evolution of a social reaction norm, or psychological response function, for determining the punishment level meted out by individuals in dependence on the cooperation level exhibited by their neighbors in a lattice-structured population. We find that (1) cooperation and punishment can undergo runaway selection, with evolution towards enhanced cooperation and an ever more demanding punishment reaction norm mutually reinforcing each other; (2) this mechanism works best when punishment is strict, so that ambiguities in defining defectors are small; (3) when the strictness of punishment can adapt jointly with the threshold and severity of punishment, evolution favors the strict-and-severe punishment of individuals who offer slightly less than average cooperation levels; (4) strict-and-severe punishment naturally evolves and leads to much enhanced cooperation when cooperation without punishment would be weak and neither cooperation nor punishment are too costly; and (5) such evolutionary dynamics enable the bootstrapping of cooperation and punishment, through which defectors who never punish gradually and steadily evolve into cooperators who punish those they define as defectors.
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
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....
Directory of Open Access Journals (Sweden)
Stefan M. Stefanov
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.
Towards a Convex-Analytic View of Impossibility Results in ...
Indian Academy of Sciences (India)
Ankur A. Kulkarni
2016-11-05
Nov 5, 2016 ... [Jose and Kulkarni, 2015, IEEE CDC], [Jose and Kulkarni, 2016, IEEE. Trans IT]. Original problem. Optimization over distributions. (Nonconvex! ) min codes. Perror(code, R, n). ⇐⇒ min distributions. Perror(distribution, R, n). ⇓. A particular LP relaxation. Convex relaxation min hyperplanes. Perror(dist, R, n).
The Fatou property in p-convex Banach lattices
Curbera, Guillermo P.; Ricker, Werner J.
2007-04-01
New features of the Banach function space , that is, the space of all [nu]-scalarly pth power integrable functions (with 1[less-than-or-equals, slant]pFatou property plays an essential role and leads to a new representation theorem for a large class of abstract p-convex Banach lattices.
Convex Combination of Multiple Statistical Models with Application to VAD
DEFF Research Database (Denmark)
Petsatodis, Theodoros; Boukis, Christos; Talantzis, Fotios
2011-01-01
This paper proposes a robust Voice Activity Detector (VAD) based on the observation that the distribution of speech captured with far-field microphones is highly varying, depending on the noise and reverberation conditions. The proposed VAD employs a convex combination scheme comprising three...
Linear inequality and convexity. Lineinye neravenstva i vypuklost
Energy Technology Data Exchange (ETDEWEB)
Astaf' ev, N.N.
1982-01-01
An examination is made of convex programming within the framework of linear inequality systems which are distinguished by constructivity and computational possibilities. Considerable attention is given to the study of various convergence situations. The book will be of interest to specialists in the field of mathmatical programming and optimization. 17 references.
On moduli of convexity and some applications | Barcenas ...
African Journals Online (AJOL)
Abstract. We provide some properties of both moduli of convexity δ and β and derive some applications of the modulus β to the geometry of Banach spaces as well as fixed point theory. Quaestiones Mathematicae 32(2009), 307–319 ...
Dynamical convexity of the Euler problem of two fixed centers
Kim, Seongchan
2016-01-01
We give thorough analysis for the rotation functions of the critical orbits from which one can understand bifurcations of periodic orbits. Moreover, we give explicit formulas of the Conley-Zehnder indices of the interior and exterior collision orbits and show that the universal cover of the regularized energy hypersurface of the Euler problem is dynamically convex for energies below the critical Jacobi energy.
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.
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...
Convexity of spheres in a manifold without conjugate points
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. For a non-compact, complete and simply connected manifold M without conjugate points, we prove that if the determinant of the second fundamental form of the geodesic spheres in M is a radial function, then the geodesic spheres are convex. We also show that if M is two or three dimensional and without ...
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.
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.
On the distance between convex-ordered random variables, with applications
Boutsikas, Michael V.; Vaggelatou, Eutichia
2002-01-01
Simple approximation techniques are developed exploiting relationships between generalized convex orders and appropriate probability metrics. In particular, the distance between s-convex ordered random variables is investigated. Results connecting positive or negative dependence concepts and convex ordering are also presented. These results lead to approximations and bounds for the distributions of sums of positively or negatively dependent random variables. Applications and ex...
Polynômes et optimisation convexe en commande robuste
Henrion, Didier
2007-01-01
A l'aide de quelques exemples illustratifs, des pistes sont évoquées pour combiner les méthodes polynomiales (algèbre, géométrie algébrique) et l'optimisation convexe (inégalités matricielles linéaires, LMI) dans le but de développer des outils numériques de résolution de problèmes basiques en automatique, et en particulier pour la commande robuste des systèmes linéaires. Dans le chapitre 2, nous évoquons les liens étroits entre ensembles semi-algébriques convexes et LMI,ainsi que la notion s...
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 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.
A Survey on Operator Monotonicity, Operator Convexity, and Operator Means
Directory of Open Access Journals (Sweden)
Pattrawut Chansangiam
2015-01-01
Full Text Available This paper is an expository devoted to an important class of real-valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations for such functions are given from the viewpoint of differential analysis in terms of matrix of divided differences. From the viewpoint of operator inequalities, various characterizations and the relationship between operator monotonicity and operator convexity are given by Hansen and Pedersen. In the viewpoint of measure theory, operator monotone functions on the nonnegative reals admit meaningful integral representations with respect to Borel measures on the unit interval. Furthermore, Kubo-Ando theory asserts the correspondence between operator monotone functions and operator means.
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.
Convex relationships in ecosystems containing mixtures of trees and grass
CSIR Research Space (South Africa)
Scholes, RJ
2003-12-01
Full Text Available of the copyright owner. Further reproduction prohibited without permission. Convex Relationships in Ecosystems Containing Mixtures of Trees and Grass R.J. Scholes Environmental and Resource Economics; Dec 2003; 26, 4; ABI/INFORM Global pg. 559 Reproduced... with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further...
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
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...... programs containing arithmetic, as well as constraint logic programs. Assignments, inequalities and equalities with arithmetic expressions can be interpreted as constraints during specialization, thus increasing the amount of specialization that can be achieved....
Free locally convex spaces with a small base
Czech Academy of Sciences Publication Activity Database
Gabriyelyan, S.; Kąkol, Jerzy
2017-01-01
Roč. 111, č. 2 (2017), s. 575-585 ISSN 1578-7303 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : compact resolution * free locally convex space * G-base Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.690, year: 2016 http://link. springer .com/article/10.1007%2Fs13398-016-0315-1
Some fixed point theorems on non-convex sets
Directory of Open Access Journals (Sweden)
Mohanasundaram Radhakrishnan
2017-10-01
Full Text Available In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\\to K$ is a nonexpansive map satisfying $\\frac{x+Tx}{2}\\in K$ for all $x\\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$
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, ma.......AG/0311149]. We investigate the cluster structure of this moduli space, and define its quantum version....
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.
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
Sequential and Parallel Algorithms for Finding a Maximum Convex Polygon
DEFF Research Database (Denmark)
Fischer, Paul
1997-01-01
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...
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 Optimization Methods for Graphs and Statistical Modeling
2011-06-01
Specifically we note that evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and...thus we can employ various tractable linear programming, spectral, and SDP relaxations of QAP [32, 122, 147]. In particular we discuss recent work [43...on exploiting group symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many
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
Speech Enhancement by Modified Convex Combination of Fractional Adaptive Filtering
Directory of Open Access Journals (Sweden)
M. Geravanchizadeh
2014-12-01
Full Text Available This paper presents new adaptive filtering techniques used in speech enhancement system. Adaptive filtering schemes are subjected to different trade-offs regarding their steady-state misadjustment, speed of convergence, and tracking performance. Fractional Least-Mean-Square (FLMS is a new adaptive algorithm which has better performance than the conventional LMS algorithm. Normalization of LMS leads to better performance of adaptive filter. Furthermore, convex combination of two adaptive filters improves its performance. In this paper, new convex combinational adaptive filtering methods in the framework of speech enhancement system are proposed. The proposed methods utilize the idea of normalization and fractional derivative, both in the design of different convex mixing strategies and their related component filters. To assess our proposed methods, simulation results of different LMS-based algorithms based on their convergence behavior (i.e., MSE plots and different objective and subjective criteria are compared. The objective and subjective evaluations include examining the results of SNR improvement, PESQ test, and listening tests for dual-channel speech enhancement. The powerful aspects of proposed methods are their low complexity, as expected with all LMS-based methods, along with a high convergence rate.
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:...
Structural robust optimization design based on convex model
Directory of Open Access Journals (Sweden)
Xuyong Chen
Full Text Available There exist a great amount of uncertain factors in actual engineering. In order to involve these uncertain factors in analytical model, they have been expressed as the convex variables. In addition, the convex model was further classified into the hyper-ellipsoidal model and the interval model. After pointing out the intrinsic difference between these two kinds of models, the principle for applying which one of the models within the analysis has been indicated according to the available testing points. After standardizing the convex variables, the difference and relation between these two models for the optimization and solution process have been presented. With the analysis mentality available from the hyper-ellipsoidal model, the basic method about the robust optimization for the interval model was emphasized. After classification of the interval variables within the optimization process, the characteristics of the robust optimization were highlighted with different constraint conditions. Using the target-performance-based analytical scheme, the algorithm, the solution step and the convergence criteria for the robust optimization have been also presented with only one reliability index. Numerical examples and engineering problems were used to demonstrate the effectiveness and correctness of the proposed approach. Keywords: Robust optimization, Non-probabilistic reliability, Interval model, Hyper-ellipsoidal model, Probabilistic index
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.
Linearithmic time sparse and convex maximum margin clustering.
Zhang, Xiao-Lei; Wu, Ji
2012-12-01
Recently, a new clustering method called maximum margin clustering (MMC) was proposed and has shown promising performances. It was originally formulated as a difficult nonconvex integer problem. To make the MMC problem practical, the researchers either relaxed the original MMC problem to inefficient convex optimization problems or reformulated it to nonconvex optimization problems, which sacrifice the convexity for efficiency. However, no approaches can both hold the convexity and be efficient. In this paper, a new linearithmic time sparse and convex MMC algorithm, called support-vector-regression-based MMC (SVR-MMC), is proposed. Generally, it first uses the SVR as the core of the MMC. Then, it is relaxed as a convex optimization problem, which is iteratively solved by the cutting-plane algorithm. Each cutting-plane subproblem is further decomposed to a serial supervised SVR problem by a new global extended-level method (GELM). Finally, each supervised SVR problem is solved in a linear time complexity by a new sparse-kernel SVR (SKSVR) algorithm. We further extend the SVR-MMC algorithm to the multiple-kernel clustering (MKC) problem and the multiclass MMC (M3C) problem, which are denoted as SVR-MKC and SVR-M3C, respectively. One key point of the algorithms is the utilization of the SVR. It can prevent the MMC and its extensions meeting an integer matrix programming problem. Another key point is the new SKSVR. It provides a linear time interface to the nonlinear kernel scenarios, so that the SVR-MMC and its extensions can keep a linearthmic time complexity in nonlinear kernel scenarios. Our experimental results on various real-world data sets demonstrate the effectiveness and the efficiency of the SVR-MMC and its two extensions. Moreover, the unsupervised application of the SVR-MKC to the voice activity detection (VAD) shows that the SVR-MKC can achieve good performances that are close to its supervised counterpart, meet the real-time demand of the VAD, and need no
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
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
Lefschetz Fixed Point Theorem and Lattice Points in Convex Polytopes
Sardo-Infirri, Sacha
1993-01-01
A simple convex lattice polytope $\\Box$ defines a torus-equivariant line bundle $\\LB$ over a toric variety $\\XB.$ Atiyah and Bott's Lefschetz fixed-point theorem is applied to the torus action on the $d''$-complex of $\\LB$ and information is obtained about the lattice points of $\\Box$. In particular an explicit formula is derived, computing the number of lattice points and the volume of $\\Box$ in terms of geometric data at its extreme points. We show this to be equivalent the results of Brion...
Convex optimization in normed spaces theory, methods and examples
Peypouquet, Juan
2015-01-01
This work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct independent research on the topic. It is also a concise, easy-to-follow and self-contained textbook, which may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. It will contain a thorough revision of the extant literature including both classical and state-of-the-art references.
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...
A *-mixing convergence theorem for convex set valued processes
Directory of Open Access Journals (Sweden)
A. de Korvin
1987-01-01
Full Text Available In this paper the concept of a *-mixing process is extended to multivalued maps from a probability space into closed, bounded convex sets of a Banach space. The main result, which requires that the Banach space be separable and reflexive, is a convergence theorem for *-mixing sequences which is analogous to the strong law of large numbers. The impetus for studying this problem is provided by a model from information science involving the utilization of feedback data by a decision maker who is uncertain of his goals. The main result is somewhat similar to a theorem for real valued processes and is of interest in its own right.
A contribution to group representations in locally convex spaces
International Nuclear Information System (INIS)
Jurzak, J.P.
1977-01-01
Let U be a continuous representation of a (connected) locally compact group G in a separated locally convex space E. It is shown that the study of U is equivalent to the study of a family Usub(i) of continuous representations of G in Frechet spaces Fsub(i). If U is equicontinuous, the Fsub(i) are Banach spaces, and the Usub(i) are realized by isomeric operators. When U is topologically irreducible, it is Naemark equivalent to a Frechet (or isomeric Banach, in the equicontinuous case) continuous representation. Similar results hold for semi-groups. (Auth.)
Vector optimization and monotone operators via convex duality recent advances
Grad, Sorin-Mihai
2014-01-01
This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.
7 CFR 28.414 - Strict Low Middling Light Spotted Color.
2010-01-01
... CONTAINER REGULATIONS COTTON CLASSING, TESTING, AND STANDARDS Standards Light Spotted Cotton § 28.414 Strict Low Middling Light Spotted Color. Strict Low Middling Light Spotted Color is color which in spot or...
Off-Grid DOA Estimation Based on Analysis of the Convexity of Maximum Likelihood Function
LIU, Liang; WEI, Ping; LIAO, Hong Shu
Spatial compressive sensing (SCS) has recently been applied to direction-of-arrival (DOA) estimation owing to advantages over conventional ones. However the performance of compressive sensing (CS)-based estimation methods decreases when true DOAs are not exactly on the discretized sampling grid. We solve the off-grid DOA estimation problem using the deterministic maximum likelihood (DML) estimation method. In this work, we analyze the convexity of the DML function in the vicinity of the global solution. Especially under the condition of large array, we search for an approximately convex range around the ture DOAs to guarantee the DML function convex. Based on the convexity of the DML function, we propose a computationally efficient algorithm framework for off-grid DOA estimation. Numerical experiments show that the rough convex range accords well with the exact convex range of the DML function with large array and demonstrate the superior performance of the proposed methods in terms of accuracy, robustness and speed.
On N. Chomsky’s strict subcategorization of verbs
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Janez Orešnik
1966-12-01
Full Text Available This paper studies the so-called strict subcategorization rules, and the theory associated with them, in the transformational grammar of. Erigl·ish as proposed by Noarn Chomsky in his Aspects. The syntactic component of English transformational grammar consists of two mutually ordered parts, viz., the base and the transformational subcomponents. The initial part of the base are the so-called categorial rules, which are of almost exclusive interest to us here. Their primary task is to generate what are usually called basic sentence patterns, and will here, with Chomsky (Aspects, p.ll3, be designated with the expression, frames of category symbols.- The rules of the transformational subcomponent modify, in various ways, the frames generated by the base. For several reasons - one of them being that the correct work of the transformational subcomponent quite often depends on the kind of lexical items with which the syntactic positions in the frames of category symbols have been filled, the lexical items must be introduced from the lexicon into the empty positions in the frames before the rules of the transformational subcomponent can be allowed to modify the frames.
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
with larger declines in V̇o2max). Furthermore, the systematic review revealed a gap in the knowledge about the cardiovascular response to extreme physical inactivity, particularly in older subjects and women of any age group. In addition to its relevance to spaceflight, this lack of data has significant....... Since 1949, 80 studies with a total of 949 participants (>90% men) have been published with data on strict bed rest and V̇o2max The studies were conducted mainly in young participants [median age (interquartile range) 24.5 (22.4-34.0) yr]. The duration of bed rest ranged from 1 to 90 days. V̇o2max...... declined linearly across bed rest duration. No statistical difference in the decline among studies reporting V̇o2max as l/min (-0.3% per day) compared with studies reporting V̇o2max normalized to body weight (ml·kg-1·min-1; -0.43% per day) was observed. Although both total body weight and lean body mass...
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
Kunt, Mehmet; İşcan, İmdat; Yazıcı, Nazlı; Gözütok, Uğur
2016-01-01
In this paper, firstly, new Hermite-Hadamard type inequalities for harmonically convex functions in fractional integral forms are given. Secondly, Hermite-Hadamard-Fejer inequalities for harmonically convex functions in fractional integral forms are built. Finally, an integral identity and some Hermite-Hadamard-Fejer type integral inequalities for harmonically convex functions in fractional integral forms are obtained. Some results presented here provide extensions of others given in earlier works.
The left Rieaman-Liouville fractional Hermite-Hadamard type inequalities for quasi-convex functions
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Dünya Karapınar
2017-08-01
Full Text Available Recently, in [5], with a new approach, the authors obtained a new fractional Hermite-Hadamard type inequality for convex functions by using only the left Riemann-Liouville fractional integral. They also had new equalities to have new fractional trapezoid and midpoint type inequalities for convex functions, In this papers, we will use the same equalities to have new fractional trapezoid and midpoint type inequalities for quasi-convex functions. Our results generalise the study [3].
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...
Convex Relaxation For Hard Problem In Data Mining And Sensor Localization
2017-04-13
AFRL-AFOSR-VA-TR-2017-0085 CONVEX RELAXATION FOR HARD PROBLEM IN DATA MINING AND SENSOR LOCALIZATION Stephen Vavasis UNIVERSITY OF WATERLOO 200...Performance 3. DATES COVERED (From - To) 15 Jun 2012 to 14 Aug 2015 4. TITLE AND SUBTITLE CONVEX RELAXATION FOR HARD PROBLEM IN DATA MINING AND SENSOR...the results. 15. SUBJECT TERMS Convex Relaxation Methods, Data Mining 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER OF
Sequential Change-Point Detection via Online Convex Optimization
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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 Deep-Cutting-Plane Technique for Reverse Convex Optimization.
Moshirvaziri, K; Amouzegar, M A
2011-08-01
A large number of problems in engineering design and in many areas of social and physical sciences and technology lend themselves to particular instances of problems studied in this paper. Cutting-plane methods have traditionally been used as an effective tool in devising exact algorithms for solving convex and large-scale combinatorial optimization problems. Its utilization in nonconvex optimization has been also promising. A cutting plane, essentially a hyperplane defined by a linear inequality, can be used to effectively reduce the computational efforts in search of a global solution. Each cut is generated in order to eliminate a large portion of the search domain. Thus, a deep cut is intuitively superior in which it will exclude a larger set of extraneous points from consideration. This paper is concerned with the development of deep-cutting-plane techniques applied to reverse-convex programs. An upper bound and a lower bound for the optimal value are found, updated, and improved at each iteration. The algorithm terminates when the two bounds collapse or all the generated subdivisions have been fathomed. Finally, computational considerations and numerical results on a set of test problems are discussed. An illustrative example, walking through the steps of the algorithm and explaining the computational process, is presented.
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.
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
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. E 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 explicit construction of binary packings
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.
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
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
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.
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.
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...
Entropies from Coarse-graining: Convex Polytopes vs. Ellipsoids
Directory of Open Access Journals (Sweden)
Nikos Kalogeropoulos
2015-09-01
Full Text Available We examine the Boltzmann/Gibbs/Shannon SBGS and the non-additive Havrda-Charvát/Daróczy/Cressie-Read/Tsallis Sq and the Kaniadakis κ-entropy Sκ from the viewpoint of coarse-graining, symplectic capacities and convexity. We argue that the functional form of such entropies can be ascribed to a discordance in phase-space coarse-graining between two generally different approaches: the Euclidean/Riemannian metric one that reflects independence and picks cubes as the fundamental cells in coarse-graining and the symplectic/canonical one that picks spheres/ellipsoids for this role. Our discussion is motivated by and confined to the behaviour of Hamiltonian systems of many degrees of freedom. We see that Dvoretzky’s theorem provides asymptotic estimates for the minimal dimension beyond which these two approaches are close to each other. We state and speculate about the role that dualities may play in this viewpoint.
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.
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)
Greedy vs. L1 Convex Optimization in Sparse Coding
DEFF Research Database (Denmark)
Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor
Sparse representation has been applied successfully in many image analysis applications, including abnormal event detection, in which a baseline is to learn a dictionary from the training data and detect anomalies from its sparse codes. During this procedure, sparse codes which can be achieved...... and action recognition, a comparative study of codes in abnormal event detection is less studied and hence no conclusion is gained on the effect of codes in detecting abnormalities. We constrict our comparison in two types of the above L0-norm solutions: greedy algorithms and convex L1-norm solutions....... Considering the property of abnormal event detection, i.e., only normal videos are used as training data due to practical reasons, effective codes in classification application may not perform well in abnormality detection. Therefore, we compare the sparse codes and comprehensively evaluate their performance...
Reachability by paths of bounded curvature in a convex polygon
Ahn, Heekap
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
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.......8% on average by applying 3D SA focusing. In-Vivo measurements show an improvement in C-scans matching what is found in simulations and wire phantoms. The method has shown the ability to improve the elevation focus and contrast for a convex rocking array. This was shown for simulations and for phantom and In...
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.
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
On some Hermite-Hadamard type inequalities for (s, QC)-convex functions.
Wu, Ying; Qi, Feng
2016-01-01
In the paper, the authors introduce a new notion "[Formula: see text]-convex function on the co-ordinates" and establish some Hermite-Hadamard type integral inequalities for [Formula: see text]-convex functions on the co-ordinates.
Sandor Type Inequalities for Sugeno Integral with respect to General α,m,r-Convex Functions
Directory of Open Access Journals (Sweden)
Dong-Qing Li
2015-01-01
Full Text Available The concept for general α,m,r-convex functions, as a generalization of convex functions, is introduced. Then, Sandor type inequalities for the Sugeno integral based on this kind of function are established. Our work generalizes the previous results in the literature. Finally, some conclusions and problems for further investigations are given.
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
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 ...
The Concept of Convexity in Fuzzy Set Theory | Rauf | Journal of the ...
African Journals Online (AJOL)
This paper investigates the concept of Fuzzy set theory in relation to the idea of convexity. Some fundamental theorems were considered. Keywords: Fuzzy Set, Mapping for Fuzzy Set, Convex Set. 2010 Mathematics Subject Classification: 03Exx, 52Axx, 94B75 Journal of the Nigerian Association of Mathematical Physics, ...
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.
Optimality Conditions and Duality for DC Programming in Locally Convex Spaces
Directory of Open Access Journals (Sweden)
Wang Xianyun
2009-01-01
Full Text Available Consider the DC programming problem where and are proper convex functions defined on locally convex Hausdorff topological vector spaces and respectively, and is a linear operator from to . By using the properties of the epigraph of the conjugate functions, the optimality conditions and strong duality of are obtained.
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.
Directory of Open Access Journals (Sweden)
Feixiang Chen
2014-01-01
Full Text Available We obtain some Hermite-Hadamard type inequalities for products of two m-convex functions via Riemann-Liouville integrals. The analogous results for (α,m-convex functions are also established.
Statistical Mechanics of Optimal Convex Inference in High Dimensions
Directory of Open Access Journals (Sweden)
Madhu Advani
2016-08-01
Full Text Available A fundamental problem in modern high-dimensional data analysis involves efficiently inferring a set of P unknown model parameters governing the relationship between the inputs and outputs of N noisy measurements. Various methods have been proposed to regress the outputs against the inputs to recover the P parameters. What are fundamental limits on the accuracy of regression, given finite signal-to-noise ratios, limited measurements, prior information, and computational tractability requirements? How can we optimally combine prior information with measurements to achieve these limits? Classical statistics gives incisive answers to these questions as the measurement density α=(N/P→∞. However, these classical results are not relevant to modern high-dimensional inference problems, which instead occur at finite α. We employ replica theory to answer these questions for a class of inference algorithms, known in the statistics literature as M-estimators. These algorithms attempt to recover the P model parameters by solving an optimization problem involving minimizing the sum of a loss function that penalizes deviations between the data and model predictions, and a regularizer that leverages prior information about model parameters. Widely cherished algorithms like maximum likelihood (ML and maximum-a posteriori (MAP inference arise as special cases of M-estimators. Our analysis uncovers fundamental limits on the inference accuracy of a subclass of M-estimators corresponding to computationally tractable convex optimization problems. These limits generalize classical statistical theorems like the Cramer-Rao bound to the high-dimensional setting with prior information. We further discover the optimal M-estimator for log-concave signal and noise distributions; we demonstrate that it can achieve our high-dimensional limits on inference accuracy, while ML and MAP cannot. Intriguingly, in high dimensions, these optimal algorithms become computationally
Privileged coding of convex shapes in human object-selective cortex.
Haushofer, Johannes; Baker, Chris I; Livingstone, Margaret S; Kanwisher, Nancy
2008-08-01
What is the neural code for object shape? Despite intensive research, the precise nature of object representations in high-level visual cortex remains elusive. Here we use functional magnetic resonance imaging (fMRI) to show that convex shapes are encoded in a privileged fashion by human lateral occipital complex (LOC), a region that has been implicated in object recognition. On each trial, two convex or two concave shapes that were either identical or different were presented sequentially. Critically, the convex and concave stimuli were the same except for a binocular disparity change that reversed the figure-ground assignment. The fMRI response in LOC for convex stimuli was higher for different than that for identical shape pairs, indicating sensitivity to differences in convex shape. However, when the same stimuli were seen as concave, the response for different and identical pairs was the same, indicating lower sensitivity to changes in concave shape than convex shape. This pattern was more pronounced in the anterior than that in the posterior portion of LOC. These results suggest that convex contours could be important elements in cortical object representations.
Non-convex shape effects on the dense random packing properties of assembled rods
Meng, Lingyi; Wang, Chao; Yao, Xiaohu
2018-01-01
The packing of rod-like particles, which is common in physical and mathematical studies, has arisen in a variety of industrial applications. Elongation effect on the packing properties of rod-like particle has been well investigated. Besides that, rod-like particles can be easily deformed into a large amount of non-convex shapes by simply bending or assembling several particles, in which effects of non-convex deformations should also be concerned. In this work, the packing behaviors of particulate systems composed of various non-convex deformations of rod-like particles are numerically simulated via the analytical model and the relaxation algorithm. The packing configurations are further optimized using the Monte Carlo method to eliminate the local ordered structures. 8 shapes of non-convex particles including 2-dimensional and 3-dimensional particles are employed in the packing systems. Independent of aspect ratio, the dense random packing densities of identical assembled rods are up to 20% higher than those of spherocylinders and are less dependent from the specific particle shape. However, the coordination numbers of various non-convex particle packings are quite different. With a parameter of convex ratio defined, a packing composed of more non-convex particles will have a higher coordination number. This indicates that for more non-convex particle packings, there are more constraints and entanglements among neighboring particles, resulting in a more stable configuration. The nearest-neighbor contact to a centered particle in 3DX-shaped particle packings is quite different from those of other shapes, which can be identified from the location of the first peak in the radial distribution function. It is also the cause to the distinct disparities of estimated excluded volumes of non-convex particles simulated in this work.
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.
Visualization of pool boiling on downward-facing convex surfaces
International Nuclear Information System (INIS)
Ei-genk, M.S.; Gao, C.
1997-01-01
Visualizations and quenching experiments were performed to investigate effect of material properties on pool boiling from downward-facing, convex stainless steel and copper surfaces in saturated water. Video images showed that more than one boiling regimes can co-exist on the surface. Maximum heat flux (MHF) occurred first at lowermost position, then propagated radially outward to higher inclination positions and its local value decreased with increased inclination. However, the wall superheats corresponding to MHF were independent of the local surface inclinations. MHF propagated ∼10 times slower on stainless-steel than on copper and was ∼12% and 40% lower on stainless-steel than on copper at θ = 0 degree and θ 7.91 degree, respectively. Results confirmed that transition boiling consisted of two distinct regions: high wall superheat, in which heat flux increased relatively slowly, and low wall superheat, in which heat flux increased precipitously with time. Nuclear boiling regime also consisted of two distinct regions: high heat flux nucleate boiling, in which heat flux decreased with increased inclination, and low heat flux nucleate boiling, in which heat flux increased with increased inclination
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.
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.
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.
[A case of rapidly growing dumbbell-shaped convexity meningioma].
Kawahara, Ichiro; Nakamoto, Morito; Matsuo, Yoshitaka; Tokunaga, Yoshiharu I; Abe, Kuniko
2009-06-01
We have had more opportunities to treat incidental meningiomas owing to the recent development of neuroradiological imaging. Generally, most of them are treated conservatively unless they grow rapidly or change to symptomatic. Rapidly growing meningiomas are unusual because meningiomas are generally benign and slow-growing tumors. Particularly, the indication of surgery in elderly patients with asymptomatic meningiomas must be considered very carefully because of the higher risks of complications or postoperative neurological deficits. The author describes a rare case of a rapidly growing dumbbell-shaped convexity meningioma in an elderly patient. The tumor was removed completely (Simpson grade II), and the pathological diagnosis was atypical meningioma. There was a difference of MIB-1 LI within the tumor, which suggests that the difference of proliferation within the meningioma may have changed it into "dumbbell-shaped". The only factor we could identify to explain the rapid growth was the high MIB-1LI. This represents an interesting example of a rapidly growing meningiomas. Although the indication of aggresive surgery in elderly patients with symptomatic meningiomas should be considered, the postoperative deterioration of quality of life must be avoided. And earlier postoperative rehabilitation can be regarded as indispensable for elderly patients.
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.
Convergence theorems for a class of nonlinear 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 be a mapping of K into itself and suppose T is an element of C (in the notation of Browder and Petryshyn; and Rhoades). It is proved that each of two well known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly to the unique fixed point of T. (author). 20 refs
Fast Bundle-Level Type Methods for Unconstrained and Ball-Constrained Convex Optimization
2014-12-01
f), C2(x,R, f) are some constants that depend on f in (2.1). For example, if f is a smooth convex function , ∇f is Lipschitz continuous in Rn with...assumed to be a simple Lipschitz continuous 13 convex function , and only Fη is approximated by the linear estimation. However in the FUSL method, we...90C22, 49M37 1. Introduction. Given a convex function f : Rn → R, the main problem of interest in this paper is: f∗ := min x∈Rn f(x). (1.1) Throughout
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...
7 CFR 28.416 - Strict Good Ordinary Light Spotted Color.
2010-01-01
... CONTAINER REGULATIONS COTTON CLASSING, TESTING, AND STANDARDS Standards Light Spotted Cotton § 28.416 Strict Good Ordinary Light Spotted Color. Strict Good Ordinary Light Spotted Color is color which in spot or... Cotton Source: 57 FR 34498, Aug. 5, 1992, unless otherwise noted. ...
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...
Directory of Open Access Journals (Sweden)
Sercan TURHAN
2016-04-01
Full Text Available In this paper, we gave the new general identity for differentiable functions. As a result of this identity some new and general inequalities for differentiable harmonically-convex functions are obtained.
CSIR Research Space (South Africa)
Govender, Nicolin
2015-09-01
Full Text Available Convex polyhedra represent granular media well. This geometric representation may be critical in obtaining realistic simulations of many industrial processes using the discrete element method (DEM). However detecting collisions between the polyhedra...
Coefficient Bounds for Some Families of Starlike and Convex Functions of Reciprocal Order
Arif, Muhammad; Darus, Maslina; Raza, Mohsan; Khan, Qaiser
2014-01-01
The aim of the present paper is to investigate coefficient estimates, Fekete-Szegő inequality, and upper bound of third Hankel determinant for some families of starlike and convex functions of reciprocal order. PMID:25506621
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...... scanner. A 3 MHz 192 elements convex array probe (pitch 0.33 mm) is used in both simulations and measurements. An F-number of 5 is used in transmit and two 32 element wide peaks are used in receive separated by 96 elements between peaks. Parabolic velocity profiles are simulated at beam-to-flow angles......) at a depth of 40 mm. Measurements have been made using the SARUS experimental ultrasound scanner and a BK Medical 8820e convex array transducer. Sixty-four elements was used in transmit and 2 x 32 elements in receive for creating a color flow map image of a flow rig phantom with a laminar, parabolic flow...
New Criteria for Functions to Be in a Class of -Valent Alpha Convex Functions
Directory of Open Access Journals (Sweden)
Muhammad Arif
2013-01-01
Full Text Available We obtain certain simple sufficiency criteria for a class of -valent alpha convex functions. Many known results appear as special consequences of our work. Some applications of our work to the generalized integral operator are also given.
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
Chierchia, Giovanni; Pustelnik, Nelly; Pesquet, Jean-Christophe; Pesquet-Popescu, Béatrice
2012-01-01
We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different, but possibly overlapping, blocks of the signal. For such constraints, the associated projection operator generally does not have a simple form. We circumvent this difficulty by splitting the lowe...
Chierchia, Giovanni; Pustelnik, Nelly; Pesquet, Jean-Christophe; Pesquet-Popescu, Béatrice
2012-01-01
We propose a proximal approach to deal with convex optimization problems involving nonlinear constraints. A large family of such constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different, but possibly overlapping, blocks of the signal. For this class of constraints, the associated projection operator generally does not have a closed form. We circumvent this difficulty by splitting the ...
Epigraphical splitting for solving constrained convex optimization problems with proximal tools
Chierchia, Giovanni; Pustelnik, Nelly; Pesquet, Jean-Christophe; Pesquet-Popescu, Béatrice
2015-01-01
International audience; We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different blocks of the linearly-transformed signal. For such constraints, the associated projection operator generally does not have a simple form. We circumvent this difficulty by ...
Optimisation convexe pour l'estimation simultanée de réponses acoustiques
Benichoux, Alexis; Vincent, Emmanuel; Gribonval, Rémi
2011-01-01
National audience; We consider the estimation of acoustic impulse responses from the simultaneous recording of several known sources. Existing techniques are restricted to the case where the number of sources is at most equal to the number of sensors. We relax this assumption in the case where the sources are known. To this aim, we propose statistical models of the filters associated with a convex log-likelihood, and we propose a convex optimization algorithm to solve the inverse problem, wit...
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.
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.
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
Kadukova, Maria; Grudinin, Sergei
2017-10-01
We present a novel optimization approach to train a free-shape distance-dependent protein-ligand scoring function called Convex-PL. We do not impose any functional form of the scoring function. Instead, we decompose it into a polynomial basis and deduce the expansion coefficients from the structural knowledge base using a convex formulation of the optimization problem. Also, for the training set we do not generate false poses with molecular docking packages, but use constant RMSD rigid-body deformations of the ligands inside the binding pockets. This allows the obtained scoring function to be generally applicable to scoring of structural ensembles generated with different docking methods. We assess the Convex-PL scoring function using data from D3R Grand Challenge 2 submissions and the docking test of the CASF 2013 study. We demonstrate that our results outperform the other 20 methods previously assessed in CASF 2013. The method is available at http://team.inria.fr/nano-d/software/Convex-PL/.
The Effect of Strict Segregation on Pseudomonas aeruginosa in Cystic Fibrosis Patients
van Mansfeld, Rosa; de Vrankrijker, Angelica; Brimicombe, Roland; Heijerman, Harry; Teding van Berkhout, Ferdinand; Spitoni, Cristian|info:eu-repo/dai/nl/304625957; Grave, Sanne; van der Ent, Cornelis; Wolfs, Tom; Willems, Rob; Bonten, Marc
2016-01-01
INTRODUCTION: Segregation of patients with cystic fibrosis (CF) was implemented to prevent chronic infection with epidemic Pseudomonas aeruginosa strains with presumed detrimental clinical effects, but its effectiveness has not been carefully evaluated. METHODS: The effect of strict segregation on
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)
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.
Plant use in the medicinal practices known as "strict diets" in Chazuta valley (Peruvian Amazon).
Sanz-Biset, Jaume; Cañigueral, Salvador
2011-09-01
Strict diets are traditional medicinal practices where plant remedies are consumed with nearly fasting and with some sort of social seclusion. The aim of this work was to describe these practices of Chazuta and the use of plants within, as well as to analyse the possible functions of the last. The information was obtained through interviews to the 6.3% of the district rural adult population (140 individuals, 75% of which was considered Quechua). In total, 122 strict diets were recorded and 106 different plant species were reported to be used. Strict diets present a characteristic structure and plant use. The main effects reported in strict diets were antinflammatory, antiinfective, brain function alteration and depuration. Strict diets are well structured traditional medicinal practices, also with a symbolic significance in the life cycle of chazutian men. Plants used in strict diets can contribute to the main effects through antinflammation, antiinfective actions, psychoactivity and depurative related activities. The correlation between literature evidence of activity of most used plants and effects reported for the correspondent diet (i.e. in which the plant was used) are 36% for antinflammatory activity, 29% for antimicrobial activity, 18% for psychoactivity and 5% for depurative related activities. The percentages go to 77%, 64%, 73% and 32%, respectively, when literature evidences on related taxa are also considered. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.
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
Chine, Abderrazek
1991-01-01
Cette thèse est consacrée a l'étude des algorithmes en optimisation non convexe, a l'implémentation des codes a l'usage industriel et aux simulations numériques dans les problèmes de grande tailles. L'étude des problèmes quadratiques (convexes ou non convexes) sous contraintes linéaires et quadratiques ainsi que celle des méthodes de région de confiance pour minimisation d'une fonction de classe c#2, font l'objet de deux premiers chapitres. Les chapitres 3 et 4 sont réservés a l'optimisation ...
Modified surface testing method for large convex aspheric surfaces based on diffraction optics.
Zhang, Haidong; Wang, Xiaokun; Xue, Donglin; Zhang, Xuejun
2017-12-01
Large convex aspheric optical elements have been widely applied in advanced optical systems, which have presented a challenging metrology problem. Conventional testing methods cannot satisfy the demand gradually with the change of definition of "large." A modified method is proposed in this paper, which utilizes a relatively small computer-generated hologram and an illumination lens with certain feasibility to measure the large convex aspherics. Two example systems are designed to demonstrate the applicability, and also, the sensitivity of this configuration is analyzed, which proves the accuracy of the configuration can be better than 6 nm with careful alignment and calibration of the illumination lens in advance. Design examples and analysis show that this configuration is applicable to measure the large convex aspheric surfaces.
A Convex Model for Nonnegative Matrix Factorization and Dimensionality Reduction on Physical Space
Esser, Ernie; Moller, Michael; Osher, Stanley; Sapiro, Guillermo; Xin, Jack
2012-07-01
A collaborative convex framework for factoring a data matrix $X$ into a non-negative product $AS$, with a sparse coefficient matrix $S$, is proposed. We restrict the columns of the dictionary matrix $A$ to coincide with certain columns of the data matrix $X$, thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. We use $l_{1,\\infty}$ regularization to select the dictionary from the data and show this leads to an exact convex relaxation of $l_0$ in the case of distinct noise free data. We also show how to relax the restriction-to-$X$ constraint by initializing an alternating minimization approach with the solution of the convex model, obtaining a dictionary close to but not necessarily in $X$. We focus on applications of the proposed framework to hyperspectral endmember and abundances identification and also show an application to blind source separation of NMR data.
Convex Formulation for Kernel PCA and Its Use in Semisupervised Learning.
Alaiz, Carlos M; Fanuel, Michael; Suykens, Johan A K
2017-06-23
In this brief, kernel principal component analysis (KPCA) is reinterpreted as the solution to a convex optimization problem. Actually, there is a constrained convex problem for each principal component, so that the constraints guarantee that the principal component is indeed a solution, and not a mere saddle point. Although these insights do not imply any algorithmic improvement, they can be used to further understand the method, formulate possible extensions, and properly address them. As an example, a new convex optimization problem for semisupervised classification is proposed, which seems particularly well suited whenever the number of known labels is small. Our formulation resembles a least squares support vector machine problem with a regularization parameter multiplied by a negative sign, combined with a variational principle for KPCA. Our primal optimization principle for semisupervised learning is solved in terms of the Lagrange multipliers. Numerical experiments in several classification tasks illustrate the performance of the proposed model in problems with only a few labeled data.
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.
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....
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...
Conditions for Bounded Closed and Convex Sets to Have a Unique Completion in Banach Spaces
Directory of Open Access Journals (Sweden)
JI Dong-hai
2017-06-01
Full Text Available In order to study the conditions for bounded closed and convex sets to have a unique completion inreal Banach spaces，known results in this direction are summarized. Based on this，a sufficient condition as well as some necessary and sufficient conditions for bounded closed and convex sets to have a unique completion areprovided. The notion of ( K，u -completeness is extended，and the relation of this notion to the uniqueness of completion in real Banach spaces is discussed.
Implementation of an optimal first-order method for strongly convex total variation regularization
DEFF Research Database (Denmark)
Jensen, Tobias Lindstrøm; Jørgensen, Jakob Heide; Hansen, Per Christian
2012-01-01
We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to μ-strongly convex objective functions with L-Lipschitz continuous gradient....... In the framework of Nesterov both μ and L are assumed known—an assumption that is seldom satisfied in practice. We propose to incorporate mechanisms to estimate locally sufficient μ and L during the iterations. The mechanisms also allow for the application to non-strongly convex functions. We discuss...
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.
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.
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)
de Klerk, Etienne; Glineur, Francois; Taylor, Adrien
2016-01-01
We consider the gradient (or steepest) descent method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-case rate of convergence of this scheme, and show that this worst-case behavior is exhibited by a certain convex
de Klerk, Etienne; Glineur, Francois; Taylor, Adrien
2017-01-01
We consider the gradient (or steepest) descent method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-case rate of convergence of this scheme, and show that this worst-case behavior is exhibited by a certain convex
Strict Monotonicity and Unique Continuation for the Third-Order Spectrum of Biharmonic Operator
Directory of Open Access Journals (Sweden)
Khalil Ben Haddouch
2012-01-01
Full Text Available We will study the spectrum for the biharmonic operator involving the laplacian and the gradient of the laplacian with weight, which we call third-order spectrum. We will show that the strict monotonicity of the eigenvalues of the operator , where , holds if some unique continuation property is satisfied by the corresponding eigenfunctions.
"Let the Master Respond": Should Schools Be Strictly Liable When Employees Sexually Abuse Children?
Fossey, Richard; DeMitchell, Todd
Although sexual abuse against children is a problem in the public schools, school officials have generally not acted aggressively to stop it. This paper argues for a strict liability standard--the assessment of liability without fault--against a school district in cases of student sexual abuse by a school employee. Part 1 explores the principle of…
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)
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
Directory of Open Access Journals (Sweden)
Atiq Ur Rehman
2016-01-01
Full Text Available We have discussed the generalization of Hermite-Hadamard inequality introduced by Lupaş for convex functions on coordinates defined in a rectangle from the plane. Also we define that mappings are related to it and their properties are discussed.
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...
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
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
Gorissen, B.L.; Blanc, J.P.C.; den Hertog, D.; Ben-Tal, A.
We propose a new way to derive tractable robust counterparts of a linear program based on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First we obtain a new convex reformulation of the dual problem of a robust linear program, and then show how to construct
Eurodollar futures and options: convexity adjustment in HJM one- factor model
Henrard Marc
2005-01-01
In this note we give pricing formulas for different instruments linked to rate futures (euro-dollar futures). We provide the future price including the convexity adjustment and the exact dates. Based on that result we price options on futures, including the mid-curve options.
The Lp Lp Lp-curvature images of convex bodies and Lp Lp Lp ...
Indian Academy of Sciences (India)
Abstract. Associated with the Lp-curvature image defined by Lutwak, some inequali- ties for extended mixed p-affine surface areas of convex bodies and the support functions of Lp-projection bodies are established. As a natural extension of a result due to Lutwak, an Lp-type affine isoperimetric inequality, whose special ...
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.
ON INEQUALITIES OF HERMITE – HADAMARD TYPE INVOLVING AN s-CONVEX FUNCTION WITH APPLICATIONS
Directory of Open Access Journals (Sweden)
Liu Zheng
2016-03-01
Full Text Available Motivated by a recent paper, the author provides some new integral inequalities of Hermite–Hadamard type involving the product of an s-convex function and a symmetric function and applies these new established inequalities to construct inequalities for special means.
On the Hadamard’s type inequalities for co-ordinated convex functions via fractional integrals
Directory of Open Access Journals (Sweden)
Abdullah Akkurt
2017-07-01
Full Text Available In this paper, we establish two identities for functions of two variables and apply them to give new Hermite–Hadamard type fractional integral inequalities for double fractional integrals involving functions whose derivatives are bounded or co-ordinates convex function on Δ≔[a,b]×[c,d] in R2 with a
Balder, E.J.
1984-01-01
This note presents a new, quick approach to existence results without convexity conditions for optimal control problems with singular components in the sense of [11.], 438–485). Starting from the resolvent kernel representation of the solutions of a linear integral equation, a version of Fatou's
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.
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.
New Criteria for Functions to Be in a Class of p-Valent Alpha Convex Functions
Arif, Muhammad; Aouf, Mohamed Kamal
2013-01-01
We obtain certain simple sufficiency criteria for a class of p-valent alpha convex functions. Many known results appear as special consequences of our work. Some applications of our work to the generalized integral operator are also given. PMID:24191138
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)
Directory of Open Access Journals (Sweden)
Chang Tong-Huei
2009-01-01
Full Text Available We use a concept of abstract convexity to define the almost - property, al- - family, and almost -spaces. We get some new approximate fixed point theorems and fixed point theorems in almost -spaces. Our results extend some results of other authors.
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.
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 pred...
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.
Principled Design and Runtime Analysis of Abstract Convex Evolutionary Search.
Moraglio, Alberto; Sudholt, Dirk
2017-01-01
Geometric crossover is a formal class of crossovers that includes many well-known recombination operators across representations. In previous work, it was shown that all evolutionary algorithms with geometric crossover (but no mutation) do the same form of convex search regardless of the underlying representation, the specific selection mechanism, offspring distribution, search space, and problem at hand. Furthermore, it was suggested that the generalised convex search could perform well on generalised forms of concave and approximately concave fitness landscapes regardless of the underlying space and representation. In this article, we deepen this line of enquiry and study the runtime of generalised convex search on concave fitness landscapes. This is a first step toward linking a geometric theory of representations and runtime analysis in the attempt to (1) set the basis for a more general, unified approach for the runtime analysis of evolutionary algorithms across representations, and (2) identify the essential matching features of evolutionary search behaviour and landscape topography that cause polynomial performance. We present a general runtime result that can be systematically instantiated to specific search spaces and representations and present its specifications to three search spaces. As a corollary, we obtain that the convex search algorithm optimises LeadingOnes in [Formula: see text] fitness evaluations, which is faster than all unbiased unary black box algorithms.
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
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.
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 Log-convexity of the poly-cauchy numbers | Komatsu ...
African Journals Online (AJOL)
In 2013, Komatsu introduced the poly-Cauchy numbers, which generalize. Cauchy numbers. Several generalizations of poly-Cauchy numbers have been con- sidered since then. One particular type of generalizations is that of multiparameter- poly-Cauchy numbers. In this paper, we study the log-convexity of the ...
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.
First-order convex feasibility algorithms for x-ray CT.
Sidky, Emil Y; Jørgensen, Jakob S; Pan, Xiaochuan
2013-03-01
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, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution-thereby facilitating the IIR algorithm design process. An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144°. The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems. 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 angular-range scanning. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application.
A Criterium for the Strict Positivity of the Density of the Law of a Poisson Process
Directory of Open Access Journals (Sweden)
Léandre Rémi
2011-01-01
Full Text Available We translate in semigroup theory our result (Léandre, 1990 giving a necessary condition so that the law of a Markov process with jumps could have a strictly positive density. This result express, that we have to jump in a finite number of jumps in a "submersive" way from the starting point to the end point if the density of the jump process is strictly positive in . We use the Malliavin Calculus of Bismut type of (Léandre, (2008;2010 translated in semi-group theory as a tool, and the interpretation in semi-group theory of some classical results of the stochastic analysis for Poisson process as, for instance, the formula giving the law of a compound Poisson process.
The effect of 8 days of strict bed rest on the incretin effect in healthy volunteers
DEFF Research Database (Denmark)
Nielsen, Signe Tellerup; Harder-Lauridsen, Nina Majlund; Benatti, Fabiana Braga
2016-01-01
in the levels of GLP-1 and Glucagon. Bed rest led to a mean loss of 2.4 kg of fat-free mass, and induced insulin resistance evaluated by the Matsuda index, but did not affect the incretin effect (P = 0.6). In conclusion, 8 days of bed rest induces insulin resistance, but we did not see evidence of an associated......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...
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.
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.
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.
Multiple-Set Split Feasibility Problems for κ-Strictly Pseudononspreading Mapping in Hilbert Spaces
Directory of Open Access Journals (Sweden)
Jing Quan
2013-01-01
Full Text Available The purpose of this paper is to prove some weak and strong convergence theorems for solving the multiple-set split feasibility problems for κ-strictly pseudononspreading mapping in infinite-dimensional Hilbert spaces by using the proposed iterative method. The main results presented in this paper extend and improve the corresponding results of Xu et al. (2006, of Osilike et al. (2011, and of many other authors.
Multiobjective Optimization for the Forecasting Models on the Base of the Strictly Binary Trees
Nadezhda Astakhova; Liliya Demidova; Evgeny Nikulchev
2016-01-01
The optimization problem dealing with the development of the forecasting models on the base of strictly binary trees has been considered. The aim of paper is the comparative analysis of two optimization variants which are applied for the development of the forecasting models. Herewith the first optimization variant assumes the application of one quality indicator of the forecasting model named as the affinity indicator and the second variant realizes the application of two quality indicators ...
Cannabis legalization with strict regulation, the overall superior policy option for public health.
Rehm, J; Fischer, B
2015-06-01
Cannabis is the most prevalently used drug globally, with many jurisdictions considering varying reform options to current policies to deal with this substance and associated harm. Three policy options are available: prohibition, decriminalization, and legalization, with prohibition currently the dominant model globally. This contribution gives reasons why legalization with strict regulation should be considered superior to other options with respect to public health in high income countries in North America. © 2015 ASCPT.
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)
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.
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.
Temporary Strict Maternal Avoidance of Cow’s Milk and Infantile Colic
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Firoozeh Sajedi
2009-12-01
Full Text Available Infant colic is a common problem characterized by excessive crying and fussing. We examined whether colic symptoms of exclusively breast-milk-fed infants would be improved by temporary strict maternal avoidance of cows milk. This study is analytic and experimental. Sixty-six subjects were recruited during winter of 2006 from a clinic in Isfahan, Iran. Breast-milk-fed in-fants with "colic", age 3-6 months and to be in otherwise good health were referred by pediatri-cians. The intervention was 1 week period of strict maternal avoidance of cows milk while they continued exclusive breast-milk-feeding. All infants showed improvement in distressed behavior (crying and fussing during intervention. The total recorded crying and fussing time was reduced by an average of 31%. A significant difference was found in cry and fuss time between first and last 2 days of intervention (P = 0.000. Cows milk proteins may play an etiologic role in colic. We propose that a brief intervention with strict maternal avoidance of cows milk may be an effective treatment for colic in some breast-milk-fed infants.
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.
DEFF Research Database (Denmark)
Huang, Shaojun; Wu, Qiuwei; Zhao, Haoran
2016-01-01
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...... penetration level of renewables is present in the distribution networks. The geometry study helps understand the fundamental nature of the OPF and its convex-relaxed problem, such as the second-order cone programming (SOCP) problem. A case study based on a three-node system is used to illustrate the geometry...
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
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)
Parthood and Convexity as the Basic Notions of a Theory of Space
DEFF Research Database (Denmark)
Robering, Klaus
, a ``pregeometry'' is described in which only the notion of convexity but no further axiom is added to that background framework. Pregeometry is extended to the full system in three steps. First the notion of a line segment is explained as the convex hull of the mereological sum of two points. In a second step two...... axioms are added which describe what it means for a thus determined line segment to be ``straight''. In the final step we deal with the order of points on a line segment and define the notion of a line. The presentation of the geometric system is concluded with a brief consideration of the geometrical...... principles known by the names of Peano and Pasch. Two additional topics are treated in short sections at the end of the article: (1) the introduction of coordinates and (2) the idea of a ``geometrical algebra''....
Analyse statique de contrôleurs à base d'optimisation convexe
Garoche, Pierre-Loïc
2016-01-01
This manuscript presents a set of works targeting the formal analysis of controller software implementation using the tools of convex optimization.; Les travaux présentés portent, d’une façon générale, sur la preuve automatique de propriétés de systèmes de contrôle-commande à l’aide d’optimisation convexe. Par exemple, pour montrer qu’un système ne va jamais se mettre dans un état indésirable, on va démontrer qu’une certaine propriété, dite invariant inductif, excluant les états indésirables,...
Ramesh, Nisha; Tasdizen, Tolga
2014-10-01
Bayesian frameworks are commonly used in tracking algorithms. An important example is the particle filter, where a stochastic motion model describes the evolution of the state, and the observation model relates the noisy measurements to the state. Particle filters have been used to track the lineage of cells. Propagating the shape model of the cell through the particle filter is beneficial for tracking. We approximate arbitrary shapes of cells with a novel implicit convex function. The importance sampling step of the particle filter is defined using the cost associated with fitting our implicit convex shape model to the observations. Our technique is capable of tracking the lineage of cells for nonmitotic stages. We validate our algorithm by tracking the lineage of retinal and lens cells in zebrafish embryos.
Seamless lamination of a concave-convex architecture with single-layer graphene
Park, Ji-Hoon; Lim, Taekyung; Baik, Jaeyoon; Seo, Keumyoung; Moon, Youngkwon; Park, Noejung; Shin, Hyun-Joon; Kyu Kwak, Sang; Ju, Sanghyun; Real Ahn, Joung
2015-10-01
Graphene has been used as an electrode and channel material in electronic devices because of its superior physical properties. Recently, electronic devices have changed from a planar to a complicated three-dimensional (3D) geometry to overcome the limitations of planar devices. The evolution of electronic devices requires that graphene be adaptable to a 3D substrate. Here, we demonstrate that chemical-vapor-deposited single-layer graphene can be transferred onto a silicon dioxide substrate with a 3D geometry, such as a concave-convex architecture. A variety of silicon dioxide concave-convex architectures were uniformly and seamlessly laminated with graphene using a thermal treatment. The planar graphene was stretched to cover the concave-convex architecture, and the resulting strain on the curved graphene was spatially resolved by confocal Raman spectroscopy; molecular dynamic simulations were also conducted and supported the observations. Changes in electrical resistivity caused by the spatially varying strain induced as the graphene-silicon dioxide laminate varies dimensionally from 2D to 3D were measured by using a four-point probe. The resistivity measurements suggest that the electrical resistivity can be systematically controlled by the 3D geometry of the graphene-silicon dioxide laminate. This 3D graphene-insulator laminate will broaden the range of graphene applications beyond planar structures to 3D materials.Graphene has been used as an electrode and channel material in electronic devices because of its superior physical properties. Recently, electronic devices have changed from a planar to a complicated three-dimensional (3D) geometry to overcome the limitations of planar devices. The evolution of electronic devices requires that graphene be adaptable to a 3D substrate. Here, we demonstrate that chemical-vapor-deposited single-layer graphene can be transferred onto a silicon dioxide substrate with a 3D geometry, such as a concave-convex architecture. A
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...
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.
Multimode Root locus for a Matrix with uncertainty using convex lowbar Hull
International Nuclear Information System (INIS)
Hussein, Mohammed Tawfik
2009-01-01
The goal of this paper is to investigate the robust stability of the uncertain system based on the edge theorem and the Bhattacharyya and Keel algorithm. Firstly, the dynamic model for the system will be derived, then, Depending on the uncertainty, which appears in the elements of matrix A, the system will generates a set of interval matrices, secondly the procedures of the proposed algorithm to find convex hull of the system by Using the method of Andrew's Monotone Chain Algorithm will be implemented, and lastly root locus method will be utilized and applied to the exposed edges of the convex polygon and yet; the sharp and tight bounds of the eigenvalues of the proposed uncertain systems will be computed. An Electrical engineering system will be presented as practical example to validate the proposed method.
Directory of Open Access Journals (Sweden)
Kechen Song
2013-01-01
Full Text Available Accurate detection of surface defect is an indispensable section in steel surface inspection system. In order to detect the micro surface defect of silicon steel strip, a new detection method based on saliency convex active contour model is proposed. In the proposed method, visual saliency extraction is employed to suppress the clutter background for the purpose of highlighting the potential objects. The extracted saliency map is then exploited as a feature, which is fused into a convex energy minimization function of local-based active contour. Meanwhile, a numerical minimization algorithm is introduced to separate the micro surface defects from cluttered background. Experimental results demonstrate that the proposed method presents good performance for detecting micro surface defects including spot-defect and steel-pit-defect. Even in the cluttered background, the proposed method detects almost all of the microdefects without any false objects.
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.
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.
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.
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
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.
Irreducible convex paving for decomposition of multi-dimensional martingale transport plans
De March, Hadrien; Touzi, Nizar
2017-01-01
Martingale transport plans on the line are known from Beiglbock & Juillet to have an irreducible decomposition on a (at most) countable union of intervals. We provide an extension of this decomposition for martingale transport plans in R^d, d larger than one. Our decomposition is a partition of R^d consisting of a possibly uncountable family of relatively open convex components, with the required measurability so that the disintegration is well-defined. We justify the relevance of our decompo...
Estimates of Covering Numbers of Convex Sets with Slowly Decaying Orthogonal Subsets
Czech Academy of Sciences Publication Activity Database
Kůrková, Věra; Sanguineti, M.
2007-01-01
Roč. 155, č. 15 (2007), s. 1930-1942 ISSN 0166-218X R&D Projects: GA MŠk(CZ) 1M0567 Institutional research plan: CEZ:AV0Z10300504 Keywords : symmetric convex hulls * lower bounds on covering numbers * power-type covering numbers * generalized Hadamard matrices * Minkowski functional Subject RIV: IN - Informatics, Computer Science Impact factor: 0.625, year: 2007
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.
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...
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]....
A Perfect Price Discrimination Market Model with Production, and a (Rational) Convex Program for It
Goel, Gagan; Vazirani, Vijay
Recent results showed PPAD-completeness of the problem of computing an equilibrium for Fisher's market model under additively separable, piecewise-linear, concave utilities. We show that introducing perfect price discrimination in this model renders its equilibrium polynomial time computable. Moreover, its set of equilibria are captured by a convex program that generalizes the classical Eisenberg-Gale program, and always admits a rational solution.
A stronger version of matrix convexity as applied to functions of Hermitian matrices
Directory of Open Access Journals (Sweden)
Kagan Abram
1999-01-01
Full Text Available A stronger version of matrix convexity, called hyperconvexity is introduced. It is shown that the function is hyperconvex on the set of Hermitian matrices and is hyperconvex on the set of positive definite Hermitian matrices. The new concept makes it possible to consider weighted averages of matrices of different orders. Proofs use properties of the Fisher information matrix, a fundamental concept of mathematical statistics.
Contact point generation for convex polytopes in interactive rigid body dynamics
DEFF Research Database (Denmark)
Silcowitz-Hansen, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny
When computing contact forces in rigid body dynamics systems, most state-of-the-art solutions use iterative methods such as the projected Gauss–Seidel (PGS) method. Methods such as the PGS method are preferred for their robustness. However, the time-critical nature of interactive applications...... for convex polytopes. A novel contact point generation method is presented, which is based on growth distances and Gauss maps. We demonstrate improvements when using our method in the context of interactive rigid body simulation...
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.
Directory of Open Access Journals (Sweden)
Xiaofei Cao
2016-11-01
Full Text Available In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theory of Lagrange multipliers.
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
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; Weiner, Michael W.; Aisen, Paul; Petersen, Ronald; Jack, Clifford R.; Jagust, William; Trojanowki, John Q.
2017-01-01
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 \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage...
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
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.
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.
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.
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.
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.
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.
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
Directory of Open Access Journals (Sweden)
M. Emin Özdemir
2015-01-01
Full Text Available In this paper, we obtain some companions of Ostrowski type inequality for absolutely continuous functions whose second derivatives absolute values are convex and concave. Finally, we give some applications for special means.
Fang, Lingling; Zhao, Wantong; Li, Xinyou; Wang, Xianghai
2017-11-01
To segment ship target in infrared (IR) images, a convex active contour model based on local image entropy is proposed in this paper. Firstly, local image entropy based on kernel function is obtained; on this basis, the convex energy functional is built using the variational level set method in the convex set. Because of the introduction of entropy, the proposed method can protect the image edge and enhance the ability to deal images with heterogeneity. At the same time, the convex energy functional can get a global minimum and has robustness against initial curve placement. Compared with the state-of-the-art methods, experiment results demonstrate the performance and effectiveness of the proposed method.
Gordon, Jacqueline M; Lauver, Lori S; Buck, Harleah G
2018-02-01
Hyperglycemia post-cardiac surgery is associated with poor clinical outcomes. Recent studies suggest maintaining liberal glycemic control (liberal CII protocol. Retrospective review of 144 strict CII patient records and 147 liberal CII patient records. Mean blood glucose was 159.8mg/dL (liberal CII) compared to 143.3mg/dL (strict CII) (p≤0.001). No surgical site infections occurred in either group. Mean ICU length of stay was 4.5days (liberal) versus 4.4days (strict) (p=0.74). Two 30-day mortalities occurred for the liberal cohort compared to no deaths in the strict group (p=0.49). Hypoglycemia incidence within 24h after surgery was 0.1% (liberal) compared to 0.3% (strict) compared to (p=0.16). Use of a nurse managed liberal CII resulted in similar outcomes with fewer incidents of hypoglycemia. Copyright © 2017. Published by Elsevier Inc.
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.
Knabel, S J; Walker, H W; Hartman, P A; Mendonca, A F
1990-02-01
Listeria monocytogenes F5069 was suspended in either Trypticase soy broth-0.6% yeast extract (TSBYE) or sterile, whole milk and heated at 62.8 degrees C in sealed thermal death time tubes. Severely heat-injured cells were recovered in TSBYE within sealed thermal death time tubes because of the formation of reduced conditions in the depths of the TSBYE. Also, the use of strictly anaerobic Hungate techniques significantly increased recovery in TSBYE containing 1.5% agar compared with aerobically incubated controls. The exogenous addition of catalase, but not superoxide dismutase, slightly increased the recovery of heat-injured cells in TSBYE containing 1.5% agar incubated aerobically. Growth of cells at 43 degrees C caused a greater increase in heat resistance as compared with cells heat shocked at 43 degrees C or cells grown at lower temperatures. Growth of L. monocytogenes at 43 degrees C and enumeration by the use of strictly anaerobic Hungate techniques resulted in D62.8 degrees C values that were at least sixfold greater than those previously obtained by using cells grown at 37 degrees C and aerobic plating. Results indicate that, under the conditions of the present study, high levels of L. monocytogenes would survive the minimum low-temperature, long-time treatment required by the U.S. Food and Drug Administration for pasteurizing milk. The possible survival of low levels of L. monocytogenes during high-temperature, short-time pasteurization and enumeration of injured cells by recovery on selective media under strictly anaerobic conditions are discussed.
RelTime Rates Collapse to a Strict Clock When Estimating the Timeline of Animal Diversification.
Lozano-Fernandez, Jesus; Dos Reis, Mario; Donoghue, Philip C J; Pisani, Davide
2017-05-01
Establishing an accurate timescale for the history of life is crucial to understand evolutionary processes. For this purpose, relaxed molecular clock models implemented in a Bayesian MCMC framework are generally used. However, these methods are time consuming. RelTime, a non-Bayesian method implementing a fast, ad hoc, algorithm for relative dating, was developed to overcome the computational inefficiencies of Bayesian software. RelTime was recently used to investigate the timing of origin of animals, yielding results consistent with early strict clock studies from the 1980s and 1990s, estimating metazoans to have a Mesoproterozoic origin-over a billion years ago. RelTime results are unexpected and disagree with the largest majority of modern, relaxed, Bayesian molecular clock analyses, which suggest animals originated in the Tonian-Cryogenian (less that 850 million years ago). Here, we demonstrate that RelTime-inferred divergence times for the origin of animals are spurious, a consequence of the inability of RelTime to relax the clock along the internal branches of the animal phylogeny. RelTime-inferred divergence times are comparable to strict-clock estimates because they are essentially inferred under a strict clock. Our results warn us of the danger of using ad hoc algorithms making implicit assumptions about rate changes along a tree. Our study roundly rejects a Mesoproterozoic origin of animals; metazoans emerged in the Tonian-Cryogenian, and diversified in the Ediacaran, in the immediate prelude to the routine fossilization of animals in the Cambrian associated with the emergence of readily preserved skeletons. © The Author 2017. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
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.
Knabel, S J; Walker, H W; Hartman, P A; Mendonca, A F
1990-01-01
Listeria monocytogenes F5069 was suspended in either Trypticase soy broth-0.6% yeast extract (TSBYE) or sterile, whole milk and heated at 62.8 degrees C in sealed thermal death time tubes. Severely heat-injured cells were recovered in TSBYE within sealed thermal death time tubes because of the formation of reduced conditions in the depths of the TSBYE. Also, the use of strictly anaerobic Hungate techniques significantly increased recovery in TSBYE containing 1.5% agar compared with aerobicall...
Alimov, A. R.
2017-07-01
In a broad class of finite-dimensional Banach spaces, we show that a closed set with lower semicontinuous metric projection is a strict sun, admits a continuous selection of the metric projection operator onto it, has contractible intersections with balls, and its (nonempty) intersection with any closed ball is a retract of this ball. For sets with continuous metric projection, a number of new results relating the solarity of such sets to the stability of the operator of best approximation are obtained. Bibliography 25 titles.
Transplanting Diseases from Organ Donors in Western Europe: Fault Liability or Strict Liability?
Broeckx, Nils; Verhoeven, Dimitri
2015-06-01
This article will examine the problem of disease transmission through organ transplantation from a civil liability perspective. Both fault liability and strict product liability might be possible. These two types of liability will be compared, while applying them to the actions of the central parties involved in organ donation and transplantation, namely the physician/hospital, the donor and the organ exchange organisation. While product liability is generally an easier way to obtain compensation than fault liability, it might nevertheless place too heavy a burden on the transplant professionals.
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.
Single Molecule Experiments Challenge the Strict Wave-Particle Dualism of Light
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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.
Fuzzy Adaptive Decentralized Optimal Control for Strict Feedback Nonlinear Large-Scale Systems.
Sun, Kangkang; Sui, Shuai; Tong, Shaocheng
2018-04-01
This paper considers the optimal decentralized fuzzy adaptive control design problem for a class of interconnected large-scale nonlinear systems in strict feedback form and with unknown nonlinear functions. The fuzzy logic systems are introduced to learn the unknown dynamics and cost functions, respectively, and a state estimator is developed. By applying the state estimator and the backstepping recursive design algorithm, a decentralized feedforward controller is established. By using the backstepping decentralized feedforward control scheme, the considered interconnected large-scale nonlinear system in strict feedback form is changed into an equivalent affine large-scale nonlinear system. Subsequently, an optimal decentralized fuzzy adaptive control scheme is constructed. The whole optimal decentralized fuzzy adaptive controller is composed of a decentralized feedforward control and an optimal decentralized control. It is proved that the developed optimal decentralized controller can ensure that all the variables of the control system are uniformly ultimately bounded, and the cost functions are the smallest. Two simulation examples are provided to illustrate the validity of the developed optimal decentralized fuzzy adaptive control scheme.
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.
Liu, Jing; He, Qiong; Luo, Jianwen
2018-03-01
According to the linear acoustic theory, the channel data of a plane wave emitted by a linear array is a linear combination of the full data set of synthetic transmit aperture (STA). Combining this relationship with compressed sensing (CS), a novel CS based ultrasound beamforming strategy, named compressed sensing based synthetic transmit aperture (CS-STA), was previously proposed to increase the frame rate of ultrasound imaging without sacrificing the image quality for a linear array. In this paper, assuming linear transfer function of a pulse-echo ultrasound system, we derived and applied the theory of CS-STA for a slightly curved array and validated CS-STA in a convex array configuration. Computer simulations demonstrated that, in the convex array configuration, the normalized root-mean-square error between the beamformed radio-frequency data of CS-STA and STA was smaller than 1% while CS-STA achieved four-fold higher frame rate than STA. In addition, CS-STA was capable of achieving good image quality at depths over 100 mm. It was validated in phantom experiments by comparing CS-STA with STA, multielement synthetic transmit aperture (ME-STA), and the conventional focused method (focal depth = 110 mm). The experimental results showed that STA and CS-STA performed better than ME-STA and the focused method at small depths. At the depth of 110 mm, CS-STA, ME-STA, and the focused methods improved the contrast and contrast-to-noise ratio of STA. The improvements in CS-STA are higher than those in ME-STA but lower than those in the focused mode. These results can also be observed qualitatively in the in vivo experiments on the liver of a healthy male volunteer. The CS-STA method is thus proved to increase the frame rate and achieve high image quality at full depth in the convex array configuration.
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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
Convex hulls of random walks in higher dimensions: A large-deviation study
Schawe, Hendrik; Hartmann, Alexander K.; Majumdar, Satya N.
2017-12-01
The distribution of the hypervolume V and surface ∂ V of convex hulls of (multiple) random walks in higher dimensions are determined numerically, especially containing probabilities far smaller than P =10-1000 to estimate large deviation properties. For arbitrary dimensions and large walk lengths T , we suggest a scaling behavior of the distribution with the length of the walk T similar to the two-dimensional case and behavior of the distributions in the tails. We underpin both with numerical data in d =3 and d =4 dimensions. Further, we confirm the analytically known means of those distributions and calculate their variances for large T .
n-Hindle-sphere arrangement with an exact ray trace for testing hyperboloid convex mirrors.
Percino-Zacarias, M E; Cordero-Dávila, A
1999-10-01
We present calculations with an exact ray trace to determine the dimensions that define one or two Hindle spheres, since the paraxial theory is incongruent for convex hyperboloid mirrors with small f numbers. The equations are generalized to calculate the dimensions of n Hindle spheres, since in this way it is possible to reduce the dimensions of the spheres more. Actual calculations are done for the secondary mirrors of the Benemerita Universidad Autonoma de Puebla and Large Milimetric Telescopes; experimental results are shown for the latter.
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.
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...
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
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...
Maximal L2 regularity for Ornstein-Uhlenbeck equation in convex sets of Banach spaces
Cappa, G.
2016-06-01
We study the elliptic equation λu -LΩ u = f in an open convex subset Ω of an infinite dimensional separable Banach space X endowed with a centered non-degenerate Gaussian measure γ, where LΩ is the Ornstein-Uhlenbeck operator. We prove that for λ > 0 and f ∈L2 (Ω , γ) the weak solution u belongs to the Sobolev space W 2 , 2 (Ω , γ). Moreover we prove that u satisfies the Neumann boundary condition in the sense of traces at the boundary of Ω. This is done by finite dimensional approximation.
International Nuclear Information System (INIS)
Sidky, Emil Y; Pan Xiaochuan; Jørgensen, Jakob H
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 modeling breast CT with low-intensity x-ray illumination is presented. (paper)
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....
Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process.
Yin, Chuancun; 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.
RECTILINEAR AND BROWNIAN MOTION FROM A RANDOM POINT IN A CONVEX REGION
Directory of Open Access Journals (Sweden)
Peter Ehlers
2011-05-01
Full Text Available A particle is projected from a point P in a subset E of a convex region H to a point Q in a uniformly random direction. The probability that Q lies in the interior of H at time t is obtained for two types of motion of the particle, rectilinear (i.e. straight-line and Brownian. In the case of rectilinear motion, the first passage time through the boundary of H is considered. Results are obtained in terms of the generalized overlap function for embedded bodies.
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
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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.
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).
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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.
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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.
Paul N. Somerville
1998-01-01
Let X' = (X1,X2, ... ,Xk) have the multivariate normal distribution f(X) = MVN(μ, ∑σ2) where ∑ is a known positive definite matrix, and σ2 is a constant. There are many problems in statistics which require the evaluation of f(x) over some convex region A. That is P = ∫A f(X) dX. If σ2 is known, then without loss of generality, set μ = 0, σ =1 and let ∑ be the correlation matrix. For the case where the region A is rectangular, the problem has been addressed by many authors. They include ...
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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.
Sheikh-Jabbari, M. M.
2016-09-01
General covariance is the cornerstone of Einstein’s general relativity (GR) and implies that any two metrics related by diffeomorphisms are physically equivalent. There are, however, many examples pointing to the fact that this strict statement of general covariance needs refinement. There are a very special (measure-zero) subset of diffeomorphisms, the residual diffeomorphisms, to which one can associate well-defined conserved charges. This would hence render these diffeomorphic geometries physically distinct. We discuss that these symmetries may be appropriately called “symplectic symmetries”. Existence of residual diffeomorphisms and symplectic symmetries can be a quite general feature and not limited to the examples discussed so far in the literature. We propose that, in the context of black holes, these diffeomorphic, but distinct, geometries may be viewed as “symplectic soft hair” on black holes. We comment on how this may remedy black hole microstate problem, which in this context are dubbed as “horizon fluffs”.
Reactions to terror attacks in ultra-orthodox jews: the cost of maintaining strict identity.
Ankri, Yael L E; Bachar, Eytan; Shalev, Arieh Y
2010-01-01
Traumatic events can shatter faith and beliefs. The responses of Ultra-Orthodox survivors of deadly terrorist attacks illustrate an effort to reconcile dreadful experiences with deeply embedded beliefs. Qualified clinicians prospectively evaluated self-reported and interviewer-generated posttraumatic stress disorder (PTSD) symptoms and cognitive appraisal in Ultra-Orthodox (n = 20) and non-Ultra-Orthodox (n = 33) survivors of suicide bus-bombing incidents in Jerusalem. Ultra-Orthodox survivors reported higher levels of PTSD symptoms and more personal guilt. Their narratives reflected an unshaken belief in Just Providence, within which being a victim of terror was perceived as a Just retribution for known or unknown wrongdoing. Survivors' reactions to trauma often reflect an effort to reconcile incongruous experiences with previously held beliefs. When treating strict believers, helpers should be sensitive to the identity-preserving function of posttraumatic cognitions.
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...
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
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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.
The Effect of Strict Segregation on Pseudomonas aeruginosa in Cystic Fibrosis Patients.
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Rosa van Mansfeld
Full Text Available Segregation of patients with cystic fibrosis (CF was implemented to prevent chronic infection with epidemic Pseudomonas aeruginosa strains with presumed detrimental clinical effects, but its effectiveness has not been carefully evaluated.The effect of strict segregation on the incidence of P. aeruginosa infection in CF patients was investigated through longitudinal protocolized follow-up of respiratory tract infection before and after segregation. In two nested cross-sectional studies in 2007 and 2011 the P. aeruginosa population structure was investigated and clinical parameters were determined in patients with and without infection with the Dutch epidemic P. aeruginosa clone (ST406.Of 784 included patients 315 and 382 were at risk for acquiring chronic P. aeruginosa infection before and after segregation. Acquisition rates were, respectively, 0.14 and 0.05 per 1,000 days at risk (HR: 0.66, 95% CI [0.2548-1.541]; p = 0.28. An exploratory subgroup analysis indicated lower acquisition after segregation in children < 15 years of age (HR: 0.43, 95% CI[0.21-0.95]; p = 0.04. P. aeruginosa population structure did not change after segregation and ST406 was not associated with lung function decline, death or lung transplantation.Strict segregation was not associated with a statistically significant lower acquisition of chronic P. aeruginosa infection and ST406 was not associated with adverse clinical outcome. After segregation there were no new acquisitions of ST406. In an unplanned exploratory analysis chronic acquisition of P. aeruginosa was lower after implementation of segregation in patients under 15 years of age.
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.
Selvester scoring in patients with strict LBBB using the QUARESS software.
Xia, Xiaojuan; Chaudhry, Uzma; Wieslander, Björn; Borgquist, Rasmus; Wagner, Galen S; Strauss, David G; Platonov, Pyotr; Ugander, Martin; Couderc, Jean-Philippe
2015-01-01
Estimation of the infarct size from body-surface ECGs in post-myocardial infarction patients has become possible using the Selvester scoring method. Automation of this scoring has been proposed in order to speed-up the measurement of the score and improving the inter-observer variability in computing a score that requires strong expertise in electrocardiography. In this work, we evaluated the quality of the QuAReSS software for delivering correct Selvester scoring in a set of standard 12-lead ECGs. Standard 12-lead ECGs were recorded in 105 post-MI patients prescribed implantation of an implantable cardiodefibrillator (ICD). Amongst the 105 patients with standard clinical left bundle branch block (LBBB) patterns, 67 had a LBBB pattern meeting the strict criteria. The QuAReSS software was applied to these 67 tracings by two independent groups of cardiologists (from a clinical group and an ECG core laboratory) to measure the Selvester score semi-automatically. Using various level of agreement metrics, we compared the scores between groups and when automatically measured by the software. The average of the absolute difference in Selvester scores measured by the two independent groups was 1.4±1.5 score points, whereas the difference between automatic method and the two manual adjudications were 1.2±1.2 and 1.3±1.2 points. Eighty-two percent score agreement was observed between the two independent measurements when the difference of score was within two point ranges, while 90% and 84% score agreements were reached using the automatic method compared to the two manual adjudications. The study confirms that the QuAReSS software provides valid measurements of the Selvester score in patients with strict LBBB with minimal correction from cardiologists. Copyright © 2015 Elsevier Inc. All rights reserved.
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Eloísa Ramos Rodríguez
2016-11-01
Full Text Available A common freshwater cryptophyte, Cryptomonas pyrenoidifera, was cultivated in batch-cultures to analyze intraspecific variation in elemental stoichiometry along a broad gradient of pulsed phosphorus (P enrichment during the early acclimation period and to determine the immediate homeostatic capacity of the nitrogen-to-phosphorus (N:P ratio of this alga when nutrients are at saturating levels. Experimental results revealed that nitrogen (N and P cell quotas significantly increased with increasing P concentration. However, despite the wide range of N:P ratios in the medium, Cryptomonas N:P ratios were highly stable at higher P-level treatments, indicating a highly conservative behavior and suggesting strict elemental homeostasis when nutrients are at saturating levels. The strictly homeostatic N:P ratio appears to be attributable to their high potential for a fast luxury consumption of both N and P after a brief and intense episode of increased resource availability and to physiological limits on their nutrient storage capacity. Most importantly, the N:P biomass ratio at nutrient saturating levels converged around 11:1, which was the observed ratio of maximum internal cell quotas for N and P (i.e. Qmax,N:Qmax,P under the prevailing experimental conditions. This value is particularly informative for C. pyrenoidifera because it represents cell storage quotients and may be a taxon-specific evolutionary optimum, providing a reference point to infer the grade of nutrient-limitation. The experimental data give ranges of variation in C. pyrenoidifera elemental composition permitting, among others, proper parameterization of cryptophyte stoichiometry models.
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....
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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.
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.
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.
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...
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.
Shen, Zhengwei; Cheng, Lishuang
2017-09-01
Total variation (TV)-based image deblurring method can bring on staircase artifacts in the homogenous region of the latent images recovered from the degraded images while a wavelet/frame-based image deblurring method will lead to spurious noise spikes and pseudo-Gibbs artifacts in the vicinity of discontinuities of the latent images. To suppress these artifacts efficiently, we propose a nonconvex composite wavelet/frame and TV-based image deblurring model. In this model, the wavelet/frame and the TV-based methods may complement each other, which are verified by theoretical analysis and experimental results. To further improve the quality of the latent images, nonconvex penalty function is used to be the regularization terms of the model, which may induce a stronger sparse solution and will more accurately estimate the relative large gradient or wavelet/frame coefficients of the latent images. In addition, by choosing a suitable parameter to the nonconvex penalty function, the subproblem that splits by the alternative direction method of multipliers algorithm from the proposed model can be guaranteed to be a convex optimization problem; hence, each subproblem can converge to a global optimum. The mean doubly augmented Lagrangian and the isotropic split Bregman algorithms are used to solve these convex subproblems where the designed proximal operator is used to reduce the computational complexity of the algorithms. Extensive numerical experiments indicate that the proposed model and algorithms are comparable to other state-of-the-art model and methods.
Designing null phase screens to test a fast plano-convex aspheric lens
DelOlmo-Márquez, Jesús; Castán-Ricaño, Diana; Avendaño-Alejo, Maximino; Díaz-Uribe, Rufino
2015-08-01
We have obtained a formula to represent the wavefront produced by a plano-convex aspheric lens with symmetry of revolution considering a plane wavefront propagating parallel to the optical axis and impinging on the refracting surface, it is called a zero-distance phase front, being it the first wavefront to be out of the optical system. Using a concept of differential geometry called parallel curves it is possible to obtain an analytic formula to represent the wavefront propagated at arbitrary distances through the optical axis. In order to evaluate qualitatively a plano-convex aspheric lens, we have modified slightly an interferometer Tywman-Green as follow: In the reference beam we use a plane mirror and the beam of test we have used a spatial light modulator (SLM) to compensate the phase produced by the lens under test. It will be called a null phase interferometer. The main idea is to recombine both wavefronts in order to get a null interferogram, otherwise we will associate the patterns of the interferogram to deformations of the lens under test. The null phase screens are formed with concentric circumferences assuming different gray levels printed on SLM.
Contribution à l'étude des algorithmes de l'optimisation non convexe et non différentiable
Benacer, Rachid
1986-01-01
Etude théorique et algorithmique des problèmes d'optimisation non convexes et non différentiables des types suivants: maximiser f(x) sur C, minimiser f(x)-g(x) sur C, minimiser f(x) lorsque x appartient à C et g(x) positive, où f, g sont convexes définies sur rn et C est une partie compacte convexe non vide de rn. Un étudie les conditions nécessaires d'optimalité du premier ordre la dualité, les méthodes de sous-gradients qui convergent vers des solutions optimales locales et les algorithmes ...
Grabovsky, Yury
2018-02-01
Examples of non-quasiconvex functions that are rank-one convex are rare. In this paper we construct a family of such functions by means of the algebraic methods of the theory of exact relations for polycrystalline composite materials, developed to identify G-closed sets of positive codimensions. The algebraic methods are used to construct a set of materials of positive codimension that is closed under lamination but is not G-closed. The well-known link between G-closed sets and quasiconvex functions and sets closed under lamination and rank-one convex functions is then used to construct a family of rotationally invariant, nonnegative, and 2-homogeneous rank-one convex functions, that are not quasiconvex.
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
de Klerk, Etienne; Glineur, François; Taylor, Adrien B.
2016-01-01
We consider the gradient (or steepest) descent method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-case rate of convergence of this scheme, and show that this worst-case behavior is exhibited by a certain convex quadratic function. We also give the tight worst-case complexity bound for a noisy variant of gradient descent method, where exact line-search is performed in a search direction that differs from negative...
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.
Rhemrev, G E; Timmerman, M F; Veldkamp, I; Van Winkelhoff, A J; Van der Velden, U
2006-01-01
To investigate (1) reduction in the number of microorganisms obtained directly after subgingival instrumentation, (2) rate of bacterial re-colonization during 2 weeks, under supragingival plaque-free conditions. Effects of subgingival instrumentation were measured at one deep pocket in 22 patients (11 smokers and 11 non-smokers). Immediately after initial therapy, experimental sites, under strict plaque control, were instrumented subgingivally. Microbiological evaluation was performed at pre-instrumentation, immediate post-instrumentation and 1 and 2 weeks post-instrumentation. Mean total anaerobic colony forming units (CFUs) dropped from 3.9 x 10(6) before to 0.09 x 10(6) immediately following instrumentation. Significant reductions were found for Tannerella forsythia, Micromonas micros, Fusobacterium nucleatum and spirochetes. Significant reductions were not observed for Actinobacillus actinomycetemcomitans, Porphyromonas gingivalis, Prevotella intermedia and Campylobacter rectus. Except for spirochetes, no reduction in prevalence of specific periodontal bacteria was found immediately after instrumentation. During follow-up, mean total CFU tended to increase. Prevalence of periodontal bacteria further reduced. No effect of smoking was found. Results indicate that subgingival mechanical cleaning in itself, has a limited effect, in actually removing bacteria. The subsequent reduction in prevalence of specific periodontal bacteria shows that it is apparently difficult for these species to survive in treated pockets.
Ferrando, A A; Stuart, C A; Brunder, D G; Hillman, G R
1995-10-01
Prolonged bed rest results in a loss of leg lean body mass. Previous studies using bed rest as a model for microgravity have shown decreases in leg mass after 12 and 14 d, 5 and 17 wk. As magnetic resonance imaging (MRI) can provide a precise and non-invasive means of determining muscle volume, we sought to determine if changes in leg muscle volume could be detected in bed rest periods as short as 7 d. Five young, healthy, male volunteers were subjected to 7 d of absolute bed rest. Each subject underwent MRI quantitation of segmental muscle volumes of the calves and thighs before and after bed rest. Eleven (calf) and nine (thigh) contiguous 1-cm thick transaxial images were generated over prescribed regions using a Technicare MRI imager with a 0.6T superconducting magnet and body coil. Image processing was performed using a generalized 8-bit medical image analysis package developed at University of Texas Medical Branch. Images were analyzed for muscle and non-muscle volumes (including fat, blood vessel, and bone marrow volumes). The MRI quantitation demonstrated bed rest-induced significant decreases in segmental thigh muscle (approximately 3.0%, p image analysis of MRI images provides a sensitive tool capable of detecting leg volume changes of as little as 3.0% over a 7-d period of strict bed rest.
Kayyal, Mohammad; Gibbs, Trevor
2012-01-01
As the world of medical education moves forward, it becomes increasingly clear that the transformative process is not as easy a process for all. Across the globe, there appears to be many barriers that obstruct or threaten innovation and change, most of which cause almost insurmountable problems to many schools. If transformative education is to result in an equitable raising of standards across such an unlevel playing field, schools have to find ways in overcoming these barriers. One seemingly common barrier to development occurs when medical schools are trapped within strict University governance structures; rules and regulations which are frequently inappropriate and obstructive to the transformation that must occur in today's medical educational paradigm. The Faculty of Medicine at Damascus University, one of the oldest and foremost medical schools in the Middle East, is one such school where rigid rules and regulations and traditional values are obstructing transformative change. This paper describes the problems, which the authors believe to be common to many, and explores how attempts have been made to overcome them and move the school into the twenty-first century. It is the ultimate purpose of this paper to raise awareness of the issue, share the lessons learned in order to assist others who are experiencing similar problems and possibly create opportunities for dialogue between schools.
On a holomorphic Lefschetz formula in strictly pseudoconvex subdomains of complex manifolds
International Nuclear Information System (INIS)
Kytmanov, A M; Myslivets, S G; Tarkhanov, N N
2004-01-01
The classical Lefschetz formula expresses the number of fixed points of a continuous map f:M→M in terms of the transformation induced by f on the cohomology of M. In 1966, Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they obtained a holomorphic Lefschetz formula on compact complex manifolds without boundary. Brenner and Shubin (1981, 1991) extended the Atiyah-Bott theory to compact manifolds with boundary. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, therefore the Atiyah-Bott theory is not applicable. Bypassing difficulties related to the boundary behaviour of Dolbeault cohomology, Donnelly and Fefferman (1986) obtained a formula for the number of fixed points in terms of the Bergman metric. The aim of this paper is to obtain a Lefschetz formula on relatively compact strictly pseudoconvex subdomains of complex manifolds X with smooth boundary, that is, to find the total Lefschetz number for a holomorphic endomorphism f * of the Dolbeault complex and to express it in terms of local invariants of the fixed points of f.
Agren, J J; Tvrzicka, E; Nenonen, M T; Helve, T; Hänninen, O
2001-02-01
The effects of a strict uncooked vegan diet on serum lipid and sterol concentrations were studied in patients with rheumatoid arthritis. The subjects were randomized into a vegan diet group (n 16), who consumed a vegan diet for 2-3 months, or into a control group (n 13), who continued their usual omnivorous diets. Serum total and LDL-cholesterol and -phospholipid concentrations were significantly decreased by the vegan diet. The levels of serum cholestanol and lathosterol also decreased, but serum cholestanol:total cholesterol and lathosterol:total cholesterol did not change. The effect of a vegan diet on serum plant sterols was divergent as the concentration of campesterol decreased while that of sitosterol increased. This effect resulted in a significantly greater sitosterol:campesterol value in the vegan diet group than in the control group (1.48 (SD 0.39) v. 0.72 (SD 0.14); P vegan diet changes the relative absorption rates of these sterols and/or their biliary clearance.
Model-Based Adaptive Event-Triggered Control of Strict-Feedback Nonlinear Systems.
Li, Yuan-Xin; Yang, Guang-Hong
2018-04-01
This paper is concerned with the adaptive event-triggered control problem of nonlinear continuous-time systems in strict-feedback form. By using the event-sampled neural network (NN) to approximate the unknown nonlinear function, an adaptive model and an associated event-triggered controller are designed by exploiting the backstepping method. In the proposed method, the feedback signals and the NN weights are aperiodically updated only when the event-triggered condition is violated. A positive lower bound on the minimum intersample time is guaranteed to avoid accumulation point. The closed-loop stability of the resulting nonlinear impulsive dynamical system is rigorously proved via Lyapunov analysis under an adaptive event sampling condition. In comparing with the traditional adaptive backstepping design with a fixed sample period, the event-triggered method samples the state and updates the NN weights only when it is necessary. Therefore, the number of transmissions can be significantly reduced. Finally, two simulation examples are presented to show the effectiveness of the proposed control method.
Brown, Spencer C; Bourge, Mickaël; Maunoury, Nicolas; Wong, Maurice; Bianchi, Michele Wolfe; Lepers-Andrzejewski, Sandra; Besse, Pascale; Siljak-Yakovlev, Sonja; Dron, Michel; Satiat-Jeunemaître, Béatrice
2017-04-13
DNA remodelling during endoreplication appears to be a strong developmental characteristic in orchids. In this study, we analysed DNA content and nuclei in 41 species of orchids to further map the genome evolution in this plant family. We demonstrate that the DNA remodelling observed in 36 out of 41 orchids studied corresponds to strict partial endoreplication. Such process is developmentally regulated in each wild species studied. Cytometry data analyses allowed us to propose a model where nuclear states 2C, 4E, 8E, etc. form a series comprising a fixed proportion, the euploid genome 2C, plus 2 to 32 additional copies of a complementary part of the genome. The fixed proportion ranged from 89% of the genome in Vanilla mexicana down to 19% in V. pompona, the lowest value for all 148 orchids reported. Insterspecific hybridisation did not suppress this phenomenon. Interestingly, this process was not observed in mass-produced epiphytes. Nucleolar volumes grow with the number of endocopies present, coherent with high transcription activity in endoreplicated nuclei. Our analyses suggest species-specific chromatin rearrangement. Towards understanding endoreplication, V. planifolia constitutes a tractable system for isolating the genomic sequences that confer an advantage via endoreplication from those that apparently suffice at diploid level. © The Author(s) 2017. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
Strictly hyperbolic models of co-current three-phase flow withgravity
Energy Technology Data Exchange (ETDEWEB)
Juanes, Ruben; Patzek, Tadeusz W.
2002-11-18
We study the character of the equations in the traditional formulation of one-dimensional immiscible three-phase flow with gravity, in the limit of negligible capillarity. We restrict our analysis to co-current flow required for a displacement process; in cases of mixed co-current and counter-current flow, capillarity effects cannot be dropped from the formulation. The model makes use of the classical multiphase extension of Darcy's equation. It is well known that, if relative permeabilities are taken as fixed functions of saturations, the model yields regions in the saturation space where the system of equations is locally elliptic. We regard elliptic behavior as a nonphysical artifact of an incomplete formulation, and derive conditions on the relative permeabilities that ensure strict hyperbolicity of the governing equations. The key point is to acknowledge that a Darcy-type formulation is insufficient to capture all the physics of three-phase flow and that, consequently, the relative permeabilities are functionals that depend on the fluid viscosity ratio and the gravity number. The derived conditions are consistent with the type of displacements that take place in porous media. By means of an illustrative example, we show how elliptic behavior can be removed, even when using simplistic relative permeability models.
Clinical impact of strict criteria for selectivity and lateralization in adrenal vein sampling.
Gasparetto, Alessandro; Angle, John F; Darvishi, Pasha; Freeman, Colbey W; Norby, Ray G; Carey, Robert M
2015-04-01
Selectivity index (SI) and lateralization index (LI) thresholds determine the adequacy of adrenal vein sampling (AVS) and the degree of lateralization. The purpose of this study was investigate the clinical outcome of patients whose adrenal vein sampling was interpreted using "strict criteria" (SC) (SIpre-stimuli≥3, SIpost-stimuli≥5 and LIpre-stimuli≥4, LIpost-stimuli≥4). A retrospective review of 73 consecutive AVS procedures was performed and 67 were technically successful. Forty-three patients showed lateralization and underwent surgery, while 24 did not lateralize and were managed conservatively. Systolic blood pressure (SBP), diastolic blood pressure (DBP), kalemia (K(+)), and the change in number of blood pressure (BP) medications were recorded for each patient before and after AVS and potential surgery were performed. In the surgery group, BP and K(+) changed respectively from 160±5.3/100±2.0 mmHg to 127±3.3/80±1.9 (p blood pressure medications were six (14.0%) in the lateralized group and 22 (91.7%) in the non-lateralized group (p <0.001). AVS interpretation with SC leads to significant clinical improvement in both patients who underwent surgery and those managed conservatively.
Fernández-de-las-Peñas, César; Arendt-Nielsen, Lars; Cuadrado, María Luz; Pareja, Juan A
2009-06-01
No study has previously analyzed pressure pain sensitivity of nerve trunks in migraine. This study aimed to examine the differences in mechanical pain sensitivity over specific nerves between patients with unilateral migraine and healthy controls. Blinded investigators assessed pressure pain thresholds (PPT) over the supra-orbital nerves (V1) and peripheral nerve trunks of both upper extremities (median, radial, and ulnar nerves) in 20 patients with strictly unilateral migraine and 20 healthy matched controls. Pain intensity after palpation over both supra-orbital nerves was also assessed. A pressure algometer was used to quantify PPT, whereas a 10-point numerical pain rate scale was used to evaluate pain to palpation over the supra-orbital nerve. The analysis of covariance revealed that pain to palpation over the supra-orbital nerve was significantly higher (P0.6). In patients with unilateral migraine, we found increased mechano-sensitivity of the supra-orbital nerve on the symptomatic side of the head. Outside the head, the same patients showed increased mechano-sensitivity of the main peripheral nerves of both upper limbs, without asymmetries. Such diffuse hypersensitivity of the peripheral nerves lends further evidence to the presence of a state of hyperexcitability of the central nervous system in patients with unilateral migraine.
International Nuclear Information System (INIS)
Gleiter, H.
1991-01-01
Nanocrystalline solids are polycrystals, the crystal size of which is a few (typically 1 to 10) nanometres so that 50% or more of the solid consists of incoherent interfaces between crystals of different orientations. Solids consisting primarily of internal interfaces represent a separate class of atomic structures because the atomic arrangement formed in the core of an interface is known to be an arrangement of minimum energy in the potential field of the two adjacent crystal lattices with different crystallographic orientations on either side of the boundary core. These boundary conditions result in atomic structures in the interfacial cores which cannot be formed elsewhere (e.g. in glasses or perfect crystals). Nanocrystalline solids are of interest for the following four reasons: (1) Nanocrystalline solids exhibit an atomic structure which differs from that of the two known solid states: the crystalline (with long-range order) and the glassy (with short-range order). (2) The properties of nanocrystalline solids differ (in some cases by several orders of magnitude) from those of glasses and/or crystals with the same chemical composition, which suggests that they may be utilized technologically in the future. (3) Nanocrystalline solids seem to permit the alloying of conventionally immiscible components. (4) If small (1 to 10 nm diameter) solid droplets with a glassy structure are consolidated (instead of small crystals), a new type of glass, called nanoglass, is obtained. Such glasses seem to differ structurally from conventional glasses. (orig.)
Angelo, Joseph A
2011-01-01
Supported by a generous quantity of full-color illustrations and interesting sidebars, Solid Matter introduces the basic characteristics and properties of solid matter. It briefly describes the cosmic connection of the elements, leading readers through several key events in human pre-history that resulted in more advanced uses of matter in the solid state. Chapters include:. -Solid Matter: An Initial Perspective. -Physical Behavior of Matter. -The Gravity of Matter. -Fundamentals of Materials Science. -Rocks and Minerals. -Metals. -Building Materials. -Carbon Earth's Most Versatile Element. -S
Differential inclusions governed by convex and nonconvex perturbation of a sweeping process
International Nuclear Information System (INIS)
Truong Xuan Duc Ha.
1992-07-01
In this paper we study the differential inclusion of the form -dx/dt is an element of N C(t) (x(t)) + F(t,x(t)), t is an element of [0,1] x(0) x 0 is an element of C(0), where C(t) is a nonempty weakly closed moving subset of a separable Hilbert space H and N C(t) (x) is the Clarke's normal cone of C(t) at the point x in C(t) and the perturbation F is satisfies one of the following assumptions: i) F is a uniformly continuous on the graph of C with nonempty compact values in H, ii) F is globally measurable, upper semicontinuous on H with nonempty convex compact values in H. (author). 21 refs
DEFF Research Database (Denmark)
Bonnevie, Rasmus; Schmidt, Mikkel Nørgaard; Mørup, Morten
2017-01-01
is marginalized. We consider the KL-corrected collapsed variational bound and apply it to Dirichlet process mixture models, allowing us to reduce the optimization space considerably. We find that the variational bound exhibits consistent and exploitable structure, allowing the application of difference......-of-convex optimization algorithms. We show how this yields an interpretable fixed-point update algorithm in the collapsed setting for the Dirichlet process mixture model. We connect this update formula to classical coordinate ascent updates, illustrating that the proposed improvement surprisingly reduces......Variational methods for approximate inference in Bayesian models optimise a lower bound on the marginal likelihood, but the optimization problem often suffers from being nonconvex and high-dimensional. This can be alleviated by working in a collapsed domain where a part of the parameter space...
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
. Furthermore, when the correlation between the a priori errors of the components is low enough, their combination is able to outperform both of them. Using energy conservation relations, we specialize the results to a combination of least mean-square filters operating both in stationary and in nonstationary......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...... is adapted by means of a stochastic gradient algorithm in order to minimize the error of the overall structure. General expressions are derived that show that the method is universal with respect to the component filters, i.e., in steady-state, it performs at least as well as the best component filter...
Analysis of the Criteria of Activation-Based Inverse Electrocardiography using Convex Optimization
Erem, Burak; van Dam, Peter M.; Brooks, Dana H.
2012-01-01
In inverse electrocardiography (ECG), the problem of finding activation times on the heart noninvasively from body surface potentials is typically formulated as a nonlinear least squares optimization problem. Current solutions rely on iterative algorithms which are sensitive to the presence of local minima. As a result, improved initialization approaches for this problem have been of considerable interest. However, in experiments conducted on a subject with Wolff-Parkinson-White syndrome, we have observed that there may be a mismatch between favorable solutions of the optimization problem and solutions with the desired physiological characteristics. In this work, we use a method based on a convex optimization framework to explore the solution space and analyze whether the optimization criteria target their intended objective. PMID:22255195
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
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......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...... minimum within the feasible region is identified. Following that finding we propose a tailored minimisation procedure that utilises the nature of the feasible region such that the minimisation can be separated into two linear programs; one for each of the control variables. These subproblems are simple...
An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State
Energy Technology Data Exchange (ETDEWEB)
Kamm, James Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-03-05
This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.