Convex optimization approach to the fusion of identity information
Li, Lingjie; Luo, Zhi-Quan; Wong, Kon M.; Bosse, Eloi
1999-03-01
We consider the problem of identity fusion for a multi- sensor target tracking system whereby sensors generate reports on the target identities. Since the sensor reports are typically fuzzy, 'incomplete' and inconsistent, the fusion approach based on the minimization of inconsistencies between the sensor reports by using a convex Quadratic Programming (QP) and linear programming (LP) formulation. In contrast to the Dempster-Shafer's evidential reasoning approach which suffers from exponentially growing completely, our approach is highly efficient. Moreover, our approach is capable of fusing 'ratio type' sensor reports, thus it is more general than the evidential reasoning theory. When the sensor reports are consistent, the solution generated by the new fusion method can be shown to converge to the true probability distribution. Simulation work shows that our method generates reasonable fusion results, and when only 'Subset type' sensor reports are presented, it produces fusion results similar to that obtained via the evidential reasoning theory.
Hamilton, D Kojo; Jones-Quaidoo, Sean M; Sansur, Charles; Shaffrey, Christopher I; Oskouian, Rod; Jane, John A
2008-05-01
Bone morphogenic protein products enable lumber spine fusion. Few outcome studies have been performed to evaluate function and pain relief after posterior lumber decompression for degenerative disease, and few studies have provided detailed results of posterior lumbar fusion in elderly patients. This retrospective analysis presents a comprehensive examination of spinal fusion, functional outcomes, and pain relief in a growing elderly population in which a BMP was used. Fifty-five patients, 25 men and 30 women (moderately disabled to bedridden), with both mean and median ages of 68 years, underwent surgery for symptoms of lumbar degenerative disease between August 2003 and June 2004. Surgery involved multilevel lumbar total laminectomies with medial facetectomies and posterior lateral fusion, which was performed using INFUSE Bone Graft (Medtronic Sofamor Dane K. Inc, Minneapolis, MN) with recombinant human BMP-2 as the active ingredient. Forty-seven patients (22 men and 25 women) were available for follow-up and participated in this study. Of these 47 patients, the average number of levels decompressed and fused was 2. Thirteen patients had 1 level, 18 patients with 2 levels, 15 patients with 3 levels, and 1 patient with 4 levels. An analysis of fusion was performed using computed tomography beginning at an average of 6 months (range, 3-36 months) postsurgery. At an average of 34 months (range, 29-36 months) of follow-up, 2 questionnaires--the Modified Oswestry Low Back Pain Disability Questionnaire and the SF-12 Health Survey--were completed by the patient. Long-term follow-up indicates that more than 85% of patients exhibited high functioning ability and had improved index scores and pain relief. Patients with improved pain and function scores also had better than average health status. In addition, grading the patients' fusion rates with the Lenke fusion scale [J Spinal Disord 5(4) (1992) 433-442] showed an 80% fusion (Lenke Grades A and B) rate. The use of rh
Scheer, Justin K; Khanna, Ryan; Lopez, Alejandro J; Fessler, Richard G; Koski, Tyler R; Smith, Zachary A; Dahdaleh, Nader S
2015-10-01
We retrospectively reviewed patient charts to compare the approach-related (convex versus concave) neurological complications and magnitude of correction in patients undergoing lateral lumbar interbody fusion (LLIF). It is yet to be quantitatively determined if correction of adult degenerative scoliosis from either side of the curve apex using a LLIF results in a reduction in complications and/or improved corrective ability. The inclusion criteria for this study were patients who underwent a LLIF for adult degenerative thoracolumbar scoliosis and had the LLIF prior to any other supplemental procedures. Patients were grouped based on the approach toward the curve apex concavity (CAVE) or the convexity (VEX). Standard coronal and sagittal radiographic measurements were made. Neurological complications and reoperation indications were also recorded. We included 32 patients for review (CAVE: 17; VEX: 15) with a mean age of 65.5 years±a standard deviation of 10.2, and mean follow-up of 17.0 months±15.7. There were eight postoperative neurological complications in eight patients (25.0%), and seven reoperations for six patients (18.8%; CAVE: 4/17 [23.5%]; VEX: 2/15 [13.3%]). The CAVE group had 6/17 neurological complications (35.3%; four ipsilateral and two contralateral to approach side) and VEX had 2/15 (13.3%; one ipsilateral and one bilateral to approach side; p>0.05). All patients significantly improved in the mean regional and segmental Cobb angles (p0.05). There were no significant differences between the groups for any of the radiographic parameters measured (p>0.05). Approaching the curve apex from either the concave or convex side resulted in significant improvements. The concave approach was associated with more postoperative neurological complications.
Gunay, Osman; Kose, Kivanc; Cetin, A Enis
2011-01-01
In this paper, an Entropy functional based online Adaptive Decision Fusion (EADF) framework is developed for image analysis and computer vision applications. In this framework, it is assumed that the compound algorithm consists of several sub-algorithms each of which yielding its own decision as a real number centered around zero, representing the confidence level of that particular sub-algorithm. Decision values are linearly combined with weights which are updated online according to an active fusion method based on performing entropic projections onto convex sets describing sub-algorithms. It is assumed that there is an oracle, who is usually a human operator, providing feedback to the decision fusion method. A video based wildfire detection system is developed to evaluate the performance of the algorithm in handling the problems where data arrives sequentially. In this case, the oracle is the security guard of the forest lookout tower verifying the decision of the combined algorithm. Simulation results are...
DEFF Research Database (Denmark)
M. Gaspar, Raquel; Murgoci, Agatha
2010-01-01
of particular importance to practitioners: yield convexity adjustments, forward versus futures convexity adjustments, timing and quanto convexity adjustments. We claim that the appropriate way to look into any of these adjustments is as a side effect of a measure change, as proposed by Pelsser (2003...
DEFF Research Database (Denmark)
Lauritzen, Niels
-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point...
Tsirikos, A I; Mataliotakis, G; Bounakis, N
2017-08-01
We present the results of correcting a double or triple curve adolescent idiopathic scoliosis using a convex segmental pedicle screw technique. We reviewed 191 patients with a mean age at surgery of 15 years (11 to 23.3). Pedicle screws were placed at the convexity of each curve. Concave screws were inserted at one or two cephalad levels and two caudal levels. The mean operating time was 183 minutes (132 to 276) and the mean blood loss 0.22% of the total blood volume (0.08% to 0.4%). Multimodal monitoring remained stable throughout the operation. The mean hospital stay was 6.8 days (5 to 15). The mean post-operative follow-up was 5.8 years (2.5 to 9.5). There were no neurological complications, deep wound infection, obvious nonunion or need for revision surgery. Upper thoracic scoliosis was corrected by a mean 68.2% (38% to 48%, p scoliosis was corrected by a mean 71% (43.5% to 8.9%, p scoliosis was corrected by a mean 72.3% (41% to 90%, p Scoliosis Research Society Outcomes Questionnaire score improved from a mean 3.6 to 4.6 (2.4 to 4, p scoliosis, an improved thoracic kyphosis and normal global sagittal balance. Both patient satisfaction and functional outcomes were excellent. Cite this article: Bone Joint J 2017;99-B:1080-7. ©2017 The British Editorial Society of Bone & Joint Surgery.
Nedjar, Sebastien; Cicchetti, Rosine; Lakhal, Lotfi; 10.3166/isi.11.6.11-31
2010-01-01
In various approaches, data cubes are pre-computed in order to answer efficiently OLAP queries. The notion of data cube has been declined in various ways: iceberg cubes, range cubes or differential cubes. In this paper, we introduce the concept of convex cube which captures all the tuples of a datacube satisfying a constraint combination. It can be represented in a very compact way in order to optimize both computation time and required storage space. The convex cube is not an additional structure appended to the list of cube variants but we propose it as a unifying structure that we use to characterize, in a simple, sound and homogeneous way, the other quoted types of cubes. Finally, we introduce the concept of emerging cube which captures the significant trend inversions. characterizations.
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
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
Uniformly convex and strictly convex Orlicz spaces
Masta, Al Azhary
2016-02-01
In this paper we define the new norm of Orlicz spaces on ℝn through a multiplication operator on an old Orlicz spaces. We obtain some necessary and sufficient conditions that the new norm to be a uniformly convex and strictly convex spaces.
Mahaffey, James A
2012-01-01
As energy problems of the world grow, work toward fusion power continues at a greater pace than ever before. The topic of fusion is one that is often met with the most recognition and interest in the nuclear power arena. Written in clear and jargon-free prose, Fusion explores the big bang of creation to the blackout death of worn-out stars. A brief history of fusion research, beginning with the first tentative theories in the early 20th century, is also discussed, as well as the race for fusion power. This brand-new, full-color resource examines the various programs currently being funded or p
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.
Uniformly Convex Metric Spaces
Kell Martin
2014-01-01
In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology called co-convex topology agrees with the usualy weak topology in Banach spaces. An example of a $CAT(0)$-spaces with weak topology which is not Hausdorff is given. This answers questions raised b...
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
Herman, Robin
1990-10-01
The book abounds with fascinating anecdotes about fusion's rocky path: the spurious claim by Argentine dictator Juan Peron in 1951 that his country had built a working fusion reactor, the rush by the United States to drop secrecy and publicize its fusion work as a propaganda offensive after the Russian success with Sputnik; the fortune Penthouse magazine publisher Bob Guccione sank into an unconventional fusion device, the skepticism that met an assertion by two University of Utah chemists in 1989 that they had created "cold fusion" in a bottle. Aimed at a general audience, the book describes the scientific basis of controlled fusion--the fusing of atomic nuclei, under conditions hotter than the sun, to release energy. Using personal recollections of scientists involved, it traces the history of this little-known international race that began during the Cold War in secret laboratories in the United States, Great Britain and the Soviet Union, and evolved into an astonishingly open collaboration between East and West.
On convexity in complex networks
Marc, Tilen
2016-01-01
Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity. We analyze the expansion of convex subsets of nodes in empirical networks and also convexity of small subgraphs known as graphlets. We demonstrate that convexity is an inherent property of complex networks not present in a random graph. According to our perception of convexity, a convex network is such in which every connected subset of nodes induces a convex subgraph. Especially convex are technological networks and social collaboration graphs, whereas food webs are the only networks studied that are truly non-convex. Many other networks can be divided into a non-convex core surrounded by a convex periphery. We interpret convexity in terms of redundancy of shortest paths in a network and discuss possible applications.
DEFF Research Database (Denmark)
Jacob, Riko
We determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage of the data structure...... is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects the convex hull......, and the tangent queries to determine whether a given point is inside the convex hull. The space usage of the data structure is O(n). We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure....
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 data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects...... the convex hull, and the tangent queries to determine whether a given point is inside the convex hull. We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure....
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...
Hörmander, Lars
1994-01-01
The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed, leading up to Trépreau’s theorem on sufficiency of condition (capital Greek letter Psi) for microlocal solvability in the analytic category. At the beginning of the book, no prerequisites are assumed beyond calculus and linear algebra. Later on, basic facts from distribution theory and functional analysis are needed. In a few places, a more extensive background in differential geometry or pseudodiffer...
Convex Geometry and Stoichiometry
Jer-Chin,
2011-01-01
We demonstrate the benefits of a convex geometric perspective for questions on chemical stoichiometry. We show that the balancing of chemical equations, the use of "mixtures" to explain multiple stoichiometry, and the half-reaction for balancing redox actions all yield nice convex geometric interpretations. We also relate some natural questions on reaction mechanisms with the enumeration of lattice points in polytopes. Lastly, it is known that a given reaction mechanism imposes linear constraints on observed stoichiometries. We consider the inverse question of deducing reaction mechanism consistent with a given set of linear stoichiometric restrictions.
SMOOTHING BY CONVEX QUADRATIC PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Bing-sheng He; Yu-mei Wang
2005-01-01
In this paper, we study the relaxed smoothing problems with general closed convex constraints. It is pointed out that such problems can be converted to a convex quadratic minimization problem for which there are good programs in software libraries.
Global approximation of convex functions
Azagra, D
2011-01-01
We show that for every (not necessarily bounded) open convex subset $U$ of $\\R^n$, every (not necessarily Lipschitz or strongly) convex function $f:U\\to\\R$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded sets to results on uniform approximation on unbounded sets, in such a way that not only convexity and $C^k$ smoothness, but also local Lipschitz constants, minimizers, order, and strict or strong convexity, are preserved. This transfer method is quite general and it can also be used to obtain new results on approximation of convex functions defined on Riemannian manifolds or Banach spaces. We also provide a characterization of the class of convex functions which can be uniformly approximated on $\\R^n$ by strongly convex functions.
Egalitarianism in Convex Fuzzy Games
Brânzei, R.; Dimitrov, D.A.; Tijs, S.H.
2002-01-01
In this paper the egalitarian solution for convex cooperative fuzzy games is introduced.The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game.This adjusted algorithm is also a f
Average Convexity in Communication Situations
Slikker, M.
1998-01-01
In this paper we study inheritance properties of average convexity in communication situations. We show that the underlying graph ensures that the graphrestricted game originating from an average convex game is average convex if and only if every subgraph associated with a component of the underlyin
Efficient Approximation of Convex Recolorings
Moran, Shlomo; Snir, Sagi
2005-01-01
A coloring of a tree is convex if the vertices that pertain to any color induce a connected subtree; a partial coloring (which assigns colors to some of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring of trees arise in areas such as phylogenetics, linguistics, etc. eg, a perfect phylogenetic tree is one in which the states of each character induce a convex coloring of the tree. Research on perfect phylogeny is usually focused on finding a tree so t...
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
Introducing the Adaptive Convex Enveloping
Yu, Sheng
2011-01-01
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an accurate, fast and reliable algorithm for solving convex dynamic programs with multivariate continuous states and actions, called Adaptive Convex Enveloping. This is a short introduction of the core technique created and used in my dissertation, so it is less formal, and misses some parts, such as literature review and reference, compared to a full journal paper.
Convex polytopes and quantum states
Energy Technology Data Exchange (ETDEWEB)
Wilmott, Colin; Kampermann, Hermann; Bruss, Dagmar [Institut fuer Theoretische Physik III, Heinrich-Heine-Universitaet Duesseldorf (Germany)
2010-07-01
A convex polytope is defined as the convex hull of a finite non-empty set of vectors. We present a theorem of Rado (1952) which characterizes the convex hull of the collection of all permutations of a given real d-tuple in terms of the Hardy-Littlewood-Polya spectral order relation prec. We give a necessary and sufficient condition to construct a d-dimensional convex polytope which utilizes Rado's original (d-1)-dimensional characterization, and we describe how the resulting polytope may be placed in a quantum mechanical framework.
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 Optimization without Projection Steps
Jaggi, Martin
2011-01-01
We study the general problem of minimizing a convex function over a compact convex domain. We will investigate a simple iterative approximation algorithm that does not need projection steps in order to stay inside the optimization domain. Instead of a projection step, the linearized problem defined by a current subgradient is solved, which gives a step direction that will naturally stay in the domain. The approach generalizes the sparse greedy algorithm of Clarkson (and the low-rank SDP solver by Hazan) to arbitrary convex domains, and to using subgradients for the case of non-differentiable convex functions. Analogously, we give a convergence proof guaranteeing {\\epsilon}-small duality gap after O(1/{\\epsilon}) iterations. The framework allows us understand the sparsity of approximate solutions for any l1-regularized convex optimization problem, expressed as a function of the approximation quality. We obtain matching upper and lower bounds of {\\Theta}(1/{\\epsilon}) for the sparsity for l1-problems. The same ...
Fabrication of Non-instrumented capsule for DUPIC simulated fuel irradiation test in HANARO
Energy Technology Data Exchange (ETDEWEB)
Kim, B.G.; Kang, Y.H.; Park, S.J.; Shin, Y.T. [Korea Atomic Energy Research Institute, Taejon (Korea)
1999-10-01
In order to develope DUPIC nuclear fuel, the irradiation test for simulated DUPIC fuel was planed using a non-instrumented capsule in HANARO. Because DUPIC fuel is highly radioactive material the non-instrumented capsule for an irradiation test of simulated DUPIC fuel in HANARO was designed to remotely assemble and disassemble in hot cell. And then, according to the design requirements the non-instrumented DUPIC capsule was successfully manufactured. Also, the manufacturing technologies of the non-instrumented capsule for irradiating the nuclear fuel in HANARO were established, and the basic technology for the development of the instrumented capsule technology was accumulated. This report describes the manufacturing of the non-instrumented capsule for simulated DUPIC fuel. And, this report will be based to develope the instrumented capsule, which will be utilized to irradiate the nuclear fuel in HANARO. 26 refs., 4 figs. (Author)
Decision Problems For Convex Languages
Brzozowski, Janusz; Xu, Zhi
2008-01-01
In this paper we examine decision problems associated with various classes of convex languages, studied by Ang and Brzozowski (under the name "continuous languages''). We show that we can decide whether a given language L is prefix-, suffix-, factor-, or subword-convex in polynomial time if L is represented by a DFA, but that the problem is PSPACE-hard if L is represented by an NFA. In the case that a regular language is not convex, we prove tight upper bounds on the length of the shortest words demonstrating this fact, in terms of the number of states of an accepting DFA. Similar results are proved for some subclasses of convex languages: the prefix-, suffix-, factor-, and subword-closed languages, and the prefix-, suffix-, factor-, and subword-free languages.
Covering Numbers for Convex Functions
Guntuboyina, Adityanand
2012-01-01
In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the $\\epsilon$-covering number of $\\C([a, b]^d, B)$, in the $L_p$-metric, $1 \\le p 0$, and $\\C([a,b]^d, B)$ denotes the set of all convex functions on $[a, b]^d$ that are uniformly bounded by $B$. We summarize previously known results on covering numbers for convex functions and also provide alternate proofs of some known results. Our results have direct implications in the study of rates of convergence of empirical minimization procedures as well as optimal convergence rates in the numerous convexity constrained function estimation problems.
Complex Convexity of Orlicz Modular Sequence Spaces
Directory of Open Access Journals (Sweden)
Lili Chen
2016-01-01
Full Text Available The concepts of complex extreme points, complex strongly extreme points, complex strict convexity, and complex midpoint locally uniform convexity in general modular spaces are introduced. Then we prove that, for any Orlicz modular sequence space lΦ,ρ, lΦ,ρ is complex midpoint locally uniformly convex. As a corollary, lΦ,ρ is also complex strictly convex.
Uniformly convex-transitive function spaces
Rambla-Barreno, Fernando; Talponen, Jarno
2009-01-01
We introduce a property of Banach spaces called uniform convex-transitivity, which falls between almost transitivity and convex-transitivity. We will provide examples of uniformly convex-transitive spaces. This property behaves nicely in connection with some Banach-valued function spaces. As a consequence, we obtain new examples of convex-transitive Banach spaces.
On Fuzzy Simplex and Fuzzy Convex Hull
Institute of Scientific and Technical Information of China (English)
Dong QIU; Wei Quan ZHANG
2011-01-01
In this paper,we discuss fuzzy simplex and fuzzy convex hull,and give several representation theorems for fuzzy simplex and fuzzy convex hull.In addition,by giving a new characterization theorem of fuzzy convex hull,we improve some known results about fuzzy convex hull.
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…
Convexity Adjustments for ATS Models
DEFF Research Database (Denmark)
Murgoci, Agatha; Gaspar, Raquel M.
Practitioners are used to value a broad class of exotic interest rate derivatives simply by preforming for what is known as convexity adjustments (or convexity corrections). We start by exploiting the relations between various interest rate models and their connections to measure changes. As a re......Practitioners are used to value a broad class of exotic interest rate derivatives simply by preforming for what is known as convexity adjustments (or convexity corrections). We start by exploiting the relations between various interest rate models and their connections to measure changes....... 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...
Compactly convex sets in linear topological spaces
Banakh, T; Ravsky, O
2012-01-01
A convex subset X of a linear topological space is called compactly convex if there is a continuous compact-valued map $\\Phi:X\\to exp(X)$ such that $[x,y]\\subset\\Phi(x)\\cup \\Phi(y)$ for all $x,y\\in X$. We prove that each convex subset of the plane is compactly convex. On the other hand, the space $R^3$ contains a convex set that is not compactly convex. Each compactly convex subset $X$ of a linear topological space $L$ has locally compact closure $\\bar X$ which is metrizable if and only if each compact subset of $X$ is metrizable.
Powers of Convex-Cyclic Operators
Directory of Open Access Journals (Sweden)
Fernando León-Saavedra
2014-01-01
Full Text Available A bounded operator T on a Banach space X is convex cyclic if there exists a vector x such that the convex hull generated by the orbit Tnxn≥0 is dense in X. In this note we study some questions concerned with convex-cyclic operators. We provide an example of a convex-cyclic operator T such that the power Tn fails to be convex cyclic. Using this result we solve three questions posed by Rezaei (2013.
A class of free locally convex spaces
Sipacheva, O. V.
2003-04-01
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.
The genealogy of convex solids
Domokos, Gabor; Szabó, Timea
2012-01-01
The shape of homogeneous, smooth convex bodies as described by the Euclidean distance from the center of gravity represents a rather restricted class M_C of Morse-Smale functions on S^2. Here we show that even M_C exhibits the complexity known for general Morse-Smale functions on S^2 by exhausting all combinatorial possibilities: every 2-colored quadrangulation of the sphere is isomorphic to a suitably represented Morse-Smale complex associated with a function in M_C (and vice versa). We prove our claim by an inductive algorithm, starting from the path graph P_2 and generating convex bodies corresponding to quadrangulations with increasing number of vertices by performing each combinatorially possible vertex splitting by a convexity- preserving local manipulation of the surface. Since convex bodies carrying Morse-Smale complexes isomorphic to P_2 exist, this algorithm not only proves our claim but also defines a hierarchical order among convex solids and general- izes the known classification scheme in [35], ...
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.
Local Routing in Convex Subdivisions
DEFF Research Database (Denmark)
Bose, Prosenjit; Durocher, Stephane; Mondal, Debajyoti;
2015-01-01
In various wireless networking settings, node locations determine a network’s topology, allowing the network to be modelled by a geometric graph drawn in the plane. Without any additional information, local geometric routing algorithms can guarantee delivery to the target node only in restricted...... classes of geometric graphs, such as triangulations. In order to guarantee delivery on more general classes of geometric graphs (e.g., convex subdivisions or planar subdivisions), previous local geometric routing algorithms required Θ(logn) state bits to be stored and passed with the message. We present...... the first local geometric routing algorithm using only one state bit to guarantee delivery on convex subdivisions and the first local geometric memoryless routing algorithm that guarantees delivery on edge-augmented monotone subdivisions (including all convex subdivisions) when the algorithm has knowledge...
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.)
Institute of Scientific and Technical Information of China (English)
Chuan Qiang CHEN; Bo Wen HU
2013-01-01
We study microscopic spacetime convexity properties of fully nonlinear parabolic partial differential equations.Under certain general structure condition,we establish a constant rank theorem for the spacetime convex solutions of fully nonlinear parabolic equations.At last,we consider the parabolic convexity of solutions to parabolic equations and the convexity of the spacetime second fundamental form of geometric flows.
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...
A Note on Permutationally Convex Games
van Velzen, S.; Hamers, H.J.M.; Norde, H.W.
2005-01-01
In this paper we generalise marginal vectors and permutational convexity.We show that if a game is generalised permutationally convex, then the corresponding generalised marginal vector is a core element.Furthermore we refine the concept of permutational convexity and show that this refinement yield
On Uniform Convexity of Banach Spaces
Institute of Scientific and Technical Information of China (English)
Qing Jin CHENG; Bo WANG; Cui Ling WANG
2011-01-01
This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.
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 expecte
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
Generalized geometrically convex functions and inequalities.
Noor, Muhammad Aslam; Noor, Khalida Inayat; Safdar, Farhat
2017-01-01
In this paper, we introduce and study a new class of generalized functions, called generalized geometrically convex functions. We establish several basic inequalities related to generalized geometrically convex functions. We also derive several new inequalities of the Hermite-Hadamard type for generalized geometrically convex functions. Several special cases are discussed, which can be deduced from our main results.
Firey linear combinations of convex bodies
Institute of Scientific and Technical Information of China (English)
XIONG Ge; XIAO Qi-ming; CHEUNG Wing-Sum
2009-01-01
For convex bodies, the Firey linear combinations were introduced and studied in several papers. In this paper the mean width of the Firey linear combinations of convex bodies is studied, and the lower bound of the mean width of the Firey linear combinations of convex body and its polar body is given.
A noncommutative convexity in C*-bimodules
Directory of Open Access Journals (Sweden)
Mohsen Kian
2017-02-01
Full Text Available Let A and B be C*-algebras. We consider a noncommutative convexity in Hilbert A-B-bimodules, called A-B-convexity, as a generalization of C*-convexity in C*-algebras. We show that if X is a Hilbert A-B-bimodule, then Mn(X is a Hilbert Mn(A-Mn(B-bimodule and apply it to show that the closed unit ball of every Hilbert A-B-bimodule is A-B-convex. Some properties of this kind of convexity and various examples have been given.
Evaluating convex roof entanglement measures.
Tóth, Géza; Moroder, Tobias; Gühne, Otfried
2015-04-24
We show a powerful method to compute entanglement measures based on convex roof constructions. In particular, our method is applicable to measures that, for pure states, can be written as low order polynomials of operator expectation values. We show how to compute the linear entropy of entanglement, the linear entanglement of assistance, and a bound on the dimension of the entanglement for bipartite systems. We discuss how to obtain the convex roof of the three-tangle for three-qubit states. We also show how to calculate the linear entropy of entanglement and the quantum Fisher information based on partial information or device independent information. We demonstrate the usefulness of our method by concrete examples.
Convex Hulls of Algebraic Sets
Gouveia, João
2010-01-01
This article describes a method to compute successive convex approximations of the convex hull of a set of points in R^n that are the solutions to a system of polynomial equations over the reals. The method relies on sums of squares of polynomials and the dual theory of moment matrices. The main feature of the technique is that all computations are done modulo the ideal generated by the polynomials defining the set to the convexified. This work was motivated by questions raised by Lov\\'asz concerning extensions of the theta body of a graph to arbitrary real algebraic varieties, and hence the relaxations described here are called theta bodies. The convexification process can be seen as an incarnation of Lasserre's hierarchy of convex relaxations of a semialgebraic set in R^n. When the defining ideal is real radical the results become especially nice. We provide several examples of the method and discuss convergence issues. Finite convergence, especially after the first step of the method, can be described expl...
The Hydraulic Test Procedure for Non-instrumented Irradiation Test Rig of Annular Fuel
Energy Technology Data Exchange (ETDEWEB)
Kim, Dae Ho; Lee, Kang Hee; Shin, Chang Hwan; Park, Chan Kook
2008-08-15
This report presents the procedure of pressure drop test, vibration test and endurance test for the non-instrumented rig using the irradiation test in HANARO of advanced PWR annular fuel which were designed and fabricated by KAERI. From the out-pile thermal hydraulic tests, confirm the flow rate at the 200 kPa pressure drop and measure the RMS displacement at this time. And the endurance test is confirmed the wear and the integrity of the non-instrumented rig at the 110% design flow rate. This out-pile test perform the Flow-Induced Vibration and Pressure Drop Experimental Tester(FIVPET) facility. The instruments in FIVPET facility was calibrated in KAERI and the pump and the thermocouple were certified by manufacturer.
Use of Convexity in Ostomy Care
Salvadalena, Ginger; Pridham, Sue; Droste, Werner; McNichol, Laurie; Gray, Mikel
2017-01-01
Ostomy skin barriers that incorporate a convexity feature have been available in the marketplace for decades, but limited resources are available to guide clinicians in selection and use of convex products. Given the widespread use of convexity, and the need to provide practical guidelines for appropriate use of pouching systems with convex features, an international consensus panel was convened to provide consensus-based guidance for this aspect of ostomy practice. Panelists were provided with a summary of relevant literature in advance of the meeting; these articles were used to generate and reach consensus on 26 statements during a 1-day meeting. Consensus was achieved when 80% of panelists agreed on a statement using an anonymous electronic response system. The 26 statements provide guidance for convex product characteristics, patient assessment, convexity use, and outcomes. PMID:28002174
CONVEX CLASS OF STARLIKE FUNCTIONS
Gupta, V. P.
1984-01-01
Let ＄S＄ denote the class of functions of the form ＄f(z)=z-￥sum_{n=2}^{￥infty}|a_{n}|z^{n}＄ that are analytic and univalent in the unit disk ＄U＄. Let ＄S(￥alpha, ￥beta)＄ and ＄K(￥alpha, ￥beta)＄ denote the subclasses of ＄S＄ consisting respectively, of starlike and close-to-convex functions of order ＄￥alpha(0￥leqq￥alpha
Finite dimensional convexity and optimization
Florenzano, Monique
2001-01-01
The primary aim of this book is to present notions of convex analysis which constitute the basic underlying structure of argumentation in economic theory and which are common to optimization problems encountered in many applications. The intended readers are graduate students, and specialists of mathematical programming whose research fields are applied mathematics and economics. The text consists of a systematic development in eight chapters, with guided exercises containing sometimes significant and useful additional results. The book is appropriate as a class text, or for self-study.
Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order
Balashov, Maxim V.; Repovš, Dušan,
2011-01-01
We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius.
Various Expressions for Modulus of Random Convexity
Institute of Scientific and Technical Information of China (English)
Xiao Lin ZENG
2013-01-01
We first prove various kinds of expressions for modulus of random convexity by using an Lo(F,R)-valued function's intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals,then establish some basic properties including continuity for modulus of random convexity.In particular,we express the modulus of random convexity of a special random normed module Lo(F,X) derived from a normed space X by the classical modulus of convexity of X.
Institute of Scientific and Technical Information of China (English)
CHENG LIXIN; TENG YANMEI
2005-01-01
This paper presents a type of variational principles for real valued w* lower semicon tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces.
A simple view on convex analysis and its applications
J. Brinkhuis (Jan); V. Tikhomirov
2005-01-01
textabstractOur aim is to give a simple view on the basics and applications of convex analysis. The essential feature of this account is the systematic use of the possibility to associate to each convex object---such as a convex set, a convex function or a convex extremal problem--- a cone, without
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 measur
Efficient Line Searching for Convex Functions
den Boef, E.; den Hertog, D.
2004-01-01
In this paper we propose two new line search methods for convex functions. These new methods exploit the convexity property of the function, contrary to existing methods.The worst method is an improved version of the golden section method.For the second method it is proven that after two evaluations
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 re
Stochastic Dominance: Convexity and Some Efficiency Tests
A.M. Lizyayev (Andrey)
2009-01-01
textabstractThis paper points out the importance of Stochastic Dominance (SD) efficient sets being convex. We review classic convexity and efficient set characterization results on SD efficiency of a given portfolio relative to a diversified set of assets and generalize them in the following
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 ...
1990-01-01
to Convex Bodies, Geometriae Dedicata 2" (1973) 225-248. 10. H. Guggenheimer, "The Analytic Geometry of the Unsymmetric Minkowski Plane," Lecture...Mathematics, Vol. 58, No. 2, 1975. 19. E. Lutwak, "On Cross-Sectional Measures of Polar Reciprocal Convex Bodies," Geometriae Dedicata 5, (1976) 79-80
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 divide...
Swanson, David
2011-01-01
We give elementary proofs of formulas for the area and perimeter of a planar convex body surrounded by a band of uniform thickness. The primary tool is a integral formula for the perimeter of a convex body which describes the perimeter in terms of the projections of the body onto lines in the plane.
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
YOE ITOKAWA; KATSUHIRO SHIOHAMA; BANKTESHWAR TIWARI
2016-10-01
The purpose of the present paper is to investigate the influence of strictly convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss the properties of the group of isometries and the exponential maps on a complete Finsler manifold admitting strictly convex functions.
Energy Technology Data Exchange (ETDEWEB)
Kim, D. H.; Lee, C. B.; Song, K. W. [Korea Atomic Energy Research Institute, Taejeon (Korea)
2002-04-01
This project is preparing to irradiation test of the developed large grain UO{sub 2} fuel pellet in HANARO for pursuit fuel safety and high burn-up in 'Advanced LWR Fuel Technology Development Project' as a part Nuclear Mid and Long-term R and D Program. On the basis test rod is performed the nuclei property and preliminary fuel performance analysis, test rod and non-instrumented capsule are designed and manufactured for irradiation test in HANARO. This non-instrumented irradiation capsule of Advanced PWR Fuel pellet was referred the non-instrumented capsule for an irradiation test of simulated DUPIC fuel in HANARO(DUPIC Rig-001) and 18-element HANARO fuel, was designed to ensure the integrity and the endurance of non-instrumented capsule during the long term(2.5 years) irradiation. To irradiate the UO{sub 2} pellets up to the burn-up 70 MWD/kgU, need the time about 60 months and ensure the integrity of non-instrumented capsule for 30 months until replace the new capsule. This non-instrumented irradiation capsule will be based to develope the non-instrumented capsule for the more long term irradiation in HANARO. 22 refs., 13 figs., 5 tabs. (Author)
Toric geometry of convex quadrilaterals
Legendre, Eveline
2009-01-01
We provide an explicit resolution of the Abreu equation on convex labeled quadrilaterals. This confirms a conjecture of Donaldson in this particular case and implies a complete classification of the explicit toric K\\"ahler-Einstein and toric Sasaki-Einstein metrics constructed in [6,23,14]. As a byproduct, we obtain a wealth of extremal toric (complex) orbi-surfaces, including K\\"ahler-Einstein ones, and show that for a toric orbi-surface with 4 fixed points of the torus action, the vanishing of the Futaki invariant is a necessary and sufficient condition for the existence of K\\"ahler metric with constant scalar curvature. Our results also provide explicit examples of relative K-unstable toric orbi-surfaces that do not admit extremal metrics.
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;
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
The set of all surface tensors of a convex body K (Minkowski tensors derived from the surface area measure of K) determine K up to translation, and hereby, the surface tensors of K contain all information on the shape of K. Here, shape means the equivalence class of all convex bodies...... 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....... 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...
Convex functions, monotone operators and differentiability
Phelps, Robert R
1993-01-01
The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition. Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space. The startlingly simple proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for subdifferentials of convex functions. The exciting new version of the useful Borwein-Preiss smooth variational principle due to Godefroy, Deville and Zizler. The material is accessible to students who have had a course in Functional Analysis; indeed, the first edition has been used in numerous graduate seminars. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational princ...
A Note on Upper Convex Density
Institute of Scientific and Technical Information of China (English)
YIN JIAN-DONG; ZHOU ZUO-LING
2010-01-01
For a self-similar set E satisfying the open set condition,upper convex density is an important concept for the computation of its Hausdorff measure,and it is well known that the set of relative interior points with upper convex density 1has a full Hausdorff measure.But whether the upper convex densities of E at all the relative interior points are equal to 1? In other words,whether there exists a relative interior point of E such that the upper convex density of E at this point is less than 1?In this paper,the authors construct a self-similar set satisfying the open set condition,which has a relative interior point with upper convex density less than 1.Thereby,the above problem is sufficiently answered.
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...
Zachos, Anastasios
2010-01-01
We obtain the plasticity equations for convex quadrilaterals on a complete convex surface with bounded specific curvature and derive a plasticity principle which states that: Given four shortest arcs which meet at the weighted Fermat-Torricelli point P_F and their endpoints form a convex quadrilateral, an increase of the weight that corresponds to a shortest arc causes a decrease to the two weights that correspond to the two neighboring shortest arcs and an increase to the weight that corresponds to the opposite shortest arc. We show a connection between the plasticity of convex quadrilaterals on a complete convex surface with bounded specific curvature with the plasticity of generalized convex quadrilaterals on a manifold which is composed by triangles located on a complete convex surface of bounded specific curvature and triangles located on a two dimensional sphere whose constant Gaussian curvature equals to the infimum or supremum of the specific curvature. Furthermore, we give some cases of geometrizatio...
Energy Technology Data Exchange (ETDEWEB)
Kim, Dae Ho; Bang, Je Geon; Lim, Ik Sung; Kim, Sun Ki; Yang, Yong Sik; Song, Kun Woo; Seo, Chul Gyo; Park, Chan Kook
2008-09-15
This project is preparing to irradiation test of the developed double cooled annular fuel pellet in HANARO for pursuit advanced performance in High Performance Fuel Technology Development as a part Nuclear Mid and Long-term R and D Program. On the basis test rod is performed the nuclei property and preliminary fuel performance analysis, test rod and non-instrumented rig designed and manufactured for irradiation test in HANARO OR hole. This non- instrumented rig was confirmed the compatibility of HANARO and the integrity of rig structure, and satisfied the quality assurance requirements. This non- instrumented rig is adopt to the irradiation test for double cooled annular fuel pellet in HANARO.
The Hydraulic Test Report for Non-instrumented Irradiation Test Rig of DUO-Cooled Annular Pellet
Energy Technology Data Exchange (ETDEWEB)
Kim, Dae Ho; Lee, Kang Hee; Shin, Chang Hwan; Yang, Yong Sik; Kim, Sun Ki; Bang, Je Geon; Song, Kun Woo
2007-08-15
This report presents the results of pressure drop test and vibration test for non-instrumented rig of Advanced PWR DUO-Fuel Annular Pellet which were designed and fabricated by KAERI. From the pressure drop test results, it is noted that the flow velocity across the non-instrumented rig of Advanced PWR DUO-Fuel Annular Pellet corresponding to the pressure drop of 200 kPa is measured to be about 8.30 kg/sec. Vibration frequency results for the non-instrumented rig at the pump spin frequency ranges from 19.0 to 32.0 Hz, RMS(Root Mean Square) displacement for the non-instrumented rig of Advanced PWR DUO-Fuel Annular Pellet is less than 7.25 m, and the maximum displacement is less than 31.27 {mu}m. This test was performed at the FIVPET facility.
Quasi-convex Functions in Carnot Groups
Institute of Scientific and Technical Information of China (English)
Mingbao SUN; Xiaoping YANG
2007-01-01
In this paper, the authors introduce the concept of h-quasiconvex functions on Carnot groups G. It is shown that the notions of h-quasiconvex functions and h-convex sets are equivalent and the L∞ estimates of first derivatives of h-quasiconvex functions are given. For a Carnot group G of step two, it is proved that h-quasiconvex functions are locally bounded from above. Furthermore, the authors obtain that h-convex functions are locally Lipschitz continuous and that an h-convex function is twice differentiable almost everywhere.
On the vertex index of convex bodies
Bezdek, Karoly
2011-01-01
We introduce the vertex index, vein(K), of a given centrally symmetric convex body K, which, in a sense, measures how well K can be inscribed into a convex polytope with small number of vertices. This index is closely connected to the illumination parameter of a body, introduced earlier by the first named author, and, thus, related to the famous conjecture in Convex Geometry about covering of a d-dimensional body by 2^d smaller positively homothetic copies. We provide asymptotically sharp estimates (up to a logarithmic term) of this index in the general case. Also, we provide sharp estimates in dimensions 2 and 3.
Watkins, N. W.; Chau, Y.; Chapman, S. C.
2010-12-01
The idea of describing animal movement by mathematical models based on diffusion and Brownian motion has a long heritage. It has thus been natural to account for those aspects of motion that depart from the Brownian by the use of models incorporating long memory & subdiffusion (“the Joseph effect”) and/or heavy tails & superdiffusion (“the Noah effect”). My own interest in this problem was originally from a geoscience perspective, and was triggered by the need to model time series in space physics where both effects coincide. Subsequently I have been involved in animal foraging studies [e.g. Edwards et al, Nature, 2007]. I will describe some recent work [Watkins et al, PRE, 2009] which studies how fixed-timestep and variable-timestep formulations of anomalous diffusion are related in the presence of heavy tails and long range memory (stable processes versus the CTRW). Quantities for which different scaling relations are predicted between the two approaches are of particular interest, to aid testability. I will also present some of work in progress on the convex hull of anomalously diffusing walkers, inspired by its possible relevance to the idea of home range in biology, and by Randon-Furling et al’s recent analytical results in the Brownian case [PRL, 2009].
Revising incompletely specified convex probabilistic belief bases
CSIR Research Space (South Africa)
Rens, G
2016-04-01
Full Text Available International Workshop on Non-Monotonic Reasoning (NMR), 22-24 April 2016, Cape Town, South Africa Revising Incompletely Specified Convex Probabilistic Belief Bases Gavin Rens CAIR_, University of KwaZulu-Natal, School of Mathematics, Statistics...
Relations between Lipschitz functions and convex functions
Institute of Scientific and Technical Information of China (English)
RUAN Yingbin
2005-01-01
We discuss the relationship between Lipschitz functions and convex functions.By these relations, we give a sufficient condition for the set of points where Lipschitz functions on a Hilbert space is Frechet differentiable to be residual.
Some integral inequalities for logarithmically convex functions
Directory of Open Access Journals (Sweden)
Mevlüt Tunç
2014-07-01
Full Text Available The main aim of the present note is to establish new Hadamard like integral inequalities involving log-convex function. We also prove some Hadamard-type inequalities, and applications to the special means are given.
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.
Linearization functors on real convex sets
Velasco, Mauricio
2012-01-01
We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to efficient computation. These operations are convex analogues of Hom functors, tensor products, symmetric powers, exterior powers and general Schur functors on vector spaces and lead to novel constructions even for polyhedra.
Deformation in locally convex topological linear spaces
Institute of Scientific and Technical Information of China (English)
DING; Yanheng
2004-01-01
We are concerned with a deformation theory in locally convex topological linear spaces. A special "nice" partition of unity is given. This enables us to construct certain vector fields which are locally Lipschitz continuous with respect to the locally convex topology. The existence, uniqueness and continuous dependence of flows associated to the vector fields are established. Deformations related to strongly indefinite functionals are then obtained. Finally, as applications, we prove some abstract critical point theorems.
The convexity radius of a Riemannian manifold
Dibble, James
2014-01-01
The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver's method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius.
Convexity conditions and normal structure of Banach spaces
Saejung, Satit
2008-08-01
We prove that F-convexity, the property dual to P-convexity of Kottman, implies uniform normal structure. Moreover, in the presence of the WORTH property, normal structure follows from a weaker convexity condition than F-convexity. The latter result improves the known fact that every uniformly nonsquare space with the WORTH property has normal structure.
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, respe
A further characteristic of abstract convexity structures on topological spaces
Xiang, Shu-Wen; Xia, Shunyou
2007-11-01
In this paper, we give a characteristic of abstract convexity structures on topological spaces with selection property. We show that if a convexity structure defined on a topological space has the weak selection property then satisfies H0-condition. Moreover, in a compact convex subset of a topological space with convexity structure, the weak selection property implies the fixed point property.
Exact and Approximate Sizes of Convex Datacubes
Nedjar, Sébastien
In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.
Hyperspectral image superresolution: An edge-preserving convex formulation
Simões, Miguel; Almeida, Luis B; Chanussot, Jocelyn
2014-01-01
Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These complementary characteristics have stimulated active research in the inference of images with high spatial and spectral resolutions from HSI-MSI pairs. In this paper, we formulate this data fusion problem as the minimization of a convex objective function containing two data-fitting terms and an edge-preserving regularizer. The data-fitting terms are quadratic and account for blur, different spatial resolutions, and additive noise; the regularizer, a form of vector Total Variation, promotes aligned discontinuities across the reconstructed hyperspectral bands. The optimization described above is rather hard, owing to its non-diagonalizable linear operators, to the non-quadratic and non-smooth nature of the regularizer, and to the very large size of the image to be inferred. We tac...
Optimal convex shapes for concave functionals
Bucur, Dorin; Lamboley, Jimmy
2011-01-01
Motivated by a long-standing conjecture of Polya and Szeg\\"o about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application to isoperimetriclike inequalities. As a byproduct of this approach we also obtain a quantitative version of the Kneser-S\\"uss inequality. Finally, for a large class of functionals involving Dirichlet energies and the surface measure, we perform a local analysis of strictly convex portions of the boundary via second order shape derivatives. This allows in particular to exclude the presence of smooth regions with positive Gauss curvature in an optimal shape for Polya-Szeg\\"o problem.
On the convexity of Relativistic Ideal Magnetohydrodynamics
Ibáñez, José-María; Aloy, Miguel-Ángel; Martí, José-María; Miralles, Juan-Antonio
2015-01-01
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity condition on the magnetic field. The result is expressed in the form of a generalized fundamental derivative written as the sum of two terms. The first one is the generalized fundamental derivative in the case of purely hydrodynamical (relativistic) flow. The second one contains the effects of the magnetic field. The analysis ...
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.
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...... problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models...
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...
Directory of Open Access Journals (Sweden)
Tamás Pardy
2017-06-01
Full Text Available Non-instrumented nucleic acid amplification tests (NINAAT are a novel paradigm in portable molecular diagnostics. They offer the high detection accuracy characteristic of nucleic acid amplification tests (NAAT in a self-contained device, without the need for any external instrumentation. These Point-of-Care tests typically employ a Lab-on-a-Chip for liquid handling functionality, and perform isothermal nucleic acid amplification protocols that require low power but high accuracy temperature control in a single well-defined temperature range. We propose temperature control solutions based on commercially available heating elements capable of meeting these challenges, as well as demonstrate the process by which such elements can be fitted to a NINAAT system. Self-regulated and thermostat-controlled resistive heating elements were evaluated through experimental characterization as well as thermal analysis using the finite element method (FEM. We demonstrate that the proposed solutions can support various NAAT protocols, as well as demonstrate an optimal solution for the loop-mediated isothermal amplification (LAMP protocol. Furthermore, we present an Arduino-compatible open-source thermostat developed for NINAAT applications.
Non-convex onion peeling using a shape hull algorithm
Fadili, Jalal M.; Melkemi, Mahmoud; Elmoataz, Abderrahim
2004-01-01
International audience; The convex onion-peeling of a set of points is the organization of these points into a sequence of interpolating convex polygons. This method is adequate to detect the shape of the “center” of a set of points when this shape is convex. However it reveals inadequate to detect non-convex shapes. Alternatively, we propose an extension of the convex onion-peeling method. It consists in representing a set of points with a sequence of non-convex polylines which are computed ...
Uniform convexity and the splitting problem for selections
Balashov, Maxim V; 10.1016/j.jmaa.2009.06.045
2009-01-01
We continue to investigate cases when the Repov\\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images.
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...
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
problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models...... such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output...
Convex functions and the rolling circle criterion
1995-01-01
Given 0≤R1≤R2≤∞, CVG(R1,R2) denotes the class of normalized convex functions f in the unit disc U, for which ∂f(U) satisfies a Blaschke Rolling Circles Criterion with radii R1 and R2. Necessary and sufficient conditions for R1=R2, growth and distortion theorems for CVG(R1,R2) and rotation theorem for the class of convex functions of bounded type, are found.
A Complete Characterization of the Gap between Convexity and SOS-Convexity
Ahmadi, Amir Ali
2011-01-01
Our first contribution in this paper is to prove that three natural sum of squares (sos) based sufficient conditions for convexity of polynomials via the definition of convexity, its first order characterization, and its second order characterization are equivalent. These three equivalent algebraic conditions, henceforth referred to as sos-convexity, can be checked by semidefinite programming whereas deciding convexity is NP-hard. If we denote the set of convex and sos-convex polynomials in $n$ variables of degree $d$ with $\\tilde{C}_{n,d}$ and $\\tilde{\\Sigma C}_{n,d}$ respectively, then our main contribution is to prove that $\\tilde{C}_{n,d}=\\tilde{\\Sigma C}_{n,d}$ if and only if $n=1$ or $d=2$ or $(n,d)=(2,4)$. We also present a complete characterization for forms (homogeneous polynomials) except for the case $(n,d)=(3,4)$ which is joint work with G. Blekherman and is to be published elsewhere. Our result states that the set $C_{n,d}$ of convex forms in $n$ variables of degree $d$ equals the set $\\Sigma C_{...
Stable anisotropic plasma confinement in magnetic configurations with convex-concave field lines
Tsventoukh, M. M.
2014-02-01
It is shown that a combination of the convex and the concave part of a field line provides a strong stabilizing action against convective (flute-interchange) plasma instability (Tsventoukh 2011 Nucl. Fusion 51 112002). This results in internal peaking of the stable plasma pressure profile that is calculated from the collisionless kinetic stability criterion for any magnetic confinement system with combination of mirrors and cusps. Connection of the convex and concave field line parts results in a reduction of the space charge that drives the unstable E × B motion, as there is an opposite direction of the particle drift in a non-uniform field at convex and concave field lines. The pressure peaking arises at the minimum of the second adiabatic invariant J that takes place at the ‘middle’ of a tandem mirror-cusp transverse cross-section. The position of the minimum in J varies with the particle pitch angle that results in a shift of the peaking position depending on plasma anisotropy. This allows one to improve a stable peaked pressure profile at a convex-concave field by changing the plasma anisotropy over the trap cross-section. Examples of such anisotropic distribution functions are found that give an additional substantial enhancement in the maximal central pressure. Furthermore, the shape of new calculated stable profiles has a wide central plasma layer instead of a narrow peak.
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
Energy Technology Data Exchange (ETDEWEB)
Kim, Dae Ho; Lee, Kang Hee; Shin, Chang Hwan
2008-09-15
This report presents the results of pressure drop test, vibration test and endurance test for the non-instrumented rig using the irradiation test in HANARO of the double cooled annular fuel which were designed and fabricated by KAERI. From the out-pile thermal hydraulic tests, corresponding to the pressure drop of 200 kPa is measured to be about 9.72 kg/sec. Vibration frequency for the non-instrumented rig ranges from 5.0 to 10.7 kg/s. RMS(Root Mean Square) displacement for non-instrumented rig is less than 11.73 m, and the maximum displacement is less than 54.87m. The flow rate for endurance test were 10.5 kg/s, which was 110% of 9.72 kg/s. And the endurance test was carried out for 3 days. The test results found not to the wear and satisfied to the limits of pressure drop, flow rate, vibration and wear in the non-instrumented rig. This test was performed at the FIVPET facility.
Tropicalized Lambda Lengths, Measured Laminations and Convexity
DEFF Research Database (Denmark)
C. Penner, R.
cell decomposition of a surface is discovered in the limit. Finally, the tropical analogue of the convex hull construction in Minkowski space is formulated as an explicit algorithm that serially simplifies a triangulation with respect to a fixed lamination and has its own independent applications....
Some Characterizations of Convex Interval Games
Brânzei, R.; Tijs, S.H.; Alparslan-Gok, S.Z.
2008-01-01
This paper focuses on new characterizations of convex interval games using the notions of exactness and superadditivity. We also relate big boss interval games with concave interval games and obtain characterizations of big boss interval games in terms of exactness and subadditivity.
A generalization of the convex Kakeya problem
Ahn, Heekap
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.
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.
Tropicalized Lambda Lengths, Measured Laminations and Convexity
DEFF Research Database (Denmark)
C. Penner, R.
This work uncovers the tropical analogue for measured laminations of the convex hull construction of decorated Teichmueller theory, namely, it is a study in coordinates of geometric degeneration to a point of Thurston's boundary for Teichmueller space. This may offer a paradigm for the extension...
On fixed points and uniformly convex spaces
Gelander, Tsachik
2008-01-01
The purpose of this note is to present two elementary, but useful, facts concerning actions on uniformly convex spaces. We demonstrate how each of them can be used in an alternative proof of the triviality of the first $L_p$-cohomology of higher rank simple Lie groups, proved in [BFGM].
Dynamic Matchings in Convex Bipartite Graphs
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Georgiadis, Loukas; Hansen, Kristoffer Arnsfelt
2007-01-01
We consider the problem of maintaining a maximum matching in a convex bipartite graph G = (V,E) under a set of update operations which includes insertions and deletions of vertices and edges. It is not hard to show that it is impossible to maintain an explicit representation of a maximum matching...
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.
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...
Estimates for oscillatory integrals with convex phase
Energy Technology Data Exchange (ETDEWEB)
Chakhkiev, M A [Moscow State Social University, Moscow (Russian Federation)
2006-02-28
We consider methods for estimating one-dimensional oscillatory integrals with convex phase and amplitudes of bounded variation or Lipschitz class amplitudes. In particular, we improve the estimate for the Piercey integral with near-caustic parameter values, and also consider estimation methods for n-dimensional oscillatory integrals.
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.
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 bodies of states and maps
Grabowski, Janusz; Ibort, Alberto; Kuś, Marek; Marmo, Giuseppe
2013-10-01
We give a general solution to the question of when the convex hulls of orbits of quantum states on a finite-dimensional Hilbert space under unitary actions of a compact group have a non-empty interior in the surrounding space of all density operators. The same approach can be applied to study convex combinations of quantum channels. The importance of both problems stems from the fact that, usually, only sets with non-vanishing volumes in the embedding spaces of all states or channels are of practical importance. For the group of local transformations on a bipartite system we characterize maximally entangled states by the properties of a convex hull of orbits through them. We also compare two partial characteristics of convex bodies in terms of the largest balls and maximum volume ellipsoids contained in them and show that, in general, they do not coincide. Separable states, mixed-unitary channels and k-entangled states are also considered as examples of our techniques.
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...
Subset Selection by Local Convex Approximation
DEFF Research Database (Denmark)
Øjelund, Henrik; Sadegh, Payman; Madsen, Henrik
1999-01-01
least squares criterion. We propose an optimization technique for the posed probelm based on a modified version of the Newton-Raphson iterations, combined with a backward elimination type algorithm. THe Newton-Raphson modification concerns iterative approximations to the non-convex cost function...
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...
Relations between Lipschitz functions and convex functions
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Zajicek, J., On the differentation of convex functions in finite and infinite dimensional spaces, Czech J. Math.,1979, 29: 340-348.[2]Hu, T. C., Klee, V. L., Larman, D. G., Optimization of globally convex functions, SIAM J. Control Optim., 1989,27: 1026-1047.[3]Cepedello Boiso, M., Approximation of Lipschitz functions by △-convex functions in Banach spaces, Israel J.Math., 1998, 106: 269-284.[4]Asplund, E., Frechet differentiability of convex functions, Acta Math., 1968, 121: 31-47.[5]Johnson, J. A., Lipschitz spaces, Pacific J. Math, 1974, 51: 177-186.[6]Stromberg, T., The operation of infimal convolution, Dissert. Math., (Rozprawy Mat.), 1996, 325: 58.[7]Kadison, R. V., Ringrose, J. R., Fundamentals of the theory of operator algebras, volume Ⅰ: Elementary Theory,Graduate Studies in Math., vol. 15, Amer. Math. Soc., 1997.[8]Phelps, R. R., Convex functions,monotone operators and differentiability, Lect. Notes in Math., vol. 1364,Springer-Verlag, 1977.[9]Lindenstrauss, J., On operators which attain their norm, Israel J. Math., 1963, 1: 139-148.[10]Press, D., Gateaux differentiable functions are somewhere Frechet differentiable, Rend. Circ. Mat. Palermo,1984, 33: 122-133.[11]Press, D., Differentiability of Lipschitz functions on Banach spaces, J. Funct. Anal., 1990, 91:312-345.[12]Lindenstrauss, J., Press, D., On Frechet differentiability of Lipschitz maps between Banach spaces, Annals of Math., 2003, 157: 257-288.[13]Press, D., Gateaux differentiable Lipschitz functions need not be Frechet differentiable on a residual set, Supplemento Rend. Circ. Mat. Palermo, Serie Ⅱ, 1982, 2: 217-222.
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.
On the convexity of N-Chebyshev sets
Borodin, Petr A.
2011-10-01
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\\ge 3 is odd and X is smooth uniformly convex.
The Identification of Convex Function on Riemannian Manifold
Directory of Open Access Journals (Sweden)
Li Zou
2014-01-01
Full Text Available The necessary and sufficient condition of convex function is significant in nonlinear convex programming. This paper presents the identification of convex function on Riemannian manifold by use of Penot generalized directional derivative and the Clarke generalized gradient. This paper also presents a method for judging whether a point is the global minimum point in the inequality constraints. Our objective here is to extend the content and proof the necessary and sufficient condition of convex function to Riemannian manifolds.
ON THE PRODUCT OF GATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
Shen Xisheng; Cheng Lixin
2005-01-01
A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Frechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.
Allometric relationships between traveltime channel networks, convex hulls, and convexity measures
Tay, Lea Tien; Sagar, B. S. Daya; Chuah, Hean Teik
2006-06-01
The channel network (S) is a nonconvex set, while its basin [C(S)] is convex. We remove open-end points of the channel connectivity network iteratively to generate a traveltime sequence of networks (Sn). The convex hulls of these traveltime networks provide an interesting topological quantity, which has not been noted thus far. We compute lengths of shrinking traveltime networks L(Sn) and areas of corresponding convex hulls C(Sn), the ratios of which provide convexity measures CM(Sn) of traveltime networks. A statistically significant scaling relationship is found for a model network in the form L(Sn) ˜ A[C(Sn)]0.57. From the plots of the lengths of these traveltime networks and the areas of their corresponding convex hulls as functions of convexity measures, new power law relations are derived. Such relations for a model network are CM(Sn) ˜ ? and CM(Sn) ˜ ?. In addition to the model study, these relations for networks derived from seven subbasins of Cameron Highlands region of Peninsular Malaysia are provided. Further studies are needed on a large number of channel networks of distinct sizes and topologies to understand the relationships of these new exponents with other scaling exponents that define the scaling structure of river networks.
Reverse convex problems: an approach based on optimality conditions
Directory of Open Access Journals (Sweden)
Ider Tseveendorj
2006-01-01
Full Text Available We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.
On Quasi E-Convex Bilevel Programming Problem
Directory of Open Access Journals (Sweden)
E. A. Youness
2005-01-01
Full Text Available Bilevel programming problems involve two optimization problems where the data of the first one is implicity determined by the solution of the second. This study introduces the notions of E-convexity and quasi E-convexity in bilevel programming problems to generalize quasi convex bilevel programming problems.
Reverse convex problems: an approach based on optimality conditions
Ider Tseveendorj
2006-01-01
We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.
Canu I, Guseva; C, Ducros; S, Ducamp; L, Delabre; S, Audignon-Durand; C, Durand; Y, Iwatsubo; D, Jezewski-Serra; Bihan O, Le; S, Malard; A, Radauceanu; M, Reynier; M, Ricaud; O, Witschger
2015-05-01
The French national epidemiological surveillance program EpiNano aims at surveying mid- and long-term health effects possibly related with occupational exposure to either carbon nanotubes or titanium dioxide nanoparticles (TiO2). EpiNano is limited to workers potentially exposed to these nanomaterials including their aggregates and agglomerates. In order to identify those workers during the in-field industrial hygiene visits, a standardized non-instrumental method is necessary especially for epidemiologists and occupational physicians unfamiliar with nanoparticle and nanomaterial exposure metrology. A working group, Quintet ExpoNano, including national experts in nanomaterial metrology and occupational hygiene reviewed available methods, resources and their practice in order to develop a standardized tool for conducting company industrial hygiene visits and collecting necessary information. This tool, entitled “Onsite technical logbook”, includes 3 parts: company, workplace, and workstation allowing a detailed description of each task, process and exposure surrounding conditions. This logbook is intended to be completed during the company industrial hygiene visit. Each visit is conducted jointly by an industrial hygienist and an epidemiologist of the program and lasts one or two days depending on the company size. When all collected information is computerized using friendly-using software, it is possible to classify workstations with respect to their potential direct and/or indirect exposure. Workers appointed to workstations classified as concerned with exposure are considered as eligible for EpiNano program and invited to participate. Since January 2014, the Onsite technical logbook has been used in ten company visits. The companies visited were mostly involved in research and development. A total of 53 workstations with potential exposure to nanomaterials were pre-selected and observed: 5 with TiO2, 16 with single-walled carbon nanotubes, 27 multiwalled
A Generalization of Uniformly Extremely Convex Banach Spaces
Suyalatu Wulede; Wurichaihu Bai; Wurina Bao
2016-01-01
We discuss a new class of Banach spaces which are the generalization of uniformly extremely convex spaces introduced by Wulede and Ha. We prove that the new class of Banach spaces lies strictly between either the classes of k-uniformly rotund spaces and k-strongly convex spaces or classes of fully k-convex spaces and k-strongly convex spaces and has no inclusive relation with the class of locally k-uniformly convex spaces. We obtain in addition some characterizations and properties of this ne...
Brasco, Lorenzo
2012-01-01
We investigate some basic properties of the {\\it heart} $\\heartsuit(\\mathcal{K})$ of a convex set $\\mathcal{K}.$ It is a subset of $\\mathcal{K},$ whose definition is based on mirror reflections of euclidean space, and is a non-local object. The main motivation of our interest for $\\heartsuit(\\mathcal{K})$ is that this gives an estimate of the location of the hot spot in a convex heat conductor with boundary temperature grounded at zero. Here, we investigate on the relation between $\\heartsuit(\\mathcal{K})$ and the mirror symmetries of $\\mathcal{K};$ we show that $\\heartsuit(\\mathcal{K})$ contains many (geometrically and phisically) relevant points of $\\mathcal{K};$ we prove a simple geometrical lower estimate for the diameter of $\\heartsuit(\\mathcal{K});$ we also prove an upper estimate for the area of $\\heartsuit(\\mathcal{K}),$ when $\\mathcal{K}$ is a triangle.
Coalescence between two convex liquid surfaces
Yang, Fan; Jian, Zhen; Li, Erqiang; Thoroddsen, S. T.
2015-11-01
We study the coalescence of two convex surfaces of the same liquid. One of the convex free surfaces is formed at a circular opening of a closed tank by imposing a negative pressure difference. The other surface is a droplet of larger curvature, which is pendant from a concentric nozzle. The coalescence starts from near-zero velocity, so the configuration can be characterized by two dimensionless numbers: the Ohnesorge number Oh = μ /√{ ργL } and the radius ratio between the two surfaces α =rd /rs . We use high-speed video, PIV and numerical simulations, using the Gerris program, to study the dynamics of the coalescence. Our focus is on the interface shapes, the growth-rate of the neck connecting the two surfaces and the formation of a vortex ring. The growth-rate is compared to earlier models for the coalescence of drops or bubbles.
Convex Modeling of Interactions with Strong Heredity
Haris, Asad; Witten, Daniela; Simon, Noah
2015-01-01
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. PMID:28316461
Convex Arrhenius plots and their interpretation
Truhlar, Donald G.; Kohen, Amnon
2001-01-01
This paper draws attention to selected experiments on enzyme-catalyzed reactions that show convex Arrhenius plots, which are very rare, and points out that Tolman's interpretation of the activation energy places a fundamental model-independent constraint on any detailed explanation of these reactions. The analysis presented here shows that in such systems, the rate coefficient as a function of energy is not just increasing more slowly than expected, it is actually decreasing. This interpretation of the data provides a constraint on proposed microscopic models, i.e., it requires that any successful model of a reaction with a convex Arrhenius plot should be consistent with the microcanonical rate coefficient being a decreasing function of energy. The implications and limitations of this analysis to interpreting enzyme mechanisms are discussed. This model-independent conclusion has broad applicability to all fields of kinetics, and we also draw attention to an analogy with diffusion in metastable fluids and glasses. PMID:11158559
On the convexity of Relativistic Hydrodynamics
Ibáñez, José María; Martí, José María; Miralles, Juan Antonio; 10.1088/0264-9381/30/5/057002
2013-01-01
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr 1989 {\\it Rev. Mod. Phys.} {\\bf 61} 75). The classical limit is recovered.
Coefficient inequalities for starlikeness and convexity
Directory of Open Access Journals (Sweden)
Ali Rosihan M.
2013-06-01
Full Text Available For an analytic function $f(z=z+\\sum_{n=2}^\\infty a_n z^n$ satisfying the inequality $\\sum_{n=2}^\\infty n(n-1|a_n|\\leq \\beta$, sharp bound on $\\beta$ is determined so that $f$ is either starlike or convex of order $\\alpha$. Several other coefficient inequalities related to certain subclasses are also investigated.
When is multidimensional screening a convex program?
Figalli, Alessio; McCann, Robert J
2009-01-01
A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis and that agents can choose only pure strategies, we identify a structural condition on the preference b(x,y) of agent type x for product type y -- and on the principal's costs c(y) -- which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal's problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal's optimum strategy -- and similarly of the strategy maximizing the expected welfare of the agents when the principal's profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under r...
On convex relaxation of graph isomorphism.
Aflalo, Yonathan; Bronstein, Alexander; Kimmel, Ron
2015-03-10
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 n2 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.
Extreme properties of quermassintegrals of convex bodies
Institute of Scientific and Technical Information of China (English)
LENG; Gangsong
2001-01-01
［1］Ball,K.,Shadows of convex bodies,Trans.Amer.Math.Soc.,1991,327:891-901.［2］Lutwak,E.,Mixed projection inequalities,Trans.Amer.Math.Soc.,1985,287:92-106.［3］Bourgain,J.,Lindenstrauss,J.,Projection bodies,Israel Seminar (G.A.F.A) 1986-1987,Lecture Notes in Math.Vol.1317,Berlin-New York:Springer-Verlag,1988,250-269.［4］Chakerian,G.D.,Lutwak,E.,Bodies with similar projections,Trans.Amer.Math.Soc.,1997,349:1811-1820.［5］Schneider,R.,Weil,W.,Zonoids and related topics,Convexity and its Applications (eds.Gruber,P.M.,Wills,J.M.),Basel:Birkhuser,1983,296-316.［6］Schneider,R.,Convex Bodies:the Brunn-Minkowski Theory,Cambridge:Cambridge University Press,1993.［7］Schneider,R.,On the determination of convex bodies by projection and girth functions,Result Math.,1998,33:155-160.［8］Thompson,A.C.,Minkowski Geometry,Cambridge:Cambridge University Press,1996.［9］Petty,C.M.,Projection bodies,in Proceedings,Coll Convexity,Copenhagen,1965,Kbenhavns Univ.Mat.Inst.,1967,234-241.［10］Schneider,R.,Zu einem problem von Shephard über die projectionen konvexer kirper,Math.Z.,1967,101:71-81.［11］Ball,K.,Volume ratios and a reverse isoprimetric inequalitity,J.London Math.Soc.,1991,44(2):351-359.［12］Gardner,R.J.,Intersection bodies and the Busemann-Petty problem,Trans.Amer.Math.Soc.,1994,342:435-445.［13］Gardner,R.J.,A positive answer to the Busemann-petty problem in three dimensions,Annals of Math.,1994,140:435-447.［14］Grinberg,E.L.,Isoperimetric inequalities and identities fork-dimensional cross-sections of convex bodies,Math.Ann.,1991,291:75-86.［15］Goodey,P.,Schneider,R.,Weil,W.,On the determination of convex bodies by projection functions,Bull.London Math.Soc.,1997,29:82-88.［16］Lutwak,E.,Intersection bodies and dual mixed volumes,Adv.Math.,1988,71:232-261.［17］Zhang,G.,Centered bodies and dual mixed volumes,Trans.Amer.Soc.,1994,345:777-801.［18］Zhang,G.,Dual Kinematic formulas,Trans.Amer.Soc.,1999,351:985-995.［19
A Mean Point Based Convex Hull Computation Algorithm
Directory of Open Access Journals (Sweden)
Digvijay Singh
2016-11-01
Full Text Available The optimal solution of a Linear Programming problem (LPP is a basic feasible solution and all basic feasible solutions are extreme or boundary points of a convex region formed by the constraint functions of the LPP. In fact, the feasible solution space is not always a convex set so the verification of extreme points for optimality is quite difficult. In order to cover the non-convex feasible points within a convex set, a convex hull is imagined so that the extreme or boundary points may be checked for evaluation of the optimum solution in the decision-making process. In this article a computer assisted convex hull computation algorithm using the Mean Point and Python code verified results of the designed algorithm are discussed.
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...
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.
Convex and Radially Concave Contoured Distributions
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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.
Width Distributions for Convex Regular Polyhedra
Finch, Steven R
2011-01-01
The mean width is a measure on three-dimensional convex bodies that enjoys equal status with volume and surface area [Rota]. As the phrase suggests, it is the mean of a probability density f. We verify formulas for mean widths of the regular tetrahedron and the cube. Higher-order moments of f_tetra and f_cube have not been examined until now. Assume that each polyhedron has edges of unit length. We deduce that the mean square width of the regular tetrahedron is 1/3+(3+sqrt(3))/(3*pi) and the mean square width of the cube is 1+4/pi.
Measuring Voting Power in Convex Policy Spaces
Directory of Open Access Journals (Sweden)
Sascha Kurz
2014-03-01
Full Text Available Classical power index analysis considers the individual’s ability to influence the aggregated group decision by changing its own vote, where all decisions and votes are assumed to be binary. In many practical applications we have more options than either “yes” or “no”. Here we generalize three important power indices to continuous convex policy spaces. This allows the analysis of a collection of economic problems like, e.g., tax rates or spending that otherwise would not be covered in binary models.
Trace-Inequalities and Matrix-Convex Functions
Directory of Open Access Journals (Sweden)
Ando Tsuyoshi
2010-01-01
Full Text Available Abstract A real-valued continuous function on an interval gives rise to a map via functional calculus from the convex set of 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: for . A related topic will be also discussed.
Recovery of Sparse Probability Measures via Convex Programming
Pilanci, Mert; El Ghaoui, Laurent; Chandrasekaran, Venkat
2012-01-01
We consider the problem of cardinality penalized optimization of a convex function over the probability simplex with additional convex constraints. The classical ℓ_1 regularizer fails to promote sparsity on the probability simplex since ℓ_1 norm on the probability simplex is trivially constant. We propose a direct relaxation of the minimum cardinality problem and show that it can be efficiently solved using convex programming. As a first application we consider recovering a spa...
Lower Bound for Convex Hull Area and Universal Cover Problems
Khandhawit, Tirasan; Sriswasdi, Sira
2011-01-01
In this paper, we provide a lower bound for an area of the convex hull of points and a rectangle in a plane. We then apply this estimate to establish a lower bound for a universal cover problem. We showed that a convex universal cover for a unit length curve has area at least 0.232239. In addition, we show that a convex universal cover for a unit closed curve has area at least 0.0879873.
Approximation of Convex Bodies by Convex Bodies%凸体间的逼近
Institute of Scientific and Technical Information of China (English)
国起; Sten Kaijser
2003-01-01
For the affine distance d(C,D)between two convex bodies C,D(∈)Rn,which reduces to the Banach-Mazur distance for symmetric convex bodies, the bounds of d(C,D)have been studied for many years. Some well known estimates for the upper-bounds are as follows: F. John proved d(C,D)≤n1/2 if one is an ellipsoid and another is symmetric,d(C,D)≤n if both are symmetric, and fromF. John's result and d(C1,C2)≤d(C1,C3)d(C2,C3) one has d(C,D)≤n2 for general convex bodies;M.Lassak proved d(C,D)≤(2n-1) if one of them is symmetric.In this paper we get an estimate which includes all the results above as special cases and refines some of them in terms of measures of asymmetry for convex bodies.
Error bound results for convex inequality systems via conjugate duality
Bot, Radu Ioan
2010-01-01
The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. We deal first of all with systems described via one convex inequality and extend the achieved results, by making use of a celebrated scalarization function, to convex inequality systems expressed by means of a general vector function. We also propose a second approach for guaranteeing the existence of global error bounds of the latter, which meanwhile sharpens the classical result of Robinson.
Long Wave Dynamics along a Convex Bottom
Didenkulova, Ira; Soomere, Tarmo
2008-01-01
Long linear wave transformation in the basin of varying depth is studied for a case of a convex bottom profile in the framework of one-dimensional shallow water equation. The existence of travelling wave solutions in this geometry and the uniqueness of this wave class is established through construction of a 1:1 transformation of the general 1D wave equation to the analogous wave equation with constant coefficients. The general solution of the Cauchy problem consists of two travelling waves propagating in opposite directions. It is found that generally a zone of a weak current is formed between these two waves. Waves are reflected from the coastline so that their profile is inverted with respect to the calm water surface. Long wave runup on a beach with this profile is studied for sine pulse, KdV soliton and N-wave. Shown is that in certain cases the runup height along the convex profile is considerably larger than for beaches with a linear slope. The analysis of wave reflection from the bottom containing a s...
Molecular Graphics of Convex Body Fluids.
Gabriel, Adrian T; Meyer, Timm; Germano, Guido
2008-03-01
Coarse-grained modeling of molecular fluids is often based on nonspherical convex rigid bodies like ellipsoids or spherocylinders representing rodlike or platelike molecules or groups of atoms, with site-site interaction potentials depending both on the distance among the particles and the relative orientation. In this category of potentials, the Gay-Berne family has been studied most extensively. However, conventional molecular graphics programs are not designed to visualize such objects. Usually the basic units are atoms displayed as spheres or as vertices in a graph. Atomic aggregates can be highlighted through an increasing amount of stylized representations, e.g., Richardson ribbon diagrams for the secondary structure of proteins, Connolly molecular surfaces, density maps, etc., but ellipsoids and spherocylinders are generally missing, especially as elementary simulation units. We fill this gap providing and discussing a customized OpenGL-based program for the interactive, rendered representation of large ensembles of convex bodies, useful especially in liquid crystal research. We pay particular attention to the performance issues for typical system sizes in this field. The code is distributed as open source.
DEFF Research Database (Denmark)
Marie Julie Møller, Anaïs; Delaissé, Jean-Marie; Søe, Kent
2017-01-01
suggesting that fusion partners may specifically select each other and that heterogeneity between the partners seems to play a role. Therefore, we set out to directly test the hypothesis that fusion factors have a heterogenic involvement at different stages of nuclearity. Therefore, we have analyzed...... on the nuclearity of fusion partners. While CD47 promotes cell fusions involving mono-nucleated pre-osteoclasts, syncytin-1 promotes fusion of two multi-nucleated osteoclasts, but also reduces the number of fusions between mono-nucleated pre-osteoclasts. Furthermore, CD47 seems to mediate fusion mostly through......Investigations addressing the molecular keys of osteoclast fusion are primarily based on end-point analyses. No matter if investigations are performed in vivo or in vitro the impact of a given factor is predominantly analyzed by counting the number of multi-nucleated cells, the number of nuclei per...
Labarre, Paul; Gerlach, Jay; Wilmoth, Jared; Beddoe, Andrew; Singleton, Jered; Weigl, Bernhard
2010-01-01
We have achieved the first complete, non-instrumented nucleic acid amplification test (NAAT) using a calcium oxide heat source thermally linked to an engineered phase change material. These two components alone maintain a thermal profile suitable for the loop-mediated isothermal amplification assay. Starting with computational fluid dynamics analysis, we identified nominal geometry for the exothermic reaction chamber, phase change material chamber, thermal insulation, and packaging. Using this model, we designed and fabricated an alpha prototype assay platform. We have verified the function of this multi-pathogen-capable platform with both fluorescent and visual turbidity indications using samples spiked with malaria DNA. Both the exothermically heated platform samples and samples heated on a Perkin-Elmer GeneAmp9600 thermocycler were first incubated at 62°C for 45 minutes, then heated to 95°C to terminate enzyme activity, then analyzed. Results from the exothermically heated, non-instrumented platform were comparable to those from the thermocycler. These developments will enable point-of-care diagnostics using accurate NAATs which until now have required a well-equipped laboratory. The aim of this research is to provide pathogen detection with NAAT-level sensitivity in low-resource settings where assays such as immunochromatographic strip tests are successfully used but where there is no access to the infrastructure and logistics required to operate and maintain instrument-based diagnostics.
Linear Minimum variance estimation fusion
Institute of Scientific and Technical Information of China (English)
ZHU Yunmin; LI Xianrong; ZHAO Juan
2004-01-01
This paper shows that a general mulitisensor unbiased linearly weighted estimation fusion essentially is the linear minimum variance (LMV) estimation with linear equality constraint, and the general estimation fusion formula is developed by extending the Gauss-Markov estimation to the random paramem of distributed estimation fusion in the LMV setting.In this setting ,the fused estimator is a weighted sum of local estimatess with a matrix quadratic optimization problem subject to a convex linear equality constraint. Second, we present a unique solution to the above optimization problem, which depends only on the covariance matrixCK. Third, if a priori information, the expectation and covariance, of the estimated quantity is unknown, a necessary and sufficient condition for the above LMV fusion becoming the best unbiased LMV estimation with dnown prior information as the above is presented. We also discuss the generality and usefulness of the LMV fusion formulas developed. Finally, we provied and off-line recursion of Ck for a class of multisensor linear systems with coupled measurement noises.
DEFF Research Database (Denmark)
Bendix, Pól Martin
2015-01-01
At Stanford University, Boxer lab, I worked on membrane fusion of small unilamellar lipid vesicles to flat membranes tethered to glass surfaces. This geometry closely resembles biological systems in which liposomes fuse to plasma membranes. The fusion mechanism was studied using DNA zippering...... between complementary strands linked to the two apposing membranes closely mimicking the zippering mechanism of SNARE fusion complexes....
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.
Finding sets of points without empty convex 6-gons
Overmars, M.H.
2001-01-01
Erdös asked whether every large enough set of points in general position in the plane contains six points that form a convex 6-gon without any points from the set in its interior. In this note we show how a set of 29 points was found that contains no empty convex 6-gon. To this end a fast
Convex bodies in Euclidean and Weil-Petersson geometries
Yamada, Sumio
2011-01-01
On a convex body in a Euclidean space, we introduce a new variational formulation for its Funk metric, a Finsler metric compatible with the tautological Finsler structure of the convex body. We generalize the metric on Teichmuller spaces with the Weil-Petersson distance function. A set of similarities the resulting metric structure shares with Thurston's asymmetric metric is noted.
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 ...
In-vivo Convex Array Vector Flow Imaging
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Brandt, Andreas Hjelm; Nielsen, Michael Bachmann
2014-01-01
In-vivo VFI scans obtained from the abdomen of a human volunteer using a convex array transducers and trans- verse oscillation vector flow imaging (VFI) are presented. A 3 MHz BK Medical 8820e (Herlev, Denmark) 192-element convex array probe is used with the SARUS experimental ultrasound scanner....
Locally uniformly convex norms in Banach spaces and their duals
Haydon, Richard
2006-01-01
It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by C^1 functions.
On a-order-convexity of Fuzzy Syntopogenous Spaces
Institute of Scientific and Technical Information of China (English)
WANG Hong
2007-01-01
In this paper,we combine L-fuzzy syntopogenous structure on X with algebraic structure on X.First,the *-increasing and *-decreasing spaces have been studied.Second,we define a-order-convexity on syntopogenous structures (X,S,≤).some important properties of a-order-convexity have been obtained.
Transverse-Mode Control of VCSELs With Convex Mirror
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
We propose the transverse-mode control of vertical-cavity surface-emitting lasers (VCSELs) with a convex mirror. A possibility of improvements on single-mode output power and higher-order mode suppression is presented by optimizing a convex mirror.
Infinitesimal nonrigidity of convex surfaces with planar boundary
Institute of Scientific and Technical Information of China (English)
LI Chunhe; HONG Jiaxing
2005-01-01
In the present paper infinitesimal nonrigidity of a class of convex surfaces with planar boundary is given. This result shows that if the image of the Gauss map of an evolution convex surface with planar boundary covers some hemisphere, this surface may be of infinitesimal nonrigidity for the isometric deformation of planar boundary.
Homotopy Method for Non-convex Programming in Unbonded Set
Institute of Scientific and Technical Information of China (English)
徐庆; 于波
2005-01-01
In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.
(Average-) convexity of common pool and oligopoly TU-games
Driessen, T.S.H.; Meinhardt, H.
2000-01-01
The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the rele
Simple sufficient conditions for starlikeness and convexity for meromorphic functions
Directory of Open Access Journals (Sweden)
Goswami Pranay
2016-01-01
Full Text Available In this paper we investigate some extensions of sufficient conditions for meromorphic multivalent functions in the open unit disk to be meromorphic multivalent starlike and convex of order α. Our results unify and extend some starlikeness and convexity conditions for meromorphic multivalent functions obtained by Xu et al. [2], and some interesting special cases are given.
Fusion rings and fusion ideals
DEFF Research Database (Denmark)
Andersen, Troels Bak
by the so-called fusion ideals. The fusion rings of Wess-Zumino-Witten models have been widely studied and are well understood in terms of precise combinatorial descriptions and explicit generating sets of the fusion ideals. They also appear in another, more general, setting via tilting modules for quantum...
Wu, Yican
2017-01-01
This book provides a systematic and comprehensive introduction to fusion neutronics, covering all key topics from the fundamental theories and methodologies, as well as a wide range of fusion system designs and experiments. It is the first-ever book focusing on the subject of fusion neutronics research. Compared with other nuclear devices such as fission reactors and accelerators, fusion systems are normally characterized by their complex geometry and nuclear physics, which entail new challenges for neutronics such as complicated modeling, deep penetration, low simulation efficiency, multi-physics coupling, etc. The book focuses on the neutronics characteristics of fusion systems and introduces a series of theories and methodologies that were developed to address the challenges of fusion neutronics, and which have since been widely applied all over the world. Further, it introduces readers to neutronics design’s unique principles and procedures, experimental methodologies and technologies for fusion systems...
The inverse moment problem for convex polytopes
Gravin, Nick; Pasechnik, Dmitrii; Robins, Sinai
2011-01-01
The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.
Convex functions, monotone operators and differentiability
Phelps, Robert R
1989-01-01
These notes start with an introduction to the differentiability of convex functions on Banach spaces, leading to the study of Asplund spaces and their intriguing relationship to monotone operators (and more general set-values maps) and Banach spaces with the Radon-Nikodym property. While much of this is classical, some of it is presented using streamlined proofs which were not available until recently. Considerable attention is paid to contemporary results on variational principles and perturbed optimization in Banach spaces, exhibiting their close connections with Asplund spaces. An introductory course in functional analysis is adequate background for reading these notes which can serve as the basis for a seminar of a one-term graduate course. There are numerous excercises, many of which form an integral part of the exposition.
non-Lipschitzian mappings without convexity
Directory of Open Access Journals (Sweden)
G. Li
1999-01-01
real Hilbert space H, and ℑ={Tt:t∈G} a representation of G as asymptotically nonexpansive type mappings of C into itself. Let L(x={z∈H:infs∈Gsupt∈G‖Tts x−z‖=inft∈G‖Tt x−z‖} for each x∈C and L(ℑ=∩x∈C L(x. In this paper, we prove that ∩s∈Gconv¯{Tts x:t∈G}∩L(ℑ is nonempty for each x∈C if and only if there exists a unique nonexpansive retraction P of C into L(ℑ such that PTs=P for all s∈G and P(x∈conv¯{Ts x:s∈G} for every x∈C. Moreover, we prove the ergodic convergence theorem for a semitopological semigroup of non-Lipschitzian mappings without convexity.
DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS
Institute of Scientific and Technical Information of China (English)
Jacek DZIOK; Ravinder Krishna RAINA; Janusz SOK(O)L
2013-01-01
This article presents some new results on the class SLMα of functions that are analytic in the open unit discu ={z:[z[＜ 1} satisfying the conditions that f(0)=0,f'(0)=1,and α (1+ zf"(z)/f'(z)) + (1-α)zf'(z)/f(x) ∈(p)(u)for all z ∈ u,where α is a real number and (p)(z) =1 + τ2z2/ 1-τz-τ2z2 (z ∈ u).The number τ =(1-√5)/2 is such that τ2 =1 + T.The class SLMα introduced by J.Dziok,R.K.Raina,and J.Sokól [3,Appl.Math.Comput.218 (2011),996-1002] is closely related to the classes of starlike and convex functions.The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.
Quantification of small, convex particles by TEM
Energy Technology Data Exchange (ETDEWEB)
Andersen, Sigmund J. [SINTEF Materials and Chemistry, Department of Synthesis and Properties, Material Physics, NO-7465 Trondheim (Norway)], E-mail: sigmund.j.andersen@sintef.no; Holme, Borge [SINTEF Materials and Chemistry, P.O. Box 124, Blindern, NO-0314 Oslo (Norway); Marioara, Calin D. [SINTEF Materials and Chemistry, Department of Synthesis and Properties, Material Physics, NO-7465 Trondheim (Norway)
2008-07-15
It is shown how size distributions of arbitrarily oriented, convex, non-overlapping particles extracted from conventional transmission electron microscopy (TEM) images may be determined by a variation of the Schwartz-Saltykov method. In TEM, particles cut at the surfaces have diminished projections, which alter the observed size distribution. We represent this distribution as a vector and multiply it with the inverse of a matrix comprising thickness-dependent Scheil or Schwartz-Saltykov terms. The result is a corrected size distribution of the projections of uncut particles. It is shown how the real (3D) distribution may be estimated when particle shape is considered. Computer code to generate the matrix is given. A log-normal distribution of spheres and a real distribution of pill-box-shaped dispersoids in an Al-Mg-Si alloy are given as examples. The errors are discussed in detail.
Weighted composition operators and locally convex algebras
Institute of Scientific and Technical Information of China (English)
Edoardo Vesentini
2005-01-01
The Gleason-Kahane-Zelazko theorem characterizes the continuous homomorphism of an associative, locally multiplicatively convex, sequentially complete algebra A into the field C among all linear forms on A. This characterization will be applied along two different directions. In the case in which A is a commutative Banach algebra, the theorem yields the representation of some classes of continuous linear maps A: A → A as weighted composition operators, or as composition operators when A is a continuous algebra endomorphism. The theorem will then be applied to explore the behaviour of continuous linear forms on quasi-regular elements, when A is either the algebra of all Hilbert-Schmidt operators or a Hilbert algebra.
The problem of convexity of Chebyshev sets
Balaganskii, V. S.; Vlasov, L. P.
1996-12-01
Contents Introduction §1. Definitions and notation §2. Reference theorems §3. Some results Chapter I. Characterization of Banach spaces by means of the relations between approximation properties of sets §1. Existence, uniqueness §2. Prom approximate compactness to 'sun'-property §3. From 'sun'-property to approximate compactness §4. Differentiability in the direction of the gradient is sufficient for Fréchet and Gâteaux differentiability §5. Sets with convex complement Chapter II. The structure of Chebyshev and related sets §1. The isolated point method §2. Restrictions of the type \\vert\\overline{W}\\vert Klee (discrete Chebyshev set) §4. A survey of some other results Conclusion Bibliography
Convex Decomposition Based Cluster Labeling Method for Support Vector Clustering
Institute of Scientific and Technical Information of China (English)
Yuan Ping; Ying-Jie Tian; Ya-Jian Zhou; Yi-Xian Yang
2012-01-01
Support vector clustering (SVC) is an important boundary-based clustering algorithm in multiple applications for its capability of handling arbitrary cluster shapes. However,SVC's popularity is degraded by its highly intensive time complexity and poor label performance.To overcome such problems,we present a novel efficient and robust convex decomposition based cluster labeling (CDCL) method based on the topological property of dataset.The CDCL decomposes the implicit cluster into convex hulls and each one is comprised by a subset of support vectors (SVs).According to a robust algorithm applied in the nearest neighboring convex hulls,the adjacency matrix of convex hulls is built up for finding the connected components; and the remaining data points would be assigned the label of the nearest convex hull appropriately.The approach's validation is guaranteed by geometric proofs.Time complexity analysis and comparative experiments suggest that CDCL improves both the efficiency and clustering quality significantly.
ANALYSIS TO NEYMAN-PEARSON CLASSIFICATION WITH CONVEX LOSS FUNCTION
Institute of Scientific and Technical Information of China (English)
Min Han; Dirong Chen; Zhaoxu Sun
2008-01-01
Neyman-Pearson classification has been studied in several articles before.But they all proceeded in the classes of indicator functions with indicator function as the loss function,which make the calculation to be difficult.This paper investigates NeymanPearson classification with convex loss function in the arbitrary class of real measurable functions.A general condition is given under which Neyman-Pearson classification with convex loss function has the same classifier as that with indicator loss function.We give analysis to NP-ERM with convex loss function and prove it's performance guarantees.An example of complexity penalty pair about convex loss function risk in terms of Rademacher averages is studied,which produces a tight PAC bound of the NP-ERM with convex loss function.
Introducing convex layers to the Traveling Salesman Problem
Liew, Sing
2012-01-01
In this paper, we will propose convex layers to the Traveling Salesman Problem (TSP). Firstly, we will focus on human performance on the TSP. Experimental data shows that untrained humans appear to have the ability to perform well in the TSP. On the other hand, experimental data also supports the hypothesis of convex hull i.e. human relies on convex hull to search for the optimal tour for the TSP. Secondly, from the paper published by Bonabeau, Dorigo and Theraulaz, social insect behavior would be able to help in some of the optimizing problems, especially the TSP. Thus, we propose convex layers to the TSP based on the argument that, by the analogy to the social insect behavior, untrained humans' cognition should be able to help in the TSP. Lastly, we will use Tour Improvement algorithms on convex layers to search for an optimal tour for a 13-cities problem to demonstrate the idea.
Efficient protocols for point-convex hull inclusion decision problems
Directory of Open Access Journals (Sweden)
Yun Ye
2010-05-01
Full Text Available Secure Multi-party Computation (SMC is dedicated to solve trust problems in cooperative computing with each participant’s private data. Privacy Preserving Computational Geometry (PPCG is a special area in SMC and being widely researched. In the real world, PPCG theories can be found being used in various occasions such as military cooperation, commercial competitions and so on. Point-convex hull inclusion problem is a practical case in PPCG and has its profound values. This paper firstly investigates the point inclusion problem with static convex hull, and then marches on to the cases of active convex hull, including the parallel moving and rotating ones. To solve the problems above, we propose a secure protocol to determine the relative position of a private point and a private convex hull in the first place. Compared with previous solutions, our protocols perform better in efficiency, especially when the number of the convex hull’s point is large.
Misunderstanding that the Effective Action is Convex under Broken Symmetry
Asanuma, Nobu-Hiko
2016-01-01
The widespread belief that the effective action is convex and has a flat bottom under broken global symmetry is shown to be wrong. We show spontaneous symmetry breaking necessarily accompanies non-convexity in the effective action for quantum field theory, or in the free energy for statistical mechanics, and clarify the magnitude of non-convexity. For quantum field theory, it is also explicitly proved that translational invariance breaks spontaneously when the system is in the non-convex region, and that different vacua of spontaneously broken symmetry cannot be superposed. As applications of non-convexity, we study the first-order phase transition which happens at the zero field limit of spontaneously broken symmetry, and we propose a simple model of phase coexistence which obeys the Born rule.
CPU timing routines for a CONVEX C220 computer system
Bynum, Mary Ann
1989-01-01
The timing routines available on the CONVEX C220 computer system in the Structural Mechanics Division (SMD) at NASA Langley Research Center are examined. The function of the timing routines, the use of the timing routines in sequential, parallel, and vector code, and the interpretation of the results from the timing routines with respect to the CONVEX model of computing are described. The timing routines available on the SMD CONVEX fall into two groups. The first group includes standard timing routines generally available with UNIX 4.3 BSD operating systems, while the second group includes routines unique to the SMD CONVEX. The standard timing routines described in this report are /bin/csh time,/bin/time, etime, and ctime. The routines unique to the SMD CONVEX are getinfo, second, cputime, toc, and a parallel profiling package made up of palprof, palinit, and palsum.
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...
Directory of Open Access Journals (Sweden)
Harry J Witchel
2016-02-01
Full Text Available Background: Estimating engagement levels from postural micromovements has been summarized by some researchers as: increased proximity to the screen is a marker for engagement, while increased postural movement is a signal for disengagement or negative affect. However, these findings are inconclusive: the movement hypothesis challenges other findings of dyadic interaction in humans, and experiments on the positional hypothesis diverge from it.Hypotheses: 1 Under controlled conditions, adding a relevant visual stimulus to an auditory stimulus will preferentially result in Non-Instrumental Movement Inhibition (NIMI of the head. 2 When instrumental movements are eliminated and computer-interaction rate is held constant, for two identically-structured stimuli, cognitive engagement (i.e. interest will result in measurable NIMI of the body generally. Methods: Twenty-seven healthy participants were seated in front of a computer monitor and speakers. Discrete three-minute stimuli were presented with interactions mediated via a handheld trackball without any keyboard, to minimize instrumental movements of the participant's body. Music videos and audio-only music were used to test hypothesis 1. Time-sensitive, highly interactive stimuli were used to test hypothesis 2. Subjective responses were assessed via visual analogue scales. The computer users' movements were quantified using video motion tracking from the lateral aspect. Repeated measures ANOVAs with Tukey post hoc comparisons were performed.Results: For two equivalently-engaging music videos, eliminating the visual content elicited significantly increased non-instrumental movements of the head (while also decreasing subjective engagement; a highly engaging user-selected piece of favorite music led to further increased non-instrumental movement. For two comparable reading tasks, the more engaging reading significantly inhibited (42% movement of the head and thigh; however, when a highly engaging
Goberna, Miguel A.; Jeyakumar, Vaithilingam; Li, Guoyin; Linh, Nguyen
2016-01-01
The radius of robust feasibility of a convex program with uncertain constraints gives a value for the maximal ‘size’ of an uncertainty set under which robust feasibility can be guaranteed. This paper provides an upper bound for the radius for convex programs with uncertain convex polynomial constraints and exact formulas for convex programs with SOS-convex polynomial constraints (or convex quadratic constraints) under affine data uncertainty. These exact formulas allow the radius to be comput...
Decomposability of Abstract and Path-Induced Convexities in Hypergraphs
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Malvestuto Francesco Mario
2015-08-01
Full Text Available An abstract convexity space on a connected hypergraph H with vertex set V (H is a family C of subsets of V (H (to be called the convex sets of H such that: (i C contains the empty set and V (H, (ii C is closed under intersection, and (iii every set in C is connected in H. A convex set X of H is a minimal vertex convex separator of H if there exist two vertices of H that are separated by X and are not separated by any convex set that is a proper subset of X. A nonempty subset X of V (H is a cluster of H if in H every two vertices in X are not separated by any convex set. The cluster hypergraph of H is the hypergraph with vertex set V (H whose edges are the maximal clusters of H. A convexity space on H is called decomposable if it satisfies the following three properties:
Exploiting Symmetry in Integer Convex Optimization using Core Points
Herr, Katrin; Schürmann, Achill
2012-01-01
We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. We define a core point of such a symmetry group as an integral point for which the convex hull of its orbit does not contain integral points other than the orbit points themselves. These core points allow us to decompose symmetric integer convex programming problems. Especially for symmetric integer linear programs we describe two algorithms based on this decomposition. Using a characterization of core points for direct products of symmetric groups, we show that prototype implementations can compete with state-of-the art commercial solvers and solve an open MIPLIB problem.
Properties of distance functions on convex surfaces and Alexandrov spaces
Rataj, Jan
2009-01-01
If $X$ is a convex surface in a Euclidean space, then the squared (intrinsic) distance function $\\dist^2(x,y)$ is d.c. (DC, delta-convex) on $X\\times X$ in the only natural extrinsic sense. For the proof we use semiconcavity (in an intrinsic sense) of $\\dist^2(x,y)$ on $X \\times X$ if $X$ is an Alexandrov space with nonnegative curvature. Applications concerning $r$-boundaries (distance spheres) and the ambiguous locus (exoskeleton) of a closed subset of a convex surface are given.
Plane geometry and convexity of polynomial stability regions
Henrion, Didier
2008-01-01
The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however that quite often for benchmark problem instances, the set of stabilizing controllers seems to be convex. In this note we use elementary techniques from real algebraic geometry (resultants and Bezoutian matrices) to explain this phenomenon. As a byproduct, we derive a convex linear matrix inequality (LMI) formulation of two-parameter fixed-order controller design problem, when possible.
Bubbles, convexity and the Black--Scholes equation
Ekström, Erik; 10.1214/08-AAP579
2009-01-01
A bubble is characterized by the presence of an underlying asset whose discounted price process is a strict local martingale under the pricing measure. In such markets, many standard results from option pricing theory do not hold, and in this paper we address some of these issues. In particular, we derive existence and uniqueness results for the Black--Scholes equation, and we provide convexity theory for option pricing and derive related ordering results with respect to volatility. We show that American options are convexity preserving, whereas European options preserve concavity for general payoffs and convexity only for bounded contracts.
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.
Quadratic growth and stability in convex programming problems
Bonnans, J. Frederic; Ioffe, Alexander D.
1994-01-01
Projet PROMATH; Given a convex program with $C^2$ functions and a convex set $S$ of solutions to the problem, we give a second order condition which guarantees that the problem does not have solutions outside of $S$. This condition is interpreted as a characterization for the quadratic growth of the cost function. The crucial role in the proofs is played by a theorem describing a certain uniform regularity property of critical cones in smooth convex programs. We apply these results to the dis...
A Note on The Convexity of Chebyshev Sets
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Sangeeta
2009-07-01
Full Text Available Perhaps one of the major unsolved problem in Approximation Theoryis: Whether or not every Chebyshev subset of a Hilbert space must be convex. Many partial answers to this problem are available in the literature. R.R. Phelps[Proc. Amer. Math. Soc. 8 (1957, 790-797] showed that a Chebyshev set in an inner product space (or in a strictly convex normed linear space is convex if the associated metric projection is non-expansive. We extend this result to metricspaces.
Global Optimization Approach to Non-convex Problems
Institute of Scientific and Technical Information of China (English)
LU Zi-fang; ZHENG Hui-li
2004-01-01
A new approach to find the global optimal solution of the special non-convex problems is proposed in this paper. The non-convex objective problem is first decomposed into two convex sub-problems. Then a generalized gradient is introduced to determine a search direction and the evolution equation is built to obtain a global minimum point. By the approach, we can prevent the search process from some local minima and search a global minimum point. Two numerical examples are given to prove the approach to be effective.
Prolonging sensor networks lifetime using convex clusters
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Payam Salehi
2013-11-01
Full Text Available Reducing the energy consumption of nodes in sensor networks and prolonging the network life time has been proposed as one of the most important challenges facing researchers in the field of sensor networks. Therefore, designing an energy-aware protocol to gather data from network level and transmitting it to sink is placed on the agenda at this paper. After presenting an analysis of the processes of clustering in sensory networks and investigating the effect of sending interval on the amount of energy consumption, We have shown that if the use of convex static casters be done such as all the communications within the cluster with the sending distance less than the optimal threshold, it Will help to increase the lifetime of nodes. also have shown that if we create a virtual backbone between cluster heads to transfer far cluster heads data from sink to sink , will has a significant impact on increasing the network lifetime. For this reason, a detailed discussion on how to determine the size of clusters and partitioning of the network environment to them is presented in Chapter 4.Simulation results show considerable improvement of the proposed algorithm.
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).
Flip to Regular Triangulation and Convex Hull.
Gao, Mingcen; Cao, Thanh-Tung; Tan, Tiow-Seng
2017-02-01
Flip is a simple and local operation to transform one triangulation to another. It makes changes only to some neighboring simplices, without considering any attribute or configuration global in nature to the triangulation. Thanks to this characteristic, several flips can be independently applied to different small, non-overlapping regions of one triangulation. Such operation is favored when designing algorithms for data-parallel, massively multithreaded hardware, such as the GPU. However, most existing flip algorithms are designed to be executed sequentially, and usually need some restrictions on the execution order of flips, making them hard to be adapted to parallel computation. In this paper, we present an in depth study of flip algorithms in low dimensions, with the emphasis on the flexibility of their execution order. In particular, we propose a series of provably correct flip algorithms for regular triangulation and convex hull in 2D and 3D, with implementations for both CPUs and GPUs. Our experiment shows that our GPU implementation for constructing these structures from a given point set achieves up to two orders of magnitude of speedup over other popular single-threaded CPU implementation of existing algorithms.
Convex weighting criteria for speaking rate estimation
Jiao, Yishan; Berisha, Visar; Tu, Ming; Liss, Julie
2015-01-01
Speaking rate estimation directly from the speech waveform is a long-standing problem in speech signal processing. In this paper, we pose the speaking rate estimation problem as that of estimating a temporal density function whose integral over a given interval yields the speaking rate within that interval. In contrast to many existing methods, we avoid the more difficult task of detecting individual phonemes within the speech signal and we avoid heuristics such as thresholding the temporal envelope to estimate the number of vowels. Rather, the proposed method aims to learn an optimal weighting function that can be directly applied to time-frequency features in a speech signal to yield a temporal density function. We propose two convex cost functions for learning the weighting functions and an adaptation strategy to customize the approach to a particular speaker using minimal training. The algorithms are evaluated on the TIMIT corpus, on a dysarthric speech corpus, and on the ICSI Switchboard spontaneous speech corpus. Results show that the proposed methods outperform three competing methods on both healthy and dysarthric speech. In addition, for spontaneous speech rate estimation, the result show a high correlation between the estimated speaking rate and ground truth values. PMID:26167516
Convexity and symmetrization in relativistic theories
Ruggeri, T.
1990-09-01
There is a strong motivation for the desire to have symmetric hyperbolic field equations in thermodynamics, because they guarantee well-posedness of Cauchy problems. A generic quasi-linear first order system of balance laws — in the non-relativistic case — can be shown to be symmetric hyperbolic, if the entropy density is concave with respect to the variables. In relativistic thermodynamics this is not so. This paper shows that there exists a scalar quantity in relativistic thermodynamics whose concavity guarantees a symmetric hyperbolic system. But that quantity — we call it —bar h — is not the entropy, although it is closely related to it. It is formed by contracting the entropy flux vector — ha with a privileged time-like congruencebar ξ _α . It is also shown that the convexity of h plus the requirement that all speeds be smaller than the speed of light c provide symmetric hyperbolic field equations for all choices of the direction of time. At this level of generality the physical meaning of —h is unknown. However, in many circumstances it is equal to the entropy. This is so, of course, in the non-relativistic limit but also in the non-dissipative relativistic fluid and even in relativistic extended thermodynamics for a non-degenerate gas.
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...
Differential subordination for meromorphic multivalent quasi-convex functions
R. W. Ibrahim; M. Darus
2010-01-01
We introduce new classes of meromorphic multivalent quasi-convex functions and find some sufficient differential subordination theorems for such classes in punctured unit disk with applications in fractional calculus.
Differential subordination for meromorphic multivalent quasi-convex functions
Directory of Open Access Journals (Sweden)
R. W. Ibrahim
2010-02-01
Full Text Available We introduce new classes of meromorphic multivalent quasi-convex functions and find some sufficient differential subordination theorems for such classes in punctured unit disk with applications in fractional calculus.
Global optimization over linear constraint non-convex programming problem
Institute of Scientific and Technical Information of China (English)
ZHANG Gui-Jun; WU Ti-Huan; YE Rong; YANG Hai-qing
2005-01-01
A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programmin g problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.
Lipschitz estimates for convex functions with respect to vector fields
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Valentino Magnani
2012-12-01
Full Text Available We present Lipschitz continuity estimates for a class of convex functions with respect to Hörmander vector fields. These results have been recently obtained in collaboration with M. Scienza, [22].
A novel neural network for nonlinear convex programming.
Gao, Xing-Bao
2004-05-01
In this paper, we present a neural network for solving the nonlinear convex programming problem in real time by means of the projection method. The main idea is to convert the convex programming problem into a variational inequality problem. Then a dynamical system and a convex energy function are constructed for resulting variational inequality problem. It is shown that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. Compared with the existing neural networks for solving the nonlinear convex programming problem, the proposed neural network has no Lipschitz condition, no adjustable parameter, and its structure is simple. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.
Entropy and convexity for nonlinear partial differential equations.
Ball, John M; Chen, Gui-Qiang G
2013-12-28
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.
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...
A Convex Optimization Approach to pMRI Reconstruction
Zhang, Cishen
2013-01-01
In parallel magnetic resonance imaging (pMRI) reconstruction without using estimation of coil sensitivity functions, one group of algorithms reconstruct sensitivity encoded images of the coils first followed by the magnitude only image reconstruction, e.g. GRAPPA, and another group of algorithms jointly compute the image and sensitivity functions by regularized optimization which is a non-convex problem with local only solutions. For the magnitude only image reconstruction, this paper derives a reconstruction formulation, which is linear in the magnitude image, and an associated convex hull in the solution space of the formulated equation containing the magnitude of the image. As a result, the magnitude only image reconstruction for pMRI is formulated into a two-step convex optimization problem, which has a globally optimal solution. An algorithm based on split-bregman and nuclear norm regularized optimizations is proposed to implement the two-step convex optimization and its applications to phantom and in-vi...
Two new definitions on convexity and related inequalities
Tunc, Mevlut
2012-01-01
We have made some new definitions using the inequalities of Young' and Nesbitt'. And we have given some features of these new definitions. After, we established new Hadamard type inequalities for convex functions in the Young and Nesbitt sense.
Continuity of Extremal Elements in Uniformly Convex Spaces
Ferguson, Timothy
2013-01-01
In this paper, we study the problem of finding the extremal element for a linear functional over a uniformly convex Banach space. We show that a unique extremal element exists and depends continuously on the linear functional, and vice versa. Using this, we simplify and clarify Ryabykh's proof that for any linear functional on a uniformly convex Bergman space with kernel in a certain Hardy space, the extremal functional belongs to the corresponding Hardy space.
Convex games, clan games, and their marginal games
Branzei , Rodica; Dimitrov, Dinko; Tijs, Stef
2005-01-01
We provide characterizations of convex games and total clan games by using properties of their corresponding marginal games. As it turns out, a cooperative game is convex if and only if all its marginal games are superadditive, and a monotonic game satisfying the veto player property with respect to the members of a coalition C is a total clan game (with clan C) if and only if all its C-based marginal games are subadditive.
Gradient of the Value Function in Parametric Convex Optimization Problems
Baotić, Mato
2016-01-01
We investigate the computation of the gradient of the value function in parametric convex optimization problems. We derive general expression for the gradient of the value function in terms of the cost function, constraints and Lagrange multipliers. In particular, we show that for the strictly convex parametric quadratic program the value function is continuously differentiable at every point in the interior of feasible space for which the Linear Independent Constraint Qualification holds.
Convex Aspherical Surface Testing Using Catadioptric Partial Compensating System
Wang, Jingxian; Hao, Qun; Hu, Yao; Wang, Shaopu; Li, Tengfei; Tian, Yuhan; Li, Lin
2016-01-01
Aspheric optical components are the indispensable part of modern optics systems. With the constant development of aspheric optical fabrication technique, the systems with large aperture convex aspheric optical components are widely used in astronomy and space optics. Thus, the measurement of the figure error of the whole convex aspherical surface with high precision comes to be a challenge in the area of optical surface manufacture, and surface testing method is also very important. This paper presents a new partial compensating system by the combination of a refractive lens and a reflective mirror for testing convex aspherical surface. The refractive lens is used to compensate the aberration of the tested convex asphere partially. The reflective mirror is a spherical mirror which is coaxial to the refractive lens and reflecting the lights reflected by the tested convex asphere back to the convex asphere itself. With the long focal length and large aperture system we can realize a lighter and more compact system than the refractive partial compensating system because the spheric reflective mirror is more easily to realize and can bending the light conveniently.
Ribeiro, Fabiana Silva; Santos, Flávia H
2017-03-01
Studies suggest that musical training enhances spatial-temporal reasoning and leads to greater learning of mathematical concepts. The aim of this prospective study was to verify the efficacy of a Non-Instrumental Musical Training (NIMT) on the Numerical Cognition systems in children with low achievement in math. For this purpose, we examined, with a cluster analysis, whether children with low scores on Numerical Cognition would be grouped in the same cluster at pre and post-NIMT. Participants were primary school children divided into two groups according to their scores on an Arithmetic test. Results with a specialized battery of Numerical Cognition revealed improvements for Cluster 2 (children with low achievement in math) especially for number production capacity compared to normative data. Besides, the number of children with low scores in Numerical Cognition decreased at post-NIMT. These findings suggest that NIMT enhances Numerical Cognition and seems to be a useful tool for rehabilitation of children with low achievement in math. Copyright © 2016 Elsevier Ltd. All rights reserved.
Spectral calibration for convex grating imaging spectrometer
Zhou, Jiankang; Chen, Xinhua; Ji, Yiqun; Chen, Yuheng; Shen, Weimin
2013-12-01
Spectral calibration of imaging spectrometer plays an important role for acquiring target accurate spectrum. There are two spectral calibration types in essence, the wavelength scanning and characteristic line sampling. Only the calibrated pixel is used for the wavelength scanning methods and he spectral response function (SRF) is constructed by the calibrated pixel itself. The different wavelength can be generated by the monochromator. The SRF is constructed by adjacent pixels of the calibrated one for the characteristic line sampling methods. And the pixels are illuminated by the narrow spectrum line and the center wavelength of the spectral line is exactly known. The calibration result comes from scanning method is precise, but it takes much time and data to deal with. The wavelength scanning method cannot be used in field or space environment. The characteristic line sampling method is simple, but the calibration precision is not easy to confirm. The standard spectroscopic lamp is used to calibrate our manufactured convex grating imaging spectrometer which has Offner concentric structure and can supply high resolution and uniform spectral signal. Gaussian fitting algorithm is used to determine the center position and the Full-Width-Half-Maximum（FWHM）of the characteristic spectrum line. The central wavelengths and FWHMs of spectral pixels are calibrated by cubic polynomial fitting. By setting a fitting error thresh hold and abandoning the maximum deviation point, an optimization calculation is achieved. The integrated calibration experiment equipment for spectral calibration is developed to enhance calibration efficiency. The spectral calibration result comes from spectral lamp method are verified by monochromator wavelength scanning calibration technique. The result shows that spectral calibration uncertainty of FWHM and center wavelength are both less than 0.08nm, or 5.2% of spectral FWHM.
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 ℓ1 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.
A convex formulation for hyperspectral image superresolution via subspace-based regularization
Simões, Miguel; Almeida, Luis B; Chanussot, Jocelyn
2014-01-01
Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer,...
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.
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.
Davis, Colin M; Grant, Caroline A; Pearcy, Mark J; Askin, Geoffrey N; Labrom, Robert D; Izatt, Maree T; Adam, Clayton J; Little, J Paige
2017-03-01
Adolescent idiopathic scoliosis is a complex three-dimensional deformity of the spine characterized by deformities in the sagittal, coronal, and axial planes. Spinal fusion using pedicle screw instrumentation is a widely used method for surgical correction in severe (coronal deformity, Cobb angle > 45°) adolescent idiopathic scoliosis curves. Understanding the anatomic difference in the pedicles of patients with adolescent idiopathic scoliosis is essential to reduce the risk of neurovascular or visceral injury through pedicle screw misplacement. To use CT scans (1) to analyze pedicle anatomy in the adolescent thoracic scoliotic spine comparing concave and convex pedicles and (2) to assess the intra- and interobserver reliability of these measurements to provide critical information to spine surgeons regarding size, length, and angle of projection. Between 2007 and 2009, 27 patients with adolescent idiopathic scoliosis underwent thoracoscopic anterior correction surgery by two experienced spinal surgeons. Preoperatively, each patient underwent a CT scan as was their standard of care at that time. Twenty-two patients (mean age, 15.7 years; SD, 2.4 years; range, 11.6-22 years) (mean Cobb angle, 53°; SD, 5.3°; range, 42°-63°) were selected. Inclusion criteria were a clinical diagnosis of adolescent idiopathic scoliosis, female, and Lenke type 1 adolescent idiopathic scoliosis with the major curve confined to the thoracic spine. Using three-dimensional image analysis software, the pedicle width, inner cortical pedicle width, pedicle height, inner cortical pedicle height, pedicle length, chord length, transverse pedicle angle, and sagittal pedicle angles were measured. Randomly selected scans were remeasured by two of the authors and the reproducibility of the measurement definitions was validated through limit of agreement analysis. The concave pedicle widths were smaller compared with the convex pedicle widths at T7, T8, and T9 by 37% (3.44 mm ± 1.16 mm vs 4
Hibbin, Rebecca
2016-01-01
The oral re-telling of traditional tales, modelled by a storyteller and taught to children in school, can be understood as "non-instrumental" practice in speaking and listening that emphasises oral language over the reading and writing of stories. While oral storytelling has significant benefits to children's education and development,…
Energy Technology Data Exchange (ETDEWEB)
Suh, Suk Yong; Sung, Ki Woong; Kang, Joo Sang; Lee, Jong Jik [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1995-02-01
So called `cold fusion phenomena` are not confirmed yet. Excess heat generation is very delicate one. Neutron generation is most reliable results, however, the records are erratic and the same results could not be repeated. So there is no reason to exclude the malfunction of testing instruments. The same arguments arise in recording {sup 4}He, {sup 3}He, {sup 3}H, which are not rich in quantity basically. An experiment where plenty of {sup 4}He were recorded is attached in appendix. The problem is that we are trying to search cold fusion which is permitted by nature or not. The famous tunneling effect in quantum mechanics will answer it, however, the most fusion rate is known to be negligible. The focus of this project is on the theme that how to increase that negligible fusion rate. 6 figs, 4 tabs, 1512 refs. (Author).
... results in predictable healing. Autograft is currently the “gold standard” source of bone for a fusion. The ... pump. With this technique, the patient presses a button that delivers a predetermined amount of narcotic pain ...
The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities
Cain, George L., Jr.; González, Luis
2008-02-01
The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.
Huppertz, Berthold; Gauster, Martin
2011-01-01
The villous trophoblast of the human placenta is the epithelial cover of the fetal chorionic villi floating in maternal blood. This epithelial cover is organized in two distinct layers, the multinucleated syncytiotrophoblast directly facing maternal blood and a second layer of mononucleated cytotrophoblasts. During pregnancy single cytotrophoblasts continuously fuse with the overlying syncytiotrophoblast to preserve this end-differentiated layer until delivery. Syncytial fusion continuously supplies the syncytiotrophoblast with compounds of fusing cytotrophoblasts such as proteins, nucleic acids and lipids as well as organelles. At the same time the input of cytotrophoblastic components is counterbalanced by a continuous release of apoptotic material from the syncytiotrophoblast into maternal blood. Fusion is an essential step in maintaining the syncytiotrophoblast. Trophoblast fusion was shown to be dependant on and regulated by multiple factors such as fusion proteins, proteases and cytoskeletal proteins as well as cytokines, hormones and transcription factors. In this chapter we focus on factors that may be involved in the fusion process of trophoblast directly or that may prepare the cytotrophoblast to fuse.
Cavitation bubbles collapse characteristics behind a convex body
Institute of Scientific and Technical Information of China (English)
李瑶; 许唯临; 张亚磊; 张敬威; 陈春祺; 阿蓉
2013-01-01
Cavitation bubbles behind a convex body were experimentally studied by a high speed camera and a hydrophone synch- ronously. The experiments were conducted in a circulating water tunnel with five various contraction ratios:b=0.497,b=0.6,b=0.697,b=0.751, andb=0.799. The distributions of the cavitation bubble collapse positions behind the five different convex bodies were obtained by combining the images taken by the high speed camera. According to the collapse positions, it was found that no cavitation bubble was collapsed in the region near the wall until the ratio of the water head loss over the convex body height was larger than 20, which can be used to predict if the cavitation damage would occur in the tunnel with orifice energy dissipaters.
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.
RESEARCH ANNOUNCEMENTS Helly Type Problems for Some Special Convex Polygons
Institute of Scientific and Technical Information of China (English)
苑立平; 丁仁
2001-01-01
@@In the combinatorial geometry of convex sets the question of how efficiently a family of convex sets can be pierced by points has led to various problems which may be regarded as extensions of the Helly-type problems. A family of sets is said to be n-pierceable (abbreviated as Пn) if there exists a set of n points such that each member of the family contains at least one of them. A family of sets is said to be Пnk if every subfamily of size k or less is Пn. The famous Helly theorem in combinatorial geometry asserts that for finite families of convex sets in the plane П13 implies П1. In a recent paper by M. Katchalski and D. Nashtir[a] the following conjecture of Griinbaum[2] was mentioned again:
Widths of some classes of convex functions and bodies
Konovalov, V. N.; Maiorov, Vitalii E.
2010-02-01
We consider classes of uniformly bounded convex functions defined on convex compact bodies in \\mathbb{R}^d and satisfying a Lipschitz condition and establish the exact orders of their Kolmogorov, entropy, and pseudo-dimension widths in the L_1-metric. We also introduce the notions of pseudo-dimension and pseudo-dimension widths for classes of sets and determine the exact orders of the entropy and pseudo-dimension widths of some classes of convex bodies in \\mathbb{R}^drelative to the pseudo-metric defined as the d-dimensional Lebesgue volume of the symmetric difference of two sets. We also find the exact orders of the entropy and pseudo-dimension widths of the corresponding classes of characteristic functions in L_p-spaces, 1\\le p\\le\\infty.
Convex minorants of random walks and L\\'evy processes
Abramson, Josh; Ross, Nathan; Bravo, Gerónimo Uribe
2011-01-01
This article provides an overview of recent work on descriptions and properties of the convex minorant of random walks and L\\'evy processes which summarize and extend the literature on these subjects. The results surveyed include point process descriptions of the convex minorant of random walks and L\\'evy processes on a fixed finite interval, up to an independent exponential time, and in the infinite horizon case. These descriptions follow from the invariance of these processes under an adequate path transformation. In the case of Brownian motion, we note how further special properties of this process, including time-inversion, imply a sequential description for the convex minorant of the Brownian meander.
Small sets in convex geometry and formal independence over ZFC
Directory of Open Access Journals (Sweden)
Menachem Kojman
2005-01-01
Full Text Available To each closed subset S of a finite-dimensional Euclidean space corresponds a σ-ideal of sets (S which is σ-generated over S by the convex subsets of S. The set-theoretic properties of this ideal hold geometric information about the set. We discuss the relation of reducibility between convexity ideals and the connections between convexity ideals and other types of ideals, such as the ideals which are generated over squares of Polish space by graphs and inverses of graphs of continuous self-maps, or Ramsey ideals, which are generated over Polish spaces by the homogeneous sets with respect to some continuous pair coloring. We also attempt to present to nonspecialists the set-theoretic methods for dealing with formal independence as a means of geometric investigations.
Dose evaluation from multiple detector outputs using convex optimisation.
Hashimoto, Makoto; Iimoto, Takeshi; Kosako, Toshiso
2011-07-01
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.
Entanglement Quantification Made Easy: Polynomial Measures Invariant under Convex Decomposition.
Regula, Bartosz; Adesso, Gerardo
2016-02-19
Quantifying entanglement in composite systems is a fundamental challenge, yet exact results are available in only a few special cases. This is because hard optimization problems are routinely involved, such as finding the convex decomposition of a mixed state with the minimal average pure-state entanglement, the so-called convex roof. We show that under certain conditions such a problem becomes trivial. Precisely, we prove by a geometric argument that polynomial entanglement measures of degree 2 are independent of the choice of pure-state decomposition of a mixed state, when the latter has only one pure unentangled state in its range. This allows for the analytical evaluation of convex roof extended entanglement measures in classes of rank-2 states obeying such a condition. We give explicit examples for the square root of the three-tangle in three-qubit states, and we show that several representative classes of four-qubit pure states have marginals that enjoy this property.
Polyominoes with nearly convex columns: A model with semidirected blocks
Feretic, Svjetlan
2009-01-01
In most of today's exactly solved classes of polyominoes, either all members are convex (in some way), or all members are directed, or both. If the class is neither convex nor directed, the exact solution uses to be elusive. This paper is focused on polyominoes with hexagonal cells. Concretely, we deal with polyominoes whose columns can have either one or two connected components. Those polyominoes (unlike the well-explored column-convex polyominoes) cannot be exactly enumerated by any of the now existing methods. It is therefore appropriate to introduce additional restrictions, thus obtaining solvable subclasses. In our recent paper, published in this same journal, the restrictions just mentioned were semidirectedness and an upper bound on the size of the gap within a column. In this paper, the semidirectedness requirement is made looser. The result is that now the exactly solved subclasses are larger and have greater growth constants. These new polyomino families also have the advantage of being invariant u...
Skala, Vaclav
2016-06-01
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees, octrees, kd-trees, bounding volume hierarchies etc. However in some applications a non-orthogonal space subdivision can offer new ways for actual speed up. In the case of convex polygon in E2 a simple Point-in-Polygon test is of the O(N) complexity and the optimal algorithm is of O(log N) computational complexity. In the E3 case, the complexity is O(N) even for the convex polyhedron as no ordering is defined. New Point-in-Convex Polygon and Point-in-Convex Polyhedron algorithms are presented based on space subdivision in the preprocessing stage resulting to O(1) run-time complexity. The presented approach is simple to implement. Due to the principle of duality, dual problems, e.g. line-convex polygon, line clipping, can be solved in a similarly.
AN EFFICIENT ALGORITHM FOR THE CONVEX HULL OF PLANAR SCATTERED POINT SET
Directory of Open Access Journals (Sweden)
Z. Fu
2012-07-01
Full Text Available Computing the convex hull of a point set is requirement in the GIS applications. This paper studies on the problem of minimum convex hull and presents an improved algorithm for the minimum convex hull of planar scattered point set. It adopts approach that dividing the point set into several sub regions to get an initial convex hull boundary firstly. Then the points on the boundary, which cannot be vertices of the minimum convex hull, are removed one by one. Finally the concave points on the boundary, which cannot be vertices of the minimum convex hull, are withdrew. Experimental analysis shows the efficiency of the algorithm compared with other methods.
Nonparametric estimation of a convex bathtub-shaped hazard function.
Jankowski, Hanna K; Wellner, Jon A
2009-11-01
In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of n(2/5) at points x(0) where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. One notable feature of the nonparametric MLE studied here is that no arbitrary choice of tuning parameter (or complicated data-adaptive selection of the tuning parameter) is required.
Convex Four Body Central Configurations with Some Equal Masses
Perez-Chavela, Ernest
2009-01-01
We prove that there is a unique convex non-collinear central configuration of the planar Newtonian four-body problem when two equal masses are located at opposite vertices of a quadrilateral and, at most, only one of the remaining masses is larger than the equal masses. Such central configuration posses a symmetry line and it is a kite shaped quadrilateral. We also show that there is exactly one convex non-collinear central configuration when the opposite masses are equal. Such central configuration also posses a symmetry line and it is a rhombus.
A working-set framework for sequential convex approximation methods
DEFF Research Database (Denmark)
Stolpe, Mathias
2008-01-01
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.......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...
Finding Convex Hulls Using Quickhull on the GPU
Tzeng, Stanley
2012-01-01
We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of problems. Our framework transforms the recursive splitting step into a permutation step that is well-suited for graphics hardware. Our convex hull algorithm of choice is Quickhull. Our parallel Quickhull implementation (for both 2D and 3D cases) achieves an order of magnitude speedup over standard computational geometry libraries.
Convexity and the "Pythagorean" metric of space(-time)
Kalogeropoulos, Nikos
2016-01-01
We address the question about the reasons why the "Wick-rotated", positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces providing the kinematic framework for the statistical or quantum treatments of gravity. We rely on particular moduli of convexity and smoothness which are extremized by Hilbert spaces. In the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a functional integral approach. The "Pythagorean" metric of space(-time) is then induced by such Hilbert spaces.
Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2013-08-01
In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π.
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...... statistical distributions - a Gaussian, a Laplacian, and a two-sided Gamma - to effectively model captured speech. This scheme shows increased ability to adapt to dynamic acoustic environments. The contribution of each distribution to this convex combination is automatically adjusted based on the statistical...
Nonparametric Least Squares Estimation of a Multivariate Convex Regression Function
Seijo, Emilio
2010-01-01
This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. Mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided. We also consider a regression function which is known to be convex and componentwise nonincreasing and discuss the characterization, computation and consistency of its least squares estimator.
Closedness type regularity conditions in convex optimization and beyond
Directory of Open Access Journals (Sweden)
Sorin-Mihai Grad
2016-09-01
Full Text Available The closedness type regularity conditions have proven during the last decade to be viable alternatives to their more restrictive interiority type counterparts, in both convex optimization and different areas where it was successfully applied. In this review article we de- and reconstruct some closedness type regularity conditions formulated by means of epigraphs and subdifferentials, respectively, for general optimization problems in order to stress that they arise naturally when dealing with such problems. The results are then specialized for constrained and unconstrained convex optimization problems. We also hint towards other classes of optimization problems where closedness type regularity conditions were successfully employed and discuss other possible applications of them.
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....
DEFF Research Database (Denmark)
Sørensen, Jakob Balslev; Milosevic, Ira
2015-01-01
the vesicular SNARE VAMP2/synaptobrevin-2 and the target (plasma membrane) SNAREs SNAP25 and syntaxin-1 results in fusion and release of neurotransmitter, synchronized to the electrical activity of the cell by calcium influx and binding to synaptotagmin. Formation of the SNARE complex is tightly regulated...... and appears to start with syntaxin-1 bound to an SM (Sec1/Munc18-like) protein. Proteins of the Munc13-family are responsible for opening up syntaxin and allowing sequential binding of SNAP-25 and VAMP2/synaptobrevin-2. N- to C-terminal “zippering” of the SNARE domains leads to membrane fusion...
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We consider the problem of minimizing a convex separable logarithmic function over a region defined by a convex inequality constraint or linear equality constraint, and two-sided bounds on the variables (box constraints. Such problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems as well as in various practical problems such as problems of production planning and scheduling, allocation of resources, decision making, facility location problems, and so forth. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.
A capacity scaling algorithm for convex cost submodular flows
Energy Technology Data Exchange (ETDEWEB)
Iwata, Satoru [Kyoto Univ. (Japan)
1996-12-31
This paper presents a scaling scheme for submodular functions. A small but strictly submodular function is added before scaling so that the resulting functions should be submodular. This scaling scheme leads to a weakly polynomial algorithm to solve minimum cost integral submodular flow problems with separable convex cost functions, provided that an oracle for exchange capacities are available.
Bounds for Minkowski Billiard Trajectories in Convex Bodies
Artstein-Avidan, Shiri
2011-01-01
In this paper we use the Ekeland-Hofer-Zehnder symplectic capacity to provide several bounds and inequalities for the length of the shortest periodic billiard trajectory in a smooth convex body in ${\\mathbb R}^{n}$. Our results hold both for classical billiards, as well as for the more general case of Minkowski billiards.
Schur convexity for a class of symmetric functions
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The Schur convexity and concavity of a class of symmetric functions are discussed, and an open problem proposed by Guan in "Some properties of a class of symmetric functions" is answered. As consequences, some inequalities are established by use of the theory of majorization.
Method for solving a convex integer programming problem
Stefanov, Stefan M.
2003-01-01
We consider a convex integer program which is a nonlinear version of the assignment problem. This problem is reformulated as an equivalent problem. An algorithm for solving the original problem is suggested which is based on solving the simple assignment problem via some of known algorithms.
The Projection Neural Network for Solving Convex Nonlinear Programming
Yang, Yongqing; Xu, Xianyun
In this paper, a projection neural network for solving convex optimization is investigated. Using Lyapunov stability theory and LaSalle invariance principle, the proposed network is showed to be globally stable and converge to exact optimal solution. Two examples show the effectiveness of the proposed neural network model.
ON A GENERALIZED MODULUS OF CONVEXITY AND UNIFORM NORMAL STRUCTURE
Institute of Scientific and Technical Information of China (English)
Yang Changsen; Wang Fenghui
2007-01-01
In this article, the authors study a generalized modulus of convexity, δ(α)(∈).Certain related geometrical properties of this modulus are analyzed. Their main result is that Banach space X has uniform normal structure if there exists ∈, 0 ≤∈≤1, such that δ(α)(1 + ∈) ＞ (1 - α)∈.
Bounded cohomology with coefficients in uniformly convex Banach spaces
Bestvina, Mladen; Bromberg, Ken; Fujiwara, Koji
2013-01-01
We show that for acylindrically hyperbolic groups $\\Gamma$ (with no nontrivial finite normal subgroups) and arbitrary unitary representation $\\rho$ of $\\Gamma$ in a (nonzero) uniformly convex Banach space the vector space $H^2_b(\\Gamma;\\rho)$ is infinite dimensional. The result was known for the regular representations on $\\ell^p(\\Gamma)$ with $1
Systematization of problems on ball estimates of a convex compactum
Dudov, S. I.
2015-09-01
We consider a class of finite-dimensional problems on the estimation of a convex compactum by a ball of an arbitrary norm in the form of extremal problems whose goal function is expressed via the function of the distance to the farthest point of the compactum and the function of the distance to the nearest point of the compactum or its complement. Special attention is devoted to the problem of estimating (approximating) a convex compactum by a ball of fixed radius in the Hausdorff metric. It is proved that this problem plays the role of the canonical problem: solutions of any problem in the class under consideration can be expressed via solutions of this problem for certain values of the radius. Based on studying and using the properties of solutions of this canonical problem, we obtain ranges of values of the radius in which the canonical problem expresses solutions of the problems on inscribed and circumscribed balls, the problem of uniform estimate by a ball in the Hausdorff metric, the problem of asphericity of a convex body, the problems of spherical shells of the least thickness and of the least volume for the boundary of a convex body. This makes it possible to arrange the problems in increasing order of the corresponding values of the radius. Bibliography: 34 titles.
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.
On a convex combination of solutions to elliptic variational inequalities
Directory of Open Access Journals (Sweden)
Sergiu Aizicovici
2007-02-01
Full Text Available We consider continuous descent methods for the minimization of convex functions defined on a general Banach space. In our previous work we showed that most of them (in the sense of Baire category converged. In the present paper we show that convergent continuous descent methods are stable under small perturbations.
QUASI-EQUILIBRIA IN MARKETS WITH NON-CONVEX PREFERENCES.
An upper bound is placed on social divergence from general equilibrium , due to non-convexity of the traders’ preference relations. Existence and significance of certain quasi-equilibria are investigated. If there is a sufficiently large number of traders in the market, the existence of a configuration arbitrarily close to equilibrium is demonstrated. (Author)
The fundamental formulas for vertices of convex hull
Directory of Open Access Journals (Sweden)
Md. Kazi Salimullah
2013-07-01
Full Text Available This paper represents four formulas for solution of convex hull problem. It aims to analyze how many points are vertices out of total input points, how many vertices lie on a horizontal or vertical lines, position of vertices and number of vertices on lower and higher lines(horizontal or vertical.
Preconditioning 2D Integer Data for Fast Convex Hull Computations.
Directory of Open Access Journals (Sweden)
José Oswaldo Cadenas
Full Text Available In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q ≤ n the algorithm executes in time within O(n; second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q ≤ n holds; the smaller the ratio min(p, q/n is in the dataset, the greater the speedup factor achieved.
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...
A subclass of close-to-convex functions
Directory of Open Access Journals (Sweden)
Zheng- Lv Zhang
2013-03-01
Full Text Available In this paper, we introduce and investigate an interesting subclass $\\mathcal {J}_\\alpha(h$ of analytic and close-to-convex function in the open unit disk D. several coefficient inequalities, growth, and distortion theorem for this class are proved. The various results presented here would generalize many know results.
Parametric R-norm directed-divergence convex function
Garg, Dhanesh; Kumar, Satish
2016-06-01
In this paper, we define parametric R-norm directed-divergence convex function and discuss their special cases and prove some properties similar to Kullback-Leibler information measure. From R-norm divergence measure new information measures have also been derived and their relations with different measures of entropy have been obtained and give its application in industrial engineering.
Visualizing Data as Objects by DC (Difference of Convex) Optimization
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
2017-01-01
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 prob...
Approximation and polynomial convexity in several complex variables
Ölçücüoğlu, Büke; Olcucuoglu, Buke
2009-01-01
This thesis is a survey on selected topics in approximation theory. The topics use either the techniques from the theory of several complex variables or those that arise in the study of the subject. We also go through elementary theory of polynomially convex sets in complex analysis.
Convex relationships in ecosystems containing mixtures of trees and grass
CSIR Research Space (South Africa)
Scholes, RJ
2003-12-01
Full Text Available The relationship between grass production and the quantity of trees in mixed tree-grass ecosystems (savannas) is convex for all or most of its range. In other words, the grass production declines more steeply per unit increase in tree quantity...
Stochastic level-value approximation for quadratic integer convex programming
Institute of Scientific and Technical Information of China (English)
PENG Zheng; WU Dong-hua
2008-01-01
We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and re-port some numerical results to illuminate its effectiveness.
Satisfying states of triangulations of a convex n-gon
Jiménez, Andrea; Loebl, Martin
2009-01-01
In this work we count the number of satisfying states of triangulations of a convex n-gon using the transfer matrix method. We show an exponential (in n) lower bound. We also give the exact formula for the number of satisfying states of a strip of triangles.
The Existence Problem for Steiner Networks in Strictly Convex Domains
Freire, Alexandre
2011-05-01
We consider the existence problem for `Steiner networks' (trivalent graphs with 2 π/3 angles at each junction) in strictly convex domains, with `Neumann' boundary conditions. For each of the three possible combinatorial possibilities, sufficient conditions on the domain are derived for existence. In addition, in each case explicit examples of nonexistence are given.
Preconditioning 2D Integer Data for Fast Convex Hull Computations.
Cadenas, José Oswaldo; Megson, Graham M; Luengo Hendriks, Cris L
2016-01-01
In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.
On Certain Subclass of Meromorphic Close-to-Convex Functions
Directory of Open Access Journals (Sweden)
Goyal S.P.
2013-05-01
Full Text Available In this paper we introduce and investigate a certain subclass of functions which are analytic in the punctured unit disk and meromorphically close-to-convex. The sub-ordination property, inclusion relationship, coefficient inequalities, distortion theorem and a sufficient condition for our subclass of functions are derived. The results presented here would provide extensions of those given in earlier works.
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 a...
Networked and Distributed Convex Optimization for Design, Estimation, and Verification
2009-10-01
IEEE Transactions on Automatic Control . 3...to appear in IEEE Transactions on Automatic Control , October 2009. 7. S. Joshi and S. Boyd, “Subspaces that Minimize the Condition Number of a Matrix...Jitter,” IEEE Transactions on Automatic Control , 54(3):652-657, March 2009. 16. A. Magnani and S. Boyd, “Convex Piecewise-Linear
Greedy vs. L1 convex optimization in sparse coding
DEFF Research Database (Denmark)
Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor;
2015-01-01
, such as face 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...
On the Coefficients Problem of Quasi-convex Mappings and Starlike Mapppings in Cn
Institute of Scientific and Technical Information of China (English)
LIUWei-xian; WANGYu-min
2003-01-01
Let Bn be the unit ball in Cn, we study quasi-convex mappings and starlike mappings on Bn.The upper bounds of second order item coefficients ofr quasi-convex mappings and starlike mappings are obtained.
Some Hermite–Hadamard Type Inequalities for Geometrically Quasi-Convex Functions
Indian Academy of Sciences (India)
Feng Qi; Bo-Yan Xi
2014-08-01
In the paper, we introduce a new concept ‘geometrically quasi-convex function’ and establish some Hermite–Hadamard type inequalities for functions whose derivatives are of geometric quasi-convexity.
Institute of Scientific and Technical Information of China (English)
武希琳; 国起
2011-01-01
Uniform convexity in every direction in locally convex spaces is introduced and several equivalent definitions are given.Every bounded closed convex set in a uniformly convex in every direction space is proved to have a normal structure.%引进了局部凸空间中方向一致凸的概念,给出了相关的几个等价定义,证明了方向一致凸的局部凸空间的任一有界闭凸集具有正规结构。
Construction of convex solutions for the second type of Feigenbaum’s functional equations
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, convex solutions for the second type of Feigenbaum’s equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1-convex solutions and C2-convex solutions of the above equation.
Magnetic fusion; La fusion magnetique
Energy Technology Data Exchange (ETDEWEB)
NONE
2002-07-01
This document is a detailed lecture on thermonuclear fusion. The basic physics principles are recalled and the technological choices that have led to tokamaks or stellarators are exposed. Different aspects concerning thermonuclear reactors such as safety, economy and feasibility are discussed. Tore-supra is described in details as well as the ITER project.
APPROXIMATION OF CONVEX TYPE FUNCTION BY PARTIAL SUMS OF FOURIER SERIES
Institute of Scientific and Technical Information of China (English)
YuGuohua
2004-01-01
The concept of convex type function is introduced in this paper,from which a kind of convex-decomposition approach is proposed. As one of applications of this approach, the approximation of the convex type function by the partial sum of its Fourier series is investigated. Moreover,the order of approximation is described with the 2th continuous modulus.
Ihlow, Dankmar; Kubein-Meesenburg, Dietmar; Hunze, Justus; Dathe, Henning; Planert, Jens; Schwestka-Polly, Rainer; Nägerl, Hans
2002-07-01
Radii for concave-convex vertical stripping instruments can be derived from measurements of the natural curvature morphology in the horizontal contact area of the mandibular dentition. The concave-convex adjustment of contacts in the anterior dental arch with a newly developed set of concave-convex stripping instruments should enable orthodontic crowding problems to be alleviated biomechanically.
Institute of Scientific and Technical Information of China (English)
S.D. Scott
2003-01-01
The first section of this paper covers preliminaries. Essentially, the next four cover units. It is shown that a compatible nearring with DCCR is Nnilpotent if and only if every maximal right N-subgroup is a right ideal. The last five sections relate to fusion (I.e., N-groups minimal for being generated by Nsubgroups, where each is N-isomorphic to a given N-group). Right N-subgroups of a tame nearring N with DCCR, minimal for not annihilating a minimal ideal from the left, are self monogenic and N-isomorphic. That this holds for any collection of minimal ideals is significant. Here, the right N-subgroup involved is a 'fusion product' of the 'components'.
2012-01-01
Carpal fusion may be seen in hereditary and nonhereditary conditions such as acrocallosal syndrome,acromegaly, Apert syndrome, arthrogryposis, Carpenter syndrome, chromosomal abnormalities, ectrodactyly-ectodermal dysplasia-cleft (EEC) syndrome, the F form of acropectorovertebral dysgenesis or the F syndrome, fetal alcohol syndrome, Holt-Oram syndrome, Leopard syndrome, multiple synostosis syndrome, oligosyndactyly syndrome, Pfeiffer-like syndrome, scleroderma, split hand and foot malformatio...
Fusion rules of equivariantizations of fusion categories
2012-01-01
We determine the fusion rules of the equivariantization of a fusion category $\\mathcal{C}$ under the action of a finite group $G$ in terms of the fusion rules of $\\mathcal{C}$ and group-theoretical data associated to the group action. As an application we obtain a formula for the fusion rules in an equivariantization of a pointed fusion category in terms of group-theoretical data. This entails a description of the fusion rules in any braided group-theoretical fusion category.
Fusion rules of equivariantizations of fusion categories
Burciu, Sebastian; Natale, Sonia
2012-01-01
We determine the fusion rules of the equivariantization of a fusion category $\\mathcal{C}$ under the action of a finite group $G$ in terms of the fusion rules of $\\mathcal{C}$ and group-theoretical data associated to the group action. As an application we obtain a formula for the fusion rules in an equivariantization of a pointed fusion category in terms of group-theoretical data. This entails a description of the fusion rules in any braided group-theoretical fusion category.
Convex half-quadratic criteria and interacting auxiliary variables for image restoration.
Idier, J
2001-01-01
This paper deals with convex half-quadratic criteria and associated minimization algorithms for the purpose of image restoration. It brings a number of original elements within a unified mathematical presentation based on convex duality. Firstly, the Geman and Yang's and Geman and Reynolds's constructions are revisited, with a view to establishing the convexity properties of the resulting half-quadratic augmented criteria, when the original nonquadratic criterion is already convex. Secondly, a family of convex Gibbsian energies that incorporate interacting auxiliary variables is revealed as a potentially fruitful extension of the Geman and Reynolds's construction.
On curves contained in convex subsets of the plane
Coppersmith, Don; Ravsky, Alex
2012-01-01
If K' and K are convex bodies of the plane such that K' is a subset of K then the perimeter of K' is not greater than the perimeter of K. We obtain the following generalization of this fact. Let K be a convex compact body of the plane with the perimeter p and the diameter d and r>1 be an integer. Let s be the smallest number such that for any curve of length greater than s contained in K there is a straight line intersecting the curve at least in r+1 different points. Then s=rp/2 if r is even and s=(r-1)p/2+d if r is odd.
Efficiency Loss in a Cournot Oligopoly with Convex Market Demand
Tsitsiklis, John N
2012-01-01
We consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand function is convex. We establish a lower bound on the efficiency of Cournot equilibria in terms of a scalar parameter derived from the inverse demand function, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium to the average slope of the inverse demand function between the Cournot equilibrium and a social optimum. Also, for the case of a single, monopolistic, profit maximizing supplier, or of multiple suppliers who collude to maximize their total profit, we establish a similar but tighter lower bound on the efficiency of the resulting output. Our results provide nontrivial quantitative bounds on the loss of social welfare for several convex inverse demand functions that appear in the economics literature.
Bouncing dynamics of impact droplets on the convex superhydrophobic surfaces
Shen, Yizhou; Liu, Senyun; Zhu, Chunling; Tao, Jie; Chen, Zhong; Tao, Haijun; Pan, Lei; Wang, Guanyu; Wang, Tao
2017-05-01
Bouncing dynamics of impact droplets on solid surfaces intensively appeal to researchers due to the importance in many industrial fields. Here, we found that droplets impacting onto dome convex superhydrophobic surfaces could rapidly bounce off with a 28.5% reduction in the contact time, compared with that on flat superhydrophobic surfaces. This is mainly determined by the retracting process of impact droplets. Under the action of dome convexity, the impact droplet gradually evolves into an annulus shape with a special hydrodynamic distribution. As a consequence, both the inner and external rims of the annulus shape droplet possess a higher retracting velocity under the actions of the inertia force and the surface energy change, respectively. Also, the numerical simulation provides a quantitative evidence to further verify the interpretation on the regimes behind the rapidly detached phenomenon of impact droplets.
Fuzzy Clustering Using the Convex Hull as Geometrical Model
Directory of Open Access Journals (Sweden)
Luca Liparulo
2015-01-01
Full Text Available A new approach to fuzzy clustering is proposed in this paper. It aims to relax some constraints imposed by known algorithms using a generalized geometrical model for clusters that is based on the convex hull computation. A method is also proposed in order to determine suitable membership functions and hence to represent fuzzy clusters based on the adopted geometrical model. The convex hull is not only used at the end of clustering analysis for the geometric data interpretation but also used during the fuzzy data partitioning within an online sequential procedure in order to calculate the membership function. Consequently, a pure fuzzy clustering algorithm is obtained where clusters are fitted to the data distribution by means of the fuzzy membership of patterns to each cluster. The numerical results reported in the paper show the validity and the efficacy of the proposed approach with respect to other well-known clustering algorithms.
Convexity and the Euclidean Metric of Space-Time
Directory of Open Access Journals (Sweden)
Nikolaos Kalogeropoulos
2017-02-01
Full Text Available We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.
Intersection patterns of convex sets via simplicial complexes, a survey
Tancer, Martin
2011-01-01
The task of this survey is to present various results on intersection patterns of convex sets. One of main tools for studying intersection patterns is a point of view via simplicial complexes. We recall the definitions of so called $d$-representable, $d$-collapsible and $d$-Leray simplicial complexes which are very useful for this study. We study the differences among these notions and we also focus on computational complexity for recognizing them. A list of Helly-type theorems is presented in the survey and it is also discussed how (important) role play the above mentioned notions for the theorems. We also consider intersection patterns of good covers which generalize collections of convex sets (the sets may be `curvy'; however, their intersections cannot be too complicated). We mainly focus on new results.
Memoryless Routing in Convex Subdivisions: Random Walks are Optimal
Chen, Dan; Dujmovic, Vida; Morin, Pat
2009-01-01
A memoryless routing algorithm is one in which the decision about the next edge on the route to a vertex t for a packet currently located at vertex v is made based only on the coordinates of v, t, and the neighbourhood, N(v), of v. The current paper explores the limitations of such algorithms by showing that, for any (randomized) memoryless routing algorithm A, there exists a convex subdivision on which A takes Omega(n^2) expected time to route a message between some pair of vertices. Since this lower bound is matched by a random walk, this result implies that the geometric information available in convex subdivisions is not helpful for this class of routing algorithms. The current paper also shows the existence of triangulations for which the Random-Compass algorithm proposed by Bose etal (2002,2004) requires 2^{\\Omega(n)} time to route between some pair of vertices.
On the convex hull of symmetric stable processes
Kampf, Jürgen
2010-01-01
Let alpha \\in (1, 2] and X be an R^d-valued alpha-stable process with independent and symmetric components starting in 0. We consider the closure S_t of the path described by X on the interval [0, t] and its convex hull Z_t. The first result of this paper provides a formula for certain mean mixed volumes of Z_t and in particular for the expected first intrinsic volume of Z_t. The second result deals with the asymptotics of the expected volume of the stable sausage Z_t+B (where B is an arbitrary convex body with interior points) as t \\to 0.
Delivering sound energy along an arbitrary convex trajectory.
Zhao, Sipei; Hu, Yuxiang; Lu, Jing; Qiu, Xiaojun; Cheng, Jianchun; Burnett, Ian
2014-10-15
Accelerating beams have attracted considerable research interest due to their peculiar properties and various applications. Although there have been numerous research on the generation and application of accelerating light beams, few results have been published on the generation of accelerating acoustic beams. Here we report on the experimental observation of accelerating acoustic beams along arbitrary convex trajectories. The desired trajectory is projected to the spatial phase profile on the boundary which is discretized and sampled spatially. The sound field distribution is formulated with the Green function and the integral equation method. Both the paraxial and the non-paraxial regimes are examined and observed in the experiments. The effect of obstacle scattering in the sound field is also investigated and the results demonstrate that the approach is robust against obstacle scattering. The realization of accelerating acoustic beams will have an impact on various applications where acoustic information and energy are required to be delivered along an arbitrary convex trajectory.
Recognition of Graphs with Convex Quadratic Stability Number
Pacheco, Maria F.; Cardoso, Domingos M.
2009-09-01
A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented.
A Unified Fixed Point Theory in Generalized Convex Spaces
Institute of Scientific and Technical Information of China (English)
Sehie PARK
2007-01-01
Let β be the class of 'better' admissible multimaps due to the author.We introduce newconcepts of admissibility (in the sense of Klee) and of Klee approximability for subsets of G-convexuniform spaces and show that any compact closed multimap in β from a G-convex space into itselfwith the Klee approximable range has a fixed point.This new theorem contains a large number ofknown results on topological vector spaces or on various subclasses.of the class of admissible G-convexspaces.Such subclasses are those of C-spaces,sets of the Zima-Hadzic type,locally G-convex spaces,and LG-spaces.Mutual relations among those subclasses and some related results are added.
A Convex Optimization Model and Algorithm for Retinex
Directory of Open Access Journals (Sweden)
Qing-Nan Zhao
2017-01-01
Full Text Available Retinex is a theory on simulating and explaining how human visual system perceives colors under different illumination conditions. The main contribution of this paper is to put forward a new convex optimization model for Retinex. Different from existing methods, the main idea is to rewrite a multiplicative form such that the illumination variable and the reflection variable are decoupled in spatial domain. The resulting objective function involves three terms including the Tikhonov regularization of the illumination component, the total variation regularization of the reciprocal of the reflection component, and the data-fitting term among the input image, the illumination component, and the reciprocal of the reflection component. We develop an alternating direction method of multipliers (ADMM to solve the convex optimization model. Numerical experiments demonstrate the advantages of the proposed model which can decompose an image into the illumination and the reflection components.
The -Curvature Images of Convex Bodies and -Projection Bodies
Indian Academy of Sciences (India)
Songjun Lv; Gangsong Leng
2008-08-01
Associated with the -curvature image defined by Lutwak, some inequalities for extended mixed -affine surface areas of convex bodies and the support functions of -projection bodies are established. As a natural extension of a result due to Lutwak, an -type affine isoperimetric inequality, whose special cases are -Busemann–Petty centroid inequality and -affine projection inequality, respectively, is established. Some -mixed volume inequalities involving -projection bodies are also established.
A toolbox for robust PID controller tuning using convex optimization
Sadeghpour, Mehdi; de Oliveira, Vinicius; Karimi, Alireza
2012-01-01
A robust PID controller design toolbox for Matlab is presented in this paper. The design is based on linearizing or convexifying the conventional non-convex constraints on the classical robustness margins or H∞ constraints. Then the existing optimization solvers can be used to compute the controller parameters. The software can be used in a wide range of controller design problems, including multi-model systems and gain-scheduled controllers. The models can be parametric or non-parametric whi...
A Partial Differential Equation for the Rank One Convex Envelope
Oberman, Adam M.; Ruan, Yuanlong
2017-02-01
A partial differential equation (PDE) for the rank one convex envelope is introduced. The existence and uniqueness of viscosity solutions to the PDE is established. Elliptic finite difference schemes are constructed and convergence of finite difference solutions to the viscosity solution of the PDE is proven. Computational results are presented and laminates are computed from the envelopes. Results include the Kohn-Strang example, the classical four gradient example, and an example with eight gradients which produces nontrivial laminates.
Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces
Kohlenbach, Ulrich; Leuştean, Laurentiu
2007-01-01
This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnoselski-Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed point theory of such mappings.
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
Non-differentiable multiobjective mixed symmetric duality under generalized convexity
Directory of Open Access Journals (Sweden)
Li Jueyou
2011-01-01
Full Text Available Abstract The objective of this paper is to obtain a mixed symmetric dual model for a class of non-differentiable multiobjective nonlinear programming problems where each of the objective functions contains a pair of support functions. Weak, strong and converse duality theorems are established for the model under some suitable assumptions of generalized convexity. Several special cases are also obtained. MS Classification: 90C32; 90C46.
Design and Implementation of Convex Analysis of Mixtures Software Suite
Meng, Fan
2012-01-01
Various convex analysis of mixtures (CAM) based algorithms have been developed to address real world blind source separation (BSS) problems and proven to have good performances in previous papers. This thesis reported the implementation of a comprehensive software CAM-Java, which contains three different CAM based algorithms, CAM compartment modeling (CAM-CM), CAM non-negative independent component analysis (CAM-nICA), and CAM non-negative well-grounded component analysis (CAM-nWCA). The imp...
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.
Institute of Scientific and Technical Information of China (English)
Caroline; 黄颖（翻译）
2009-01-01
“Fusion World”科技展示体验中心是英国设计公司MET Studio为新加坡科技研究局（A＊Star）的科学工程委员会（SERC）所设计的,位于启汇城的办公地点，用于展示该委员会的精选技术作品，以吸引潜在的客户和启汇城内的学生购买群体。
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.
Convex-Faced Combinatorially Regular Polyhedra of Small Genus
Directory of Open Access Journals (Sweden)
Jörg M. Wills
2011-12-01
Full Text Available Combinatorially regular polyhedra are polyhedral realizations (embeddings in Euclidean 3-space E3 of regular maps on (orientable closed compact surfaces. They are close analogues of the Platonic solids. A surface of genus g ≥ 2 admits only finitely many regular maps, and generally only a small number of them can be realized as polyhedra with convex faces. When the genus g is small, meaning that g is in the historically motivated range 2 ≤ g ≤ 6, only eight regular maps of genus g are known to have polyhedral realizations, two discovered quite recently. These include spectacular convex-faced polyhedra realizing famous maps of Klein, Fricke, Dyck, and Coxeter. We provide supporting evidence that this list is complete; in other words, we strongly conjecture that in addition to those eight there are no other regular maps of genus g, with 2 ≤ g ≤ 6, admitting realizations as convex-faced polyhedra in E3. For all admissible maps in this range, save Gordan’s map of genus 4, and its dual, we rule out realizability by a polyhedron in E3.
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:...
Multi-class DTI Segmentation: A Convex Approach.
Xie, Yuchen; Chen, Ting; Ho, Jeffrey; Vemuri, Baba C
2012-10-01
In this paper, we propose a novel variational framework for multi-class DTI segmentation based on global convex optimization. The existing variational approaches to the DTI segmentation problem have mainly used gradient-descent type optimization techniques which are slow in convergence and sensitive to the initialization. This paper on the other hand provides a new perspective on the often difficult optimization problem in DTI segmentation by providing a reasonably tight convex approximation (relaxation) of the original problem, and the relaxed convex problem can then be efficiently solved using various methods such as primal-dual type algorithms. To the best of our knowledge, such a DTI segmentation technique has never been reported in literature. We also show that a variety of tensor metrics (similarity measures) can be easily incorporated in the proposed framework. Experimental results on both synthetic and real diffusion tensor images clearly demonstrate the advantages of our method in terms of segmentation accuracy and robustness. In particular, when compared with existing state-of-the-art methods, our results demonstrate convincingly the importance as well as the benefit of using more refined and elaborated optimization method in diffusion tensor MR image segmentation.
A Faster Algorithm for Quasi-convex Integer Polynomial Optimization
Hildebrand, Robert
2010-01-01
We present a faster exponential-time algorithm for integer optimization over quasi-convex polynomials. We study the minimization of a quasi-convex polynomial subject to s quasi-convex polynomial constraints and integrality constraints for all variables. The new algorithm is an improvement upon the best known algorithm due to Heinz (Journal of Complexity, 2005). A lower time complexity is reached through applying a stronger ellipsoid rounding method and applying a recent advancement in the shortest vector problem to give a smaller exponential-time complexity of a Lenstra-type algorithm. For the bounded case, our algorithm attains a time-complexity of s (r l M d)^{O(1)} 2^{2n\\log_2(n) + O(n)} when M is a bound on the number of monomials in each polynomial and r is the binary encoding length of a bound on the feasible region. In the general case, s l^{O(1)} d^{O(n)} 2^{2n\\log_2(n)}. In each we assume d>=2 is a bound on the total degree of the polynomials and l bounds the maximum binary encoding size of the input...
Gauss images of hyperbolic cusps with convex polyhedral boundary
Fillastre, François
2009-01-01
We prove that a 3--dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by its Gauss image. Furthermore, any spherical metric on the torus with cone singularities of negative curvature and all closed contractible geodesics of length greater than $2\\pi$ is the metric of the Gauss image of some convex polyhedral cusp. This result is an analog of the Rivin-Hodgson theorem characterizing compact convex hyperbolic polyhedra in terms of their Gauss images. The proof uses a variational method. Namely, a cusp with a given Gauss image is identified with a critical point of a functional on the space of cusps with cone-type singularities along a family of half-lines. The functional is shown to be concave and to attain maximum at an interior point of its domain. As a byproduct, we prove rigidity statements with respect to the Gauss image for cusps with or without cone-type singularities. In a special case, our theorem is equivalent to existence of a circle pattern on the torus, with prescrib...
Constrained spacecraft reorientation using mixed integer convex programming
Tam, Margaret; Glenn Lightsey, E.
2016-10-01
A constrained attitude guidance (CAG) system is developed using convex optimization to autonomously achieve spacecraft pointing objectives while meeting the constraints imposed by on-board hardware. These constraints include bounds on the control input and slew rate, as well as pointing constraints imposed by the sensors. The pointing constraints consist of inclusion and exclusion cones that dictate permissible orientations of the spacecraft in order to keep objects in or out of the field of view of the sensors. The optimization scheme drives a body vector towards a target inertial vector along a trajectory that consists solely of permissible orientations in order to achieve the desired attitude for a given mission mode. The non-convex rotational kinematics are handled by discretization, which also ensures that the quaternion stays unity norm. In order to guarantee an admissible path, the pointing constraints are relaxed. Depending on how strict the pointing constraints are, the degree of relaxation is tuneable. The use of binary variables permits the inclusion of logical expressions in the pointing constraints in the case that a set of sensors has redundancies. The resulting mixed integer convex programming (MICP) formulation generates a steering law that can be easily integrated into an attitude determination and control (ADC) system. A sample simulation of the system is performed for the Bevo-2 satellite, including disturbance torques and actuator dynamics which are not modeled by the controller. Simulation results demonstrate the robustness of the system to disturbances while meeting the mission requirements with desirable performance characteristics.
Directory of Open Access Journals (Sweden)
Jalal Jalalshokouhi*
2012-05-01
Full Text Available Carpal fusion may be seen in hereditary and nonhereditary conditions such as acrocallosal syndrome,acromegaly, Apert syndrome, arthrogryposis, Carpenter syndrome, chromosomal abnormalities, ectrodactyly-ectodermal dysplasia-cleft (EEC syndrome, the F form of acropectorovertebral dysgenesis or the F syndrome, fetal alcohol syndrome, Holt-Oram syndrome, Leopard syndrome, multiple synostosis syndrome, oligosyndactyly syndrome, Pfeiffer-like syndrome, scleroderma, split hand and foot malformation, Stickler syndrome, thalidomide embryopathy, Turner syndrome and many other conditions as mentioned in Rubinstein-Taybi's book. Sometimes there is no known causative disease.Diagnosis is usually made by plain X-ray during studying a syndrome or congenital disease or could be an incidental finding like our patients. Hand bone anomalies are more common in syndromes or other congenital or non-hereditary conditions, but polydactyly, syndactyly or oligodactyly and carpal fusions are interesting. X-ray is the modality of choice, but MRI and X-ray CT with multiplanar reconstructions may be used for diagnosis.
Triangulation Algorithm Based on Empty Convex Set Condition
Directory of Open Access Journals (Sweden)
Klyachin Vladimir Aleksandrovich
2015-11-01
Full Text Available The article is devoted to generalization of Delaunay triangulation. We suggest to consider empty condition for special convex sets. For given finite set P ⊂ Rn we shall say that empty condition for convex set B ⊂ Rn is fullfiled if P ∩ B = P ∩ ∂B. Let Φ = Φα, α ∈ A be a family of compact convex sets with non empty inner. Consider some nondegenerate simplex S ⊂ Rn with vertexes p0,...,pn. We define the girth set B(S ∈ Φ if qi ∈ ∂B(S, i = 0, 1, ..., n. We suppose that the family Φ has the property: for arbitrary nondegenerate simplex S there is only one the girth set B(S. We prove the following main result. Theorem 1. If the family Φ = Φα, α ∈ A of convex sets have the pointed above property then for the girth sets it is true: 1. The set B(S is uniquely determined by any simplex with vertexes on ∂B(S. 2. Let S1, S2 be two nondegenerate simplexes such that B(S1 ≠ B(S2. If the intersection B(S1 ∩ B(S2 is not empty, then the intersection of boundaries B(S1, B(S2 is (n − 2-dimensional convex surface, lying in some hyperplane. 3. If two simplexes S1 and S2 don’t intersect by inner points and have common (n − 1-dimensional face G and A, B are vertexes don’t belong to face G and vertex B of simplex B(S2 such that B ∉ B(S1 then B(S2 does not contain the vertex A of simplex S1. These statements allow us to define Φ-triangulation correctly by the following way. The given triangulation T of finite set P ⊂ Rn is called Φ-triangulation if for all simlex S ∈ T the girth set B(S ∈ Φ is empty. In the paper we give algorithm for construct Φ-triangulation arbitrary finite set P ⊂ Rn. Besides we describe examples of families Φ for which we prove the existence and uniqueness of girth set B(S for arbitrary nondegenerate simplex S.
Jiménez, A
2012-01-01
An $n-1$--dimensional tropical simplex $\\TT_A$ is the set of points tropically spanned by $n$ points in $n-1$--dimensional space, when they are not contained in any tropical hyperplane. The coordinates of the points are written as the columns of an $n\\times n$ real matrix $A$. In theorem \\ref{thm:convexity}, we show that convexity of $\\TT_A$ is equivalent to normality and tropical idempotency of $A$. A description of $\\TT_A$ by $n(n-1)$ linear inequalities is immediate from $A$. Set $n=4$. We study \\textbf{tropical tetrahedra} which are \\textbf{convex} and \\textbf{maximal} (i.e., having the maximal number of extremal points, which is 20, and maximal number of facets, which is 12). By tropicality, the facets in $\\TT_A$ are $m$--gons, with $m=3,4,5,6$. In corollary \\ref{cor:no(0,0,12,0)ni(0,1,10,1)}, we show that a polyhedron $\\TT_A$ combinatorially equivalent to the regular dodecahedron does not occur, i.e., the polygon--vector $(f_3,f_4,f_5,f_6)$ of $\\TT_A$ (with $12=f_3+f_4+f_5+f_6$) cannot be $(0,0,12,0)$. ...
A new algorithm for computing the convex hull of a planar point set
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
When the edges of a convex polygon are traversed along one direction, the interior of the convex polygon is always on the same side of the edges. Based on this characteristic of convex polygons, a new algorithm for computing the convex hull of a simple polygon is proposed in this paper, which is then extended to a new algorithm for computing the convex hull of a planar point set. First, the extreme points of the planar point set are found, and the subsets of point candidate for vertex of the convex hull between extreme points are obtained. Then, the ordered convex hull point sequences between extreme points are constructed separately and concatenated by removing redundant extreme points to get the convex hull. The time complexity of the new planar convex hull algorithm is O(nlogh), which is equal to the time complexity of the best output-sensitive planar convex hull algorithms.Compared with the algorithm having the same complexity, the new algorithm is much faster.
Farley, Francis
2012-01-01
A sizzling romance and a romp with subatomic particles at CERN. Love, discovery and adventure in the city where nations meet and beams collide. Life in a large laboratory. As always, the challenges are the same. Who leads? Who follows? Who succeeds? Who gets the credit? Who gets the women or the men? Young Jeremy arrives in CERN and joins the quest for green energy. Coping with baffling jargon and manifold dangers, he is distracted by radioactive rats, lovely ladies and an unscrupulous rival. Full of doubts and hesitations, he falls for a dazzling Danish girl, who leads him astray. His brilliant idea leads to a discovery and a new route to cold fusion. But his personal life is scrambled. Does it bring fame or failure? Tragedy or triumph?
PENGKLASIFIKASIAN DEBITUR DENGAN MENGGUNAKAN ALGORITMA GRAHAM SCAN DALAM PENGAPLIKASIAN CONVEX HULL
Directory of Open Access Journals (Sweden)
AGUS EKA ARIESTA
2014-01-01
Full Text Available Computational geometry is the mathematical science of computation by using the algorithm analysis to solve the problems of geometry. The problems of computational include polygon triangulations, convex hulls, Voronoi diagrams, and motion planning. Convex hull is the set of points that form a convex polygon that covers the entire set of points. The algorithms for determining the convex hull, among others, Graham Scan, Jarvis March, and Divide and Conquer. In the two-dimensional case, Graham Scan algorithm is highly efficient in the use of time complexity. This article discusses the quest convex hull of the data bank debtors, some of the data used to look at the classification accuracy of the convex hull formed. The coordinates of all the data found by using principal component analysis.After the data are analyzed, we get the accuracy of classification by 74%.
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.
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.
Fluctuations of collective coordinates and convexity theorems for energy surfaces
Giraud, B G; Sami, T
2016-01-01
Constrained energy minimizations of a many-body Hamiltonian return energy landscapes e(b) where b= representes the average value(s) of one (or several) collective operator(s), B, in an "optimized" trial state Phi_b, and e = is the average value of the Hamiltonian in this state Phi_b. It is natural to consider the uncertainty, Delta e, given that Phi_b usually belongs to a restricted set of trial states. However, we demonstrate that the uncertainty, Delta b, must also be considered, acknowledging corrections to theoretical models. We also find a link between fluctuations of collective coordinates and convexity properties of energy surfaces.
Nonlinear Non-convex Optimization of Hydraulic Networks
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Kallesøe, Carsten; Leth, John-Josef
2013-01-01
Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption...... in pumps and also to regulate the pressure at the end-user valves to a desired value. The optimization problem which is solved is a nonlinear and non-convex optimization. The barrier method is used to solve this problem. The modeling framework and the optimization technique which are used are general...
Iterative Schemes for Convex Minimization Problems with Constraints
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2014-01-01
Full Text Available We first introduce and analyze one implicit iterative algorithm for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: the generalized mixed equilibrium problem, the system of generalized equilibrium problems, and finitely many variational inclusions in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another implicit iterative algorithm for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.
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.
Probabilistic Guidance of Swarms using Sequential Convex Programming
2014-01-01
as follows (for spacecraft j). Problem 2 (Convex Problem): min uj T−1∑ k=0 ‖uj [k]‖2∆t subject to (12) xj [k + 1] = Axj [k] + Buj [k], k = 0, . . . , T...k]‖2∆t1 + T−1∑ k=k0+TH ‖uj [k]‖2∆t2 (21) subject to xj [k + 1] = Axj [k] + Buj [k], k = k0, . . . , T − 1 (22) ‖uj [k]‖2 ≤ Umax, k = k0, . . . , T − 1
PRECONDITIONED SPECTRAL PROJECTED GRADIENT METHOD ON CONVEX SETS
Institute of Scientific and Technical Information of China (English)
Lenys Bello; Marcos Raydan
2005-01-01
The spectral gradient method has proved to be effective for solving large-scale unconstrained optimization problems. It has been recently extended and combined with the projected gradient method for solving optimization problems on convex sets. This combination includes the use of nonmonotone line search techniques to preserve the fast local convergence. In this work we further extend the spectral choice of steplength to accept preconditioned directions when a good preconditioner is available. We present an algorithm that combines the spectral projected gradient method with preconditioning strategies to increase the local speed of convergence while keeping the global properties. We discuss implementation details for solving large-scale problems.
Design of convex hull plate forming by pure line heating
Institute of Scientific and Technical Information of China (English)
ZHANG Xue-biao; JI Zhuo-shang; LIU Yu-jun
2004-01-01
This paper presents a ship-hull plate forming way by pure line heating. The heating lines forming the required bending angle is determined by curvature analysis method. Heating along the calculated heating lines results in bland plate with initial transverse curvature. Then, the plate with desired convex shape can be obtained by heating in the longitudinal edge. This is the whole forming process by pure line heating. This paper presents a method of plane development for ship-hull plate with B-spline surface representation, and provides the shrinkage heating lines in the forming process. This forming way would facilitate temperature control and make plate forming automatically easy.
Left ventricle segmentation in MRI via convex relaxed distribution matching.
Nambakhsh, Cyrus M S; Yuan, Jing; Punithakumar, Kumaradevan; Goela, Aashish; Rajchl, Martin; Peters, Terry M; Ayed, Ismail Ben
2013-12-01
A fundamental step in the diagnosis of cardiovascular diseases, automatic left ventricle (LV) segmentation in cardiac magnetic resonance images (MRIs) is still acknowledged to be a difficult problem. Most of the existing algorithms require either extensive training or intensive user inputs. This study investigates fast detection of the left ventricle (LV) endo- and epicardium surfaces in cardiac MRI via convex relaxation and distribution matching. The algorithm requires a single subject for training and a very simple user input, which amounts to a single point (mouse click) per target region (cavity or myocardium). It seeks cavity and myocardium regions within each 3D phase by optimizing two functionals, each containing two distribution-matching constraints: (1) a distance-based shape prior and (2) an intensity prior. Based on a global measure of similarity between distributions, the shape prior is intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive a fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed algorithm relaxes the need for costly pose estimation (or registration) procedures and large training sets, and can tolerate shape deformations, unlike template (or atlas) based priors. Our formulation leads to a challenging problem, which is not directly amenable to convex-optimization techniques. For each functional, we split the problem into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Unlike related graph-cut approaches, the proposed convex-relaxation solution can be parallelized to reduce substantially the computational time for 3D domains (or higher), extends directly to high dimensions, and does not have the grid-bias problem. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm
Optimal convex correcting procedures in problems of high dimension
Dokukin, A. A.; Senko, O. V.
2011-09-01
The properties of convex correcting procedures (CCPs) over sets of predictors are examined. It is shown that the minimization of the generalized error in a CCP is reduced to a quadratic programming problem. The conditions are studied under which a set of predictors cannot be reduced without degrading the accuracy of the corresponding optimal CCP. Experimental studies of the prognostic properties of CCPs for samples of one-dimensional linear regressions showed that CCP optimization can be an effective tool for regression variable selection.
Sparse Signal Recovery from Quadratic Measurements via Convex Programming
Li, Xiaodong; Voroninski, Vladislav
2012-01-01
In this paper we consider a system of quadratic equations ||^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be underdetermined, i.e., m < n. We prove that if there exists a sparse solution x, i.e., at most k components of x are non-zero, then by solving a convex optimization program, we can solve for x up to a multiplicative constant with high probability, provided that k
Multi-Stage Convex Relaxation Methods for Machine Learning
2013-03-01
relaxation with Lasso (L1 regularization), the multi-stage convex relaxation method can 3 Initialize v̂ = 1 Repeat the following two steps until convergence...observations using the following sparse regression method: ŵ = arg min w 1 n ‖Xw − y‖22 + λ d∑ j=1 g(|wj |) , (9) where g(|wj |) is a...estimation problems. Statistical Science, 27:576–593, 2012. Tong Zhang. Some sharp performance bounds for least squares regression with L1
Convexity of Spheres in a Manifold without Conjugate Points
Indian Academy of Sciences (India)
Akhil Ranjan; Hemangi Shah
2002-11-01
For a non-compact, complete and simply connected manifold without conjugate points, we prove that if the determinant of the second fundamental form of the geodesic spheres in is a radial function, then the geodesic spheres are convex. We also show that if is two or three dimensional and without conjugate points, then, at every point there exists a ray with no focal points on it relative to the initial point of the ray. The proofs use a result from the theory of vector bundles combined with the index lemma.
Reconstructing Shapes with Guarantees by Unions of Convex Sets
Attali, Dominique; Lieutier, André
2010-01-01
33 pages; A simple way to reconstruct a shape $A$ from a sample $P$ is to output an $r$-offset $P + r B$, where $B$ designates the unit Euclidean ball centered at the origin. Recently, it has been proved that the output $P + r B$ is homotopy equivalent to the shape $A$, for a dense enough sample $P$ of $A$ and for a suitable value of the parameter $r$. In this paper, we extend this result and find convex sets $C$, besides the unit Euclidean ball $B$, for which $P + r C$ reconstructs the topol...
Stienen, Martin N; Joswig, Holger; Smoll, Nicolas R; Tessitore, Enrico; Schaller, Karl; Hildebrandt, Gerhard; Gautschi, Oliver P
2016-03-01
A myriad of negative bodily health effects related to tobacco smoking is known while its detrimental effects on the spine in particular are less defined. The goal of the current study is to compare long-term outcome between smokers and non-smokers after non-instrumented lumbar spine surgery. Prospective observational study on n=172 consecutive patients undergoing non-instrumented spine surgery for lumbar disc herniation (LDH) or lumbar spinal stenosis (LSS) with a follow-up (FU) of 4.5 years. Patients were dichotomized according to their smoking status at the time of surgery. Back pain and health-related quality of life (HRQoL) were assessed using the visual analogue scale (VAS) and the Short-Form (SF)-12. Any subsequent lumbar spine surgeries since the index surgery were registered. Logistic regression analysis was used to estimate the effect size of the relationship between smoking and the responder status to surgery in terms of pain and HRQoL-metrics. Complete FU data was available for n=29 (55%) smokers and n=75 (63%) non-smokers. At discharge, 1 month, 1 year and 4.5 years, smokers were as likely as non-smokers to achieve a favourable response to surgery in terms of VAS back pain and the SF-12 mental and physical component scale metric. A subgroup analysis on active smokers throughout the entire study interval did not find an inferior responder rate than in never-smokers. A trend for additional lumbar spine surgery performed in 17.2% of the smoking and 8.2% of the non-smoking patients during FU was observed (OR 2.39, 95% CI 0.67-8.57, p=0.179). Up to 4.5 years following non-instrumented lumbar spine surgery, there was no difference in the pain or HRQoL-responder status of smokers and non-smokers. Smokers may be more likely to undergo re-do surgery in the long term, but more data is needed to confirm this statistical trend. Copyright © 2016 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Ajab Akbarally
2007-06-01
Full Text Available A new subclass of analytic functions $ k-SP_\\lambda(\\alpha $ is introduced by applying certain operators of fractional calculus to $k$-uniformly starlike and $ k $-uniformly convex functions of order $ \\alpha $. Some theorems on coefficient bounds and growth and distortion theorems for this subclass are found. The radii of close to convexity, starlikeness and convexity for this subclass is also derived.
Shape Preserving Positive and Convex Data Visualization using Rational Bi-cubic Functions
Directory of Open Access Journals (Sweden)
Tahira Sumbal Shaikh
2012-01-01
Full Text Available This paper is concerned with the problem of positive and convex data visualization in the form of positive and convex surfaces. A rational bi-cubic partially blended function with eight free parameters in its description is introduced and applied to visualize the shape of positive data and convex data. The developed schemes in this paper have unique representations. Visual models of surfaces attain smoothness.
Maximum matching by convex quadratic programming based o an adverse graph conjecture
Pacheco, Maria F.; Cardoso, Domingos Moreira; Luz, Carlos J.
2012-01-01
In this talk, we describe a procedure for determining a maximum stable set in a graph with convex-$QP$ stability number (which is a graph whose stability number can be determined by solving a convex quadratic programming problem) unless there is a subgraph for which neither the optimal value of the convex quadratic program nor the least adjacency eigenvalue changes when the neighborhood of any vertex is deleted. Such a graph is called adverse. Assuming the trueness of the adver...
2014-10-31
constrained quadratic program can be lifted to a convex conic optimization prob- lem. We have shown that a complementarity approach can be used to find sparse...students who were partially supported by this grant have graduated from RPI or UIUC: • Lijie Bai, On convex quadratic programs with complementarity...conferences and universities. In paper [A], we show that any quadratically constrained quadratic program is equivalent to a convex optimization problem
Convex quadratic programming applied to the stability number of a graph
Pacheco, Maria F.; Cardoso, Domingos Moreira; Luz, Carlos J.
2012-01-01
We deal with graphs whose stability number can be determined by a convex quadratic program and describe algorithmic techniques for the determination of maximum stabe sets in such graphs (except there is an induced subgraph with least adjacency eigenvalue and optimal value of the convex quadratic program not changing if the neighbourhood of any vertex is deleted). Such a graph is called adverse. Assuming that every adverse graph has convex-QP stability number, an algorithm for the recognition ...
Further Development in the Global Resolution of Convex Programs with Complementarity Constraints
2014-04-09
variables, we have investigated the class of convex quadratic programs with complementarity constraints (QPCCs) and be- gun to explore the global...published; all are available from http://www.rpi. edu/~mitchj: • L. Bai, J.E. Mitchell, and J.S. Pang. On convex quadratic programs with linear...relationship of a pair of convex quadratic programs and on a logical Benders scheme, an extreme ray/point generation procedure is developed, which
A Generalization on Weighted Means and Convex Functions with respect to the Non-Newtonian Calculus
Directory of Open Access Journals (Sweden)
Uğur Kadak
2016-01-01
Full Text Available This paper is devoted to investigating some characteristic features of weighted means and convex functions in terms of the non-Newtonian calculus which is a self-contained system independent of any other system of calculus. It is shown that there are infinitely many such useful types of weighted means and convex functions depending on the choice of generating functions. Moreover, some relations between classical weighted mean and its non-Newtonian version are compared and discussed in a table. Also, some geometric interpretations of convex functions are presented with respect to the non-Newtonian slope. Finally, using multiplicative continuous convex functions we give an application.
Favorov, S
2012-01-01
We introduce a new geometric characteristic of compact sets on the plane called $r$-convexity, which fits nicely into the concept of generalized convexity and extends essentially the conventional convexity. For a class of subharmonic functions on unbounded domains with $r$-convex compact complement, with the growth governed by the distance to the boundary, we obtain the Blaschke--type condition for their Riesz' measures. The result is applied to the study of the convergence of the discrete spectrum for the Schatten-von Neumann perturbations.
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.
Rationally convex sets on the unit sphere in ℂ2
Wermer, John
2008-04-01
Let X be a rationally convex compact subset of the unit sphere S in ℂ2, of three-dimensional measure zero. Denote by R( X) the uniform closure on X of the space of functions P/ Q, where P and Q are polynomials and Q≠0 on X. When does R( X)= C( X)? Our work makes use of the kernel function for the bar{δ}b operator on S, introduced by Henkin in [5] and builds on results obtained in Anderson Izzo Wermer [3]. We define a real-valued function ɛ X on the open unit ball int B, with ɛ X ( z, w) tending to 0 as ( z, w) tends to X. We give a growth condition on ɛ X ( z, w) as ( z, w) approaches X, and show that this condition is sufficient for R( X)= C( X) (Theorem 1.1). In Section 4, we consider a class of sets X which are limits of a family of Levi-flat hypersurfaces in int B. For each compact set Y in ℂ2, we denote the rationally convex hull of Y by widehat{Y}. A general reference is Rudin [8] or Aleksandrov [1].
Zone diagrams in compact subsets of uniformly convex normed spaces
Kopecká, Eva; Reich, Simeon
2010-01-01
A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matousek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and proved the existence and uniqueness of zone diagrams there. In the present paper we prove the existence of zone diagrams with respect to finitely many pairwise disjoint compact sites contained in a compact and convex subset of a uniformly convex normed space. The proof is based on the Schauder fixed point theorem, the Curtis-Schori theorem regarding the Hilbert cube, and on recent results concerning the characterization of Voronoi cells as a collection of line segments and their geometric stability with respect to small changes of the corresponding sites. Along the way we obtain the continuity of the Dom mapping as wel...
Convex foundations for generalized MaxEnt models
Frongillo, Rafael; Reid, Mark D.
2014-12-01
We present an approach to maximum entropy models that highlights the convex geometry and duality of generalized exponential families (GEFs) and their connection to Bregman divergences. Using our framework, we are able to resolve a puzzling aspect of the bijection of Banerjee and coauthors between classical exponential families and what they call regular Bregman divergences. Their regularity condition rules out all but Bregman divergences generated from log-convex generators. We recover their bijection and show that a much broader class of divergences correspond to GEFs via two key observations: 1) Like classical exponential families, GEFs have a "cumulant" C whose subdifferential contains the mean: Eo˜pθ[φ(o)]∈∂C(θ) ; 2) Generalized relative entropy is a C-Bregman divergence between parameters: DF(pθ,pθ')= D C(θ,θ') , where DF becomes the KL divergence for F = -H. We also show that every incomplete market with cost function C can be expressed as a complete market, where the prices are constrained to be a GEF with cumulant C. This provides an entirely new interpretation of prediction markets, relating their design back to the principle of maximum entropy.
Midpoint locally uniformly convexity on locally convex spaces%关于局部凸空间的中点局部一致凸性
Institute of Scientific and Technical Information of China (English)
陈利国; 罗成
2011-01-01
The notions of（weakly） midpoint locally uniformly convexity on locally convex spaces are introduced.It is proved that the dual property between（weakly） midpoint locally uniformly convexity and（weakly） midpoint locally uniformly smoothness,and disscuss the relationship between them and other convexity.Corresponding notions and results in Banach space is generalized.%给出局部凸空间的（弱）中点局部一致凸性,证明了它与（弱）中点局部一致光滑性具有对偶性质,讨论它们与其它凸性之间的关系,推广了Banach空间相应概念和结果.
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
Effect of dental arch convexity and type of archwire on frictional forces
Fourie, Zacharias; Ozcan, Mutlu; Sandham, John
2009-01-01
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
M. Dyer; R. Kannan; L. Stougie (Leen)
2014-01-01
htmlabstractWe consider maximising a concave function over a convex set by a simplerandomised algorithm. The strength of the algorithm is that it requires only approximatefunction evaluations for the concave function and a weak membership oraclefor the convex set. Under smoothness conditions on the
A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES
Institute of Scientific and Technical Information of China (English)
Binayak S. Choudhury
2003-01-01
In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extension of a known theorem in the corresponding non-random case.
On Convex Hull of Orthogonal Scalar Spectral Functions of a Carleman Operator
Directory of Open Access Journals (Sweden)
S. M. Bahri
2008-11-01
Full Text Available In this paper we describe the closed convex hull of orthogonal resolvents of an abstract symmetric operator of defect indices (1; 1, then we study the convex hull of orthogonal spectral functions of a Carleman operator in the Hilbert space L^2(X;mu.
Directory of Open Access Journals (Sweden)
Simon Larson
2016-04-01
Full Text Available Abstract We prove geometric $$L^p$$ L p versions of Hardy’s inequality for the sub-elliptic Laplacian on convex domains $$\\Omega $$ Ω in the Heisenberg group $$\\mathbb {H}^n$$ H n , where convex is meant in the Euclidean sense. When $$p=2$$ p = 2 and $$\\Omega $$ Ω is the half-space given by $$\\langle \\xi , \
Hermite-Hadamard type inequalities for GA-s-convex functions
Directory of Open Access Journals (Sweden)
İmdat İşcan
2014-10-01
Full Text Available In this paper, The author introduces the concepts of the GA-s-convex functions in the first sense and second sense and establishes some integral inequalities of Hermite-Hadamard type related to the GA-s-convex functions. Some applications to special means of real numbers are also given.
Pospelov, A. I.
2016-08-01
Adaptive methods for the polyhedral approximation of the convex Edgeworth-Pareto hull in multiobjective monotone integer optimization problems are proposed and studied. For these methods, theoretical convergence rate estimates with respect to the number of vertices are obtained. The estimates coincide in order with those for filling and augmentation H-methods intended for the approximation of nonsmooth convex compact bodies.
Inequalities of Hadamard Type for r-Convex Functions in Carnot Groups
Institute of Scientific and Technical Information of China (English)
Ming-bao Sun; Xiao-ping Yang
2004-01-01
For a Carnot group G,we establish the relationship between extended mean values and r-convex functions which is introduced in this paper,which is a class of inequalities of Hadamard type for r-convex function on G.
Guo, Peng; Cao, Jiannong; Zhang, Kui
2015-01-01
In critical event (e.g., fire or gas) monitoring applications of wireless sensor networks (WSNs), convex hull of the event region is an efficient tool in handling the usual tasks like event report, routes reconstruction and human motion planning. Existing works on estimating convex hull of event
Matrix convex functions with applications to weighted centers for semidefinite programming
J. Brinkhuis (Jan); Z-Q. Luo; S. Zhang (Shuzhong)
2005-01-01
textabstractIn this paper, we develop various calculus rules for general smooth matrix-valued functions and for the class of matrix convex (or concave) functions first introduced by Loewner and Kraus in 1930s. Then we use these calculus rules and the matrix convex function -log X to study a new
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
Homotopy formulas and ■-equation on local q- convex domains in Stein manifolds
Institute of Scientific and Technical Information of China (English)
钟同德
1997-01-01
The homotopy formulas of (r,s) differential forms and the solution of equation of type (r,s) on local q-convex domains in Stein manifolds are obtained.The homotopy formulas on local q-convex domains have important applications in uniform estimates of equation and holomorphic extension of CR-manifolds.
Measures of Asymmetry Dual to Mean Minkowski Measures of Asymmetry for Convex Bo dies
Institute of Scientific and Technical Information of China (English)
Yao Dan; Guo Qi
2016-01-01
We introduce a family of measures (functions) of asymmetry for convex bodies and discuss their properties. It turns out that this family of measures shares many nice properties with the mean Minkowski measures. As the mean Minkowski measures describe the symmetry of lower dimensional sections of a convex body, these new measures describe the symmetry of lower dimensional orthogonal projections.
Guo, Peng; Cao, Jiannong; Zhang, Kui
2015-01-01
In critical event (e.g., fire or gas) monitoring applications of wireless sensor networks (WSNs), convex hull of the event region is an efficient tool in handling the usual tasks like event report, routes reconstruction and human motion planning. Existing works on estimating convex hull of event reg
Global convergence of a non-convex Douglas-Rachford iteration
Artacho, Francisco J Aragón
2012-01-01
We establish a region of convergence for the proto-typical non-convex Douglas-Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration [2] was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given.
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...
Rocking convex array used for 3D synthetic aperture focusing
DEFF Research Database (Denmark)
Andresen, Henrik; Nikolov, Svetoslav; Pedersen, M M
2008-01-01
Volumetric imaging can be performed using 1D arrays in combination with mechanical motion. Outside the elevation focus of the array, the resolution and contrast quickly degrade compared to the azimuth plane, because of the fixed transducer focus. The purpose of this paper is to use synthetic...... aperture focusing (SAF) for enhancing the elevation focusing for a convex rocking array, to obtain a more isotropic point spread function. This paper presents further development of the SAF method, which can be used with curved array combined with a rocking motion. The method uses a virtual source (VS...... Kretztechnik, Zipf, Austria). The array has an elevation focus at 60 mm of depth, and the angular rocking velocity is up to 140deg/s. The scan sequence uses an fprf of 4500 - 7000 Hz allowing up to 15 cm of penetration. The full width at half max (FWHM) and main-lobe to side-lobe ratio (MLSL) is used...
Nonlinear Non-convex Optimization of Hydraulic Networks
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Kallesøe, Carsten; Leth, John-Josef
2013-01-01
Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption...... in pumps and also to regulate the pressure at the end-user valves to a desired value. The optimization problem which is solved is a nonlinear and non-convex optimization. The barrier method is used to solve this problem. The modeling framework and the optimization technique which are used are general....... They can be used for a general hydraulic networks to optimize the leakage and energy consumption and to satisfy the demands at the end-users. The results in this paper show that the power consumption of the pumps is reduced....
Optimal placement of convex polygons to maximize point containment
Energy Technology Data Exchange (ETDEWEB)
Dickerson, M. [Middlebury College, VT (United States); Scharstein, D. [Cornell Univ., Ithaca, NY (United States)
1996-12-31
Given a convex polygon P with m vertices and a set S of n points in the plane, we consider the problem of finding a placement of P that contains the maximum number of points in S. We allow both translation and rotation. Our algorithm is self-contained and utilizes the geometric properties of the containing regions in the parameter space of transformations. The algorithm requires O(nk{sup 2} m{sup 2} log(mk)) time and O(n + m) space, where k is the maximum number of points contained. This provides a linear improvement over the best previously known algorithm when k is large ({Theta}(n)) and a cubic improvement when k is small. We also show that the algorithm can be extended to solve bichromatic and general weighted variants of the problem.
Sharp recovery bounds for convex deconvolution, with applications
McCoy, Michael B
2012-01-01
Deconvolution refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. A standard example is the problem of separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis. Another familiar case is the problem of decomposing an observed matrix into a low-rank matrix plus a sparse matrix. This paper describes and analyzes a framework, based on convex optimization, for solving these deconvolution problems and many others. This work introduces a randomized signal model which ensures that the two structures are incoherent, i.e., generically oriented. For an observation from this model, the calculus of spherical integral geometry provides an exact formula that describes when the optimization problem will succeed (or fail) to deconvolve the two constituent signals with high probability. This approach identifies a summary statistic that reflects the complexity of a particu...
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.
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.
In-vivo evaluation of convex array synthetic aperture imaging
DEFF Research Database (Denmark)
Pedersen, Morten Høgholm; Gammelmark, Kim Løkke; Jensen, Jørgen Arendt
2007-01-01
This paper presents an in-vivo study of synthetic transmit aperture (STA) imaging in comparison to conventional imaging, evaluating whether STA imaging is feasible in-vivo, and whether the image quality obtained is comparable to traditional scanned imaging in terms of penetration depth, spatial...... resolution, contrast resolution, and artifacts. Acquisition was performed using our research scanner RASMUS and a 5.5 MHz convex array transducer. STA imaging was acquired using circular wave emulation by 33-element subapertures and a 20 us linear FM signal as excitation pulse. For conventional imaging a 64...... element aperture was used in transmit and receive with a 1.5 cycle sinusoid excitation pulse. Conventional and STA images were acquired interleaved ensuring that the exact same anatomical location was scanned. Image sequences were recorded in real-time and processed off-line. Seven male volunteers were...
Identification of community structure in networks with convex optimization
Hildebrand, Roland
2008-01-01
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous one. A semidefinite relaxation of this conic program then allows to compute upper bounds on the maximum modularity of the network. Based on the solution of the corresponding semidefinite program, we design a randomized algorithm generating partitions of the network with suboptimal modularities. We apply this algorithm to several benchmark networks, demonstrating that it is competitive in accuracy with the best algorithms previously known. We use our method to provide the first proof of optimality of a partition for a real-world network.
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.
Bankruptcy Problem Allocations and the Core of Convex Games
Directory of Open Access Journals (Sweden)
William Olvera-Lopez
2014-01-01
Full Text Available A well-known result related to bankruptcy problems establishes that a vector is a bankruptcy allocation if and only if it belongs to the core of the associated O’Neill’s bankruptcy game. In this paper we show that this game is precisely the unique TU-game based on convex functions that satisfies the previous result. In addition, given a bankruptcy problem, we show a way for constructing bankruptcy games such that the set of bankruptcy allocations is a subset of their core or their core is a subset of the set of bankruptcy allocations. Also, we show how these results can be applied for finding new bankruptcy solutions.
Convexity at finite temperature and non-extensive thermodynamics
Alexandre, J.
2016-09-01
Assuming that tunnel effect between two degenerate bare minima occurs, in a scalar field theory at finite volume, this article studies the consequences for the effective potential, to all loop orders. Convexity is achieved only if the two bare minima are taken into account in the path integral, and a new derivation of the effective potential is given, in the large volume limit. The effective potential then has a universal form, it is suppressed by the space time volume, and does not feature spontaneous symmetry breaking as long as the volume is finite. The finite temperature analysis leads to surprising thermal properties, following from the non-extensive expression for the free energy. Although the physical relevance of these results is not clear, the potential application to ultra-light scalar particles is discussed.
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.
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...
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......-description problem. We finally present the contributions of the thesis. The remaining parts of the thesis consist of five research papers. The first paper addresses non-smooth first-order convex optimization and the trade-off between accuracy and smoothness of the approximating smooth function. The second and third...
Convex preserving scattered data interpolation using bivariate C1 cubic splines
Lai, Ming-Jun
2000-07-01
We use bivariate C1 cubic splines to deal with convexity preserving scattered data interpolation problem. Using a necessary and sufficient condition on Bernstein-Bézier polynomials, we set the convexity-preserving interpolation problem into a quadratically constraint quadratic programming problem. We show the existence of convexity preserving interpolatory surfaces under certain conditions on the data. That is, under certain conditions on the data, there always exists a convexity preservation C1 cubic spline interpolation if the triangulation is refined sufficiently many times. We then replace the quadratical constrains by three linear constrains and formulate the problem into linearly constraint quadratic programming problems in order to be able to solve it easily. Certainly, the existence of convexity preserving interpolatory surfaces is equivalent to the feasibility of the linear constrains. We present a numerical experiment to test which of these three linear constraints performs the best.
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.
National Research Council Canada - National Science Library
Huang Zhenqiang Huang Yuxiang
2013-01-01
...... And with a magnetic moment of light nuclei controlled cold nuclear collide fusion, belongs to the nuclear energy research and development in the field of applied technology "cold nuclear collide fusion...
Institute of Scientific and Technical Information of China (English)
唐献秀; 林尤武; 吴建功
2011-01-01
给出局部凸空间平均一致凸性的一些等价刻画与某些凸性的关系.%We obtained some necessary and sufficient conditions for average uniform convexity in locally converx spaces.At the same time,we discussed the relationship between this convexity and some other convexity.
Energy Technology Data Exchange (ETDEWEB)
None
1989-11-01
I am pleased to forward to you the Final Report of the Cold Fusion Panel. This report reviews the current status of cold fusion and includes major chapters on Calorimetry and Excess Heat, Fusion Products and Materials Characterization. In addition, the report makes a number of conclusions and recommendations, as requested by the Secretary of Energy.
Ayupov, Sh A
2011-01-01
In the present article we prove a fixed point theorem for reflections of compact convex sets and give a new characterization of state space of JB-algebras among compact convex sets. Namely they are exactly those compact convex sets which are strongly spectral and symmetric.
Institute of Scientific and Technical Information of China (English)
Liu Xiaosong; Liu Taishun
2009-01-01
In this article, the authors obtain an inequality of homogeneous expansion for f, where f is a quasi-convex mapping (including quasi-convex mapping of type A and quasi-convex mapping of type B) defined on the open unit polydisk in Cn. Meanwhile, the authors also investigate its application.
Gunay, Osman; Toreyin, Behçet Ugur; Kose, Kivanc; Cetin, A Enis
2012-05-01
In this paper, an entropy-functional-based online adaptive decision fusion (EADF) framework is developed for image analysis and computer vision applications. In this framework, it is assumed that the compound algorithm consists of several subalgorithms, each of which yields its own decision as a real number centered around zero, representing the confidence level of that particular subalgorithm. Decision values are linearly combined with weights that are updated online according to an active fusion method based on performing entropic projections onto convex sets describing subalgorithms. It is assumed that there is an oracle, who is usually a human operator, providing feedback to the decision fusion method. A video-based wildfire detection system was developed to evaluate the performance of the decision fusion algorithm. In this case, image data arrive sequentially, and the oracle is the security guard of the forest lookout tower, verifying the decision of the combined algorithm. The simulation results are presented.
Energy Technology Data Exchange (ETDEWEB)
Harrison, Stephen C., E-mail: harrison@crystal.harvard.edu
2015-05-15
Membrane fusion is an essential step when enveloped viruses enter cells. Lipid bilayer fusion requires catalysis to overcome a high kinetic barrier; viral fusion proteins are the agents that fulfill this catalytic function. Despite a variety of molecular architectures, these proteins facilitate fusion by essentially the same generic mechanism. Stimulated by a signal associated with arrival at the cell to be infected (e.g., receptor or co-receptor binding, proton binding in an endosome), they undergo a series of conformational changes. A hydrophobic segment (a “fusion loop” or “fusion peptide”) engages the target-cell membrane and collapse of the bridging intermediate thus formed draws the two membranes (virus and cell) together. We know of three structural classes for viral fusion proteins. Structures for both pre- and postfusion conformations of illustrate the beginning and end points of a process that can be probed by single-virion measurements of fusion kinetics. - Highlights: • Viral fusion proteins overcome the high energy barrier to lipid bilayer merger. • Different molecular structures but the same catalytic mechanism. • Review describes properties of three known fusion-protein structural classes. • Single-virion fusion experiments elucidate mechanism.
Statistical Mechanics of Optimal Convex Inference in High Dimensions
Advani, Madhu; Ganguli, Surya
2016-07-01
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 simpler than
LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies
Habert, Luc; Pocchiola, Michel
2011-01-01
We extend the classical LR characterization of chirotopes of finite planar families of points to chirotopes of finite planar families of pairwise disjoint convex bodies: a map \\c{hi} on the set of 3-subsets of a finite set I is a chirotope of finite planar families of pairwise disjoint convex bodies if and only if for every 3-, 4-, and 5-subset J of I the restriction of \\c{hi} to the set of 3-subsets of J is a chirotope of finite planar families of pairwise disjoint convex bodies. Our main to...
GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS IN LOCALLY G-CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
DING Xie-ping
2005-01-01
Some classes of generalized vector quasi-equilibrium problems (in short,GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems, generalized vector variational inequality problems,quasi-equilibrium problems and quasi-variational inequality problems as special cases. First,an equilibrium existence theorem for one person games is proved in locally G-convex spaces.As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.
A proximal point method for nonsmooth convex optimization problems in Banach spaces
Directory of Open Access Journals (Sweden)
Y. I. Alber
1997-01-01
Full Text Available In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.
Fast Bundle-Level Type Methods for Unconstrained and Ball-Constrained Convex Optimization
2014-12-01
of half- spaces , hence it is convex and closed. Therefore, the subproblem (3.4) always has a unique solution as long as Qk is non-empty. To finish the...pixels in the image. The ‖u‖TV is convex and non-smooth. Table 5.1 Uniformly distributed QP instances A : n = 4000,m = 3000, L = 2.0e6, e0 = 2.89e4 Alg...generation. Mathematical pro- gramming, 118(1):177–206, 2009. [14] G. Lan. Bundle-level type methods uniformly optimal for smooth and non-smooth convex
A New Representation and Algorithm for Constructing Convex Hulls in Higher Dimensional Spaces
Institute of Scientific and Technical Information of China (English)
吕伟; 梁友栋
1992-01-01
This paper presents a new and simple scheme to describe the convex hull in Rd,which only uses three kinds of the faces of the convex hull.i.e.,the d-1-faces,d-2-faces and 0-faces.Thus,we develop and efficient new algorithm for constructing the convex hull of a finite set of points incrementally.This algorithm employs much less storage and time than that of the previously-existing approaches.The analysis of the runniing time as well as the storage for the new algorithm is also theoretically made.The algorithm is optimal in the worst case for even d.
On Prop erties of p-critical Points of Convex Bo dies
Institute of Scientific and Technical Information of China (English)
Huang Xing; Guo Qi
2015-01-01
Properties of the p-measures of asymmetry and the corresponding aﬃne equivariant p-critical points, defined recently by the second author, for convex bodies are discussed in this article. In particular, the continuity of p-critical points with respect to p on (1,+∞) is confirmed, and the connections between general p-critical points and the Minkowski-critical points (∞-critical points) are investigated. The behavior of p-critical points of convex bodies approximating a convex bodies is studied as well.
Input Design for System Identification via Convex Relaxation
Manchester, Ian R
2010-01-01
This paper proposes a new framework for the optimization of excitation inputs for system identification. The optimization problem considered is to maximize a reduced Fisher information matrix in any of the classical D-, E-, or A-optimal senses. In contrast to the majority of published work on this topic, we consider the problem in the time domain and subject to constraints on the amplitude of the input signal. This optimization problem is nonconvex. The main result of the paper is a convex relaxation that gives an upper bound accurate to within $2/\\pi$ of the true maximum. A randomized algorithm is presented for finding a feasible solution which, in a certain sense is expected to be at least $2/\\pi$ as informative as the globally optimal input signal. In the case of a single constraint on input power, the proposed approach recovers the true global optimum exactly. Extensions to situations with both power and amplitude constraints on both inputs and outputs are given. A simple simulation example illustrates th...
A Localization Method for Multistatic SAR Based on Convex Optimization.
Directory of Open Access Journals (Sweden)
Xuqi Zhong
Full Text Available In traditional localization methods for Synthetic Aperture Radar (SAR, the bistatic range sum (BRS estimation and Doppler centroid estimation (DCE are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function's maximum is on the circumference of the ellipse which is the iso-range for its model function's T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment.
A Localization Method for Multistatic SAR Based on Convex Optimization.
Zhong, Xuqi; Wu, Junjie; Yang, Jianyu; Sun, Zhichao; Huang, Yuling; Li, Zhongyu
2015-01-01
In traditional localization methods for Synthetic Aperture Radar (SAR), the bistatic range sum (BRS) estimation and Doppler centroid estimation (DCE) are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R) pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function's maximum is on the circumference of the ellipse which is the iso-range for its model function's T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment.
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 coordinate-free condition number for convex programming
Amelunxen, Dennis
2011-01-01
We introduce and analyze a natural geometric version of Renegar's condition number R, which we call Grassmann condition number, for the homogeneous convex feasibility problem associated with a regular cone C\\subseteq R^n. Let Gr_{n,m} denote the Grassmann manifold of m-dimensional linear subspaces of R^n with the Riemannian distance metric d_g. The set of ill-posed instances \\Sigma_m\\subset Gr_{n,m} consists of the linear subspaces W touching C. We define the Grassmann condition number \\CG(W) of an m-dimensional subspace W\\in\\Gr_{n,m} as \\CG(W)^{-1} := sin d_g(W,\\Sigma_m). We also provide other characterizations of \\CG(W) and prove that \\CG(W) <= R(A) <= \\CG(W) \\kappa(A), where W =\\im A^T, and where \\kappa(A) =||A|| ||A^\\dagger|| denotes the matrix condition number. This extends work by Belloni and Freund in Math. Program. 119:95-107 (2009). Based on the Grassmann condition number, in a forthcoming paper, we shall provide, for the first time, a probabilistic analysis of Renegar's condition number for an...
Optimal Orthogonal Graph Drawing with Convex Bend Costs
Bläsius, Thomas; Wagner, Dorothea
2012-01-01
Traditionally, the quality of orthogonal planar drawings is quantified by either the total number of bends, or the maximum number of bends per edge. However, this neglects that in typical applications, edges have varying importance. Moreover, as bend minimization over all planar embeddings is NP-hard, most approaches focus on a fixed planar embedding. We consider the problem OptimalFlexDraw that is defined as follows. Given a planar graph G on n vertices with maximum degree 4 and for each edge e a cost function cost_e : N_0 --> R defining costs depending on the number of bends on e, compute an orthogonal drawing of G of minimum cost. Note that this optimizes over all planar embeddings of the input graphs, and the cost functions allow fine-grained control on the bends of edges. In this generality OptimalFlexDraw is NP-hard. We show that it can be solved efficiently if 1) the cost function of each edge is convex and 2) the first bend on each edge does not cause any cost (which is a condition similar to the posi...
Nontraumatic convexal subarachnoid hemorrhage concomitant with acute ischemic stroke.
Nakajima, Makoto; Inatomi, Yuichiro; Yonehara, Toshiro; Hirano, Teruyuki; Ando, Yukio
2014-07-01
Nontraumatic convexal subarachnoid hemorrhage (cSAH) rarely occurs subsequent to acute ischemic stroke. The incidence, clinical background characteristics, and outcomes in acute ischemic stroke patients with cSAH were investigated. Our stroke center database was reviewed to identify patients with acute ischemic stroke/transient ischemic attack (TIA) who demonstrated acute cSAH within 14 days of admission between 2005 and 2011. Background characteristics, clinical course, and outcomes at discharge and 3 months after onset were investigated in these patients. Of 4953 acute stroke/TIA patients, cSAH was observed in 8 (.14%) patients (7 men, mean age 71 years): 7 were detected incidentally, and the other was found immediately after a convulsion. Two patients died during their hospital stay, 1 died after discharge, and 3 were dependent at 3 months. Major artery occlusion or severe stenosis was observed in 5 patients. Two patients subsequently developed subcortical hemorrhage. On gradient echo imaging, lobar cerebral microbleeds were observed in 2 patients, and chronic superficial siderosis was observed in 2 patients. In this retrospective review of cases with ischemic stroke and cSAH, over half of patients had occlusion of major arteries. Cerebral amyloid angiopathy was suggested by magnetic resonance imaging findings and subsequent events in 3 patients. The overall outcome was unfavorable although the causal relationship with cSAH was unclear. Copyright © 2014 National Stroke Association. Published by Elsevier Inc. All rights reserved.
Asynchronous Code-Division Random Access Using Convex Optimization
Applebaum, Lorne; Duarte, Marco F; Calderbank, Robert
2011-01-01
Many applications in cellular systems and sensor networks involve a random subset of a large number of users asynchronously reporting activity to a base station. This paper examines the problem of multiuser detection (MUD) in random access channels for such applications. Traditional orthogonal signaling ignores the random nature of user activity in this problem and limits the total number of users to be on the order of the number of signal space dimensions. Contention-based schemes, on the other hand, suffer from delays caused by colliding transmissions and the hidden node problem. In contrast, this paper presents a novel asynchronous (non-orthogonal) code-division random access scheme along with a convex optimization-based MUD algorithm that overcomes the issues associated with orthogonal signaling and contention-based methods. Two key distinguishing features of the proposed algorithm are that it does not require knowledge of the delay or channel state information of every user and it has polynomial-time com...
Optimization-based mesh correction with volume and convexity constraints
D'Elia, Marta; Ridzal, Denis; Peterson, Kara J.; Bochev, Pavel; Shashkov, Mikhail
2016-05-01
We consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. This volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.
Energy Technology Data Exchange (ETDEWEB)
None, None
1977-10-15
This report provides the results of a study of methods of economic analysis applied to the evaluation of fusion research. The study recognizes that a hierarchy of economic analyses of research programs exists: standard benefit-cost analysis, expected value of R and D information, and expected utility analysis. It is shown that standard benefit-cost analysis, as commonly applied to research programs, is inadequate for the evaluation of a high technology research effort such as fusion research. A methodology for performing an expected value analysis is developed and demonstrated and an overview of an approach to perform an expected utility analysis of fusion research is presented. In addition, a potential benefit of fusion research, not previously identified, is discussed and rough estimates of its magnitude are presented. This benefit deals with the effect of a fusion research program on optimal fossil fuel consumption patterns. The results of this study indicate that it is both appropriate and possible to perform an expected value analysis of fusion research in order to assess the economics of a fusion research program. The results indicate further that the major area of benefits of fusion research is likely due to the impact of a fusion research program on optimal fossil fuel consumption patterns and it is recommended that this benefit be included in future assessments of fusion research economics.
Knaster, J.; Moeslang, A.; Muroga, T.
2016-05-01
Fusion materials research started in the early 1970s following the observation of the degradation of irradiated materials used in the first commercial fission reactors. The technological challenges of fusion energy are intimately linked with the availability of suitable materials capable of reliably withstanding the extremely severe operational conditions of fusion reactors. Although fission and fusion materials exhibit common features, fusion materials research is broader. The harder mono-energetic spectrum associated with the deuterium-tritium fusion neutrons (14.1 MeV compared to hydrogen and helium as transmutation products that might lead to a (at present undetermined) degradation of structural materials after a few years of operation. Overcoming the historical lack of a fusion-relevant neutron source for materials testing is an essential pending step in fusion roadmaps. Structural materials development, together with research on functional materials capable of sustaining unprecedented power densities during plasma operation in a fusion reactor, have been the subject of decades of worldwide research efforts underpinning the present maturity of the fusion materials research programme.
Li, Qian; Kutz, J. Nathan; Wai, P. K. A.
2013-08-01
We consider the non-adiabatic pulse compression of cascaded soliton propagating in three consecutive optical fiber segments, each of which has a convex dispersion profile with two zero-dispersion wavelengths. The convex dispersion profile provides an accurate description of the chromatic dispersion over the whole frequency range, thus allowing for a comprehensive theoretical treatment of the cascaded third order soliton compression when ultrashort pulses (DFDF) has a convex curvature in its dispersion profile which varies along length of fiber. Compared to DFDF, the cascading of fiber segments with convex dispersion that stays constant along the fiber length greatly reduces the manufacture difficulties and provides a much simpler engineering design in practice. High-degree pulse compression and high-coherence supercontinuum generation are demonstrated.
Ishikawa iteration process with errors for nonexpansive mappings in uniformly convex Banach spaces
Deng Lei; Li Shenghong
2000-01-01
We shall consider the behaviour of Ishikawa iteration with errors in a uniformly convex Banach space. Then we generalize the two theorems of Tan and Xu without the restrictions that C is bounded and limsupnsn
Remarks on quasi-isometric non-embeddability into uniformly convex Banach spaces
Nowak, Piotr W.
2005-01-01
We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of $c_0$ and superreflexivity are discussed.
Extreme Points of the Convex Set of Joint Probability Distributions with Fixed Marginals
Indian Academy of Sciences (India)
K R Parthasarathy
2007-11-01
By using a quantum probabilistic approach we obtain a description of the extreme points of the convex set of all joint probability distributions on the product of two standard Borel spaces with fixed marginal distributions.
Pratt, J; Mueller, W -C; Chapman, S C; Watkins, N W
2014-01-01
Local regions of anomalous particle dispersion, and intermittent events that occur in turbulent flows can greatly influence the global statistical description of the flow. These local behaviors can be identified and analyzed by comparing the growth of neighboring convex hulls of Lagrangian tracer particles. Although in our simulations of homogeneous turbulence the convex hulls generally grow in size, after the Lagrangian particles that define the convex hulls begin to disperse, our analysis reveals short periods when the convex hulls of the Lagrangian particles shrink, evidence that particles are not dispersing simply. Shrinkage can be associated with anisotropic flows, since it occurs most frequently in the presence of a mean magnetic field or thermal convection. We compare dispersion between a wide range of statistically homogeneous and stationary turbulent flows ranging from homogeneous isotropic Navier-Stokes turbulence over different configurations of magnetohydrodynamic turbulence and Boussinesq convect...
Generalizing the Convex Hull of a Sample: The R Package alphahull
Directory of Open Access Journals (Sweden)
Beatriz Pateiro-López
2010-10-01
Full Text Available This paper presents the R package alphahull which implements the α-convex hull and the α-shape of a finite set of points in the plane. These geometric structures provide an informative overview of the shape and properties of the point set. Unlike the convex hull, the α-convex hull and the α-shape are able to reconstruct non-convex sets. This flexibility make them specially useful in set estimation. Since the implementation is based on the intimate relation of theses constructs with Delaunay triangulations, the R package alphahull also includes functions to compute Voronoi and Delaunay tesselations. The usefulness of the package is illustrated with two small simulation studies on boundary length estimation.
Radius model of convex vertical curve of freeway based on attachment coefficient
Institute of Scientific and Technical Information of China (English)
LI Song-ling; PEI Yu-long
2008-01-01
A longitudinal slope brake model was established for the radius calculation of vertical curve of free-way through analyzing the dynamics of brake-running of vehicles running on the longitudinal slope road section. To satisfy the requirement of sight distance, a relation model was established for the attachment coefficient and the convex vertical curve radius. Using MATLAB simulation technique, the convex vertical curve radius at different attachment conditions was calculated accurately and a three-dimensional figure was drawn to describe the relation between the adhesive coefficient, the driving velocity and the radius of vertical curve. The correlation between the convex vertical curve radius and the adhesive coefficient was further analyzed and compared with National Technical Standards. The suggested radius of vertical curve was then put forward to provide a theoretical platform for the security design of the convex vertical curve.
Convex integration theory solutions to the h-principle in geometry and topology
Spring, David
1998-01-01
This book provides a comprehensive study of convex integration theory in immersion-theoretic topology. Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to optimal control theory. Though topological in nature, the theory is based on a precise analytical approximation result for higher order derivatives of functions, proved by M. Gromov. This book is the first to present an exacting record and exposition of all of the basic concepts and technical results of convex integration theory in higher order jet spaces, including the theory of iterated convex hull extensions and the theory of relative h-principles. A second feature of the book is its detailed presentation of applications of the general theory to topics in symplectic topology, divergence free vector fields on 3-manifolds, isometric immersions, totally real embeddings, u...
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks
DEFF Research Database (Denmark)
Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui;
2016-01-01
This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed...... sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal...... 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....
凸体的包含测度(Ⅱ)%Inclusion measures of convex bodies (Ⅱ)
Institute of Scientific and Technical Information of China (English)
熊革
2007-01-01
In this paper, several inequalities for inclusion measures of convex bodies were obtained. The inclusion measure was proved to have concavity by considering the property of relative inner parallel body.
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...... sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal...... 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....
On Certain New Subclass of Meromorphic Close-to-Convex Functions
Directory of Open Access Journals (Sweden)
Jing-Ping Yi
2013-01-01
Full Text Available We introduce a certain new subclass of meromorphic close-to-convex functions. Such results as inclusion relationship, coefficient inequalities, distortion, and growth theorems for this class of functions are derived.
New Fixed Point Results for Fractal Generation in Jungck Noor Orbit with s-Convexity
Directory of Open Access Journals (Sweden)
Shin Min Kang
2015-01-01
Full Text Available We establish new fixed point results in the generation of fractals (Julia sets, Mandelbrot sets, and Tricorns and Multicorns for linear or nonlinear dynamics by using Jungck Noor iteration with s-convexity.
NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
DING Xie-ping(丁协平); Park Jong-yeoul
2002-01-01
By applying the technique of continuous partition of unity and Tychonoff's fixed point theorem, some new collectively fixed point theorems for a family of set-valued mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G-convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence theorems of abstract economies are also obtained in G-convex spaces. Our theorems improve, unify and generalized many important known results in recent literature.
Armour, Edward A.G.
2007-01-01
Muon catalyzed fusion is a process in which a negatively charged muon combines with two nuclei of isotopes of hydrogen, e.g, a proton and a deuteron or a deuteron and a triton, to form a muonic molecular ion in which the binding is so tight that nuclear fusion occurs. The muon is normally released after fusion has taken place and so can catalyze further fusions. As the muon has a mean lifetime of 2.2 microseconds, this is the maximum period over which a muon can participate in this process. This article gives an outline of the history of muon catalyzed fusion from 1947, when it was first realised that such a process might occur, to the present day. It includes a description of the contribution that Drachrnan has made to the theory of muon catalyzed fusion and the influence this has had on the author's research.
Footstep Planning on Uneven Terrain with Mixed-Integer Convex Optimization
2014-08-01
variables to absorb any non-convex constraints. We handle orientation of the footstep placements by approximating the trigonometric sin and cos...must enforce that sj and cj approximate sin and cos without introducing non-convex trigonometric constraints. We choose instead to create a simple...goal and identical cost weights on the displacement from each footstep to the next. To control the number of footsteps used in the plan, and thus the
Institute of Scientific and Technical Information of China (English)
Qin Ni; Ch. Zillober; K. Schittkowski
2005-01-01
In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming (SCP). A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.
A Generalization on Weighted Means and Convex Functions with respect to the Non-Newtonian Calculus
Uğur Kadak; Yusuf Gürefe
2016-01-01
This paper is devoted to investigating some characteristic features of weighted means and convex functions in terms of the non-Newtonian calculus which is a self-contained system independent of any other system of calculus. It is shown that there are infinitely many such useful types of weighted means and convex functions depending on the choice of generating functions. Moreover, some relations between classical weighted mean and its non-Newtonian version are compared and discussed in a table...
Bot, Radu Ioan
2010-01-01
A fruitful idea, when providing subdifferential formulae and dual representations for convex risk measures, is to make use of the conjugate duality theory in convex optimization. In this paper we underline the outstanding role played by the qualification conditions in the context of different problem formulations in this area. We show that not only the meanwhile classical generalized interiority point ones come here to bear, but also a recently introduced one formulated by means of the quasi-relative interior.
Directory of Open Access Journals (Sweden)
Messaoud Bounkhel
2015-01-01
Full Text Available The present paper is devoted to the study of the generalized projection πK:X∗→K, where X is a uniformly convex and uniformly smooth Banach space and K is a nonempty closed (not necessarily convex set in X. Our main result is the density of the points x∗∈X∗ having unique generalized projection over nonempty close sets in X. Some minimisation principles are also established. An application to variational problems with nonconvex sets is presented.
Messaoud Bounkhel
2015-01-01
The present paper is devoted to the study of the generalized projection πK:X∗→K, where X is a uniformly convex and uniformly smooth Banach space and K is a nonempty closed (not necessarily convex) set in X. Our main result is the density of the points x∗∈X∗ having unique generalized projection over nonempty close sets in X. Some minimisation principles are also established. An application to variational problems with nonconvex sets is presented.
Measure of Segments which Intersect a Convex Body from Rotational Formulae
Institute of Scientific and Technical Information of China (English)
Ximo GUAL-ARNAU; Silena HEROLD-GARC´IA
2015-01-01
Classical problems in integral geometry and geometric probability involve the kinematic measure of congruent segments of fixed length within a convex body in R3. We give this measure from rotational formulae; that is, from isotropic plane sections through a fixed point. From this result we also obtain a new rotational formula for the volume of a convex body;which is proved to be equivalent to the wedge formula for the volume.
Assessing 3-D Uncertain System Stability by Using MATLAB Convex Hull Functions
Mohammed Tawfik Hussein
2011-01-01
This paper is dealing with the robust stability of an uncertain three dimensional (3-D) system using existence MATLAB convex hull functions. Hence, the uncertain model of plant will be simulated by INTLAB Toolbox; furthermore, the root loci of the characteristic polynomials of the convex hull are obtained to judge whether the uncertain system is stable or not. A design third order example for uncertain parameters is given to validate the proposed approach.
Sharp Convex Bounds on the Aggregate Sums–An Alternative Proof
Directory of Open Access Journals (Sweden)
Chuancun Yin
2016-09-01
Full Text Available It is well known that a random vector with given marginals is comonotonic if and only if it has the largest convex sum, and that a random vector with given marginals (under an additional condition is mutually exclusive if and only if it has the minimal convex sum. This paper provides an alternative proof of these two results using the theories of distortion risk measure and expected utility.
Some Fejer Type Inequalities for Harmonically-Convex Functions with Applications to Special Means
Directory of Open Access Journals (Sweden)
M. A. Latif
2017-01-01
Full Text Available In this paper, the notion of harmonic symmetricity of functions is introduced. A new identity involving harmonically symmetric functions is established and some new Fejer type integral inequalities are presented for the class of harmonically convex functions. The results presented in this paper are better than those established in recent literature concerning harmonically convex functions. Applications of our results to special means of positive real numbers are given as well.
Cyclic pairs and common best proximity points in uniformly convex Banach spaces
Directory of Open Access Journals (Sweden)
Gabeleh Moosa
2017-06-01
Full Text Available In this article, we survey the existence, uniqueness and convergence of a common best proximity point for a cyclic pair of mappings, which is equivalent to study of a solution for a nonlinear programming problem in the setting of uniformly convex Banach spaces. Finally, we provide an extension of Edelstein’s fixed point theorem in strictly convex Banach spaces. Examples are given to illustrate our main conclusions.
On the rate of convergence for multi-category classification based on convex losses
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The multi-category classification algorithms play an important role in both theory and practice of machine learning.In this paper,we consider an approach to the multi-category classification based on minimizing a convex surrogate of the nonstandard misclassification loss.We bound the excess misclassification error by the excess convex risk.We construct an adaptive procedure to search the classifier and furthermore obtain its convergence rate to the Bayes rule.
Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces
Directory of Open Access Journals (Sweden)
Kim JongKyu
2010-01-01
Full Text Available The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi- -asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.
Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces
Directory of Open Access Journals (Sweden)
Shih-sen Chang
2010-01-01
Full Text Available The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi-ϕ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.
Acker, A.
Under reasonably general assumptions, we prove the existence of convex classical solutions for the Prandtl-Batchelor free boundary problem in fluid dynamics, in which a flow of constant vorticity density is embedded in a potential flow, with a vortex sheet of constant vorticity density as the flow interface. These results apply to Batchelor flows which are confined to a bounded, convex vessel, and for which the limiting interior flow-speed exceeds the limiting exterior flow-speed along the interface.
Xuewen Mu; Yaling Zhang
2015-01-01
An alternating direction method is proposed for convex quadratic second-order cone programming problems with bounded constraints. In the algorithm, the primal problem is equivalent to a separate structure convex 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 ...
Dolan, Thomas J
2014-01-01
Magnetic Fusion Technology describes the technologies that are required for successful development of nuclear fusion power plants using strong magnetic fields. These technologies include: ? magnet systems, ? plasma heating systems, ? control systems, ? energy conversion systems, ? advanced materials development, ? vacuum systems, ? cryogenic systems, ? plasma diagnostics, ? safety systems, and ? power plant design studies. Magnetic Fusion Technology will be useful to students and to specialists working in energy research.
Dolan, Thomas James
2013-01-01
Fusion Research, Volume I: Principles provides a general description of the methods and problems of fusion research. The book contains three main parts: Principles, Experiments, and Technology. The Principles part describes the conditions necessary for a fusion reaction, as well as the fundamentals of plasma confinement, heating, and diagnostics. The Experiments part details about forty plasma confinement schemes and experiments. The last part explores various engineering problems associated with reactor design, vacuum and magnet systems, materials, plasma purity, fueling, blankets, neutronics
A new method for automatically constructing convexity-preserving interpolatory splines
Institute of Scientific and Technical Information of China (English)
PAN Yongjuan; WANG Guojin
2004-01-01
Constructing a convexity-preserving interpolating curve according to the given planar data points is a problem to be solved in computer aided geometric design (CAGD). So far, almost all methods must solve a system of equations or recur to a complicated iterative process, and most of them can only generate some function-form convexity-preserving interpolating curves which are unaccommodated with the parametric curves, commonly used in CAGD systems. In order to overcome these drawbacks, this paper proposes a new method that can automatically generate some parametric convexity-preserving polynomial interpolating curves but dispensing with solving any system of equations or going at any iterative computation. The main idea is to construct a family of interpolating spline curves first with the shape parameter a as its family parameter; then, using the positive conditions of Bernstein polynomial to respectively find a range in which the shape parameter a takes its value for two cases of global convex data points and piecewise convex data points so as to make the corresponding interpolating curves convexity-preserving and C2(or G1) continuous. The method is simple and convenient, and the resulting interpolating curves possess smooth distribution of curvature. Numerical examples illustrate the correctness and the validity of theoretical reasoning.
Magnetic fusion reactor economics
Energy Technology Data Exchange (ETDEWEB)
Krakowski, R.A.
1995-12-01
An almost primordial trend in the conversion and use of energy is an increased complexity and cost of conversion systems designed to utilize cheaper and more-abundant fuels; this trend is exemplified by the progression fossil fission {yields} fusion. The present projections of the latter indicate that capital costs of the fusion ``burner`` far exceed any commensurate savings associated with the cheapest and most-abundant of fuels. These projections suggest competitive fusion power only if internal costs associate with the use of fossil or fission fuels emerge to make them either uneconomic, unacceptable, or both with respect to expensive fusion systems. This ``implementation-by-default`` plan for fusion is re-examined by identifying in general terms fusion power-plant embodiments that might compete favorably under conditions where internal costs (both economic and environmental) of fossil and/or fission are not as great as is needed to justify the contemporary vision for fusion power. Competitive fusion power in this context will require a significant broadening of an overly focused program to explore the physics and simbiotic technologies leading to more compact, simplified, and efficient plasma-confinement configurations that reside at the heart of an attractive fusion power plant.
Kikuchi, Mitsuru
2011-01-01
Frontiers in Fusion Research provides a systematic overview of the latest physical principles of fusion and plasma confinement. It is primarily devoted to the principle of magnetic plasma confinement, that has been systematized through 50 years of fusion research. Frontiers in Fusion Research begins with an introduction to the study of plasma, discussing the astronomical birth of hydrogen energy and the beginnings of human attempts to harness the Sun's energy for use on Earth. It moves on to chapters that cover a variety of topics such as: * charged particle motion, * plasma kinetic theory, *
Ongena, J.; Koch, R.; Wolf, R.; Zohm, H.
2016-05-01
Our modern society requires environmentally friendly solutions for energy production. Energy can be released not only from the fission of heavy nuclei but also from the fusion of light nuclei. Nuclear fusion is an important option for a clean and safe solution for our long-term energy needs. The extremely high temperatures required for the fusion reaction are routinely realized in several magnetic-fusion machines. Since the early 1990s, up to 16 MW of fusion power has been released in pulses of a few seconds, corresponding to a power multiplication close to break-even. Our understanding of the very complex behaviour of a magnetized plasma at temperatures between 150 and 200 million °C surrounded by cold walls has also advanced substantially. This steady progress has resulted in the construction of ITER, a fusion device with a planned fusion power output of 500 MW in pulses of 400 s. ITER should provide answers to remaining important questions on the integration of physics and technology, through a full-size demonstration of a tenfold power multiplication, and on nuclear safety aspects. Here we review the basic physics underlying magnetic fusion: past achievements, present efforts and the prospects for future production of electrical energy. We also discuss questions related to the safety, waste management and decommissioning of a future fusion power plant.
DEFF Research Database (Denmark)
Bulut, Sanja; Oskolkova, M. Z.; Schweins, R.
2010-01-01
We present an experimental study of vesicle fusion using light and neutron scattering to monitor fusion events. Vesicles are reproducibly formed with an extrusion procedure using an single amphiphile triethylene glycol mono-n-decyl ether in water. They show long-term stability for temperatures...... around 20 C, but at temperatures above 26 C we observe an increase in the scattered intensity due to fusion. The system is unusually well suited for the study of basic mechanisms of vesicle fusion. The vesicles are flexible with a bending rigidity of only a few k(H)T. The monolayer spontaneous curvature...
On the minima and convexity of Epstein zeta function
Lim, S. C.; Teo, L. P.
2008-07-01
Let Zn(s ;a1,…,an) be the Epstein zeta function defined as the meromorphic continuation of the function ∑k εZn{0}(∑i =1n[aiki]2)-s, Re s>n/2 to the complex plane. We show that for fixed s ≠n/2, the function Zn(s ;a1,…,an) as a function of (a1,…,an)ε(R+)n with fixed ∏i =1nai has a unique minimum at the point a1=⋯=an. When ∑i =1nci is fixed, the function (c1,…,cn)↦Zn(s ;ec1,…,ecn) can be shown to be a convex function of any (n -1) of the variables {c1,…,cn}. These results are then applied to the study of the sign of Zn(s ;a1,…,an) when s is in the critical range (0,n/2). It is shown that when 1≤n≤9, Zn(s ;a1,…,an) as a function of (a1,…,an)ε(R+)n can be both positive and negative for every s ε(0,n/2). When n ≥10, there are some open subsets In,+ of s ε(0,n/2), where Zn(s ;a1,…,an) is positive for all (a1,…,an)ε(R+)n. By regarding Zn(s ;a1,…,an) as a function of s, we find that when n ≥10, the generalized Riemann hypothesis is false for all (a1,…,an).
Asymptotic Performance of Sparse Signal Detection Using Convex Programming Method
Institute of Scientific and Technical Information of China (English)
LEI Chuan; ZHANG Jun
2012-01-01
The detection of sparse signals against background noise is considered.Detecting signals of such kind is difficult since only a small portion of the signal carries information.Prior knowledge is usually assumed to ease detection.In this paper,we consider the general unknown and arbitrary sparse signal detection problem when no prior knowledge is available.Under a Neyman-Pearson hypothesis-testing framework,a new detection scheme is proposed by combining a generalized likelihood ratio test (GLRT)-like test statistic and convex programming methods which directly exploit sparsity in an underdetermined system of linear equations.We characterize large sample behavior of the proposed method by analyzing its asymptotic performance.Specifically,we give the condition for the Chernoff-consistent detection which shows that the proposed method is very sensitive to the (e)2 norm energy of the sparse signals.Both the false alarm rate and the miss rate tend to zero at vanishing signal-to-noise ratio (SNR),as long as the signal energy grows at least logarithmically with the problem dimension.Next we give a large deviation analysis to characterize the error exponent for the Neyman-Pearson detection.We derive the oracle error exponent assuming signal knowledge.Then we explicitly derive the error exponent of the proposed scheme and compare it with the oracle exponent.We complement our study with numerical experiments,showing that the proposed method performs in the vicinity of the likelihood ratio test (LRT) method in the finite sample scenario and the error probability degrades exponentially with the number of observations.
Disc height and anteroposterior translation in fused and adjacent segments after lumbar spine fusion
Directory of Open Access Journals (Sweden)
Frobin, Wolfgang
2003-09-01
Full Text Available In a series of 46 patients the effects of spinal fusion upon intervertebral height and sagittal alignment in operated and non-operated segments were retrospectively evaluated on digitized radiographs. Data was compared with age- and gender-normalized standard values. The objective was to evaluate the influence of different types of spine fusions primarily upon adjacent segments, particularly in terms of degeneration and sagittal profile of the lumbar spine. Incidence of adjacent segment degeneration (ASD is still highly controversial. However, not every degeneration adjacent to spinal fusion must be caused by the fusion and responsibility of the fusion for ASD may vary with its range and type. Distortion Corrected Roentgen Analysis (DCRA was utilized. DCRA is a proven valid, reliable, observer-independent, and accurate tool for assessment of these parameters over time and in comparison with "normal" cohorts. With this method the exact posture of the patients needs not to be known.There was little evidence for serious fusion-related ASD within an average of 40 months follow-up. No difference could be detected for rigid vs. non-rigid fusion and instrumented vs. non-instrumented techniques. Temporary postoperative distraction effects could be detected in operated and non-operated segments. Absolute preoperative values for intervertebral height and vertebral slip were age-related. Retrospectively, the choice of segments for fusion was clearly based upon radiological criteria. Thus we conclude that radiological parameters have an obvious clinical relevance for decision-making and need to be quantified. Within the limitations of this pilot study, true fusion related ASD seems to be infrequent.
Directory of Open Access Journals (Sweden)
Lorraine Lillis
Full Text Available Sensitive diagnostic tests for infectious diseases often employ nucleic acid amplification technologies (NAATs. However, most NAAT assays, including many isothermal amplification methods, require power-dependent instrumentation for incubation. For use in low resource settings (LRS, diagnostics that do not require consistent electricity supply would be ideal. Recombinase polymerase amplification (RPA is an isothermal amplification technology that has been shown to typically work at temperatures ranging from 25-43°C, and does not require a stringent incubation temperature for optimal performance. Here we evaluate the ability to incubate an HIV-1 RPA assay, intended for use as an infant HIV diagnostic in LRS, at ambient temperatures or with a simple non-instrumented heat source. To determine the range of expected ambient temperatures in settings where an HIV-1 infant diagnostic would be of most use, a dataset of the seasonal range of daily temperatures in sub Saharan Africa was analyzed and revealed ambient temperatures as low as 10°C and rarely above 43°C. All 24 of 24 (100% HIV-1 RPA reactions amplified when incubated for 20 minutes between 31°C and 43°C. The amplification from the HIV-1 RPA assay under investigation at temperatures was less consistent below 30°C. Thus, we developed a chemical heater to incubate HIV-1 RPA assays when ambient temperatures are between 10°C and 30°C. All 12/12 (100% reactions amplified with chemical heat incubation from ambient temperatures of 15°C, 20°C, 25°C and 30°C. We also observed that incubation at 30 minutes improved assay performance at lower temperatures where detection was sporadic using 20 minutes incubation. We have demonstrated that incubation of the RPA HIV-1 assay via ambient temperatures or using chemical heaters yields similar results to using electrically powered devices. We propose that this RPA HIV-1 assay may not need dedicated equipment to be a highly sensitive tool to diagnose
Cell fusion and nuclear fusion in plants.
Maruyama, Daisuke; Ohtsu, Mina; Higashiyama, Tetsuya
2016-12-01
Eukaryotic cells are surrounded by a plasma membrane and have a large nucleus containing the genomic DNA, which is enclosed by a nuclear envelope consisting of the outer and inner nuclear membranes. Although these membranes maintain the identity of cells, they sometimes fuse to each other, such as to produce a zygote during sexual reproduction or to give rise to other characteristically polyploid tissues. Recent studies have demonstrated that the mechanisms of plasma membrane or nuclear membrane fusion in plants are shared to some extent with those of yeasts and animals, despite the unique features of plant cells including thick cell walls and intercellular connections. Here, we summarize the key factors in the fusion of these membranes during plant reproduction, and also focus on "non-gametic cell fusion," which was thought to be rare in plant tissue, in which each cell is separated by a cell wall.
Nuclear fusion inside condense matters
Institute of Scientific and Technical Information of China (English)
HE Jing-tang
2007-01-01
This article describes in detail the nuclear fusion inside condense matters--the Fleischmann-Pons effect, the reproducibility of cold fusions, self-consistentcy of cold fusions and the possible applications.
Fusion of biological membranes
Indian Academy of Sciences (India)
K Katsov; M Müller; M Schick
2005-06-01
The process of membrane fusion has been examined by Monte Carlo simulation, and is found to be very different than the conventional picture. The differences in mechanism lead to several predictions, in particular that fusion is accompanied by transient leakage. This prediction has recently been verified. Self-consistent field theory is applied to examine the free energy barriers in the different scenarios.
DEFF Research Database (Denmark)
Plascencia, Alfredo; Stepán, Petr
2006-01-01
The main contribution of this paper is to present a sensor fusion approach to scene environment mapping as part of a Sensor Data Fusion (SDF) architecture. This approach involves combined sonar array with stereo vision readings. Sonar readings are interpreted using probability density functions...
Complementary Advanced Fusion Exploration
2005-08-01
homographic computer vision image fusion, out-of-sequence measurement and track data handling, Nash bargaining approaches to sensor management... homographic fusion notions are identified together with the Nash approach, the pursuit-evasion approach to threat situation outcome determination, and the
Glasstone, Samuel
This publication is one of a series of information booklets for the general public published by The United States Atomic Energy Commission. Among the topics discussed are: Importance of Fusion Energy; Conditions for Nuclear Fusion; Thermonuclear Reactions in Plasmas; Plasma Confinement by Magnetic Fields; Experiments With Plasmas; High-Temperature…
Controlled thermonuclear fusion
Bobin, Jean Louis
2014-01-01
The book is a presentation of the basic principles and main achievements in the field of nuclear fusion. It encompasses both magnetic and inertial confinements plus a few exotic mechanisms for nuclear fusion. The state-of-the-art regarding thermonuclear reactions, hot plasmas, tokamaks, laser-driven compression and future reactors is given.
DEFF Research Database (Denmark)
Larsson, Lars-Inge; Bjerregaard, Bolette; Talts, Jan Fredrik
2008-01-01
Cell fusions are important to fertilization, placentation, development of skeletal muscle and bone, calcium homeostasis and the immune defense system. Additionally, cell fusions participate in tissue repair and may be important to cancer development and progression. A large number of factors appe...
CERN. Geneva
2015-01-01
Fusion research is currently to a large extent focused on tokamak (ITER) and inertial confinement (NIF) research. In addition to these large international or national efforts there are private companies performing fusion research using much smaller devices than ITER or NIF. The attempt to achieve fusion energy production through relatively small and compact devices compared to tokamaks decreases the costs and building time of the reactors and this has allowed some private companies to enter the field, like EMC2, General Fusion, Helion Energy, Lawrenceville Plasma Physics and Lockheed Martin. Some of these companies are trying to demonstrate net energy production within the next few years. If they are successful their next step is to attempt to commercialize their technology. In this presentation an overview of compact fusion reactor concepts is given.
Material Removal Model Considering Influence of Curvature Radius in Bonnet Polishing Convex Surface
Institute of Scientific and Technical Information of China (English)
SONG Jianfeng; YAO Yingxue
2015-01-01
The bonnet tool polishing is a novel, advanced and ultra-precise polishing process, by which the freeform surface can be polished. However, during the past few years, not only the key technology of calculating the dwell time and controlling the surface form in the bonnet polishing has been little reported so far, but also little attention has been paid to research the material removal function of the convex surface based on the geometry model considering the influence of the curvature radius. Firstly in this paper, for realizing the control of the freeform surface automatically by the bonnet polishing, on the basis of the simplified geometric model of convex surface, the calculation expression of the polishing contact spot on the convex surface considering the influence of the curvature radius is deduced, and the calculation model of the pressure distribution considering the influence of the curvature radius on the convex surface is derived by the coordinate transformation. Then the velocity distribution model is built in the bonnet polishing the convex surface. On the basis of the above research and the semi-experimental modified Preston equation obtained from the combination method of experimental and theoretical derivation, the material removal model of the convex surface considering the influence of the curvature radius in the bonnet polishing is established. Finally, the validity of the model through the simulation method has been validated. This research presents an effective prediction model and the calculation method of material removal for convex surface in bonnet polishing and prepares for the bonnet polishing the free surface numerically and automatically.
Energy Technology Data Exchange (ETDEWEB)
Badocco, Denis; Lavagnini, Irma; Mondin, Andrea; Tapparo, Andrea; Pastore, Paolo, E-mail: paolo.pastore@unipd.it
2015-05-01
In this paper the detection limit was estimated when signals were affected by two error contributions, namely instrumental errors and operational-non-instrumental errors. The detection limit was theoretically obtained following the hypothesis testing schema implemented with the calibration curve methodology. The experimental calibration design was based on J standards measured I times with non-instrumental errors affecting each standard systematically but randomly among the J levels. A two-component variance regression was performed to determine the calibration curve and to define the detection limit in these conditions. The detection limit values obtained from the calibration at trace levels of 41 elements by ICP-MS resulted larger than those obtainable from a one component variance regression. The role of the reagent impurities on the instrumental errors was ascertained and taken into account. Environmental pollution was studied as source of non-instrumental errors. The environmental pollution role was evaluated by Principal Component Analysis technique (PCA) applied to a series of nine calibrations performed in fourteen months. The influence of the seasonality of the environmental pollution on the detection limit was evidenced for many elements usually present in the urban air particulate. The obtained results clearly indicated the need of using the two-component variance regression approach for the calibration of all the elements usually present in the environment at significant concentration levels. - Highlights: • Limit of detection was obtained considering a two variance component regression. • Calibration data may be affected by instrumental and operational conditions errors. • Calibration model was applied to determine 41 elements at trace level by ICP-MS. • Non instrumental errors were evidenced by PCA analysis.
Pratt, J; Müller, W -C; Chapman, S C; Watkins, N W
2016-01-01
We investigate the utility of the convex hull to analyze physical questions related to the dispersion of a group of much more than four Lagrangian tracer particles in a turbulent flow. Validation of standard dispersion behaviors is a necessary preliminary step for use of the convex hull to describe turbulent flows. In simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection we show that the convex hull can be used to reasonably capture the dispersive behavior of a large group of tracer particles. We validate dispersion results produced with convex hull analysis against scalings for Lagrangian particle pair dispersion. In addition to this basic validation study, we show that convex hull analysis provides information that particle pair dispersion does not, in the form of a extreme value statistics, surface area, and volume for a cluster of particles. We use the convex hull surface area and volume to examine the degree of...
Patient Reported Outcomes from Sacroiliac Joint Fusion
McGowan, Shane M.; Audley, Brittany N.; Sokunbi, Gbolabo; Puccio, Steven T.
2017-01-01
radicular pain. Conclusions Percutaneous SIJ fusion offers minimal morbidity and acceptable functional outcomes. While women and those with a prior history of lumbar instrumentation may be at increased risk of having SIJ dysfunction requiring surgical intervention, it was not found to affect postoperative functional outcomes when compared to the non-instrumented group. PMID:28243380
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.
Ogawa, Yuichi
2016-05-01
A new strategic energy plan decided by the Japanese Cabinet in 2014 strongly supports the steady promotion of nuclear fusion development activities, including the ITER project and the Broader Approach activities from the long-term viewpoint. Atomic Energy Commission (AEC) in Japan formulated the Third Phase Basic Program so as to promote an experimental fusion reactor project. In 2005 AEC has reviewed this Program, and discussed on selection and concentration among many projects of fusion reactor development. In addition to the promotion of ITER project, advanced tokamak research by JT-60SA, helical plasma experiment by LHD, FIREX project in laser fusion research and fusion engineering by IFMIF were highly prioritized. Although the basic concept is quite different between tokamak, helical and laser fusion researches, there exist a lot of common features such as plasma physics on 3-D magnetic geometry, high power heat load on plasma facing component and so on. Therefore, a synergetic scenario on fusion reactor development among various plasma confinement concepts would be important.
Trading Regret for Efficiency: Online Convex Optimization with Long Term Constraints
Mahdavi, Mehrdad; Yang, Tianbao
2011-01-01
In this paper we propose a framework for solving constrained online convex optimization problem. Our motivation stems from the observation that most algorithms proposed for online convex optimization require a projection onto the convex set $\\mathcal{K}$ from which the decisions are made. While for simple shapes (e.g. Euclidean ball) the projection is straightforward, for arbitrary complex sets this is the main computational challenge and may be inefficient in practice. In this paper, we consider an alternative online convex optimization problem. Instead of requiring decisions belong to $\\mathcal{K}$ for all rounds, we only require that the constraints which define the set $\\mathcal{K}$ be satisfied in the long run. We show that our framework can be utilized to solve a relaxed version of online learning with side constraints addressed in \\cite{DBLP:conf/colt/MannorT06} and \\cite{DBLP:conf/aaai/KvetonYTM08}. By turning the problem into an online convex-concave optimization problem, we propose an efficient algo...
Switched Systems Reduction Framework Based on Convex Combination of Generalized Gramians
Directory of Open Access Journals (Sweden)
Hamid Reza Shaker
2009-01-01
Full Text Available A general method for model-order reduction of switched linear dynamical systems is presented. The proposed technique uses convex generalized gramian which is a convex combination of the generalized gramians. It is shown that different classical reduction methods can be developed into the generalized gramian framework for model reduction of linear systems and further for the reduction of switched systems by construction of the convex generalized gramian. Balanced reduction within specified frequency bound is taken as an example which is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, convex generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the method preserves the stability of the original switched system at least for stabilizing switching signal and it is also less conservative than the method which is based on the common generalized gramian. Some discussions on the coefficient of the vertices of the convex variables are presented. The performance of the proposed method is illustrated by numerical examples.
Phase behaviour and gravity-directed self assembly of hard convex spherical caps.
McBride, John M; Avendaño, Carlos
2017-03-08
We investigate the phase behaviour and self-assembly of convex spherical caps using Monte Carlo simulations. This model is used to represent the main features observed in experimental colloidal particles with mushroom-cap shape [Riley et al., Langmuir, 2010, 26, 1648]. The geometry of this non-centrosymmetric convex model is fully characterized by the aspect ratio χ* defined as the spherical cap height to diameter ratio. We use NPT Monte Carlo simulations combined with free energy calculations to determine the most stable crystal structures and the phase behaviour of convex spherical caps with different aspect ratios. We find a variety of crystal structures at each aspect ratio, including plastic and dimer-based crystals; small differences in chemical potential between the structures with similar morphology suggest that convex spherical caps have the tendency to form polycrystalline phases rather than crystallising into a single uniform structure. With the exception of plastic crystals observed at large aspect ratios (χ* > 0.75), crystallisation kinetics seem to be too slow, hindering the spontaneous formation of ordered structures. As an alternative, we also present a study of directing the self-assembly of convex spherical caps via sedimentation onto solid substrates. This study contributes to show how small changes to particle shape can significantly alter the self-assembly of crystal structures, and how a simple gravity field and a template can substantially enhance the process.
On growth and covering theorems of quasi-convex mappings in the unit ball of a complex Banach space
Institute of Scientific and Technical Information of China (English)
张文俊; 刘太顺
2002-01-01
A class of biholomorphic mappings named "quasi-convex mapping" is introduced in the unitball of a complex Banach space. It is proved that this class of mappings is a proper subset of the class ofstarlike mappings and contains the class of convex mappings properly, and it has the same growth and coveringtheorems as the convex mappings. Furthermore, when the Banach space is confined to Cn, the "quasi-convexmapping" is exactly the "quasi-convex mapping of type A" introduced by K. A. Roper and T. J. Suffridge.
Dinh, Quoc Tran; Michiels, Wim; Diehl, Moritz
2011-01-01
A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem.Applications to various output feedback controller synthesis problems are presented. In these applications the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from COMPleib library.
Directory of Open Access Journals (Sweden)
Cui Yunan
2011-01-01
Full Text Available Abstract Uniformly convex W-hyperbolic spaces with monotone modulus of uniform convexity are a natural generalization of both uniformly convexnormed spaces and CAT(0 spaces. In this article, we discuss the existence of fixed points and demiclosed principle for mappings of asymptotically non-expansive type in uniformly convex W-hyperbolic spaces with monotone modulus of uniform convexity. We also obtain a Δ-convergence theorem of Krasnoselski-Mann iteration for continuous mappings of asymptotically nonexpansive type in CAT(0 spaces. MSC: 47H09; 47H10; 54E40
Control of Fusion and Solubility in Fusion Systems
Craven, David A
2009-01-01
In this article, we consider the control of fusion in fusion systems, proving three previously known, non-trivial results in a new, largely elementary way. We then reprove a result of Aschbacher, that the product of two strongly closed subgroups is strongly closed; to do this, we consolidate the theory of quotients of fusion systems into a consistent theory. We move on considering p-soluble fusion systems, and prove that they are constrained, allowing us to effectively characterize fusion systems of p-soluble groups. This leads us to recast Thompson Factorization for Qd(p)-free fusion systems, and consider Thompson Factorization for more general fusion systems.
Alparone, Luciano; Baronti, Stefano; Garzelli, Andrea
2015-01-01
A synthesis of more than ten years of experience, Remote Sensing Image Fusion covers methods specifically designed for remote sensing imagery. The authors supply a comprehensive classification system and rigorous mathematical description of advanced and state-of-the-art methods for pansharpening of multispectral images, fusion of hyperspectral and panchromatic images, and fusion of data from heterogeneous sensors such as optical and synthetic aperture radar (SAR) images and integration of thermal and visible/near-infrared images. They also explore new trends of signal/image processing, such as
Directory of Open Access Journals (Sweden)
T. Venkata Rama Krishna
2008-01-01
Full Text Available This paper presented a theoretical and numerical assessment for nonidentical segmented exponential- (NISE- convex and NISE-concave serrated plane CATRs by changing number of serrations. The investigation was based on diffraction theory and, more specifically, on the diffraction formulation of Fresnel. The compact antenna test range (CATR provides uniform illumination within the Fresnel region to the test antenna. Application of serrated edges has been shown to be a good method to control diffraction at the edges of the reflectors. In this paper, the Fresnel fields of NISE-convex and NISE-concave serrated CATRs are analyzed using physical optics (PO technique. The PO analysis is applied in this paper for plane reflector serrated CATR only. The same analysis is applied to any type of reflector. In this paper, lens-based reflector is not considered. It is observed that NISE-concave serrated CATR gives less ripple and enhanced quiet zone width than NISE-convex.
A New Hybrid Shuffled Frog Leaping Algorithm to Solve Non-convex Economic Load Dispatch Problem
Directory of Open Access Journals (Sweden)
Ehsan Bijami
2011-11-01
Full Text Available This paper presents a New Hybrid Shuffled Frog Leaping (NHSFL algorithm applied to solve Economic Load Dispatch (ELD problem. Practical ELD has non-convex cost function and various equality and inequality constraints that convert the ELD problem as a nonlinear, non-convex and non-smooth optimization problem. In this paper, a new frog leaping rule is proposed to improve the local exploration and the performance of the conventional SFL algorithm. Also a genetic mutation operator is used for the creation of new frogs instead of random frog creation that improves the convergence. To show the efficiency of the proposed approach, the non-convex ELD problem is solved using conventional SFL and an improved SFL method proposed by other researchers. Then the results of SFL methods are compared to the results obtained by the proposed NHSFL algorithm. Simulation studies show that the results obtained by NHSFL are more effective and better compared with these algorithms.
The role of convexity for solving some shortest path problems in plane without triangulation
An, Phan Thanh; Hai, Nguyen Ngoc; Hoai, Tran Van
2013-09-01
Solving shortest path problems inside simple polygons is a very classical problem in motion planning. To date, it has usually relied on triangulation of the polygons. The question: "Can one devise a simple O(n) time algorithm for computing the shortest path between two points in a simple polygon (with n vertices), without resorting to a (complicated) linear-time triangulation algorithm?" raised by J. S. B. Mitchell in Handbook of Computational Geometry (J. Sack and J. Urrutia, eds., Elsevier Science B.V., 2000), is still open. The aim of this paper is to show that convexity contributes to the design of efficient algorithms for solving some versions of shortest path problems (namely, computing the convex hull of a finite set of points and convex rope on rays in 2D, computing approximate shortest path between two points inside a simple polygon) without triangulation on the entire polygons. New algorithms are implemented in C and numerical examples are presented.
Lp stability for entropy solutions of scalar conservation laws with strict convex flux
Adimurthi; Ghoshal, Shyam Sundar; Veerappa Gowda, G. D.
Here we consider the scalar convex conservation laws in one space dimension with strictly convex flux which is in C1. Existence, uniqueness and L1 contractivity were proved by Kružkov [14]. Using the relative entropy method, Leger showed that for a uniformly convex flux and for the shock wave solutions, the L2 norm of a perturbed solution relative to the shock wave is bounded by the L2 norm of the initial perturbation. Here we generalize the result to Lp norm for all 1⩽p<∞. Also we show that for the non-shock wave solution, Lp norm of the perturbed solution relative to the modified N-wave is bounded by the Lp norm of the initial perturbation for all 1⩽p<∞.
Local polynomial convexity of the union of two totally real surfaces at their intersection
Gorai, Sushil
2010-01-01
We consider the following question: Let $S_1$ and $S_2$ be two smooth, totally-real surfaces in $\\mathbb{C}^2$ that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is $S_1 \\cup S_2$ locally polynomially convex at the origin? If $T_0S_1 \\cap T_0S_2=\\{0\\}$, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dimension of $T_0S_1 \\cap T_0S_2$ over the field of real numbers is 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.
A high-performance feedback neural network for solving convex nonlinear programming problems.
Leung, Yee; Chen, Kai-Zhou; Gao, Xing-Bao
2003-01-01
Based on a new idea of successive approximation, this paper proposes a high-performance feedback neural network model for solving convex nonlinear programming problems. Differing from existing neural network optimization models, no dual variables, penalty parameters, or Lagrange multipliers are involved in the proposed network. It has the least number of state variables and is very simple in structure. In particular, the proposed network has better asymptotic stability. For an arbitrarily given initial point, the trajectory of the network converges to an optimal solution of the convex nonlinear programming problem under no more than the standard assumptions. In addition, the network can also solve linear programming and convex quadratic programming problems, and the new idea of a feedback network may be used to solve other optimization problems. Feasibility and efficiency are also substantiated by simulation examples.
Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures
Bobkov, Sergey
2011-01-01
We develop a reverse entropy power inequality for convex measures, which may be seen as an affine-geometric inverse of the entropy power inequality of Shannon and Stam. The specialization of this inequality to log-concave measures may be seen as a version of Milman's reverse Brunn-Minkowski inequality. The proof relies on a demonstration of new relationships between the entropy of high dimensional random vectors and the volume of convex bodies, and on a study of effective supports of convex measures, both of which are of independent interest, as well as on Milman's deep technology of $M$-ellipsoids and on certain information-theoretic inequalities. As a by-product, we also give a continuous analogue of some Pl\\"unnecke-Ruzsa inequalities from additive combinatorics.
Schur-Convexity for a Class of Symmetric Functions and Its Applications
Directory of Open Access Journals (Sweden)
Wei-Feng Xia
2009-01-01
Full Text Available For x=(x1,x2,…,xn∈R+n, the symmetric function ϕn(x,r is defined by ϕn(x,r=ϕn(x1,x2,…,xn;r=∏1≤i1
Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach
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Rodman, Leiba [Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795 (United States); Spitkovsky, Ilya M., E-mail: ims2@nyu.edu, E-mail: ilya@math.wm.edu [Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795 (United States); Division of Science and Mathematics, New York University Abu Dhabi, Saadiyat Island, P.O. Box 129188, Abu Dhabi (United Arab Emirates); Szkoła, Arleta, E-mail: szkola@mis.mpg.de; Weis, Stephan, E-mail: maths@stephan-weis.info [Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig (Germany)
2016-01-15
We study the continuity of an abstract generalization of the maximum-entropy inference—a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for 3 × 3 matrices.
On the Convexity of the MSE Region of Single-Antenna Users
Hunger, Raphael
2008-01-01
We prove convexity of the sum-power constrained mean square error (MSE) region in case of two single-antenna users communicating with a multi-antenna base station. Due to the MSE duality this holds both for the vector broadcast channel and the dual multiple access channel. Increasing the number of users to more than two, we show by means of a simple counter-example that the resulting MSE region is not necessarily convex any longer, even under the assumption of single-antenna users. In conjunction with our former observation that the two user MSE region is not necessarily convex for two multi-antenna users, this extends and corrects the hitherto existing notion of the MSE region geometry.
Non-convex prior image constrained compressed sensing (NC-PICCS)
Ramírez Giraldo, Juan Carlos; Trzasko, Joshua D.; Leng, Shuai; McCollough, Cynthia H.; Manduca, Armando
2010-04-01
The purpose of this paper is to present a new image reconstruction algorithm for dynamic data, termed non-convex prior image constrained compressed sensing (NC-PICCS). It generalizes the prior image constrained compressed sensing (PICCS) algorithm with the use of non-convex priors. Here, we concentrate on perfusion studies using computed tomography examples in simulated phantoms (with and without added noise) and in vivo data, to show how the NC-PICCS method holds potential for dramatic reductions in radiation dose for time-resolved CT imaging. We show that NC-PICCS can provide additional undersampling compared to conventional convex compressed sensing and PICCS, as well as, faster convergence under a quasi-Newton numerical solver.
Sampling Based Average Classifier Fusion
Directory of Open Access Journals (Sweden)
Jian Hou
2014-01-01
fusion algorithms have been proposed in literature, average fusion is almost always selected as the baseline for comparison. Little is done on exploring the potential of average fusion and proposing a better baseline. In this paper we empirically investigate the behavior of soft labels and classifiers in average fusion. As a result, we find that; by proper sampling of soft labels and classifiers, the average fusion performance can be evidently improved. This result presents sampling based average fusion as a better baseline; that is, a newly proposed classifier fusion algorithm should at least perform better than this baseline in order to demonstrate its effectiveness.