#### Sample records for convex mirrors

1. Improved methods for dewarping images in convex mirrors in fine art: applications to van Eyck and Parmigianino

Usami, Yumi; Stork, David G.; Fujiki, Jun; Hino, Hideitsu; Akaho, Shotaro; Murata, Noboru

2011-03-01

We derive and demonstrate new methods for dewarping images depicted in convex mirrors in artwork and for estimating the three-dimensional shapes of the mirrors themselves. Previous methods were based on the assumption that mirrors were spherical or paraboloidal, an assumption unlikely to hold for hand-blown glass spheres used in early Renaissance art, such as Johannes van Eyck's Portrait of Giovanni (?) Arnolfini and his wife (1434) and Robert Campin's Portrait of St. John the Baptist and Heinrich von Werl (1438). Our methods are more general than such previous methods in that we assume merely that the mirror is radially symmetric and that there are straight lines (or colinear points) in the actual source scene. We express the mirror's shape as a mathematical series and pose the image dewarping task as that of estimating the coefficients in the series expansion. Central to our method is the plumbline principle: that the optimal coefficients are those that dewarp the mirror image so as to straighten lines that correspond to straight lines in the source scene. We solve for these coefficients algebraically through principal component analysis, PCA. Our method relies on a global figure of merit to balance warping errors throughout the image and it thereby reduces a reliance on the somewhat subjective criterion used in earlier methods. Our estimation can be applied to separate image annuli, which is appropriate if the mirror shape is irregular. Once we have found the optimal image dewarping, we compute the mirror shape by solving a differential equation based on the estimated dewarping function. We demonstrate our methods on the Arnolfini mirror and reveal a dewarped image superior to those found in prior work|an image noticeably more rectilinear throughout and having a more coherent geometrical perspective and vanishing points. Moreover, we find the mirror deviated from spherical and paraboloidal shape; this implies that it would have been useless as a concave

2. Mirroring

Wegener, Charlotte; Wegener, Gregers

2016-01-01

and metaphorical value of mirroring for creativity theory across two different research fields — neuroscience and learning. We engage in a mutual (possibly creative) exploration of mirroring from ‘mirror neurons’ to mirroring in social learning theory. One of the most fascinating aspects of mirroring...... as a neurobiological and as a learning phenomenon is that it points to the embodied and unconscious aspects of social interaction. Thus, mirroring should not be reduced to the non-creative, mechanical repetition of the original, outstanding creativity. To mirror is a human capability built into our capacity to create......Most definitions of creativity emphasise originality. The creative product is recognised as distinct from other products and the creative person as someone who stands out from the crowd. What tend to be overlooked are acts of mirroring as a crucial element of the creative process. The human ability...

M. Gaspar, Raquel; Murgoci, Agatha

2010-01-01

A convexity adjustment (or convexity correction) in fixed income markets arises when one uses prices of standard (plain vanilla) products plus an adjustment to price nonstandard products. We explain the basic and appealing idea behind the use of convexity adjustments and focus on the situations...

Lauritzen, Niels

-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point......Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier...

Lauritzen, Niels

Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier-Motzkin elimin......Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier......-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point...... algorithm....

6. Convex analysis

Rockafellar, Ralph Tyrell

2015-01-01

Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and

Lauritzen, Niels

Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier-Motzkin elimin...

8. Convex surfaces

Busemann, Herbert

2008-01-01

This exploration of convex surfaces focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. It also examines intrinsic geometry and the realization of intrinsic metrics. 1958 edition.

9. Convex polytopes

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...

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

11. Convex Lattice Polygons

Scott, Paul

2006-01-01

A "convex" polygon is one with no re-entrant angles. Alternatively one can use the standard convexity definition, asserting that for any two points of the convex polygon, the line segment joining them is contained completely within the polygon. In this article, the author provides a solution to a problem involving convex lattice polygons.

12. Two-convex polygons

Aichholzer, Oswin; Aurenhammer, Franz; Hurtado Díaz, Fernando Alfredo; Ramos, Pedro A.; Urrutia, J.

2009-01-01

We introduce a notion of k-convexity and explore some properties of polygons that have this property. In particular, 2-convex polygons can be recognized in O(n log n) time, and k-convex polygons can be triangulated in O(kn) time.

13. Analytic aspects of convexity

Colesanti, Andrea; Gronchi, Paolo

2018-01-01

This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016. It offers a collection of selected articles, written by some of the world’s leading experts in the field of Convex Geometry, on recent developments in this area: theory of valuations; geometric inequalities; affine geometry; and curvature measures. The book will be of interest to a broad readership, from those involved in Convex Geometry, to those focusing on Functional Analysis, Harmonic Analysis, Differential Geometry, or PDEs. The book is a addressed to PhD students and researchers, interested in Convex Geometry and its links to analysis.

14. Theory of convex structures

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

15. Convexity and Marginal Vectors

van Velzen, S.; Hamers, H.J.M.; Norde, H.W.

2002-01-01

In this paper we construct sets of marginal vectors of a TU game with the property that if the marginal vectors from these sets are core elements, then the game is convex.This approach leads to new upperbounds on the number of marginal vectors needed to characterize convexity.An other result is that

16. Convex Interval Games

Alparslan-Gok, S.Z.; Brânzei, R.; Tijs, S.H.

2008-01-01

In this paper, convex interval games are introduced and some characterizations are given. Some economic situations leading to convex interval games are discussed. The Weber set and the Shapley value are defined for a suitable class of interval games and their relations with the interval core for

17. Dynamic Planar Convex Hull

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....

18. Stereotype locally convex spaces

Akbarov, S S

2000-01-01

We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis

19. Stereotype locally convex spaces

Akbarov, S S

2000-08-31

We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.

20. Stereotype locally convex spaces

Akbarov, S. S.

2000-08-01

We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.

1. Generalized Convexity and Inequalities

Anderson, G. D.; Vamanamurthy, M. K.; Vuorinen, M.

2007-01-01

Let R+ = (0,infinity) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 in M, we say that a function f : R+ to R+ is (m1,m2)-convex if f(m1(x,y)) < or = m2(f(x),f(y)) for all x, y in R+ . The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m1,m2)-convexity on m1 and m2 and give sufficient conditions for (m1,m2)-convexity of functions defined...

2. Dynamic Planar Convex Hull

Brodal, Gerth Stølfting; Jacob, Rico

2002-01-01

In this paper we determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage of the d......In this paper we determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage...... of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects...... the convex hull, and the tangent queries to determine whether a given point is inside the convex hull. We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure....

3. Notions of convexity

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...

4. Some Aspects of Convexity

for all t E [0,1] and all x, y (in the domain of definition of f). ... Proof: (a) is a consequence of the definition. (b) Define conv(S) ... More generally, a set F is said to be a face of the convex .... and bounded, and assume the validity (for a proof, see.

5. Convex Optimization in R

Roger Koenker

2014-09-01

Full Text Available Convex optimization now plays an essential role in many facets of statistics. We briefly survey some recent developments and describe some implementations of these methods in R . Applications of linear and quadratic programming are introduced including quantile regression, the Huber M-estimator and various penalized regression methods. Applications to additively separable convex problems subject to linear equality and inequality constraints such as nonparametric density estimation and maximum likelihood estimation of general nonparametric mixture models are described, as are several cone programming problems. We focus throughout primarily on implementations in the R environment that rely on solution methods linked to R, like MOSEK by the package Rmosek. Code is provided in R to illustrate several of these problems. Other applications are available in the R package REBayes, dealing with empirical Bayes estimation of nonparametric mixture models.

6. On convex complexity measures

Hrubeš, P.; Jukna, S.; Kulikov, A.; Pudlák, Pavel

2010-01-01

Roč. 411, 16-18 (2010), s. 1842-1854 ISSN 0304-3975 R&D Projects: GA AV ČR IAA1019401 Institutional research plan: CEZ:AV0Z10190503 Keywords : boolean formula * complexity measure * combinatorial rectangle * convexity Subject RIV: BA - General Mathematics Impact factor: 0.838, year: 2010 http://www.sciencedirect.com/science/article/pii/S0304397510000885

7. Subordination by convex functions

Rosihan M. Ali

2006-01-01

Full Text Available For a fixed analytic function g(z=z+∑n=2∞gnzn defined on the open unit disk and γ<1, let Tg(γ denote the class of all analytic functions f(z=z+∑n=2∞anzn satisfying ∑n=2∞|angn|≤1−γ. For functions in Tg(γ, a subordination result is derived involving the convolution with a normalized convex function. Our result includes as special cases several earlier works.

8. Convex games versus clan games

Brânzei, R.; Dimitrov, D.A.; Tijs, S.H.

2008-01-01

In this paper we provide characterizations of convex games and total clan games by using properties of their corresponding marginal games. We show that a "dualize and restrict" procedure transforms total clan games with zero worth for the clan into monotonic convex games. Furthermore, each monotonic

9. 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

10. Convexity Adjustments for ATS Models

Murgoci, Agatha; Gaspar, Raquel M.

. As a result we classify convexity adjustments into forward adjustments and swaps adjustments. We, then, focus on affine term structure (ATS) models and, in this context, conjecture convexity adjustments should be related of affine functionals. In the case of forward adjustments, we show how to obtain exact...

11. Nested convex bodies are chaseable

N. Bansal (Nikhil); M. Böhm (Martin); M. Eliáš (Marek); G. Koumoutsos (Grigorios); S.W. Umboh (Seeun William)

2018-01-01

textabstractIn the Convex Body Chasing problem, we are given an initial point v0 2 Rd and an online sequence of n convex bodies F1; : : : ; Fn. When we receive Fi, we are required to move inside Fi. Our goal is to minimize the total distance traveled. This fundamental online problem was first

12. θ-convex nonlinear programming problems

Emam, T.

2008-01-01

A class of sets and a class of functions called θ-convex sets and θ-convex functions are introduced by relaxing the definitions of convex sets and operator θ on the sets and domain of definition of the functions. The optimally results for θ-convex programming problems are established.

13. A class of free locally convex spaces

Sipacheva, O V

2003-01-01

Stratifiable spaces are a natural generalization of metrizable spaces for which Dugundji's theorem holds. It is proved that the free locally convex space of a stratifiable space is stratifiable. This means, in particular, that the space of finitely supported probability measures on a stratifiable space is a retract of a locally convex space, and that each stratifiable convex subset of a locally convex space is a retract of a locally convex space

14. Geometry of isotropic convex bodies

Brazitikos, Silouanos; Valettas, Petros; Vritsiou, Beatrice-Helen

2014-01-01

The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lov�sz-Simonovits conjecture. This book prov...

15. A new convexity measure for polygons.

Zunic, Jovisa; Rosin, Paul L

2004-07-01

Abstract-Convexity estimators are commonly used in the analysis of shape. In this paper, we define and evaluate a new convexity measure for planar regions bounded by polygons. The new convexity measure can be understood as a "boundary-based" measure and in accordance with this it is more sensitive to measured boundary defects than the so called "area-based" convexity measures. When compared with the convexity measure defined as the ratio between the Euclidean perimeter of the convex hull of the measured shape and the Euclidean perimeter of the measured shape then the new convexity measure also shows some advantages-particularly for shapes with holes. The new convexity measure has the following desirable properties: 1) the estimated convexity is always a number from (0, 1], 2) the estimated convexity is 1 if and only if the measured shape is convex, 3) there are shapes whose estimated convexity is arbitrarily close to 0, 4) the new convexity measure is invariant under similarity transformations, and 5) there is a simple and fast procedure for computing the new convexity measure.

16. NP-completeness of weakly convex and convex dominating set decision problems

Joanna Raczek

2004-01-01

Full Text Available The convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are \\(NP\\-complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can verify in polynomial time whether a given subset of vertices of a graph is convex or weakly convex.

17. Chromatic aberrations of two-electrode transaxial mirrors

Bejzina, L.G.; Karetskaya, S.P.

1991-01-01

Second order chromatic aberrations of electrostatic two-electrode transaxial mirrors in case the beam axial trajectory of charged particles is curvilinear are considered. Interrelations between coefficients of linear and angular chromatic aberrations are determined. Values of these coefficients for concave and convex transaxial mirrors with plane electrodes in dependence on potential ratio on electrodes by different onnular clearance radii are presented

18. Nonsmooth Mechanics and Convex Optimization

Kanno, Yoshihiro

2011-01-01

"This book concerns matter that is intrinsically difficult: convex optimization, complementarity and duality, nonsmooth analysis, linear and nonlinear programming, etc. The author has skillfully introduced these and many more concepts, and woven them into a seamless whole by retaining an easy and consistent style throughout. The book is not all theory: There are many real-life applications in structural engineering, cable networks, frictional contact problems, and plasticity! I recommend it to any reader who desires a modern, authoritative account of nonsmooth mechanics and convex optimiz

19. Quantum information and convex optimization

Reimpell, Michael

2008-01-01

This thesis is concerned with convex optimization problems in quantum information theory. It features an iterative algorithm for optimal quantum error correcting codes, a postprocessing method for incomplete tomography data, a method to estimate the amount of entanglement in witness experiments, and it gives necessary and sufficient criteria for the existence of retrodiction strategies for a generalized mean king problem. (orig.)

20. On the Moduli of Convexity

Guirao, A. J.; Hájek, Petr Pavel

2007-01-01

Roč. 135, č. 10 (2007), s. 3233-3240 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190502 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach spaces * moduli of convexity * uniformly rotund norms Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007

1. Quantum information and convex optimization

Reimpell, Michael

2008-07-01

This thesis is concerned with convex optimization problems in quantum information theory. It features an iterative algorithm for optimal quantum error correcting codes, a postprocessing method for incomplete tomography data, a method to estimate the amount of entanglement in witness experiments, and it gives necessary and sufficient criteria for the existence of retrodiction strategies for a generalized mean king problem. (orig.)

2. Convexity of the effective potential

1978-01-01

The effective potential V(phi) in field theories is a convex function of phi. V(lambda phi 1 + (1 - lambda)phi 2 ) less than or equal to lambdaV(phi 1 ) + (1 - lambda)V(phi 2 ), 0 less than or equal to lambda less than or equal to 1, all phi 1 , phi 2 . A linear interpolation of V(phi) is always larger than or equal to V(phi). There are numerous examples in the tree approximation and in perturbation theory for which this is not the case, the most notorious example being the double dip potential. More complete solutions may or may not show this property automatically. However, a non-convex V(phi) simply indicates that an unstable vacuum state was used in implementing the definition of V(phi). A strict definition will instruct one to replace V(phi) with its linear interpolation in such a way as to make it convex. (Alternatively one can just as well take the view that V(phi) is undefined in these domains.) In this note, attention is called to a very simple argument for convexity based on a construction described by H. Callen in his classic book Thermodynamics

3. Einstein's Mirror

Gjurchinovski, Aleksandar; Skeparovski, Aleksandar

2008-01-01

Reflection of light from a plane mirror in uniform rectilinear motion is a century-old problem, intimately related to the foundations of special relativity. The problem was first investigated by Einstein in his famous 1905 paper by using the Lorentz transformations to switch from the mirror's rest frame to the frame where the mirror moves at a…

4. Chiral mirrors

Plum, Eric; Zheludev, Nikolay I.

2015-01-01

Mirrors are used in telescopes, microscopes, photo cameras, lasers, satellite dishes, and everywhere else, where redirection of electromagnetic radiation is required making them arguably the most important optical component. While conventional isotropic mirrors will reflect linear polarizations without change, the handedness of circularly polarized waves is reversed upon reflection. Here, we demonstrate a type of mirror reflecting one circular polarization without changing its handedness, while absorbing the other. The polarization-preserving mirror consists of a planar metasurface with a subwavelength pattern that cannot be superimposed with its mirror image without being lifted out of its plane, and a conventional mirror spaced by a fraction of the wavelength from the metasurface. Such mirrors enable circularly polarized lasers and Fabry-Pérot cavities with enhanced tunability, gyroscopic applications, polarization-sensitive detectors of electromagnetic waves, and can be used to enhance spectroscopies of chiral media

5. 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

6. A noncommutative convexity in C*-bimodules

Mohsen Kian

2017-02-01

Full Text Available Let A and B be C*-algebras. We consider a noncommutative convexity in Hilbert A-B-bimodules, called A-B-convexity, as a generalization of C*-convexity in C*-algebras. We show that if X is a Hilbert A-B-bimodule, then Mn(X is a Hilbert Mn(A-Mn(B-bimodule and apply it to show that the closed unit ball of every Hilbert A-B-bimodule is A-B-convex. Some properties of this kind of convexity and various examples have been given.

7. Quantum logics and convex geometry

Bunce, L.J.; Wright, J.D.M.

1985-01-01

The main result is a representation theorem which shows that, for a large class of quantum logics, a quantum logic, Q, is isomorphic to the lattice of projective faces in a suitable convex set K. As an application we extend our earlier results, which, subject to countability conditions, gave a geometric characterization of those quantum logics which are isomorphic to the projection lattice of a von Neumann algebra or a JBW-algebra. (orig.)

8. Learning Convex Inference of Marginals

Domke, Justin

2012-01-01

Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this paper, the inference process is first defined to be the minimization of a convex function, inspired by free energy approximations. Learning is then done directly in terms of the performance of the inference process at univariate marginal prediction. The main ...

9. Diameter 2 properties and convexity

Abrahamsen, T. A.; Hájek, Petr Pavel; Nygaard, O.; Talponen, J.; Troyanski, S.

2016-01-01

Roč. 232, č. 3 (2016), s. 227-242 ISSN 0039-3223 R&D Projects: GA ČR GA16-07378S Institutional support: RVO:67985840 Keywords : diameter 2 property * midpoint locally uniformly rotund * Daugavet property Subject RIV: BA - General Mathematics Impact factor: 0.535, year: 2016 https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia- mathematica /all/232/3/91534/diameter-2-properties-and-convexity

10. Sequential Change-Point Detection via Online Convex Optimization

Yang Cao

2018-02-01

Full Text Available Sequential change-point detection when the distribution parameters are unknown is a fundamental problem in statistics and machine learning. When the post-change parameters are unknown, we consider a set of detection procedures based on sequential likelihood ratios with non-anticipating estimators constructed using online convex optimization algorithms such as online mirror descent, which provides a more versatile approach to tackling complex situations where recursive maximum likelihood estimators cannot be found. When the underlying distributions belong to a exponential family and the estimators satisfy the logarithm regret property, we show that this approach is nearly second-order asymptotically optimal. This means that the upper bound for the false alarm rate of the algorithm (measured by the average-run-length meets the lower bound asymptotically up to a log-log factor when the threshold tends to infinity. Our proof is achieved by making a connection between sequential change-point and online convex optimization and leveraging the logarithmic regret bound property of online mirror descent algorithm. Numerical and real data examples validate our theory.

11. Advanced Optical Metrology for XRAY Replication Mandrels and Mirrors, Phase I

National Aeronautics and Space Administration — Advanced x-ray observatories such as IXO and GenX will require thousands of thin shell mirror segments produced by replication using convex mandrels. Quality and...

12. Mirror symmetry

Voisin, Claire

1999-01-01

This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry. The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the ...

13. Einstein's Mirror

Gjurchinovski, Aleksandar; Skeparovski, Aleksandar

2008-10-01

Reflection of light from a plane mirror in uniform rectilinear motion is a century-old problem, intimately related to the foundations of special relativity.1-4 The problem was first investigated by Einstein in his famous 1905 paper by using the Lorentz transformations to switch from the mirror's rest frame to the frame where the mirror moves at a constant velocity.5 Einstein showed an intriguing fact that the usual law of reflection would not hold in the case of a uniformly moving mirror, that is, the angles of incidence and reflection of the light would not equal each other. Later on, it has been shown that the law of reflection at a moving mirror can be obtained in various alternative ways,6-10 but none of them seems suitable for bringing this interesting subject into the high school classroom.

14. 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.

15. 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

16. Reconstruction of convex bodies from moments

Hörrmann, Julia; Kousholt, Astrid

We investigate how much information about a convex body can be retrieved from a finite number of its geometric moments. We give a sufficient condition for a convex body to be uniquely determined by a finite number of its geometric moments, and we show that among all convex bodies, those which......- rithm that approximates a convex body using a finite number of its Legendre moments. The consistency of the algorithm is established using the stabil- ity result for Legendre moments. When only noisy measurements of Legendre moments are available, the consistency of the algorithm is established under...

17. Entropy coherent and entropy convex measures of risk

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

18. Pluripotential theory and convex bodies

Bayraktar, T.; Bloom, T.; Levenberg, N.

2018-03-01

A seminal paper by Berman and Boucksom exploited ideas from complex geometry to analyze the asymptotics of spaces of holomorphic sections of tensor powers of certain line bundles L over compact, complex manifolds as the power grows. This yielded results on weighted polynomial spaces in weighted pluripotential theory in {C}^d. Here, motivated by a recent paper by the first author on random sparse polynomials, we work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body in ({R}^+)^d. These classes of polynomials need not occur as sections of tensor powers of a line bundle L over a compact, complex manifold. We follow the approach of Berman and Boucksom to obtain analogous results. Bibliography: 16 titles.

19. 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;

20. Characterizing Convexity of Games using Marginal Vectors

van Velzen, S.; Hamers, H.J.M.; Norde, H.W.

2003-01-01

In this paper we study the relation between convexity of TU games and marginal vectors.We show that if specfic marginal vectors are core elements, then the game is convex.We characterize sets of marginal vectors satisfying this property, and we derive the formula for the minimum number of marginal

1. Convex trace functions of several variables

Hansen, Frank

2002-01-01

We prove that the function (x1,...,xk)¿Tr(f(x1,...,xk)), defined on k-tuples of symmetric matrices of order (n1,...,nk) in the domain of f, is convex for any convex function f of k variables. The matrix f(x1,...,xk) is defined by the functional calculus for functions of several variables, and it ...

2. Differential analysis of matrix convex functions II

Hansen, Frank; Tomiyama, Jun

2009-01-01

We continue the analysis in [F. Hansen, and J. Tomiyama, Differential analysis of matrix convex functions. Linear Algebra Appl., 420:102--116, 2007] of matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided...

3. Strictly convex functions on complete Finsler manifolds

convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss ... map expp at some point p ∈ M (and hence at every point on M) is defined on the whole tangent space Mp to M at ... The influence of the existence of convex functions on the metric and topology of under- lying manifolds has ...

4. 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

5. Convexity of oligopoly games without transferable technologies

Driessen, Theo; Meinhardt, Holger I.

2005-01-01

We present sufficient conditions involving the inverse demand function and the cost functions to establish the convexity of oligopoly TU-games without transferable technologies. For convex TU-games it is well known that the core is relatively large and that it is generically nonempty. The former

6. Convex bodies with many elliptic sections

Arelio, Isaac; Montejano, Luis

2014-01-01

{We show in this paper that two normal elliptic sections through every point of the boundary of a smooth convex body essentially characterize an ellipsoid and furthermore, that four different pairwise non-tangent elliptic sections through every point of the $C^2$-differentiable boundary of a convex body also essentially characterize an ellipsoid.

7. 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...

8. Two generalizations of column-convex polygons

Feretic, Svjetlan; Guttmann, Anthony J

2009-01-01

Column-convex polygons were first counted by area several decades ago, and the result was found to be a simple, rational, generating function. In this work we generalize that result. Let a p-column polyomino be a polyomino whose columns can have 1, 2, ..., p connected components. Then column-convex polygons are equivalent to 1-convex polyominoes. The area generating function of even the simplest generalization, namely 2-column polyominoes, is unlikely to be solvable. We therefore define two classes of polyominoes which interpolate between column-convex polygons and 2-column polyominoes. We derive the area generating functions of those two classes, using extensions of existing algorithms. The growth constants of both classes are greater than the growth constant of column-convex polyominoes. Rather tight lower bounds on the growth constants complement a comprehensive asymptotic analysis.

9. Mirror, mirror on the wall

2005-01-01

RICH 2, one of the two Ring Imaging Cherenkov detectors of the LHCb experiment, is being prepared to join the other detector elements ready for the first proton-proton collisions at LHC. The mirrors of the RICH2 detector are meticulously assembled in a clean room.In a large dark room, men in white move around an immense structure some 7 metres high, 10 metres wide and nearly 2.5 metres deep. Apparently effortlessly, they are installing the two large high-precision spherical mirrors. These mirrors will focus Cherenkov light, created by the charged particles that will traverse this detector, onto the photon detectors. Each spherical mirror wall is made up of facets like a fly's eye. Twenty-eight individual thin glass mirrors will all point to the same point in space to within a few micro-radians. The development of these mirrors has been technically demanding : Ideally they should be massless, sturdy, precise and have high reflectivity. In practice, though not massless, they are made from a mere 6 mm thin gl...

10. Alpha-Concave Hull, a Generalization of Convex Hull

2013-01-01

Bounding hull, such as convex hull, concave hull, alpha shapes etc. has vast applications in different areas especially in computational geometry. Alpha shape and concave hull are generalizations of convex hull. Unlike the convex hull, they construct non-convex enclosure on a set of points. In this paper, we introduce another generalization of convex hull, named alpha-concave hull, and compare this concept with convex hull and alpha shape. We show that the alpha-concave hull is also a general...

11. Duality and calculus of convex objects (theory and applications)

Brinkhuis, Ya; Tikhomirov, V M

2007-01-01

A new approach to convex calculus is presented, which allows one to treat from a single point of view duality and calculus for various convex objects. This approach is based on the possibility of associating with each convex object (a convex set or a convex function) a certain convex cone without loss of information about the object. From the duality theorem for cones duality theorems for other convex objects are deduced as consequences. The theme 'Duality formulae and the calculus of convex objects' is exhausted (from a certain precisely formulated point of view). Bibliography: 5 titles.

12. [Mirror neurons].

Rubia Vila, Francisco José

2011-01-01

Mirror neurons were recently discovered in frontal brain areas of the monkey. They are activated when the animal makes a specific movement, but also when the animal observes the same movement in another animal. Some of them also respond to the emotional expression of other animals of the same species. These mirror neurons have also been found in humans. They respond to or "reflect" actions of other individuals in the brain and are thought to represent the basis for imitation and empathy and hence the neurobiological substrate for "theory of mind", the potential origin of language and the so-called moral instinct.

13. Mirror systems.

Fogassi, Leonardo; Ferrari, Pier Francesco

2011-01-01

Mirror neurons are a class of visuomotor neurons, discovered in the monkey premotor cortex and in an anatomically connected area of the inferior parietal lobule, that activate both during action execution and action observation. They constitute a circuit dedicated to match actions made by others with the internal motor representations of the observer. It has been proposed that this matching system enables individuals to understand others' behavior and motor intentions. Here we will describe the main features of mirror neurons in monkeys. Then we will present evidence of the presence of a mirror system in humans and of its involvement in several social-cognitive functions, such as imitation, intention, and emotion understanding. This system may have several implications at a cognitive level and could be linked to specific social deficits in humans such as autism. Recent investigations addressed the issue of the plasticity of the mirror neuron system in both monkeys and humans, suggesting also their possible use in rehabilitation. WIREs Cogn Sci 2011 2 22-38 DOI: 10.1002/wcs.89 For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.

14. Convex sets in probabilistic normed spaces

2008-01-01

In this paper we obtain some results on convexity in a probabilistic normed space. We also investigate the concept of CSN-closedness and CSN-compactness in a probabilistic normed space and generalize the corresponding results of normed spaces

15. Designing Camera Networks by Convex Quadratic Programming

Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao

2015-01-01

be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution

16. ON THE GENERALIZED CONVEXITY AND CONCAVITY

Bhayo B.

2015-11-01

Full Text Available A function ƒ : R+ → R+ is (m1, m2-convex (concave if ƒ(m1(x,y ≤ (≥ m2(ƒ(x, ƒ(y for all x,y Є R+ = (0,∞ and m1 and m2 are two mean functions. Anderson et al. [1] studies the dependence of (m1, m2-convexity (concavity on m1 and m2 and gave the sufficient conditions of (m1, m2-convexity and concavity of a function defined by Maclaurin series. In this paper, we make a contribution to the topic and study the (m1, m2-convexity and concavity of a function where m1 and m2 are identric mean, Alzer mean mean. As well, we prove a conjecture posed by Bruce Ebanks in [2].

17. On convexity and Schoenberg's variation diminishing splines

Feng, Yuyu; Kozak, J.

1992-11-01

In the paper we characterize a convex function by the monotonicity of a particular variation diminishing spline sequence. The result extends the property known for the Bernstein polynomial sequence. (author). 4 refs

18. Recent characterizations of generalized convexity in convexity in cooperative game thoery

Driessen, T.

1994-12-31

The notion of convexity for a real-valued function on the power set of the finite set N (the so-called cooperative game with player set N) is defined as in other mathematical fields. The study of convexity plays an important role within the field of cooperative game theory because the application of the solution part of game theory to convex games provides elegant results for the solution concepts involved. Especially, the well known solution concept called core is, for convex games, very well characterized. The current paper focuses on a notion of generalized convexity, called k- convexity, for cooperative n-person games. Due to very recent characterizations of convexity for cooperative games, the goal is to provide similar new characterizations of k-convexity. The main characterization states that for the k-convexity of an n-person game it is both necessary and sufficient that half of all the so-called marginal worth vectors belong to the core of the game. Here it is taken into account whether a marginal worth vector corresponds to an even or odd ordering of k elements of the n-person player set N. Another characterization of k-convexity is presented in terms of a so-called finite min-modular decomposition. That is, some specific cover game of a k-convex game can be decomposed as the minimum of a finite number of modular (or additive) games. Finally it is established that the k-convexity of a game can be characterized in terms of the second order partial derivates of the so-called multilinear extension of the game.

19. Hermitian harmonic maps into convex balls

Li Zhenyang; Xi Zhang

2004-07-01

In this paper, we consider Hermitian harmonic maps from Hermitian manifolds into convex balls. We prove that there exist no non-trivial Hermitian harmonic maps from closed Hermitian manifolds into convex balls, and we use the heat flow method to solve the Dirichlet problem for Hermitian harmonic maps when the domain is compact Hermitian manifold with non-empty boundary. The case where the domain manifold is complete(noncompact) is also studied. (author)

20. Counting convex polygons in planar point sets

Mitchell, J.S.B.; Rote, G.; Sundaram, Gopalakrishnan; Woeginger, G.J.

1995-01-01

Given a set S of n points in the plane, we compute in time O(n3) the total number of convex polygons whose vertices are a subset of S. We give an O(m · n3) algorithm for computing the number of convex k-gons with vertices in S, for all values k = 3,…, m; previously known bounds were exponential

1. Bypassing the Limits of Ll Regularization: Convex Sparse Signal Processing Using Non-Convex Regularization

Parekh, Ankit

Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the ℓ1 norm is used to induce sparsity, so much so that ℓ1 regularization is considered to be `modern least-squares'. The use of ℓ1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the ℓ1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal

2. What do mirror neurons mirror?

Uithol, S.; Rooij, I.J.E.I. van; Bekkering, H.; Haselager, W.F.G.

2011-01-01

Single cell recordings in monkeys provide strong evidence for an important role of the motor system in action understanding. This evidence is backed up by data from studies of the (human) mirror neuron system using neuroimaging or TMS techniques, and behavioral experiments. Although the data

3. Entropy Coherent and Entropy Convex Measures of Risk

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,

4. On Hadamard-Type Inequalities Involving Several Kinds of Convexity

Dragomir SeverS

2010-01-01

Full Text Available We do not only give the extensions of the results given by Gill et al. (1997 for log-convex functions but also obtain some new Hadamard-type inequalities for log-convex -convex, and -convex functions.

5. Mirror monochromator

Mankos, Marian [Electron Optica, Inc., Palo Alto, CA (United States); Shadman, Khashayar [Electron Optica, Inc., Palo Alto, CA (United States)

2014-12-02

In this SBIR project, Electron Optica, Inc. (EOI) is developing a mirror electron monochromator (MirrorChrom) attachment to new and retrofitted electron microscopes (EMs) for improving the energy resolution of the EM from the characteristic range of 0.2-0.5 eV to the range of 10-50 meV. This improvement will enhance the characterization of materials by imaging and spectroscopy. In particular, the monochromator will refine the energy spectra characterizing materials, as obtained from transmission EMs [TEMs] fitted with electron spectrometers, and it will increase the spatial resolution of the images of materials taken with scanning EMs (SEMs) operated at low voltages. EOI’s MirrorChrom technology utilizes a magnetic prism to simultaneously deflect the electron beam off the axis of the microscope column by 90° and disperse the electrons in proportional to their energies into a module with an electron mirror and a knife-edge. The knife-edge cuts off the tails of the energy distribution to reduce the energy spread of the electrons that are reflected, and subsequently deflected, back into the microscope column. The knife-edge is less prone to contamination, and thereby charging, than the conventional slits used in existing monochromators, which improves the reliability and stability of the module. The overall design of the MirrorChrom exploits the symmetry inherent in reversing the electron trajectory in order to maintain the beam brightness – a parameter that impacts how well the electron beam can be focused downstream onto a sample. During phase I, EOI drafted a set of candidate monochromator architectures and evaluated the trade-offs between energy resolution and beam current to achieve the optimum design for three particular applications with market potential: increasing the spatial resolution of low voltage SEMs, increasing the energy resolution of low voltage TEMs (beam energy of 5-20 keV), and increasing the energy resolution of conventional TEMs (beam

6. Mirror systems

Howells, M.R.

1985-12-01

The physics of VUV and x-ray reflection is reviewed. The main functions of mirrors in synchrotron beamlines are stated briefly and include deflection, filtration, power absorption, formation of a real image of the source, focusing, and collimation. Methods of fabrication of optical surfaces are described. Types of imperfections are discussed, including, aberrations, surface figure inaccuracy, roughness, and degradation due to use. Calculation of the photon beam thermal load, including computer modelling, is considered. 50 refs., 7 figs

7. Convex Banding of the Covariance Matrix.

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

8. Reconstruction of convex bodies from surface tensors

Kousholt, Astrid; Kiderlen, Markus

. The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available...... tensors up to rank s. This is used to establish consistency of the developed reconstruction algorithm....

9. 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...

10. 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.

11. Mirror fusion reactors

Anon.

1978-01-01

Conceptual design studies were made of fusion reactors based on the three current mirror-confinement concepts: the standard mirror, the tandem mirror, and the field-reversed mirror. Recent studies of the standard mirror have emphasized its potential as a fusion-fission hybrid reactor, designed to produce fuel for fission reactors. We have designed a large commercial hybrid and a small pilot-plant hybrid based on standard mirror confinement. Tandem mirror designs include a commercial 1000-MWe fusion power plant and a nearer term tandem mirror hybrid. Field-reversed mirror designs include a multicell commercial reactor producing 75 MWe and a single-cell pilot plant

12. Mirror fusion reactors

Carlson, G.A.; Moir, R.W.

1978-01-01

We have carried out conceptual design studies of fusion reactors based on the three current mirror confinement concepts: the standard mirror, the tandem mirror, and the field-reversed mirror. Recent studies of the standard mirror have emphasized its potential as a fusion-fission hybrid reactor, designed to produce fission fuel for fission reactors. We have designed a large commercial hybrid based on standard mirror confinement, and also a small pilot plant hybrid. Tandem mirror designs include a commercial 1000 MWe fusion power plant and a nearer term tandem mirror hybrid. Field-reversed mirror designs include a multicell commercial reactor producing 75 MWe and a single cell pilot plant

13. Reconstruction of convex bodies from surface tensors

Kousholt, Astrid; Kiderlen, Markus

We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based...

14. Probing convex polygons with X-rays

Edelsbrunner, H.; Skiena, S.S.

1988-01-01

An X-ray probe through a polygon measures the length of intersection between a line and the polygon. This paper considers the properties of various classes of X-ray probes, and shows how they interact to give finite strategies for completely describing convex n-gons. It is shown that (3n/2)+6 probes are sufficient to verify a specified n-gon, while for determining convex polygons (3n-1)/2 X-ray probes are necessary and 5n+O(1) sufficient, with 3n+O(1) sufficient given that a lower bound on the size of the smallest edge of P is known

15. Recovering convexity in non-associated plasticity

Francfort, Gilles A.

2018-03-01

We quickly review two main non-associated plasticity models, the Armstrong-Frederick model of nonlinear kinematic hardening and the Drucker-Prager cap model. Non-associativity is commonly thought to preclude any kind of variational formulation, be it in a Hencky-type (static) setting, or when considering a quasi-static evolution because non-associativity destroys convexity. We demonstrate that such an opinion is misguided: associativity (and convexity) can be restored at the expense of the introduction of state variable-dependent dissipation potentials.

16. Improved Mirror Source Method in Roomacoustics

Mechel, F. P.

2002-10-01

Most authors in room acoustics qualify the mirror source method (MS-method) as the only exact method to evaluate sound fields in auditoria. But evidently nobody applies it. The reason for this discrepancy is the abundantly high numbers of needed mirror sources which are reported in the literature, although such estimations of needed numbers of mirror sources mostly are used for the justification of more or less heuristic modifications of the MS-method. The present, intentionally tutorial article accentuates the analytical foundations of the MS-method whereby the number of needed mirror sources is reduced already. Further, the task of field evaluation in three-dimensional spaces is reduced to a sequence of tasks in two-dimensional room edges. This not only allows the use of easier geometrical computations in two dimensions, but also the sound field in corner areas can be represented by a single (directional) source sitting on the corner line, so that only this "corner source" must be mirror-reflected in the further process. This procedure gives a drastic reduction of the number of needed equivalent sources. Finally, the traditional MS-method is not applicable in rooms with convex corners (the angle between the corner flanks, measured on the room side, exceeds 180°). In such cases, the MS-method is combined below with the second principle of superposition(PSP). It reduces the scattering task at convex corners to two sub-tasks between one flank and the median plane of the room wedge, i.e., always in concave corner areas where the MS-method can be applied.

17. Foundations of complex analysis in non locally convex spaces function theory without convexity condition

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

18. Differential analysis of matrix convex functions

Hansen, Frank; Tomiyama, Jun

2007-01-01

We analyze matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus [F. Kraus, Über konvekse Matrixfunktionen, Math. Z. 41 (1936) 18-42]. We obtain for each order conditions for ma...

19. 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...

20. Robust Utility Maximization Under Convex Portfolio Constraints

Matoussi, Anis; Mezghani, Hanen; Mnif, Mohamed

2015-01-01

We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption–investment strategy by studying the associated quadratic backward stochastic differential equation. We characterize the optimal control by using the duality method and deriving a dynamic maximum principle

1. Localized Multiple Kernel Learning A Convex Approach

2016-11-22

data. All the aforementioned approaches to localized MKL are formulated in terms of non-convex optimization problems, and deep the- oretical...learning. IEEE Transactions on Neural Networks, 22(3):433–446, 2011. Jingjing Yang, Yuanning Li, Yonghong Tian, Lingyu Duan, and Wen Gao. Group-sensitive

2. A generalization of the convex Kakeya problem

Ahn, Heekap; Bae, Sangwon; Cheong, Otfried; Gudmundsson, Joachim; Tokuyama, Takeshi; Vigneron, Antoine E.

2013-01-01

segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then placing the segments with their midpoint at the origin and taking their convex hull results in an optimal solution. Finally, we show that for any

3. Minimizing convex functions by continuous descent methods

Sergiu Aizicovici

2010-01-01

Full Text Available We study continuous descent methods for minimizing convex functions, defined on general Banach spaces, which are associated with an appropriate complete metric space of vector fields. We show that there exists an everywhere dense open set in this space of vector fields such that each of its elements generates strongly convergent trajectories.

4. 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

5. 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...

6. 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.

7. A generalization of the convex Kakeya problem

Ahn, Heekap; Bae, Sangwon; Cheong, Otfried; Gudmundsson, Joachim; Tokuyama, Takeshi; Vigneron, Antoine E.

2012-01-01

We consider the following geometric alignment problem: Given a set of line segments in the plane, find a convex region of smallest area that contains a translate of each input segment. This can be seen as a generalization of Kakeya's problem

8. 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.

9. Dynamic Matchings in Convex Bipartite Graphs

Brodal, Gerth Stølting; Georgiadis, Loukas; Hansen, Kristoffer Arnsfelt

2007-01-01

We consider the problem of maintaining a maximum matching in a convex bipartite graph G = (V,E) under a set of update operations which includes insertions and deletions of vertices and edges. It is not hard to show that it is impossible to maintain an explicit representation of a maximum matching...

10. Cost Allocation and Convex Data Envelopment

Hougaard, Jens Leth; Tind, Jørgen

such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output...

11. Tropicalized Lambda Lengths, Measured Laminations and Convexity

C. Penner, R.

This work uncovers the tropical analogue for measured laminations of the convex hull construction of decorated Teichmueller theory, namely, it is a study in coordinates of geometric degeneration to a point of Thurston's boundary for Teichmueller space. This may offer a paradigm for the extension ...

12. Fast approximate convex decomposition using relative concavity

Ghosh, Mukulika; Amato, Nancy M.; Lu, Yanyan; Lien, Jyh-Ming

2013-01-01

Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.

13. 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.

14. Schur Convexity of Generalized Heronian Means Involving Two Parameters

Bencze Mihály

2008-01-01

Full Text Available Abstract The Schur convexity and Schur-geometric convexity of generalized Heronian means involving two parameters are studied, the main result is then used to obtain several interesting and significantly inequalities for generalized Heronian means.

15. A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES

程立新; 腾岩梅

2003-01-01

This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.

16. Displacement Convexity for First-Order Mean-Field Games

Seneci, Tommaso

2018-01-01

Finally, we identify a large class of functions, that depend on solutions of MFGs, which are convex in time. Among these, we find several norms. This convexity gives bounds for the density of solutions of the planning problem.

17. Convex stoma appliances: an audit of stoma care nurses.

Perrin, Angie

2016-12-08

This article observes the complexities surrounding the use of convex appliances within the specialist sphere of stoma care. It highlights some of the results taken from a small audit carried out with 24 stoma care nurses examining the general use of convex appliances and how usage of convex products has evolved, along with specialist stoma care practice.

18. Fastest Rates for Stochastic Mirror Descent Methods

Hanzely, Filip

2018-03-20

Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In this work we are taking ideas from well studied field of stochastic convex optimization and using them in order to obtain faster algorithms for minimizing relatively smooth functions. We propose and analyze two new algorithms: Relative Randomized Coordinate Descent (relRCD) and Relative Stochastic Gradient Descent (relSGD), both generalizing famous algorithms in the standard smooth setting. The methods we propose can be in fact seen as a particular instances of stochastic mirror descent algorithms. One of them, relRCD corresponds to the first stochastic variant of mirror descent algorithm with linear convergence rate.

19. Fastest Rates for Stochastic Mirror Descent Methods

Hanzely, Filip; Richtarik, Peter

2018-01-01

Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In this work we are taking ideas from well studied field of stochastic convex optimization and using them in order to obtain faster algorithms for minimizing relatively smooth functions. We propose and analyze two new algorithms: Relative Randomized Coordinate Descent (relRCD) and Relative Stochastic Gradient Descent (relSGD), both generalizing famous algorithms in the standard smooth setting. The methods we propose can be in fact seen as a particular instances of stochastic mirror descent algorithms. One of them, relRCD corresponds to the first stochastic variant of mirror descent algorithm with linear convergence rate.

20. Convexity, gauge-dependence and tunneling rates

Plascencia, Alexis D.; Tamarit, Carlos [Institute for Particle Physics Phenomenology, Durham University,South Road, DH1 3LE (United Kingdom)

2016-10-19

We clarify issues of convexity, gauge-dependence and radiative corrections in relation to tunneling rates. Despite the gauge dependence of the effective action at zero and finite temperature, it is shown that tunneling and nucleation rates remain independent of the choice of gauge-fixing. Taking as a starting point the functional that defines the transition amplitude from a false vacuum onto itself, it is shown that decay rates are exactly determined by a non-convex, false vacuum effective action evaluated at an extremum. The latter can be viewed as a generalized bounce configuration, and gauge-independence follows from the appropriate Nielsen identities. This holds for any election of gauge-fixing that leads to an invertible Faddeev-Popov matrix.

1. Reconstruction of convex bodies from surface tensors

Kousholt, Astrid; Kiderlen, Markus

2016-01-01

We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy...... measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise...

2. Exact generating function for 2-convex polygons

James, W R G; Jensen, I; Guttmann, A J

2008-01-01

Polygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their 'concavity index', m. Such polygons are called m-convex polygons and are characterized by having up to m indentations in their perimeter. We first describe how we conjectured the (isotropic) generating function for the case m = 2 using a numerical procedure based on series expansions. We then proceed to prove this result for the more general case of the full anisotropic generating function, in which steps in the x and y directions are distinguished. In doing so, we develop tools that would allow for the case m > 2 to be studied

3. Solving ptychography with a convex relaxation

Horstmeyer, Roarke; Chen, Richard Y.; Ou, Xiaoze; Ames, Brendan; Tropp, Joel A.; Yang, Changhuei

2015-05-01

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that currently solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the ptychographic reconstruction algorithm that is currently in widespread use.

4. Convex nonnegative matrix factorization with manifold regularization.

Hu, Wenjun; Choi, Kup-Sze; Wang, Peiliang; Jiang, Yunliang; Wang, Shitong

2015-03-01

Nonnegative Matrix Factorization (NMF) has been extensively applied in many areas, including computer vision, pattern recognition, text mining, and signal processing. However, nonnegative entries are usually required for the data matrix in NMF, which limits its application. Besides, while the basis and encoding vectors obtained by NMF can represent the original data in low dimension, the representations do not always reflect the intrinsic geometric structure embedded in the data. Motivated by manifold learning and Convex NMF (CNMF), we propose a novel matrix factorization method called Graph Regularized and Convex Nonnegative Matrix Factorization (GCNMF) by introducing a graph regularized term into CNMF. The proposed matrix factorization technique not only inherits the intrinsic low-dimensional manifold structure, but also allows the processing of mixed-sign data matrix. Clustering experiments on nonnegative and mixed-sign real-world data sets are conducted to demonstrate the effectiveness of the proposed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

5. Convexity, gauge-dependence and tunneling rates

Plascencia, Alexis D.; Tamarit, Carlos

2016-01-01

We clarify issues of convexity, gauge-dependence and radiative corrections in relation to tunneling rates. Despite the gauge dependence of the effective action at zero and finite temperature, it is shown that tunneling and nucleation rates remain independent of the choice of gauge-fixing. Taking as a starting point the functional that defines the transition amplitude from a false vacuum onto itself, it is shown that decay rates are exactly determined by a non-convex, false vacuum effective action evaluated at an extremum. The latter can be viewed as a generalized bounce configuration, and gauge-independence follows from the appropriate Nielsen identities. This holds for any election of gauge-fixing that leads to an invertible Faddeev-Popov matrix.

6. An easy path to convex analysis and applications

Mordukhovich, Boris S

2013-01-01

Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to cl

7. Convex geometry of quantum resource quantification

Regula, Bartosz

2018-01-01

We introduce a framework unifying the mathematical characterisation of different measures of general quantum resources and allowing for a systematic way to define a variety of faithful quantifiers for any given convex quantum resource theory. The approach allows us to describe many commonly used measures such as matrix norm-based quantifiers, robustness measures, convex roof-based measures, and witness-based quantifiers together in a common formalism based on the convex geometry of the underlying sets of resource-free states. We establish easily verifiable criteria for a measure to possess desirable properties such as faithfulness and strong monotonicity under relevant free operations, and show that many quantifiers obtained in this framework indeed satisfy them for any considered quantum resource. We derive various bounds and relations between the measures, generalising and providing significantly simplified proofs of results found in the resource theories of quantum entanglement and coherence. We also prove that the quantification of resources in this framework simplifies for pure states, allowing us to obtain more easily computable forms of the considered measures, and show that many of them are in fact equal on pure states. Further, we investigate the dual formulation of resource quantifiers, which provide a characterisation of the sets of resource witnesses. We present an explicit application of the results to the resource theories of multi-level coherence, entanglement of Schmidt number k, multipartite entanglement, as well as magic states, providing insight into the quantification of the four resources by establishing novel quantitative relations and introducing new quantifiers, such as a measure of entanglement of Schmidt number k which generalises the convex roof-extended negativity, a measure of k-coherence which generalises the \

8. On the convexity of relativistic hydrodynamics

Ibáñez, José M; Martí, José M; Cordero-Carrión, Isabel; Miralles, Juan A

2013-01-01

The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 Relativistic Fluids and Magneto-Fluids (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr1989 Rev. Mod. Phys. 61 75). The classical limit is recovered. Communicated by L Rezzolla (note)

9. Dynamic Convex Duality in Constrained Utility Maximization

Li, Yusong; Zheng, Harry

2016-01-01

In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual problems in terms of FBSDEs plus additional conditions. Such formulation then allows us to explicitly characterize the primal optimal control as a function of the adjoint process coming from the dual FBSDEs in a dynamic fashion and vice versa. Moreover, we also...

10. Optimal skill distribution under convex skill costs

Tin Cheuk Leung

2018-03-01

Full Text Available This paper studies optimal distribution of skills in an optimal income tax framework with convex skill constraints. The problem is cast as a social planning problem where a redistributive planner chooses how to distribute a given amount of aggregate skills across people. We find that optimal skill distribution is either perfectly equal or perfectly unequal, but an interior level of skill inequality is never optimal.

11. The occipital lobe convexity sulci and gyri.

Alves, Raphael V; Ribas, Guilherme C; Párraga, Richard G; de Oliveira, Evandro

2012-05-01

The anatomy of the occipital lobe convexity is so intricate and variable that its precise description is not found in the classic anatomy textbooks, and the occipital sulci and gyri are described with different nomenclatures according to different authors. The aim of this study was to investigate and describe the anatomy of the occipital lobe convexity and clarify its nomenclature. The configurations of sulci and gyri on the lateral surface of the occipital lobe of 20 cerebral hemispheres were examined in order to identify the most characteristic and consistent patterns. The most characteristic and consistent occipital sulci identified in this study were the intraoccipital, transverse occipital, and lateral occipital sulci. The morphology of the transverse occipital sulcus and the intraoccipital sulcus connection was identified as the most important aspect to define the gyral pattern of the occipital lobe convexity. Knowledge of the main features of the occipital sulci and gyri permits the recognition of a basic configuration of the occipital lobe and the identification of its sulcal and gyral variations.

12. Convex Hull Aided Registration Method (CHARM).

Fan, Jingfan; Yang, Jian; Zhao, Yitian; Ai, Danni; Liu, Yonghuai; Wang, Ge; Wang, Yongtian

2017-09-01

Non-rigid registration finds many applications such as photogrammetry, motion tracking, model retrieval, and object recognition. In this paper we propose a novel convex hull aided registration method (CHARM) to match two point sets subject to a non-rigid transformation. First, two convex hulls are extracted from the source and target respectively. Then, all points of the point sets are projected onto the reference plane through each triangular facet of the hulls. From these projections, invariant features are extracted and matched optimally. The matched feature point pairs are mapped back onto the triangular facets of the convex hulls to remove outliers that are outside any relevant triangular facet. The rigid transformation from the source to the target is robustly estimated by the random sample consensus (RANSAC) scheme through minimizing the distance between the matched feature point pairs. Finally, these feature points are utilized as the control points to achieve non-rigid deformation in the form of thin-plate spline of the entire source point set towards the target one. The experimental results based on both synthetic and real data show that the proposed algorithm outperforms several state-of-the-art ones with respect to sampling, rotational angle, and data noise. In addition, the proposed CHARM algorithm also shows higher computational efficiency compared to these methods.

13. Generalized vector calculus on convex domain

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

14. Convexities move because they contain matter.

Barenholtz, Elan

2010-09-22

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

15. Convex and Radially Concave Contoured Distributions

Wolf-Dieter Richter

2015-01-01

Full Text Available Integral representations of the locally defined star-generalized surface content measures on star spheres are derived for boundary spheres of balls being convex or radially concave with respect to a fan in Rn. As a result, the general geometric measure representation of star-shaped probability distributions and the general stochastic representation of the corresponding random vectors allow additional specific interpretations in the two mentioned cases. Applications to estimating and testing hypotheses on scaling parameters are presented, and two-dimensional sample clouds are simulated.

16. On conditional independence and log-convexity

Matúš, František

2012-01-01

Roč. 48, č. 4 (2012), s. 1137-1147 ISSN 0246-0203 R&D Projects: GA AV ČR IAA100750603; GA ČR GA201/08/0539 Institutional support: RVO:67985556 Keywords : Conditional independence * Markov properties * factorizable distributions * graphical Markov models * log-convexity * Gibbs- Markov equivalence * Markov fields * Gaussian distributions * positive definite matrices * covariance selection model Subject RIV: BA - General Mathematics Impact factor: 0.933, year: 2012 http://library.utia.cas.cz/separaty/2013/MTR/matus-0386229.pdf

17. Mirror Neurons and Mirror-Touch Synesthesia.

Linkovski, Omer; Katzin, Naama; Salti, Moti

2016-05-30

Since mirror neurons were introduced to the neuroscientific community more than 20 years ago, they have become an elegant and intuitive account for different cognitive mechanisms (e.g., empathy, goal understanding) and conditions (e.g., autism spectrum disorders). Recently, mirror neurons were suggested to be the mechanism underlying a specific type of synesthesia. Mirror-touch synesthesia is a phenomenon in which individuals experience somatosensory sensations when seeing someone else being touched. Appealing as it is, careful delineation is required when applying this mechanism. Using the mirror-touch synesthesia case, we put forward theoretical and methodological issues that should be addressed before relying on the mirror-neurons account. © The Author(s) 2016.

18. Topological mirror superconductivity.

Zhang, Fan; Kane, C L; Mele, E J

2013-08-02

We demonstrate the existence of topological superconductors (SCs) protected by mirror and time-reversal symmetries. D-dimensional (D=1, 2, 3) crystalline SCs are characterized by 2(D-1) independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z(2) index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa and that a DIII SC with a mirror plane is always time-reversal trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out.

19. 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...

20. CVXPY: A Python-Embedded Modeling Language for Convex Optimization

Diamond, Steven; Boyd, Stephen

2016-01-01

CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at http://www.cvxpy.org/ under the GPL license, along with documentation and examples.

1. CVXPY: A Python-Embedded Modeling Language for Convex Optimization.

Diamond, Steven; Boyd, Stephen

2016-04-01

CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at http://www.cvxpy.org/ under the GPL license, along with documentation and examples.

2. Convex blind image deconvolution with inverse filtering

Lv, Xiao-Guang; Li, Fang; Zeng, Tieyong

2018-03-01

Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption.

3. Effective potential for non-convex potentials

Fujimoto, Y.; O'Raifeartaigh, L.; Parravicini, G.

1983-01-01

It is shown that the well-known relationship between the effective potential GAMMA and the vacuum graphs μ of scalar QFT follows directly from the translational invariance of the measure, and that it holds for all values of the fields phi if, and only if, the classical potential is convex. In the non-convex case μ appears to become complex for some values of phi, but it is shown that the complexity is only apparent and is due to the failure of the loop expansion. The effective potential actually remains real and well-defined for all phi, and reduces to μ in the neighbourhood of the classical minima. A number of examples are considered, notably potentials which are spontaneously broken. In particular the mechanism by which a spontaneous breakdown may be generated by radiative corrections is re-investigated and some new insights obtained. Finally, it is shown that the renormalization group equations for the parameters may be obtained by inspection from the effective potential, and among the examples considered are SU(n) fields and supermultiplets. In particular, it is shown that for supermultiplets the effective potential is not only real but positive. (orig.)

4. INdAM Workshop on Analytic Aspects of Convexity

Colesanti, Andrea; Gronchi, Paolo

2018-01-01

This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016. It offers a collection of selected articles, written by some of the world’s leading experts in the field of Convex Geometry, on recent developments in this area: theory of valuations; geometric inequalities; affine geometry; and curvature measures. The book will be of interest to a broad readership, from those involved in Convex Geometry, to those focusing on Functional Analysis, Harmonic Analysis, Differential Geometry, or PDEs. The book is a addressed to PhD students and researchers, interested in Convex Geometry and its links to analysis.

5. Mirror machine reactors

Carlson, G.A.; Moir, R.W.

1976-01-01

Recent mirror reactor conceptual design studies are described. Considered in detail is the design of ''standard'' Yin-Yang fusion power reactors with classical and enhanced confinement. It is shown that to be economically competitive with estimates for other future energy sources, mirror reactors require a considerable increase in Q, or major design simplifications, or preferably both. These improvements may require a departure from the ''standard'' configuration. Two attractive possibilities, both of which would use much of the same physics and technology as the ''standard'' mirror, are the field reversed mirror and the end-stoppered mirror

6. The mirror neuron system.

Cattaneo, Luigi; Rizzolatti, Giacomo

2009-05-01

Mirror neurons are a class of neurons, originally discovered in the premotor cortex of monkeys, that discharge both when individuals perform a given motor act and when they observe others perform that same motor act. Ample evidence demonstrates the existence of a cortical network with the properties of mirror neurons (mirror system) in humans. The human mirror system is involved in understanding others' actions and their intentions behind them, and it underlies mechanisms of observational learning. Herein, we will discuss the clinical implications of the mirror system.

7. Multi-Period Trading via Convex Optimization

Boyd, Stephen; Busseti, Enzo; Diamond, Steve

2017-01-01

We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades oﬀ expected return, risk......, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the ﬁrst one executed, using estimates of future quantities that are unknown when the trades....... In this paper, we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software...

8. Conditionally exponential convex functions on locally compact groups

Okb El-Bab, A.S.

1992-09-01

The main results of the thesis are: 1) The construction of a compact base for the convex cone of all conditionally exponential convex functions. 2) The determination of the extreme parts of this cone. Some supplementary lemmas are proved for this purpose. (author). 8 refs

9. Approximate convex hull of affine iterated function system attractors

Mishkinis, Anton; Gentil, Christian; Lanquetin, Sandrine; Sokolov, Dmitry

2012-01-01

Highlights: ► We present an iterative algorithm to approximate affine IFS attractor convex hull. ► Elimination of the interior points significantly reduces the complexity. ► To optimize calculations, we merge the convex hull images at each iteration. ► Approximation by ellipses increases speed of convergence to the exact convex hull. ► We present a method of the output convex hull simplification. - Abstract: In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy.

10. Entropy coherent and entropy convex measures of risk

2010-01-01

We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized

11. Convexity-preserving Bernstein–Bézier quartic scheme

Maria Hussain

2014-07-01

Full Text Available A C1 convex surface data interpolation scheme is presented to preserve the shape of scattered data arranged over a triangular grid. Bernstein–Bézier quartic function is used for interpolation. Lower bound of the boundary and inner Bézier ordinates is determined to guarantee convexity of surface. The developed scheme is flexible and involves more relaxed constraints.

12. Convergence of Algorithms for Reconstructing Convex Bodies and Directional Measures

Gardner, Richard; Kiderlen, Markus; Milanfar, Peyman

2006-01-01

We investigate algorithms for reconstructing a convex body K in Rn from noisy measurements of its support function or its brightness function in k directions u1, . . . , uk. The key idea of these algorithms is to construct a convex polytope Pk whose support function (or brightness function) best...

13. On approximation and energy estimates for delta 6-convex functions.

2018-01-01

The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted [Formula: see text]-norm.

14. On approximation and energy estimates for delta 6-convex functions

2018-02-01

Full Text Available Abstract The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted L2 $L^{2}$-norm.

15. STRICT CONVEXITY THROUGH EQUIVALENT NORMS IN SEPARABLES BANACH SPACES

Willy Zubiaga Vera

2016-12-01

Full Text Available Let E be a separable Banach space with norm || . ||. In the present work, the objective is to construct a norm || . ||1 that is equivalent to || . || in E, such that || . ||1 is strictly convex. In addition it is shown that its dual conjugate norm is also strictly convex.

16. 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...

17. Small mirror fusion reactors

Carlson, G.A.; Schultz, K.R.; Smith, A.C. Jr.

1978-01-01

Basic requirements for the pilot plants are that they produce a net product and that they have a potential for commercial upgrade. We have investigated a small standard mirror fusion-fission hybrid, a two-component tandem mirror hybrid, and two versions of a field-reversed mirror fusion reactor--one a steady state, single cell reactor with a neutral beam-sustained plasma, the other a moving ring field-reversed mirror where the plasma passes through a reaction chamber with no energy addition

18. U. S. Mirror Program

Fowler, T.K.

1978-01-01

The mirror approach is now the principal alternate to the tokamak in the U.S. magnetic fusion energy program. The program is now focused on two new concepts that can obtain high values of Q, defined as the ratio of fusion power output to the neutral beam power injected to sustain the reaction. These are the tandem mirror and field reversed mirror concepts. Theoretically both concepts should be able to attain Q = 5 or more, as compared with Q approximately 1 in previous mirror designs. Success with either or both of these approaches would point the way toward fusion power plants with many attractive features. The linear geometry of mirror systems offers a distinct alternative to the toroidal tokamak. As a direct consequence of this difference in geometry, it is generally possible to build mirror systems in smaller units of modular construction that can probably be made to operate in steady-state. During the next 5 years the main mirror facilities in the U.S. will be the 2XIIB (renamed Beta II); a tandem mirror experiment caled TMX; and the Mirror Fusion Test Facility (MFTF) scheduled to be completed in 1981 at a cost of $94 million. As a background for discussing this program and mirror reactor concepts in later lectures, the current status of mirror physics will be reviewed by comparing theory and experimental data in four critical areas. These are adiabatic confinement of individual ions, electron heat losses out of the ends of the machine, the achievement of beta values of order unity; and stabilization of ''loss cone'' modes 19. Decomposability and convex structure of thermal processes Mazurek, Paweł; Horodecki, Michał 2018-05-01 We present an example of a thermal process (TP) for a system of d energy levels, which cannot be performed without an instant access to the whole energy space. This TP is uniquely connected with a transition between some states of the system, that cannot be performed without access to the whole energy space even when approximate transitions are allowed. Pursuing the question about the decomposability of TPs into convex combinations of compositions of processes acting non-trivially on smaller subspaces, we investigate transitions within the subspace of states diagonal in the energy basis. For three level systems, we determine the set of extremal points of these operations, as well as the minimal set of operations needed to perform an arbitrary TP, and connect the set of TPs with thermomajorization criterion. We show that the structure of the set depends on temperature, which is associated with the fact that TPs cannot increase deterministically extractable work from a state—the conclusion that holds for arbitrary d level system. We also connect the decomposability problem with detailed balance symmetry of an extremal TPs. 20. 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). ​ 1. Visualizing Data as Objects by DC (Difference of Convex) Optimization Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero 2018-01-01 In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value, as convex objects. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization...... problem whose objective is the difference of two convex functions (DC). Suitable DC decompositions allow us to use the Difference of Convex Algorithm (DCA) in a very efficient way. Our algorithmic approach is used to visualize two real-world datasets.... 2. Bronze rainbow hologram mirrors Dawson, P. 2006-02-01 This project draws on holographic embossing techniques, ancient artistic conventions of bronze mirror design and modelling and casting processes to accomplish portraiture of reflection. Laser scanning, 3D computer graphics and holographic imaging are employed to enable a permanent 3D static holographic image to appear integrated with the real-time moving reflection of a viewer's face in a polished bronze disc. The disc and the figure which holds it (caryatid) are cast in bronze from a lost wax model, a technique which has been used for millennia to make personal mirrors. The Caryatid form of bronze mirror which went through many permutations in ancient Egyptian, Greece and Rome shows a plethora of expressive figure poses ranging from sleek nudes to highly embellished multifigure arrangements. The prototype of this series was made for Australian choreographer Graeme Murphy, Artistic Director of the Sydney Dance Company. Each subsequent mirror will be unique in figure and holographic imagery as arranged between artist and subject. Conceptually this project references both the modern experience of viewing mirrors retrieved from ancient tombs, which due to deterioration of the surface no longer reflect, and the functioning of Chinese Magic mirrors, which have the ability to project a predetermined image. Inspired by the metaphorical potential of these mirrors, which do not reflect the immediate reality of the viewer, this bronze hologram mirror series enables each viewer to reflect upon himself or herself observing simultaneously the holographic image and their own partially obliterated reflection. 3. Mirror fusion reactor design Neef, W.S. Jr.; Carlson, G.A. 1979-01-01 Recent conceptual reactor designs based on mirror confinement are described. Four components of mirror reactors for which materials considerations and structural mechanics analysis must play an important role in successful design are discussed. The reactor components are: (a) first-wall and thermal conversion blanket, (b) superconducting magnets and their force restraining structure, (c) neutral beam injectors, and (d) plasma direct energy converters 4. Tandem mirror plasma confinement apparatus Fowler, T.K. 1978-01-01 Apparatus and method are described for confining a plasma in a center mirror cell by use of two end mirror cells as positively charged end stoppers to minimize leakage of positive particles from the ends of the center mirror cell 5. Tandem mirror plasma confinement apparatus Fowler, T. Kenneth 1978-11-14 Apparatus and method for confining a plasma in a center mirror cell by use of two end mirror cells as positively charged end stoppers to minimize leakage of positive particles from the ends of the center mirror cell. 6. A survey on locally uniformly A-convex algebras Oudadess, M. 1984-12-01 Using a bornological technic of M. Akkar, we reduce the study of classical questions (spectrum, boundedness of characters, functional calculus, etc.) in locally uniformly A-convex algebras to the Banach case. (author) 7. Lipschitz estimates for convex functions with respect to vector fields Valentino Magnani 2012-12-01 Full Text Available We present Lipschitz continuity estimates for a class of convex functions with respect to Hörmander vector fields. These results have been recently obtained in collaboration with M. Scienza, [22]. 8. A note on supercyclic operators in locally convex spaces Albanese, Angela A.; Jornet, David 2018-01-01 We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some examples are given. 9. Convex solutions of systems arising from Monge-Ampere equations Haiyan Wang 2009-10-01 Full Text Available We establish two criteria for the existence of convex solutions to a boundary value problem for weakly coupled systems arising from the Monge-Ampère equations. We shall use fixed point theorems in a cone. 10. 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. 11. Displacement Convexity for First-Order Mean-Field Games Seneci, Tommaso 2018-05-01 In this thesis, we consider the planning problem for first-order mean-field games (MFG). These games degenerate into optimal transport when there is no coupling between players. Our aim is to extend the concept of displacement convexity from optimal transport to MFGs. This extension gives new estimates for solutions of MFGs. First, we introduce the Monge-Kantorovich problem and examine related results on rearrangement maps. Next, we present the concept of displacement convexity. Then, we derive first-order MFGs, which are given by a system of a Hamilton-Jacobi equation coupled with a transport equation. Finally, we identify a large class of functions, that depend on solutions of MFGs, which are convex in time. Among these, we find several norms. This convexity gives bounds for the density of solutions of the planning problem. 12. Multi-objective convex programming problem arising in multivariate ... user Multi-objective convex programming problem arising in ... However, although the consideration of multiple objectives may seem a novel concept, virtually any nontrivial ..... Solving multiobjective programming problems by discrete optimization. 13. Mirror boxes and mirror mounts for photophysics beamline Raja Rao, P.M.; Raja Sekhar, B.N.; Das, N.C.; Khan, H.A.; Bhattacharya, S.S.; Roy, A.P. 1996-01-01 Photophysics beamline makes use of one metre Seya-Namioka monochromator and two toroidal mirrors in its fore optics. The first toroidal mirror (pre mirror) focuses light originating from the tangent point of the storage ring onto the entrance slit of the monochromator and second toroidal mirror (post mirror) collects light from the exit slit of the monochromator and focuses light onto the sample placed at a distance of about one metre away from the 2nd mirror. To steer light through monochromator and to focus it on the sample of 1mm x 1mm size require precision rotational and translational motion of the mirrors and this has been achieved with the help of precision mirror mounts. Since Indus-1 operates at pressures less than 10 -9 m.bar, the mirror mounts should be manipulated under similar ultra high vacuum conditions. Considering these requirements, two mirror boxes and two mirror mounts have been designed and fabricated. The coarse movements to the mirrors are imparted from outside the mirror chamber with the help of x-y tables and precision movements to the mirrors are achieved with the help of mirror mounts. The UHV compatibility and performance of the mirror mounts connected to mirror boxes under ultra high vacuum condition is evaluated. The details of the design, fabrication and performance evaluation are discussed in this report. 5 refs., 9 figs., 1 tab 14. Surgical treatment of convexity focal epilepsy Shimizu, Hiroyuki; Ishijima, Buichi; Iio, Masaaki. 1987-01-01 We have hitherto applied PET study in 72 epileptic patients. The main contents of their seizures consists of complex partial in 32, elementary partial in 32, generalized in 6, and others in 3 cases. We administered perorally 10 mCi glucose labeled with C11 produced in the JSW Baby Cyclotron for the study of CMRG(cerebral metabolic rate of glucose). The continuous inhalation method of CO 2 and O 2 labeled with O15 produced in the same cyclotron was also employed for measurement of rCBE(cerebral blood flow) and CMRO 2 (cerebral metabolic rate of oxygen). In both studies, epileptic foci were shown as well demarcated hypometabolic zones with decreased CMRG, rCBF or CMRO 2 . The locations of PET diagnosed foci were not contradictory with the clinical symptoms, scalp EEGs or X-ray CT findings. Of the 32 patients with the convexity epileptic foci, 8 patients underwent surgical treatment. Prior to the surgical intervention, subdural strip electrodes were inserted in the four cases for further assessment of focus locations. Subdural EEG disclosed very active brain activity with high amplitude 4 to 5 times scalp EEG and revealed epileptiform discharges most of which were not detected by scalp recording. PET scans did not characterize epileptogenic nature of a lesion. Subdural recording therefore was useful for detecting the foci responsible for habitual seizures in the cases with multiple PET foci. Ambiguous hypometabolic zones on PECT images also could be confirmed by the subdural technique. Of the 8 operated cases, five patients are seizure free, one is signigicantly improved and two are not improved although the postoperative follow-up is too short for precise evaluation. (J.P.N.) 15. Efficiency and Generalized Convex Duality for Nondifferentiable Multiobjective Programs Bae KwanDeok 2010-01-01 Full Text Available We introduce nondifferentiable multiobjective programming problems involving the support function of a compact convex set and linear functions. The concept of (properly efficient solutions are presented. We formulate Mond-Weir-type and Wolfe-type dual problems and establish weak and strong duality theorems for efficient solutions by using suitable generalized convexity conditions. Some special cases of our duality results are given. 16. Two examples of non strictly convex large deviations De Marco, Stefano; Jacquier, Antoine; Roome, Patrick 2016-01-01 We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex large deviations. For one of these examples, we show that the rate function of the Cramer-type of large deviations coincides with that of the Freidlin-Wentzell when contraction principles are applied. 17. Classical mirror symmetry Jinzenji, Masao 2018-01-01 This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov–Witten invariants of a Calabi–Yau threefold by using the Picard–Fuchs differential equation of period integrals of its mirror Calabi–Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold. First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold. On the B-model side, the process of construct... 18. Mirror plasma apparatus Moir, R.W. 1981-01-01 A mirror plasma apparatus which utilizes shielding by arc discharge to form a blanket plasma and lithium walls to reduce neutron damage to the wall of the apparatus. An embodiment involves a rotating liquid lithium blanket for a tandem mirror plasma apparatus wherein the first wall of the central mirror cell is made of liquid lithium which is spun with angular velocity great enough to keep the liquid lithium against the first material wall, a blanket plasma preventing the lithium vapor from contaminating the plasma 19. Mesmerising mirror neurons. Heyes, Cecilia 2010-06-01 Mirror neurons have been hailed as the key to understanding social cognition. I argue that three currents of thought-relating to evolution, atomism and telepathy-have magnified the perceived importance of mirror neurons. When they are understood to be a product of associative learning, rather than an adaptation for social cognition, mirror neurons are no longer mesmerising, but they continue to raise important questions about both the psychology of science and the neural bases of social cognition. Copyright 2010 Elsevier Inc. All rights reserved. 20. Decompositions, partitions, and coverings with convex polygons and pseudo-triangles Aichholzer, O.; Huemer, C.; Kappes, S.; Speckmann, B.; Tóth, Cs.D. 2007-01-01 We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex 1. Surgery for convexity/parasagittal/falx meningiomas Ochi, Takashi; Saito, Nobuhito 2013-01-01 Incidence of the complication related with the surgical treatment of meningiomas in the title was reviewed together with consideration of data about progress observation and stereotactic radiosurgery. MEDLINE papers in English were on line searched with keywords contained in above using PubMed System. For the convexity meningioma, 50-141 cases (mean age, 48-58.9 y) with 1.9-3.6 cm or 146.3 mL of the tumor size or volume were reported in 6 literatures (2006-2011), presenting 0% of surgery related death, 1-5.9% of internal medical or 5.5-37.4% of surgical complication, 0-2% of postoperative hemorrhage, 0-15.4% of neurological and 0-15.4% of prolonged/permanent deficits. For the parasagittal/falx meningioma, 46-108 cases (age, 55-58 y) with 1.9-4 cm tumor were reported in 8 literatures (2004-2011), presenting 0-5.7% death, 2-7.4% medical or 5.4-31% surgical complication, 0-3% hemorrhage, 0-15.4 neurologic and 0-15.4% prolonged deficits. For complications after the radiosurgery of the all 3 meningiomas, 41-832 cases (50-60 y) with tumors of 24.7-28 mm or 4.7-7.4 mL were reported in 8 literatures (2003-2012), presenting the incidence of 6.8-26.8% of radiation-related complications like headache, seizures and paralysis necessary for steroid treatment, and 1.20 or 4.80% of permanent morbidity. For the natural history of incidental meningiomas involving tentorium one, 16-144 cases in 6 literatures (2000-2012) revealed the growth rate/y of 1.9-3.9 mm or 0.54-1.15 mL. The outcome of surgical treatment of the meningiomas, a representative benign tumor, was concluded to be rather good as surgery was generally needed only when the disease became symptomatic due to the tumor growth. (T.T.) 2. Cryogenic Active Mirrors National Aeronautics and Space Administration — This effort seeks to develop active mirrors that can correct for thermally-induced figure deformations upon cooling from room-temperature at the time of manufacture,... 3. Manufacturing parabolic mirrors CERN PhotoLab 1975-01-01 The photo shows the construction of a vertical centrifuge mounted on an air cushion, with a precision of 1/10000 during rotation, used for the manufacture of very high=precision parabolic mirrors. (See Annual Report 1974.) 4. Mirror reactor surface study Hunt, A. L.; Damm, C. C.; Futch, A. H.; Hiskes, J. R.; Meisenheimer, R. G.; Moir, R. W.; Simonen, T. C.; Stallard, B. W.; Taylor, C. E. 1976-09-01 A general survey is presented of surface-related phenomena associated with the following mirror reactor elements: plasma first wall, ion sources, neutral beams, director converters, vacuum systems, and plasma diagnostics. A discussion of surface phenomena in possible abnormal reactor operation is included. Several studies which appear to merit immediate attention and which are essential to the development of mirror reactors are abstracted from the list of recommended areas for surface work. The appendix contains a discussion of the fundamentals of particle/surface interactions. The interactions surveyed are backscattering, thermal desorption, sputtering, diffusion, particle ranges in solids, and surface spectroscopic methods. A bibliography lists references in a number of categories pertinent to mirror reactors. Several complete published and unpublished reports on surface aspects of current mirror plasma experiments and reactor developments are also included. 5. Mirror fermions and cosmology Senjanovic, G.; Virginia Polytechnic Inst. and State Univ., Blacksburg 1984-07-01 Extended supersymmetry, Kaluza-Klein theory and family unification all suggest the existence of mirror fermions, with same quantum numbers but opposite helicities from ordinary fermions. The laboratory and especially cosmological implications of such particles are reviewed and summarized. (author) 6. Mirror reactor surface study Hunt, A.L.; Damm, C.C.; Futch, A.H.; Hiskes, J.R.; Meisenheimer, R.G.; Moir, R.W.; Simonen, T.C.; Stallard, B.W.; Taylor, C.E. 1976-01-01 A general survey is presented of surface-related phenomena associated with the following mirror reactor elements: plasma first wall, ion sources, neutral beams, director converters, vacuum systems, and plasma diagnostics. A discussion of surface phenomena in possible abnormal reactor operation is included. Several studies which appear to merit immediate attention and which are essential to the development of mirror reactors are abstracted from the list of recommended areas for surface work. The appendix contains a discussion of the fundamentals of particle/surface interactions. The interactions surveyed are backscattering, thermal desorption, sputtering, diffusion, particle ranges in solids, and surface spectroscopic methods. A bibliography lists references in a number of categories pertinent to mirror reactors. Several complete published and unpublished reports on surface aspects of current mirror plasma experiments and reactor developments are also included 7. The obsidian mirror The obsidian mirror Maria do Socorro Reis Amorin 2008-04-01 Full Text Available The author James Norman is an American who has always lived in Mexico during the summer. He seems to love Mexican - Indian traditions and he is well acquainted with the pre-historic culture as it is shown in his book: "The Obsidian Mirror". "The Obsidian Mirror" is a mysterious story about an archeologist: Quigley that lives in a small village in Mexico-San Marcos. He is searching for antiques that belong to some tribes of pre-historic Indians in order to find out their mysteries. Quigley becomes so engaged in his work that his mind has reached a stage that is impossible to separate between Quigley the archeologist, and Quigley as an ancient Indian. The culture, the myth, the sensation of Omen - characteristics of the Indians are within himself. As a result, Quigley acts sometimes as a real Indian. The author James Norman is an American who has always lived in Mexico during the summer. He seems to love Mexican - Indian traditions and he is well acquainted with the pre-historic culture as it is shown in his book: "The Obsidian Mirror". "The Obsidian Mirror" is a mysterious story about an archeologist: Quigley that lives in a small village in Mexico-San Marcos. He is searching for antiques that belong to some tribes of pre-historic Indians in order to find out their mysteries. Quigley becomes so engaged in his work that his mind has reached a stage that is impossible to separate between Quigley the archeologist, and Quigley as an ancient Indian. The culture, the myth, the sensation of Omen - characteristics of the Indians are within himself. As a result, Quigley acts sometimes as a real Indian. 8. Geometry of mirror manifolds Aspinwall, P.S.; Luetken, C.A. 1991-01-01 We analyze the mirror manifold hypothesis in one and three dimensions using the simplest available representations of the N = 2 superconformal algebra. The symmetries of these tensor models can be divided out to give an explicit representation of the mirror, and we give a simple group theoretical algorithm for determining which symmetries should be used. We show that the mirror of a superconformal field theory does not always have a geometrical interpretation, but when it does, deformations of complex structure of one manifold are reflected in deformations of the Kaehler form of the mirror manifold, and we show how the large radius limit of a manifold corresponds to a large complex structure limit in the mirror manifold. The mirror of the Tian-Yau three generation model is constructed both as a conformal field theory and as an algebraic variety with Euler number six. The Hodge numbers of this manifolds are fixed, but the intersection numbes are highly ambiguous, presumably reflected a rich structure of multicritical points in the moduli space of the field theory. (orig.) 9. Convex unwraps its first grown-up supercomputer Manuel, T. 1988-03-03 Convex Computer Corp.'s new supercomputer family is even more of an industry blockbuster than its first system. At a tenfold jump in performance, it's far from just an incremental upgrade over its first minisupercomputer, the C-1. The heart of the new family, the new C-2 processor, churning at 50 million floating-point operations/s, spawns a group of systems whose performance could pass for some fancy supercomputers-namely those of the Cray Research Inc. family. When added to the C-1, Convex's five new supercomputers create the C series, a six-member product group offering a performance range from 20 to 200 Mflops. They mark an important transition for Convex from a one-product high-tech startup to a multinational company with a wide-ranging product line. It's a tough transition but the Richardson, Texas, company seems to be doing it. The extended product line propels Convex into the upper end of the minisupercomputer class and nudges it into the low end of the big supercomputers. It positions Convex in an uncrowded segment of the market in the$500,000 to $1 million range offering 50 to 200 Mflops of performance. The company is making this move because the minisuper area, which it pioneered, quickly became crowded with new vendors, causing prices and gross margins to drop drastically. 10. Inhibitory competition in figure-ground perception: context and convexity. Peterson, Mary A; Salvagio, Elizabeth 2008-12-15 Convexity has long been considered a potent cue as to which of two regions on opposite sides of an edge is the shaped figure. Experiment 1 shows that for a single edge, there is only a weak bias toward seeing the figure on the convex side. Experiments 1-3 show that the bias toward seeing the convex side as figure increases as the number of edges delimiting alternating convex and concave regions increases, provided that the concave regions are homogeneous in color. The results of Experiments 2 and 3 rule out a probability summation explanation for these context effects. Taken together, the results of Experiments 1-3 show that the homogeneity versus heterogeneity of the convex regions is irrelevant. Experiment 4 shows that homogeneity of alternating regions is not sufficient for context effects; a cue that favors the perception of the intervening regions as figures is necessary. Thus homogeneity alone does not alone operate as a background cue. We interpret our results within a model of figure-ground perception in which shape properties on opposite sides of an edge compete for representation and the competitive strength of weak competitors is further reduced when they are homogeneous. 11. Optical calibration and test of the VLT Deformable Secondary Mirror Briguglio, Runa; Xompero, Marco; Riccardi, Armando; Andrighettoni, Mario; Pescoller, Dietrich; Biasi, Roberto; Gallieni, Daniele; Vernet, Elise; Kolb, Johann; Arsenault, Robin; Madec, Pierre-Yves 2013-12-01 The Deformable Secondary Mirror (DSM) for the VLT (ESO) represents the state-of-art of the large-format deformable mirror technology with its 1170 voice-coil actuators and its internal metrology based on actuator co-located capacitive sensors to control the shape of the 1.12m-diameter 2mm-thick convex shell. The present paper reports the results of the optical characterization of the mirror unit with the ASSIST facility located at ESO-Garching and executed in a collaborative effort by ESO, INAF-Osservatorio Astrofisico di Arcetri and the DSM manufacturing companies (Microgate s.r.l. and A.D.S. International s.r.l.). The main purposes of the tests are the optical characterization of the shell flattening residuals, the corresponding calibration of flattening commands, the optical calibration of the capacitive sensors and the optical calibration of the mirror influence functions. The results are used for the optical acceptance of the DSM and to allow the next test phase coupling the DSM with the wave-front sensor modules of the new Adaptive Optics Facility (AOF) of ESO. 12. Helically linked mirror arrangement Ranjan, P. 1986-08-01 A scheme is described for helical linking of mirror sections, which endeavors to combine the better features of toroidal and mirror devices by eliminating the longitudinal loss of mirror machines, having moderately high average β and steady state operation. This scheme is aimed at a device, with closed magnetic surfaces having rotational transform for equilibrium, one or more axisymmetric straight sections for reduced radial loss, a simple geometrical axis for the links and an overall positive magnetic well depth for stability. We start by describing several other attempts at linking of mirror sections, made both in the past and the present. Then a description of our helically linked mirror scheme is given. This example has three identical straight sections connected by three sections having helical geometric axes. A theoretical analysis of the magnetic field and single-particle orbits in them leads to the conclusion that most of the passing particles would be confined in the device and they would have orbits independent of pitch angle under certain conditions. Numerical results are presented, which agree well with the theoretical results as far as passing particle orbits are concerned 13. Physics of mirror systems Post, R.F. 1982-05-01 In recent years the emphasis in research on the magnetic mirror approach to fusion has been shifted to address what are essentially economically-motivated issues. The introduction of the Tandem Mirror idea solved in principal the problem of low Q (low fusion power gain) of mirror-based fusion systems. In order to optimize the tandem mirror idea from an economic standpoint, some important improvements have been suggested. These improvements include the thermal barrier idea of Baldwin and Logan and the axicell concept of Kesner. These new modifications introduce some special physics considerations. Among these are (1) The MHD stability properties of high energy electron components in the end cells; (2) The optimization of end-cell magnetic field configurations with the objective of minimizing equilibrium parallel currents; (3) The suppression of microstabilities by use of sloshing ion distributions. Following a brief outline of tandem mirror concepts, the above three topics are discussed, with illustrative examples taken from earlier work or from recent design studies 14. Dose evaluation from multiple detector outputs using convex optimisation Hashimoto, M.; Iimoto, T.; Kosako, T. 2011-01-01 A dose evaluation using multiple radiation detectors can be improved by the convex optimisation method. It enables flexible dose evaluation corresponding to the actual radiation energy spectrum. An application to the neutron ambient dose equivalent evaluation is investigated using a mixed-gas proportional counter. The convex derives the certain neutron ambient dose with certain width corresponding to the true neutron energy spectrum. The range of the evaluated dose is comparable to the error of conventional neutron dose measurement equipments. An application to the neutron individual dose equivalent measurement is also investigated. Convexes of particular dosemeter combinations evaluate the individual dose equivalent better than the dose evaluation of a single dosemeter. The combinations of dosemeters with high orthogonality of their response characteristics tend to provide a good suitability for dose evaluation. (authors) 15. Convexity and concavity constants in Lorentz and Marcinkiewicz spaces Kaminska, Anna; Parrish, Anca M. 2008-07-01 We provide here the formulas for the q-convexity and q-concavity constants for function and sequence Lorentz spaces associated to either decreasing or increasing weights. It yields also the formula for the q-convexity constants in function and sequence Marcinkiewicz spaces. In this paper we extent and enhance the results from [G.J.O. Jameson, The q-concavity constants of Lorentz sequence spaces and related inequalities, Math. Z. 227 (1998) 129-142] and [A. Kaminska, A.M. Parrish, The q-concavity and q-convexity constants in Lorentz spaces, in: Banach Spaces and Their Applications in Analysis, Conference in Honor of Nigel Kalton, May 2006, Walter de Gruyter, Berlin, 2007, pp. 357-373]. 16. Transient disturbance growth in flows over convex surfaces Karp, Michael; Hack, M. J. Philipp 2017-11-01 Flows over curved surfaces occur in a wide range of applications including airfoils, compressor and turbine vanes as well as aerial, naval and ground vehicles. In most of these applications the surface has convex curvature, while concave surfaces are less common. Since monotonic boundary-layer flows over convex surfaces are exponentially stable, they have received considerably less attention than flows over concave walls which are destabilized by centrifugal forces. Non-modal mechanisms may nonetheless enable significant disturbance growth which can make the flow susceptible to secondary instabilities. A parametric investigation of the transient growth and secondary instability of flows over convex surfaces is performed. The specific conditions yielding the maximal transient growth and strongest instability are identified. The effect of wall-normal and spanwise inflection points on the instability process is discussed. Finally, the role and significance of additional parameters, such as the geometry and pressure gradient, is analyzed. 17. A working-set framework for sequential convex approximation methods Stolpe, Mathias 2008-01-01 We present an active-set algorithmic framework intended as an extension to existing implementations of sequential convex approximation methods for solving nonlinear inequality constrained programs. The framework is independent of the choice of approximations and the stabilization technique used...... to guarantee global convergence of the method. The algorithm works directly on the nonlinear constraints in the convex sub-problems and solves a sequence of relaxations of the current sub-problem. The algorithm terminates with the optimal solution to the sub-problem after solving a finite number of relaxations.... 18. Convex Hull Abstraction in Specialisation of CLP Programs Peralta, J.C.; Gallagher, John Patrick 2003-01-01 We introduce an abstract domain consisting of atomic formulas constrained by linear arithmetic constraints (or convex hulls). This domain is used in an algorithm for specialization of constraint logic programs. The algorithm incorporates in a single phase both top-down goal directed propagation...... and bottom-up answer propagation, and uses a widening on the convex hull domain to ensure termination. We give examples to show the precision gained by this approach over other methods in the literature for specializing constraint logic programs. The specialization method can also be used for ordinary logic... 19. Closedness type regularity conditions in convex optimization and beyond Sorin-Mihai Grad 2016-09-01 Full Text Available The closedness type regularity conditions have proven during the last decade to be viable alternatives to their more restrictive interiority type counterparts, in both convex optimization and different areas where it was successfully applied. In this review article we de- and reconstruct some closedness type regularity conditions formulated by means of epigraphs and subdifferentials, respectively, for general optimization problems in order to stress that they arise naturally when dealing with such problems. The results are then specialized for constrained and unconstrained convex optimization problems. We also hint towards other classes of optimization problems where closedness type regularity conditions were successfully employed and discuss other possible applications of them. 20. Distribution functions of sections and projections of convex bodies Kim, Jaegil; Yaskin, Vladyslav; Zvavitch, Artem 2015-01-01 Typically, when we are given the section (or projection) function of a convex body, it means that in each direction we know the size of the central section (or projection) perpendicular to this direction. Suppose now that we can only get the information about the sizes of sections (or projections), and not about the corresponding directions. In this paper we study to what extent the distribution function of the areas of central sections (or projections) of a convex body can be used to derive ... 1. 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. 2. Relaxation Methods for Strictly Convex Regularizations of Piecewise Linear Programs Kiwiel, K. C. 1998-01-01 We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that occur in entropy maximization, quadratic programming, and network flows. In particular, it may solve exact penalty versions of such (possibly inconsistent) problems, and subproblems of bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity, and in certain cases is highly parallelizable. Its global convergence is established in the recent framework of B -functions (generalized Bregman functions) 3. A Conceptual Mirror Badie, Farshad 2017-01-01 The multilevel interactions between a mentor and her/his learner could exchange various conceptions between them that are supported by their own conceptualisations. Producing the own realisation of a world and developing it in the context of interactions could be said to be the most valuable prod...... will analyse the logical dependencies between learner and men- tor and will check their reflectional symmetrical relationship in a conceptual mirror. The conceptual mirror is a phenomenon that represents the meeting point of the mentor’s and the learner’s conceptual knowledge.... 4. The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases Gomes, Diogo A.; Mitake, Hiroyoshi; Tran, Hung V. 2018-01-01 Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton–Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton–Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton–Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not directly apply. In this case, we establish the convergence by a direct approach. 5. The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases Gomes, Diogo A. 2018-01-26 Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton–Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton–Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton–Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not directly apply. In this case, we establish the convergence by a direct approach. 6. An efficient method for minimizing a convex separable logarithmic function subject to a convex inequality constraint or linear equality constraint 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. 7. Amorphous Metals and Composites as Mirrors and Mirror Assemblies Hofmann, Douglas C. (Inventor); Davis, Gregory L. (Inventor); Agnes, Gregory S. (Inventor); Shapiro, Andrew A. (Inventor) 2016-01-01 A mirror or mirror assembly fabricated by molding, pressing, assembling, or depositing one or more bulk metal glass (BMG), bulk metal glass composite (BMGMC), or amorphous metal (AM) parts and where the optical surface and backing of the mirror can be fabricated without machining or polishing by utilizing the unique molding capabilities of this class of materials. 8. Tandem mirror reactor Moir, R.W.; Barr, W.L.; Carlson, G.A. 1977-01-01 A parametric analysis and a preliminary conceptual design for a 1000 MWe Tandem Mirror Reactor (TMR) are described. The concept is sufficiently attractive to encourage further work, both for a pure fusion TMR and a low technology TMR Fusion-Fission Hybrid 9. Advanced Curvature Deformable Mirrors 2010-09-01 ORGANIZATION NAME(S) AND ADDRESS(ES) University of Hawaii ,Institute for Astronomy,640 North A‘ohoku Place, #209 , Hilo ,HI,96720-2700 8. PERFORMING...Advanced Curvature Deformable Mirrors Christ Ftaclas1,2, Aglae Kellerer2 and Mark Chun2 Institute for Astronomy, University of Hawaii 10. Mirror reactor blankets Lee, J.D.; Barmore, W.L.; Bender, D.J.; Doggett, J.N.; Galloway, T.R. 1976-01-01 The general requirements of a breeding blanket for a mirror reactor are described. The following areas are discussed: (1) facility layout and blanket maintenance, (2) heat transfer and thermal conversion system, (3) materials, (4) tritium containment and removal, and (5) nuclear performance 11. Minimal mirror twin Higgs Barbieri, Riccardo [Institute of Theoretical Studies, ETH Zurich,CH-8092 Zurich (Switzerland); Scuola Normale Superiore,Piazza dei Cavalieri 7, 56126 Pisa (Italy); Hall, Lawrence J.; Harigaya, Keisuke [Department of Physics, University of California,Berkeley, California 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory,Berkeley, California 94720 (United States) 2016-11-29 In a Mirror Twin World with a maximally symmetric Higgs sector the little hierarchy of the Standard Model can be significantly mitigated, perhaps displacing the cutoff scale above the LHC reach. We show that consistency with observations requires that the Z{sub 2} parity exchanging the Standard Model with its mirror be broken in the Yukawa couplings. A minimal such effective field theory, with this sole Z{sub 2} breaking, can generate the Z{sub 2} breaking in the Higgs sector necessary for the Twin Higgs mechanism. The theory has constrained and correlated signals in Higgs decays, direct Dark Matter Detection and Dark Radiation, all within reach of foreseen experiments, over a region of parameter space where the fine-tuning for the electroweak scale is 10-50%. For dark matter, both mirror neutrons and a variety of self-interacting mirror atoms are considered. Neutrino mass signals and the effects of a possible additional Z{sub 2} breaking from the vacuum expectation values of B−L breaking fields are also discussed. 12. On the polarizability dyadics of electrically small, convex objects Lakhtakia, Akhlesh 1993-11-01 This communication on the polarizability dyadics of electrically small objects of convex shapes has been prompted by a recent paper published by Sihvola and Lindell on the polarizability dyadic of an electrically gyrotropic sphere. A mini-review of recent work on polarizability dyadics is appended. 13. Riemann solvers and undercompressive shocks of convex FPU chains Herrmann, Michael; Rademacher, Jens D M 2010-01-01 We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space–time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax shocks are replaced by so-called dispersive shocks. For convex–concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave–convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions 14. On the Convexity of Step out - Step in Sequencing Games Musegaas, Marieke; Borm, Peter; Quant, Marieke 2016-01-01 The main result of this paper is the convexity of Step out - Step in (SoSi) sequencing games, a class of relaxed sequencing games first analyzed by Musegaas, Borm, and Quant (2015). The proof makes use of a polynomial time algorithm determining the value and an optimal processing order for an 15. 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. 16. Convex relationships in ecosystems containing mixtures of trees and grass Scholes, RJ 2003-12-01 Full Text Available The relationship between grass production and the quantity of trees in mixed tree-grass ecosystems (savannas) is convex for all or most of its range. In other words, the grass production declines more steeply per unit increase in tree quantity... 17. Positive definite functions and dual pairs of locally convex spaces Daniel Alpay 2018-01-01 Full Text Available Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions. 18. Intracranial Convexity Lipoma with Massive Calcification: Case Report Kim, Eung Tae; Park, Dong Woo; Ryu, Jeong Ah; Park, Choong Ki; Lee, Young Jun; Lee, Seung Ro [Dept. of Radiology, Hanyang University College of Medicine, Seoul (Korea, Republic of) 2011-12-15 Intracranial lipoma is a rare entity, accounting for less than 0.5% of intracranial tumors, which usually develops in the callosal cisterns. We report a case of lipoma with an unusual location; in the high parietal convexity combined with massive calcification, and no underlying vascular malformation or congenital anomaly. 19. A duality recipe for non-convex variational problems Bouchitté, Guy; Phan, Minh 2018-03-01 The aim of this paper is to present a general convexification recipe that can be useful for studying non-convex variational problems. In particular, this allows us to treat such problems by using a powerful primal-dual scheme. Possible further developments and open issues are given. xml:lang="fr" 20. A note on the nucleolus for 2-convex TU games Driessen, Theo; Hou, D. For 2-convex n-person cooperative TU games, the nucleolus is determined as some type of constrained equal award rule. Its proof is based on Maschler, Peleg, and Shapley’s geometrical characterization for the intersection of the prekernel with the core. Pairwise bargaining ranges within the core are 1. A convex optimization approach for solving large scale linear systems Debora Cores 2017-01-01 Full Text Available The well-known Conjugate Gradient (CG method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems. 2. Transonic shock wave. Boundary layer interaction at a convex wall Koren, B.; Bannink, W.J. 1984-01-01 A standard finite element procedure has been applied to the problem of transonic shock wave – boundary layer interaction at a convex wall. The method is based on the analytical Bohning-Zierep model, where the boundary layer is perturbed by a weak normal shock wave which shows a singular pressure 3. Computing Convex Coverage Sets for Faster Multi-Objective Coordination Roijers, D.M.; Whiteson, S.; Oliehoek, F.A. 2015-01-01 In this article, we propose new algorithms for multi-objective coordination graphs (MO-CoGs). Key to the efficiency of these algorithms is that they compute a convex coverage set (CCS) instead of a Pareto coverage set (PCS). Not only is a CCS a sufficient solution set for a large class of problems, 4. Flat tori in three-dimensional space and convex integration. Borrelli, Vincent; Jabrane, Saïd; Lazarus, Francis; Thibert, Boris 2012-05-08 It is well-known that the curvature tensor is an isometric invariant of C(2) Riemannian manifolds. This invariant is at the origin of the rigidity observed in Riemannian geometry. In the mid 1950s, Nash amazed the world mathematical community by showing that this rigidity breaks down in regularity C(1). This unexpected flexibility has many paradoxical consequences, one of them is the existence of C(1) isometric embeddings of flat tori into Euclidean three-dimensional space. In the 1970s and 1980s, M. Gromov, revisiting Nash's results introduced convex integration theory offering a general framework to solve this type of geometric problems. In this research, we convert convex integration theory into an algorithm that produces isometric maps of flat tori. We provide an implementation of a convex integration process leading to images of an embedding of a flat torus. The resulting surface reveals a C(1) fractal structure: Although the tangent plane is defined everywhere, the normal vector exhibits a fractal behavior. Isometric embeddings of flat tori may thus appear as a geometric occurrence of a structure that is simultaneously C(1) and fractal. Beyond these results, our implementation demonstrates that convex integration, a theory still confined to specialists, can produce computationally tractable solutions of partial differential relations. 5. Mirror fusion--fission hybrids Lee, J.D. 1978-01-01 The fusion-fission concept and the mirror fusion-fission hybrid program are outlined. Magnetic mirror fusion drivers and blankets for hybrid reactors are discussed. Results of system analyses are presented and a reference design is described 6. Physics of mirror fusion systems Post, R.F. 1976-01-01 Recent experimental results with the 2XIIB mirror machine at Lawrence Livermore Laboratory have demonstrated the stable confinement of plasmas at fusion temperatures and with energy densities equaling or exceeding that of the confining fields. The physics of mirror confinement is discussed in the context of these new results. Some possible approaches to further improving the confinement properties of mirror systems and the impact of these new approaches on the prospects for mirror fusion reactors are discussed 7. Mirror fusion test facility Post, R.F. 1978-01-01 The MFTF is a large new mirror facility under construction at Livermore for completion in 1981--82. It represents a scaleup, by a factor of 50 in plasma volume, a factor of 5 or more in ion energy, and a factor of 4 in magnetic field intensity over the Livermore 2XIIB experiment. Its magnet, employing superconducting NbTi windings, is of Yin-Yang form and will weigh 200 tons. MFTF will be driven by neutral beams of two levels of current and energy: 1000 amperes of 20 keV (accelerating potential) pulsed beams for plasma startup; 750 amperes of 80 keV beams of 0.5 second duration for temperature buildup and plasma sustainment. Two operating modes for MFTF are envisaged: The first is operation as a conventional mirror cell with n/sup tau/ approximately equal to 10 12 cm -3 sec, W/sub i/ = 50 keV, where the emphasis will be on studying the physics of mirror cells, particularly the issues of improved techniques of stabilization against ion cyclotron modes and of maximization of the electron temperature. The second possible mode is the further study of the Field Reversed Mirror idea, using high current neutral beams to sustain the field-reversed state. Anticipating success in the coming Livermore Tandem Mirror Experiment (TMX) MFTF has been oriented so that it could comprise one end cell of a scaled up TM experiment. Also, if MFTF were to succeed in achieving a FR state it could serve as an essentially full-sized physics prototype of one cell of a FRM fusion power plant 8. Mirror reactor studies Moir, R.W.; Barr, W.L.; Bender, D.J. 1977-01-01 Design studies of a fusion mirror reactor, a fusion-fission mirror reactor, and two small mirror reactors are summarized. The fusion reactor uses 150-keV neutral-beam injectors based on the acceleration of negative ions. The injectors provide over 1 GW of continuous power at an efficiency greater than 80%. The fusion reactor has three-stage, modularized, Venetian blind, plasma direct converter with a predicted efficiency of 59% and a new concept for removal of the lune-shaped blanket: a crane is brought between the two halves of the Yin-Yang magnet, which are separated by a float. The design has desirable features such as steady-state operation, minimal impurity problems, and low first-wall thermal stress. The major disadvantage is low Q resulting in high re-circulating power and hence high cost of electrical power. However, the direct capital cost per unit of gross electrical power is reasonable [$1000/kW(e)]. By contrast, the fusion-fission reactor design is not penalized by re-circulating power and uses relatively near-term fusion technology being developed for the fusion power program. New results are presented on the Th- 233 U and the U- 239 Pu fuel cycles. The purpose of this hybrid is fuel production, with projected costs at $55/g of Pu or$127/g of 233 U. Blanket and cooling system designs, including an emergency cooling system, by General Atomic Company, lead us to the opinion that the reactor can meet expected safety standards for licensing. The smallest mirror reactor having only a shield between the plasma and the coil is the 4.2-m long fusion engineering research facility (FERF) designed for material irradiation. The smallest mirror reactor having both a blanket and shield is the 7.5-m long experimental power reactor (EPR), which has both a fusion and a fusion-fission version. (author)

9. Short Run Profit Maximization in a Convex Analysis Framework

Ilko Vrankic

2017-03-01

Full Text Available In this article we analyse the short run profit maximization problem in a convex analysis framework. The goal is to apply the results of convex analysis due to unique structure of microeconomic phenomena on the known short run profit maximization problem where the results from convex analysis are deductively applied. In the primal optimization model the technology in the short run is represented by the short run production function and the normalized profit function, which expresses profit in the output units, is derived. In this approach the choice variable is the labour quantity. Alternatively, technology is represented by the real variable cost function, where costs are expressed in the labour units, and the normalized profit function is derived, this time expressing profit in the labour units. The choice variable in this approach is the quantity of production. The emphasis in these two perspectives of the primal approach is given to the first order necessary conditions of both models which are the consequence of enveloping the closed convex set describing technology with its tangents. The dual model includes starting from the normalized profit function and recovering the production function, and alternatively the real variable cost function. In the first perspective of the dual approach the choice variable is the real wage, and in the second it is the real product price expressed in the labour units. It is shown that the change of variables into parameters and parameters into variables leads to both optimization models which give the same system of labour demand and product supply functions and their inverses. By deductively applying the results of convex analysis the comparative statics results are derived describing the firm's behaviour in the short run.

10. Review of mirror fusion reactor designs

Bender, D.J.

1977-01-01

Three magnetic confinement concepts, based on the mirror principle, are described. These mirror concepts are summarized as follows: (1) fusion-fission hybrid reactor, (2) tandem mirror reactor, and (3) reversed field mirror reactor

11. Mirror image agnosia.

Chandra, Sadanandavalli Retnaswami; Issac, Thomas Gregor

2014-10-01

Gnosis is a modality-specific ability to access semantic knowledge of an object or stimulus in the presence of normal perception. Failure of this is agnosia or disorder of recognition. It can be highly selective within a mode. self-images are different from others as none has seen one's own image except in reflection. Failure to recognize this image can be labeled as mirror image agnosia or Prosopagnosia for reflected self-image. Whereas mirror agnosia is a well-recognized situation where the person while looking at reflected images of other objects in the mirror he imagines that the objects are in fact inside the mirror and not outside. Five patients, four females, and one male presented with failure to recognize reflected self-image, resulting in patients conversing with the image as a friend, fighting because the person in mirror is wearing her nose stud, suspecting the reflected self-image to be an intruder; but did not have prosopagnosia for others faces, non living objects on self and also apraxias except dressing apraxia in one patient. This phenomena is new to our knowledge. Mirror image agnosia is an unique phenomena which is seen in patients with parietal lobe atrophy without specificity to a category of dementing illness and seems to disappear as disease advances. Reflected self-images probably have a specific neural substrate that gets affected very early in posterior dementias specially the ones which predominantly affect the right side. At that phase most patients are mistaken as suffering from psychiatric disorder as cognition is moderately preserved. As disease becomes more widespread this symptom becomes masked. A high degree of suspicion and proper assessment might help physicians to recognize the organic cause of the symptom so that early therapeutic interventions can be initiated. Further assessment of the symptom with FMRI and PET scan is likely to solve the mystery of how brain handles reflected self-images. A new observation involving failure

12. Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes

Sarıkaya, Mehmet Zeki, E-mail: sarikayamz@gmail.com [Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce (Turkey); Kiriş, Mehmet Eyüp, E-mail: kiris@aku.edu.tr [Department of Mathematics, Institute of Science and Arts, Afyon Kocatepe University, Afyonkarahisar (Turkey); Çelik, Nuri, E-mail: ncelik@bartin.edu.tr [Department of Statistics, Faculty of Science, Bartın University, Bartın-Turkey (Turkey)

2016-04-18

The main aim of the present paper is to introduce φ{sub h}-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φ{sub h}-convex stochastic processes. We also give some new general inequalities for φ{sub h}-convex stochastic processes.

13. Dynamic coherent backscattering mirror

Zeylikovich, I.; Xu, M., E-mail: mxu@fairfield.edu [Physics Department, Fairfield University, Fairfield, CT 06824 (United States)

2016-02-15

The phase of multiply scattered light has recently attracted considerable interest. Coherent backscattering is a striking phenomenon of multiple scattered light in which the coherence of light survives multiple scattering in a random medium and is observable in the direction space as an enhancement of the intensity of backscattered light within a cone around the retroreflection direction. Reciprocity also leads to enhancement of backscattering light in the spatial space. The random medium behaves as a reciprocity mirror which robustly converts a diverging incident beam into a converging backscattering one focusing at a conjugate spot in space. Here we first analyze theoretically this coherent backscattering mirror (CBM) phenomenon and then demonstrate the capability of CBM compensating and correcting both static and dynamic phase distortions occurring along the optical path. CBM may offer novel approaches for high speed dynamic phase corrections in optical systems and find applications in sensing and navigation.

14. Neutral beams for mirrors

Fink, J.H.

1983-01-01

An important demonstration of negative ion technology is proposed for FY92 in the MFTF-α+T, an upgrade of the Mirror Fusion Test Facility at the Lawrence Livermore National Laboratory. This facility calls for 200-keV negative ions to form neutral beams that generate sloshing ions in the reactor end plugs. Three different beam lines are considered for this application. Their advantages and disadvantages are discussed

15. Mirrors for High Resolution X-Ray Optics---Figure Preserving IR/PT Coating

Chan, Kai-Wing; Olsen, Lawrence; Sharpe, Marton; Numata, Ai; McClelland, Ryan; Saha, Timo; Zhang, Will

2016-01-01

Coating stress of 10 - 20 nm of Ir is sufficiently high to distort the figure of arc-second thin lightweight mirrors. For iridium: --Stress sigma 4 GPa for 15 nm film implies 60 Nm integrated stress-- Need less than 3 N/m (or stress less than 200 MPa) for sub-arcsecond optics. Basic Approaches for Mitigation. A. Annealing the film-- Glass can be heat up to 400 C without distortion. Silicon is even more resistant.-- It was found that recovery is limited by residual thermal stress from taking the mirror down from high T. B. Coating bi-layer films with compressive stress with tensile stress. C. Front-and-back coating with magnetron sputtering or atomic layer deposition-- Sputtering involve spanning of substrates. Geometric difference in setup (convexness/concaveness of curved mirrors) does not permit precise front-and-back matching-- Atomic layer deposition can provide a uniform deposition front and back simultaneously.

16. Mirror reactor studies

Moir, R.W.; Barr, W.L.; Bender, D.J.

1976-01-01

Design studies of a fusion mirror reactor, a fusion-fission mirror reactor, and two small mirror reactors are summarized. The fusion reactor uses 150-keV neutral-beam injectors based on the acceleration of negative ions. The injectors provide over 1 GW of continuous power at an efficiency greater than 80 percent. The fusion reactor has three-stage, modularized, Venetian blind, plasma direct converter with a predicted efficiency of 59 percent and a new concept for removal of the lune-shaped blanket: a crane is brought between the two halves of the Yin-Yang magnet, which are separated by a float. The design has desirable features such as steady-state operation, minimal impurity problems, and low first-wall thermal stress. The major disadvantage is low Q resulting in high recirculating power and hence high cost of electrical power. However, the direct capital cost per unit of gross electrical power is reasonable [$1000/kW(e) 17. Mirror-Image Equivalence and Interhemispheric Mirror-Image Reversal. Corballis, Michael C 2018-01-01 Mirror-image confusions are common, especially in children and in some cases of neurological impairment. They can be a special impediment in activities such as reading and writing directional scripts, where mirror-image patterns (such as b and d ) must be distinguished. Treating mirror images as equivalent, though, can also be adaptive in the natural world, which carries no systematic left-right bias and where the same object or event can appear in opposite viewpoints. Mirror-image equivalence and confusion are natural consequences of a bilaterally symmetrical brain. In the course of learning, mirror-image equivalence may be established through a process of symmetrization, achieved through homotopic interhemispheric exchange in the formation of memory circuits. Such circuits would not distinguish between mirror images. Learning to discriminate mirror-image discriminations may depend either on existing brain asymmetries, or on extensive learning overriding the symmetrization process. The balance between mirror-image equivalence and mirror-image discrimination may nevertheless be precarious, with spontaneous confusions or reversals, such as mirror writing, sometimes appearing naturally or as a manifestation of conditions like dyslexia. 18. Mirror-Image Equivalence and Interhemispheric Mirror-Image Reversal Michael C. Corballis 2018-04-01 Full Text Available Mirror-image confusions are common, especially in children and in some cases of neurological impairment. They can be a special impediment in activities such as reading and writing directional scripts, where mirror-image patterns (such as b and d must be distinguished. Treating mirror images as equivalent, though, can also be adaptive in the natural world, which carries no systematic left-right bias and where the same object or event can appear in opposite viewpoints. Mirror-image equivalence and confusion are natural consequences of a bilaterally symmetrical brain. In the course of learning, mirror-image equivalence may be established through a process of symmetrization, achieved through homotopic interhemispheric exchange in the formation of memory circuits. Such circuits would not distinguish between mirror images. Learning to discriminate mirror-image discriminations may depend either on existing brain asymmetries, or on extensive learning overriding the symmetrization process. The balance between mirror-image equivalence and mirror-image discrimination may nevertheless be precarious, with spontaneous confusions or reversals, such as mirror writing, sometimes appearing naturally or as a manifestation of conditions like dyslexia. 19. A Convex Optimization Model and Algorithm for Retinex Qing-Nan Zhao 2017-01-01 Full Text Available Retinex is a theory on simulating and explaining how human visual system perceives colors under different illumination conditions. The main contribution of this paper is to put forward a new convex optimization model for Retinex. Different from existing methods, the main idea is to rewrite a multiplicative form such that the illumination variable and the reflection variable are decoupled in spatial domain. The resulting objective function involves three terms including the Tikhonov regularization of the illumination component, the total variation regularization of the reciprocal of the reflection component, and the data-fitting term among the input image, the illumination component, and the reciprocal of the reflection component. We develop an alternating direction method of multipliers (ADMM to solve the convex optimization model. Numerical experiments demonstrate the advantages of the proposed model which can decompose an image into the illumination and the reflection components. 20. Convexity and the Euclidean Metric of Space-Time Nikolaos Kalogeropoulos 2017-02-01 Full Text Available We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces. 1. On the stretch factor of convex Delaunay graphs Prosenjit Bose 2010-06-01 Full Text Available Let C be a compact and convex set in the plane that contains the origin in its interior, and let S be a finite set of points in the plane. The Delaunay graph DGC(S of S is defined to be the dual of the Voronoi diagram of S with respect to the convex distance function defined by C. We prove that DGC(S is a t-spanner for S, for some constant t that depends only on the shape of the set C. Thus, for any two points p and q in S, the graph DGC(S contains a path between p and q whose Euclidean length is at most t times the Euclidean distance between p and q. 2. A Survey on Operator Monotonicity, Operator Convexity, and Operator Means Pattrawut Chansangiam 2015-01-01 Full Text Available This paper is an expository devoted to an important class of real-valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations for such functions are given from the viewpoint of differential analysis in terms of matrix of divided differences. From the viewpoint of operator inequalities, various characterizations and the relationship between operator monotonicity and operator convexity are given by Hansen and Pedersen. In the viewpoint of measure theory, operator monotone functions on the nonnegative reals admit meaningful integral representations with respect to Borel measures on the unit interval. Furthermore, Kubo-Ando theory asserts the correspondence between operator monotone functions and operator means. 3. Convex variational problems linear, nearly linear and anisotropic growth conditions Bildhauer, Michael 2003-01-01 The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions. This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems. 4. Moduli spaces of convex projective structures on surfaces Fock, V. V.; Goncharov, A. B. 2007-01-01 We introduce explicit parametrisations of the moduli space of convex projective structures on surfaces, and show that the latter moduli space is identified with the higher Teichmüller space for defined in [V.V. Fock, A.B. Goncharov, Moduli spaces of local systems and higher Teichmüller theory, math.......AG/0311149]. We investigate the cluster structure of this moduli space, and define its quantum version.... 5. Constrained convex minimization via model-based excessive gap Tran Dinh, Quoc; Cevher, Volkan 2014-01-01 We introduce a model-based excessive gap technique to analyze first-order primal- dual methods for constrained convex minimization. As a result, we construct new primal-dual methods with optimal convergence rates on the objective residual and the primal feasibility gap of their iterates separately. Through a dual smoothing and prox-function selection strategy, our framework subsumes the augmented Lagrangian, and alternating methods as special cases, where our rates apply. 6. Free locally convex spaces with a small base Gabriyelyan, S.; Kąkol, Jerzy 2017-01-01 Roč. 111, č. 2 (2017), s. 575-585 ISSN 1578-7303 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : compact resolution * free locally convex space * G-base Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.690, year: 2016 http://link.springer.com/article/10.1007%2Fs13398-016-0315-1 7. A formulation of combinatorial auction via reverse convex programming Henry Schellhorn 2005-01-01 of this problem, where orders are aggregated and integrality constraints are relaxed. It was proved that this problem could be solved efficiently in two steps by calculating two fixed points, first the fixed point of a contraction mapping, and then of a set-valued function. In this paper, we generalize the problem to incorporate constraints on maximum price changes between two auction rounds. This generalized problem cannot be solved by the aforementioned methods and necessitates reverse convex programming techniques. 8. Some fixed point theorems on non-convex sets Mohanasundaram Radhakrishnan 2017-10-01 Full Text Available In this paper, we prove that if$K$is a nonempty weakly compact set in a Banach space$X$,$T:K\\to K$is a nonexpansive map satisfying$\\frac{x+Tx}{2}\\in K$for all$x\\in K$and if$X$is$3-$uniformly convex or$X$has the Opial property, then$T$has a fixed point in$K.$9. PENNON: A code for convex nonlinear and semidefinite programming Kočvara, Michal; Stingl, M. 2003-01-01 Roč. 18, č. 3 (2003), s. 317-333 ISSN 1055-6788 R&D Projects: GA ČR GA201/00/0080 Grant - others:BMBF(DE) 03ZOM3ER Institutional research plan: CEZ:AV0Z1075907 Keywords : convex programming * semidefinite programming * large-scale problems Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.306, year: 2003 10. 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 11. 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. 12. Speech Enhancement by Modified Convex Combination of Fractional Adaptive Filtering M. Geravanchizadeh 2014-12-01 Full Text Available This paper presents new adaptive filtering techniques used in speech enhancement system. Adaptive filtering schemes are subjected to different trade-offs regarding their steady-state misadjustment, speed of convergence, and tracking performance. Fractional Least-Mean-Square (FLMS is a new adaptive algorithm which has better performance than the conventional LMS algorithm. Normalization of LMS leads to better performance of adaptive filter. Furthermore, convex combination of two adaptive filters improves its performance. In this paper, new convex combinational adaptive filtering methods in the framework of speech enhancement system are proposed. The proposed methods utilize the idea of normalization and fractional derivative, both in the design of different convex mixing strategies and their related component filters. To assess our proposed methods, simulation results of different LMS-based algorithms based on their convergence behavior (i.e., MSE plots and different objective and subjective criteria are compared. The objective and subjective evaluations include examining the results of SNR improvement, PESQ test, and listening tests for dual-channel speech enhancement. The powerful aspects of proposed methods are their low complexity, as expected with all LMS-based methods, along with a high convergence rate. 13. 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:... 14. Measurement system for diffraction efficiency of convex gratings Liu, Peng; Chen, Xin-hua; Zhou, Jian-kang; Zhao, Zhi-cheng; Liu, Quan; Luo, Chao; Wang, Xiao-feng; Tang, Min-xue; Shen, Wei-min 2017-08-01 A measurement system for diffraction efficiency of convex gratings is designed. The measurement system mainly includes four components as a light source, a front system, a dispersing system that contains a convex grating, and a detector. Based on the definition and measuring principle of diffraction efficiency, the optical scheme of the measurement system is analyzed and the design result is given. Then, in order to validate the feasibility of the designed system, the measurement system is set up and the diffraction efficiency of a convex grating with the aperture of 35 mm, the curvature-radius of 72mm, the blazed angle of 6.4°, the grating period of 2.5μm and the working waveband of 400nm-900nm is tested. Based on GUM (Guide to the Expression of Uncertainty in Measurement), the uncertainties in the measuring results are evaluated. The measured diffraction efficiency data are compared to the theoretical ones, which are calculated based on the grating groove parameters got by an atomic force microscope and Rigorous Couple Wave Analysis, and the reliability of the measurement system is illustrated. Finally, the measurement performance of the system is analyzed and tested. The results show that, the testing accuracy, the testing stability and the testing repeatability are 2.5%, 0.085% and 3.5% , respectively. 15. Active Mirror Predictive and Requirements Verification Software (AMP-ReVS) Basinger, Scott A. 2012-01-01 This software is designed to predict large active mirror performance at various stages in the fabrication lifecycle of the mirror. It was developed for 1-meter class powered mirrors for astronomical purposes, but is extensible to other geometries. The package accepts finite element model (FEM) inputs and laboratory measured data for large optical-quality mirrors with active figure control. It computes phenomenological contributions to the surface figure error using several built-in optimization techniques. These phenomena include stresses induced in the mirror by the manufacturing process and the support structure, the test procedure, high spatial frequency errors introduced by the polishing process, and other process-dependent deleterious effects due to light-weighting of the mirror. Then, depending on the maturity of the mirror, it either predicts the best surface figure error that the mirror will attain, or it verifies that the requirements for the error sources have been met once the best surface figure error has been measured. The unique feature of this software is that it ties together physical phenomenology with wavefront sensing and control techniques and various optimization methods including convex optimization, Kalman filtering, and quadratic programming to both generate predictive models and to do requirements verification. This software combines three distinct disciplines: wavefront control, predictive models based on FEM, and requirements verification using measured data in a robust, reusable code that is applicable to any large optics for ground and space telescopes. The software also includes state-of-the-art wavefront control algorithms that allow closed-loop performance to be computed. It allows for quantitative trade studies to be performed for optical systems engineering, including computing the best surface figure error under various testing and operating conditions. After the mirror manufacturing process and testing have been completed, the 16. Thermal effects on beryllium mirrors Weinswig, S. 1989-01-01 Beryllium is probably the most frequently used material for spaceborne system scan mirrors. Beryllium's properties include lightweightedness, high Young's modulus, high stiffness value, high resonance value. As an optical surface, beryllium is usually nickel plated in order to produce a higher quality surface. This process leads to the beryllium mirror acting like a bimetallic device. The mirror's deformation due to the bimetallic property can possibly degrade the performance of the associated optical system. As large space borne systems are designed and as temperature considerations become more crucial in the instruments, the concern about temporal deformation of the scan mirrors becomes a prime consideration. Therefore, two sets of tests have been conducted in order to ascertain the thermal effects on nickel plated beryllium mirrors. These tests are categorized. The purpose of this paper is to present the values of the bimetallic effect on typical nickel plated beryllium mirrors 17. Mirror symmetry II Greene, Brian R 1997-01-01 Mirror symmetry has undergone dramatic progress during the last five years. Tremendous insight has been gained on a number of key issues. This volume surveys these results. Some of the contributions in this work have appeared elsewhere, while others were written specifically for this collection. The areas covered are organized into 4 sections, and each presents papers by both physicists and mathematicians. This volume collects the most important developments that have taken place in mathematical physics since 1991. It is an essential reference tool for both mathematics and physics libraries and for students of physics and mathematics. 18. Introduction: Mirrors of Passing Seebach, Sophie Hooge; Willerslev, Rane How is death, time, and materiality interconnected? How to approach an understanding of the world of the dead? In this introduction, we seek to understand how the experience of material decay, of the death of those around us, makes us aware of the passing of time. Through the literary lens of Neil...... Gaiman’s The Graveyard Book, we explore how the world of the dead and the world of the living can intersect; how time and materiality shifts and changes depending on who experiences it. These revelations, based on fiction, provide a mirror through which the reader can experience the varied chapters... 19. Complex/Symplectic Mirrors Chuang, Wu-yen; Kachru, Shamit; /Stanford U., ITP /SLAC; Tomasiello, Alessandro; /Stanford U., ITP 2005-10-28 We construct a class of symplectic non-Kaehler and complex non-Kaehler string theory vacua, extending and providing evidence for an earlier suggestion by Polchinski and Strominger. The class admits a mirror pairing by construction. Comparing hints from a variety of sources, including ten-dimensional supergravity and KK reduction on SU(3)-structure manifolds, suggests a picture in which string theory extends Reid's fantasy to connect classes of both complex non-Kaehler and symplectic non-Kaehler manifolds. 20. Trieste lectures on mirror symmetry Hori, K [Department of Physics and Department of Mathematics, University of Toronto, Toronto, Ontario (Canada) 2003-08-15 These are pedagogical lectures on mirror symmetry given at the Spring School in ICTP, Trieste, March 2002. The focus is placed on worldsheet descriptions of the physics related to mirror symmetry. We start with the introduction to general aspects of (2,2) supersymmetric field theories in 1 + 1 dimensions. We next move on to the study and applications of linear sigma model. Finally, we provide a proof of mirror symmetry in a class of models. (author) 1. Mirror Fusion Test Facility (MFTF) Thomassen, K.I. 1978-01-01 A large, new Mirror Fusion Test Facility is under construction at LLL. Begun in FY78 it will be completed at the end of FY78 at a cost of$94.2M. This facility gives the mirror program the flexibility to explore mirror confinement principles at a signficant scale and advances the technology of large reactor-like devices. The role of MFTF in the LLL program is described here

2. Gasdynamic Mirror Fusion Propulsion Experiment

Emrich, Bill; Rodgers, Stephen L. (Technical Monitor)

2000-01-01

A gasdynamic mirror (GDM) fusion propulsion experiment is currently being constructed at the NASA Marshall Space Flight Center (MSFC) to test the feasibility of this particular type of fusion device. Because of the open magnetic field line configuration of mirror fusion devices, they are particularly well suited for propulsion system applications since they allow for the easy ejection of thrust producing plasma. Currently, the MSFC GDM is constructed in three segments. The vacuum chamber mirror segment, the plasma injector mirror segment, and the main plasma chamber segment. Enough magnets are currently available to construct up to three main plasma chamber segments. The mirror segments are also segmented such that they can be expanded to accommodate new end plugging strategies with out requiring the disassembly of the entire mirror segment. The plasma for the experiment is generated in a microwave cavity located between the main magnets and the mirror magnets. Ion heating is accomplished through ambipolar diffusion. The objective of the experiment is to investigate the stability characteristics of the gasdynamic mirror and to map a region of parameter space within which the plasma can be confined in a stable steady state configuration. The mirror ratio, plasma density, and plasma "b" will be varied over a range of values and measurements subsequently taken to determine the degree of plasma stability.

3. Mirror profile optimization for nano-focusing KB mirror

Zhang Lin; Baker, Robert; Barrett, Ray; Cloetens, Peter; Dabin, Yves

2010-01-01

A KB focusing mirror width profile has been optimized to achieve nano-focusing for the nano-imaging end-station ID22NI at the ESRF. The complete mirror and flexure bender assembly has been modeled in 3D with finite element analysis using ANSYS. Bender stiffness, anticlastic effects and geometrical non-linear effects have been considered. Various points have been studied: anisotropy and crystal orientation, stress in the mirror and bender, actuator resolution and the mirror-bender adhesive bonding... Extremely high performance of the mirror is expected with residual slope error smaller than 0.6 μrad, peak-to-valley, compared to the bent slope of 3000 μrad.

4. The role of convexity in perceptual completion: beyond good continuation.

Liu, Z; Jacobs, D W; Basri, R

1999-01-01

Since the seminal work of the Gestalt psychologists, there has been great interest in understanding what factors determine the perceptual organization of images. While the Gestaltists demonstrated the significance of grouping cues such as similarity, proximity and good continuation, it has not been well understood whether their catalog of grouping cues is complete--in part due to the paucity of effective methodologies for examining the significance of various grouping cues. We describe a novel, objective method to study perceptual grouping of planar regions separated by an occluder. We demonstrate that the stronger the grouping between two such regions, the harder it will be to resolve their relative stereoscopic depth. We use this new method to call into question many existing theories of perceptual completion (Ullman, S. (1976). Biological Cybernetics, 25, 1-6; Shashua, A., & Ullman, S. (1988). 2nd International Conference on Computer Vision (pp. 321-327); Parent, P., & Zucker, S. (1989). IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 823-839; Kellman, P. J., & Shipley, T. F. (1991). Cognitive psychology, Liveright, New York; Heitger, R., & von der Heydt, R. (1993). A computational model of neural contour processing, figure-ground segregation and illusory contours. In Internal Conference Computer Vision (pp. 32-40); Mumford, D. (1994). Algebraic geometry and its applications, Springer, New York; Williams, L. R., & Jacobs, D. W. (1997). Neural Computation, 9, 837-858) that are based on Gestalt grouping cues by demonstrating that convexity plays a strong role in perceptual completion. In some cases convexity dominates the effects of the well known Gestalt cue of good continuation. While convexity has been known to play a role in figure/ground segmentation (Rubin, 1927; Kanizsa & Gerbino, 1976), this is the first demonstration of its importance in perceptual completion.

5. Virtual Mirror gaming in libraries

Speelman, M.; Kröse, B.; Nijholt, A.; Poppe, R.

2008-01-01

This paper presents a study on a natural interface game in the context of a library. We developed a camera-based Virtual Mirror (VM) game, in which the player can see himself on the screen as if he looks at a mirror image. We present an overview of the different aspects of VM games and technologies

6. TCV mirrors cleaned by plasma

L. Marot

2017-08-01

Full Text Available Metallic mirrors exposed in TCV tokamak were cleaned by plasma in laboratory. A gold (Au mirror was deposited with 185–285nm of amorphous carbon (aC:D film coming from the carbon tiles of TCV. Another molybdenum (Mo mirror had a thicker deposit due to a different location within the tokamak. The thickness measurements were carried out using ellipsometry and the reflectivity measurements performed by spectrophotometry revealed a decrease of the specular reflectivity in the entire range (250–2500nm for the Mo mirror and specifically in the visible spectrum for the Au. Comparison of the simulated reflectivity using a refractive index of 1.5 and a Cauchy model for the aC:D gives good confidence on the estimated film thickness. Plasma cleaning using radio frequency directly applied to a metallic plate where the mirrors were fixed demonstrated the ability to remove the carbon deposits. A mixture of 50% hydrogen and 50% helium was used with a −200V self-bias. Due to the low sputtering yield of He and the low chemical erosion of hydrogen leading to volatile molecules, 20h of cleaning were needed for Au mirror and more than 60h for Mo mirror. Recovery of the reflectivity was not complete for the Au mirror most likely due to damage of the surface during tokamak exposure (breakdown phenomena.

7. Blaschke- and Minkowski-endomorphisms of convex bodies

Kiderlen, Markus

2006-01-01

We consider maps of the family of convex bodies in Euclidean d-dimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d>2, a representation theorem for such maps......-endomorphisms, where additivity is now understood with respect to Blaschke-addition. Using a special mixed volume, an adjoining operator can be introduced. This operator allows one to identify the class of Blaschke-endomorphisms with the class of weakly monotonic, non-degenerate and translation-covariant Minkowski...

8. Convex models and probabilistic approach of nonlinear fatigue failure

Qiu Zhiping; Lin Qiang; Wang Xiaojun

2008-01-01

This paper is concerned with the nonlinear fatigue failure problem with uncertainties in the structural systems. In the present study, in order to solve the nonlinear problem by convex models, the theory of ellipsoidal algebra with the help of the thought of interval analysis is applied. In terms of the inclusion monotonic property of ellipsoidal functions, the nonlinear fatigue failure problem with uncertainties can be solved. A numerical example of 25-bar truss structures is given to illustrate the efficiency of the presented method in comparison with the probabilistic approach

9. Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities

Imre, C.; Matúš, František

2012-01-01

Roč. 48, č. 4 (2012), s. 637-689 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539; GA ČR GAP202/10/0618 Institutional support: RVO:67985556 Keywords : maximum entropy * moment constraint * generalized primal/dual solutions * normal integrand * convex duality * Bregman projection * inference principles Subject RIV: BA - General Mathematics Impact factor: 0.619, year: 2012 http://library.utia.cas.cz/separaty/2012/MTR/matus-0381750.pdf

10. Iterative Schemes for Convex Minimization Problems with Constraints

Lu-Chuan Ceng

2014-01-01

Full Text Available We first introduce and analyze one implicit iterative algorithm for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: the generalized mixed equilibrium problem, the system of generalized equilibrium problems, and finitely many variational inclusions in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another implicit iterative algorithm for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.

11. Gröbner bases and convex polytopes

Sturmfels, Bernd

1995-01-01

This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gröbner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.

12. On the structure of self-affine convex bodies

Voynov, A S [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2013-08-31

We study the structure of convex bodies in R{sup d} that can be represented as a union of their affine images with no common interior points. Such bodies are called self-affine. Vallet's conjecture on the structure of self-affine bodies was proved for d = 2 by Richter in 2011. In the present paper we disprove the conjecture for all d≥3 and derive a detailed description of self-affine bodies in R{sup 3}. Also we consider the relation between properties of self-affine bodies and functional equations with a contraction of an argument. Bibliography: 10 titles.

13. Mirroring patients – or not

Davidsen, Annette Sofie; Fosgerau, Christina Fogtmann

2015-01-01

on studies of imitative behaviour within linguistics and psychology, we argue that interactional mirroring is an important aspect of displaying implicit mentalization. We aimed to explore if, and in that case how, mirroring is displayed by general practitioners (GPs) and psychiatrists in consultations...... with patients with depression. We wanted to see how implicit mentalizing unfolds in physician–patient interactions. Consultations were videorecorded and analysed within the framework of conversation analysis. GPs and psychiatrists differed substantially in their propensity to mirror body movements and verbal...... and acoustic features of speech. GPs mirrored their patients more than psychiatrists in all modalities and were more flexible in their interactional behaviour. Psychiatrists seemed more static, regardless of the emotionality displayed by patients. Implicitly mirroring and attuning to patients could signify...

14. Introduction to tandem mirror physics

Kesner, J.; Gerver, M.J.; Lane, B.G.; McVey, B.D.; Catto, P.J.; D'Ippolito, D.A.; Myra, J.R.

1983-09-01

This monograph, prepared jointly by the MIT Plasma Fusion Center Mirror Fusion group and SAI, Boulder, Colorado, presents a review of the development of mirror fusion theory from its conception some thirty years ago to the present. Pertinent historic experiments and their contribution are discussed to set the stage for a detailed analysis of current experiments and the problems which remain to be solved in bringing tandem mirror magnetic confinement fusion to fruition. In particular, Chapter III discusses in detail the equilibrium and stability questions which must be dealt with before tandem mirror reactors become feasible, while Chapters IV and V discuss some of the current machines and those under construction which will help to resolve critical issues in both physics and engineering whose solutions are necessary to the commercialization of tandem mirror fusion

15. Potential measurements in tandem mirrors

Glowienka, J.C.

1985-11-01

The US mirror program has begun conducting experiments with a thermal barrier tandem mirror configuration. This configuration requires a specific axial potential profile and implies measurements of potential for documentation and optimization of the configuration. This report briefly outlines the motivation for the thermal barrier tandem mirror and then outlines the techniques used to document the potential profile in conventional and thermal barrier tandem mirrors. Examples of typical data sets from the world's major tandem mirror experiments, TMX and TMX-U at Lawrence Livermore National Laboratory (LLNL) and Gamma 10 at Tsukuba University in Japan, and the current interpretation of the data are discussed together with plans for the future improvement of measurements of plasma potential

16. LLL mirror fusion program: summary

Fowler, T.K.

1977-01-01

During 1976, new Mirror Program plans have been laid out to take into account the significant advances during the last 18 months. The program is now focused on two new mirror concepts, field reversal and the tandem mirror, that can obtain high Q, defined as the ratio of fusion power output to the neutral-beam power injected to sustain the reaction. Theoretically, both concepts can attain Q = 5 or more, as compared to Q = 1 in previous mirror designs. Experimental planning for the next 5 years is complete in broad outline, and we are turning attention to what additional steps are necessary to reach our long-range goal of an experimental mirror reactor operating by 1990. Highlights of the events that have led to the above circumstance are listed, and experimental program plans are outlined

17. Genetics Home Reference: congenital mirror movement disorder

... Health Conditions Congenital mirror movement disorder Congenital mirror movement disorder Printable PDF Open All Close All Enable ... view the expand/collapse boxes. Description Congenital mirror movement disorder is a condition in which intentional movements ...

18. Use of Convexity in Ostomy Care: Results of an International Consensus Meeting.

Hoeflok, Jo; Salvadalena, Ginger; Pridham, Sue; Droste, Werner; McNichol, Laurie; Gray, Mikel

Ostomy skin barriers that incorporate a convexity feature have been available in the marketplace for decades, but limited resources are available to guide clinicians in selection and use of convex products. Given the widespread use of convexity, and the need to provide practical guidelines for appropriate use of pouching systems with convex features, an international consensus panel was convened to provide consensus-based guidance for this aspect of ostomy practice. Panelists were provided with a summary of relevant literature in advance of the meeting; these articles were used to generate and reach consensus on 26 statements during a 1-day meeting. Consensus was achieved when 80% of panelists agreed on a statement using an anonymous electronic response system. The 26 statements provide guidance for convex product characteristics, patient assessment, convexity use, and outcomes.

19. Canonical Primal-Dual Method for Solving Non-convex Minimization Problems

Wu, Changzhi; Li, Chaojie; Gao, David Yang

2012-01-01

A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a convex-concave saddle point optimization problem, which is then solved by a quadratically perturbed primal-dual method. %It is proved that the popular SDP method is indeed a special case of the canonical duality theory. Numerical examples are illustrated. Comparing...

20. 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.

1. Sequential and Parallel Algorithms for Finding a Maximum Convex Polygon

Fischer, Paul

1997-01-01

This paper investigates the problem where one is given a finite set of n points in the plane each of which is labeled either ?positive? or ?negative?. We consider bounded convex polygons, the vertices of which are positive points and which do not contain any negative point. It is shown how...... such a polygon which is maximal with respect to area can be found in time O(n³ log n). With the same running time one can also find such a polygon which contains a maximum number of positive points. If, in addition, the number of vertices of the polygon is restricted to be at most M, then the running time...... becomes O(M n³ log n). It is also shown how to find a maximum convex polygon which contains a given point in time O(n³ log n). Two parallel algorithms for the basic problem are also presented. The first one runs in time O(n log n) using O(n²) processors, the second one has polylogarithmic time but needs O...

2. Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and -convexity

Briec, Walter; Horvath, Charles

2008-05-01

-convexity was introduced in [W. Briec, C. Horvath, -convexity, Optimization 53 (2004) 103-127]. Separation and Hahn-Banach like theorems can be found in [G. Adilov, A.M. Rubinov, -convex sets and functions, Numer. Funct. Anal. Optim. 27 (2006) 237-257] and [W. Briec, C.D. Horvath, A. Rubinov, Separation in -convexity, Pacific J. Optim. 1 (2005) 13-30]. We show here that all the basic results related to fixed point theorems are available in -convexity. Ky Fan inequality, existence of Nash equilibria and existence of equilibria for abstract economies are established in the framework of -convexity. Monotone analysis, or analysis on Maslov semimodules [V.N. Kolokoltsov, V.P. Maslov, Idempotent Analysis and Its Applications, Math. Appl., volE 401, Kluwer Academic, 1997; V.P. Litvinov, V.P. Maslov, G.B. Shpitz, Idempotent functional analysis: An algebraic approach, Math. Notes 69 (2001) 696-729; V.P. Maslov, S.N. Samborski (Eds.), Idempotent Analysis, Advances in Soviet Mathematics, Amer. Math. Soc., Providence, RI, 1992], is the natural framework for these results. From this point of view Max-Plus convexity and -convexity are isomorphic Maslov semimodules structures over isomorphic semirings. Therefore all the results of this paper hold in the context of Max-Plus convexity.

3. Generalized Bregman distances and convergence rates for non-convex regularization methods

Grasmair, Markus

2010-01-01

We generalize the notion of Bregman distance using concepts from abstract convexity in order to derive convergence rates for Tikhonov regularization with non-convex regularization terms. In particular, we study the non-convex regularization of linear operator equations on Hilbert spaces, showing that the conditions required for the application of the convergence rates results are strongly related to the standard range conditions from the convex case. Moreover, we consider the setting of sparse regularization, where we show that a rate of order δ 1/p holds, if the regularization term has a slightly faster growth at zero than |t| p

4. Processing convexity and concavity along a 2-D contour: figure-ground, structural shape, and attention.

Bertamini, Marco; Wagemans, Johan

2013-04-01

Interest in convexity has a long history in vision science. For smooth contours in an image, it is possible to code regions of positive (convex) and negative (concave) curvature, and this provides useful information about solid shape. We review a large body of evidence on the role of this information in perception of shape and in attention. This includes evidence from behavioral, neurophysiological, imaging, and developmental studies. A review is necessary to analyze the evidence on how convexity affects (1) separation between figure and ground, (2) part structure, and (3) attention allocation. Despite some broad agreement on the importance of convexity in these areas, there is a lack of consensus on the interpretation of specific claims--for example, on the contribution of convexity to metric depth and on the automatic directing of attention to convexities or to concavities. The focus is on convexity and concavity along a 2-D contour, not convexity and concavity in 3-D, but the important link between the two is discussed. We conclude that there is good evidence for the role of convexity information in figure-ground organization and in parsing, but other, more specific claims are not (yet) well supported.

5. First-order Convex Optimization Methods for Signal and Image Processing

Jensen, Tobias Lindstrøm

2012-01-01

In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can...... be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple...

6. Advanced Mirror & Modelling Technology Development

Effinger, Michael; Stahl, H. Philip; Abplanalp, Laura; Maffett, Steven; Egerman, Robert; Eng, Ron; Arnold, William; Mosier, Gary; Blaurock, Carl

2014-01-01

The 2020 Decadal technology survey is starting in 2018. Technology on the shelf at that time will help guide selection to future low risk and low cost missions. The Advanced Mirror Technology Development (AMTD) team has identified development priorities based on science goals and engineering requirements for Ultraviolet Optical near-Infrared (UVOIR) missions in order to contribute to the selection process. One key development identified was lightweight mirror fabrication and testing. A monolithic, stacked, deep core mirror was fused and replicated twice to achieve the desired radius of curvature. It was subsequently successfully polished and tested. A recently awarded second phase to the AMTD project will develop larger mirrors to demonstrate the lateral scaling of the deep core mirror technology. Another key development was rapid modeling for the mirror. One model focused on generating optical and structural model results in minutes instead of months. Many variables could be accounted for regarding the core, face plate and back structure details. A portion of a spacecraft model was also developed. The spacecraft model incorporated direct integration to transform optical path difference to Point Spread Function (PSF) and between PSF to modulation transfer function. The second phase to the project will take the results of the rapid mirror modeler and integrate them into the rapid spacecraft modeler.

7. Survey of mirror machine reactors

Condit, W.C.

1978-01-01

The Magnetic Mirror Fusion Program is one of the two main-line fusion efforts in the United States. Starting from the simple axisymmetric mirror concept in the 1950's, the program has successfully overcome gross flute-type instabilities (using minimum-B magnetic fields), and the most serious of the micro-instabilities which plagued it (the drift-cyclotron loss-cone mode). Dense plasmas approaching the temperature range of interest for fusion have been created (n/sub p/ = 10 14 /cc at 10 to 12 keV). At the same time, rather extensive conceptual design studies of possible mirror configurations have led to three principle designs of interest: the standard mirror fission-fusion hybrid, tandem mirror, and the field-reversed mirror. The lectures will discuss these three concepts in turn. There will be no discussion of diagnostics for the mirror machine in these lectures, but typical plasma parameters will be given for each type of machine, and the diagnostic requirements will be apparent. In a working fusion reactor, diagnostics will be required for operational control, and remarks will be made on this subject

8. Tandem mirror and field-reversed mirror experiments

Coensgen, F.H.; Simonen, T.C.; Turner, W.C.

1979-08-21

This paper is largely devoted to tandem mirror and field-reversed mirror experiments at the Lawrence Livermore Laboratory (LLL), and briefly summarizes results of experiments in which field-reversal has been achieved. In the tandem experiment, high-energy, high-density plasmas (nearly identical to 2XIIB plasmas) are located at each end of a solenoid where plasma ions are electrostatically confined by the high positive poentials arising in the end plug plasma. End plug ions are magnetically confined, and electrons are electrostatically confined by the overall positive potential of the system. The field-reversed mirror reactor consists of several small field-reversed mirror plasmas linked together for economic reasons. In the LLL Beta II experiment, generation of a field-reversed plasma ring will be investigated using a high-energy plasma gun with a transverse radial magnetic field. This plasma will be further heated and sustained by injection of intense, high-energy neutral beams.

9. Edificio Daily Mirror

Williams, Owen

1963-07-01

Full Text Available The building has 18 levels. The Press occupies the 4 basement floors. The ground floor is taken up with the entrance hall, and an indoor carriage way. A snack bar and the telephone operators are situated on the second floor. The production department and the medical services are located on the third storey, whilst the fourth is occupied by the offices and library. The fifth floor is the beginning of the higher section of the building. This floor and up to including the 11th floor are devoted to office space, except for the 10th storey, which contains the office apartments of the directors and the Council Chamber. Equipment related to various services of the building is housed on the 12th storey. Finally, this tall building constitutes a fine landmark in the London skyline. The Daily Mirror building is outstanding for the appropriate nature, the completeness and the quality of its installations, which thus provide the most widely read paper in the world with outstandingly efficient offices.Este edificio consta de 18 plantas. El cuerpo de Prensa se aloja en los cuatro sótanos; los vestíbulos de entrada y una calzada interior para vehículos se hallan en la planta baja; la primera alberga un snack-bar y centralita telefónica; la segunda, el departamento de producción y centro de asistencia médica, y la tercera, las oficinas y biblioteca principales. La cuarta planta señala el comienzo del bloque alto; esta planta, junto con las quinta, sexta, séptima, octava y décima, están dedicadas a oficinas. La novena contiene las oficinas-apartamentos de los directores y salas de Consejo, y la undécima, la maquinaria para las diversas instalaciones del edificio. La elevada torre constituye un grandioso hito de referencia en esta zona de Londres. El «Daily Mirror» se distingue por el acierto, número y perfección de sus instalaciones, que proporcionan, al periódico de mayor actualidad mundial, las más adecuadas y amplias oficinas modernas.

10. Kodak AMSD Mirror Development Program

Matthews, Gary; Dahl, Roger; Barrett, David; Bottom, John; Russell, Kevin (Technical Monitor)

2002-01-01

The Advanced Mirror System Demonstration Program is developing minor technology for the next generation optical systems. Many of these systems will require extremely lightweight and stable optics due to the overall size of the primary mirror. These segmented, deployable systems require new technology that AMSD is developing. The on-going AMSD program is a critical enabler for Next Generation Space Telescope (NGST) which will start in 2002. The status of Kodak's AMSD mirror and future plans will be discussed with respect to the NGST program.

11. Tinbergen on mirror neurons

Heyes, Cecilia

2014-01-01

Fifty years ago, Niko Tinbergen defined the scope of behavioural biology with his four problems: causation, ontogeny, survival value and evolution. About 20 years ago, there was another highly significant development in behavioural biology—the discovery of mirror neurons (MNs). Here, I use Tinbergen's original four problems (rather than the list that appears in textbooks) to highlight the differences between two prominent accounts of MNs, the genetic and associative accounts; to suggest that the latter provides the defeasible ‘best explanation’ for current data on the causation and ontogeny of MNs; and to argue that functional analysis, of the kind that Tinbergen identified somewhat misleadingly with studies of ‘survival value’, should be a high priority for future research. In this kind of functional analysis, system-level theories would assign MNs a small, but potentially important, role in the achievement of action understanding—or another social cognitive function—by a production line of interacting component processes. These theories would be tested by experimental intervention in human and non-human animal samples with carefully documented and controlled developmental histories. PMID:24778376

12. Photocatalytic, antifogging mirror

Takagi, K.; Makimoto, T.; Hiraiwa, H.; Negishi, T.

2001-01-01

This article is about the coating of thin titanium dioxide film by sputter deposition. When irradiated with solar light, thin titanium dioxide film exhibits high oxidizing power and provides sterilizing, cleaning, decomposing, and hydrophylic effects. This technique has already been used for coating building walls by the sol-gel method and by others and has been partly commercialized to make automotive sideview mirrors. There have been no practical applications of the sputter deposition method so far, but establishment of the coating method is expected because of its excellent properties of film production techniques such as film thickness uniformity, film quality durability, and freedom from environmental pollution. In this article we discuss the establishment of the method of evaluating the quality of thin titanium dioxide film, establishment of sputter-deposition conditions, and the results of observation by x-ray diffraction and atomic force microscopy of the thin film. It was found that titanium dioxide films, 200 nm or more in thickness, have the above mentioned performance and that sputter deposition allows the film to form without heating

13. Stabilized thermally compensated mirror

Dunn, C. III; Tobin, R.D.; Bergstreser, N.E.; Heinz, T.A.

1975-01-01

A thermally compensated mirror is described that is formed by a laminated structure. The structure is comprised of a front plate having a reflective front surface and having a plurality of grooves formed in the rear surface for conducting coolant fluid in heat exchanging relation with said reflective surface, a rear plate having coolant inlet and coolant outlet openings extending therethrough, a minimum temperature plate interposed between said front and rear plates and formed with a plurality of coolant distribution passageways coupled to receive coolant fluid from said coolant inlet and oriented to distribute said coolant fluid in a manner to establish a minimum temperature plane parallel to said reflective surface, a temperature stabilization plate interposed between said front plate and said minimum temperature plate and formed with a plurality of coolant distribution channels coupled to receive said coolant fluid after said coolant fluid has passed in heat exchanging relation with said reflective surface and oriented to distribute said coolant fluid in a manner to establish a uniform temperature plane parallel to said reflective surface, and means for circulating said coolant fluid through said structure in a predetermined path. (U.S.)

14. Tinbergen on mirror neurons.

Heyes, Cecilia

2014-01-01

Fifty years ago, Niko Tinbergen defined the scope of behavioural biology with his four problems: causation, ontogeny, survival value and evolution. About 20 years ago, there was another highly significant development in behavioural biology-the discovery of mirror neurons (MNs). Here, I use Tinbergen's original four problems (rather than the list that appears in textbooks) to highlight the differences between two prominent accounts of MNs, the genetic and associative accounts; to suggest that the latter provides the defeasible 'best explanation' for current data on the causation and ontogeny of MNs; and to argue that functional analysis, of the kind that Tinbergen identified somewhat misleadingly with studies of 'survival value', should be a high priority for future research. In this kind of functional analysis, system-level theories would assign MNs a small, but potentially important, role in the achievement of action understanding-or another social cognitive function-by a production line of interacting component processes. These theories would be tested by experimental intervention in human and non-human animal samples with carefully documented and controlled developmental histories.

15. 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

16. Transmission X-ray mirror

Lairson, B.M.; Bilderback, D.H.

1982-01-01

Transmission X-ray mirrors have been made from 400 A to 10 000 A thick soap films and have been shown to have novel properties. Using grazing angles of incidence, low energy X-rays were reflected from the front surface while more energetic X-rays were transmitted through the mirror largely unattenuated. A wide bandpass monochromator was made from a silicon carbide mirror followed by a soap film transmission mirror and operated in the white beam at the cornell High Energy Synchrotron Source (CHESS). Bandpasses of ΔE/E=12% to 18% were achieved at 13 keV with peak efficiencies estimated to be between 55% and 75%, respectively. Several wide angle scattering photographs of stretched polyethylene and a phospholipid were obtained in 10 s using an 18% bandpass. (orig.)

17. Mirror symmetry and loop operators

Assel, Benjamin [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Gomis, Jaume [Perimeter Institute for Theoretical Physics,Waterloo, Ontario, N2L 2Y5 (Canada)

2015-11-09

Wilson loops in gauge theories pose a fundamental challenge for dualities. Wilson loops are labeled by a representation of the gauge group and should map under duality to loop operators labeled by the same data, yet generically, dual theories have completely different gauge groups. In this paper we resolve this conundrum for three dimensional mirror symmetry. We show that Wilson loops are exchanged under mirror symmetry with Vortex loop operators, whose microscopic definition in terms of a supersymmetric quantum mechanics coupled to the theory encode in a non-trivial way a representation of the original gauge group, despite that the gauge groups of mirror theories can be radically different. Our predictions for the mirror map, which we derive guided by branes in string theory, are confirmed by the computation of the exact expectation value of Wilson and Vortex loop operators on the three-sphere.

18. Mirror Neurons from Associative Learning

Catmur, Caroline; Press, Clare; Heyes, Cecilia

2016-01-01

Mirror neurons fire both when executing actions and observing others perform similar actions. Their sensorimotor matching properties have generally been considered a genetic adaptation for social cognition; however, in the present chapter we argue that the evidence in favor of this account is not compelling. Instead we present evidence supporting an alternative account: that mirror neurons’ matching properties arise from associative learning during individual development. Notably, this proces...

19. MARS: Mirror Advanced Reactor Study

Logan, B.G.

1984-01-01

A recently completed two-year study of a commercial tandem mirror reactor design [Mirror Advanced Reactor Study (MARS)] is briefly reviewed. The end plugs are designed for trapped particle stability, MHD ballooning, balanced geodesic curvature, and small radial electric fields in the central cell. New technologies such as lithium-lead blankets, 24T hybrid coils, gridless direct converters and plasma halo vacuum pumps are highlighted

20. Nonparametric instrumental regression with non-convex constraints

Grasmair, M; Scherzer, O; Vanhems, A

2013-01-01

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, such as integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition. (paper)

1. 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.

2. Elastic energy of liquid crystals in convex polyhedra

Majumdar, A; Robbins, J M; Zyskin, M

2004-01-01

We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants. For a right rectangular prism and a large class of topologies, we derive upper bounds by introducing test configurations constructed from local conformal solutions of the Euler-Lagrange equation. The ratio of the upper and lower bounds depends only on the aspect ratios of the prism. As the aspect ratios are varied, the minimum-energy conformal state undergoes a sharp transition from being smooth to having singularities on the edges. (letter to the editor)

3. 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...

4. Reachability by paths of bounded curvature in a convex polygon

Ahn, Heekap; Cheong, Otfried; Matoušek, Jiřǐ; Vigneron, Antoine E.

2012-01-01

Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n2) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment. © 2011 Elsevier B.V.

5. Rocking convex array used for 3D synthetic aperture focusing

Andresen, Henrik; Nikolov, Svetoslav; Pedersen, M M

2008-01-01

Volumetric imaging can be performed using 1D arrays in combination with mechanical motion. Outside the elevation focus of the array, the resolution and contrast quickly degrade compared to the azimuth plane, because of the fixed transducer focus. The purpose of this paper is to use synthetic...... aperture focusing (SAF) for enhancing the elevation focusing for a convex rocking array, to obtain a more isotropic point spread function. This paper presents further development of the SAF method, which can be used with curved array combined with a rocking motion. The method uses a virtual source (VS...... Kretztechnik, Zipf, Austria). The array has an elevation focus at 60 mm of depth, and the angular rocking velocity is up to 140deg/s. The scan sequence uses an fprf of 4500 - 7000 Hz allowing up to 15 cm of penetration. The full width at half max (FWHM) and main-lobe to side-lobe ratio (MLSL) is used...

6. Approximating convex Pareto surfaces in multiobjective radiotherapy planning

Craft, David L.; Halabi, Tarek F.; Shih, Helen A.; Bortfeld, Thomas R.

2006-01-01

Radiotherapy planning involves inherent tradeoffs: the primary mission, to treat the tumor with a high, uniform dose, is in conflict with normal tissue sparing. We seek to understand these tradeoffs on a case-to-case basis, by computing for each patient a database of Pareto optimal plans. A treatment plan is Pareto optimal if there does not exist another plan which is better in every measurable dimension. The set of all such plans is called the Pareto optimal surface. This article presents an algorithm for computing well distributed points on the (convex) Pareto optimal surface of a multiobjective programming problem. The algorithm is applied to intensity-modulated radiation therapy inverse planning problems, and results of a prostate case and a skull base case are presented, in three and four dimensions, investigating tradeoffs between tumor coverage and critical organ sparing

7. 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.

8. Neural network for solving convex quadratic bilevel programming problems.

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

2014-03-01

In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.

9. Entropies from Coarse-graining: Convex Polytopes vs. Ellipsoids

Nikos Kalogeropoulos

2015-09-01

Full Text Available We examine the Boltzmann/Gibbs/Shannon SBGS and the non-additive Havrda-Charvát/Daróczy/Cressie-Read/Tsallis Sq and the Kaniadakis κ-entropy Sκ from the viewpoint of coarse-graining, symplectic capacities and convexity. We argue that the functional form of such entropies can be ascribed to a discordance in phase-space coarse-graining between two generally different approaches: the Euclidean/Riemannian metric one that reflects independence and picks cubes as the fundamental cells in coarse-graining and the symplectic/canonical one that picks spheres/ellipsoids for this role. Our discussion is motivated by and confined to the behaviour of Hamiltonian systems of many degrees of freedom. We see that Dvoretzky’s theorem provides asymptotic estimates for the minimal dimension beyond which these two approaches are close to each other. We state and speculate about the role that dualities may play in this viewpoint.

10. Advances in telescope mirror cleaning

Blanken, Maarten F.; Chopping, Alan K.; Dee, Kevin M.

2004-09-01

Metrology and cleaning techniques for telescope mirrors are generally well established. CO2 cleaning and water washing are mainly used. Water washing has proven to be the best method of removing oil and water stains and restoring the aluminium to nearly fresh values. The risk of water getting to unwanted places such as electronics or other optics prevents this method from being employed more often. Recently the Isaac Newton Group introduced a new cleaning technique for their telescope mirrors, which reduces the risks discussed above. This technique uses water vapour instead of water to wash the mirror. The advantage of this method is that the amount of water needed is drastically reduced. In addition the pressure of the vapour will blow away any large dust particles on the mirror and the temperature shock between the vapour and the mirror will help to de-bond the dust particles. Adding a soapy solution will help to clean oil and watermarks of the mirror. This paper describes the vapour cleaning method, tests that have been done and the overall findings.

11. Evolution of the mirror machine

Damm, C.C.

1983-01-01

The history of the magnetic-mirror approach to a fusion reactor is primarily the history of our understanding and control of several crucial physics issues, coupled with progress in the technology of heating and confining a reacting plasma. The basic requirement of an MHD-stable plasma equilibrium was achieved following the early introduction of minimum-B multipolar magnetic fields. In refined form, the same magnetic-well principle carries over to our present experiments and to reactor designs. The higher frequency microinstabilities, arising from the non-Maxwellian particle distributions inherent in mirror machines, have gradually come under control as theoretical prescriptions for distribution functions have been applied in the experiments. Even with stability, the classical plasma leakage through the mirrors posed a serious question for reactor viability until the principle of electrostatic axial stoppering was applied in the tandem mirror configuration. Experiments to test this principle successfully demonstrated the substantial improvement in confinement predicted. Concurrent with advances in mirror plasma physics, development of both high-power neutral beam injectors and high-speed vacuum pumping techniques has played a crucial role in ongoing experiments. Together with superconducting magnets, cryogenic pumping, and high-power radiofrequency heating, these technologies have evolved to a level that extrapolates readily to meet the requirements of a tandem mirror fusion reactor

12. 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.

13. Hermite-Hadamard type inequalities for GA-s-convex functions

İmdat İşcan

2014-10-01

Full Text Available In this paper, The author introduces the concepts of the GA-s-convex functions in the first sense and second sense and establishes some integral inequalities of Hermite-Hadamard type related to the GA-s-convex functions. Some applications to special means of real numbers are also given.

14. Distributed Topological Convex Hull Estimation of Event Region in Wireless Sensor Networks without Location Information

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

15. On the Lasserre hierarchy of semidefinite programming relaxations of convex polynomial optimization problems

de Klerk, E.; Laurent, M.

2011-01-01

The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization problems is known to converge finitely under some assumptions. [J. B. Lasserre, Convexity in semialgebraic geometry and polynomial optimization, SIAM J. Optim., 19 (2009), pp. 1995–2014]. We give a

16. The Concept of Convexity in Fuzzy Set Theory | Rauf | Journal of the ...

The notions of convex analysis are indispensable in theoretical and applied Mathematics especially in the study of Calculus where it has a natural generalization for the several variables case. This paper investigates the concept of Fuzzy set theory in relation to the idea of convexity. Some fundamental theorems were ...

17. 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

18. A canonical process for estimation of convex functions : The "invelope" of integrated Brownian motion +t4

Groeneboom, P.; Jongbloed, G.; Wellner, J.A.

2001-01-01

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely

19. Issues facing the U. S. mirror program

George, T.V.

1978-07-01

Some of the current issues associated with the U.S. Magnetic Mirror Program are analyzed. They are presented as five separate papers entitled: (1) Relevant Issues Broughtup by the Mirror Reactor Design Studies. (2) An Assessment of the Design Study of the 1 MeV Neutral Beam Injector Required for a Tandem Mirror Reactor. (3) The Significance of the Radial Plasma Size Measured in Units of Ion Gyroradii in Tandem Mirrors and Field Reversed Mirrors. (4) Producing Field Reversed Mirror Plasmas by Methods used in Field Reversed Theta Pinch. (5) RF Stoppering of Mirror Confined Plasma.

20. The spectral positioning algorithm of new spectrum vehicle based on convex programming in wireless sensor network

Zhang, Yongjun; Lu, Zhixin

2017-10-01

Spectrum resources are very precious, so it is increasingly important to locate interference signals rapidly. Convex programming algorithms in wireless sensor networks are often used as localization algorithms. But in view of the traditional convex programming algorithm is too much overlap of wireless sensor nodes that bring low positioning accuracy, the paper proposed a new algorithm. Which is mainly based on the traditional convex programming algorithm, the spectrum car sends unmanned aerial vehicles (uses) that can be used to record data periodically along different trajectories. According to the probability density distribution, the positioning area is segmented to further reduce the location area. Because the algorithm only increases the communication process of the power value of the unknown node and the sensor node, the advantages of the convex programming algorithm are basically preserved to realize the simple and real-time performance. The experimental results show that the improved algorithm has a better positioning accuracy than the original convex programming algorithm.

1. The mirror-neuron system.

Rizzolatti, Giacomo; Craighero, Laila

2004-01-01

A category of stimuli of great importance for primates, humans in particular, is that formed by actions done by other individuals. If we want to survive, we must understand the actions of others. Furthermore, without action understanding, social organization is impossible. In the case of humans, there is another faculty that depends on the observation of others' actions: imitation learning. Unlike most species, we are able to learn by imitation, and this faculty is at the basis of human culture. In this review we present data on a neurophysiological mechanism--the mirror-neuron mechanism--that appears to play a fundamental role in both action understanding and imitation. We describe first the functional properties of mirror neurons in monkeys. We review next the characteristics of the mirror-neuron system in humans. We stress, in particular, those properties specific to the human mirror-neuron system that might explain the human capacity to learn by imitation. We conclude by discussing the relationship between the mirror-neuron system and language.

2. Metamaterial mirrors in optoelectronic devices

Esfandyarpour, Majid

2014-06-22

The phase reversal that occurs when light is reflected from a metallic mirror produces a standing wave with reduced intensity near the reflective surface. This effect is highly undesirable in optoelectronic devices that use metal films as both electrical contacts and optical mirrors, because it dictates a minimum spacing between the metal and the underlying active semiconductor layers, therefore posing a fundamental limit to the overall thickness of the device. Here, we show that this challenge can be circumvented by using a metamaterial mirror whose reflection phase is tunable from that of a perfect electric mirror († = €) to that of a perfect magnetic mirror († = 0). This tunability in reflection phase can also be exploited to optimize the standing wave profile in planar devices to maximize light-matter interaction. Specifically, we show that light absorption and photocurrent generation in a sub-100 nm active semiconductor layer of a model solar cell can be enhanced by ∼20% over a broad spectral band. © 2014 Macmillan Publishers Limited.

3. Metamaterial mirrors in optoelectronic devices

Esfandyarpour, Majid; Garnett, Erik C.; Cui, Yi; McGehee, Michael D.; Brongersma, Mark L.

2014-01-01

The phase reversal that occurs when light is reflected from a metallic mirror produces a standing wave with reduced intensity near the reflective surface. This effect is highly undesirable in optoelectronic devices that use metal films as both electrical contacts and optical mirrors, because it dictates a minimum spacing between the metal and the underlying active semiconductor layers, therefore posing a fundamental limit to the overall thickness of the device. Here, we show that this challenge can be circumvented by using a metamaterial mirror whose reflection phase is tunable from that of a perfect electric mirror († = €) to that of a perfect magnetic mirror († = 0). This tunability in reflection phase can also be exploited to optimize the standing wave profile in planar devices to maximize light-matter interaction. Specifically, we show that light absorption and photocurrent generation in a sub-100 nm active semiconductor layer of a model solar cell can be enhanced by ∼20% over a broad spectral band. © 2014 Macmillan Publishers Limited.

4. Vertex algebras and mirror symmetry

Borisov, L.A.

2001-01-01

Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish the relation between these vertex algebras for mirror Calabi-Yau manifolds. This should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras. Our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra, as well as some basic results of the theory of vertex algebras. Ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties.This paper could also be of interest to physicists, because it contains explicit description of holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in terms of free bosons and fermions. (orig.)

5. Multiple-mirror plasma confinement

Lichtenberg, A.J.; Lieberman, M.A.; Logan, B.G.

1975-01-01

A large enhancement of the confinement time can be achieved in a straight system of multiple mirrors over an equal length uniform magnetic field. The scaling is diffusive rather than that of flow, thereby scaling the square of the system length rather than linear with system length. Probably the most economic mode of operation for a reactor occurs when lambda/M is approximately l/sub c/, where lambda is the mean free path, M the mirror ratio, and l/sub c/ the length between mirrors; but where the scale length of the mirror field l/sub m/ is much less than lambda. The axial confinement time has been calculated theoretically and numerically for all important parameter regimes, and confirmed experimentally. A typical reactor calculation gives Q/sub E/ = 2 for a 400 meter system with 3000 MW(e) output. The main concern of a multiple-mirror system is stability. Linked quadrupoles can achieve average minimum-B stabilization of flute modes, and experiments have demonstrated this stabilization. Localized instabilities at finite β and enhanced diffusion resulting from the distorted flux surfaces and possibly from turbulent higher order modes still remain to be investigated

6. Anomalous transport in mirror systems

Post, R.F.

1979-01-01

As now being explored for fusion applications confinement systems based on the mirror principle embody two kinds of plasma regimes. These two regimes are: (a) high-beta plasmas, stabilized against MHD and other low frequency plasma instabilities by magnetic-well fields, but characterized by non-Maxwellian ion distributions; (b) near-Maxwellian plasmas, confined electrostatically (as in the tandem mirror) or in a field-reversed region within the mirror cell. Common to both situations are the questions of anomalous transport owing to high frequency instabilities in the non-maxwellian portions of the plasmas. This report will summarize the status of theory and of experimental data bearing on these questions, with particular reference to the high temperature regimes of interest for fusion power

7. Fokker-Planck equation in mirror research

Post, R.F.

1983-01-01

Open confinement systems based on the magnetic mirror principle depend on the maintenance of particle distributions that may deviate substantially from Maxwellian distributions. Mirror research has therefore from the beginning relied on theoretical predictions of non-equilibrium rate processes obtained from solutions to the Fokker-Planck equation. The F-P equation plays three roles: Design of experiments, creation of classical standards against which to compare experiment, and predictions concerning mirror based fusion power systems. Analytical and computational approaches to solving the F-P equation for mirror systems will be reviewed, together with results and examples that apply to specific mirror systems, such as the tandem mirror

8. Neoclassical resonant transport of a mirror cell

Ito, T.; Katanuma, I.

2005-01-01

The neoclassical resonant plateau transport in a mirror cell is studied theoretically. The analytical expression for a non-square-well magnetic field is obtained. The analytical result is applied to the GAMMA10 tandem mirror [T. Cho, M. Yoshida, J. Kohagura et al., Phys. Rev. Lett. 94, 085002-1 (2005)], which consists of several mirror cells in it, and the confinement time due to the neoclassical resonant plateau transport is determined in each mirror cell. It is found that the neoclassical resonant transport of ions trapped in the nonaxisymmetric anchor mirror cell and transition mirror cells is significantly smaller than those trapped in the central cell

9. Mirror Advanced Reactor Study (MARS)

Logan, B.G.

1983-01-01

Progress in a two year study of a 1200 MWe commercial tandem mirror reactor (MARS - Mirror Advanced Reactor Study) has reached the point where major reactor system technologies are identified. New design features of the magnets, blankets, plug heating systems and direct converter are described. With the innovation of radial drift pumping to maintain low plug density, reactor recirculating power fraction is reduced to 20%. Dominance of radial ion and impurity losses into the halo permits gridless, circular direct converters to be dramatically reduced in size. Comparisons of MARS with the Starfire tokamak design are made

10. The Mirror in the Ground

Shepherd, Nick

An important and original contribution to the study of the archive, The Mirror in the Ground approaches the discipline of archaeology in South Africa from the perspective of an interest in visualities. Author Nick Shepherd argues that it makes sense to talk about an archaeological aesthetics...... at the University of Cape Town, where he convenes a graduate programme on Public Culture and Heritage. The Mirror in the Ground is the first volume in the relaunched Series in Visual Histories, produced by the Centre for Curating the Archive (CCA) at the University of Cape Town....

11. Mirror Fusion Test Facility magnet

Henning, C.H.; Hodges, A.J.; Van Sant, J.H.; Hinkle, R.E.; Horvath, J.A.; Hintz, R.E.; Dalder, E.; Baldi, R.; Tatro, R.

1979-01-01

The Mirror Fusion Test Facility (MFTF) is the largest of the mirror program experiments for magnetic fusion energy. It seeks to combine and extend the near-classical plasma confinement achieved in 2XIIB with the most advanced neutral-beam and magnet technologies. The product of ion density and confinement time will be improved more than an order of magnitude, while the superconducting magnet weight will be extrapolated from the 15 tons in Baseball II to 375 tons in MFTF. Recent reactor studies show that the MFTF will traverse much of the distance in magnet technology towards the reactor regime. Design specifics of the magnet are given

12. Precision platform for convex lens-induced confinement microscopy

Berard, Daniel; McFaul, Christopher M. J.; Leith, Jason S.; Arsenault, Adriel K. J.; Michaud, François; Leslie, Sabrina R.

2013-10-01

We present the conception, fabrication, and demonstration of a versatile, computer-controlled microscopy device which transforms a standard inverted fluorescence microscope into a precision single-molecule imaging station. The device uses the principle of convex lens-induced confinement [S. R. Leslie, A. P. Fields, and A. E. Cohen, Anal. Chem. 82, 6224 (2010)], which employs a tunable imaging chamber to enhance background rejection and extend diffusion-limited observation periods. Using nanopositioning stages, this device achieves repeatable and dynamic control over the geometry of the sample chamber on scales as small as the size of individual molecules, enabling regulation of their configurations and dynamics. Using microfluidics, this device enables serial insertion as well as sample recovery, facilitating temporally controlled, high-throughput measurements of multiple reagents. We report on the simulation and experimental characterization of this tunable chamber geometry, and its influence upon the diffusion and conformations of DNA molecules over extended observation periods. This new microscopy platform has the potential to capture, probe, and influence the configurations of single molecules, with dramatically improved imaging conditions in comparison to existing technologies. These capabilities are of immediate interest to a wide range of research and industry sectors in biotechnology, biophysics, materials, and chemistry.

13. Neural network for nonsmooth pseudoconvex optimization with general convex constraints.

Bian, Wei; Ma, Litao; Qin, Sitian; Xue, Xiaoping

2018-05-01

In this paper, a one-layer recurrent neural network is proposed for solving a class of nonsmooth, pseudoconvex optimization problems with general convex constraints. Based on the smoothing method, we construct a new regularization function, which does not depend on any information of the feasible region. Thanks to the special structure of the regularization function, we prove the global existence, uniqueness and "slow solution" character of the state of the proposed neural network. Moreover, the state solution of the proposed network is proved to be convergent to the feasible region in finite time and to the optimal solution set of the related optimization problem subsequently. In particular, the convergence of the state to an exact optimal solution is also considered in this paper. Numerical examples with simulation results are given to show the efficiency and good characteristics of the proposed network. In addition, some preliminary theoretical analysis and application of the proposed network for a wider class of dynamic portfolio optimization are included. Copyright © 2018 Elsevier Ltd. All rights reserved.

14. On asphericity of convex bodies in linear normed spaces.

Faried, Nashat; Morsy, Ahmed; Hussein, Aya M

2018-01-01

In 1960, Dvoretzky proved that in any infinite dimensional Banach space X and for any [Formula: see text] there exists a subspace L of X of arbitrary large dimension ϵ -iometric to Euclidean space. A main tool in proving this deep result was some results concerning asphericity of convex bodies. In this work, we introduce a simple technique and rigorous formulas to facilitate calculating the asphericity for each set that has a nonempty boundary set with respect to the flat space generated by it. We also give a formula to determine the center and the radius of the smallest ball containing a nonempty nonsingleton set K in a linear normed space, and the center and the radius of the largest ball contained in it provided that K has a nonempty boundary set with respect to the flat space generated by it. As an application we give lower and upper estimations for the asphericity of infinite and finite cross products of these sets in certain spaces, respectively.

15. JPEG2000-coded image error concealment exploiting convex sets projections.

Atzori, Luigi; Ginesu, Giaime; Raccis, Alessio

2005-04-01

Transmission errors in JPEG2000 can be grouped into three main classes, depending on the affected area: LL, high frequencies at the lower decomposition levels, and high frequencies at the higher decomposition levels. The first type of errors are the most annoying but can be concealed exploiting the signal spatial correlation like in a number of techniques proposed in the past; the second are less annoying but more difficult to address; the latter are often imperceptible. In this paper, we address the problem of concealing the second class or errors when high bit-planes are damaged by proposing a new approach based on the theory of projections onto convex sets. Accordingly, the error effects are masked by iteratively applying two procedures: low-pass (LP) filtering in the spatial domain and restoration of the uncorrupted wavelet coefficients in the transform domain. It has been observed that a uniform LP filtering brought to some undesired side effects that negatively compensated the advantages. This problem has been overcome by applying an adaptive solution, which exploits an edge map to choose the optimal filter mask size. Simulation results demonstrated the efficiency of the proposed approach.

16. Link Prediction via Convex Nonnegative Matrix Factorization on Multiscale Blocks

Enming Dong

2014-01-01

Full Text Available Low rank matrices approximations have been used in link prediction for networks, which are usually global optimal methods and lack of using the local information. The block structure is a significant local feature of matrices: entities in the same block have similar values, which implies that links are more likely to be found within dense blocks. We use this insight to give a probabilistic latent variable model for finding missing links by convex nonnegative matrix factorization with block detection. The experiments show that this method gives better prediction accuracy than original method alone. Different from the original low rank matrices approximations methods for link prediction, the sparseness of solutions is in accord with the sparse property for most real complex networks. Scaling to massive size network, we use the block information mapping matrices onto distributed architectures and give a divide-and-conquer prediction method. The experiments show that it gives better results than common neighbors method when the networks have a large number of missing links.

17. Convergence theorems for quasi-contractive maps in uniformly convex spaces

Chidume, C.E.; Osilike, M.O.

1992-04-01

Let K be a nonempty closed convex and bounded subset of a real uniformly convex Banach space E of modulus of convexity of power type q≥2. Let T by a quasi-contractive mapping of K into itself. It is proved that each of two well known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of T in K. Our theorems generalize important known results. (author). 22 refs

18. A One-Layer Recurrent Neural Network for Constrained Complex-Variable Convex Optimization.

Qin, Sitian; Feng, Jiqiang; Song, Jiahui; Wen, Xingnan; Xu, Chen

2018-03-01

In this paper, based on calculus and penalty method, a one-layer recurrent neural network is proposed for solving constrained complex-variable convex optimization. It is proved that for any initial point from a given domain, the state of the proposed neural network reaches the feasible region in finite time and converges to an optimal solution of the constrained complex-variable convex optimization finally. In contrast to existing neural networks for complex-variable convex optimization, the proposed neural network has a lower model complexity and better convergence. Some numerical examples and application are presented to substantiate the effectiveness of the proposed neural network.

19. Timecourse of mirror and counter-mirror effects measured with transcranial magnetic stimulation.

Cavallo, Andrea; Heyes, Cecilia; Becchio, Cristina; Bird, Geoffrey; Catmur, Caroline

2014-08-01

The human mirror system has been the subject of much research over the past two decades, but little is known about the timecourse of mirror responses. In addition, it is unclear whether mirror and counter-mirror effects follow the same timecourse. We used single-pulse transcranial magnetic stimulation to investigate the timecourse of mirror and counter-mirror responses in the human brain. Experiment 1 demonstrated that mirror responses can be measured from around 200 ms after observed action onset. Experiment 2 demonstrated significant effects of counter-mirror sensorimotor training at all timepoints at which a mirror response was found in Experiment 1 (i.e. from 200 ms onward), indicating that mirror and counter-mirror responses follow the same timecourse. By suggesting similarly direct routes for mirror and counter-mirror responses, these results support the associative account of mirror neuron origins whereby mirror responses arise as a result of correlated sensorimotor experience during development. More generally, they contribute to theorizing regarding mirror neuron function by providing some constraints on how quickly mirror responses can influence social cognition. © The Author (2013). Published by Oxford University Press. For Permissions, please email: journals.permissions@oup.com.

20. On four dimensional mirror symmetry

Losev, A.; Nekrasov, N.; Shatashvili, S.

2000-01-01

A conjecture relating instanton calculus in four dimensional supersymmetric theories and the deformation theory of Lagrangian submanifolds in C 2r invariant under a (subgroup of) Sp(2r,Z) is formulated. This is a four dimensional counterpart of the mirror symmetry of topological strings (relating Gromov-Witten invariants and generalized variations of Hodge structure). (orig.)

1. Mirror model for sterile neutrinos

Berezinsky, Veniamin; Narayan, Mohan; Vissani, Francesco

2003-01-01

Sterile neutrinos are studied as subdominant contribution to solar neutrino physics. The mirror-matter neutrinos are considered as sterile neutrinos. We use the symmetric mirror model with gravitational communication between mirror and visible sectors. This communication term provides mixing between visible and mirror neutrinos with the basic scale μ=v EW 2 /M Pl =2.5x10 -6 eV, where v EW =174 GeV is the vacuum expectation value of the standard electroweak group and M Pl is the Planckian mass. It is demonstrated that each mass eigenstate of active neutrinos splits into two states separated by small Δm 2 . Unsuppressed oscillations between active and sterile neutrinos (ν a ↔ν s ) occur only in transitions between each of these close pairs ('windows'). These oscillations are characterized by very small Δm 2 and can suppress the flux and distort spectrum of pp-neutrinos in detectable way. The other observable effect is anomalous seasonal variation of neutrino flux, which appears in LMA solution. The considered subdominant neutrino oscillations ν a ↔ν s can reveal itself as big effects in observations of supernova neutrinos and high-energy (HE) neutrinos. In the case of HE neutrinos they can provide a very large diffuse flux of active neutrinos unconstrained by the e-m cascade upper limit

2. Mirror Confinement Systems: project summaries

1980-07-01

This report contains descriptions of the projects supported by the Mirror Confinement Systems (MCS) Division of the Office of Fusion Energy. The individual project summaries were prepared by the principal investigators, in collaboration with MCS staff office, and include objectives and milestones for each project. In addition to project summaries, statements of Division objectives and budget summaries are also provided

3. MHD stability of tandem mirrors

Poulsen, P.; Molvik, A.; Shearer, J.

1982-01-01

The TMX-Upgrade experiment was described, and the manner in which various plasma parameters could be affected was discussed. The initial analysis of the MHD stability of the tandem mirror was also discussed, with emphasis on the negative tandem configuration

4. Status of tandem mirror theory

Baldwin, D.E.

1979-01-01

This report contains the text and slides used for the review talk on tandem mirror theory presented at the meeting of the Division of Plasma Physics, A.P.S., Boston, MA, November 12-16, 1979. Topics covered include classical confinement, equilibria, MHD- and micro-stability, radial transport, and thermal barriers

5. Mirror research: status and prospects

Baldwin, D.E.

1983-01-01

The tandem mirror program has evolved considerably in the last decade. Of significance is the viable reactor concept embodied in the MARS design. An aggressive experimental program culminating in the operation of MFTF-B in late 1986, will provide a firm basis for refining the MARS design as necessary for constructing a reactor prototype in the 1990s

6. Three mirror pairs of fermion families

Montvay, I.

1988-01-01

A simple model with three mirror pairs of fermion families is considered which allows for a substantial mixing between the mirror fermion partners without conflicting with known phenomenology. (orig.)

7. Globally convergent optimization algorithm using conservative convex separable diagonal quadratic approximations

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

2009-01-01

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

8. Cohesive granular media modelization with non-convex particles shape: Application to UO2 powder compaction

Saint-Cyr, B.

2011-01-01

We model in this work granular materials composed of non-convex and cohesive aggregates, in view of application to the rheology of UO 2 powders. The effect of non convexity is analyzed in terms of bulk quantities (Coulomb internal friction and cohesion) and micromechanical parameters such as texture anisotropy and force transmission. In particular, we find that the packing fraction evolves in a complex manner with the shape non convexity and the shear strength increases but saturates due to interlocking between the aggregates. We introduce simple models to describe these features in terms of micro-mechanical parameters. Furthermore, a systematic investigation of shearing, uniaxial compaction and simple compression of cohesive packings show that bulk cohesion increases with non-convexity but is strongly influenced by the boundary conditions and shear bands or stress concentration. (author) [fr

9. 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...

10. A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks

Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui

2016-01-01

This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed...... solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....... sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal...

11. The Axisymmetric Tandem Mirror: A Magnetic Mirror Concept Game Changer Magnet Mirror Status Study Group

Simonen, T.; Cohen, R.; Correll, D.; Fowler, K.; Post, D.; Berk, H.; Horton, W.; Hooper, E.B.; Fisch, N.; Hassam, A.; Baldwin, D.; Pearlstein, D.; Logan, G.; Turner, B.; Moir, R.; Molvik, A.; Ryutov, D.; Ivanov, A.A; Kesner, J.; Cohen, B.; McLean, H.; Tamano, T.; Tang, X.Z.; Imai, T.

2008-01-01

Experimental results, theory and innovative ideas now point with increased confidence to the possibility of a Gas Dynamic Trap (GDT) neutron source which would be on the path to an attractively simple Axisymmetric Tandem Mirror (ATM) power plant. Although magnetic mirror research was terminated in the US 20 years ago, experiments continued in Japan (Gamma 10) and Russia (GDT), with a very small US effort. This research has now yielded data, increased understanding, and generated ideas resulting in the new concepts described here. Early mirror research was carried out with circular axisymmetric magnets. These plasmas were MHD unstable due to the unfavorable magnetic curvature near the mid-plane. Then the minimum-B concept emerged in which the field line curvature was everywhere favorable and the plasma was situated in a MHD stable magnetic well (70% average beta in 2XII-B). The Ioffe-bar or baseball-coil became the standard for over 40 years. In the 1980's, driven by success with minimum-B stabilization and the control of ion cyclotron instabilities in PR6 and 2XII-B, mirrors were viewed as a potentially attractive concept with near-term advantages as a lower Q neutron source for applications such as a hybrid fission fuel factory or toxic waste burner. However there are down sides to the minimum-B geometry: coil construction is complex; restraining magnetic forces limit field strength and mirror ratios. Furthermore, the magnetic field lines have geodesic curvature which introduces resonant and neoclassical radial transport as observed in early tandem mirror experiments. So what now leads us to think that simple axisymmetric mirror plasmas can be stable? The Russian GDT experiment achieves on-axis 60% beta by peaking of the kinetic plasma pressure near the mirror throat (where the curvature is favorable) to counter-balance the average unfavorable mid-plane curvature. Then a modest augmentation of plasma pressure in the expander results in stability. The GDT

12. The Axisymmetric Tandem Mirror: A Magnetic Mirror Concept Game Changer Magnet Mirror Status Study Group

Simonen, T; Cohen, R; Correll, D; Fowler, K; Post, D; Berk, H; Horton, W; Hooper, E B; Fisch, N; Hassam, A; Baldwin, D; Pearlstein, D; Logan, G; Turner, B; Moir, R; Molvik, A; Ryutov, D; Ivanov, A A; Kesner, J; Cohen, B; McLean, H; Tamano, T; Tang, X Z; Imai, T

2008-10-24

Experimental results, theory and innovative ideas now point with increased confidence to the possibility of a Gas Dynamic Trap (GDT) neutron source which would be on the path to an attractively simple Axisymmetric Tandem Mirror (ATM) power plant. Although magnetic mirror research was terminated in the US 20 years ago, experiments continued in Japan (Gamma 10) and Russia (GDT), with a very small US effort. This research has now yielded data, increased understanding, and generated ideas resulting in the new concepts described here. Early mirror research was carried out with circular axisymmetric magnets. These plasmas were MHD unstable due to the unfavorable magnetic curvature near the mid-plane. Then the minimum-B concept emerged in which the field line curvature was everywhere favorable and the plasma was situated in a MHD stable magnetic well (70% average beta in 2XII-B). The Ioffe-bar or baseball-coil became the standard for over 40 years. In the 1980's, driven by success with minimum-B stabilization and the control of ion cyclotron instabilities in PR6 and 2XII-B, mirrors were viewed as a potentially attractive concept with near-term advantages as a lower Q neutron source for applications such as a hybrid fission fuel factory or toxic waste burner. However there are down sides to the minimum-B geometry: coil construction is complex; restraining magnetic forces limit field strength and mirror ratios. Furthermore, the magnetic field lines have geodesic curvature which introduces resonant and neoclassical radial transport as observed in early tandem mirror experiments. So what now leads us to think that simple axisymmetric mirror plasmas can be stable? The Russian GDT experiment achieves on-axis 60% beta by peaking of the kinetic plasma pressure near the mirror throat (where the curvature is favorable) to counter-balance the average unfavorable mid-plane curvature. Then a modest augmentation of plasma pressure in the expander results in stability. The GDT

13. Mounting and Alignment of IXO Mirror Segments

Chan, Kai-Wing; Zhang, William; Evans, Tyler; McClelland, Ryan; Hong, Melinda; Mazzarella, James; Saha, Timo; Jalota, Lalit; Olsen, Lawrence; Byron, Glenn

2010-01-01

A suspension-mounting scheme is developed for the IXO (International X-ray Observatory) mirror segments in which the figure of the mirror segment is preserved in each stage of mounting. The mirror, first fixed on a thermally compatible strongback, is subsequently transported, aligned and transferred onto its mirror housing. In this paper, we shall outline the requirement, approaches, and recent progress of the suspension mount processes.

14. Plasma impact on diagnostic mirrors in JET

A. Garcia-Carrasco; P. Petersson; M. Rubel; A. Widdowson; E. Fortuna-Zalesna; S. Jachmich; M. Brix; L. Marot

2017-01-01

Metallic mirrors will be essential components of all optical systems for plasma diagnosis in ITER. This contribution provides a comprehensive account on plasma impact on diagnostic mirrors in JET with the ITER-Like Wall. Specimens from the First Mirror Test and the lithium-beam diagnostic have been studied by spectrophotometry, ion beam analysis and electron microscopy. Test mirrors made of molybdenum were retrieved from the main chamber and the divertor after exposure to the 2013–2014 experi...

15. Graph Design via Convex Optimization: Online and Distributed Perspectives

Meng, De

Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation

16. A one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion

Suidan, T M

2001-01-01

The surprising connection between a one-dimensional gravitationally interacting gas of sticky particles and the convex minorant process generated by Brownian motion on [0,1] is studied. A study is made of the dynamics of this 1-D gas system by identifying three distinct clustering regimes and the time scales at which they occur. At the critical moment of time the mass distribution of the gas can be computed in terms of functionals of the convex minorant process

17. Perturbation of convex risk minimization and its application in differential private learning algorithms

Weilin Nie

2017-01-01

Full Text Available Abstract Convex risk minimization is a commonly used setting in learning theory. In this paper, we firstly give a perturbation analysis for such algorithms, and then we apply this result to differential private learning algorithms. Our analysis needs the objective functions to be strongly convex. This leads to an extension of our previous analysis to the non-differentiable loss functions, when constructing differential private algorithms. Finally, an error analysis is then provided to show the selection for the parameters.

18. X-ray imaging with toroidal mirror

1978-01-01

X-ray imaging is made with a single toroidal mirror or two successive toroidal mirrors. Geometrical images at the Gaussian image plane are described by the ray trace. Application of a single toroidal mirror to small-angle scattering is presented. (author)

19. Connection between adiabaticity and the mirror mode

Cohen, R.H.

1976-01-01

The size of magnetic moment jumps of a particle in a long, thin equilibrium magnetic mirror field is shown to be related to the complex zeroes of the mirror mode parameter B + 4πdP/sub perpendicular//dB. A consequence is that adiabaticity places a lower limit on β than does the mirror mode

20. A generalized construction of mirror manifolds

Berglund, P.; Huebsch, T.

1993-01-01

We generalize the known method for explicit construction of mirror pairs of (2,2)-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in weighted projective spaces. This generalization makes it possible to construct the mirror partners of many manifolds for which the mirror was not previously known. (orig.)

1. The mirror neuron system : New frontiers

2008-01-01

Since the discovery of mirror neurons, much effort has been invested into Studying their location and properties in the human brain. Here we review these original findings and introduce the Main topics of this special issue of Social Neuroscience. What does the mirror system code? How is the mirror

2. Tandem mirror next step conceptual design

Doggett, J.N.; Damm, C.C.; Bulmer, R.H.

1980-01-01

A study was made to define the features of the experimental mirror fusion device - The Tandem Mirror Next Step, or TMNS - that will bridge the gap between present mirror confinement experiments and a power-producing reactor. We outline the project goals, describe some initial device parameters, and relate the technological requirements to ongoing development programs

3. A Fast Algorithm of Convex Hull Vertices Selection for Online Classification.

Ding, Shuguang; Nie, Xiangli; Qiao, Hong; Zhang, Bo

2018-04-01

Reducing samples through convex hull vertices selection (CHVS) within each class is an important and effective method for online classification problems, since the classifier can be trained rapidly with the selected samples. However, the process of CHVS is NP-hard. In this paper, we propose a fast algorithm to select the convex hull vertices, based on the convex hull decomposition and the property of projection. In the proposed algorithm, the quadratic minimization problem of computing the distance between a point and a convex hull is converted into a linear equation problem with a low computational complexity. When the data dimension is high, an approximate, instead of exact, convex hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples. In addition, the impact of outliers is also considered, and the proposed algorithm is improved by deleting the outliers in the initial procedure. Furthermore, a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems. An upper bound is theoretically proved for the difference between the support vector machines based on the approximate convex hull vertices selected and all the training samples. Experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm.

4. Pattern Discovery in Brain Imaging Genetics via SCCA Modeling with a Generic Non-convex Penalty.

Du, Lei; Liu, Kefei; Yao, Xiaohui; Yan, Jingwen; Risacher, Shannon L; Han, Junwei; Guo, Lei; Saykin, Andrew J; Shen, Li

2017-10-25

Brain imaging genetics intends to uncover associations between genetic markers and neuroimaging quantitative traits. Sparse canonical correlation analysis (SCCA) can discover bi-multivariate associations and select relevant features, and is becoming popular in imaging genetic studies. The L1-norm function is not only convex, but also singular at the origin, which is a necessary condition for sparsity. Thus most SCCA methods impose [Formula: see text]-norm onto the individual feature or the structure level of features to pursuit corresponding sparsity. However, the [Formula: see text]-norm penalty over-penalizes large coefficients and may incurs estimation bias. A number of non-convex penalties are proposed to reduce the estimation bias in regression tasks. But using them in SCCA remains largely unexplored. In this paper, we design a unified non-convex SCCA model, based on seven non-convex functions, for unbiased estimation and stable feature selection simultaneously. We also propose an efficient optimization algorithm. The proposed method obtains both higher correlation coefficients and better canonical loading patterns. Specifically, these SCCA methods with non-convex penalties discover a strong association between the APOE e4 rs429358 SNP and the hippocampus region of the brain. They both are Alzheimer's disease related biomarkers, indicating the potential and power of the non-convex methods in brain imaging genetics.

5. Study on IAEA international emergency response exercise convEx-3

Yamamoto, Kazuya

2007-05-01

The International Atomic Energy Agency (IAEA) carried out a large-scale international emergency response exercise in 2005 under the designated name of ConvEx-3(2005), at Romania. This review report summarizes a study about ConvEx-3(2005) based on several related open literature. The ConvEx-3 was conducted in accordance with Agency's safety standard series and requirements in the field of Emergency Preparedness and Response. The study on the preparation, conduct and evaluation of ConvEx-3(2005) exercise is expected to provide very useful knowledge for development of drills and educational programs conducted by Nuclear Emergency Assistance and Training Center (NEAT). Especially, study on the exercise evaluations is instrumental in improving evaluations of drills planned by the national government and local governments. As international cooperation among Asian countries in the field of nuclear emergency preparedness and response is going to realize, it is very useful to survey and consider scheme and methodology about international emergency preparedness, response and exercise referring the knowledge of this ConvEx-3 study. The lessons learned from this study of ConvEx-3(2005) are summarized in four chapters; methodology of exercises and educational programs, exercise evaluation process, amendments/verification of the emergency response plan of NEAT, and technical issues of systems for emergency response and assistance of NEAT relevant to interface for international emergency communication. (author)

6. EUV multilayer mirror, optical system including a multilayer mirror and method of manufacturing a multilayer mirror

Huang, Qiushi; Louis, Eric; Bijkerk, Frederik; de Boer, Meint J.; von Blanckenhagen, G.

2016-01-01

A multilayer mirror (M) reflecting extreme ultraviolet (EUV) radiation from a first wave-length range in a EUV spectral region comprises a substrate (SUB) and a stack of layers (SL) on the substrate, the stack of layers comprising layers comprising a low index material and a high index material, the

7. Physics issues in mirror and tandem mirror systems

Post, R.F.

1984-01-01

Over the years the study of the confinement of high temperature plasma in magnetic mirror systems has presented researchers with many unusual physics problems. Many of these issues are by now understood theoretically and documented experimentally. With the advent of the tandem mirror idea, some new issues have emerged and are now under intensive study. These include: (1) the generation and control of ambipolar confining potentials and their effect on axial confinement and, (2) the combined influence of nonaxisymmetric magnetic fields (used to ensure MHD stability) and electric magnetic particle drifts on radial transport. Physics considerations associated with these two categories of issues will be reviewed, including concepts for the control of radial transport, under study or proposed

8. Mirror hybrid reactor optimization studies

Bender, D.J.

1976-01-01

A system model of the mirror hybrid reactor has been developed. The major components of the model include (1) the reactor description, (2) a capital cost analysis, (3) various fuel management schemes, and (4) an economic analysis that includes the hybrid plus its associated fission burner reactors. The results presented describe the optimization of the mirror hybrid reactor, the objective being to minimize the cost of electricity from the hybrid fission-burner reactor complex. We have examined hybrid reactors with two types of blankets, one containing natural uranium, the other thorium. The major difference between the two optimized reactors is that the uranium hybrid is a significant net electrical power producer, whereas the thorium hybrid just about breaks even on electrical power. Our projected costs for fissile fuel production are approximately 50 $/g for 239 Pu and approximately 125$/g for 233 U

9. Mirror Fusion vacuum technology developments

Batzer, T.H.; Call, W.R.

1983-01-01

Magnetic Mirror Fusion experiments, such as MFTF-B+T (Mirror Fusion Test Facility-B, Tritium Upgrade) and foreseeable follow-on devices, have operational and maintenance requirements that have not yet been fully demonstrated. Among those associated with vacuum technology are the very-high continuous-pumping speeds, 10 7 to 10 8 l/s for D 2 , T 2 and, to a lesser extent, He; the early detection of water leaks from the very-high heat-flux neutral-beam dumps and the detection and location of leaks in the superconducting magnets not protected by guard vacuums. Possible solutions to these problems have been identified and considerable progress has been made toward successfully demonstrating their feasibility

10. Mirror fusion vacuum technology developments

Batzer, T.H.; Call, W.R.

1983-01-01

Magnetic Mirror Fusion experiments, such as MFTF-B+T (Mirror Fusion Test Facility-B, Tritium Upgrade) and foreseeable follow-on devices, have operational and maintenance requirements that have not yet been fully demonstrated. Among those associated with vacuum technology are the very-high continuous-pumping speeds, 10 7 to 10 8 l/s for D 2 , T 2 and, to a lesser extent, He; the early detection of water leaks from the very-high heat-flux neutral-beam dumps and the detection and location of leaks in the superconducting magnets not protected by guard vacuums. Possible solutions to these problems have been identified and considerable progress has been made toward successfully demonstrating their feasibility

11. Imitation, empathy, and mirror neurons.

Iacoboni, Marco

2009-01-01

There is a convergence between cognitive models of imitation, constructs derived from social psychology studies on mimicry and empathy, and recent empirical findings from the neurosciences. The ideomotor framework of human actions assumes a common representational format for action and perception that facilitates imitation. Furthermore, the associative sequence learning model of imitation proposes that experience-based Hebbian learning forms links between sensory processing of the actions of others and motor plans. Social psychology studies have demonstrated that imitation and mimicry are pervasive, automatic, and facilitate empathy. Neuroscience investigations have demonstrated physiological mechanisms of mirroring at single-cell and neural-system levels that support the cognitive and social psychology constructs. Why were these neural mechanisms selected, and what is their adaptive advantage? Neural mirroring solves the "problem of other minds" (how we can access and understand the minds of others) and makes intersubjectivity possible, thus facilitating social behavior.

12. Mirror decay of $^{75}$Sr

Huikari, J; Algora, A; Cederkäll, J; Courtin, S; Dessagne, P; Fraile-Prieto, L M; Franchoo, S; Fynbo, H O U; Huang Wan Xia; Jokinen, A; Knipper, A; Maréchal, F; Miehé, C; Nácher, E; Peräjärvi, K; Poirier, E; Weissman, L; Äystö, J

2003-01-01

The beta -decay of /sup 75/Sr to its mirror nucleus /sup 75/Rb was studied at the ISOLDE PSB facility at CERN by means of beta -delayed gamma and proton spectroscopy. The decay Q-value and beta -delayed gamma intensity were measured for the first time. These results, 10.60+or-0.22 MeV and 4.5/sub -0.7//sup +1.9/%, together with accurate measurements of the beta -decay half-life and beta -delayed proton branching ratio yielded the Gamow-Teller strength 0.35+or-0.05 for the mirror transition. Implications of the results on studies of deformation effects and on the path of the rapid proton capture process are discussed. (24 refs).

13. MINIMARS tandem mirror reactor study

Perkins, L.J.; Logan, B.G.; Doggett, J.N.

1986-01-01

During 1985-1986, Lawrence Livermore National Lab., in partnership with the Fusion Engineering Design Center of Oak Ridge National Lab., the Univ. of Wisconsin, TRW, Grumman Aerospace Corporation, General Dynamics/Convair, Argonne National Lab., and the Canadian Fusion Fuels Technology Project, has conducted the conceptual design of MINIMARS, a small commercial tandem mirror reactor with novel octopole end plugs. With a net electric output of 600 MW(e), MINIMARS is expressly designed for short (∼4- to 5-yr) construction time, factory-built modules, and a passively safe blanket and thermal cycle. In this way, we intend to achieve a small reactor based on the tandem mirror principle that will minimize utility financial risk, thereby providing an attractive alternative to the more conventional large fusion plant designs encountered to date

14. Open trap with ambipolar mirrors

Dimov, G.I.; Zakajdakov, V.V.; Kishinevskij, M.E.

1977-01-01

Results of numerical calculations on the behaviour of a thermonuclear plasma, allowing for α-particles in a trap with longitudinal confinement of the main ions by ambipolar electric fields are presented. This trap is formed by connecting two small-volume ''mirrortrons'' to an ordinary open trap. Into the extreme mirrortrons, approximately 1-MeV ions are introduced continuously by ionization of atomic beams on the plasma, and approximately 10-keV ions are similarly introduced into the main central region of the trap. By a suitable choice of injection currents, the plasma density established in the extreme mirrortrons is higher than in the central region. As a result of the quasi-neutrality condition, a longitudinal ambipolar field forming a potential well not only for electrons but also for the central ions is formed in the plasma. When the depth of the well for the central ions is much greater than their temperature, their life-time considerably exceeds the time of confinement by the magnetic mirrors. As a result, the plasma density is constant over the entire length of the central mirrortron, including the regions near the mirrors, and an ambipolar field is formed only in the extreme mirrortrons. The distribution of central ions and ambipolar potential in the extreme mirrortrons is uniquely determined by the density distribution of fast extreme ions. It is shown in the present study that an amplification coefficient Q as high as desired can, in principle, be reached in the trap under consideration, allowing for α-particles. However, this requires high magnetic fields in the mirrors and a sufficient length of the central mirrotron. It is shown that for moderate values of Q=3-8, it is desirable not to confine the central fast α-particles. To achieve a coefficient of Q=5, it is necessary to create fields of 250 kG in the mirrors, and the length of the trap must not be greater than 100 m. (author)

15. Imitation, mirror neurons and autism

Williams, Justin H.G.; Whiten, Andrew; Suddendorf, Thomas; Perrett, David I.

2001-01-01

Various deficits in the cognitive functioning of people with autism have been documented in recent years but these provide only partial explanations for the condition. We focus instead on an imitative disturbance involving difficulties both in copying actions and in inhibiting more stereotyped mimicking, such as echolalia. A candidate for the neural basis of this disturbance may be found in a recently discovered class of neurons in frontal cortex, 'mirror neurons' (MNs). These neurons show ac...

16. Manufacturability of compact synchrotron mirrors

Douglas, Gary M.

1997-11-01

While many of the government funded research communities over the years have put their faith and money into increasingly larger synchrotrons, such as Spring8 in Japan, and the APS in the United States, a viable market appears to exist for smaller scale, research and commercial grade, compact synchrotrons. These smaller, and less expensive machines, provide the research and industrial communities with synchrotron radiation beamline access at a portion of the cost of their larger and more powerful counterparts. A compact synchrotron, such as the Aurora-2D, designed and built by Sumitomo Heavy Industries, Ltd. of japan (SHI), is a small footprint synchrotron capable of sustaining 20 beamlines. Coupled with a Microtron injector, with 150 MeV of injection energy, an entire facility fits within a 27 meter [88.5 ft] square floorplan. The system, controlled by 2 personal computers, is capable of producing 700 MeV electron energy and 300 mA stored current. Recently, an Aurora-2D synchrotron was purchased from SHI by the University of Hiroshima. The Rocketdyne Albuquerque Operations Beamline Optics Group was approached by SHI with a request to supply a group of 16 beamline mirrors for this machine. These mirrors were sufficient to supply 3 beamlines for the Hiroshima machine. This paper will address engineering issues which arose during the design and manufacturing of these mirrors.

17. The deformable secondary mirror of VLT: final electro-mechanical and optical acceptance test results

Briguglio, Runa; Biasi, Roberto; Xompero, Marco; Riccardi, Armando; Andrighettoni, Mario; Pescoller, Dietrich; Angerer, Gerald; Gallieni, Daniele; Vernet, Elise; Kolb, Johann; Arsenault, Robin; Madec, Pierre-Yves

2014-07-01

The Deformable Secondary Mirror (DSM) for the VLT ended the stand-alone electro-mechanical and optical acceptance process, entering the test phase as part of the Adaptive Optics Facility (AOF) at the ESO Headquarter (Garching). The VLT-DSM currently represents the most advanced already-built large-format deformable mirror with its 1170 voice-coil actuators and its internal metrology based on co-located capacitive sensors to control the shape of the 1.12m-diameter 2mm-thick convex shell. The present paper reports the final results of the electro-mechanical and optical characterization of the DSM executed in a collaborative effort by the DSM manufacturing companies (Microgate s.r.l. and A.D.S. International s.r.l.), INAF-Osservatorio Astrofisico di Arcetri and ESO. The electro-mechanical acceptance tests have been performed in the company premises and their main purpose was the dynamical characterization of the internal control loop response and the calibration of the system data that are needed for its optimization. The optical acceptance tests have been performed at ESO (Garching) using the ASSIST optical test facility. The main purpose of the tests are the characterization of the optical shell flattening residuals, the corresponding calibration of flattening commands, the optical calibration of the capacitive sensors and the optical calibration of the mirror influence functions.

18. Mirror agnosia and the mirrored-self misidentification delusion: a hypnotic analogue.

Connors, Michael H; Cox, Rochelle E; Barnier, Amanda J; Langdon, Robyn; Coltheart, Max

2012-05-01

Mirrored-self misidentification is the delusional belief that one's reflection in the mirror is a stranger. Current theories suggest that one pathway to the delusion is mirror agnosia (a deficit in which patients are unable to use mirror knowledge when interacting with mirrors). This study examined whether a hypnotic suggestion for mirror agnosia can recreate features of the delusion. Ten high hypnotisable participants were given either a suggestion to not understand mirrors or to see the mirror as a window. Participants were asked to look into a mirror and describe what they saw. Participants were tested on their understanding of mirrors and received a series of challenges. Participants then received a detailed postexperimental inquiry. Three of five participants given the suggestion to not understand mirrors reported seeing a stranger and maintained this belief when challenged. These participants also showed signs of mirror agnosia. No participants given the suggestion to see a window reported seeing a stranger. Results indicate that a hypnotic suggestion for mirror agnosia can be used to recreate the mirrored-self misidentification delusion. Factors influencing the effectiveness of hypnotic analogues of psychopathology, such as participants' expectations and interpretations, are discussed.

19. linear time algorithm for finding the convex ropes between two vertices of a simple polygon without triangulation

Phan Thanh An

2008-06-01

The convex rope problem, posed by Peshkin and Sanderson in IEEE J. Robotics Automat, 2 (1986) pp. 53-58, is to find the counterclockwise and clockwise convex ropes starting at the vertex a and ending at the vertex b of a simple polygon, where a is on the boundary of the convex hull of the polygon and b is visible from infinity. In this paper, we present a linear time algorithm for solving this problem without resorting to a linear-time triangulation algorithm and without resorting to a convex hull algorithm for the polygon. The counterclockwise (clockwise, respectively) convex rope consists of two polylines obtained in a basic incremental strategy described in convex hull algorithms for the polylines forming the polygon from a to b. (author)

20. Smart Makeup Mirror: Computer Augmented Mirror to Aid Makeup Application

岩渕, 絵里子; 椎尾, 一郎

2008-01-01

In this paper, we present the system that aids people in wearing makeup easily and make the process enjoyable. The proposed system is the Smart Makeup Mirror device, which is an electronic dressing table that facilitates the process of makeup application. In this system, we place a high-resolution camera on top of a computer display. We developed some functions such as Automatic zoom to a specific part of the face, Display our face from various angles , and Simulation of the lighting conditio...

1. On the complexity of a combined homotopy interior method for convex programming

Yu, Bo; Xu, Qing; Feng, Guochen

2007-03-01

In [G.C. Feng, Z.H. Lin, B. Yu, Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem, Nonlinear Anal. 32 (1998) 761-768; G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics, Proceedings of the Second Japan-China Seminar on Numerical Mathematics, Lecture Notes in Numerical and Applied Analysis, vol. 14, Kinokuniya, Tokyo, 1995, pp. 9-16; Z.H. Lin, B. Yu, G.C. Feng, A combined homotopy interior point method for convex programming problem, Appl. Math. Comput. 84 (1997) 193-211.], a combined homotopy was constructed for solving non-convex programming and convex programming with weaker conditions, without assuming the logarithmic barrier function to be strictly convex and the solution set to be bounded. It was proven that a smooth interior path from an interior point of the feasible set to a K-K-T point of the problem exists. This shows that combined homotopy interior point methods can solve the problem that commonly used interior point methods cannot solveE However, so far, there is no result on its complexity, even for linear programming. The main difficulty is that the objective function is not monotonically decreasing on the combined homotopy path. In this paper, by taking a piecewise technique, under commonly used conditions, polynomiality of a combined homotopy interior point method is given for convex nonlinear programming.

2. Passivation coating for flexible substrate mirrors

Tracy, C. Edwin; Benson, David K.

1990-01-01

A protective diffusion barrier for metalized mirror structures is provided by a layer or coating of silicon nitride which is a very dense, transparent, dielectric material that is impervious to water, alkali, and other impurities and corrosive substances that typically attack the metal layers of mirrors and cause degradation of the mirrors' reflectivity. The silicon nitride layer can be deposited on the substrate before metal deposition thereon to stabilize the metal/substrate interface, and it can be deposited over the metal to encapsulate it and protect the metal from corrosion or other degradation. Mirrors coated with silicon nitride according to this invention can also be used as front surface mirrors. Also, the silver or other reflective metal layer on mirrors comprising thin, lightweight, flexible substrates of metal or polymer sheets coated with glassy layers can be protected with silicon nitride according to this invention.

3. Standard specification for silvered flat glass mirror

American Society for Testing and Materials. Philadelphia

2008-01-01

1.1 This specification covers the requirements for silvered flat glass mirrors of rectangular shape supplied as cut sizes, stock sheets or as lehr ends and to which no further processing (such as edgework or other fabrication) has been done. 1.2 This specification covers the quality requirements of silvered annealed monolithic clear and tinted flat glass mirrors up to 6 mm (¼ in.) thick. The mirrors are intended to be used indoors for mirror glazing, for components of decorative accessories or for similar uses. 1.3 This specification does not address safety glazing materials nor requirements for mirror applications. Consult model building codes and other applicable standards for safety glazing applications. 1.4 Mirrors covered in this specification are not intended for use in environments where high humidity or airborne corrosion promoters, or both, are consistently present (such as swimming pool areas, ocean-going vessels, chemical laboratories and other corrosive environments). 1.5 The dimensional val...

4. Magnetic mirror fusion: status and prospects

Post, R.F.

1980-01-01

Two improved mirror systems, the tandem mirror (TM) and the field-reversed mirror (FRM) are being intensively studied. The twin practical aims of these studies: to improve the economic prospects for mirror fusion power plants and to reduce the size and/or complexity of such plants relative to earlier approaches to magnetic fusion. While at the present time the program emphasis is still strongly oriented toward answering scientific questions, the emphasis is shifting as the data accumulates and as larger facilities - ones with a heavy technological and engineering orientation - are being prepared. The experimental and theoretical progress that led to the new look in mirror fusion research is briefly reviewed, the new TM and the FRM ideas are outlined, and the projected future course of mirror fusion research is discussed

5. Torus knots and mirror symmetry

Brini, Andrea; Marino, Marcos

2012-01-01

We propose a spectral curve describing torus knots and links in the B-model. In particular, the application of the topological recursion to this curve generates all their colored HOMFLY invariants. The curve is obtained by exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved conifold, and should be regarded as the mirror of the topological D-brane associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we derive the curve as the large N limit of the matrix model computing torus knot invariants.

6. Ring mirror fiber laser gyroscope

Shalaby, Mohamed Y.; Khalil, Kamal; Afifi, Abdelrahman E.; Khalil, Diaa

2017-02-01

In this work we present a new architecture for a laser gyroscope based on the use of a Sagnac fiber loop mirror. The proposed system has the unique property that its scale factor can be increased by increasing the gain of the optical amplifier used in the system as demonstrated experimentally using standard single mode fiber and explained physically by the system operation. The proposed gyroscope system is also capable of identifying the direction of rotation. This new structure opens the door for a new category of low cost optical gyroscopes.

7. Tandem mirror technology demonstration facility

1983-10-01

This report describes a facility for generating engineering data on the nuclear technologies needed to build an engineering test reactor (ETR). The facility, based on a tandem mirror operating in the Kelley mode, could be used to produce a high neutron flux (1.4 MW/M/sup 2/) on an 8-m/sup 2/ test area for testing fusion blankets. Runs of more than 100 h, with an average availability of 30%, would produce a fluence of 5 mW/yr/m/sup 2/ and give the necessary experience for successful operation of an ETR.

8. Tandem mirror technology demonstration facility

1983-10-01

This report describes a facility for generating engineering data on the nuclear technologies needed to build an engineering test reactor (ETR). The facility, based on a tandem mirror operating in the Kelley mode, could be used to produce a high neutron flux (1.4 MW/M 2 ) on an 8-m 2 test area for testing fusion blankets. Runs of more than 100 h, with an average availability of 30%, would produce a fluence of 5 mW/yr/m 2 and give the necessary experience for successful operation of an ETR

9. Mirror advanced reactor study (MARS)

Henning, C.D.; Logan, B.G.; Carlson, G.A.

1982-01-01

The agenda for the meeting is as follows: (1) basic Tandem Mirror approach, (2) baseline design, (3) transition and Yin-Yang coils, (4) drift pump physics, (5) drift pump coil, (6) Fokker-Planck analysis, (7) ignition-alpha pumping, (8) neutral beam status, (9) axicell layout, (10) axicell radiation levels, (11) ICRH system, (12) central cell cost optimization, (13) central cell coil design, (14) gridless direct converter, (15) direct converter directions, (16) end cell structure, (17) corrosion-double wall HX, (18) central cell maintenance, (19) radioactivity, (20) PbLi blanket design, and (21) MARS schedule

10. Field-reversed mirror reactor

Carlson, G.A.

1978-01-01

The reactor design is a multicell arrangement wherein a series of field-reversed plasma layers are arranged along the axis of a long superconducting solenoid which provides the background magnetic field. Normal copper mirror coils and Ioffe bars placed at the first wall radius provide shallow axial and radial magnetic wells for each plasma layer. Each of 11 plasma layers requires the injection of 3.6 MW of 200 keV deuterium and tritium and produces 20 MW of fusion power. The reactor has a net electric output of 74 MWe and an estimated direct capital cost of $1200/kWe 11. Field reversal in mirror machines Pearlstein, L.D.; Anderson, D.V.; Boozer, A.H. 1978-01-01 This report discusses some of the physics issues anticipated in field-reversed mirrors. The effect of current cancellation due to electrons is described. An estimate is made of the required impurity level to maintain a field-reversed configuration. The SUPERLAYER code is used to simulate the high-β 2XIIB results, and favorable comparisons require inclusion of quasilinear RF turbulence. Impact of a quadrupole field on field-line closure and resonant transport is discussed. A simple self-consistent model of ion currents is presented. Conditions for stability of field-reversed configurations to E x B driven rotations are determined 12. Charged particle confinement in magnetic mirror Bora, D.; John, P.I.; Saxena, Y.C.; Varma, R.K. 1982-01-01 The behaviour of single charged particle trapped in a magnetic mirror has been investigated experimentally. The particle injected off axis and trapped in a magnetic mirror, leak out of the mirror with the leakage characterized by multiple decay times. The observed decay times are in good agreement with predictions of a ''wave mechanical like'' model by Varma, over a large range of relevant parameters. (author) 13. Mirror neurons: From origin to function Cook, R; Bird, G; Catmur, C; Press, C; Heyes, C 2014-01-01 This article argues that mirror neurons originate in sensorimotor associative learning and therefore a new approach is needed to investigate their functions. Mirror neurons were discovered about 20 years ago in the monkey brain, and there is now evidence that they are also present in the human brain. The intriguing feature of many mirror neurons is that they fire not only when the animal is performing an action, such as grasping an object using a power grip, but also when the animal passively... 14. Anomalous dynamics triggered by a non-convex equation of state in relativistic flows Ibáñez, J. M.; Marquina, A.; Serna, S.; Aloy, M. A. 2018-05-01 The non-monotonicity of the local speed of sound in dense matter at baryon number densities much higher than the nuclear saturation density (n0 ≈ 0.16 fm-3) suggests the possible existence of a non-convex thermodynamics which will lead to a non-convex dynamics. Here, we explore the rich and complex dynamics that an equation of state (EoS) with non-convex regions in the pressure-density plane may develop as a result of genuinely relativistic effects, without a classical counterpart. To this end, we have introduced a phenomenological EoS, the parameters of which can be restricted owing to causality and thermodynamic stability constraints. This EoS can be regarded as a toy model with which we may mimic realistic (and far more complex) EoSs of practical use in the realm of relativistic hydrodynamics. 15. Convex polyhedral abstractions, specialisation and property-based predicate splitting in Horn clause verification Kafle, Bishoksan; Gallagher, John Patrick 2014-01-01 We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of query-answer transformed clauses, and refinement by splitting...... in conjunction with specialisation for propagating constraints it can frequently solve challenging verification problems. This is a contribution in itself, but refinement is needed when it fails, and the question of how to refine convex polyhedral analyses has not been studied much. We present a refinement...... technique based on interpolants derived from a counterexample trace; these are used to drive a property-based specialisation that splits predicates, leading in turn to more precise convex polyhedral analyses. The process of specialisation, analysis and splitting can be repeated, in a manner similar... 16. Uniform estimate of a compact convex set by a ball in an arbitrary norm Dudov, S I; Zlatorunskaya, I V 2000-01-01 The problem of the best uniform approximation of a compact convex set by a ball with respect to an arbitrary norm in the Hausdorff metric corresponding to that norm is considered. The question is reduced to a convex programming problem, which can be studied by means of convex analysis. Necessary and sufficient conditions for the solubility of this problem are obtained and several properties of its solution are described. It is proved, in particular, that the centre of at least one ball of best approximation lies in the compact set under consideration; in addition, conditions ensuring that the centres of all balls of best approximation lie in this compact set and a condition for unique solubility are obtained 17. Schur-Convexity for a Class of Symmetric Functions and Its Applications Wei-Feng Xia 2009-01-01 Full Text Available For x=(x1,x2,…,xn∈R+n, the symmetric function ϕn(x,r is defined by ϕn(x,r=ϕn(x1,x2,…,xn;r=∏1≤i1convexity, Schur multiplicative convexity and Schur harmonic convexity of ϕn(x,r are discussed. As applications, some inequalities are established by use of the theory of majorization. 18. Analytic solution for a quartic electron mirror Straton, Jack C., E-mail: straton@pdx.edu 2015-01-15 A converging electron mirror can be used to compensate for spherical and chromatic aberrations in an electron microscope. This paper presents an analytical solution to a diode (two-electrode) electrostatic mirror including the next term beyond the known hyperbolic shape. The latter is a solution of the Laplace equation to second order in the variables perpendicular to and along the mirror's radius (z{sup 2}−r{sup 2}/2) to which we add a quartic term (kλz{sup 4}). The analytical solution is found in terms of Jacobi cosine-amplitude functions. We find that a mirror less concave than the hyperbolic profile is more sensitive to changes in mirror voltages and the contrary holds for the mirror more concave than the hyperbolic profile. - Highlights: • We find the analytical solution for electron mirrors whose curvature has z4 dependence added to the usual z{sup 2} – r{sup 2}/2 terms. • The resulting Jacobi cosine-amplitude function reduces to the well-known cosh solution in the limit where the new term is 0. • This quartic term gives a mirror designer additional flexibility for eliminating spherical and chromatic aberrations. • The possibility of using these analytical results to approximately model spherical tetrode mirrors close to axis is noted. 19. Mirror neurons and language in schizophrenia Bendová, Marie 2016-01-01 Mirror neurons are a specific kind of visuomotor neurons that are involved in action execution and also in action perception. The mirror mechanism is linked to a variety of complex psychological functions such as social-cognitive functions and language. People with schizophrenia have often difficulties both in mirror neuron system and in language skills. In the first part of our research we studied the connectivity of mirror neuron areas (such as IFG, STG, PMC, SMC and so on) by fMRI in resti... 20. Sensorimotor learning configures the human mirror system. Catmur, Caroline; Walsh, Vincent; Heyes, Cecilia 2007-09-04 Cells in the "mirror system" fire not only when an individual performs an action but also when one observes the same action performed by another agent [1-4]. The mirror system, found in premotor and parietal cortices of human and monkey brains, is thought to provide the foundation for social understanding and to enable the development of theory of mind and language [5-9]. However, it is unclear how mirror neurons acquire their mirror properties -- how they derive the information necessary to match observed with executed actions [10]. We address this by showing that it is possible to manipulate the selectivity of the human mirror system, and thereby make it operate as a countermirror system, by giving participants training to perform one action while observing another. Before this training, participants showed event-related muscle-specific responses to transcranial magnetic stimulation over motor cortex during observation of little- and index-finger movements [11-13]. After training, this normal mirror effect was reversed. These results indicate that the mirror properties of the mirror system are neither wholly innate [14] nor fixed once acquired; instead they develop through sensorimotor learning [15, 16]. Our findings indicate that the human mirror system is, to some extent, both a product and a process of social interaction. 1. A parallel Discrete Element Method to model collisions between non-convex particles Rakotonirina Andriarimina Daniel 2017-01-01 Full Text Available In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called “glued-convex method” (in the sense clumping convex bodies together, as an extension of the popular “glued-spheres” method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i the collapse of a granular column made of convex particles and (i the microstructure of a heap of non-convex particles in a cylindrical reactor. 2. Method of convex rigid frames and applications in studies of multipartite quNit pure states Zhong Zaizhe 2005-01-01 In this letter, we suggest a method of convex rigid frames in the studies of multipartite quNit pure states. We illustrate what the convex rigid frames are, and what is their method. As applications, we use this method to solve some basic problems and give some new results (three theorems): the problem of the partial separability of the multipartite quNit pure states and its geometric explanation; the problem of the classification of multipartite quNit pure states, giving a perfect explanation of the local unitary transformations; thirdly, we discuss the invariants of classes and give a possible physical explanation. (letter to the editor) 3. Optimization of Transverse Oscillating Fields for Vector Velocity Estimation with Convex Arrays Jensen, Jørgen Arendt 2013-01-01 A method for making Vector Flow Images using the transverse oscillation (TO) approach on a convex array is presented. The paper presents optimization schemes for TO fields for convex probes and evaluates their performance using Field II simulations and measurements using the SARUS experimental...... from 90 to 45 degrees in steps of 15 degrees. The optimization routine changes the lateral oscillation period lx to yield the best possible estimates based on the energy ratio between positive and negative spatial frequencies in the ultrasound field. The basic equation for lx gives 1.14 mm at 40 mm... 4. The canonical partial metric and the uniform convexity on normed spaces S. Oltra 2005-10-01 Full Text Available In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm. We prove that these geometric properties can be considered, in this sense, as topological properties that appear when we compare the natural metric topology of the space with the non translation invariant topology induced by the canonical partial metric in the normed space. 5. License or entry decision for innovator in international duopoly with convex cost functions Hattori, Masahiko; Tanaka, Yasuhito 2017-01-01 We consider a choice of options for a foreign innovating firm to license its new cost-reducing technology to a domestic incumbent firm or to enter the domestic market with or without license under convex cost functions. With convex cost functions the domestic market and the foreign market are not separated, and the results depend on the relative size of those markets. In a specific case with linear demand and quadratic cost, entry without license strategy is never the optimal strategy for the... 6. Coherent dynamics of plasma mirrors Thaury, C; George, H; Quere, F; Monot, P; Martin, Ph [CEA, DSM, IRAMIS, Serv Photons Atomes and Mol, F-91191 Gif Sur Yvette, (France); Loch, R [Univ Twente, Laser Phys and Nonlinear Opt Grp, Fac Sci and Technol, MESA Inst Nanotechnol, NL-7500 AE Enschede, (Netherlands); Geindre, J P [Ecole Polytech, Lab Pour Utilisat Lasers Intenses, CNRS, F-91128 Palaiseau, (France) 2008-07-01 Coherent ultrashort X-ray pulses provide new ways to probe matter and its ultrafast dynamics. One of the promising paths to generate these pulses consists of using a nonlinear interaction with a system to strongly and periodically distort the waveform of intense laser fields, and thus produce high-order harmonics. Such distortions have so far been induced by using the nonlinear polarizability of atoms, leading to the production of atto-second light bursts, short enough to study the dynamics of electrons in matter. Shorter and more intense atto-second pulses, together with higher harmonic orders, are expected by reflecting ultra intense laser pulses on a plasma mirror - a dense (approximate to 10{sup 23} electrons cm{sup -3}) plasma with a steep interface. However, short-wavelength-light sources produced by such plasmas are known to generally be incoherent. In contrast, we demonstrate that like in usual low-intensity reflection, the coherence of the light wave is preserved during harmonic generation on plasma mirrors. We then exploit this coherence for interferometric measurements and thus carry out a first study of the laser-driven coherent dynamics of the plasma electrons. (authors) 7. Neurodegeneration and Mirror Image Agnosia Chandra, Sadanandavalli Retnaswami; Issac, Thomas Gregor 2014-01-01 Background: Normal Percept with abnormal meaning (Agnosias) has been described from nineteenth century onwards. Later literature became abundant with information on the spectrum of Prosopagnosias. However, selective difficulty in identifying reflected self images with relatively better cognitive functions leads to problems in differentiating it from non-organic psychosis. Aim: In the present study, we investigated patients with dementia who showed difficulty in identifying reflected self images while they were being tested for problems in gnosis with reference to identification of reflected objects, animals, relatives, and themselves and correlate with neuropsychological and radiological parameters. Patients and Methods: Five such patients were identified and tested with a 45 cm × 45 cm mirror kept at 30-cm distance straight ahead of them. Results: Mirror image agnosia is seen in patients with moderate stage posterior dementias who showed neuropsychological and radiological evidence of right parietal dysfunction. Conclusion: Interpretation of reflected self images perception in real time probably involves distinct data-linking circuits in the right parietal lobe, which may get disrupted early in the course of the disease. PMID:25317393 8. Plasma confinement apparatus using solenoidal and mirror coils Fowler, T.K.; Condit, W.C. 1979-01-01 A plasma confinement apparatus is described, wherein multiple magnetic mirror cells are linked by magnetic field lines inside of a solenoid with the mirroring regions for adjacent magnetic mirror cells each formed by a separate mirror coil inside of the solenoid. The magnetic mirror cells may be field reversed 9. Plasma confinement apparatus using solenoidal and mirror coils Fowler, T. Kenneth; Condit, William C. 1979-01-01 A plasma confinement apparatus, wherein multiple magnetic mirror cells are linked by magnetic field lines inside of a solenoid with the mirroring regions for adjacent magnetic mirror cells each formed by a separate mirror coil inside of the solenoid. The magnetic mirror cells may be field reversed. 10. Tandem mirror magnet system for the mirror fusion test facility Bulmer, R.H.; Van Sant, J.H. 1980-01-01 The Tandem Mirror Fusion Test Facility (MFTF-B) will be a large magnetic fusion experimental facility containing 22 supercounducting magnets including solenoids and C-coils. State-of-the-art technology will be used extensively to complete this facility before 1985. Niobium titanium superconductor and stainless steel structural cases will be the principle materials of construction. Cooling will be pool boiling and thermosiphon flow of 4.5 K liquid helium. Combined weight of the magnets will be over 1500 tonnes and the stored energy will be over 1600 MJ. Magnetic field strength in some coils will be more than 8 T. Detail design of the magnet system will begin early 1981. Basic requirements and conceptual design are disclosed in this paper 11. Generalization of the fejer-hadamard type inequalities for p-convex functions via k-fractional integrals Ghulam Farid 2017-10-01 Full Text Available The aim of this paper is to obtain some more general fractional integral inequalities of Fejer Hadamard type for p-convex functions via Riemann-Liouville k-fractional integrals. Also in particular fractional inequalities for p-convex functions via Riemann-Liouville fractional integrals have been deduced. 12. Magnetic mirrors: history, results, and future prospects Beklemishev, A.D.; Ivanov, A.A.; Kruglyakov, E.P.; Burdakov, A.V.; Ivanov, A.A.; Beklemishev, A.D.; Ivanov, A.A.; Burdakov, A.V. 2012-01-01 The evolution of open traps brought them from simple solenoids to highly sophisticated and huge tandem mirrors with quadrupole magnetic stabilizers. They tried to compete with toroidal devices using ambipolar confinement and thermal barriers, but were too late and failed, and are almost extinct. A side branch of open traps went for simplicity and good fast-ion confinement inherent in axially symmetric mirrors. Since simplicity means lower cost of construction and servicing, and lower engineering and materials demands, such type of traps might still have an edge. Axially symmetric mirrors at the Budker Institute of Nuclear Physics in Novosibirsk currently represent the front line of mirror research. We discuss recent experimental results from the multiple-mirror trap, GOL-3, and the gas-dynamic trap, GDT. The next step in this line of research is the GDMT program that will combine the GDT-style fast-ion-dominated central mirror with multiple-mirror end plugs. This superconducting device will be modular and built in stages. The first stage, GDMT-T, will be based on 5m, 7T superconducting solenoid (multiple-mirror plug of the full device). Its 3-year scientific program is oriented primarily on PMI studies. 13. Foil Panel Mirrors for Nonimaging Applications Kuyper, D. J.; Castillo, A. A. 1984-01-01 Large durable, lightweight mirrors made by bonding thick aluminum foil to honeycomb panels or other rigid, flat backings. Mirrors suitable for use as infrared shields, telescope doors, solar-furnance doors, advertising displays, or other reflectors that require low thermal emissivity and high specularity but do not require precise surface figure necessary for imaging. 14. Parametric studies of tandem mirror reactors Carlson, G.A.; Boghosian, B.M.; Fink, J.H.; Myall, J.O.; Neef, W.S. Jr. 1979-01-01 This report, along with its companion, An Improved Tandem Mirror Reactor, discusses the recent progress and present status of our tandem mirror reactor studies. This report presents the detailed results of parametric studies up to, but not including, the very new ideas involving thermal barriers 15. Dynamic characteristics of mirrors' kinematic mount Wu Wenkai; Du Qiang; Li Jingze; Chen Gang; Chen Xiaojuan; Xu Yuanli 2002-01-01 Applying exact constrain design principles, kinematic mount for precision positioning large aperture mirrors is designed; theoretical method is introduced to analyze its dynamic characteristics and the result of the experiment for mirrors, stability; accordingly, the methods to improve design are put forward 16. The Mirror Neuron System and Action Recognition Buccino, Giovanni; Binkofski, Ferdinand; Riggio, Lucia 2004-01-01 Mirror neurons, first described in the rostral part of monkey ventral premotor cortex (area F5), discharge both when the animal performs a goal-directed hand action and when it observes another individual performing the same or a similar action. More recently, in the same area mirror neurons responding to the observation of mouth actions have been… 17. Unbroken Mirror Neurons in Autism Spectrum Disorders Fan, Yang-Teng; Decety, Jean; Yang, Chia-Yen; Liu, Ji-Lin; Cheng, Yawei 2010-01-01 Background: The "broken mirror" theory of autism, which proposes that a dysfunction of the human mirror neuron system (MNS) is responsible for the core social and cognitive deficits in individuals with autism spectrum disorders (ASD), has received considerable attention despite weak empirical evidence. Methods: In this electroencephalographic… 18. Where do mirror neurons come from? Heyes, Cecilia 2010-03-01 Debates about the evolution of the 'mirror neuron system' imply that it is an adaptation for action understanding. Alternatively, mirror neurons may be a byproduct of associative learning. Here I argue that the adaptation and associative hypotheses both offer plausible accounts of the origin of mirror neurons, but the associative hypothesis has three advantages. First, it provides a straightforward, testable explanation for the differences between monkeys and humans that have led some researchers to question the existence of a mirror neuron system. Second, it is consistent with emerging evidence that mirror neurons contribute to a range of social cognitive functions, but do not play a dominant, specialised role in action understanding. Finally, the associative hypothesis is supported by recent data showing that, even in adulthood, the mirror neuron system can be transformed by sensorimotor learning. The associative account implies that mirror neurons come from sensorimotor experience, and that much of this experience is obtained through interaction with others. Therefore, if the associative account is correct, the mirror neuron system is a product, as well as a process, of social interaction. (c) 2009 Elsevier Ltd. All rights reserved. 19. 21 CFR 886.1500 - Headband mirror. 2010-04-01 ... DEVICES OPHTHALMIC DEVICES Diagnostic Devices § 886.1500 Headband mirror. (a) Identification. A headband mirror is a device intended to be strapped to the head of the user to reflect light for use in examination of the eye. (b) Classification. Class I (general controls). The device is exempt from the... 20. Mirror neurons and their clinical relevance. Rizzolatti, Giacomo; Fabbri-Destro, Maddalena; Cattaneo, Luigi 2009-01-01 One of the most exciting events in neurosciences over the past few years has been the discovery of a mechanism that unifies action perception and action execution. The essence of this 'mirror' mechanism is as follows: whenever individuals observe an action being done by someone else, a set of neurons that code for that action is activated in the observers' motor system. Since the observers are aware of the outcome of their motor acts, they also understand what the other individual is doing without the need for intermediate cognitive mediation. In this Review, after discussing the most pertinent data concerning the mirror mechanism, we examine the clinical relevance of this mechanism. We first discuss the relationship between mirror mechanism impairment and some core symptoms of autism. We then outline the theoretical principles of neurorehabilitation strategies based on the mirror mechanism. We conclude by examining the relationship between the mirror mechanism and some features of the environmental dependency syndromes. 1. Mirror Objects in the Solar System? Silagadze, Z.K. 2002-01-01 This talk was given at the Tunguska-2001 international conference but it is not about the Tunguska event. Instead we tried to give some flavor of mirror matter, which is predicted to exist if parity is an unbroken symmetry of nature, to non-experts. The possible connection of the mirror matter ideas to the Tunguska phenomenon was indicated by Foot and Gninenko some time ago and was elaborated by Foot in the separate talk at this conference. If the mirror world interpretation of the Tunguska like events is indeed correct then the most fascinating (but very speculative) possibility is that some well known celestial bodies with strange properties are in fact made mostly from mirror matter, and so maybe the mirror world was discovered long ago and we just have not suspected this. (author) 2. The mirror neuron system: new frontiers. Keysers, Christian; Fadiga, Luciano 2008-01-01 Since the discovery of mirror neurons, much effort has been invested into studying their location and properties in the human brain. Here we review these original findings and introduce the main topics of this special issue of Social Neuroscience. What does the mirror system code? How is the mirror system embedded into the mosaic of circuits that compose our brain? How does the mirror system contribute to communication, language and social interaction? Can the principle of mirror neurons be extended to emotions, sensations and thoughts? Papers using a wide range of methods, including single cell recordings, fMRI, TMS, EEG and psychophysics, collected in this special issue, start to give us some impressive answers. 3. Mirror neurons and motor intentionality. Rizzolatti, Giacomo; Sinigaglia, Corrado 2007-01-01 Our social life rests to a large extent on our ability to understand the intentions of others. What are the bases of this ability? A very influential view is that we understand the intentions of others because we are able to represent them as having mental states. Without this meta-representational (mind-reading) ability their behavior would be meaningless to us. Over the past few years this view has been challenged by neurophysiological findings and, in particular, by the discovery of mirror neurons. The functional properties of these neurons indicate that intentional understanding is based primarily on a mechanism that directly matches the sensory representation of the observed actions with one's own motor representation of those same actions. These findings reveal how deeply motor and intentional components of action are intertwined, suggesting that both can be fully comprehended only starting from a motor approach to intentionality. 4. Imitation, mirror neurons and autism. Williams, J H; Whiten, A; Suddendorf, T; Perrett, D I 2001-06-01 Various deficits in the cognitive functioning of people with autism have been documented in recent years but these provide only partial explanations for the condition. We focus instead on an imitative disturbance involving difficulties both in copying actions and in inhibiting more stereotyped mimicking, such as echolalia. A candidate for the neural basis of this disturbance may be found in a recently discovered class of neurons in frontal cortex, 'mirror neurons' (MNs). These neurons show activity in relation both to specific actions performed by self and matching actions performed by others, providing a potential bridge between minds. MN systems exist in primates without imitative and 'theory of mind' abilities and we suggest that in order for them to have become utilized to perform social cognitive functions, sophisticated cortical neuronal systems have evolved in which MNs function as key elements. Early developmental failures of MN systems are likely to result in a consequent cascade of developmental impairments characterised by the clinical syndrome of autism. 5. Tandem mirrors for neutron production Doggett, J.N. 1983-01-01 Two mirror machine concepts are being studied as early-time, low-cost, neutron-producing devices for testing and demonstrating reactor-relevant fusion technology. The first of these concepts is for a new, small, driven, steady-state, D-T reactor, called the Technology Demonstration Facility (TDF). The second concept is for upgrades to the MFTF-B machine that burn tritium and run for pulse lengths of some hours. Both devices operate in the Kelley mode in order to provide high-wall loadings of 14-MeV neutrons, thereby providing a valuable test bed for reactor-relevant hardware and subsystems. Either one of these devices could be running in the early 1990's with first wall fluxes between 1.4 and 2.0 MW m -2 6. Convexity of Energy-Like Functions: Theoretical Results and Applications to Power System Operations Dvijotham, Krishnamurthy [California Inst. of Technology (CalTech), Pasadena, CA (United States); Low, Steven [California Inst. of Technology (CalTech), Pasadena, CA (United States); Chertkov, Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States) 2015-01-12 Power systems are undergoing unprecedented transformations with increased adoption of renewables and distributed generation, as well as the adoption of demand response programs. All of these changes, while making the grid more responsive and potentially more efficient, pose significant challenges for power systems operators. Conventional operational paradigms are no longer sufficient as the power system may no longer have big dispatchable generators with sufficient positive and negative reserves. This increases the need for tools and algorithms that can efficiently predict safe regions of operation of the power system. In this paper, we study energy functions as a tool to design algorithms for various operational problems in power systems. These have a long history in power systems and have been primarily applied to transient stability problems. In this paper, we take a new look at power systems, focusing on an aspect that has previously received little attention: Convexity. We characterize the domain of voltage magnitudes and phases within which the energy function is convex in these variables. We show that this corresponds naturally with standard operational constraints imposed in power systems. We show that power of equations can be solved using this approach, as long as the solution lies within the convexity domain. We outline various desirable properties of solutions in the convexity domain and present simple numerical illustrations supporting our results. 7. Perimeter generating functions for the mean-squared radius of gyration of convex polygons Jensen, Iwan 2005-01-01 We have derived long series expansions for the perimeter generating functions of the radius of gyration of various polygons with a convexity constraint. Using the series we numerically find simple (algebraic) exact solutions for the generating functions. In all cases the size exponent ν 1. (letter to the editor) 8. A Convex Variational Model for Restoring Blurred Images with Multiplicative Noise Dong, Yiqiu; Tieyong Zeng 2013-01-01 In this paper, a new variational model for restoring blurred images with multiplicative noise is proposed. Based on the statistical property of the noise, a quadratic penalty function technique is utilized in order to obtain a strictly convex model under a mild condition, which guarantees... 9. Modeling IrisCode and its variants as convex polyhedral cones and its security implications. Kong, Adams Wai-Kin 2013-03-01 IrisCode, developed by Daugman, in 1993, is the most influential iris recognition algorithm. A thorough understanding of IrisCode is essential, because over 100 million persons have been enrolled by this algorithm and many biometric personal identification and template protection methods have been developed based on IrisCode. This paper indicates that a template produced by IrisCode or its variants is a convex polyhedral cone in a hyperspace. Its central ray, being a rough representation of the original biometric signal, can be computed by a simple algorithm, which can often be implemented in one Matlab command line. The central ray is an expected ray and also an optimal ray of an objective function on a group of distributions. This algorithm is derived from geometric properties of a convex polyhedral cone but does not rely on any prior knowledge (e.g., iris images). The experimental results show that biometric templates, including iris and palmprint templates, produced by different recognition methods can be matched through the central rays in their convex polyhedral cones and that templates protected by a method extended from IrisCode can be broken into. These experimental results indicate that, without a thorough security analysis, convex polyhedral cone templates cannot be assumed secure. Additionally, the simplicity of the algorithm implies that even junior hackers without knowledge of advanced image processing and biometric databases can still break into protected templates and reveal relationships among templates produced by different recognition methods. 10. Unifying kinetic approach to phoretic forces and torques onto moving and rotating convex particles Kröger, M.; Hütter, M. 2006-01-01 We derive general expressions and present several examples for the phoretic forces and torques acting on a translationally moving and rotating convex tracer particle, usually a submicrosized aerosol particle, assumed to be small compared to the mean free path of the surrounding nonequilibrium gas. 11. Convex hull and tour crossings in the Euclidean traveling salesperson problem : implications for human performance studies Rooij, van I.; Stege, U.; Schactman, A. 2003-01-01 Recently there has been growing interest among psychologists in human performance on the Euclidean traveling salesperson problem (E-TSP). A debate has been initiated on what strategy people use in solving visually presented E-TSP instances. The most prominent hypothesis is the convex-hull 12. On the convex hull of the simple integer recourse objective function Klein Haneveld, Willem K.; Stougie, L.; van der Vlerk, Maarten H. 1995-01-01 We consider the objective function of a simple integer recourse problem with fixed technology matrix. Using properties of the expected value function, we prove a relation between the convex hull of this function and the expected value function of a continuous simple recourse program. We present an 13. On evolving deformation microstructures in non-convex partially damaged solids Gurses, Ercan; Miehe, Christian 2011-01-01 . These microstructures can be resolved by use of relaxation techniques associated with the construction of convex hulls. We propose a particular relaxation method for partially damaged solids and investigate it in one- and multi-dimensional settings. To this end, we 14. Convex Bodies With Minimal Volume Product in R^2 --- A New Proof Lin, Youjiang 2010-01-01 In this paper, a new proof of the following result is given: The product of the volumes of an origin symmetric convex bodies$K$in R^2 and of its polar body is minimal if and only if$K\$ is a parallelogram.

15. Multiobjective optimization of classifiers by means of 3D convex-hull-based evolutionary algorithms

Zhao, J.; Basto, Fernandes V.; Jiao, L.; Yevseyeva, I.; Asep, Maulana A.; Li, R.; Bäck, T.H.W.; Tang, T.; Michael, Emmerich T. M.

2016-01-01

The receiver operating characteristic (ROC) and detection error tradeoff(DET) curves are frequently used in the machine learning community to analyze the performance of binary classifiers. Recently, the convex-hull-based multiobjective genetic programming algorithm was proposed and successfully

16. Deformation patterning driven by rate dependent non-convex strain gradient plasticity

Yalcinkaya, T.; Brekelmans, W.A.M.; Geers, M.G.D.

2011-01-01

A rate dependent strain gradient plasticity framework for the description of plastic slip patterning in a system with non-convex energetic hardening is presented. Both the displacement and the plastic slip fields are considered as primary variables. These fields are determined on a global level by

17. Parthood and Convexity as the Basic Notions of a Theory of Space

Robering, Klaus

A deductive system of geometry is presented which is based on atomistic mereology ("mereology with points'') and the notion of convexity. The system is formulated in a liberal many-sorted logic which makes use of class-theoretic notions without however adopting any comprehension axioms. The geome...

18. Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization

2015-01-01

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled, the dual decomposition scheme involves local parallel

19. An Alternating Direction Method for Convex Quadratic Second-Order Cone Programming with Bounded Constraints

Xuewen Mu

2015-01-01

quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is efficient for the convex quadratic second-order cone programming problems with bounded constraints.

20. A DEEP CUT ELLIPSOID ALGORITHM FOR CONVEX-PROGRAMMING - THEORY AND APPLICATIONS

FRENK, JBG; GROMICHO, J; ZHANG, S

1994-01-01

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent

1. On the rank 1 convexity of stored energy functions of physically linear stress-strain relations

Šilhavý, Miroslav; Bertram, A.; Böhlke, T.

2007-01-01

Roč. 86, č. 3 (2007), s. 235-243 ISSN 0374-3535 Institutional research plan: CEZ:AV0Z10190503 Keywords : generalized linear elastic law s * generalized strain measures * rank 1 convexity Subject RIV: BA - General Mathematics Impact factor: 0.743, year: 2007

2. The Distortion Theorems for Harmonic Mappings with Analytic Parts Convex or Starlike Functions of Order β

Mengkun Zhu

2015-01-01

Full Text Available Some sharp estimates of coefficients, distortion, and growth for harmonic mappings with analytic parts convex or starlike functions of order β are obtained. We also give area estimates and covering theorems. Our main results generalise those of Klimek and Michalski.

3. On the Monotonicity and Log-Convexity of a Four-Parameter Homogeneous Mean

Yang Zhen-Hang

2008-01-01

Full Text Available Abstract A four-parameter homogeneous mean is defined by another approach. The criterion of its monotonicity and logarithmically convexity is presented, and three refined chains of inequalities for two-parameter mean values are deduced which contain many new and classical inequalities for means.

4. Convex order approximations in case of cash flows of mixed signs

Dhaene, J.; Goovaerts, M.J.; Vanmaele, M.; van Weert, K.

2012-01-01

In Van Weert et al. (2010), results are obtained showing that, when allowing some of the cash flows to be negative, convex order lower bound approximations can still be used to solve general investment problems in a context of provisioning or terminal wealth. In this paper, a correction and further

5. From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation

Egozcue, J.; Meziat, R.; Pedregal, P.

2002-01-01

We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature

6. Headache as a crucial symptom in the etiology of convexal subarachnoid hemorrhage.

Rico, María; Benavente, Lorena; Para, Marta; Santamarta, Elena; Pascual, Julio; Calleja, Sergio

2014-03-01

Convexal subarachnoid hemorrhage has been associated with different diseases, reversible cerebral vasoconstriction syndrome and cerebral amyloid angiopathy being the 2 main causes. To investigate whether headache at onset is determinant in identifying the underlying etiology for convexal subarachnoid hemorrhage. After searching in the database of our hospital, 24 patients were found with convexal subarachnoid hemorrhage in the last 10 years. The mean age of the sample was 69.5 years. We recorded data referring to demographics, symptoms and neuroimaging. Cerebral amyloid angiopathy patients accounted for 46% of the sample, 13% were diagnosed with reversible cerebral vasoconstriction syndrome, 16% with several other etiologies, and in 25%, the cause remained unknown. Mild headache was present only in 1 (9%) of the 11 cerebral amyloid angiopathy patients, while severe headache was the dominant feature in 86% of cases of the remaining etiologies. Headache is a key symptom allowing a presumptive etiological diagnosis of convexal subarachnoid hemorrhage. While the absence of headache suggests cerebral amyloid angiopathy as the more probable cause, severe headache obliges us to rule out other etiologies, such as reversible cerebral vasoconstriction syndrome. © 2013 American Headache Society.

7. Neuro-genetic hybrid approach for the solution of non-convex economic dispatch problem

Malik, T.N.; Asar, A.U.

2009-01-01

ED (Economic Dispatch) is non-convex constrained optimization problem, and is used for both on line and offline studies in power system operation. Conventionally, it is solved as convex problem using optimization techniques by approximating generator input/output characteristic. Curves of monotonically increasing nature thus resulting in an inaccurate dispatch. The GA (Genetic Algorithm) has been used for the solution of this problem owing to its inherent ability to address the convex and non-convex problems equally. This approach brings the solution to the global minimum region of search space in a short time and then takes longer time to converge to near optimal results. GA based hybrid approaches are used to fine tune the near optimal results produced by GA. This paper proposes NGH (Neuro Genetic Hybrid) approach to solve the economic dispatch with valve point effect. The proposed approach combines the GA with the ANN (Artificial Neural Network) using SI (Swarm Intelligence) learning rule. The GA acts as a global optimizer and the neural network fine tunes the GA results to the desired targets. Three machines standard test system has been tested for validation of the approach. Comparing the results with GA and NGH model based on back-propagation learning, the proposed approach gives contrast improvements showing the promise of the approach. (author)

8. Extreme points of the convex set of joint probability distributions with ...

Here we address the following problem: If G is a standard ... convex set of all joint probability distributions on the product Borel space (X1 ×X2, F1 ⊗. F2) which .... cannot be identically zero when X and Y vary in A1 and u and v vary in H2. Thus.

9. Mean-square performance of a convex combination of two adaptive filters

Garcia, Jeronimo; Figueiras-Vidal, A.R.; Sayed, A.H.

2006-01-01

Combination approaches provide an interesting way to improve adaptive filter performance. In this paper, we study the mean-square performance of a convex combination of two transversal filters. The individual filters are independently adapted using their own error signals, while the combination i...

10. Sufficient Descent Conjugate Gradient Methods for Solving Convex Constrained Nonlinear Monotone Equations

San-Yang Liu

2014-01-01

Full Text Available Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large-scale nonsmooth equations.

11. Robust Nearfield Wideband Beamforming Design Based on Adaptive-Weighted Convex Optimization

Guo Ye-Cai

2017-01-01

Full Text Available Nearfield wideband beamformers for microphone arrays have wide applications in multichannel speech enhancement. The nearfield wideband beamformer design based on convex optimization is one of the typical representatives of robust approaches. However, in this approach, the coefficient of convex optimization is a constant, which has not used all the freedom provided by the weighting coefficient efficiently. Therefore, it is still necessary to further improve the performance. To solve this problem, we developed a robust nearfield wideband beamformer design approach based on adaptive-weighted convex optimization. The proposed approach defines an adaptive-weighted function by the adaptive array signal processing theory and adjusts its value flexibly, which has improved the beamforming performance. During each process of the adaptive updating of the weighting function, the convex optimization problem can be formulated as a SOCP (Second-Order Cone Program problem, which could be solved efficiently using the well-established interior-point methods. This method is suitable for the case where the sound source is in the nearfield range, can work well in the presence of microphone mismatches, and is applicable to arbitrary array geometries. Several design examples are presented to verify the effectiveness of the proposed approach and the correctness of the theoretical analysis.

12. A Deep Cut Ellipsoid Algorithm for convex Programming: theory and Applications

Frenk, J.B.G.; Gromicho Dos Santos, J.A.; Zhang, S.

1994-01-01

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent

13. A deep cut ellipsoid algorithm for convex programming : Theory and applications

J.B.G. Frenk (Hans); J.A.S. Gromicho (Joaquim); S. Zhang (Shuzhong)

1994-01-01

textabstractThis paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules

14. Study on feed forward neural network convex optimization for LiFePO4 battery parameters

Liu, Xuepeng; Zhao, Dongmei

2017-08-01

Based on the modern facility agriculture automatic walking equipment LiFePO4 Battery, the parameter identification of LiFePO4 Battery is analyzed. An improved method for the process model of li battery is proposed, and the on-line estimation algorithm is presented. The parameters of the battery are identified using feed forward network neural convex optimization algorithm.

15. An Efficient Algorithm to Calculate the Minkowski Sum of Convex 3D Polyhedra

Bekker, Henk; Roerdink, Jos B.T.M.

2001-01-01

A new method is presented to calculate the Minkowski sum of two convex polyhedra A and B in 3D. These graphs are given edge attributes. From these attributed graphs the attributed graph of the Minkowski sum is constructed. This graph is then transformed into the Minkowski sum of A and B. The running

16. The Lp Lp Lp-curvature images of convex bodies and Lp Lp Lp ...

Associated with the -curvature image defined by Lutwak, some inequalities for extended mixed -affine surface areas of convex bodies and the support functions of -projection bodies are established. As a natural extension of a result due to Lutwak, an -type affine isoperimetric inequality, whose special cases are ...

17. On the Fermat-Lagrange principle for mixed smooth convex extremal problems

Brinkhuis, Ya

2001-01-01

A simple geometric condition that can be attached to an extremal problem of a fairly general form included in a family of problems is indicated. This is used to demonstrate that the task of formulating a uniform condition for smooth convex problems can be satisfactorily accomplished. On the other hand, the necessity of this new condition of optimality is proved under certain technical assumptions

18. [Motion control of moving mirror based on fixed-mirror adjustment in FTIR spectrometer].

Li, Zhong-bing; Xu, Xian-ze; Le, Yi; Xu, Feng-qiu; Li, Jun-wei

2012-08-01

The performance of the uniform motion of the moving mirror, which is the only constant motion part in FTIR spectrometer, and the performance of the alignment of the fixed mirror play a key role in FTIR spectrometer, and affect the interference effect and the quality of the spectrogram and may restrict the precision and resolution of the instrument directly. The present article focuses on the research on the uniform motion of the moving mirror and the alignment of the fixed mirror. In order to improve the FTIR spectrometer, the maglev support system was designed for the moving mirror and the phase detection technology was adopted to adjust the tilt angle between the moving mirror and the fixed mirror. This paper also introduces an improved fuzzy PID control algorithm to get the accurate speed of the moving mirror and realize the control strategy from both hardware design and algorithm. The results show that the development of the moving mirror motion control system gets sufficient accuracy and real-time, which can ensure the uniform motion of the moving mirror and the alignment of the fixed mirror.

19. Mirror neurons: from origin to function.

Cook, Richard; Bird, Geoffrey; Catmur, Caroline; Press, Clare; Heyes, Cecilia

2014-04-01

This article argues that mirror neurons originate in sensorimotor associative learning and therefore a new approach is needed to investigate their functions. Mirror neurons were discovered about 20 years ago in the monkey brain, and there is now evidence that they are also present in the human brain. The intriguing feature of many mirror neurons is that they fire not only when the animal is performing an action, such as grasping an object using a power grip, but also when the animal passively observes a similar action performed by another agent. It is widely believed that mirror neurons are a genetic adaptation for action understanding; that they were designed by evolution to fulfill a specific socio-cognitive function. In contrast, we argue that mirror neurons are forged by domain-general processes of associative learning in the course of individual development, and, although they may have psychological functions, they do not necessarily have a specific evolutionary purpose or adaptive function. The evidence supporting this view shows that (1) mirror neurons do not consistently encode action "goals"; (2) the contingency- and context-sensitive nature of associative learning explains the full range of mirror neuron properties; (3) human infants receive enough sensorimotor experience to support associative learning of mirror neurons ("wealth of the stimulus"); and (4) mirror neurons can be changed in radical ways by sensorimotor training. The associative account implies that reliable information about the function of mirror neurons can be obtained only by research based on developmental history, system-level theory, and careful experimentation.

20. A new corrective technique for adolescent idiopathic scoliosis (Ucar′s convex rod rotation

Bekir Yavuz Ucar

2014-01-01

Full Text Available Study Design: Prospective single-center study. Objective: To analyze the efficacy and safety of a new technique of global vertebral correction with convex rod rotation performed on the patients with adolescent idiopathic scoliosis. Summary of Background Data: Surgical goal is to obtain an optimal curve correction in scoliosis surgery. There are various correction techniques. This report describes a new technique of global vertebral correction with convex rod rotation. Materials and Methods: A total of 12 consecutive patients with Lenke type I adolescent idiopathic scoliosis and managed by convex rod rotation technique between years 2012 and 2013 having more than 1 year follow-up were included. Mean age was 14.5 (range = 13-17 years years at the time of operation. The hospital charts were reviewed for demographic data. Measurements of curve magnitude and balance were made on 36-inch standing anteroposterior and lateral radiographs taken before surgery and at most recent follow up to assess deformity correction, spinal balance, and complications related to the instrumentation. Results: Preoperative coronal plane major curve of 62° (range = 50°-72° with flexibility of less than 30% was corrected to 11.5°(range = 10°-14° showing a 81% scoliosis correction at the final follow-up. Coronal imbalance was improved 72% at the most recent follow-up assessment. No complications were found. Conclusion: The new technique of global vertebral correction with Ucar′s convex rod rotation is an effective technique. This method is a vertebral rotation procedure from convex side and it allows to put screws easily to the concave side.

1. Plasma impact on diagnostic mirrors in JET

A. Garcia-Carrasco

2017-08-01

Full Text Available Metallic mirrors will be essential components of all optical systems for plasma diagnosis in ITER. This contribution provides a comprehensive account on plasma impact on diagnostic mirrors in JET with the ITER-Like Wall. Specimens from the First Mirror Test and the lithium-beam diagnostic have been studied by spectrophotometry, ion beam analysis and electron microscopy. Test mirrors made of molybdenum were retrieved from the main chamber and the divertor after exposure to the 2013–2014 experimental campaign. In the main chamber, only mirrors located at the entrance of the carrier lost reflectivity (Be deposition, while those located deeper in the carrier were only slightly affected. The performance of mirrors in the JET divertor was strongly degraded by deposition of beryllium, tungsten and other species. Mirrors from the lithium-beam diagnostic have been studied for the first time. Gold coatings were severely damaged by intense arcing. As a consequence, material mixing of the gold layer with the stainless steel substrate occurred. Total reflectivity dropped from over 90% to less than 60%, i.e. to the level typical for stainless steel.

2. A comparison of performance of lightweight mirrors

Cho, Myung K.; Richard, Ralph M.; Hileman, Edward A.

1990-01-01

Four lightweight solid contoured back mirror shapes (a double arch, a single arch, a modified single arch, and a double concave mirror) and a cellular sandwich lightweight meniscus mirror, have been considered for the primary mirror of the Space Infrared Telescope Facility (SIRTF). A parametric design study using these shapes for the SIRTF 40 inch primary mirror with a focal ratio f/2 is presented. Evaluations of the optical performance and fundamental frequency analyses are performed to compare relative merits of each mirror configuration. Included in these are structural, optical, and frequency analyses for (1) different back contour shapes, (2) different number and location of the support points, and (3) two gravity orientations (ZENITH and HORIZON positions). The finite element program NASTRAN is used to obtain the structural deflections of the optical surface. For wavefront error analysis, FRINGE and PCFRINGE programs are used to evaluate the optical performance. A scaling law relating the optical and structural performance for various mirror contoured back shapes is developed.

3. Laser cleaning of ITER's diagnostic mirrors

Skinner, C. H.; Gentile, C. A.; Doerner, R.

2012-10-01

Practical methods to clean ITER's diagnostic mirrors and restore reflectivity will be critical to ITER's plasma operations. We report on laser cleaning of single crystal molybdenum mirrors coated with either carbon or beryllium films 150 - 420 nm thick. A 1.06 μm Nd laser system provided 220 ns pulses at 8 kHz with typical power densities of 1-2 J/cm^2. The laser beam was fiber optically coupled to a scanner suitable for tokamak applications. The efficacy of mirror cleaning was assessed with a new technique that combines microscopic imaging and reflectivity measurements [1]. The method is suitable for hazardous materials such as beryllium as the mirrors remain sealed in a vacuum chamber. Excellent restoration of reflectivity for the carbon coated Mo mirrors was observed after laser scanning under vacuum conditions. For the beryllium coated mirrors restoration of reflectivity has so far been incomplete and modeling indicates that a shorter duration laser pulse is needed. No damage of the molybdenum mirror substrates was observed.[4pt][1] C.H. Skinner et al., Rev. Sci. Instrum. at press.

4. Magneto-hydrodynamically stable axisymmetric mirrors

Ryutov, D. D.; Cohen, B. I.; Molvik, A. W. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Berk, H. L. [University of Texas, Austin, Texas 78712 (United States); Simonen, T. C. [University of California, Berkeley, California 94720 (United States)

2011-09-15

Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.

5. Mirror dark matter and large scale structure

Ignatiev, A.Yu.; Volkas, R.R.

2003-01-01

Mirror matter is a dark matter candidate. In this paper, we reexamine the linear regime of density perturbation growth in a universe containing mirror dark matter. Taking adiabatic scale-invariant perturbations as the input, we confirm that the resulting processed power spectrum is richer than for the more familiar cases of cold, warm and hot dark matter. The new features include a maximum at a certain scale λ max , collisional damping below a smaller characteristic scale λ S ' , with oscillatory perturbations between the two. These scales are functions of the fundamental parameters of the theory. In particular, they decrease for decreasing x, the ratio of the mirror plasma temperature to that of the ordinary. For x∼0.2, the scale λ max becomes galactic. Mirror dark matter therefore leads to bottom-up large scale structure formation, similar to conventional cold dark matter, for x(less-or-similar sign)0.2. Indeed, the smaller the value of x, the closer mirror dark matter resembles standard cold dark matter during the linear regime. The differences pertain to scales smaller than λ S ' in the linear regime, and generally in the nonlinear regime because mirror dark matter is chemically complex and to some extent dissipative. Lyman-α forest data and the early reionization epoch established by WMAP may hold the key to distinguishing mirror dark matter from WIMP-style cold dark matter

6. Mirror neurons: functions, mechanisms and models.

Oztop, Erhan; Kawato, Mitsuo; Arbib, Michael A

2013-04-12

Mirror neurons for manipulation fire both when the animal manipulates an object in a specific way and when it sees another animal (or the experimenter) perform an action that is more or less similar. Such neurons were originally found in macaque monkeys, in the ventral premotor cortex, area F5 and later also in the inferior parietal lobule. Recent neuroimaging data indicate that the adult human brain is endowed with a "mirror neuron system," putatively containing mirror neurons and other neurons, for matching the observation and execution of actions. Mirror neurons may serve action recognition in monkeys as well as humans, whereas their putative role in imitation and language may be realized in human but not in monkey. This article shows the important role of computational models in providing sufficient and causal explanations for the observed phenomena involving mirror systems and the learning processes which form them, and underlines the need for additional circuitry to lift up the monkey mirror neuron circuit to sustain the posited cognitive functions attributed to the human mirror neuron system. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

7. Mirror and (absence of) counter-mirror responses to action sounds measured with TMS.

Ticini, Luca F; Schütz-Bosbach, Simone; Waszak, Florian

2017-11-01

To what extent is the mirror neuron mechanism malleable to experience? The answer to this question can help characterising its ontogeny and its role in social cognition. Some suggest that it develops through sensorimotor associations congruent with our own actions. Others argue for its extreme volatility that will encode any sensorimotor association in the environment. Here, we added to this debate by exploring the effects of short goal-directed 'mirror' and 'counter-mirror' trainings (a 'mirror' training is defined as the first type of training encountered by the participants) on human auditory mirror motor-evoked potentials (MEPs). We recorded MEPs in response to two tones void of previous motor meaning, before and after mirror and counter-mirror trainings in which participants generated two tones of different pitch by performing free-choice button presses. The results showed that mirror MEPs, once established, were protected against an equivalent counter-mirror experience: they became manifest very rapidly and the same number of training trials that lead to the initial association did not suffice to reverse the MEP pattern. This steadiness of the association argues that, by serving direct-matching purposes, the mirror mechanism is a good solution for social cognition. © The Author (2017). Published by Oxford University Press.

8. Multilayer active shell mirrors for space telescopes

Steeves, John; Jackson, Kathryn; Pellegrino, Sergio; Redding, David; Wallace, J. Kent; Bradford, Samuel Case; Barbee, Troy

2016-07-01

A novel active mirror technology based on carbon fiber reinforced polymer (CFRP) substrates and replication techniques has been developed. Multiple additional layers are implemented into the design serving various functions. Nanolaminate metal films are used to provide a high quality reflective front surface. A backing layer of thin active material is implemented to provide the surface-parallel actuation scheme. Printed electronics are used to create a custom electrode pattern and flexible routing layer. Mirrors of this design are thin (traditional optics. Such mirrors could be used as lightweight primaries for small CubeSat-based telescopes or as meter-class segments for future large aperture observatories. Multiple mirrors can be produced under identical conditions enabling a substantial reduction in manufacturing cost and complexity. An overview of the mirror design and manufacturing processes is presented. Predictions on the actuation performance have been made through finite element simulations demonstrating correctabilities on the order of 250-300× for astigmatic modes with only 41 independent actuators. A description of the custom metrology system used to characterize the active mirrors is also presented. The system is based on a Reverse Hartmann test and can accommodate extremely large deviations in mirror figure (> 100 μm PV) down to sub-micron precision. The system has been validated against several traditional techniques including photogrammetry and interferometry. The mirror performance has been characterized using this system, as well as closed-loop figure correction experiments on 150 mm dia. prototypes. The mirrors have demonstrated post-correction figure accuracies of 200 nm RMS (two dead actuators limiting performance).

9. Near-field flat focusing mirrors

Cheng, Yu-Chieh; Staliunas, Kestutis

2018-03-01

This article reviews recent progress towards the design of near-field flat focusing mirrors, focusing/imaging light patterns in reflection. An important feature of such flat focusing mirrors is their transverse invariance, as they do not possess any optical axis. We start with a review of the physical background to the different focusing mechanisms of near- and far-field focusing. These near-field focusing devices like flat lenses and the reviewed near-field focusing mirrors can implement planar focusing devices without any optical axis. In contrast, various types of far-field planar focusing devices, such as high-contrast gratings and metasurfaces, unavoidably break the transverse invariance due to their radially symmetrical structures. The particular realizations of near-field flat focusing mirrors including Bragg-like dielectric mirrors and dielectric subwavelength gratings are the main subjects of the review. The first flat focusing mirror was demonstrated with a chirped mirror and was shown to manage an angular dispersion for beam focusing, similar to the management of chromatic dispersion for pulse compression. Furthermore, the reviewed optimized chirped mirror demonstrated a long near-field focal length, hardly achieved by a flat lens or a planar hyperlens. Two more different configurations of dielectric subwavelength gratings that focus a light beam at normal or oblique incidence are also reviewed. We also summarize and compare focusing performance, limitations, and future perspectives between the reviewed flat focusing mirrors and other planar focusing devices including a flat lens with a negative-index material, a planar hyperlens, a high-contrast grating, and a metasurface.

10. Coulomb energy differences in mirror nuclei

Lenzi, Silvia M

2006-01-01

By comparing the excitation energies of analogue states in mirror nuclei, several nuclear structure properties can be studied as a function of the angular momentum up to high spin states. They can be described in the shell model framework by including electromagnetic and nuclear isospin-non-conserving interactions. Calculations for the mirror energy differences in nuclei of the f 7/2 shell are described and compared with recent experimental data. These studies are extended to mirror nuclei in the upper sd and fp shells

11. Present status of mirror stability theory

Baldwin, D.E.; Berk, H.L.; Byers, J.A.

1976-01-01

A status report of microinstability as it applies to 2XIIB and MX theory for mirror machines is presented. It is shown that quasilinear computations reproduce many of the parameters observed in the 2XIIB experiment. In regard to large mirror machines, there are presented detailed calculations of the linear theory of the drift cyclotron loss-cone mode, with inhomogeneous geometry and nonlinear diffusive effects. Further, the stability of a mirror machine to the Alfven ion-cyclotron instability is assessed, and the Baldwin-Callen diffusion is estimated for a spatially varying plasma

12. Tandem Mirror Reactor Systems Code (Version I)

Reid, R.L.; Finn, P.A.; Gohar, M.Y.

1985-09-01

A computer code was developed to model a Tandem Mirror Reactor. Ths is the first Tandem Mirror Reactor model to couple, in detail, the highly linked physics, magnetics, and neutronic analysis into a single code. This report describes the code architecture, provides a summary description of the modules comprising the code, and includes an example execution of the Tandem Mirror Reactor Systems Code. Results from this code for two sensitivity studies are also included. These studies are: (1) to determine the impact of center cell plasma radius, length, and ion temperature on reactor cost and performance at constant fusion power; and (2) to determine the impact of reactor power level on cost

13. Black Mirror. Distopie del vedere

Daniela Panosetti

2012-02-01

Full Text Available The essay discusses the second episode of Black Mirror (2011, the miniseries produced by Charlie Brooker for British TV, by analysing the complex relationship between the special regime of visibility that regulates the possible world and the deeply rooted system of values adopted or rejected by those concerned. The author endeavours to demonstrate how, in the evident attempt at contemporary reinterpretation of certain recurring topoi in so-called dystopian narrations (especially of their modern archetype, George Orwell's novel Nineteen Eighty-Four, the text stages an original representation, albeit set in the future, of today's media scenario, problematising the different issues within a single, tendentially dysphoric projective dimension: declining phenomena (the screen vision as up-down "administration", emerging phenomena (augmented reality and dominating phenomena (the prevalent "virtual sociality" in all web 2.0 expressions. A series of reversals and shifting of the dystopian topoi recalled for another reason emerges from the global sense effect produced by speech (specifically in the final scenes: the issue switches from an obsessive de-individualization to an excess of personalization, from the tyranny of being / having to be seen/ to that of seeing / having to see, from the search for reality and truth to that of authenticity, this latter presented as principal isotopy and true epistemic architrave of the entire narration.

14. Europe in the Balkan mirror

Milutinović Zoran

2015-01-01

Full Text Available The article discusses the three dominant, Europe-wide, constructions of Europe in the nineteenth and twentieth centuries, and claims that all three found their proponents in the Balkans in the same period, while no specifically Balkan construction of Europe can be identified. The discourses which constructed Europe were transnational, and every search for national discourses must recognize that they are always fractured and contradictory, composed of various elements originating in Europe-wide discourses on Europe. Throughout this period the dominant discourse of Europe was shaped by the discourse of modernity and modernization, not only in Europe but in other parts of the globe as well. Several commentators have already noted that the current challenge of the interwar construction of Europe - peace, prosperity, democracy and human rights - mirrors the crisis of Yugoslavia, and many examples point to the unsustainability of this construction at the beginning of the twenty-first century. Gadamer’s hermeneutics offers a valuable lesson in humility and defines the oft-repeated phrase of “belonging together” as listening to the other in the belief that the other may be right, which should be taken as a starting point for any future construction of Europe.

15. [Infantile autism and mirror neurons].

Cornelio-Nieto, J O

2009-02-27

Infantile autism is a disorder that is characterised by alterations affecting reciprocal social interactions, abnormal verbal and non-verbal communication, poor imaginative activity and a restricted repertoire of activities and interests. The causes of autism remain unknown, but there are a number of different approaches that attempt to explain the neurobiological causes of the syndrome. A recent theory that has been considered is that of a dysfunction in the mirror neuron system (MNS). The MNS is a neuronal complex, originally described in monkeys and also found in humans, that is related with our movements and which offers specific responses to the movements and intended movements of other subjects. This system is believed to underlie processes of imitation and our capacity to learn by imitation. It is also thought to play a role in language acquisition, in expressing the emotions, in understanding what is happening to others and in empathy. Because these functions are altered in children with autism, it has been suggested that there is some dysfunction present in the MNS of those with autism. Dysfunction of the MNS could account for the symptoms that are observed in children with autism.

16. Fabrication Process Development for Light Deformable Mirrors

National Aeronautics and Space Administration — The project objective is to develop robust, reproductibble fabrication processes to realize functional deformable membrane mirrors (DM) for a space mission in which...

17. The mirror mechanism in the parietal lobe.

Rizzolatti, Giacomo; Rozzi, Stefano

2018-01-01

The mirror mechanism is a basic mechanism that transforms sensory representations of others' actions into motor representations of the same actions in the brain of the observer. The mirror mechanism plays an important role in understanding actions of others. In the present chapter we discuss first the basic organization of the posterior parietal lobe in the monkey, stressing that it is best characterized as a motor scaffold, on the top of which sensory information is organized. We then describe the location of the mirror mechanism in the posterior parietal cortex of the monkey, and its functional role in areas PFG, and anterior, ventral, and lateral intraparietal areas. We will then present evidence that a similar functional organization is present in humans. We will conclude by discussing the role of the mirror mechanism in the recognition of action performed with tools. Copyright © 2018 Elsevier B.V. All rights reserved.

18. The mirror mechanism: recent findings and perspectives

Rizzolatti, Giacomo; Fogassi, Leonardo

2014-01-01

Mirror neurons are a specific type of visuomotor neuron that discharge both when a monkey executes a motor act and when it observes a similar motor act performed by another individual. In this article, we review first the basic properties of these neurons. We then describe visual features recently investigated which indicate that, besides encoding the goal of motor acts, mirror neurons are modulated by location in space of the observed motor acts, by the perspective from which the others’ motor acts are seen, and by the value associated with the object on which others’ motor acts are performed. In the last part of this article, we discuss the role of the mirror mechanism in planning actions and in understanding the intention underlying the others’ motor acts. We also review some human studies suggesting that motor intention in humans may rely, as in the monkey, on the mirror mechanism. PMID:24778385

19. From quantum entanglement to mirror neuron

Zak, Michail

2007-01-01

It is proposed that two fundamental phenomena: quantum entanglement in physics, and mirror neuron in biopsychology, can be described by using the same mathematical formalism, namely, the feedback from the Liouville equation to equation of motion

20. Electrostatic axisymmetric mirror with removable spherical aberration

Birmuzaev, S.B.; Serikbaeva, G.S.; Hizirova, M.A.

1999-01-01

The electrostatic axisymmetric mirror, assembled from three coaxial cylinders with an equal diameter d and under the potential v1, v2 and v3, was computed. The proportions of geometrical and electric parameters of the mirror, with which the spherical 3-order aberration may be eliminated, were determined. The computation outcomes of the case, when the focal power of the mirror is enough large and the object plane in the focus is out of its field, are presented (Fig. 1 - potentials proportion that makes elimination of the spherical aberration possible; Fig. 2 - the focus coordinates when the spherical aberration is eliminated). The geometrical values are presented by d, and the electric ones are presented by v1. The figures on the curves present a length of the second (middle) electrode. The zero point is located in the middle of the gap between the first and second electrodes The investigated mirror may be used as a lens for the transmission electron microscope

1. Mirror Advanced Reactor Study interim design report

1983-04-01

The status of the design of a tenth-of-a-kind commercial tandem-mirror fusion reactor is described at the midpoint of a two-year study. When completed, the design is to serve as a strategic goal for the mirror fusion program. The main objectives of the Mirror Advanced Reactor Study (MARS) are: (1) to design an attractive tandem-mirror fusion reactor producing electricity and synfuels (in alternate versions), (2) to identify key development and technology needs, and (3) to exploit the potential of fusion for safety, low activation, and simple disposal of radioactive waste. In the first year we have emphasized physics and engineering of the central cell and physics of the end cell. Design optimization and trade studies are continuing, and we expect additional modifications in the end cells to further improve the performance of the final design.

2. Cosmological Constraints on Mirror Matter Parameters

Wallemacq, Quentin; Ciarcelluti, Paolo

2014-01-01

Up-to-date estimates of the cosmological parameters are presented as a result of numerical simulations of cosmic microwave background and large scale structure, considering a flat Universe in which the dark matter is made entirely or partly of mirror matter, and the primordial perturbations are scalar adiabatic and in linear regime. A statistical analysis using the Markov Chain Monte Carlo method allows to obtain constraints of the cosmological parameters. As a result, we show that a Universe with pure mirror dark matter is statistically equivalent to the case of an admixture with cold dark matter. The upper limits for the ratio of the temperatures of ordinary and mirror sectors are around 0.3 for both the cosmological models, which show the presence of a dominant fraction of mirror matter, 0.06≲Ω_m_i_r_r_o_rh"2≲0.12.

3. Four-Mirror Freeform Reflective Imaging Systems

National Aeronautics and Space Administration — Central Objectives: The research involves a revelation of the solution space for revolutionary families of four-mirror freeform reflective imaging systems. A...

4. Silicon Wafer X-ray Mirror Project

National Aeronautics and Space Administration — We propose to undertake the initial development of a Kirkpatrick-Baez (K-B) type X-ray mirror using the relatively recent availability of high quality, inexpensive,...

5. Distortion compensation in interferometric testing of mirrors

Robinson, Brian M.; Reardon, Patrick J.

2009-01-01

We present a method to compensate for the imaging distortion encountered in interferometric testing of mirrors, which is introduced by interferometer optics as well as from geometric projection errors. Our method involves placing a mask, imprinted with a regular square grid, over the mirror and finding a transformation that relates the grid coordinates to coordinates in the base plane of the parent surface. This method can be used on finished mirrors since no fiducials have to be applied to the surfaces. A critical step in the process requires that the grid coordinates be projected onto the mirror base plane before the regression is performed. We apply the method successfully during a center-of-curvature null test of an F/2 off-axis paraboloid

6. Mirror Fusion Test Facility magnet system

VanSant, J.H.; Kozman, T.A.; Bulmer, R.H.; Ng, D.S.

1981-01-01

In 1979, R.H. Bulmer of Lawrence Livermore National Laboratory (LLNL) discussed a proposed tandem-mirror magnet system for the Mirror Fusion Test Facility (MFTF) at the 8th symposium on Engineering Problems in Fusion Research. Since then, Congress has voted funds for expanding LLNL's MFTF to a tandem-mirror facility (designated MFTF-B). The new facility, scheduled for completion by 1985, will seek to achieve two goals: (1) Energy break-even capability (Q or the ratio of fusion energy to plasma heating energy = 1) of mirror fusion, (2) Engineering feasibility of reactor-scale machines. Briefly stated, 22 superconducting magnets contained in a 11-m-diam by 65-m-long vacuum vessel will confine a fusion plasma fueled by 80 axial streaming-plasma guns and over 40 radial neutral beams. We have already completed a preliminary design of this magnet system

7. Mirror Advanced Reactor Study interim design report

1983-04-01

The status of the design of a tenth-of-a-kind commercial tandem-mirror fusion reactor is described at the midpoint of a two-year study. When completed, the design is to serve as a strategic goal for the mirror fusion program. The main objectives of the Mirror Advanced Reactor Study (MARS) are: (1) to design an attractive tandem-mirror fusion reactor producing electricity and synfuels (in alternate versions), (2) to identify key development and technology needs, and (3) to exploit the potential of fusion for safety, low activation, and simple disposal of radioactive waste. In the first year we have emphasized physics and engineering of the central cell and physics of the end cell. Design optimization and trade studies are continuing, and we expect additional modifications in the end cells to further improve the performance of the final design

8. Silicon Wafer X-ray Mirror

National Aeronautics and Space Administration — We propose to undertake the initial development of a Kirkpatrick-Baez (K-B) type X-ray mirror using the relatively recent availability of high quality, inexpensive,...

9. Reflections on mirror neurons and speech perception

Lotto, Andrew J.; Hickok, Gregory S.; Holt, Lori L.

2010-01-01

The discovery of mirror neurons, a class of neurons that respond when a monkey performs an action and also when the monkey observes others producing the same action, has promoted a renaissance for the Motor Theory (MT) of speech perception. This is because mirror neurons seem to accomplish the same kind of one to one mapping between perception and action that MT theorizes to be the basis of human speech communication. However, this seeming correspondence is superficial, and there are theoretical and empirical reasons to temper enthusiasm about the explanatory role mirror neurons might have for speech perception. In fact, rather than providing support for MT, mirror neurons are actually inconsistent with the central tenets of MT. PMID:19223222

10. Auditory-vocal mirroring in songbirds.

Mooney, Richard

2014-01-01

Mirror neurons are theorized to serve as a neural substrate for spoken language in humans, but the existence and functions of auditory-vocal mirror neurons in the human brain remain largely matters of speculation. Songbirds resemble humans in their capacity for vocal learning and depend on their learned songs to facilitate courtship and individual recognition. Recent neurophysiological studies have detected putative auditory-vocal mirror neurons in a sensorimotor region of the songbird's brain that plays an important role in expressive and receptive aspects of vocal communication. This review discusses the auditory and motor-related properties of these cells, considers their potential role on song learning and communication in relation to classical studies of birdsong, and points to the circuit and developmental mechanisms that may give rise to auditory-vocal mirroring in the songbird's brain.

11. Auditory–vocal mirroring in songbirds

Mooney, Richard

2014-01-01

Mirror neurons are theorized to serve as a neural substrate for spoken language in humans, but the existence and functions of auditory–vocal mirror neurons in the human brain remain largely matters of speculation. Songbirds resemble humans in their capacity for vocal learning and depend on their learned songs to facilitate courtship and individual recognition. Recent neurophysiological studies have detected putative auditory–vocal mirror neurons in a sensorimotor region of the songbird's brain that plays an important role in expressive and receptive aspects of vocal communication. This review discusses the auditory and motor-related properties of these cells, considers their potential role on song learning and communication in relation to classical studies of birdsong, and points to the circuit and developmental mechanisms that may give rise to auditory–vocal mirroring in the songbird's brain. PMID:24778375

12. Additive Manufacturing of Telescope Mirrors, Phase I

National Aeronautics and Space Administration — This Phase 1 SBIR is to demonstrate feasibility of using selective laser melting (SLM) to produce a 3-meter symmetrical radius of curvature (ROC) isogrid mirror...

13. Coating considerations for mirrors of CPV devices

Schmauder, Torsten; Sauer, Peter; Ickes, Gerd

2014-01-01

One of the different optical concepts for concentrator devices is to place a focussing primary mirror behind a transparent front plate. In addition (also in case of Fresnel-diffractive main optics), further 'secondary' reflectors may be used further along the beam path. Such mirrors are usually implemented as coating stacks of a highly reflective metal - usually silver - and protective layers. The protective layers are preferably designed as reflection enhancing interference stack. The design of such protective layer stacks yields two difficulties, which are addressed in this paper: (a) vacuum coating of three-dimensional parts will result in a thickness distribution and the optical design of the stack should thus be tolerant to layer thickness variations, and (b) different places of the mirror will have different angle-of-incidence of the sunlight under operating conditions. As result, the layer stack has a different design at different places of the mirror

14. On the convex closed set-valued operators in Banach spaces and their applications in control problems

Vu Ngoc Phat; Jong Yeoul Park

1995-10-01

The paper studies a class of set-values operators with emphasis on properties of their adjoints and existence of eigenvalues and eigenvectors of infinite-dimensional convex closed set-valued operators. Sufficient conditions for existence of eigenvalues and eigenvectors of set-valued convex closed operators are derived. These conditions specify possible features of control problems. The results are applied to some constrained control problems of infinite-dimensional systems described by discrete-time inclusions whose right-hand-sides are convex closed set- valued functions. (author). 8 refs

15. Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization.

Craft, David

2010-10-01

A discrete set of points and their convex combinations can serve as a sparse representation of the Pareto surface in multiple objective convex optimization. We develop a method to evaluate the quality of such a representation, and show by example that in multiple objective radiotherapy planning, the number of Pareto optimal solutions needed to represent Pareto surfaces of up to five dimensions grows at most linearly with the number of objectives. The method described is also applicable to the representation of convex sets. Copyright © 2009 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

16. Nonlinear mirror mode dynamics: Simulations and modeling

Califano, F.; Hellinger, Petr; Kuznetsov, E.; Passot, T.; Sulem, P. L.; Trávníček, Pavel

2008-01-01

Roč. 113, - (2008), A08219/1-A08219/20 ISSN 0148-0227 R&D Projects: GA AV ČR IAA300420702; GA AV ČR IAA300420602 Grant - others:PECS(CZ) 98024 Institutional research plan: CEZ:AV0Z30420517 Keywords : mirror instability * nonlinear evolution * numerical simulations * magnetic holes * mirror structures * kinetic plasma instabilities Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 3.147, year: 2008

17. Quantum locking of mirrors in interferometers.

Courty, Jean-Michel; Heidmann, Antoine; Pinard, Michel

2003-02-28

We show that quantum noise in very sensitive interferometric measurements such as gravitational-wave detectors can be drastically modified by quantum feedback. We present a new scheme based on active control to lock the motion of a mirror to a reference mirror at the quantum level. This simple technique allows one to reduce quantum effects of radiation pressure and to greatly enhance the sensitivity of the detection.

18. Mirror Writing and a Dissociative Identity Disorder

Le, Catherine; Smith, Joyce; Cohen, Lewis

2009-01-01

Individuals with dissociative identity disorder (DID) have been known to show varied skills and talents as they change from one dissociative state to another. For example, case reports have described people who have changed their handedness or have spoken foreign languages during their dissociative states. During an interview with a patient with DID, a surprising talent emerged when she wrote a sentence for the Folstein Mini-Mental State Exam—mirror writing. It is not known whether her mirror...

19. Fabrication of off-axis parabolic mirrors

Bezik, M.J.; Gerth, H.L.; Sladky, R.E.; Washington, C.A.

1978-08-01

The report describes the fabrication process, including metal preparation, copper electroplating, single-crystal-diamond turning, optical inspection, and polishing, used to manufacture the focusing mirrors for the 10-kJ laser fusion experiment being conducted by the Los Alamos Scientific Laboratory. Fabrication of these mirrors by the techniques described resulted in diffraction-limited optics at a 10.6 μm wavelength

20. On horizonless temperature with an accelerating mirror

Good, Michael R.R.; Yelshibekov, Khalykbek [Department of Physics, School of Science and Technology, Nazarbayev University,53 Kabanbay Batyr Ave., Astana, 010000 Republic of (Kazakhstan); Ong, Yen Chin [Center for Astronomy and Astrophysics, Department of Physics and Astronomy,Shanghai Jiao Tong University, Shanghai, 200240 (China); Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, Stockholm, SE-106 91 (Sweden)

2017-03-03

A new solution of a unitary moving mirror is found to produce finite energy and emit thermal radiation despite the absence of an acceleration horizon. In the limit that the mirror approaches the speed of light, the model corresponds to a black hole formed from the collapse of a null shell. For speeds less than light, the black hole correspondence, if it exists, is that of a remnant.