Showing papers on "Operator (computer programming) published in 1999"

Implicit fairing of irregular meshes using diffusion and curvature flow

Abstract: In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high-fidelity computer graphics objects using imperfectly-measured data from the real world. Our approach contains three novel features: an implicit integration method to achieve efficiency, stability, and large time-steps; a scale-dependent Laplacian operator to improve the diffusion process; and finally, a robust curvature flow operator that achieves a smoothing of the shape itself, distinct from any parameterization. Additional features of the algorithm include automatic exact volume preservation, and hard and soft constraints on the positions of the points in the mesh. We compare our method to previous operators and related algorithms, and prove that our curvature and Laplacian operators have several mathematically-desirable qualities that improve the appearance of the resulting surface. In consequence, the user can easily select the appropriate operator according to the desired type of fairing. Finally, we provide a series of examples to graphically and numerically demonstrate the quality of our results.

Induced ordered weighted averaging operators

Abstract: We briefly describe the Ordered Weighted Averaging (OWA) operator and discuss a methodology for learning the associated weighting vector from observational data. We then introduce a more general type of OWA operator called the Induced Ordered Weighted Averaging (IOWA) Operator. These operators take as their argument pairs, called OWA pairs, in which one component is used to induce an ordering over the second components which are then aggregated. A number of different aggregation situations have been shown to be representable in this framework. We then show how this tool can be used to represent different types of aggregation models.

Coherence-Enhancing Diffusion Filtering

Abstract: The completion of interrupted lines or the enhancement of flow-like structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so-called interest operator (second-moment matrix, structure tensor). An m-dimensional formulation of this method is analysed with respect to its well-posedness and scale-space properties. An efficient scheme is presented which uses a stabilization by a semi-implicit additive operator splitting (AOS), and the scale-space behaviour of this method is illustrated by applying it to both 2-D and 3-D images.

D-branes and Deformation Quantization

Abstract: In this note we explain how world-volume geometries of D-branes can be reconstructed within the microscopic framework where D-branes are described through boundary conformal field theory. We extract the (non-commutative) world-volume algebras from the operator product expansions of open string vertex operators. For branes in a flat background with constant non-vanishing B-field, the operator products are computed perturbatively to all orders in the field strength. The resulting series coincides with Kontsevich's presentation of the Moyal product. After extending these considerations to fermionic fields we conclude with some remarks on the generalization of our approach to curved backgrounds.

On the Approximation of Complicated Dynamical Behavior

Abstract: We present efficient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow us to approximate Sinai--Ruelle--Bowen (SRB)-measures as well as (almost) cyclic behavior of a dynamical system. The methods are based on an appropriate discretization of the Frobenius--Perron operator, and two essentially different mathematical concepts are used: our idea is to combine classical convergence results for finite dimensional approximations of compact operators with results from ergodic theory concerning the approximation of SRB-measures by invariant measures of stochastically perturbed systems. The efficiency of the methods is illustrated by several numerical examples.

A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications

Abstract: In this paper we present a comprehensive account of a manifestly size-consistent coupled cluster formalism for a specific state, which is based on a reference function composed of determinants spanning a complete active space (CAS). The method treats all the reference determinants on the same footing and is hence expected to provide uniform description over a wide range of molecular geometry. The combining coefficients are determined by diagonalizing an effective operator in the CAS and are thus completely flexible, not constrained to preassigned values. A separate exponential-type excitation operator is invoked to induce excitations to all the virtual functions from each reference determinant. The linear dependence inherent in this choice of cluster operators is eliminated by invoking suitable sufficiency conditions, which in a transparent manner leads to manifest size extensivity. The use of a CAS also guarantees size consistency. We also discuss the relation of our method with the extant state-specific...

Non-Markovian evolution of the density operator in the presence of strong laser fields

Abstract: We present an accurate, efficient, and flexible method for propagating spatially distributed density matrices in anharmonic potentials interacting with solvent and strong fields. The method is based on the Nakajima–Zwanzig projection operator formalism with a correlated reference state of the bath that takes memory effects and initial/final correlations to second order in the system–bath interaction into account. A key feature of the method proposed is a special parametrization of the bath spectral density leading to a set of coupled equations for primary and N auxiliary density matrices. These coupled master equations can be solved numerically by representing the density operator in eigenrepresentation or on a coordinate space grid, using the Fourier method to calculate the action of the kinetic and potential energy operators, and a combination of split operator and Cayley implicit method to compute the time evolution. The key advantages of the method are: (1) The system potential may consist of any numb...

Sturm-liouville operators with singular potentials

Abstract: This paper deals with Sturm-Liouville operators generated on a finite interval and on the whole axis by the differential expressionl(y)=−y " +q(x)y, whereq(x) is a distribution of first order, such that $$\smallint q(\varepsilon )d\varepsilon \in L_{{\text{2,loc}}} $$ . The minimal and maximal operators corresponding to potentials of this type on a finite interval are constructed. All self-adjoint extensions of the minimal operator are described and the asymptotics of the eigenvalues of these extensions is found. It is proved that the constructed operator coincides with the norm resolvent limit of the Sturm-Liouville operators generated by smooth potentialsq n , provided that the condition $$\smallint |\smallint (q_n - q)d\varepsilon |^{\text{2}} dx \to 0$$ holds. The convergence of the spectra of these operators to the spectrum of the limit operator is also proved. Similar results are obtained in the case of the whole axis.

Positivity of dunkl's intertwining operator

Abstract: For a finite reflection group on $\b R^N,$ the associated Dunkl operators are parametrized first-order differential-difference operators which generalize the usual partial derivatives They generate a commutative algebra which is - under weak assumptions - intertwined with the algebra of partial differential operators by a unique linear and homogeneous isomorphism on polynomials In this paper it is shown that for non-negative parameter values, this intertwining operator is positivity-preserving on polynomials and allows a positive integral representation on certain algebras of analytic functions This result in particular implies that the generalized exponential kernel of the Dunkl transform is positive-definite

Concatenating decoherence-free subspaces with quantum error correcting codes

Abstract: An operator sum representation is derived for a decoherence-free subspace (DFS) and used to (i) show that DFS’s are the class of quantum error correcting codes (QECC’s) with fixed, unitary recovery operators and (ii) find explicit representations for the Kraus operators of collective decoherence. We demonstrate how this can be used to construct a concatenated DFS-QECC code which protects against collective decoherence perturbed by independent decoherence. The code yields an error threshold which depends only on the perturbing independent decoherence rate. [S0031-9007(99)09301-1]

Landscapes, operators and heuristic search

Abstract: Heuristic search methods have been increasingly applied to combinatorial optimizationproblems. While a specific problem defines a unique search space, different “landscapes”are created by the different heuristic search operators used to search it. In this paper, asimple example will be used to illustrate the fact that the landscape structure changes withthe operator; indeed, it often depends even on the way the operators are applied. Recentattention has focused on trying to better understand the nature of these “landscapes”. Recentwork by Boese et al. [2] has shown that instances of the TSP are often characterised by a“big valley” structure in the case of a 2‐opt exchange operator, and a particular distancemetric. In this paper, their work is developed by investigating the question of how landscapeschange under different search operators in the case of the n/m/P/Cmax flowshop problem.Six operators and four distance metrics are defined, and the resulting landscapes examined.The work is further extended by proposing a statistical randomisation test to provide anumerical assessment of the landscape. Other conclusions relate to the existence of ultra‐metricity,and to the usefulness or otherwise of hybrid neighbourhood operators.

Magnetically-controllable, semi-active haptic interface system and apparatus

Abstract: A haptic interface system or force feedback system having a magnetically-controllable device that provides resistance forces opposing movement. The magnetically-controllable device is adapted for use with a force feedback computer system to provide force feedback sensations to the system's operator. The magnetically-controllable device contains a magnetically-controllable medium beneficially providing variable resistance forces in proportion to the strength of an applied magnetic field. The system further comprises a computer system that runs an interactive program or event, a video display display, and a haptic interface device (e.g. joystick, steering wheel) in operable contact with an operator for controlling inputs and responses to the interactive program. Based on the received inputs and on processing the interactive program, the computer system provides a variable output signal, corresponding to a feedback force, to control the magnetically-controllable device for providing dissipative resistance forces to oppose the movement of the haptic interface device and to provide the operator with a force feedback sensation.

Inexact implicit methods for monotone general variational inequalities

Abstract: Solving a variational inequality problem is equivalent to finding a solution of a system of nonsmooth equations Recently, we proposed an implicit method, which solves monotone variational inequality problem via solving a series of systems of nonlinear smooth (whenever the operator is smooth) equations It can exploit the facilities of the classical Newton–like methods for smooth equations In this paper, we extend the method to solve a class of general variational inequality problems $$ Q\big(u^*\big) \in \Omega, \qquad \bigl( v - Q\big(u^*\big) \bigr)^T F\big(u^*\big) \ge 0, \qquad \forall v\in \Omega $$ Moreover, we improve the implicit method to allow inexact solutions of the systems of nonlinear equations at each iteration The method is shown to preserve the same convergence properties as the original implicit method

Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques [for EM field analysis]

Abstract: In this paper, some structures which underlie the numerical treatment of second-order boundary value problems are studied using magnetostatics as an example. The authors show that the construction of a discrete Hodge is a central problem. In this light, they interpret finite element techniques as a realization of the discrete Hodge operator in the Whitney complex. This enables one to view the Galerkin method as a way to set up circuit equations, the metric of space being encoded in the values of branch impedances.

The field theoretic renormalization group in fully developed turbulence

Abstract: 1 The Renormalization Group Method in the Stochastic Model of Isotropic Turbulence 2 Composite Operators, Operator Expansions, and the First Kolmogorov Hypothesis 3 Multicharge Problems in the Stochastic Theory of Turbulence

Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems

Abstract: Numerical experiments are presented whereby the effect of reorderings on the convergence of preconditioned Krylov subspace methods for the solution of nonsymmetric linear systems is shown. The preconditioners used in this study are different variants of incomplete factorizations. It is shown that certain reorderings for direct methods, such as reverse Cuthill--McKee, can be very beneficial. The benefit can be seen in the reduction of the number of iterations and also in measuring the deviation of the preconditioned operator from the identity.

Scattering in anti-de Sitter space and operator product expansion

Abstract: We develop a formalism to evaluate generic scalar exchange diagrams in AdS_{d+1} relevant for the calculation of four-point functions in AdS/CFT correspondence. The result may be written as an infinite power series of functions of cross-ratios. Logarithmic singularities appear in all orders whenever the dimensions of involved operators satisfy certain relations. We show that the AdS_{d+1} amplitude can be written in a form recognisable as the conformal partial wave expansion of a four-point function in CFT_{d} and identify the spectrum of intermediate operators. We find that, in addition to the contribution of the scalar operator associated with the exchanged field in the AdS diagram, there are also contributions of some other operators which may possibly be identified with two-particle bound states in AdS. The CFT interpretation also provides a useful way to ``regularize'' the logarithms appearing in AdS amplitude.

Explaining Differences in Multidimensional Aggregates

Abstract: Our goal is to enhance multidimensional database systems with advanced mining primitives. Current Online Analytical Processing (OLAP) products provide a minimal set of basic aggregate operators like sum and average and a set of basic navigational operators like drill-downs and roll-ups. These operators have to be driven entirely by the analyst’s intuition. Such ad hoc exploration gets tedious and error-prone as data dimensionality and size increases. In earlier work we presented one such advanced primitive where we premined OLAP data for exceptions, summarized the exceptions at appropriate levels, and used them to lead the analyst to the interesting regions. In this paper we present a second enhancement: a single operator that lets the analyst get summarized reasons for drops or increases observed at an aggregated level. This eliminates the need to manually drill-down for such reasons. We develop an information theoretic formulation for expressing the reasons that is compact and easy to interpret. We design a dynamic programming algorithm that requires only one pass of the data improving significantly over our initial greedy algorithm that required multiple passes. In addition, the algorithm uses a small amount of

On the strong maximum principle for fully nonlinear degenerate elliptic equations

Abstract: We prove a Strong Maximum Principle for semicontinuous viscosity subsolutions or supersolutions of fully nonlinear degenerate elliptic PDE's, which complements the results of [17]. Our assumptions and conclusions are different from those in [17], in particular our maximum principle implies the nonexistence of a dead core. We test the assumptions on several examples involving the p-Laplacian and the minimal surface operator, and they turn out to be sharp in all cases where the existence of a dead core is known. We can also cover equations that are singular for p = 0$ and very degenerate operators such as the $\infty $ -Laplacian and some first order Hamilton-Jacobi operators.

Density Operators for Fermions

Abstract: The mathematical methods that have been used to analyze the statistical properties of boson fields, and in particular the coherence of photons in quantum optics, have their counterparts for Fermi fields. The coherent states, the displacement operators, the P representation, and the other operator expansions all possess surprisingly close fermionic analogues. These methods for describing the statistical properties of fermions are based upon a practical calculus of anticommuting variables. They are used to calculate correlation functions and counting distributions for general systems of fermions.

Conformal Field Theory Techniques in Random Matrix models

Abstract: In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an explicit operator construction of the corresponding collective field theory in terms of a bosonic field on a hyperelliptic Riemann surface, with special operators associated with the branch points. The quasiclassical expressions for the spectral kernel and the joint eigenvalue probabilities are then easily obtained as correlation functions of current, fermionic and twist operators. The result for the spectral kernel is valid both in macroscopic and microscopic scales. At the end we briefly consider generalizations in different directions.

L2-boundedness of the Cauchy integral operator for continuous measures

Abstract: 1. Introduction. Let µ be a continuous (i.e., without atoms) positive Radon measure on the complex plane. The truncated Cauchy integral of a compactly supported function f in L p (µ), 1 ≤ p ≤ +∞, is defined by Ꮿ ε f (z) = |ξ −z|>ε f (ξ) ξ − z dµ(ξ), z ∈ C, ε > 0. In this paper, we consider the problem of describing in geometric terms those measures µ for which |Ꮿ ε f | 2 dµ ≤ C |f | 2 dµ, (1) for all (compactly supported) functions f ∈ L 2 (µ) and some constant C independent of ε > 0. If (1) holds, then we say, following David and Semmes [DS2, pp. 7–8], that the Cauchy integral is bounded on L 2 (µ). A special instance to which classical methods apply occurs when µ satisfies the doubling condition µ(2) ≤ Cµ((), for all discs centered at some point of spt(µ), where 2 is the disc concentric with of double radius. In this case, standard Calderón-Zygmund theory shows that (1) is equivalent to Ꮿ * f 2 dµ ≤ C |f | 2 dµ, (2) where Ꮿ * f (z) = sup ε>0 |Ꮿ ε f (z)|. If, moreover, one can find a dense subset of L 2 (µ) for which Ꮿf (z) = lim ε→0 Ꮿ ε f (z) (3) 269 270 XAVIER TOLSA exists a.e. (µ) (i.e., almost everywhere with respect to µ), then (2) implies the a.e. (µ) existence of (3), for any f ∈ L 2 (µ), and |Ꮿf | 2 dµ ≤ C |f | 2 dµ, for any function f ∈ L 2 (µ) and some constant C. For a general µ, we do not know if the limit in (3) exists for f ∈ L 2 (µ) and almost all (µ) z ∈ C. This is why we emphasize the role of the truncated operators Ꮿ ε. Proving (1) for particular choices of µ has been a relevant theme in classical analysis in the last thirty years. Calderón's paper [Ca] is devoted to the proof of (1) when µ is the arc length on a Lipschitz graph with small Lipschitz constant. The result for a general Lipschitz graph was obtained by Coifman, McIntosh, and Meyer in 1982 in the celebrated paper [CMM]. The rectifiable curves , for which (1) holds for the arc length measure µ on …

A Volterra Type Operator on Spaces of Analytic Functions

Abstract: The main results are conditions on g such that the Volterra type operator Jg(f)(z) = ∫ z

The Spectrum of coupled random matrices

Abstract: The study of the spectrum of coupled random matrices has received rather little attention. To the best of our knowledge, coupled random matrices have been studied, to some extent, by Mehta. In this work, we explain how the integrable technology can be brought to bear to gain insight into the nature of the distribution of the spectrum of coupled Hermitean random matrices and the equations the associated probabilities satisfy. In particular, the two-Toda lattice, its algebra of symmetries and its vertex operators will play a prominent role in this interaction. Namely, the method is to introduce time parameters, in an artificial way, and to dress up a certain matrix integral with a vertex integral operator, for which we find Virasoro-like differential equations. These methods lead to very simple nonlinear third-order partial differential equations for the joint statistics of the spectra of two coupled Gaussian random matrices. Comment: 56 pages, published version, abstract added in migration

Categories of Operator Modules: Morita Equivalence and Projective Modules

Abstract: Introduction Preliminaries Morita contexts Duals and projective modules Representations of the linking algebra $C^*$-algebras and Morita contexts Stable isomorphisms Examples Appendix-More recent developments Bibliography

Movable barrier operator

Abstract: A movable barrier operator having improved safety and energy efficiency features automatically detects line voltage frequency and uses that information to set a worklight shut-off time. The operator automatically detects the type of door (single panel or segmented) and uses that information to set a maximum speed of door travel. The operator moves the door with a linearly variable speed from start of travel to stop for smooth and quiet performance. The operator provides for full door closure by driving the door into the floor when the DOWN limit is reached and no auto-reverse condition has been detected. The operator provides for user selection of a minimum stop speed for easy starting and stopping of sticky or binding doors.