Showing papers on "Operator (computer programming) published in 1995"

Hilbert c*-modules-a toolkit for operator algebraists

Abstract: Hilbert C*-modules are objects like Hilbert spaces, except that the inner product, instead of being complex valued, takes its values in a C*-algebra. The theory of these modules, together with their bounded and unbounded operators, is not only rich and attractive in its own right but forms an infrastructure for some of the most important research topics in operator algebras. This book is based on a series of lectures given by Professor Lance at a summer school at the University of Trondheim. It provides, for the first time, a clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material. It will be welcomed as an excellent resource for all graduate students and researchers working in operator algebras.

Flat zones filtering, connected operators, and filters by reconstruction

Abstract: This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described. >

Context-free attentional operators: the generalized symmetry transform

Abstract: Active vision systems, and especially foveated vision systems, depend on efficient attentional mechanisms. We propose that machine visual attention should consist of both high-level, context-dependent components, and low-level, context free components. As a basis for the context-free component, we present an attention operator based on the intuitive notion of symmetry, which generalized many of the existing methods of detecting regions of interest. It is a low-level operator that can be applied successfully without a priori knowledge of the world. The resultingsymmetry edge map can be applied in various low, intermediate-and high- level tasks, such as extraction of interest points, grouping, and object recognition. In particular, we have implemented an algorithm that locates interest points in real time, and can be incorporated in active and purposive vision systems. The results agree with some psychophysical findings concerning symmetry as well as evidence concerning selection of fixation points. We demonstrate the performance of the transform on natural, cluttered images.

Frames and Stable Bases for Shift-Invariant Subspaces of L2(IRd)

Abstract: Let X be a countable fundamental set in a Hilbert space H, and let T be the operator Whenever T is well-defined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is injective is a stable basis (also known as a Riesz basis). This paper considers the above three properties for subspaces H of L2(ℝd), and for sets X of the form with Φ either a singleton, a finite set, or, more generally, a countable set. The analysis is performed on the Fourier domain, where the two operators TT* and T* T are decomposed into a collection of simpler "fiber" operators. The main theme of the entire analysis is the characterization of each of the above three properties in terms of the analogous property of these simpler operators.

The choice of a zeroth-order Hamiltonian for second-order perturbation theory with a complete active space self-consistent-field reference function

Abstract: The choice of a zeroth‐order Hamiltonian, H0, for second‐order perturbation theory with a complete active space self‐consistent‐field (CASSCF) reference function is discussed in detail, in the context of the inclusion of the denominator shifts found to be important in recent single‐reference high‐spin open‐shell theories and the formulation of a computationally efficient method. Using projection operators and second quantization algebra, an operator is constructed which consists of the complete active space Hamiltonian in the active space and the Mo/ller–Plesset zeroth‐order Hamiltonian in the inactive and secondary spaces. This operator, designated CAS/A, has the reference as an eigenfunction without the necessity of projection, it naturally incorporates denominator shifts which appear in terms of active space Fock operators, it does not give rise to intruder states, and it costs little more than other CASSCF perturbation theories. The incorporation of the complete active space Hamiltonian introduces additional active space two‐particle terms into the zeroth‐order energies over the Fock operators, which may be regarded as an inconsistency. To achieve an approximate consistency, they may be removed or supplemented with other particle–particle and hole–hole terms. The results of test calculations indicate that supplementation is not advisable and that removal has only a modest effect. The test calculations are compared with other results and experiment, and support the effectiveness of the proposed CAS/A H0.

Quantitative analysis of floating point arithmetic on FPGA based custom computing machines

Abstract: Many algorithms rely on floating point arithmetic for the dynamic range of representations and require millions of calculations per second. Such computationally intensive algorithms are candidates for acceleration using custom computing machines (CCMs) being tailored for the application. Unfortunately, floating point operators require excessive area (or time) for conventional implementations. Instead, custom formats, derived for individual applications, are feasible on CCMs, and can be implemented on a fraction of a single FPGA. Using higher-level languages, like VHDL, facilitates the development of custom operators without significantly impacting operator performance or area. Properties, including area consumption and speed of working arithmetic operator units used in real-time applications, are discussed.

Mirror manifolds in higher dimension

Abstract: We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We isolate certain simplifying features present only in dimension three, and supply alternative methods that do not rely on these special characteristics and hence can be generalized to other dimensions. Although the moduli spaces for Calabi-Yaud-folds are not “special Kahler manifolds” whend>3, they still have a restricted geometry, and we indicate the new geometrical structures which arise. We formulate and apply procedures which allow for the construction of mirror maps and the calculation of order-by-order instanton corrections to Yukawa couplings. Mathematically, these corrections are expected to correspond to calculating Chern classes of various parameter spaces (Hilbert schemes) for rational curves on Calabi-Yau manifolds. Our mirror-aided calculations agree with those Chern class calculations in the limited number of cases for which the latter can be carried out with current mathematical tools. Finally, we make explicit some striking relations between instanton corrections for various Yukawa couplings, derived from the associativity of the operator product algebra.

Ill-posed problems with a priori information

Abstract: Part 1 Unstable problems: base formulations of problems ill-posed problems examples and its stability analysis the classification of methods for unstable problems with a priori information. Part 2 Iterative methods for approximation of fixed points and their application to ill-posed problems: basic classes of mappings convergence theorems for iterative processes iterations with correcting multipliers applications to problems of mathematical programming regularizing properties of iterations iterative processes with averaging iterative regularization of variation inequalities and of operator equations with monotone operators iterative regularization of operator equations in the partially-ordered spaces iterative schemes based on the Gauss-Newton method. Part 3 Regularization methods for symmetric spectral problems: L-basis of linear operator kernel analogies of Tikhonov's and Lavent'ev's methods the variational residual method and the quasisolutions method regularization of generalized spectral problem. Part 4 The finite-moment problem and systems of operators equations: statement of the problem and convergence of finite-dimensional approximations iterative methods on the basis of projections the Fejer processes with correcting multipliers FMP regularization in Hilbert spaces with reproducing kernels iterative approximation of solution of linear operator equation system. Part 5 Discrete approximation of regularizing algorithms: discrete convergence of elements and operators convergence of discrete approximations for Tikhonov's regularizing algorithm applications to integral and operator equations interpolation of discrete approximate solutions by splines discrete approximation of reconstuction of linear operator kernel basis finite-dimensional approximation of regularized algorithms on discontinuous functions classes. Part 6 Numerical applications: iterative algorithms for solving gravimetry problem computing schemes for finite-moment problem methods for experiment data processing in structure investigations of amorphous alloys. Appendix: correction parameters methods for solving integral equations of the first kind.

Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems

Abstract: This paper introduces a class of pseudodifferential operators depending on a parameter in a particular way. The main application is a complete expansion of the trace of the resolvent of a Dirac-type operator with nonlocal boundary conditions of the kind introduced by Atiyah, Patodi, and Singer [APS]. This extends the partial expansion in [G2] to a complete one, and extends the complete expansion in [GS 1 ] to the case where the Dirac operator does not have a product structure near the boundary. A secondary application is to obtain a complete expansion of the resolvent of a ~bdo on a compact manifold, essentially reproving a result of Agranovich [Agr]. The resolvent expansion yields immediately an expansion of the trace of the heat kernel, and determines the singularities of the zeta function; moreover, a pseudodifferential factor can be allowed. A major motive for these expansions is to obtain index formulas for elliptic operators; there are many such applications in the physics and geometry literature. The index formula comes from one particular term in the expansion, but each term is a spectral invariant, and they have been used for other purposes as well as for the index. In particular, Branson and Gilkey have a number of papers (e.g. [BG] and [Gi]) analyzing these invariants, and drawing geometric consequences. Interest in the asymptotic behavior of the resolvent goes back to Carleman [C]. More recently, Agmon [Agm] developed it extensively for analytic applications; he introduced the fundamental idea of treating the resolvent parameter essentially as another cotangent variable. This idea was developed in [S1] to analyze the singularities of the zeta function of an elliptic Odo on a compact manifold, and in [$3] to analyze the resolvent of a differential operator with differential boundary conditions. The technique works smoothly for differential operators, producing so-called local invariants, integrals over the underlying

Singular continuous spectrum for palindromic schrodinger operators

Abstract: We give new examples of discrete Schrodinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potentialx in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A sufficient condition for the existence of such anx is that there is a z ∈ X that contains arbitrarily long palindromes. Thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset in X. The class includes well-known substitutions like Fibonacci, Thue-Morse, Period Doubling, binary non-Pisot and ternary non-Pisot. We also show that the operator has no absolutely continuous spectrum for all x ∈ X if X derives from a primitive substitution. For potentials defined by circle maps, x_n = 1_J (θ_0 + nα), we show that the operator has purely singular continuous spectrum for a generic subset in X for all irrational α and every half-open interval J.

Darboux transformation, factorization, and supersymmetry in one-dimensional quantum mechanics

Abstract: We introduce an N-order Darboux transformation operator as a particular case of general transformation operators. It is shown that this operator can always be represented as a product of N first-order Darboux transformation operators. The relationship between this transformation and the factorization method is investigated. Supercharge operators are introduced. They are differential operators of order N. It is shown that these operators and super-Hamiltonian form a superalgebra of order N. For N=2, we have a quadratic superalgebra analogous to the Sklyanin quadratic algebras. The relationship between the transformation introduced and the inverse scattering problem in quantum mechanics is established. An elementary N-parametric potential that has exactly N predetermined discrete spectrum levels is constructed. The paper concludes with some examples of new exactly soluble potentials.

Approximate inverse for linear and some nonlinear problems

Abstract: In this paper we present a method for solving problems such as Af = g by constructing an approximate inverse which maps the data g to a regularized solution of this equation of the first kind. No discretization for f is needed. The solution operator can be precomputed independently of the data. This works for linear problems and for nonlinear problems with a special structure. The regularization is achieved by computing mollified versions of the (minimum-norm) solution. It is shown that this class of regularization operators contains, as special cases, the classical methods such as Tikhonov - Phillips, iteration methods and also discretization methods. In the case where the operator has some invariance properties the storage needs are dramatically reduced.

The Technique of Pseudodifferential Operators

Abstract: Pseudodifferential operators arise naturally in the solution of boundary problems for partial differential equations. The formalism of these operators serves to make the Fourier-Laplace method applicable for nonconstant coefficient equations. This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses 'Leibniz formulas' with integral remainders or as asymptotic series. A pseudodifferential operator may also be described by invariance under action of a Lie-group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution and the relation of the hyperbolic theory to the propagation of maximal ideals. This book will be of particular interest to researchers in partial differential equations and mathematical physics.

The structure of the reverse Hölder classes

Abstract: In this paper we study the structure of the class of functions (RHS) which satisfy the reverse Holder inequality with exponent s > I. To do so we introduce a new operator, the minimal operator, which is analogous to the Hardy-Littlewood maximal operator, and a new class of functions, {RHcc), which plays the same role for (RHS) that the class (Ax) does for the (Ap) classes.

Learning by Observation and Practice: An Incremental Approach for Planning Operator Acquisition

Abstract: This paper describes an approach to automatically learn planning operators by observing expert solution traces and to further refine the operators through practice in a learning-by-doing paradigm. This approach uses the knowledge naturally observable when experts solve problems, without need of explicit instruction or interrogation. The inputs to our learning system are: the description language for the domain, experts' problem solving traces, and practice problems to allow learning-by-doing operator refinement. Given these inputs, our system automatically acquires the preconditions and effects (including conditional effects and preconditions) of the operators. We present empirical results to demonstrate the validity of our approach in the process planning domain. These results show that the system learns operators in this domain well enough to solve problems as effectively as human-expert coded operators. Our approach differs from knowledge acquisition tools in that it does not require a considerable amount of direct interactions with domain experts. It differs from other work on automatically learning operators in that it does not require initial approximate planning operators or strong background knowledge.

Quantum observables and recollapsing dynamics

Abstract: Within a simple quantization scheme, observables for a large class of finite-dimensional time reparametrization invariant systems may be constructed by integration over the manifold of time labels. This procedure is shown to produce a complete set of densely defined operators on a physical Hilbert space, for which an inner product is identified, and to provide reasonable results for simple test cases. Furthermore, many of these observables have a clear interpretation in the classical limit and we use this to demonstrate that, for a class of minisuperspace models including LRS Bianchi IX and the Kantowski--Sachs model, this quantization agrees with classical physics in predicting that such spacetimes recollapse.

The Replace Operator

Abstract: This paper introduces to the calculus of regular expressions a replace operator, ->, and defines a set of replacement expressions that concisely encode several alternate variations of the operation. The basic case is unconditional obligatory replacement: UPPER -> LOWER Conditional versions of replacement, such as, UPPER -> LOWER || LEFT _ RIGHT constrain the operation by left and right contexts. UPPER, LOWER, LEFT, and RIGHT may be regular expressions of any complexity. Replace expressions denote regular relations. The replace operator is defined in terms of other regular expression operators using techniques introduced by Ronald M. Kaplan and Martin Kay in "Regular Models of Phonological Rule Systems" (Computational Linguistics 20:3 331-378. 1994).

Operator expansion for high-energy scattering

Abstract: I demonstrate that the leading logarithms for high-energy scattering can be obtained as a result of evolution of the nonlocal operators - straight-line ordered gauge factors - with respect to the slope of the straight line.

FR-operator approach to the H/sub 2/ analysis and synthesis of sampled-data systems

Abstract: Recently, a frequency-domain operator called frequency response (FR) operator was defined and shown to represent the transfer characteristics of a stable sampled-data system. Using this novel frequency-domain notion and introducing its extended notion called hybrid FR-operator, we define an H/sub 2/-norm for sampled-data systems in this paper. Then, sampled-data H/sub 2/ control problems are formulated and solved, whereby the usefulness of these frequency-domain notions is demonstrated both in the analysis and synthesis aspects of sampled-data systems. For the case of sampled-data systems with hybrid (i.e., both continuous-time and discrete-time) input and output signals, the H/sub 2/-norm defined by a hybrid FR-operator turns out to be slightly different from that defined in previous studies. The source of the discrepancy is also identified. >

A fuzzy operator for the enhancement of blurred and noisy images

Abstract: Rule-based fuzzy operators are a novel class of operators specifically designed in order to apply the principles of approximate reasoning to digital image processing. This paper shows how a fuzzy operator that is able to perform detail sharpening but is insensitive to noise can be designed. The results obtainable by the proposed technique in the enhancement of a real image are presented. >

Higher order differential energy operators

Abstract: Instantaneous signal operators /spl Upsi//sub k/(x)=x/spl dot/x/sup (k-1)/-xx/sup (k)/ of integer orders k are proposed to measure the cross energy between a signal x and its derivatives. These higher order differential energy operators contain as a special case, for k=2, the Teager-Kaiser (1990) operator. When applied to (possibly modulated) sinusoids, they yield several new energy measurements useful for parameter estimation or AM-FM demodulation. Applying them to sampled signals involves replacing derivatives with differences that lead to several useful discrete energy operators defined on an extremely short window of samples. >

Method for generating performance ratings for a vehicle operator

Abstract: In one aspect of the present invention, a method for generating performance ratings that indicate the driving performance of a vehicle operator is disclosed. The method senses various operating parameters of the vehicle and produces representative signals. Sensed signals are compared to corresponding target values. A plurality of is performance ratings are determined. Finally, an operator summary report illustrating the performance ratings is generated. The report includes recommended actions to improve the performance of the operator.