Showing papers on "Operator (computer programming) published in 1983"

A complex gradient operator and its application in adaptive array theory

Abstract: The problem of minimising a real scalar quantity (for example array output power, or mean square error) as a function of a complex vector (the set of weights) frequently arises in adaptive array theory. A complex gradient operator is defined in the paper for this purpose and its use justified. Three examples of its application to array theory problems are given.

Optimal perceptual inference

Abstract: When a vision system creates an interpretation of some input datn, it assigns truth values or probabilities to intcrnal hypothcses about the world. We present a non-dctcrministic method for assigning truth values that avoids many of the problcms encountered by existing relaxation methods. Instead of rcprcscnting probabilitics with realnumbers, we usc a more dircct encoding in which thc probability \ associated with a hypotlmis is rcprcscntcd by the probability hat it is in one of two states, true or false. Wc give a particular nondeterministic operator, based on statistical mechanics, for updating the truth values of hypothcses. The operator ensures that the probability of discovering a particular combination of hypothcscs is a simplc function of how good that combination is. Wc show that thcrc is a simple relationship bctween this operator and Bayesian inference, and we describe a learning rule which allows a parallel system to converge on a set ofweights that optimizes its perccptt~al inferences.

Werner deconvolution for automated magnetic interpretation and its refinement using Marquardt's inverse modeling

Abstract: We present a deconvolution for automated magnetic interpretation based on Werner’s (1953) simplified thin‐dike assumption which leads to the linearization of complex nonlinear magnetic problems. The usefulness of the method is expanded by the fact that the horizontal gradient of the total field caused by the edge of a thick interface body is equivalent to the total field from a thin dike. Statistical decision, numerical iteration, and a seven‐point operator are used to improve approximations of susceptibility, dip, depth, and horizontal location of the source. Marquardt’s nonlinear least‐squares method for inverse modeling is then used to refine automatically the first approximation provided by the deconvolution. Synthetic and real total‐field data are used to demonstrate the process.

Learning to solve problems by searching for macro-operators

Abstract: This thesis explores the idea of learning efficient strategies for solving problems by searching for macro-operators. A macro-operator, or macro for short, is simply a sequence of operators chosen from the primitive operators provided by a problem. The technique is particularly useful for problems with non-serializable subgoals, such as Rubik's Cube, for which other weak methods fail. Both a problem solving program and a learning program are described in detail. The performance of these programs is analyzed in terms of the number of macros required to solve all problem instances, the length of the resulting solutions expressed as the number of primitive moves, and the amount of time necessary to learn the macros. In addition, a theory of why the method works, and a characterization of the range of problems for which it is useful are presented. The theory introduces a new type of problem structure called operator decomposability. Finally, it is concluded that the macro technique is a valuable addition to the class of weak methods, that macro-operators constitute an interesting and important type of knowledge, and that searching for macros may be a useful general learning paradigm.

The use of single-spin operator basis sets in the N.M.R. spectroscopy of scalar-coupled spin systems

Abstract: The use of a complete set comprising products of single-spin angular momentum operators is introduced as a basis for the expansion of the density operators of typical simple nuclear spin systems encountered in double-resonance high-resolution liquid state nuclear magnetic resonance experiments. Some simple rules are presented for calculating the evolution of the density operator due to arbitrary sequences of unselective radio frequency pulses and periods of free precession due to chemical shifts and scalar couplings. The proportions and nature of the zero-, single- and multiple-quantum order excited by such pulse sequences can readily be predicted, as can the form of the N.M.R. signal itself, when all relaxation effects are neglected. The evolution of some of the basic product operators is interpreted in terms of pictorial models. Some important restrictions on the nature of the states which can be produced by arbitrary pulse sequences are discussed and the possible states of the AX spin system are analys...

Random linear operators

Abstract: 1. Random Operators in Hilbert Space.- 1. Basic Definitions.- 1.1 Strong Random Operator.- 1.2 Weak Random Operator.- 1.3 Product of Random Operators.- 2. Characteristic Functions of Random Operators.- 2.1 Definition.- 2.2 Characteristic Functions of Strong and Bounded Operators.- 2.3 Gaussian Random Operators.- 3. Convergence of Random Operators.- 3.1 Weak Convergence of Random Operators.- 3.2 Strong Convergence of Random Operators.- 3.3 Convergence of Distributions corresponding to Random Operators.- 2. Functions of Random Operators.- 4. Spectral Representation for Symmetric Random Operators.- 4.1 Symmetric Random Operators and Selfadjoint Extensions.- 4.2 Spectral Representation of a Selfadjoint Random Operator.- 4.3 Spectral Representation of a Strong Symmetric Operator.- 5. Equations with Symmetric Random Operators.- 5.1 Evolution Equations.- 5.2 Schrodinger-type Equations.- 5.3 Spectral Moment Functions.- 5.4 Equation of Fredholm Type.- 6. Equations with Semi-Bounded Random Operators.- 6.1 Nonnegative Closed Random Operators.- 6.2 Resolvent of a Nonnegative Operator.- 6.3 Resolvent of a Nonnegative Random Operator.- 6.4 Equations of Fredholm Type.- 6.5 Equations of Evolution Type.- 3. Operator-Valued Martingales.- 7. Operator-Valued Martingale Sequences.- 7.1 Weak Operator-valued Martingale.- 7.2 Strong Operator-valued Martingales.- 7.3 Operator-valued Martingale.- 8. Convergence of Infinite Products of Independent Random Operators.- 8.1 Infinite Products as Martingales.- 8.2 Convergence of Infinite Products given the Existence of Two Moments.- 8.3 Convergence of Infinite Products in Absolute Norm.- 9. Continuous Operator-Valued Martingales.- 9.1 Some Properties of Continuous Real-valued Local Martingales.- 9.2 Continuous Martingales with values in X.- 9.3 Operator-valued Continuous Martingales.- 9.4 Strong Operator-valued Wiener Processes.- 4. Stochastic Integrals and Equations.- 10. Stochastic Integrals with Respect to an X-Valued Martingale.- 10.1 Definition.- 10.2 Integrals for Processes with Regular Characteristics.- 10.3 Stochastic Integral with respect to a Wiener Process.- 11. Stochastic Integral with Respect to an Operator-Valued Martingale.- 11.1 Integrals of X-valued Functions.- 11.2 Integrals of Operator-valued Functions.- 12. Stochastic Operator Equations.- 12.1 Operator-valued Functions of Random Operators.- 12.2 Stochastic Equations Involving I(Z, Y)t.- 12.3 Stochastic Equations Involving I*(Z, Y)t.- 12.4 Some Generalizations.- 5. Linear Stochastic Operator Equations.- 13. Generalization of the Stochastic Operator Integral.- 13.1 General Form of the Linear Equation.- 13.2 A Generalization of the Stochastic Integral.- 14. Linear Differential Operator Equations.- 14.1 Definition of a Linear Equation.- 14.2 Existence of Uniqueness of Solution.- 14.3 Linear Transformations of Solutions.- 14.4 Equations for Moments of the Solution of a Stochastic Equation.- 15. Continuous Stochastic Semigroups.- 15.1 Solutions of Simple Linear Equations -Stochastic Semigroups.- 15.2 Time Reversal in Stochastic Differential Equations.- 15.3 Definition of Stochastic Semigroups.- 15.4 Semigroups which are Martingales.

Relativistic integrals over Breit–Pauli operators using general Cartesian Gaussian functions. I. One‐electron interactions

Abstract: Cartesian Gaussian functions are employed to derive general expressions for integrals over all one‐electron operators of the Breit–Pauli Hamiltonian. It is shown that in atoms of higher atomic number p6, p8, ⋅⋅⋅ operators can be important in determining relativistic corrections to the kinetic energy. All other operators of this Hamiltonian can be expressed as some derivative of 1/r. Thus, a general expression is derived for the integral over the operator (∂1/∂x1) (∂m/∂ym) (∂n/∂zn) (1/r) by employing its Fourier transform. The operator and charge‐distribution‐dependent parts can be separately identified in the resulting expression and hence for a given charge distribution, integrals over any number of operators that can be expressed in the above form can be obtained simultaneously. In addition to nuclear attraction, these operators include the spin‐orbit and Darwin terms of the Breit‐Pauli Hamiltonian, as well as the electric field components and their derivatives, and other interactions over operators req...

Computer controlled by voice input

Abstract: A computer controlled by a voice input has a speech recognition section for converting a keyword of a program which is entered by the voice input and corresponds to a start number, thereby obtaining a digital code. The digital code data which indicates the keyword selects the start number corresponding to the storage content of a table stored in a program memory. The start number data is used to access a start address of the corresponding program, thereby starting and executing the program. Also disclosed is a system wherein when a chosen key of a key input device is operated while a voice operator guidance is generated, a key-in signal is produced to forcibly stop the ongoing guidance. In particular, when a plurality of voice operator guidances are provided, the computer learns the state of the operation by the operator from the manner of the forcible stop, and automatically stops the generation of the voice guidance on a specific item from the next processing.

Pseudojump operators. I. The r.e. case

Abstract: Call an operator J on the power set of co a pseudo jump operator if J(A) is uniformly recursively enumerable in A and A is recursive in J(A) for all subsets A of c. Thus the (Turing) jump operator is a pseudo jump operator, and any existence proof in the theory of r.e. degrees yields, when relativized, one or more pseudo jump operators. Extending well-known results about the jump, we show that for any pseudo jump operator J, every degree > 0' has a representative in the range of J, and that there is a nonrecursive r.e. set A with J(A) of degree 0'. The latter result yields a finite injury proof in two steps that there is an incomplete high r.e. degree, and by iteration analogous results for other levels of the H", Ln hierarchy of r.e. degrees. We also establish a result on pairs of pseudo jump operators. This is combined with Lachlan's result on the impossibility of combining splitting and density for r.e. degrees to yield a new proof of Harrington's result that 0' does not split over all lower r.e. degrees. 1. We prove some generalizations of theorems about the Turing jump operator (denoted A H A') to theorems about operators of the form A * A ED WA, for an arbitrary fixed Godel number e. (Here A ED B is the recursive join of A and B and WA is the eth set r.e. in A in a fixed standard enumeration.) For instance, Friedberg (see (25, Theorem 4.1)) showed that there is a nonrecursive r.e. set A with A' TK (where K is a complete r.e. set). We prove by a finite injury priority argument similar to Friedberg's that for every e there is a nonrecursive r.e. set A with A ED WA-T K. Now Friedberg's argument relative to an arbitrary oracle B yields a fixed Godel

Detection of moving edges

Abstract: A technique requiring only two frames is presented for finding time-varying edges in a dynamic scene. The frames need not be contiguous. The proposed operator picks up moving edge points which are not easily detected with simple static edge operators. The operator includes both change and edge detection in a way that improves overall performance. Also presented are arguments against the use of three-dimensional operators for scenes where the third dimension is temporal rather than spatial.

A variational approach to edge detection

Abstract: The problem of detecting intensity changes in images is canonical in vision. Edge detection operators are typically designed to optimally estimate first or second derivative over some (usually small) support. Other criteria such as output signal to noise ratio or bandwidth have also been argued for. This paper describes an attempt to formulate a set of edge detection criteria that capture as directly as possible the desirable properties of the detector. Variational techniques are used to find a solution over the space of all possible functions. The first criterion is that the detector have low probability of error i.e. failing to mark edges or falsely marking non-edges. The second is that the marked points should be as close as possible to the centre of the true edge. The third criterion is that there should be low probability of more than one response to a single edge. The third criterion is claimed to be new, and it became necessary when an operator designed using the first two criteria was found to have excessive multiple responses. The edge model that will be considered here is a one-dimensional step edge in white Gaussian noise although the same technique has been applied to an extended impulse or ridge profile. The result is a one dimensional operator that approximates the first derivative of a Gaussian. Its extension to two dimensions is also discussed.

Nonperturbative Weak Coupling Analysis of the Liouville Quantum Field Theory

Abstract: A systematic weak-coupling expansion is developed for the Liouville quantum field theory on a periodic spatial interval. Matrix elements of various Liouville operators are computed to order g/sup 8/ by perturbation in nonzero modes about the exact solution of the zero-mode problem. To this order the results agree with the explicit operator solution given previously by Braaten, Curtright, and Thorn, in which the Liouville field was expressed in terms of a free pseudoscalar field by means of an operator Baaumlcklund transformation.

Proving Precedence Properties: The Temporal Way

Abstract: This paper explores the three important classes of temporal properties of concurrent programs: invariance, liveness and precedence. It presents the first methodological approach to the precedence properties, while providing a review of the invariance and liveness properties. The approach is based on the ''unless'' operator, which is a weak version of the ''until'' operator. For each class of properties, we present a single complete proof principle. Finally, we show that the properties of each class are decidable over finite state programs.

Ladder networks, fixpoints, and the geometric mean

Abstract: Using fixed-point arguments, existence and uniqueness results are obtained for the joint resistance of infinite positive operator networks with noncommuting operators in the branches. Explicit representations for the joint resistance are given using the geometric mean of positive operators.

Positive definite kernels

Abstract: Keywords: factorization theorem;;; positive-definite operator valued kernels Reference GPRO-ARTICLE-1983-001 Record created on 2010-05-25, modified on 2016-08-08

A stationary formulation of time‐dependent problems in quantum mechanics

Abstract: A unifying framework is presented which treats time‐dependent problems in nonrelativistic quantum mechanics on equal footing with stationary ones. This is accomplished by elevating time t to the role of a dynamical variable and considering evolution in an extended space with respect to a progress variable τ. Among the new objects in the extended space are the time operator as well as operators, such as energy, that are not diagonal in time. The latter bear, e.g., on the question of ‘‘quantum chaos.’’ Only τ‐stationary states in the extended space are necessary to recover all of the Schrodinger time evolution. In particular, time‐dependent constants of the motion (and these include time‐evolved density matrices) elevate to stationary constants of the τ motion. Time‐dependent problems, which may also involve time‐dependent Hamiltonians, can then be solved by stationary‐state methods. Special attention is given to applications based on time‐dependent constants of the motion and to maximum‐entropy states subject to time‐dependent constraints. Two examples (rank‐one perturbation, damped harmonic oscillator) illustrate some of these ideas. Scattering theory in the extended space is discussed in two appendices. It furnishes a picture of Hamiltonian τ evolution which promises to embrace also irreversible dynamics.

On Essential Selfadjointness, Distinguished Selfadjoint Extension and Essential Spectrum of Dirac Operators with Matrix Valued Potentials

Abstract: (1.2) ajak+akaj=2djkl (/, fe = l, 2, 3, 4). We denote by HQ the operator H with We denote by and | | the usual inner product and norm in C, respectively, and by ( , ) and || || the inner product and norm in the Hilbert space «#=[L2CR )II, respectively. We also denote by | | and || || the operator norm of a 4x4 matrix and a bounded linear operator in «#, respectively. We denote by / the 4x4 identity matrix, which at times implies the 2x2 identity matrix, but no confusion will occur. For a closable operator T in JC, we denote by T its closure. For an (formal) operator T, we denote by T the restriction of T to the domain

Camera status and diagnostics display system

Abstract: An operator is provided with a continuous display, on a single convenient monitor, of the extent of progress, the status, etc., of each camera in a multi-camera system, during a microprocessor controlled automatic setup procedure. The display is superimposed on a video picture generated by the selected camera, which corresponds to one of various video signals selectable by the operator.

A study of the various methods for computing electromagnetic field utilizing thin wire integral equations

Abstract: In this paper we analyze the numerical aspects of the various methods that have been utilized to analyze thin wire antennas. First, we derive the properties of the operators for Pocklington's and Hallen's integral equation. On the basis of these properties, we discuss the various iterative methods used to find current distribution on thin wire structures. An attempt has been made to resolve the question of numerical stability associated with various entire domain and subdomain expansion functions in Galerkin's method. It has been shown that the sequence of solutions generated by the iterative methods monotonically approaches the exact solution provided the excitations chosen for these problems are in the range of the operator. Such a statement may not hold for Galerkin's methods if the inverse operator is unbounded. Moreover, if the excitation function is not in the range of the operator, then the sequence of solutions forms an asymptotic series. Examples have been presented to illustrate this point.

Electronic cash register

Abstract: An electronic cash register inhibits registration of information associated with a commodity unless an operator code comprised of a plurality of digits and identifying an operator is inputted. A preset code further allows selection of the manner of indicating and printing the inputted operator code. When an operator code comprised of a plurality of digits is entered by operating a decimal keyboard or ten-key (1) and an operator code key and when a first mode is set through a mode selection key (7), all the digits of the operator code are displayed in a display (11) and printed in a printer (12). If and when a second mode is set, only a predetermined partial digit or digits of the operator code comprised of a plurality of digits are printed and none of digits are displayed. If a third mode is set, both displaying and printing of the operator code are inhibited. Thus, a user can arbitrarily select whether the operator code should be displayed and printed, by switching the mode.

On the stability problem of a pair of adjoint operators

Abstract: As an introduction, the eigenvalue problem for a linear operator T having a discrete point spectrum and a complete set of eigenfunctions is studied. The bivariational principle for T and its adjoint operator T° is derived, and the biorthogonal properties of their eigenfunctions are discussed. The main part of the paper is then concerned with the problem whether these features can be extended also to a general pair of adjoint operators, T and T°, in which case the eigenvalue problem is replaced by the more general stability problem. The stability problem for a pair of adjoint operators—T and T°—is first formulated in terms of nonorthogonal projectors—O and O°—which decompose these operators and satisfy the commutation relations TO=OT and T°O°=O°T°. In the case of a finite space, these skew‐projectors may be explicitly expressed in product forms derived from the reduced Cayley–Hamilton equation for the operator T. It is shown that, if the stable subspaces defined by these projectors are properly classified ...

Design Strategies for Computer-Based Information Displays in Real-Time Control Systems

Abstract: Two strategies are defined for the design of integrated, computer-based information displays for real-time control systems. Subjects controlled a simulated system using a conventional display console or one of two integrated displays. The effects of display type on operator performance were considered. Integrated displays tended to degrade performance unless the display preprocessed information, synthesizing and presenting it in a form more compatible with an operator's high-level information needs.