Showing papers on "Operator (computer programming) published in 2003"

Soliton Equations and Hamiltonian Systems

Abstract: Integrable Systems Generated by Linear Differential nth Order Operators Hamiltonian Structures Hamiltonian Structure of the GD Hierarchies Modified KdV and GD. The Kupershmidt-Wilson Theorem The KP Hierarchy Baker Function, t-Function Additional Symmetries, String Equation Grassmannian. Algebraic-Geometrical Krichever Solutions Matrix First-Order Operator, AKNS-D Hierarchy Generalization of the AKNS-D Hierarchy: Single-Pole and Multi-Pole Matrix Hierarchies Isomonodromic Deformations and the Most General Matrix Hierarchy Tau Functions of Matrix Hierarchies KP, Modified KP, Constrained KP, Discrete KP, and q-KP Another Chain of KP Hierarchies and Integrals Over Matrix Varieties Transformational Properties of a Differential Operator under Diffeomorphisms and Classical W-Algebras Further Restrictions of the KP, Stationary Equations Stationary Equations of the Matrix Hierarchy Field Lagrangian and Hamiltonian Formalism Further Examples and Applications.

Introduction to Operator Space Theory

Abstract: The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C*-algebras. The third (and shorter) part of the book describes applications to non self-adjoint operator algebras, and similarity problems. In particular the author's counterexample to the 'Halmos problem' is presented, as well as work on the new concept of 'length' of an operator algebra. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer.

An overview of operators for aggregating information

Abstract: In this work, we first make a survey of the existing main aggregation operators and then propose some new aggregation operators such as the induced ordered weighted geometric averaging (IOWGA) operator, generalized induced ordered weighted averaging (GIOWA) operator, hybrid weighted averaging (HWA) operator, etc., and study their desirable properties. Finally, we briefly classify all of these aggregation operators. © 2003 Wiley Periodicals, Inc.

Symmetric Informationally Complete Quantum Measurements

Abstract: We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal. Such a set is called a ``symmetric, informationally complete'' POVM (SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d. SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions two, three, and four. We further conjecture that a particular kind of group-covariant SIC-POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.

The Dilatation Operator of N=4 Super Yang-Mills Theory

Abstract: We argue that existing methods for the perturbative computation of anomalous dimensions and the disentanglement of mixing in N = 4 gauge theory can be considerably simplified, systematized and extended by focusing on the theory's dilatation operator. The efficiency of the method is first illustrated at the one-loop level for general non-derivative scalar states. We then go on to derive, for pure scalar states, the two-loop structure of the dilatation operator. This allows us to obtain a host of new results. Among these are an infinite number of previously unknown two-loop anomalous dimensions, new subtleties concerning 't Hooft's large N expansion due to mixing effects of degenerate single and multiple trace states, two-loop tests of various protected operators, as well as two-loop non-planar results for two-impurity operators in BMN gauge theory. We also put to use the recently discovered integrable spin chain description of the planar one-loop dilatation operator and show that the associated Yang-Baxter equation explains the existence of a hitherto unknown planar ``axial'' symmetry between infinitely many gauge theory states. We present evidence that this integrability can be extended to all loops, with intriguing consequences for gauge theory, and that it leads to a novel integrable deformation of the XXX Heisenberg spin chain. Assuming that the integrability structure extends to more than two loops, we determine the planar three-loop contribution to the dilatation operator.

Stringing Spins and Spinning Strings

Abstract: We apply recently developed integrable spin chain and dilatation operator techniques in order to compute the planar one-loop anomalous dimensions for certain operators containing a large number of scalar fields in N = 4 Super Yang-Mills. The first set of operators, belonging to the SO(6) representations [J,L 2J,J], interpolate smoothly between the BMN case of two impurities (J = 2) and the extreme case where the number of impurities equals half the total number of fields (J = L/2). The result for this particular [J,0,J] operator is smaller than the anomalous dimension derived by Frolov and Tseytlin [hep-th/0304255] for a semiclassical string configuration which is the dual of a gauge invariant operator in the same representation. We then identify a second set of operators which also belong to [J,L 2J,J] representations, but which do not have a BMN limit. In this case the anomalous dimension of the [J,0,J] operator does match the Frolov-Tseytlin prediction. We also show that the fluctuation spectra for this [J,0,J] operator is consistent with the string prediction.

Flux: an adaptive partitioning operator for continuous query systems

Abstract: The long-running nature of continuous queries poses new scalability challenges for dataflow processing. CQ systems execute pipelined dataflows that may be shared across multiple queries. The scalability of these dataflows is limited by their constituent, stateful operators - e.g. windowed joins or grouping operators. To scale such operators, a natural solution is to partition them across a shared-nothing platform. But in the CQ context, traditional, static techniques for partitioned parallelism can exhibit detrimental imbalances as workload and runtime conditions evolve. Long-running CQ dataflows must continue to function robustly in the face of these imbalances. To address this challenge, we introduce a dataflow operator called flux that encapsulates adaptive state partitioning and dataflow routing. Flux is placed between producer-consumer stages in a dataflow pipeline to repartition stateful operators while the pipeline is still executing. We present the flux architecture, along with repartitioning policies that can be used for CQ operators under shifting processing and memory loads. We show that the flux mechanism and these policies can provide several factors improvement in throughput and orders of magnitude improvement in average latency over the static case.

A taxonomy for the crossover operator for real-coded genetic algorithms: An experimental study

Abstract: The main real-coded genetic algorithm (RCGA) research effort has been spent on developing efficient crossover operators. This study presents a taxonomy for this operator that groups its instances in different categories according to the way they generate the genes of the offspring from the genes of the parents. The empirical study of representative crossovers of all the categories reveals concrete features that allow the crossover operator to have a positive influence on RCGA performance. They may be useful to design more effective crossover models. © 2003 Wiley Periodicals, Inc. Genetic algorithms (GAs) are adaptive methods based on natural evolution that may be used for search and optimization problems. They process a population of search space solutions with three operations: selection, crossover, and mutation. 1‐3 Under their initial formulation, the search space solutions are coded using the binary alphabet; however, other coding types have been taken into account for the representation issue such as real coding. The real coding approach seems particularly natural when tackling optimization problems of parameters with variables in continuous domains. A chromosome is a vector of floating point numbers in which their size is kept the same as the length of the vector, which is the solution to the problem. GAs based on real-number representation are called real-coded GAs

Dunkl Operators: Theory and Applications

Abstract: These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics We start with an outline of the general concepts: Dunkl operators, the intertwining operator, the Dunkl kernel and the Dunkl transform We point out the connection with integrable particle systems of Calogero-Moser-Sutherland type, and discuss some systems of orthogonal polynomials associated with them A major part is devoted to positivity results for the intertwining operator and the Dunkl kernel, the Dunkl-type heat semigroup, and related probabilistic aspects The notes conclude with recent results on the asymptotics of the Dunkl kernel

Operator ordering in quantum optics theory and the development of Dirac's symbolic method

Abstract: We present a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering (or symmetric ordering)) by fashioning Dirac's symbolic method and representation theory. We propose the technique of integration within an ordered product (IWOP) of operators to realize our goal. The IWOP makes Dirac's representation theory and the symbolic method more transparent and consequently more easily understood. The beauty of Dirac's symbolic method is further revealed. Various applications of the IWOP technique, such as in developing the entangled state representation theory, nonlinear coherent state theory, Wigner function theory, etc, are presented.

Maximizing the output rate of multi-way join queries over streaming information sources

Abstract: Recently there has been a growing interest in join query evaluation for scenarios in which inputs arrive at highly variable and unpredictable rates. In such scenarios, the focus shifts from completing the computation as soon as possible to producing a prefix of the output as soon as possible. To handle this shift in focus, most solutions to date rely upon some combination of streaming binary operators and "on-the-fly" execution plan reorganization. In contrast, we consider the alternative of extending existing symmetric binary join operators to handle more than two inputs. Toward this end, we have completed a prototype implementation of a multi-way join operator, which we term the "MJoin" operator, and explored its performance. Our results show that in many instances the MJoin produces outputs sooner than any tree of binary operators. Additionally, since MJoins are completely symmetric with respect to their inputs, they can reduce the need for expensive runtime plan reorganization. This suggests that supporting multiway joins in a single, symmetric, streaming operator may be a useful addition to systems that support queries over input streams from remote sites.

A Quasi-Newton Algorithm Based on a Reduced Model for Fluid-Structure Interaction Problems in Blood Flows

Abstract: We propose a quasi-Newton algorithm for solving fluid-structure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We present 2D and 3D fluid-structure simulations performed either with a simple 1D structure model or with shells in large displacements.

Linear Sobolev type equations and degenerate semigroups of operators

Abstract: Auxiliary material Banach spaces and linear operators Theorems on infinitesimal generators Functional spaces and differential operators Relatively p-radial operators and degenerate strongly continuous semigroups of operators Introduction Relative resolvents Relatively p-radial operators Degenerate strongly continuous semigroups of operators Approximations of Hille-Widder-Post type Splitting of spaces Infinitesimal generators and phase spaces Generators of degenerate strongly continuous semigroups of operators Degenerate strongly continuous groups of operators Relatively p-sectorial operators and degenerate analytic semigroups of operators Introduction Relatively p-sectorial operators Degenerate analytic semigroups of operators Phase spaces for the case of degenerate analytic semigroups Space splitting Generators of degenerate analytic semigroups of operators Degenerate infinitely differentiable semigroups of operators Phase spaces for the case of degenerate infinitely continuously differentiable semigroups Kernels and images of degenerate infinitely differential semigroups of operators Relatively ?-bounded operators and degenerate analytic groups of operators Introduction Relatively ?-bounded operators Relative ?-boundedness and relative p-sectoriality Relative ?-boundedness and relatively adjoint vectors Degenerate analytical groups of operators Sufficient conditions of the relative ?-boundedness The case of a Fredholm operator Analytical semigroups of operators degenerating on the chains of relatively adjoint vectors of an arbitrary length Cauchy problem for inhomogeneous Sobolev-type equations Introduction Case of a relatively ?-bounded operator The case of a relatively p-sectorial operator Case of a relatively p-radial operator Strong solution of Cauchy problem Cauchy problem for an equation with Banach-adjoint operators Propagators Inhomogeneous Cauchy problem for high-order Sobolev-type equations Bounded solutions of Sobolev-type equations Introduction Relatively spectral theorem Bounded relaxed solutions of a homogeneous equation Bounded solutions of the inhomogeneous equation Examples Optimal control Introduction Strong solution of Cauchy problem for an equation with Hilbert-adjoint operators Problem of optimal control for an equation with relatively ?-bounded operator Problem of optimal control for quatino with a relatively p-sectorial operator Barenblatt-Zheltov-Kochina equation System of ordinary differential equations Equation of the evolution of the free filtered-fluid surface Bibliography Index

The loop algorithm

Abstract: A review of the loop algorithm , its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a quantum Monte Carlo procedure that employs non-local changes of worldline configurations, determined by local stochastic decisions. It is based on a formulation of quantum models of any dimension in an extended ensemble of worldlines and graphs, and is related to Swendsen-Wang algorithms. It can be represented directly on an operator level, both with a continuous imaginary time path integral and with the stochastic series expansion. It overcomes many of the difficulties of traditional worldline simulations. Autocorrelations are reduced by orders of magnitude. Grand-canonical ensembles, off-diagonal operators, and variance reduced estimators are accessible. In some cases, infinite systems can be simulated. For a restricted class of models, the fermion sign problem can be overcome. Transverse magnetic fields are handled efficiently, in contrast to strong diagonal fiel...

Double-trace operators and one-loop vacuum energy in AdS/CFT

Abstract: We perform a one-loop calculation of the vacuum energy of a tachyon field in anti\char21{}de Sitter space with boundary conditions corresponding to the presence of a double-trace operator in the dual field theory Such an operator can lead to a renormalization group flow between two different conformal field theories related to each other by a Legendre transformation in the large N limit The calculation of the one-loop vacuum energy enables us to verify the holographic c theorem one step beyond the classical supergravity approximation

Power assist method for HAL-3 estimating operator's intention based on motion information

Abstract: This paper describes the recognition method and the control method to realize the power assist which reflects operator's intention by grasping the interaction between operator's intention and motion information. The basic control method for HAL had been performed by using myoelectricity which reflects operator's intention. As the application of the basic method, we considered the control method of power assist based on another information by considering the relation between myoelectricity and another information of motion, and the recognition method for the control method. We adopted phase sequence control which generated a series of assist motions by the transition of some fundamental motions called phase. The result of experiments showed the effective power assist which reflected operator's intention by using this control method.

Soliton Equations And Hamiltonian Systems

Abstract: Integrable Systems Generated by Linear Differential nth Order Operators Hamiltonian Structures Hamiltonian Structure of the GD Hierarchies Modified KdV and GD. The Kupershmidt-Wilson Theorem The KP Hierarchy Baker Function, t-Function Additional Symmetries, String Equation Grassmannian. Algebraic-Geometrical Krichever Solutions Matrix First-Order Operator, AKNS-D Hierarchy Generalization of the AKNS-D Hierarchy: Single-Pole and Multi-Pole Matrix Hierarchies Isomonodromic Deformations and the Most General Matrix Hierarchy Tau Functions of Matrix Hierarchies KP, Modified KP, Constrained KP, Discrete KP, and q-KP Another Chain of KP Hierarchies and Integrals Over Matrix Varieties Transformational Properties of a Differential Operator under Diffeomorphisms and Classical W-Algebras Further Restrictions of the KP, Stationary Equations Stationary Equations of the Matrix Hierarchy Field Lagrangian and Hamiltonian Formalism Further Examples and Applications.

Designing optimal quantum detectors via semidefinite programming

Abstract: We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing among a collection of quantum states, represented by a set of density operators. We show that the design of the optimal detector can be formulated as a semidefinite programming problem. Based on this formulation, we derive a set of necessary and sufficient conditions for an optimal quantum measurement. We then show that the optimal measurement can be found by solving a standard (convex) semidefinite program. By exploiting the many well-known algorithms for solving semidefinite programs, which are guaranteed to converge to the global optimum, the optimal measurement can be computed very efficiently in polynomial time within any desired accuracy. Using the semidefinite programming formulation, we also show that the rank of each optimal measurement operator is no larger than the rank of the corresponding density operator. In particular, if the quantum state ensemble is a pure-state ensemble consisting of (not necessarily independent) rank-one density operators, then we show that the optimal measurement is a pure-state measurement consisting of rank-one measurement operators.

Double operator integrals in a Hilbert space

Abstract: Double operator integrals are a convenient tool in many problems arising in the theory of self-adjoint operators, especially in the perturbation theory. They allow to give a precise meaning to operations with functions of two ordered operator-valued non-commuting arguments. In a different language, the theory of double operator integrals turns into the problem of scalarvalued multipliers for operator-valued kernels of integral operators. The paper gives a short survey of the main ideas, technical tools and results of the theory. Proofs are given only in the rare occasions, usually they are replaced by references to the original papers. Various applications are discussed.

Comments on the Stress-Energy Tensor Operator in Curved Spacetime

Abstract: The technique based on a *-algebra of Wick products of field operators in curved spacetime, in the local covariant version proposed by Hollands and Wald, is strightforwardly generalized in order to define the stress-energy tensor operator in curved globally hyperbolic spacetimes. In particular, the locality and covariance requirement is generalized to Wick products of differentiated quantum fields. Within the proposed formalism, there is room to accomplish all of the physical requirements provided that known problems concerning the conservation of the stress-energy tensor are assumed to be related to the interface between the quantum and classical formalism. The proposed stress-energy tensor operator turns out to be conserved and reduces to the classical form if field operators are replaced by classical fields satisfying the equation of motion. The definition is based on the existence of convenient counterterms given by certain local Wick products of differentiated fields. These terms are independent from the arbitrary length scale (and any quantum state) and they classically vanish on solutions of the Klein-Gordon equation. Considering the averaged stress-energy tensor with respect to Hadamard quantum states, the presented definition turns out to be equivalent to an improved point-splitting renormalization procedure which makes use of the nonambiguous part of the Hadamard parametrix only that is determined by the local geometry and the parameters which appear in the Klein-Gordon operator. In particular, no extra added-by-hand term g αβQ and no arbitrary smooth part of the Hadamard parametrix (generated by some arbitrary smooth term ``ω 0 '') are involved. The averaged stress-energy tensor obtained by the point-splitting procedure also coincides with that found by employing the local ζ-function approach whenever that technique can be implemented.

For real! XCS with continuous-valued inputs

Abstract: Many real-world problems are not conveniently expressed using the ternary representation typically used by Learning Classifier Systems and for such problems an interval-based representation is preferable. We analyse two interval-based representations recently proposed for XCS, together with their associated operators and find evidence of considerable representational and operator bias. We propose a new interval-based representation that is more straightforward than the previous ones and analyse its bias. The representations presented and their analysis are also applicable to other Learning Classifier System architectures.We discuss limitations of the real multiplexer problem, a benchmark problem used for Learning Classifier Systems that have a continuous-valued representation, and propose a new test problem, the checkerboard problem, that matches many classes of real-world problem more closely than the real multiplexer.Representations and operators are compared using both the real multiplexer and checkerboard problems and we find that representational, operator and sampling bias all affect the performance of XCS in continuous-valued environments.