Showing papers on "Operator (computer programming) published in 2005"

Signal recovery by proximal forward-backward splitting ∗

Abstract: We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems. Recent results on monotone operator splitting methods are applied to establish the convergence of a forward-backward algorithm to solve the generic problem. In turn, we recover, extend, and provide a simplified analysis for a variety of existing iterative methods. Applications to geometry/texture image decomposition schemes are also discussed. A novelty of our framework is to use extensively the notion of a proximity operator, which was introduced by Moreau in the 1960s.

An overview of methods for determining OWA weights

Abstract: The ordered weighted aggregation (OWA) operator has received more and more attention since its appearance. One key point in the OWA operator is to determine its associated weights. In this article, I first briefly review existing main methods for determining the weights associated with the OWA operator, and then, motivated by the idea of normal distribution, I develop a novel practical method for obtaining the OWA weights, which is distinctly different from the existing ones. The method can relieve the influence of unfair arguments on the decision results by weighting these arguments with small values. Some of its desirable properties have also been investigated. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 843–865, 2005.

The factorized S-matrix of CFT/AdS

Abstract: We argue that the recently discovered integrability in the large-N CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory's dilatation operator nor the string sigma model's quantum hamiltonian, but instead the respective factorized S-matrix. To illustrate the idea, we focus on the closed fermionic (1|1) sector of the = 4 gauge theory. We introduce a new technique, the perturbative asymptotic Bethe ansatz, and use it to extract this sector's three-loop S-matrix from Beisert's involved algebraic work on the three-loop (2|3) sector. We then show that the current knowledge about semiclassical and near-plane-wave quantum strings in the (2), (1|1) and (2) sectors of AdS5 × S5 is fully consistent with the existence of a factorized S-matrix. Analyzing the available information, we find an intriguing relation between the three associated S-matrices. Assuming that the relation also holds in gauge theory, we derive the three-loop S-matrix of the (2) sector even though this sector's dilatation operator is not yet known beyond one loop. The resulting Bethe ansatz reproduces the three-loop anomalous dimensions of twist-two operators recently conjectured by Kotikov, Lipatov, Onishchenko and Velizhanin, whose work is based on a highly complex QCD computation of Moch, Vermaseren and Vogt.

The Multiple-Sets Split Feasibility Problem and Its Applications for Inverse Problems

Abstract: The multiple-sets split feasibility problem requires finding a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator's range. It generalizes the convex feasibility problem as well as the two-sets split feasibility problem. We propose a projection algorithm that minimizes a proximity function that measures the distance of a point from all sets. The formulation, as well as the algorithm, generalize earlier work on the split feasibility problem. We offer also a generalization to proximity functions with Bregman distances. Application of the method to the inverse problem of intensity-modulated radiation therapy treatment planning is studied in a separate companion paper and is here only described briefly.

Efficient and accurate approximations to the molecular spin-orbit coupling operator and their use in molecular g-tensor calculations.

Abstract: Approximations to the Breit-Pauli form of the spin-orbit coupling (SOC) operator are examined. The focus is on approximations that lead to an effective quasi-one-electron operator which leads to efficient property evaluations. In particular, the accurate spin-orbit mean-field (SOMF) method developed by Hess, Marian, Wahlgren, and Gropen is examined in detail. It is compared in detail with the “effective potential” spin-orbit operator commonly used in density functional theory (DFT) and which has been criticized for not including the spin-other orbit (SOO) contribution. Both operators contain identical one-electron and Coulomb terms since the SOO contribution to the Coulomb term vanishes exactly in the SOMF treatment. Since the DFT correlation functional only contributes negligibly to the SOC the only difference between the two operators is in the exchange part. In the SOMF approximation, the SOO part is equal to two times the spin-same orbit contribution. The DFT exchange contribution is of the wrong sign...

Articulated Body Motion Capture by Stochastic Search

Abstract: We develop a modified particle filter which is shown to be effective at searching the high-dimensional configuration spaces (c. 30 + dimensions) encountered in visual tracking of articulated body motion. The algorithm uses a continuation principle, based on annealing, to introduce the influence of narrow peaks in the fitness function, gradually. The new algorithm, termed annealed particle filtering, is shown to be capable of recovering full articulated body motion efficiently. A mechanism for achieving a soft partitioning of the search space is described and implemented, and shown to improve the algorithm's performance. Likewise, the introduction of a crossover operator is shown to improve the effectiveness of the search for kinematic trees (such as a human body). Results are given for a variety of agile motions such as walking, running and jumping.

Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck operators

Abstract: This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all points, we define a diffusion distance between any two data points and show that the low dimensional representation of the data by the first few eigenvectors of the corresponding Markov matrix is optimal under a certain mean squared error criterion. Furthermore, assuming that data points are random samples from a density $p(\x) = e^{-U(\x)}$ we identify these eigenvectors as discrete approximations of eigenfunctions of a Fokker-Planck operator in a potential $2U(\x)$ with reflecting boundary conditions. Finally, applying known results regarding the eigenvalues and eigenfunctions of the continuous Fokker-Planck operator, we provide a mathematical justification for the success of spectral clustering and dimensional reduction algorithms based on these first few eigenvectors. This analysis elucidates, in terms of the characteristics of diffusion processes, many empirical findings regarding spectral clustering algorithms.

Detecting primary receivers for cognitive radio applications

Abstract: In this paper we develop a framework for competition of future operators likely to operate in a mixed commons/property-rights regime under the regulation of a spectrum policy server (SPS). The operators dynamically compete for customers as well as portions of available spectrum. The operators are charged by the SPS for the amount of bandwidth they use in their services. Through demand responsive pricing, the operators try to come up with convincing service offers for the customers, while trying to maximize their profits. We first consider a single-user system as an illustrative example. We formulate the competition between the operators as a non-cooperative game and propose an SPS-based iterative bidding scheme that results in Nash equilibrium of the game. Numerical results suggest that, competition increases the user's (customer's) acceptance probability of the offered service, while reducing the profits achieved by the operators. It is also observed that as the cost of unit bandwidth increases relative to the cost of unit infrastructure (fixed cost), the operator with superior technology (higher fixed cost) becomes more competitive. We then extend the framework to a multiuser setting where the operators are competing for a number of users at once. We propose an SPS-based bandwidth allocation scheme in which the SPS optimally allocates bandwidth portions for each user-operator session to maximize its overall expected revenue resulting from the operator payments. Comparison of the performance of this scheme to one in which the bandwidth is equally shared between the user-operator pairs reveals that such an SPS-based scheme improves the user acceptance probabilities and the bandwidth utilization in multiuser systems

Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians

Abstract: Kohn's Proof of the Hypoellipticity of the Hormander Operators.- Compactness Criteria for the Resolvent of Schrodinger Operators.- Global Pseudo-differential Calculus.- Analysis of some Fokker-Planck Operator.- Return to Equillibrium for the Fokker-Planck Operator.- Hypoellipticity and Nilpotent Groups.- Maximal Hypoellipticity for Polynomial of Vector Fields and Spectral Byproducts.- On Fokker-Planck Operators and Nilpotent Techniques.- Maximal Microhypoellipticity for Systems and Applications to Witten Laplacians.- Spectral Properties of the Witten-Laplacians in Connection with Poincare Inequalities for Laplace Integrals.- Semi-classical Analysis for the Schrodinger Operator: Harmonic Approximation.- Decay of Eigenfunctions and Application to the Splitting.- Semi-classical Analysis and Witten Laplacians: Morse Inequalities.- Semi-classical Analysis and Witten Laplacians: Tunneling Effects.- Accurate Asymptotics for the Exponentially Small Eigenvalues of the Witten Laplacian.- Application to the Fokker-Planck Equation.- Epilogue.- Index.

Mond-Pecaric Method in Operator Inequalities

Abstract: In Chapter 1 a very brief and rapid review of some basic topics in Jensen's inequality for positive linear maps and Kantorovich inequality for several types are given. Some basic ideas and the viewpoints of the Mond-Peceric method are given. In Chapter 2 general converses of Jensen's inequality are considered. The Mond-Peceric method is used to obtain the bounds. Many interesting inequalities are particularly considered. In Chapter 3 a generalization of a theorem of Li-Mathias for the normalized positive linear maps as an application of the Mond-Peceric method is considered. Lower and upper bounds in converses of Jensen's type inequalities are given. The cases of the sharp inequalities are investigated. The conversions of Jensen's inequality and other inequalities are particularly considered. In Chapter 4 the previous results and the same methods are applied to obtain the inequalities for the means. Reverse inequalities of power operator means on positive linear maps are studied. Several properties of power operator means under the chaotic order are considered. New bounds in inequalities for power operator means are given. In chapter 5 the theory of operator means established by Kubo and Ando assocaiated with the operator monotone functions is introduced. Based on complementary inequalities to Jensen's inequalities on positive linear maps, complementary inequalities to Ando's inequalities assocaiated with operator means are studied. In Chapter 6 the results and the same methods in the chapter 2 are applied to obtain the inequalities for the Hadamard product. Then the reverses inequalities on the Hadamard product of operators and operator means are considered. General inequalities for the Hadamard product of operators are observed. In chapter 7 a brief survey of several applications of both Furuta inequality and generalized Furuta inequality is given. In Chapter 8 the claims preserving the operator order and the chaotic order are considered as an application of the Mond-Peceric method. The overall results on the functions which preserve the operator order and the chaotic order are particularly considered.

Demand responsive pricing and competitive spectrum allocation via a spectrum server

Abstract: In this paper we develop a framework for competition of future operators likely to operate in a mixed commons/property-rights regime under the regulation of a spectrum policy server (SPS). The operators dynamically compete for customers as well as portions of available spectrum. The operators are charged by the SPS for the amount of bandwidth they use in their services. Through demand responsive pricing, the operators try to come up with convincing service offers for the customers, while trying to maximize their profits. We first consider a single-user system as an illustrative example. We formulate the competition between the operators as a non-cooperative game and propose an SPS-based iterative bidding scheme that results in a Nash equilibrium of the game. Numerical results suggest that, competition increases the user's (customer's) acceptance probability of the offered service, while reducing the profits achieved by the operators. It is also observed that as the cost of unit bandwidth increases relative to the cost of unit infrastructure (fixed cost), the operator with superior technology (higher fixed cost) becomes more competitive. We then extend the framework to a multiuser setting where the operators are competing for a number of users at once. We propose an SPS-based bandwidth allocation scheme in which the SPS optimally allocates bandwidth portions for each user-operator session to maximize its overall expected revenue resulting from the operator payments. Comparison of the performance of this scheme to one in which the bandwidth is equally shared between the user-operator pairs reveals that such an SPS-based scheme improves the user acceptance probabilities and the bandwidth utilization in multiuser systems

Operator placement for in-network stream query processing

Abstract: In sensor networks, data acquisition frequently takes place at low-capability devices. The acquired data is then transmitted through a hierarchy of nodes having progressively increasing network band-width and computational power. We consider the problem of executing queries over these data streams, posed at the root of the hierarchy. To minimize data transmission, it is desirable to perform "in-network" query processing: do some part of the work at intermediate nodes as the data travels to the root. Most previous work on in-network query processing has focused on aggregation and inexpensive filters. In this paper, we address in-network processing for queries involving possibly expensive conjunctive filters, and joins. We consider the problem of placing operators along the nodes of the hierarchy so that the overall cost of computation and data transmission is minimized. We show that the problem is tractable, give an optimal algorithm, and demonstrate that a simpler greedy operator placement algorithm can fail to find the optimal solution. Finally we define a number of interesting variations of the basic operator placement problem and demonstrate their hardness.

CIXL2: a crossover operator for evolutionary algorithms based on population features

Abstract: In this paper we propose a crossover operator for evolutionary algorithms with real values that is based on the statistical theory of population distributions The operator is based on the theoretical distribution of the values of the genes of the best individuals in the population The proposed operator takes into account the localization and dispersion features of the best individuals of the population with the objective that these features would be inherited by the offspring Our aim is the optimization of the balance between exploration and exploitation in the search process In order to test the efficiency and robustness of this crossover, we have used a set of functions to be optimized with regard to different criteria, such as, multimodality, separability, regularity and epistasis With this set of functions we can extract conclusions in function of the problem at hand We analyze the results using ANOVA and multiple comparison statistical tests As an example of how our crossover can be used to solve artificial intelligence problems, we have applied the proposed model to the problem of obtaining the weight of each network in a ensemble of neural networks The results obtained are above the performance of standard methods

An adaptive pursuit strategy for allocating operator probabilities

Abstract: Learning the optimal probabilities of applying an exploration operator from a set of alternatives can be done by self-adaptation or by adaptive allocation rules In this paper we consider the latter option The allocation strategies discussed in the literature basically belong to the class of probability matching algorithms These strategies adapt the operator probabilities in such a way that they match the reward distribution In this paper we introduce an alternative adaptive allocation strategy, called the adaptive pursuit method We compare this method with the probability matching approach in a non-stationary environment Calculations and experimental results show the superior performance of the adaptive pursuit algorithm If the reward distributions stay stationary for some time, the adaptive pursuit method converges rapidly and accurately to an operator probability distribution that results in a much higher probability of selecting the current optimal operator and a much higher average reward than with the probability matching strategy Yet most importantly, the adaptive pursuit scheme remains sensitive to changes in the reward distributions, and reacts swiftly to non-stationary shifts in the environment

BMO spaces related to Schrödinger operators with potentials satisfying a reverse Hölder inequality

Abstract: We identify the dual space of the Hardy-type space related to the time independent Schrodinger operator =−Δ+V, with V a potential satisfying a reverse Holder inequality, as a BMO-type space . We prove the boundedness in this space of the versions of some classical operators associated to (Hardy-Littlewood, semigroup and Poisson maximal functions, square function, fractional integral operator). We also get a characterization of in terms of Carlesson measures.

Dispersive estimates for principally normal pseudodifferential operators

Abstract: The aim of these notes is to describe some recent re- sults concerning dispersive estimates for principally normal pseu- dodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used to prove L q Carleman inequalities, which in turn yield unique continuation results for various partial differential operators with rough poten- tials. Dispersive estimates are L q estimates for nonelliptic partial differ- ential operators which are a consequence of the decay properties of their fundamental solutions. These decay properties follow from spa- tial spreading of the singularities of the solutions. Since solutions prop- agate in directions conormal to the characteristic set of the operator, this spreading can be related to nonzero curvatures of the characteristic set. Dispersive estimates for constant coefficient operators are closely related to the restriction theorem in harmonic analysis. Various types of dispersive estimates are known to be true for op- erators such as the wave operator, the Schrodinger operator and the linear KdV, see Ginibre-Velo (4), Keel-Tao (11). They have proved to be useful in the study of nonlinear problems, as well as of problems with unbounded potentials. More recently, similar estimates have been obtained for wave op- erators with variable coefficients, beginning with the smooth case in Kapitanskii (10), Mockenhaupt, Seeger and Sogge (14), up to operators with C 2 coefficients in Smith (15) and Tataru (21), (23). Similar results were obtained for the Schrodinger equation in Staffilani-Tataru (19) (C 2 coefficients) and in Burq-Gerard-Tzvetkov (1) (smooth coeffic ients). In the variable coefficient elliptic case one should also mention Sogge's L q

A multivariate balance operator for variational ocean data assimilation

Abstract: It is common in meteorological applications of variational assimilation to specify the error covariances of the model background state implicitly via a transformation from model space where variables are highly correlated to a control space where variables can be considered to be approximately uncorrelated. An important part of this transformation is a balance operator which effectively establishes the multivariate component of the error covariances. The use of this technique in ocean data assimilation is less common. This paper describes a balance operator that can be used in a variable transformation for oceanographic applications of three- and four-dimensional variational assimilation. The proposed balance operator has been implemented in an incremental variational data assimilation system for a global ocean general-circulation model. Evidence that the balance operator can explain a significant percentage of background-error variance is presented. The multivariate analysis structures implied by the balance operator are illustrated using single-observation experiments. Copyright © 2005 Royal Meteorological Society

Inverse spectral problems for Sturm–Liouville operators on graphs

Abstract: Sturm–Liouville differential operators on compact graphs without cycles (i.e. on trees) are studied. We establish properties of the spectral characteristics and investigate two inverse problems of recovering the operator from the so-called Weyl functions and from a system of spectra. For these inverse problems, we prove the uniqueness theorems and obtain a procedure for constructing the solution by the method of spectral mappings.

An overview of methods for determining OWA weights: Research Articles

Abstract: The ordered weighted aggregation (OWA) operator has received more and more attention since its appearance. One key point in the OWA operator is to determine its associated weights. In this article, I first briefly review existing main methods for determining the weights associated with the OWA operator, and then, motivated by the idea of normal distribution, I develop a novel practical method for obtaining the OWA weights, which is distinctly different from the existing ones. The method can relieve the influence of unfair arguments on the decision results by weighting these arguments with small values. Some of its desirable properties have also been investigated. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 843–865, 2005.

Well-founded and Stable Semantics of Logic Programs with Aggregates

Abstract: In this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define extensions of the Kripke-Kleene, the well-founded and the stable semantics for aggregate programs. The semantics is based on the concept of a three-valued immediate consequence operator of an aggregate program. Such an operator approximates the standard two-valued immediate consequence operator of the program, and induces a unique Kripke-Kleene model, a unique well-founded model and a collection of stable models. We study different ways of defining such operators and thus obtain a framework of semantics, offering different trade-offs between precision and tractability. In particular, we investigate conditions on the operator that guarantee that the computation of the three types of semantics remains on the same level as for logic programs without aggregates. Other results show that, in practice, even efficient three-valued immediate consequence operators which are very low in the precision hierarchy, still provide optimal precision.

CR invariant powers of the sub-Laplacian

Abstract: CR invariant differential operators on densities with leading part a power of the sub-Laplacian are derived. One family of such operators is constructed from the ``conformally invariant powers of the Laplacian'' via the Fefferman metric; the powers which arise for these operators are bounded in terms of the dimension. A second family is derived from a CR tractor calculus which is developed here; this family includes operators for every positive power of the sub-Laplacian. This result together with work of Cap, Slovak and Soucek imply in three dimensions the existence of a curved analogue of each such operator in flat space.

Hybrid crossover operators for real-coded genetic algorithms: an experimental study

Abstract: Most real-coded genetic algorithm research has focused on developing effective crossover operators, and as a result, many different types have been proposed. Some forms of crossover operators are more suitable to tackle certain problems than others, even at the different stages of the genetic process in the same problem. For this reason, techniques which combine multiple crossovers have been suggested as alternative schemes to the common practice of applying only one crossover model to all the elements in the population. Therefore, the study of the synergy produced by combining the different styles of the traversal of solution space associated with the different crossover operators is an important one. The aim is to investigate whether or not the combination of crossovers perform better than the best single crossover amongst them. In this paper we have undertaken an extensive study in which we have examined the synergetic effects among real-parameter crossover operators with different search biases. This has been done by means of hybrid real-parameter crossover operators, which generate two offspring for every pair of parents, each one with a different crossover operator. Experimental results show that synergy is possible among real-parameter crossover operators, and in addition, that it is responsible for improving performance with respect to the use of a single crossover operator.

A Borg-Levinson theorem for trees

Abstract: We prove that the Dirichelet-to-Neumann map for a Schrodinger operator on a finite simply connected tree determines uniquely the potential on that tree.

Error bounds for approximate value iteration

Abstract: Approximate Value Iteration (AVI) is an method for solving a Markov Decision Problem by making successive calls to a supervised learning (SL) algorithm. Sequence of value representations Vn are processed iteratively by Vn+1 = ATVn where T is the Bellman operator and A an approximation operator. Bounds on the error between the performance of the policies induced by the algorithm and the optimal policy are given as a function of weighted Lp-norms (p ≥ 1) of the approximation errors. The results extend usual analysis in L∞-norm, and allow to relate the performance of AVI to the approximation power (usually expressed in Lp-norm, for p = 1 or 2) of the SL algorithm. We illustrate the tightness of these bounds on an optimal replacement problem.

Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials

Abstract: This paper deals with explicit spectral gap estimates for the linearized Boltzmann operator with hard potentials (and hard spheres). We prove that it can be reduced to the Maxwellian case, for which explicit estimates are already known. Such a method is constructive, does not rely on Weyl's Theorem and thus does not require Grad's splitting. The more physical idea of the proof is to use geometrical properties of the whole collision operator. In a second part, we use the fact that the Landau operator can be expressed as the limit of the Boltzmann operator as collisions become grazing in order to deduce explicit spectral gap estimates for the linearized Landau operator with hard potentials.