Operator (computer programming)

About: Operator (computer programming) is a research topic. Over the lifetime, 40896 publications have been published within this topic receiving 671452 citations. The topic is also known as: operator symbol & operator name.

Distributed Pareto Optimization via Diffusion Strategies

Abstract: We consider solving multi-objective optimization problems in a distributed manner by a network of cooperating and learning agents. The problem is equivalent to optimizing a global cost that is the sum of individual components. The optimizers of the individual components do not necessarily coincide and the network therefore needs to seek Pareto optimal solutions. We develop a distributed solution that relies on a general class of adaptive diffusion strategies. We show how the diffusion process can be represented as the cascade composition of three operators: two combination operators and a gradient descent operator. Using the Banach fixed-point theorem, we establish the existence of a unique fixed point for the composite cascade. We then study how close each agent converges towards this fixed point, and also examine how close the Pareto solution is to the fixed point. We perform a detailed mean-square error analysis and establish that all agents are able to converge to the same Pareto optimal solution within a sufficiently small mean-square-error (MSE) bound even for constant step-sizes. We illustrate one application of the theory to collaborative decision making in finance by a network of agents.

Operator mixing and the BMN correspondence

Abstract: In this note we update the discussion of the BMN correspondence and string interactions in [4] to incorporate the effects of operator mixing. We diagonalize the matrix of two point functions of single and double trace operators, and compute the eigen-operators and their anomalous dimensions to order g22λ'. Operators in different R symmetry multiplets remain degenerate at this order; we propose this is a consequence of supersymmetry. We also calculate the corresponding energy shifts in string theory, and find a discrepancy with field theory results, indicating possible new effects in light-cone string field theory.

Short characteristic solution of the non-LTE line transfer problem by operator perturbation—II. The two-dimensional planar slab

Abstract: We present the formal solution of the transfer problem in terms of the exponential short characteristic method and derive approximate operators that allow for the iterative solution of the non-LTE two-level atom problem. An eigenvalue analysis for the convergence rate of these operators and several approximate operators proposed by other authors is presented. The family of operators presented for the short characteristic approach range from local diagonal approximations to tridiagonal and pentadiagonal operators. The extension to multidimensions of the several proposed approximate operators is discussed.

Nonlinear Diffusion with Fractional Laplacian Operators

Abstract: We describe two models of flow in porous media including nonlocal (long-range) diffusion effects. The first model is based on Darcy’s law and the pressure is related to the density by an inverse fractional Laplacian operator. We prove existence of solutions that propagate with finite speed. The model has the very interesting property that mass preserving self-similar solutions can be found by solving an elliptic obstacle problem with fractional Laplacian for the pair pressure-density. We use entropy methods to show that these special solutions describe the asymptotic behavior of a wide class of solutions.