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.

Traces and determinants of linear operators

Abstract: A general theory of tracestr D A and determinantsdet D (I+A) in normed algebrasD of operators acting in Banach spacesB is proposed. In this approach trace and determinant are defined as continuous extensions of the corresponding functionals from finite dimensional operators. We characterize the algebras for which such extensions exist and describe sets of possible values of traces and determinants for the same operator in different algebras. In spite of the fact that the extended traces and determinants may differ in different algebrasD, operatorI+A (withA ∈D) is invertible inB if and only ifdet D (I+A) does not vanish. Cramer's rule and formulas for the resolvent are obtained and they are expressed in different algebras by the same formulas viadet D (I+A) andtr D (A). A large set of examples and illustrations are also presented.

Ten equivalent definitions of the fractional laplace operator

Abstract: This article reviews several definitions of the fractional Laplace operator (-Delta)^{alpha/2} (0 < alpha < 2) in R^d, also known as the Riesz fractional derivative operator, as an operator on Lebesgue spaces L^p, on the space C_0 of continuous functions vanishing at infinity and on the space C_{bu} of bounded uniformly continuous functions. Among these definitions are ones involving singular integrals, semigroups of operators, Bochner's subordination and harmonic extensions. We collect and extend known results in order to prove that all these definitions agree: on each of the function spaces considered, the corresponding operators have common domain and they coincide on that common domain.

OWA aggregation over a continuous interval argument with applications to decision making

Abstract: We briefly describe the ordered weighted average (OWA) operator. We discuss its role in decision making under uncertainty. We provide an extension of the OWA operator to the case in which our argument is a continuous valued interval rather than a finite set of values. We look at some examples of this type of aggregation. We show how it can be used in some tasks that arise in decision making. We consider the extension of the continuous interval argument OWA operator to the more general case in which the argument values have importance weights. We use this to introduce the idea of an attitudinal-based expected value associated with a continuous random variable.

Integrating scale out and fault tolerance in stream processing using operator state management

Abstract: As users of "big data" applications expect fresh results, we witness a new breed of stream processing systems (SPS) that are designed to scale to large numbers of cloud-hosted machines. Such systems face new challenges: (i) to benefit from the "pay-as-you-go" model of cloud computing, they must scale out on demand, acquiring additional virtual machines (VMs) and parallelising operators when the workload increases; (ii) failures are common with deployments on hundreds of VMs-systems must be fault-tolerant with fast recovery times, yet low per-machine overheads. An open question is how to achieve these two goals when stream queries include stateful operators, which must be scaled out and recovered without affecting query results.Our key idea is to expose internal operator state explicitly to the SPS through a set of state management primitives. Based on them, we describe an integrated approach for dynamic scale out and recovery of stateful operators. Externalised operator state is checkpointed periodically by the SPS and backed up to upstream VMs. The SPS identifies individual operator bottlenecks and automatically scales them out by allocating new VMs and partitioning the checkpointed state. At any point, failed operators are recovered by restoring checkpointed state on a new VM and replaying unprocessed tuples. We evaluate this approach with the Linear Road Benchmark on the Amazon EC2 cloud platform and show that it can scale automatically to a load factor of L=350 with 50 VMs, while recovering quickly from failures.