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.

Operator growth in the SYK model

Abstract: We discuss the probability distribution for the “size” of a time-evolving operator in the SYK model. Scrambling is related to the fact that as time passes, the distribution shifts towards larger operators. Initially, the rate is exponential and determined by the infinite-temperature chaos exponent. We evaluate the size distribution numerically for N = 30, and show how to compute it in the large-N theory using the dressed fermion propagator. We then evaluate the distribution explicitly at leading nontrivial order in the large-q expansion.

On a Fractional Operator Combining Proportional and Classical Differintegrals

Abstract: The Caputo fractional derivative has been one of the most useful operators for modelling non-local behaviours by fractional differential equations. It is defined, for a differentiable function f ( t ) , by a fractional integral operator applied to the derivative f ′ ( t ) . We define a new fractional operator by substituting for this f ′ ( t ) a more general proportional derivative. This new operator can also be written as a Riemann–Liouville integral of a proportional derivative, or in some important special cases as a linear combination of a Riemann–Liouville integral and a Caputo derivative. We then conduct some analysis of the new definition: constructing its inverse operator and Laplace transform, solving some fractional differential equations using it, and linking it with a recently described bivariate Mittag-Leffler function.

Analysis Operator Learning and its Application to Image Reconstruction

Abstract: Exploiting a priori known structural information lies at the core of many image reconstruction methods that can be stated as inverse problems. The synthesis model, which assumes that images can be decomposed into a linear combination of very few atoms of some dictionary, is now a well established tool for the design of image reconstruction algorithms. An interesting alternative is the analysis model, where the signal is multiplied by an analysis operator and the outcome is assumed to be sparse. This approach has only recently gained increasing interest. The quality of reconstruction methods based on an analysis model severely depends on the right choice of the suitable operator. In this paper, we present an algorithm for learning an analysis operator from training images. Our method is based on lp-norm minimization on the set of full rank matrices with normalized columns. We carefully introduce the employed conjugate gradient method on manifolds, and explain the underlying geometry of the constraints. Moreover, we compare our approach to state-of-the-art methods for image denoising, inpainting, and single image super-resolution. Our numerical results show competitive performance of our general approach in all presented applications compared to the specialized state-of-the-art techniques.

Operator loading tasks.

Abstract: The purpose of this paper is: (1) To review the rationale of measuring operator workload in terms of auxiliary, or secondary task performance scores; (2) To summarize the important characteristics ...

Method of response synthesis in a driver assistance system

Abstract: A method (600) of synthesizing a response to an operating situation of a vehicle includes the step of generating a master condition list (602), determining the existence of an operating situation (604), determining an operator cognitive load (606) and determining a response to the operating situation based in part on the master condition list and the operator cognitive load (608). The master condition list is a fusion of sensor data gathered within and around the vehicle. The operator cognitive load is a measure of the operator's ability to handle tasks within the vehicle.