Related papers: G-coupling functions
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
An explicit formula is given for a fundamental solution for a class of semielliptic operators. The fundamental solution is used to investigate properties of these operators as mappings between weighted function spaces. Necessary and…
Flow- and context-sensitive points-to analysis is difficult to scale; for top-down approaches, the problem centers on repeated analysis of the same procedure; for bottom-up approaches, the abstractions used to represent procedure summaries…
Gauge-fixed correlation functions are a valuable tool in intermediate steps when determining gauge-invariant physics. However, when obtaining them in different calculations, it is necessary to use exactly the same definition of the gauge to…
In this paper we introduce new generalizations of the zeta function, the Tricomi functions; their main properties are studied. This opens the way to a deeper, better application of these functions both in the theory of special functions,…
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…
Gaussian processes (GPs) are the main surrogate functions used for sequential modelling such as Bayesian Optimization and Active Learning. Their drawbacks are poor scaling with data and the need to run an optimization loop when using a…
Analytic functions represent the state-of-the-art way of performing complex data analysis within a single SQL statement. In particular, an important class of analytic functions that has been frequently used in commercial systems to support…
Parallel coordinate plots (PCP) are a useful tool in exploratory data analysis of high-dimensional numerical data. The use of PCPs is limited when working with categorical variables or a mix of categorical and continuous variables. In this…
Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from…
Deep Reinforcement Learning has shown significant progress in extracting useful representations from high-dimensional inputs albeit using hand-crafted auxiliary tasks and pseudo rewards. Automatically learning such representations in an…
The idea of calibrated recommendations is that the properties of the items that are suggested to users should match the distribution of their individual past preferences. Calibration techniques are therefore helpful to ensure that the…
The convolution of a function with an isotropic Gaussian appears in many contexts such as differential equations, computer vision, signal processing, and numerical optimization. Although this convolution does not always have a closed form…
This article highlights some of the key operating principles of Grover algorithm. These principles were used to develop a new oracle function, that illustrates the possibility of using Grover algorithm for solving more realistic and…
In product design, a decomposition of the overall product function into a set of smaller, interacting functions is usually considered a crucial first step for any computer-supported design tool. Here, we propose a new approach for the…
Structural parameters are normally extracted from observed galaxies by fitting analytic light profiles to the observations. Obtaining accurate fits to high-resolution images is a computationally expensive task, requiring many model…
Productions functions map the inputs of a firm or a productive system onto its outputs. This article expounds generalizations of the production function that include state variables, organizational structures and increasing returns to…
Genetic Algorithms (GAs) are used to solve search and optimization problems in which an optimal solution can be found using an iterative process with probabilistic and non-deterministic transitions. However, depending on the problem's…
Inspired by biological neurons, the activation functions play an essential part in the learning process of any artificial neural network commonly used in many real-world problems. Various activation functions have been proposed in the…
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…