On Infinitesimal Approximation of a Continuous Function

Insertion of a gamma-continuous function

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

Continuous Piecewise Linear Approximation of BV Function

Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be selfadaptively chosen by balancing the total variation of the target function. In this paper, we adopt continuous piecewise linear approximation instead of the existing piecewise constants approximation. The re...

A continuous approximation fitting to the discrete distributions using ODE

The probability density functions fitting to the discrete probability functions has always been needed, and very important. This paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. The main key in these fittings is the use of the derivative concept and common differential ...

On Continuous-Action Q-Learning via Tile Coding Function Approximation

Reinforcement learning (RL) is a powerful machine-learning methodology that has an established theoretical foundation and has proven effective in a variety of small, simulated domains. There has been considerable work on applying RL, a method originally conceived for discrete state-action spaces, to problems with continuous states. The extension of RL to allow continuous actions, on the other h...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles