Discrete versus continuous domain models for disease mapping

Discrete-Time versus Continuous-Time Models of Neural Networks

In mathematical modeling, very often discrete-time (DT) models are taken from, or can be viewed as numerical discretizations of, certain continuous-time (CT) models. In this paper, a general criterion, the asymptotic consistency criterion, for these DT models to inherit the dynamical behavior of their CT counterparts is derived. Detailed instances of this criterion are established for several c...

Continuous versus Discrete Market Games

De Meyer and Moussa Saley [4] provide an endogenous justification for the appearance of Brownian Motion in Finance by modeling the strategic interaction between two asymmetrically informed market makers with a zero-sum repeated game with one-sided information. The crucial point of this justification is the appearance of the normal distribution in the asymptotic behavior of Vn(P ) √ n . In De Me...

Improved Continuous Models for Discrete Media

Surrogate Models for Mixed Discrete-Continuous Variables

Large-scale computational models have become common tools for analyzing complex manmade systems. However, when coupled with optimization or uncertainty quantification methods in order to conduct extensive model exploration and analysis, the computational expense quickly becomes intractable. Furthermore, these models may have both continuous and discrete parameters. One common approach to mitiga...

Discrete versus continuous models in evolutionary dynamics: From simple to simpler-and even simpler-models

There are many different models—both continuous and discrete— used to describe gene mutation fixation. In particular, the Moran process, the Kimura equation and the replicator dynamics are all well known models, that might lead to different conclusions. We present a discussion of a unified framework to embrace all these models, in the large population regime.