The study of monotone Boolean functions (MBFs) has a long history. We explore connection between MBFs and ordinary differential equation (ODE) models gene regulation, and, in particular, problem the realization an MBF as function describing state transition graph ODE. formulate joint realizability finite collections by establishing parameterized dynamics class ODEs collection MBFs. pose questio...

A second-order total variation diminishing (TVD) method with variable flux limiters is proposed to overcome the non-realizability issue, which has been one of major obstacles in applying conventional TVD schemes moment transport equations. In present method, a realizable set at cell face reconstructed by allowing flexible selection limiter values within region. Necessary conditions for scheme s...

Despite their long history in experiment, simulation, and analytical theory, pair correlation functions that describe local order in many-body systems still retain a legacy of mathematical mysteries. One such open question concerns “realizability” of a given candidate pair correlation function, namely whether it actually represents the pair correlation for some spatial distribution of particles...

During the last twenty years or so a wide range of realizability interpretations of classical analysis have been developed. In many cases, these are achieved by extending the base interpreting system of primitive recursive functionals with some form of bar recursion, which realizes the negative translation of either countable or countable dependent choice. In this work we present the many varia...

Abstract Requirements formalization has become increasingly popular in industrial settings as an effort to disambiguate designs and optimize development time costs for critical system components. Formal requirements elicitation also enables the employment of analysis tools prove important properties, such consistency realizability. In this paper, we present realizability framework that develope...

In this paper we propose a new approach to realizability interpretations for nonstandard arithmetic. We deal with analysis in the context of (semi)intuitionistic realizability, focusing on Lightstone-Robinson construction model through an ultrapower. particular, consider extension $\lambda$-calculus memory cell, that contains integer (the state), order indicate which slice ultrapower $\cal{M}^{...

Introduction The purpose of this short paper is to sketch the development of a few basic topics in the history of Realizability. The number of topics is quite limited and reeects very much my own personal taste, prejudices and area of competence. Realizability has, over the past 60 years, developed into a subject of such dimensions that a comprehensive overview would require a fat book. Maybe s...