Comprehensive understanding of gene regulatory networks (GRNs) is a major challenge in the field of systems biology. Currently, there are two main approaches in GRN analysis using time-course observation data, namely an ordinary differential equation (ODE)-based approach and a statistical model-based approach. The ODE-based approach can generate complex dynamics of GRNs according to biologicall...

We propose in this paper a new nonlinear mathematical model of an oscillating water column (OWC). The one-dimensional shallow equations the presence device are reformulated as transmission problem related to interaction between waves and fixed partially immersed structure. By imposing conservation total fluid-OWC energy non-damped scenario, we able derive condition that involves time-dependent ...

This paper concerns a general class of PDE-ODE reaction-diffusion systems, which features singular fast-reaction limit towards equation coupled to scalar hysteresis operator. As prototypical application, we present PDE model for the growth population according given food supply an ODE turnover stock. Under realistic conditions stock is much faster than yielding intrinsic scaling parameter. We...

Ordinary differential equation (ODE) systems are commonly used many different fields. The de-facto method to implement an ODE system in Python programming using SciPy requires the entire system to be implemented as a single function, which only allow for inline documentation. Although each equation can be broken up into sub-equations, there is no compart-mentalization of sub-equations to its OD...

<abstract><p>In this note we study existence of positive radial solutions in annuli and exterior domains for a class nonlinear equations driven by Pucci extremal operators subject to Hénon type weight. Our approach is based on the shooting method applied corresponding ODE problem, energy arguments, associated flow an autonomous quadratic dynamical system.</p></abstract>

In this work, we investigate invariance analysis, conservation laws, and exact power series solutions of time fractional generalized Drinfeld–Sokolov systems (GDSS) using Lie group analysis. Using point symmetries the Erdelyi–Kober (EK) differential operator, GDSS equation is reduced to a nonlinear ordinary (ODE) order. Moreover, have constructed laws for obtained explicit ODEs that converge. L...

BACKGROUND/AIMS 9-[2-(phosphonomethoxy)ethyl]guanine (PMEG) is one of the most active antiproliferative compounds in a series of acyclic nucleoside phosphonates and is active in intraperitoneal P388 tumors in mice. METHODS We synthesized octadecyloxyethyl (ODE) and hexadecyloxypropyl esters of PMEG and compared their antiproliferative activity with unmodified PMEG in primary human fibroblasts...