•Neural ODE method predicts future gene expression states of single cells•We demonstrate prediction not observed in training data•Performance is validated by tracking cell cycle over 3 days•Dimensionality reduction required for estimation dynamics Single-cell transcriptomics data yield snapshots levels at the moment cells were killed prior to sequencing. The lack temporal context each hampers a...

Implementation of model-based fault diagnosis systems can be a difficult task due to the complex dynamics most systems, an appealing alternative avoiding modeling is use machine learning-based techniques for which implementation more affordable nowadays. However, latter approach often requires extensive data processing. In this paper, hybrid using recent developments in neural ordinary differen...

In this paper, we consider a mathematical model motivated by patterned growth of bacteria. The model is a system of differential equations that consists of two sub-systems. One is a system of ordinary differential equations and the other one is a reaction-diffusion system. Pattern formation in this model is caused by an initial instability of the ordinary differential equations. However, nonlin...

The effect of a transverse magnetic field on the boundary layer flow and heat transfer of anisothermal stretching cylinder is analyzed. The governing partial differential equations for themagnetohydrodynamic, temperature, and concentration boundary layers are transformed into a setof ordinary differential equations using similarity transformations. The obtained ordinarydifferential equations ar...

DIFFERENTIAL EQUATIONS By H. W. REDDICK, Professor and Head of the Department of Mathematics, Cooper Union School of Engineering. Covers the methods of solving ordinary differential equations, and problems in applied mathematics involving ordinary differential equations. Partial differential equations are not discussed. Noted for the clarity of treatment, the many illustrative examples, and the...

Boundary Layer Flow past a stretching surface with constant wall temperature, of a nanofluid is studied for heat transfer characteristics. The system of partial differential equations describing such a flow is subjected to similarity transformations gives rise to a boundary value problem involving a system of ordinary differential equations. This system is solved by a shooting method. Effect of...