The literature on quantum mechanics in a finite-dimensional Hilbert space is substantial. This paper is devoted to an algebraic model for a quantum oscillator allowing finite-dimensional representations, thus leading to a finite oscillator model. The canonical one-dimensional quantum oscillator (in the convention m = ω = ~ = 1) is described by a position operator q̂, a momentum operator p̂ and a ...

The currently accepted interpretation of the clock and wavefront model of somitogenesis is that a posteriorly moving molecular gradient sequentially slows the rate of clock oscillations, resulting in a spatial readout of temporal oscillations. However, while molecular components of the clocks and wavefronts have now been identified in the pre-somitic mesoderm (PSM), there is not yet conclusive ...

Phase response curves (PRCs) are widely used in circadian clocks, neuroscience, and heart physiology. They quantify the response of an oscillator to pulse-like perturbations. Phase response curves provide valuable information on the properties of oscillators and their synchronization. This chapter discusses biological self-sustained oscillators (circadian clock, physiological rhythms, etc.) in ...