Finding accurate reduced descriptions for large, complex, dynamically evolving networks is a crucial enabler to their simulation, analysis, and ultimately design. Here, we propose and illustrate a systematic and powerful approach to obtaining good collective coarse-grained observables-variables successfully summarizing the detailed state of such networks. Finding such variables can naturally le...

Recent advances in understanding circadian (daily) rhythms in the genera Neurospora, Gonyaulax, and Synechococcus are reviewed and new complexities in their circadian systems are described. The previous model, consisting of a unidirectional flow of information from input to oscillator to output, has now expanded to include multiple input pathways, multiple oscillators, multiple outputs; and fee...

OF THE THESIS OSCILLATOR STRENGTHS FROM TIME-DEPENDENT DENSITY FUNCTIONAL THEORY by Heiko Appel Thesis Director: Kieron Burke We consider different forms of single-pole approximations (SPA) for oscillator-strengths in the response formalism of time-dependent density functional theory. Numerical calculations of oscillator strengths are presented for a simple model system, Hooke’s atom, and vario...

In its most basic form an oscillator consists of a resonator driven on resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic regime. Contrary to this conventional ...

A Lie algebra is said to be metric if it admits a symmetric, invariant, and non-degenerate bilinear form. The harmonic oscillator algebra, which arises in the quantum mechanical description of oscillator, smallest solvable non-abelian example. This first step countable series algebras that support invariant Lorentzian forms. Generalizing this situation, paper, we arrive at K-algebras as double ...

A new conceptual model for ENSO has been constructed based upon the positive feedback of tropical ocean– atmosphere interaction proposed by Bjerknes as the growth mechanism and the recharge–discharge of the equatorial heat content as the phase-transition mechanism suggested by Cane and Zebiak and by Wyrtki. This model combines SST dynamics and ocean adjustment dynamics into a coupled basinwide ...