34 research outputs found
Asymptotic analysis of noisy fitness maximization, applied to metabolism and growth
We consider a population dynamics model coupling cell growth to a diffusion
in the space of metabolic phenotypes as it can be obtained from realistic
constraints-based modelling. In the asymptotic regime of slow diffusion, that
coincides with the relevant experimental range, the resulting non-linear
Fokker-Planck equation is solved for the steady state in the WKB approximation
that maps it into the ground state of a quantum particle in an Airy potential
plus a centrifugal term. We retrieve scaling laws for growth rate fluctuations
and time response with respect to the distance from the maximum growth rate
suggesting that suboptimal populations can have a faster response to
perturbations.Comment: 24 pages, 6 figure
Bethe Ansatz and the Spectral Theory of affine Lie algebra--valued connections II. The non simply--laced case
We assess the ODE/IM correspondence for the quantum -KdV model,
for a non-simply laced Lie algebra . This is done by studying a
meromorphic connection with values in the Langlands dual algebra of the affine
Lie algebra , and constructing the relevant -system
among subdominant solutions. We then use the -system to prove that the
generalized spectral determinants satisfy the Bethe Ansatz equations of the
quantum -KdV model. We also consider generalized Airy functions
for twisted Kac--Moody algebras and we construct new explicit solutions to the
Bethe Ansatz equations. The paper is a continuation of our previous work on the
ODE/IM correspondence for simply-laced Lie algebras.Comment: 37 pages, 1 figure. Continuation of arXiv:1501.07421. Minor change in
the title. New subsection 5.1 on the action of the Weyl group on the Bethe
Ansatz solution