arXiv subjects

Alain Kangabire

Publications and source records attributed to Alain Kangabire.

2 recordsLinked to original sources

arXiv2024

Bounds on the fractal uncertainty exponent and a spectral gap

We prove two results on Fractal Uncertainty Principle (FUP) for discrete Cantor sets with large alphabets. First, we give an example of an alphabet with dimension $δ\in (\frac12,1)$ where the FUP exponent is exponentially small as the size of the alphabet grows. Secondly, for $δ\in (0,\frac12]$ we show that a similar alphabet has a large FUP exponent, arbitrarily close to the optimal upper bound of $\frac12-\frac\delta2$, if we dilate the Fourier transform by a factor satisfying a generic Diophantine condition. We give an application of the latter result to spectral gaps for open quantum baker's maps.

math.AP↗

arXiv2021

A Dynamical Model for the Origin of Anisogamy

The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Using theoretical analysis and numerical simulation, we demonstrate that competition between individuals that is linked to the mean gamete size will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.

q-bio.PE↗