Tootfinder

Note on the asymptotic of the auxiliary function
Juan Arias de Reyna
https://arxiv.org/abs/2406.06066 https://arxiv.org/pdf/2406.0606…

Note on the asymptotic of the auxiliary function
To define an explicit regions without zeros of $\mathop{\mathcal R}(s)$, in a previous paper we obtained an approximation to $\mathop{\mathcal R}(s)$ of type $f(s)(1+U)$ with $|U|< 1$. But this $U$ do not tend to zero when $t\to+\infty$. In the present paper we get an approximation of the form $f(s)(1+o(t))$. We precise here Siegel's result, following his reasoning. This is essential to get the last Theorems in Siegel's paper about $\mathop{\mathcal R}(s)$.

I'm feeling extremely 90's today
#retrogaming

This https://arxiv.org/abs/2401.04843 has been replaced.
initial toot: https://mastoxiv.page/@…

Simulation of time crystal behavior for a few boson chiral soliton model in a ring
We present numerical simulations for a chiral soliton model with N=2,3 bosons in a ring, this being a few-particle version of our previous mean-field model for a quantum time crystal. Following Syrwid, Kosior, and Sacha (SKS), the notion is that a precise position measurement of one particle can lead to spontaneous formation of a bright soliton that in a time crystal should rotate intact for at least a few revolutions around the ring. In their work SKS find spontaneous formation of a soliton du…

Implementing engrams from a machine learning perspective: XOR as a basic motif
Jesus Marco de Lucas, Maria Pe\~na Fernandez, Lara Lloret Iglesias
https://arxiv.org/abs/2406.09940 …

Implementing engrams from a machine learning perspective: XOR as a basic motif
We have previously presented the idea of how complex multimodal information could be represented in our brains in a compressed form, following mechanisms similar to those employed in machine learning tools, like autoencoders. In this short comment note we reflect, mainly with a didactical purpose, upon the basic question for a biological implementation: what could be the mechanism working as a loss function, and how it could be connected to a neuronal network providing the required feedback to …