drivers – Which is more stable distro or Tensorflow GPU support on NVIDIA Ti

I am moving from Windows to UBUNTU as I got a lot of positive feedback on its stability and performance with TensorFlow.

  • Which version is more stable with NVIDIA driver for Geforce 1050 Ti, 16.04, 18.04, or 20.04?

I installed 20.04 but when browsing, the driver seems to cause some lag when scrolling pages. Tensorflow works great but that lag is tellimg me the driver is not fully compatible. I don’t know if this is normal or no.

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formatting – Are there ways to make Google Docs page layout more stable across browser & platform?

When I open a Google Doc on different computers, or even different browsers on the same computer, the line, column, & page breaks often (but not always) change. When I use “download” to export the doc to another format, the line, column, & page breaks often (but not always) change.

I’ve tried a variety of different fonts: built-in system fonts, Google fonts installed onto the computer, Google fonts not installed onto the computer. They all seem to change size.

Are there tricks or techniques to reduce this problem?

reference request – Is Fourier dimension finitely stable?

Let $A,B$ be compact subsets of $mathbb R$. Let $a=mathrm{dim}_F(A)$, $b=mathrm{dim}_F(B)$ be their Fourier dimensions, respectively. My questions are as follows:

  1. Is it true that $mathrm{dim}_F(Acup B)=max{a,b}$?

  2. If $A$ and $B$ are positively separated, is it true that $mathrm{dim}_F(Acup B)=max{a,b}$?

  3. In addition to 2, if $Asubseteq (0,1)$ and $Bsubseteq (2,3)$, is it true that $mathrm{dim}_F(Acup B)=max{a,b}$?

  4. In addition to 3, if $a=0$, is it true that $mathrm{dim}_F(Acup B)=b$?

I have searched online but I cannot find any references for that.

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algebraic geometry – Morphism from Automorphism group of stable curve to automorphism group of its dual graph surjective

I currently study the strata of the moduli stack of algebraic curves and have understood, that for a stable curve with markings $p_1, dots, p_n$ there is a morphism of groups $Aut(C, p_1, dots, p_n) to Aut(Gamma)$, where $Gamma$ is the associated stable graph. I also see, that because of automorphisms of the connected components of the normalisation that are not “seen” by the graph, in general this morphism is not injective.

But is it surjective? In all the examples I have considered I think it is, but I do not see a general argument to show that, so I am thankful for any hints.

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algebraic topology – Basic Application of Hirzebruch Signature Theorem in Stable Parallelizability of Homotopy Spheres (Kervaire-Milnor paper)

I am struggling to understand a step in Kervaire-Milnor’s proof of the fact that homotopy spheres are stably parallelizable. (Bottom of p.508, Proof of Theorem 3.1 Case 2 in Kervaire-Milnor, “Groups of Homotopy Spheres: I“).

Let $Sigma$ be a homotopy $4k$-sphere. We are interested in cohomology class $mathfrak{o}_{4}(Sigma)in H^{4k}(Sigma,mathbb{Z})$ which is an obstruction class to the triviality of the vector bundle $TSigma oplus varepsilon^1$ (or equivalently, an obstruction to the stable parallelizability of $Sigma$). It turns out that $mathfrak{o}_{4k}$ is a non-zero multiple of the Pontrjagin class $p_k(TSigma)$.

What I do not understand: supposedly, an application of Hirzebruch signature theorem implies that $p_k(TSigma)$ is a multiple of the signature $sigma(Sigma)$. Why is this the case? Hirzebruch says that the signature is given by a complicated polynomial of Pontrjagin classes (the $L$-genus) evaluated on the fundamental class of $Sigma$. But I do not know where all the terms other than $p_k(TSigma)$ go for the above to be true.