Tootfinder

Equivalence criteria for the two--term functional equations for Herglotz--Zagier functions
Sumukha Sathyanarayana, N. Guru Sharan
https://arxiv.org/abs/2510.10088 https://

Equivalence criteria for the two--term functional equations for Herglotz--Zagier functions
We establish Kronecker limit type formula for the generalized Mordell-Tornheim zeta function $Θ(r,r,t,x)$ as a function of the third argument around $t=1-r$. We then show that the above Kronecker limit type formula is equivalent to the two-term functional equation for the higher Herglotz function obtained by Vlasenko and Zagier. We also show the equivalence between a previously known Kronecker limit type formula for $Θ(1,1,t,x)$ around $t=0$ and the two-term functional equation for the Herglo…

Just finished "Beasts Made of Night" by Tochi Onyebuchi...
Indirect CW for fantasy police state violence.
So I very much enjoyed Onyebuchi's "Riot Baby," and when I grabbed this at the library, I was certain it would be excellent. But having finished it, I'm not sure I like it that much overall?
The first maybe third is excellent, including the world-building, which is fascinating. I feel like Onyebuchi must have played "Shadow of the Colossus" at some point. Onyebuchi certainly does know how to make me care for his characters.
Some spoilers from here on out...
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I felt like it stumbles towards the middle, with Bo's reactions neither making sense in the immediate context, nor in retrospect by the end when we've learned more. Things are a bit floaty in the middle with an unclear picture of what exactly is going on politics-wise and what the motivations are. Here I think there were some nuances that didn't make it to the page, or perhaps I'm just a bit thick and not getting stuff I should be? More is of course revealed by the end, but I still wasn't satisfied with the explanations of things. For example, (spoilers) I don't feel I understand clearly what kind of power the army of aki was supposed to represent within the city? Perhaps necessary to wield the threat of offensive inisisia use? In that case, a single scene somewhere of Izu's faction deploying that tactic would have been helpful I think.
Then towards the end, for me things really started to jumble, with unclear motivations, revelations that didn't feel well-paced or -structured, and a finale where both the action & collapsing concerns felt stilted and disjointed. Particularly the mechanics/ethics of the most important death that set the finale in motion bothered me, and the unexplained mechanism by which that led to what came next? I can read a couple of possible interesting morals into the whole denouement, but didn't feel that any of them were sufficiently explored. Especially if we're supposed to see some personal failing in the protagonist's actions, I don't think it's made clear enough what that is, since I feel his reasons to reject each faction are pretty solid, and if we're meant to either pity or abjure his indecision, I don't think the message lands clearly enough.
There *is* a sequel, which honestly I wasn't sure of after the last page, and which I now very interested in. Beasts is Onyebuchi's debut, which maybe makes sense of me feeling that Riot Baby didn't have the same plotting issues. It also maybe means that Onyebuchi couldn't be sure a sequel would make it to publication in terms of setting up the ending.
Overall I really enjoyed at least 80% of this, but was expecting even better (especially politically) given Onyebuchi's other work, and I didn't feel like I found it.
#AmReading

Division algebras of slice-Nash functions
Cinzia Bisi, Antonio Carbone
https://arxiv.org/abs/2510.09779 https://arxiv.org/pdf/2510.09779

Division algebras of slice-Nash functions
The purpose of this paper is to introduce the notion of Nash functions in the context of slice regular functions of one quaternionic or octonionic variable. We begin with a detailed analysis of the possible definitions of Nash slice regular functions which leads us to the definition of \textit{slice-Nash} function proposed in this paper (and which we strongly believe to be the natural generalisation of the classical real and complex Nash functions to this context). Once the `correct' definition…

Reinforced sequential Monte Carlo for amortised sampling
Sanghyeok Choi, Sarthak Mittal, V\'ictor Elvira, Jinkyoo Park, Nikolay Malkin
https://arxiv.org/abs/2510.11711 https…

Reinforced sequential Monte Carlo for amortised sampling
This paper proposes a synergy of amortised and particle-based methods for sampling from distributions defined by unnormalised density functions. We state a connection between sequential Monte Carlo (SMC) and neural sequential samplers trained by maximum-entropy reinforcement learning (MaxEnt RL), wherein learnt sampling policies and value functions define proposal kernels and twist functions. Exploiting this connection, we introduce an off-policy RL training procedure for the sampler that uses …

Continuous Inverse Ambiguous Functions on Lie Groups
David Schmitz, Sadman Rahman, Anthony Kindness
https://arxiv.org/abs/2510.09958 https://arxiv.org/pdf/…

Continuous Inverse Ambiguous Functions on Lie Groups
In a previous study, the first author defines an inverse ambiguous function on a group $G$ to be a bijective function $f : G \to G$ satisfying the functional equation $f^{-1}(x) = f(x^{-1})$ for all $x \in G$. In this paper, we investigate the existence of continuous inverse ambiguous functions on classical Lie groups. In particular, we look at tori, elliptic curves over various fields, vector spaces, additive matrix groups, and multiplicative matrix groups.

On the construction of Hadamard states from Feynman propagators
Christopher J. Fewster, Alexander Strohmaier
https://arxiv.org/abs/2510.11492 https://arxiv…

On the construction of Hadamard states from Feynman propagators
The Wightman two-point function of any Hadamard state of a linear quantum field theory determines a corresponding Feynman propagator. Conversely, however, a Feynman propagator determines a state only if certain positivity conditions are fulfilled. We point out that the construction of a state from a Feynman propagator involves a slightly subtle point that we address and resolve. Starting from a recent generalisation of the Duistermaat-Hörmander theory of distinguished parametrices to normally …

TyDe 2025 continues:
Jeremy Siek presenting "Gradual Metaprogramming" with proofs in Agda.
https://conf.researchr.org/details/icfp-splash-2025/tyde-2025-papers/1/Gradual-Metaprogramming

Viscosity CBFs: Bridging the Control Barrier Function and Hamilton-Jacobi Reachability Frameworks in Safe Control Theory
Dylan Hirsch, Jaime Fern\'andez Fisac, Sylvia Herbert
https://arxiv.org/abs/2510.09929

Viscosity CBFs: Bridging the Control Barrier Function and Hamilton-Jacobi Reachability Frameworks in Safe Control Theory
Control barrier functions (CBFs) and Hamilton-Jacobi reachability (HJR) are central frameworks in safe control. Traditionally, these frameworks have been viewed as distinct, with the former focusing on optimally safe controller design and the latter providing sufficient conditions for safety. A previous work introduced the notion of a control barrier value function (CB-VF), which is defined similarly to the other value functions studied in HJR but has certain CBF-like properties. In this work, …

An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function
Karin Ikeda
https://arxiv.org/abs/2510.10598 https://

An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function
In 1997, Báez-Duarte gave a probabilistic proof of the asymptotic formula for the partition function, which had originally been proved by Hardy-Ramanujan. Based on the probabilistic approach, this paper proves an asymptotic formula for the coefficients of the elliptic modular $j$-function using various expressions in terms of modular functions having simple infinite products.

Arithmetic Hirzebruch-Zagier divisors and central derivative values of Rankin-Selberg $L$-functions
Jeanine Van Order
https://arxiv.org/abs/2510.10303 https://

Arithmetic Hirzebruch-Zagier divisors and central derivative values of Rankin-Selberg $L$-functions
We give two distinct proofs of the Gross-Zagier formula in terms of sums of automorphic Green's functions realized as regularized theta lifts, including one involving arithmetic Hirzebruch-Zagier divisors on the Hilbert modular surface $X_0(N) \times X_0(N)$. We then describe applications to the refined conjecture of Birch and Swinnerton-Dyer. Through these calculations, we also describe known and conjectural relations of the central derivative values of Rankin-Selberg $L$-functions that appear…