Tootfinder

from my link log —
Sum types in Julia and Rust.
https://andreaskroepelin.de/blog/sum_types/
saved 2020-08-31 https://dotat.at/:/D7RR…

Infinite families of congruences for the second order mock theta function $\mathcal{B}(q)$
Hemjyoti Nath, Hirakjyoti Das
https://arxiv.org/abs/2509.20708 https://

Infinite families of congruences for the second order mock theta function $\mathcal{B}(q)$
The arithmetic properties of the second order mock theta function $\mathcal{B}(q)$, introduced by McIntosh, defined by \begin{equation*} \mathcal{B}(q) := \sum_{n \geq 0} \frac{q^n (-q;q^2)_n}{(q;q^2)_{n+1}} = \sum_{n \geq 0}b(n)q^n, \end{equation*} have been extensively studied. For instance, for all $n\ge0$, Kaur and Rana established congruences such as for all $n\ge0$, \begin{align*} b(12n+10) &\equiv 0 \pmod{36}, \quad b(18n+16) \equiv 0 \pmod{72}, \end{align*} Chen and Mao proved tha…

Quantum statistical mechanical gauge invariance
Johanna M\"uller, Matthias Schmidt
https://arxiv.org/abs/2509.20494 https://arxiv.org/pdf/2509.20494…

Quantum statistical mechanical gauge invariance
We address gauge invariance in the statistical mechanics of quantum many-body systems. The gauge transformation acts on the position and momentum degrees of freedom and it is represented by a quantum shifting superoperator that maps quantum observables onto each other. The shifting superoperator is anti-self-adjoint and it has noncommutative Lie algebra structure. These properties induce exact equilibrium sum rules that connect locally-resolved force and hyperforce densities for any given obser…

1/ C has a wealthy grandmother who has offered us a large sum of money towards a house. She’s even agreed to make up the difference from her estate if she dies within 7 years, to cover off inheritance tax. She has however insisted that that sum be ringfenced so that it ‘stays within the family’ - meaning C and her 2 biological kids. I don’t really know how to feel about this. I that since I earn more than double what C does, we call the sum ‘ours’ if we’re together 10 or more years.

Towards mixed phase correlators in monomial matrix models
A. Popolitov
https://arxiv.org/abs/2509.21218 https://arxiv.org/pdf/2509.21218

Towards mixed phase correlators in monomial matrix models
Correlators in monomial Hermitian matrix model strongly depend on the choice of eigenvalue integration contours. We express Schur correlator in case of several different integration contours (mixed phase case) as a sum over products of Schur correlators for just one type of contour (pure phase), where expansion coefficients are manifestly made from Littlewood-Richardson and Mugnaghan-Nakayama coefficients. Further, for pure phase Schur correlators we find concise superintegrability formulas t…

Purity of generalized affine Springer fibers from generic planar curve singularities
Taiwang Deng, Tao Su
https://arxiv.org/abs/2509.20800 https://arxiv.or…

Purity of generalized affine Springer fibers from generic planar curve singularities
We prove the cohomological purity of punctual Hilbert schemes of points on generic irreducible planar curve singularities, by constructing an explicit affine paving. Via their identification with generalized $GL_N$-affine Springer fibers attached to the direct sum of the adjoint and standard representations, this establishes a new case of the purity conjecture for generalized affine Springer fibers. The combinatorics of the paving - cell indices and dimensions - are controlled by $(dn,dm)$-Dyck…

Fundamental Limits of Noncoherent Massive Random Access Networks
Grace Villacr\'es, Tobias Koch, Gonzalo Vazquez-Vilar
https://arxiv.org/abs/2509.21300 https://

Fundamental Limits of Noncoherent Massive Random Access Networks
This paper studies the capacity of massive random-access cellular networks, modeled as a MIMO fading channel with an infinite number of interfering cells. To characterize the symmetric sum rate of the network, a random-coding argument is invoked together with the assumption that in all cells users draw their codebooks according to the same distribution. This can be viewed as a generalization of the assumption of Gaussian codebooks, often encountered in the literature. The network is further ass…

Coinbase agrees to acquire prediction markets startup The Clearing Company for an undisclosed sum; the startup was founded in 2025 and raised a $15M seed (Yogita Khatri/The Block)
https://www.theblock.co/post/383497/coinbase-to-acquire-…

Spectrum of Light Hexaquark States in Triquark-antitriquark Configuration
Xuan-Heng Zhang, Sheng-Qi Zhang, Cong-Feng Qiao
https://arxiv.org/abs/2509.20711 https://

Spectrum of Light Hexaquark States in Triquark-antitriquark Configuration
To understand the nature of $X(2075)$ and $X(2085)$ observed by the BESIII collaboration in the $p\barΛ$ system, we systematically investigate the possibility that these states are compact hexaquark with triquark-antitriquark configurations for the first time. Within the framework of QCD sum rules, the mass spectrum and decay constants of such hexaquark states with quantum numbers $J^P=0^-, 0^+, 1^-, 1^+$ are studied. Consequently, six independent and nondegenerate hexaquark candidates are obt…

Invariants of stably trivial vector bundles with connection
Sergiu Moroianu
https://arxiv.org/abs/2509.21288 https://arxiv.org/pdf/2509.21288

Invariants of stably trivial vector bundles with connection
We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for connections defined on a direct sum of bundles, under a certain block-diagonality condition on the curvature. As a corollary, we deduce an obstruction for conformally immersing a $n$-dimensional Riemannian manifold in a translation manifold of dimension $n+1$.

Was watching a talk by Sarah Wilson at TEDxSydney: "How to respond to a societal collapse"
Takeaway: If you're looking for an alternate word for "clusterfuck" (like if you're doing an RCA for US-EAST-1) I'm here to share that with you.
#ClusterFuck #Metacrisis

On the convergence of a numerical scheme for a boundary controlled 1D linear parabolic PIDE
Soham Chatterjee, Vivek Natarajan
https://arxiv.org/abs/2509.20960 https://

On the convergence of a numerical scheme for a boundary controlled 1D linear parabolic PIDE
We consider an 1D partial integro-differential equation (PIDE) comprising of an 1D parabolic partial differential equation (PDE) and a nonlocal integral term. The control input is applied on one of the boundaries of the PIDE. Partitioning the spatial interval into $n+1$ subintervals and approximating the spatial derivatives and the integral term with their finite-difference approximations and Riemann sum, respectively, we derive an $n^{\rm th}$-order semi-discrete approximation of the PIDE. The…

🇺🇦 #NowPlaying on #BBC6Music's #CraigCharles
ROSALÍA:
🎵 Porcelana
#ROSALÍA
https://beatsbyalpaca.bandcamp.com/track/rosal-a-porcelana-alpacas-ego-sum-mix
https://open.spotify.com/track/3hETtcSLmNncBjPMLHtVZs

If $\sum_n n! c_n z^n$ is entire and $c_n$ does not terminate, then $\sum_n c_n z^n$ has infinitely many zeros
Alann Rosas
https://arxiv.org/abs/2510.10054 https://

If $\sum_n n! c_n z^n$ is entire and $c_n$ does not terminate, then $\sum_n c_n z^n$ has infinitely many zeros
We prove that if $\sum_n n! c_n z^n$ is entire and $c_n$ does not terminate, then $\sum_n c_n z^n$ has infinitely many zeros. We then use this result to give alternative proofs that the Le Roy functions $f_r(z)=\sum_{n=0}^\infty \frac{z^n}{(n!)^r}$ for $r>1$ and Bessel functions $J_α(z)=\sum_{m=0}^\infty \frac{(-1)^m}{m!Γ(m+α+1)}\left(\frac{z}{2}\right)^{2m+α}$ for $α\in\mathbb R$ have infinitely many zeros.

The $40 billion Trump is sending Argentina is roughly on par with the $41.8 billion it owes the International Monetary Fund
— by far the largest debt on the organization’s books,
half of which was taken out under Milei earlier this year.
There is no benefit to working Americans from this,
and the president isn’t even pretending there is.

Trump: no money for health care, plenty for Argentina
Argentina’s libertarian president, Javier Milei, is the lucky winner of $40 billion that Donald Trump managed to conjure from thin air. Less lucky are the Americans who rely on the government programs Trump has gutted to be able to “save” that sum.

Small-$b$ expansion of the DOZZ formula for light operators
Franco Ferrari, Marcin R. Piatek, Artur R. Pietrykowski
https://arxiv.org/abs/2509.21182 https://

Small-$b$ expansion of the DOZZ formula for light operators
We present a systematic small-$b$ expansion of the Liouville DOZZ three-point structure constant in the light-operator regime $α_i = bσ_i$ as $b\to 0$. In this limit, the exact DOZZ function factorizes into a prefactor $\mathcal{P}(b;σ_1,σ_2,σ_3)$ and a power series in $b^2$, \[ C(bσ_1,bσ_2,bσ_3) =\mathcal{P}(b;σ_i)\Bigl[1+\sum_{n=1}^\infty b^{2n}\,Ω_n(σ_1,σ_2,σ_3)\Bigr]. \] Using Thorn's asymptotic expansion of the $Υ_b$-function, we derive closed-form expressions for the leading…

🇺🇦 #NowPlaying on KEXP's #DriveTime
ROSALÍA:
🎵 Porcelana
#ROSALÍA
https://beatsbyalpaca.bandcamp.com/track/rosal-a-porcelana-alpacas-ego-sum-mix
https://open.spotify.com/track/3hETtcSLmNncBjPMLHtVZs

Tight Regret Upper and Lower Bounds for Optimistic Hedge in Two-Player Zero-Sum Games
Taira Tsuchiya
https://arxiv.org/abs/2510.11691 https://arxiv.org/pdf…

Tight Regret Upper and Lower Bounds for Optimistic Hedge in Two-Player Zero-Sum Games
In two-player zero-sum games, the learning dynamic based on optimistic Hedge achieves one of the best-known regret upper bounds among strongly-uncoupled learning dynamics. With an appropriately chosen learning rate, the social and individual regrets can be bounded by $O(\log(mn))$ in terms of the numbers of actions $m$ and $n$ of the two players. This study investigates the optimality of the dependence on $m$ and $n$ in the regret of optimistic Hedge. To this end, we begin by refining existing …

Created two small linters improving an ergonomics of type switches in Go by adding exhaustive match check. With those tools adding a new case become a lint error.
https://github.com/gomoni/sumlint
1. oneoflint does an exhaustive check for code implementing protobuf's oneof

GitHub - gomoni/sumlint: Exhaustiveness checks for your interface "sum types" using a lightweight naming convention + `go vet`.
Exhaustiveness checks for your interface "sum types" using a lightweight naming convention + `go vet`. - gomoni/sumlint

The whole day so far, after doing some chores around the city, is depressing a few layers high ∑ and a few layers deep ↓
I am somewhere in the middle ∝ and miraculously alright, but I don't like it.

Crypto trading firm FalconX agrees to acquire 21shares, one of the main crypto ETF managers, for an undisclosed sum; 21shares had $11B in assets in September (Vicky Ge Huang/Wall Street Journal)
https://www.wsj.com/fin…

🇺🇦 #NowPlaying on #BBC6Music's #CraigCharles
ROSALÍA:
🎵 Porcelana
#ROSALÍA
https://beatsbyalpaca.bandcamp.com/track/rosal-a-porcelana-alpacas-ego-sum-mix
https://open.spotify.com/track/3hETtcSLmNncBjPMLHtVZs

00
=
@@
\(\Sigma\lambda\)
#meme

Re$^3$MCN: Cubic Newton Variance Reduction Momentum Quadratic Regularization for Finite-sum Non-convex Problems
Dmitry Pasechnyuk-Vilensky, Dmitry Kamzolov, Martin Tak\'a\v{c}
https://arxiv.org/abs/2510.08714

Re$^3$MCN: Cubic Newton + Variance Reduction + Momentum + Quadratic Regularization for Finite-sum Non-convex Problems
We analyze a stochastic cubic regularized Newton method for finite sum optimization $\textstyle\min_{x\in\mathbb{R}^d} F(x) \;=\; \frac{1}{n}\sum_{i=1}^n f_i(x)$, that uses SARAH-type recursive variance reduction with mini-batches of size $b\sim n^{1/2}$ and exponential moving averages (EMA) for gradient and Hessian estimators. We show that the method achieves a $(\varepsilon,\sqrt{L_2\varepsilon})$-second-order stationary point (SOSP) with total stochastic oracle calls $n + \widetilde{\mathcal…

Bigraded Polynomials for the Cohomology of Wild Hitchin Systems
Dan Xie
https://arxiv.org/abs/2509.20872 https://arxiv.org/pdf/2509.20872

Bigraded Polynomials for the Cohomology of Wild Hitchin Systems
We introduce a bi-graded polynomial that encodes the cohomology groups of the wild Hitchin system of type~$A_{n-1}$, constructed using an irregular singularity (determined by an integer~$m$) and an arbitrary regular singularity~$f$. When the regular singularity is of the form~$f = [1, \ldots, 1]$, the bi-graded polynomial~$C_{m,n}(q,t)$ coincides with the bigraded rational parking function defined combinatorially, admitting a Schur expansion~$C_{m,n}(q,t) = \sum_λf_λ(q,t) s_λ(x)$. For genera…

On the Exact Sum PDF and CDF of {\alpha}-{\mu} Variates
Fernando Dar\'io Almeida Garc\'ia, Francisco Raimundo Albuquerque Parente, Michel Daoud Yacoub, Jose C\^andido Silveira Santos Filho
https://arxiv.org/abs/2510.03850

On the Exact Sum PDF and CDF of α-μ Variates
The sum of random variables (RVs) appears extensively in wireless communications, at large, both conventional and advanced, and has been subject of longstanding research. The statistical characterization of the referred sum is crucial to determine the performance of such communications systems. Although efforts have been undertaken to unveil these sum statistics, e.g., probability density function (PDF) and cumulative distribution function (CDF), no general efficient nor manageable solutions ca…

k-SUM Hardness Implies Treewidth-SETH
Michael Lampis
https://arxiv.org/abs/2510.08185 https://arxiv.org/pdf/2510.08185

k-SUM Hardness Implies Treewidth-SETH
We show that if k-SUM is hard, in the sense that the standard algorithm is essentially optimal, then a variant of the SETH called the Primal Treewidth SETH is true. Formally: if there is an $\varepsilon>0$ and an algorithm which solves SAT in time $(2-\varepsilon)^{tw}|ϕ|^{O(1)}$, where $tw$ is the width of a given tree decomposition of the primal graph of the input, then there exists a randomized algorithm which solves k-SUM in time $n^{(1-δ)\frac{k}{2}}$ for some $δ>0$ and all su…

Larry Summers "stepping back" from public roles after Epstein files release (Rebecca Falconer/Axios)
https://www.axios.com/2025/11/18/larry-summers-harvard-epstein
http://www.memeorandum.com/251117/p166#a251117p166

🇺🇦 #NowPlaying on KEXP's #MiddayShow
Rochelle Jordan:
🎵 Sum
#RochelleJordan
https://rochellejordan.bandcamp.com/track/sum
https://open.spotify.com/track/3MIVJlKGcLfYNLso4pp6dn

N-Parties Private Structure and Parameter Learning for Sum-Product Networks
Xenia Heilmann, Ernst Althaus, Mattia Cerrato, Nick Johannes Peter Rassau, Mohammad Sadeq Dousti, Stefan Kramer
https://arxiv.org/abs/2510.05946

N-Parties Private Structure and Parameter Learning for Sum-Product Networks
A sum-product network (SPN) is a graphical model that allows several types of probabilistic inference to be performed efficiently. In this paper, we propose a privacy-preserving protocol which tackles structure generation and parameter learning of SPNs. Additionally, we provide a protocol for private inference on SPNs, subsequent to training. To preserve the privacy of the participants, we derive our protocol based on secret sharing, which guarantees privacy in the honest-but-curious setting ev…

Sum of elements preceding records in set partitions
Walaa Asakly, Noor Kezil
https://arxiv.org/abs/2510.06521 https://arxiv.org/pdf/2510.06521

Sum of elements preceding records in set partitions
In this paper, we aim to derive an explicit formula for the total number of elements preceding records over all set partitions of $[n]$ with exactly $k$ blocks, as well as an asymptotic estimate for the total sum of elements preceding records in all set partitions of $[n]$, expressed in terms of Bell numbers. To achieve this, we analyze the generating function that enumerates set partitions of $[n]$ according to this statistic, which we denote by $\sumelements$.

Improved Bounds for the Index Conjecture in Zero-Sum Theory
Andrew Pendleton
https://arxiv.org/abs/2510.11976 https://arxiv.org/pdf/2510.11976

Improved Bounds for the Index Conjecture in Zero-Sum Theory
The Index Conjecture in zero-sum theory states that when $n$ is coprime to $6$ and $k$ equals $4$, every minimal zero-sum sequence of length $k$ modulo $n$ has index $1$. While other values of $(k,n)$ have been studied thoroughly in the last 30 years, it is only recently that the conjecture has been proven for $n>10^{20}$. In this paper, we prove that said upper bound can be reduced to $4.6\cdot10^{13}$, and lower under certain coprimality conditions. Further, we verify the conjecture for $n<1.…

🇺🇦 Auf radioeins läuft...
Rosalía:
🎵 Porcelana
#NowPlaying #Rosalía
#newRelease 🆕 album
https://beatsbyalpaca.bandcamp.com/track/rosal-a-porcelana-alpacas-ego-sum-mix
https://open.spotify.com/track/3hETtcSLmNncBjPMLHtVZs

Did you choose your major poorly in college, and are so obsessed with being in London that you are willing to accept a sub-living wage to reside there? Or is your partner well enough paid to maintain you, but you don't want to be bored at home? Are you independently wealthy, perhaps? Please consider subsidizing the British State with your labor in exchange for a token sum of £38k per year.

Scale-Invariant Regret Matching and Online Learning with Optimal Convergence: Bridging Theory and Practice in Zero-Sum Games
Brian Hu Zhang, Ioannis Anagnostides, Tuomas Sandholm
https://arxiv.org/abs/2510.04407

Scale-Invariant Regret Matching and Online Learning with Optimal Convergence: Bridging Theory and Practice in Zero-Sum Games
A considerable chasm has been looming for decades between theory and practice in zero-sum game solving through first-order methods. Although a convergence rate of $T^{-1}$ has long been established since Nemirovski's mirror-prox algorithm and Nesterov's excessive gap technique in the early 2000s, the most effective paradigm in practice is *counterfactual regret minimization*, which is based on *regret matching* and its modern variants. In particular, the state of the art across most benchmarks …

Sum rules via large deviations: polynomial potentials and multi-cut regime on the unit circle
Fabrice Gamboa, Jan Nagel, Alain Rouault
https://arxiv.org/abs/2509.23814 https://

Sum rules via large deviations: polynomial potentials and multi-cut regime on the unit circle
Sum rules are elegant formulas that relate entropy functionals to coefficients associated with orthogonal polynomials [Sim11]. In a series of paper (see for example [GNR16], [GNR17], [BSZ18a], [BSZ18b]), interesting connections have been established between the large theory of spectral measures built on random matrices and sum rules. In this work, we extend this approach by studying sum rules within random matrix models with polynomial potentials on the unit circle, with a particular focus on c…

On stability of restricted center properties and continuity of restricted center map under $\ell_p$-direct sum
Gayathri P, V Thota
https://arxiv.org/abs/2510.01955 https://

On stability of restricted center properties and continuity of restricted center map under $\ell_p$-direct sum
We study the stability of various restricted center properties and certain continuity properties of the restricted center map. We observe that restricted center property, property-$(P_1)$ and semi-continuity properties of the restricted center map are preserved under $\ell_p$-direct sum $(1 \leq p < \infty).$ It is shown that property-$(P_2)$ is stable under finite $\ell_p$-direct sum, but not under infinite $\ell_p$-direct sum. Additionally, we introduce a notion called property-$(lP_2)$ as a …

That’s a fascinating website by @…
https://nonzerosum.games/

NON-ZERO-SUM GAMES
~ a world-help site ~

The Online Submodular Cover Problem
Anupam Gupta, Roie Levin
https://arxiv.org/abs/2510.08883 https://arxiv.org/pdf/2510.08883

The Online Submodular Cover Problem
In the submodular cover problem, we are given a monotone submodular function $f$, and we want to pick the min-cost set $S$ such that $f(S) = f(N)$. Motivated by problems in network monitoring and resource allocation, we consider the submodular cover problem in an online setting. As a concrete example, suppose at each time $t$, a nonnegative monotone submodular function $g_t$ is given to us. We define $f^{(t)} = \sum_{s \leq t} g_s$ as the sum of all functions seen so far. We need to maintain a …

On some conjectural supercongruences involving the sequence $t_n(x)$
Hui-Li Han, Chen Wang
https://arxiv.org/abs/2510.11338 https://arxiv.org/pdf/2510.1133…

On some conjectural supercongruences involving the sequence $t_n(x)$
In this paper, we study some supercongruences involving the sequence $$ t_n(x)=\sum_{k=0}^n\binom{n}{k}\binom{x}{k}\binom{x+k}{k}2^k $$ and solve some open problems. For any odd prime $p$ and $p$-adic integer $x$, we determine $\sum_{n=0}^{p-1}t_n(x)^2$ and $\sum_{n=0}^{p-1}(n+1)t_n(x)^2$ modulo $p^2$; for example, we establish that \begin{align*} \sum_{n=0}^{p-1}t_n(x)^2\equiv\begin{cases} \left(\dfrac{-1}{p}\right)\pmod{p^2},&\text{if }2x\equiv-1\pmod{p},\\[8pt] (-1)^{\langle x\rangle…

Yeah, Jimmy “I’m actually quite in favour of business and capitalism and all that”* Wales, the surveillance capitalist and Fandom-president adtech man who once told me he doesn’t believe in any form of government regulation – not even in food standards or healthcare – can go fuck himself.
Find better heroes. Or even better yet, get over the whole stupid concept itself.
*

🇺🇦 #NowPlaying on #BBC6Music's #ChrisHawkins
ROSALÍA:
🎵 Porcelana
#ROSALÍA
https://beatsbyalpaca.bandcamp.com/track/rosal-a-porcelana-alpacas-ego-sum-mix
https://open.spotify.com/track/3hETtcSLmNncBjPMLHtVZs

“Notes on Being a Man”, by Scott Galloway. An interview by Jordan Klepper on The Daily Show.
Nearly one in five men in their 30s still live with their parents, and 15% report having no close friends. Men are also four times more likely to die by suicide than women.
“Guiding boys to become men is not a zero sum game. Everyone benefits.”
htt…

“Would it be particularly helpful to have some text that would be •typical• in a given context, even if the text is possibly •incorrect•?”
∑ vet potential applications of LLMs with this one weird question!

Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvatures
Abigail Hickok, Andrew J. Blumberg
https://arxiv.org/abs/2510.04936 https://arxiv.…

Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvatures
We study the relationship between discrete analogues of Ricci and scalar curvature that are defined for point clouds and graphs. In the discrete setting, Ricci curvature is replaced by Ollivier-Ricci curvature. Scalar curvature can be computed as the trace of Ricci curvature for a Riemannian manifold; this motivates a new definition of a scalar version of Ollivier-Ricci curvature. We show that our definition converges to scalar curvature for nearest neighbor graphs obtained by sampling from a m…

A summit has begun in Brussels to decide the fate of aid to Ukraine #shorts: https://benborges.xyz/2025/12/03/a-summit-has-begun-in.html

Bounded Littlewood identities with fixed number of odd rows or odd columns
JiSun Huh, Jang Soo Kim, Christian Krattenthaler, Soichi Okada
https://arxiv.org/abs/2510.11054 https:…

Bounded Littlewood identities with fixed number of odd rows or odd columns
A Littlewood identity is an identity equating a sum of Schur functions with an infinite product. A bounded Littlewood identity is one where the sum is taken over the partitions with a bounded number of rows or columns. The price to pay is that the infinite product has to be replaced by a determinant. The focus of this article is on refinements of such bounded Littlewood identities where one also prescribes the number of odd-length rows or columns of the partitions. Goulden [{\it Discrete Math.}…

A new elementary proof of the formula $\sum\limits_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$
Jia Li
https://arxiv.org/abs/2510.03233 https://arxiv.org/p…

A new elementary proof of the formula $\sum\limits_{n=1}^{\infty}\frac{1}{n^2}=\frac{π^2}{6}$
In this article, we provide a new elementary proof of the Basel problem.

Sum of short exponential sums with prime numbers
Firuz Rakhmonov
https://arxiv.org/abs/2510.09102 https://arxiv.org/pdf/2510.09102

Sum of short exponential sums with prime numbers
For sufficiently large integers $K$, $x$, $y$, and $q$ satisfying $K \le y < x$, where $f(u) = αu^n + α_{n-1}u^{n-1} + \ldots + α_1 u$ is a polynomial of degree $n$ with real coefficients, $n$ is a fixed positive integer, $α$ is a real number such that $\left|α- \frac{a}{q}\right| \le \frac{1}{q^2}$, $(a, q) = 1$, $q \ge 1$ and $\mathscr{L} = \ln x$, an estimate of the form $$ \sum_{k=1}^K \left| \sum_{x - y < p \le x} e(kf(p)) \right| \ll K y \left( \frac{1}{q} + \frac…

The Jones Polynomial of a Connect Sum is Multiplicative: A New Approach Via Trip Matrices
Molly A. Moran, Emerson Worrell
https://arxiv.org/abs/2510.00211 https://

The Jones Polynomial of a Connect Sum is Multiplicative: A New Approach Via Trip Matrices
We utilize the trip matrix method of calculating the Jones Polynomial to give an alternative proof that the Jones Polynomial is multiplicative under connect sums.

VeritasFi: An Adaptable, Multi-tiered RAG Framework for Multi-modal Financial Question Answering
Zhenghan Tai, Hanwei Wu, Qingchen Hu, Jijun Chi, Hailin He, Lei Ding, Tung Sum Thomas Kwok, Bohuai Xiao, Yuchen Hua, Suyuchen Wang, Peng Lu, Muzhi Li, Yihong Wu, Liheng Ma, Jerry Huang, Jiayi Zhang, Gonghao Zhang, Chaolong Jiang, Jingrui Tian, Sicheng Lyu, Zeyu Li, Boyu Han, Fengran Mo, Xinyue Yu, Yufei Cui, Ling Zhou, Xinyu Wang

VeritasFi: An Adaptable, Multi-tiered RAG Framework for Multi-modal Financial Question Answering
Retrieval-Augmented Generation (RAG) is becoming increasingly essential for Question Answering (QA) in the financial sector, where accurate and contextually grounded insights from complex public disclosures are crucial. However, existing financial RAG systems face two significant challenges: (1) they struggle to process heterogeneous data formats, such as text, tables, and figures; and (2) they encounter difficulties in balancing general-domain applicability with company-specific adaptation. To…

Structured covariance estimation via tensor-train decomposition
Artsiom Patarusau, Nikita Puchkin, Maxim Rakhuba, Fedor Noskov
https://arxiv.org/abs/2510.08174 https://

Structured covariance estimation via tensor-train decomposition
We consider a problem of covariance estimation from a sample of i.i.d. high-dimensional random vectors. To avoid the curse of dimensionality we impose an additional assumption on the structure of the covariance matrix $Σ$. To be more precise we study the case when $Σ$ can be approximated by a sum of double Kronecker products of smaller matrices in a tensor train (TT) format. Our setup naturally extends widely known Kronecker sum and CANDECOMP/PARAFAC models but admits richer interaction acros…

"Debt does matter, but the debt that matters in a capitalist economy is not so much public debt, but corporate debt. The latest estimates are that in the major economies, some 30%-plus of companies have so much debt that they do not earn enough profits to service that debt."
...
"the stock market may be booming ... but the rest of the economy is not so buoyant; and there appear to be cockroaches eating into the clean running of the world of debt. "
Michae…

Debt and the cockroaches
Let the Financial Times sum it up: “US stocks ride AI hype and trade truce to 6-month winning streak S&P 500 and Nasdaq post longest runs of monthly gains in years.” The FT points out that US s…

Resonance sum rules: an application to the square well potential
Zi-Xi Ou-Yang, Philipp Gubler, Makoto Oka, Guang-Juan Wang, Jia-Jun Wu
https://arxiv.org/abs/2509.24336 https://…

Resonance sum rules: an application to the square well potential
We propose an extension of the Quantum Chromodynamics (QCD) sum rules, termed the Resonance sum rules (RSR), to access resonance poles in the complex energy plane. By strategically introducing a contour in the complex plane and conformal mapping, the method intends to reach resonance poles on the second Riemann sheet. To validate this approach, we apply RSR to the square-well potential model, for which the pole locations are known. The analysis demonstrates a successful extraction of the pole p…

Slant sums of quiver gauge theories
Hunter Dinkins, Vasily Krylov, Reese Lance
https://arxiv.org/abs/2510.02496 https://arxiv.org/pdf/2510.02496

Slant sums of quiver gauge theories
We define a notion of slant sum of quiver gauge theories, a type of surgery on the underlying quiver. Under some mild assumptions, we relate torus fixed points on the corresponding Higgs branches, which are Nakajima quiver varieties. Then we prove a formula relating the quasimap vertex functions before and after a slant sum, which is a type of ``branching rule" for vertex functions. Our construction is motivated by a conjecture, which we make here, for the factorization of the vertex function…

The $\alpha$--regression for compositional data: a unified framework for standard, spatially-lagged, and geographically-weighted regression models
Michail Tsagris
https://arxiv.org/abs/2510.12663

The $α$--regression for compositional data: a unified framework for standard, spatially-lagged, and geographically-weighted regression models
Compositional data-vectors of non--negative components summing to unity--frequently arise in scientific applications where covariates influence the relative proportions of components, yet traditional regression approaches struggle with the unit-sum constraint and zero values. This paper revisits the $α$--regression framework, which uses a flexible power transformation parameterized by $α$ to interpolate between raw data analysis and log-ratio methods, naturally handling zeros without imputati…

I made a nice sum of money on the prediction markets betting on the winner of this year's FIFA Peace Prize.

""Rousseau invites endless introspection. Franklin invites progress. The first is about how you feel; the second is about what you build.
I find the Franklin model far more useful. Not because it’s truer in some cosmic sense, but because it gives you agency. You can’t always change how you feel, but you can always decide what to do next.""

Sonnet 004 - IV
Unthrifty loveliness, why dost thou spend
Upon thy self thy beauty's legacy?
Nature's bequest gives nothing, but doth lend,
And being frank she lends to those are free:
Then, beauteous niggard, why dost thou abuse
The bounteous largess given thee to give?
Profitless usurer, why dost thou use
So great a sum of sums, yet canst not live?
For having traffic with thy self alone,
Thou of thy self thy sweet self dos…

Crosslisted article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[2/8]:
- Adversarial Reinforcement Learning for Offensive and Defensive Agents in a Simulated Zero-Sum Net...
Abrar Shahid, Ibteeker Mahir Ishum, AKM Tahmidul Haque, M Sohel Rahman, A. B. M. Alim Al Islam

Harnack inequality for Bessel operators
Giorgio Metafune, Luigi Negro, Chiara Spina
https://arxiv.org/abs/2510.12529 https://arxiv.org/pdf/2510.12529

Harnack inequality for Bessel operators
We prove uniqueness results and Harnack inequality for Bessel operators \begin{align*} %\label{def L transf alpha} D_t-Δ_{x} -2a\cdot\nabla_xD_y- D_{yy}- \frac cy D_y % \nonumber \\[1ex]&=y^α\sum_{i,j=1}^{N+1}a_{ij}D_{ij}+y^{α-1}\left(v,\nabla\right)-by^{α-2}. \end{align*} in the strip $[0,T]\times \mathbb{R}^{N+1}_+=\{0 \leq t \leq T, x \in \mathbb{R}^N, y>0\}$ under Neumann boundary conditions at $y=0$.

Real-congruence canonical forms of real matrices
Fernando De Ter\'an, Froil\'an M. Dopico
https://arxiv.org/abs/2510.07288 https://arxiv.org/pdf/25…

Real-congruence canonical forms of real matrices
We present two new canonical forms for real congruence of a real square matrix $A$. The first one is a direct sum of canonical matrices of four different types and is obtained from the canonical form under $^*$congruence of complex matrices provided by Horn and Sergeichuk in [Linear Algebra Appl. 416 (2006) 1010-1032]. The second one is a direct sum of canonical matrices of three different types, has a block tridiagonal structure and is obtained from the canonical form under $^*$congruence of c…

Affine-Orthogonal Manifolds and Deformation to Levi-Civita Connections
Mihail Cocos
https://arxiv.org/abs/2510.09648 https://arxiv.org/pdf/2510.09648

Affine-Orthogonal Manifolds and Deformation to Levi-Civita Connections
We study a class of affine manifolds equipped with a flat affine connection $\nabla$ and a global Riemannian metric $g$ that is diagonal in local affine coordinates. These structures are closely related to \emph{Hessian manifolds}, where the metric locally arises as the Hessian of a smooth potential. For example, the Hopf manifold $(\mathbb{R}^{n+1}\setminus \{0\}) / \langle x \mapsto 2x \rangle$ with metric $g = (\sum_i x_i^2)^{-1} \sum_i dx_i^2$ admits a proper deformation of $\nabla$ into it…

Layered Normalized Min-Sum Decoding with Bit Flipping for FDPC Codes
Niloufar Hosseinzadeh, Mohsen Moradi, Hessam Mahdavifar
https://arxiv.org/abs/2510.01019 https://

Layered Normalized Min-Sum Decoding with Bit Flipping for FDPC Codes
Fair-density parity-check (FDPC) codes have been recently introduced demonstrating improved performance compared to low-density parity-check (LDPC) codes standardized in 5G systems particularly in high-rate regimes. In this paper, we introduce a layered normalized min-sum (LNMS) message-passing decoding algorithm for the FDPC codes. We also introduce a syndrome-guided bit flipping (SGBF) method to enhance the error-correction performance of our proposed decoder. The LNMS decoder leverages confl…

Ultra-Reliable Risk-Aggregated Sum Rate Maximization via Model-Aided Deep Learning
Hassaan Hashmi, Spyridon Pougkakiotis, Dionysis Kalogerias
https://arxiv.org/abs/2509.26311 ht…

Ultra-Reliable Risk-Aggregated Sum Rate Maximization via Model-Aided Deep Learning
We consider the problem of maximizing weighted sum rate in a multiple-input single-output (MISO) downlink wireless network with emphasis on user rate reliability. We introduce a novel risk-aggregated formulation of the complex WSR maximization problem, which utilizes the Conditional Value-at-Risk (CVaR) as a functional for enforcing rate (ultra)-reliability over channel fading uncertainty/risk. We establish a WMMSE-like equivalence between the proposed precoding problem and a weighted risk-aver…

A degree sum condition for the existence of a quasi 5-contractible edge in a quasi 5-connected graph
Shuai Kou, Chengfu Qin, Weihua Yang, Mingzu Zhang, Shuang Zhao
https://arxiv.org/abs/2509.25809

A degree sum condition for the existence of a quasi 5-contractible edge in a quasi 5-connected graph
An edge of a quasi $k$-connected graph is said to be quasi $k$-contractible if the contraction of the edge results in a quasi $k$-connected graph. We show that every 5-connected graph contains a quasi 5-contractible edge. Furthermore, we prove that a quasi 5-connected graph possesses a quasi 5-contractible edge, if the degree sum of any two vertices with distance at most two is at least 9. This result strengthens a theorem proved by Kriesell when $k=4$ (M. Kriesell, A degree sum condition for t…

Breaking $1/\epsilon$ Barrier in Quantum Zero-Sum Games: Generalizing Metric Subregularity for Spectraplexes
Yiheng Su, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Pucheng Xiong
https://arxiv.org/abs/2509.21570

Breaking $1/ε$ Barrier in Quantum Zero-Sum Games: Generalizing Metric Subregularity for Spectraplexes
Long studied as a toy model, quantum zero-sum games have recently resurfaced as a canonical playground for modern areas such as non-local games, quantum interactive proofs, and quantum machine learning. In this simple yet fundamental setting, two competing quantum players send iteratively mixed quantum states to a referee, who performs a joint measurement to determine their payoffs. In 2025, Vasconcelos et al. [arXiv:2311.10859] connected quantum communication channels with a hierarchy of quant…

SoftBank-owned PayPay takes a 40% stake in Binance Japan for an undisclosed sum, to capitalize on Japan's crypto boom; PayPay filed for a US IPO in August (Mayumi Negishi/Bloomberg)
https://www.bloomberg.com/news/articles/20

Hardness and Algorithmic Results for Roman \{3\}-Domination
Sangam Balchandar Reddy
https://arxiv.org/abs/2509.23615 https://arxiv.org/pdf/2509.23615

Hardness and Algorithmic Results for Roman \{3\}-Domination
A Roman $\{3\}$-dominating function on a graph $G = (V, E)$ is a function $f: V \rightarrow \{0, 1, 2, 3\}$ such that for each vertex $u \in V$, if $f(u) = 0$ then $\sum_{v \in N(u)} f(v) \geq 3$ and if $f(u) = 1$ then $\sum_{v \in N(u)} f(v) \geq 2$. The weight of a Roman $\{3\}$-dominating function $f$ is $\sum_{u \in V} f(u)$. The objective of \rtd{} is to compute a Roman $\{3\}$-dominating function of minimum weight. The problem is known to be NP-complete on chordal graphs, star-convex bipa…

Accelerated stochastic first-order method for convex optimization under heavy-tailed noise
Chuan He, Zhaosong Lu
https://arxiv.org/abs/2510.11676 https://a…

Accelerated stochastic first-order method for convex optimization under heavy-tailed noise
We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex function whose subgradients are estimated under heavy-tailed noise. Existing work often employs gradient clipping or normalization techniques in stochastic first-order methods to address heavy-tailed noise. In this paper, we demonstrate that a vanilla stochastic algorithm -- without additional modifications such as clipping or normalization -- can achieve op…

New representations of the Hu-Meyer formulas and series expansion of iterated Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process
Dmitriy F. Kuznetsov
https://arxiv.org/abs/2510.06981

New representations of the Hu-Meyer formulas and series expansion of iterated Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process
The article is devoted to the systematic derivation of new representations of the Hu-Meyer formulas. The formula expressing a multiple Wiener stochastic integral through the sum of multiple Stratonovich stochastic integrals and the formula expressing a multiple Stratonovich stochastic integral through the sum of multiple Wiener stochastic integrals are derived for the case of a multidimensional Wiener process. The proof method proposed by the author in 2006 is applied. At that a different defin…

Quantum Deception: Honey-X Deception using Quantum Games
Efstratios Reppas, Ali Wadi, Brendan Gould, Kyriakos G. Vamvoudakis
https://arxiv.org/abs/2510.11848 https://

Quantum Deception: Honey-X Deception using Quantum Games
In this paper, we develop a framework for deception in quantum games, extending the Honey-X paradigm from classical zero-sum settings into the quantum domain. Building on a view of deception in classical games as manipulation of a player's perception of the payoff matrix, we formalize quantum deception as controlled perturbations of the payoff Hamiltonian subject to a deception budget. We show that when victims are aware of possible deception, their equilibrium strategies surprisingly coincide …

Divergent Infinite Series -- Ramanujan's Initial Intuition
Mario M. Attard
https://arxiv.org/abs/2510.08652 https://arxiv.org/pdf/2510.08652

Divergent Infinite Series -- Ramanujan's Initial Intuition
This paper investigates Srinivasa Ramanujan's initial intuitive methodology for assigning the finite value -1/12 to the sum of the divergent infinite series of all positive integers. We systematically examine Ramanujan's initial method, originally sketched in his notebooks, and set the methodology into an algebraic framework. The methodology has limited applicability to other classes of divergent series. The methodology is extended to assign a Ramanujan smoothed sum to the infinite sequences of…

On the Ratat-Goormaghtigh equation and integer points close to the graph of a smooth function
Tomohiro Yamada
https://arxiv.org/abs/2510.11252 https://arxi…

On the Ratat-Goormaghtigh equation and integer points close to the graph of a smooth function
We prove that the sum of reciprocals $1/x$ of integer solutions of $(x^m-1)/(x-1)=N$ with $x, m\geq 2$ for a given integer $N$ except the smallest $x$ is smaller than $5.9037$. If we limit $x$ to be prime, then the sum is smaller than $0.73194$.

Verizon agrees to buy Starry, which provides home internet via millimeter wave tech to ~100K customers and filed for bankruptcy in 2023, for an undisclosed sum (Masha Abarinova/Fierce Network)
https://www.fierce-network.com/broadband/verizon-buys-starry-what-y…

The annual fundraiser support for Wikimedia from the richest man in the world is a dystopian right-wing infused parody site of #Wikipedia.
So if you‘d rather support free access to the sum of all human knowledge instead of billionaire tech bros, you get a chance to donate out of spite.

Sublinear Algorithms for Estimating Single-Linkage Clustering Costs
Pan Peng, Christian Sohler, Yi Xu
https://arxiv.org/abs/2510.11547 https://arxiv.org/pd…

Sublinear Algorithms for Estimating Single-Linkage Clustering Costs
Single-linkage clustering is a fundamental method for data analysis. Algorithmically, one can compute a single-linkage $k$-clustering (a partition into $k$ clusters) by computing a minimum spanning tree and dropping the $k-1$ most costly edges. This clustering minimizes the sum of spanning tree weights of the clusters. This motivates us to define the cost of a single-linkage $k$-clustering as the weight of the corresponding spanning forest, denoted by $\mathrm{cost}_k$. Besides, if we consider …

Periods detecting Eisenstein series and sums of $L$-values I
Weixiao Lu, Guodong Xi
https://arxiv.org/abs/2510.12446 https://arxiv.org/pdf/2510.12446

Periods detecting Eisenstein series and sums of $L$-values I
We study the automorphic period associated to a $G$-Hamiltonian variety $M$ whose dual is $\check{M} = T^*(\check{G}/\check{L})$, where $\check{G}$ is a general linear group and $\check{L}$ is a Levi subgroup. For certain cuspidal Eisenstein series, we prove that their period is equal to a finite sum of special values of $L$-functions. This sum is indexed by the fixed points of the associated extended $L$-parameter on $\check{M}$, confirming a conjecture by Ben-Zvi-Sakellaridis-Venkatesh in thi…

Qualcomm acquires Italian open-source electronics platform Arduino for an undisclosed sum and will retain the Arduino brand; Arduino releases a Pi-like board (Emma Roth/The Verge)
https://www.theverge.com/news/794452/qualcomm-arduino-acquisition-uno-q
…

Qualcomm is acquiring DIY electronics platform Arduino
Qualcomm is acquiring the DIY electronics platform Arduino, and launching a new Uno Q that connects to a new App Lab platform.

Hamilton-Jacobi Reachability for Viability Analysis of Constrained Waste-to-Energy Systems under Adversarial Uncertainty
Achraf Bouhmady, Othman Cherkaoui Dekkaki
https://arxiv.org/abs/2510.11396

Hamilton-Jacobi Reachability for Viability Analysis of Constrained Waste-to-Energy Systems under Adversarial Uncertainty
This paper investigates the problem of maintaining the safe operation of Waste-to-Energy (WtE) systems under operational constraints and uncertain waste inflows. We model this as a robust viability problem, formulated as a zero-sum differential game between a control policy and an adversarial disturbance. Within a Hamilton-Jacobi framework, the viability kernel is characterized as the zero sublevel set of a value function satisfying a constrained Hamilton-Jacobi-Bellman (HJB) equation in the vi…

🇺🇦 #NowPlaying on #BBC6Music's #CraigCharles
ROSALÍA:
🎵 Porcelana
#ROSALÍA
https://beatsbyalpaca.bandcamp.com/track/rosal-a-porcelana-alpacas-ego-sum-mix
https://open.spotify.com/track/3hETtcSLmNncBjPMLHtVZs

Hybrid centralized-distributed precoding in fronthaul-constrained CF-mMIMO systems
Zahra Mobini, Hien Quoc Ngo, Ardavan Rahimian, Anvar Tukmanov, David Townend, Michail Matthaiou, Simon L. Cotton
https://arxiv.org/abs/2510.12406

Hybrid centralized-distributed precoding in fronthaul-constrained CF-mMIMO systems
We investigate a fronthaul-limited cell-free massive multiple-input multiple-output (CF-mMIMO) system and propose a hybrid centralized-distributed precoding strategy that dynamically adapts to varying fronthaul and spectral efficiency (SE) requirements. The proposed approach divides users into two groups: one served by centralized precoding and the other by distributed precoding. We formulate a novel optimization problem for user grouping and power control aimed at maximizing the sum SE, subjec…

Improved prediction of the mass splitting for $P$-wave $\Omega$ baryons
Niu Su, Hua-Xing Chen, Philipp Gubler, Atsushi Hosaka
https://arxiv.org/abs/2510.01979 https://

Improved prediction of the mass splitting for $P$-wave $Ω$ baryons
Using the QCD sum rule method, we investigate the mass splitting for the spin-orbit partner states of the $Ω(2012)$ baryon assuming that it is a $P$-wave excitation with $J^P=3/2^-$. This study is an extension of the previous work [1] in which the masses of these states were estimated with uncertainties too large to extract the reliable mass splitting. In the present study, by directly formulating a sum rule for the mass splitting, we obtain an improved prediction, $δM = M_{3/2^-} - M_{1/2^-}…

Active IRS Assisted Joint Uplink and Downlink Communications
Qiaoyan Peng, Qingqing Wu, Guangji Chen, Wen Chen, Shaodan Ma
https://arxiv.org/abs/2510.10045 https://

Active IRS Assisted Joint Uplink and Downlink Communications
In this paper, we investigate an intelligent reflecting surface (IRS) aided wireless communication system, where active IRSs (AIRSs) are deployed to assist communication between a base station (BS) and users of both the uplink (UL) and downlink (DL). We aim to maximize the weighted sum rate (WSR) of UL and DL communications through joint optimization of BS, AIRS beamforming, and AIRS element allocation. First, we study three deployment schemes, namely distributed AIRSs, BS-side AIRS, and user-s…

On the $p$-adic transcendence of $\sum_{k=1}^\infty p^{-1/p^k}$
Shanwen Wang, Yijun Yuan
https://arxiv.org/abs/2509.24609 https://arxiv.org/pdf/2509.24609

On the $p$-adic transcendence of $\sum_{k=1}^\infty p^{-1/p^k}$
Let $p$ be a prime number. In this article, we prove that the $p$-adic Hahn series $\sum_{k=1}^\infty p^{-1/p^k}$, which is the mixed-characteristic analogue of Abhyankar's solution $\sum_{k=1}^\infty t^{-1/p^k}$ to the Artin-Schreier equation $X^p-X-t^{-1}=0$ over $\mathbf{F}_p\left(\!\left(t\right)\!\right)$, is a $p$-adic complex number, but not a $p$-adic algebraic number. Based on this result, we formulate a conjecture about the possible order type of the support of an algebraic $p$-adic H…

🇺🇦 #NowPlaying on #BBC6Music's #LaurenLaverne
HAIM:
🎵 Summer Girl
#HAIM
https://tresfou.bandcamp.com/track/summer-girl-haim
https://open.spotify.com/track/4O3ob7NxMcZLgJ8ucIahPS

A note on the distribution of the sum of lengths of the initial longest increasing sequences in cycles of random permutations
Ljuben Mutafchiev
https://arxiv.org/abs/2509.26129 …

A note on the distribution of the sum of lengths of the initial longest increasing sequences in cycles of random permutations
Let $S_n$ be the set of all permutations of $\{1,2,\ldots,n\}$ and let $σ=(σ_1,σ_2,\ldots,σ_n)\in S_n$. The {\it initial longest increasing sequence} (ILIS) in $σ$ has length $m$ if, for $1\le m\le n-1$, $σ_1<σ_2<\ldots<σ_m, σ_m>σ_{m+1}$, and has length $n$ if $σ=(1,2,\ldots,n)$. Let $l(σ)$ be the length of the ILIS in $σ$. We assume that $σ$ is represented in cycle notation, so that the first number in each cycle is the minimum number of this cycle. We also assume that $σ$ is ch…

Movable Antenna Enhanced Covert Dual-Functional Radar-Communication: Joint Beamforming and Antenna Position Optimization
Ran Yang, Zheng Dong, Peng Cheng, Lin Zhang, Wanting Lyu, Yue Xiu, Ning Wei, Chadi Assi
https://arxiv.org/abs/2510.09949

Movable Antenna Enhanced Covert Dual-Functional Radar-Communication: Joint Beamforming and Antenna Position Optimization
Movable antenna (MA) has emerged as a promising technology to flexibly reconfigure wireless channels by adjusting antenna placement. In this paper, we study a dual-functional radar-communication (DFRC) system enhanced with movable antennas. To ensure communication security, we aim to maximize the achievable sum rate by jointly optimizing the transmit beamforming vectors, receiving filter, and antenna placement, subject to radar signal-to-noise ratio (SNR) performance and transmission covertness…

Polynomials and asymptotic constants in a resurgent problem from 't Hooft
David Broadhurst
https://arxiv.org/abs/2509.26297 https://arxiv.org/pdf/2509.…

Polynomials and asymptotic constants in a resurgent problem from 't Hooft
In a recent study of the quantum theory of harmonic oscillators, Gerard 't Hooft proposed the following problem: given $G(z)=\sum_{n>0}\sqrt{n}z^n$ for $|z|<1$, find its analytic continuation for $|z|\ge1$, excluding a branch-cut $z\in[1,\,\infty)$. A solution is provided by the bilateral convergent sum $G(z)=\frac12\sqrtπ\sum_{n\in{\mathbb Z}}(2nπ{\rm i}-\log(z))^{-3/2}$. On the negative real axis, $G(-e^u)$ has a sign-constant asymptotic expansion in $1/u^2$, for large p…

Vandermonde Cells Through the Lens of Positive Geometry
Fatemeh Mohammadi, Sebastian Seemann
https://arxiv.org/abs/2510.11614 https://arxiv.org/pdf/2510.11…

Vandermonde Cells Through the Lens of Positive Geometry
We study the geometric and algebraic structure of Vandermonde cells, defined as images of the standard probability simplex under the Vandermonde map given by consecutive power sum polynomials. Motivated by their combinatorial equivalence to cyclic polytopes, which are well-known examples of positive geometries and tree amplituhedra, we investigate whether Vandermonde cells admit the structure of positive geometries. We derive explicit parametrizations and algebraic equations for their boundary …

eBay agrees to acquire Tise, a social marketplace for secondhand fashion and interior design items that has raised $45M in funding, for an undisclosed sum (Aisha Malik/TechCrunch)
https://techcrunch.com/2025/09/22/ebay-to-acquire-social-marketplace-platfor…

eBay to acquire social marketplace platform Tise | TechCrunch
eBay’s acquisition of Tise indicates that it's looking to modernize its platform to attract younger shoppers, expand its social commerce tools, and build a stronger presence in the sustainable retail market.

Sums of the floor function related to class numbers of imaginary quadratic fields
Marc Chamberland, Karl Dilcher
https://arxiv.org/abs/2510.04387 https://a…

Sums of the floor function related to class numbers of imaginary quadratic fields
A curious identity of Bunyakovsky (1882), made more widely known by Pólya and Szeg{\H o} in their ``Problems and Theorems in Analysis", gives an evaluation of a sum of the floor function of square roots involving primes $p\equiv 1\pmod{4}$. We evaluate this sum also in the case $p\equiv 3\pmod{4}$, obtaining an identity in terms of the class number of the imaginary quadratic field ${\mathbb Q}(\sqrt{-p})$. We also consider certain cases where the prime $p$ is replaced by a composite integer. C…

Equal knapsack identities between symmetric group character degrees
David J. Hemmer, Armin Straub, Karlee J. Westrem
https://arxiv.org/abs/2510.00301 https://

Equal knapsack identities between symmetric group character degrees
We prove a series of ``knapsack'' type equalities for irreducible character degrees of symmetric groups. That is, we find disjoint subsets of the partitions of $n$ so that the two corresponding character-degree sums are equal. Our main result refines our recent description of the Riordan numbers as the sum of all character degrees $f^λ$ where $λ$ is a partition of $n$ into three parts of the same parity. In particular, the sum of the ``fat-hook'' degrees $f^{(k,k,1^{n-2k})}+f^{(k+1,k+1,1^{n-2…

The nonsymmetric shuffle theorem
Jonah Blasiak, Mark Haiman, Jennifer Morse, Anna Pun, George H. Seelinger
https://arxiv.org/abs/2509.24040 https://arxiv.o…

The nonsymmetric shuffle theorem
The shuffle conjecture of Haglund et al. expresses the symmetric function $\nabla e_n$ as a sum over labeled Dyck paths. Here $\nabla$ is an operator on symmetric functions defined in terms of its diagonal action on the basis of modified Macdonald polynomials. The shuffle conjecture was later refined by Haglund-Morse-Zabrocki to the compositional shuffle conjecture, expressing $\nabla C_α$ as a sum over labeled Dyck paths with touchpoints specified by $α$, where $C_α$ is a compositional Hall…

Gauss and p-adic numbers
Franz Lemmermeyer
https://arxiv.org/abs/2510.11559 https://arxiv.org/pdf/2510.11559

Gauss and p-adic numbers
In his notebooks, Gauss recorded various calculations with "infinite congruences". These infinite congruences are p-adic numbers; Gauss computes a square root of $5$ in the $11$-adic integers in order to find an $11$-adic approximation to a quadratic Gauss sum, computes a nontrivial square root of $1$ in $10$-adic integers, and computes the $10$-adic logarithms of small natural numbers.

On The Roots of Independence Polynomial: Quantifying The Gap
Om Prakash, Vikram Sharma
https://arxiv.org/abs/2510.09197 https://arxiv.org/pdf/2510.09197

On The Roots of Independence Polynomial: Quantifying The Gap
The independence polynomial of a graph $G$ is the generating polynomial corresponding to its independent sets of different sizes. More formally, if $a_k(G)$ denotes the number of independent sets of $G$ of size $k$ then \[I(G,z) \as \sum_{k}^{} (-1)^k a_k(G) z^k.\] The study of evaluating $I(G,z)$ has several deep connections to problems in combinatorics, complexity theory and statistical physics. Consequently, the roots of the independence polynomial have been studied in detail. In particula…

On the distinction between Kloosterman sums and multiplicative functions
Yang Zhang
https://arxiv.org/abs/2510.10721 https://arxiv.org/pdf/2510.10721

On the distinction between Kloosterman sums and multiplicative functions
Let $S(a,b;n)$ be the Kloosterman sum. For any integers $a\neq0,b\neq0,k\geqslant2$, any given complex number $η\not=0$ and multiplicative function $f: \mathbb{N} \rightarrow \mathbb{C}$, we show that \[ |\{n\leqslant X:S(a,b;n)=ηf(n), n \text{ square-free }k\text{-almost prime}\}|\leqslant π(\dfrac{X}{L_k})+O(X^{1-\frac{1}{2k}}) \] and \[ |\{n\leqslant X:S(a,b;n)=ηf(n), n \text{ square-free}\}|\leqslant π(X)+O(Xe^{-\sqrt{\log X}}) \] as $X\rightarrow \infty$. Here, $L_…

Multiparty equality in the local broadcast model
Louis Esperet, Jean-Florent Raymond
https://arxiv.org/abs/2510.09143 https://arxiv.org/pdf/2510.09143

Multiparty equality in the local broadcast model
In this paper we consider the multiparty equality problem in graphs, where every vertex of a graph $G$ is given an input, and the goal of the vertices is to decide whether all inputs are equal. We study this problem in the local broadcast model, where a message sent by a vertex is received by all its neighbors and the total cost of a protocol is the sum of the lengths of the messages sent by the vertices. This setting was studied by Khan and Vaidya, who gave in 2021 a protocol achieving a 4-app…

Congruences Relating Regular Partition Functions, a Genearalised Tau Function and Partition Function Weighted Composition Sums
S. Sriram, A. David Christopher
https://arxiv.org/abs/2509.26559

Congruences Relating Regular Partition Functions, a Genearalised Tau Function and Partition Function Weighted Composition Sums
Let $n$ and $t$ be positive integers with $t\geq 2$. Let $R_t(n)$ be the number of $t$-regular partitions of $n$. A class of functions, denoted $τ_k(n)$, is defined as follows: \[q\prod_{m=1}^{\infty}(1-q^m)^k=\sum_{n=1}^{\infty}τ_k(n)q^n, \] where $k$ is an integer. We express $τ_k(n)$ as a binomial coefficient weighted partition sum. Consequently, we obtain congruence identities that relate $τ_k(n)$, $R_t(n)$ and partition function weighted composition sums.