Had Fun

Bought a car/micro-camper

Bought a van to do up as a micro-camper, and did a temporary rush job of that conversion myself while waiting in the list for the pro to do it.
Then the pro gave himself a health criss the week it was booked so I took apart my temp job and only got another temp kit-job in it's place.
Went out in it like four times during that and then broke my wrist and couldn't really use it or improve it.
Then had to take it apart even more to try
and figure out where the ad-blue hole was.
I will do a proper permanent job of the
floor and walls and ceiling and adjustments to the kit-job to make it the nicest it's been so far during the spring next year.
My assumption that the prior conversion
into a van and for wheelchair-access meant the microcamper conversion was half-done already turned out to be false.
If I buy a new one, it'll be one that has never been wheelchair adapted.
But it's going okay. Only scraped it once so far.
Fewer than aimed for or booked, but I broke my wrist and had to cancel the second half of the summer.
Went to a conference about money and computers and fringe decentralized social media and it wasn't as boring as you might expect and felt pretty much like a festival.
Exactly the target number! It's lovely.
Took 3 times longer than I'd hoped and
50% more money than I'd planned for really.
Still improvements to make but they will
be incremental and gradual over the coming year or two now.
It's been interest-only for 20 years so a big old lump sum payment that I never really expected to be able to make. Expected to have to sell and move at the end of the mortgage term.
But surprisingly the stocks ISA got high enough to pay it off after all, so I did that.
Cash-flow ruined by that and the bedroom but should start to feel a bit richer next year.

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

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.

""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.""

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.

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.

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-…

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.…

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

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 …

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…

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

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

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 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…

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.

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…

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.

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 $\sumelements$.

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…

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

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

🇺🇦 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

🇺🇦 #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

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…

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 …

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 …

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…

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.
*

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.

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…

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 …

“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!

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…

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 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…

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

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.

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.

"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…

🇺🇦 #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

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…

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^-}…

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…

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…

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…

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…

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

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 …

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

🤼‍♂️ Japan's sumo association turns 100, but the sport's rituals have a much older role shaping ideas about the country
https://theconversation.com/japans-sumo-association-turns-100-but…

Japan’s sumo association turns 100 – but the sport’s rituals have a much older role shaping ideas about the country
As Japan’s national sport, sumo has shaped perceptions of its culture since the mid-1800s.

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…

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…

Revisiting generalized inverses of a sum with a radical element
Yukun Zhou, Nestor Thome
https://arxiv.org/abs/2510.00901 https://arxiv.org/pdf/2510.00901

Revisiting generalized inverses of a sum with a radical element
Let $R$ be a ring with identity and $J(R)$ be its Jacobson radical. Assume that $a\in R$ is $(b,c)$-invertible and $j_a,j_b,j_c\in J(R)$. This paper provides necessary and sufficient conditions for $a+j_a$ to be $(b+j_b,c+j_c)$-invertible. As an application, corresponding results on generalized inverses of dual matrices are derived.

Examining Solidarity Against AI-Enabled Surveillance at the Intersection of Workplace and Carceral Realities
Morgan McErlean, Cella M. Sum, Sukrit Venkatagiri, Sarah Fox
https://arxiv.org/abs/2510.06537

Examining Solidarity Against AI-Enabled Surveillance at the Intersection of Workplace and Carceral Realities
As panoptical, AI-driven surveillance becomes a norm, everyone is impacted. In a reality where all people fall victim to these technologies, establishing links and solidarity is essential to fighting back. Two groups facing rising and targeted surveillance are workers and individuals impacted by the carceral system. Through preliminary data collection from a worker-surveillance lens, our findings reveal several cases of these surveillance infrastructures intersecting. Continuation of our work w…

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

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

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…

On elastic and non-elastic wave superpositions for the Euler system
{\L}ukasz Chomienia, Alfred Michel Grundland
https://arxiv.org/abs/2510.09576 https://a…

On elastic and non-elastic wave superpositions for the Euler system
The paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. This system admits entropic solutions and two types of sound wave solutions. It is shown that the smallest real Lie algebra containing vector fields (associated with these waves) is isomorphic to a semidirect sum of the infinite-dimensional Abelian real Lie algebra and the non-Abelian finite-dimensional real Lie algebra. Based on …

A study of 80 known pulsars at 185 MHz using MWA incoherent drift-scan observations
Ting Yu, Hongyu Gong, Zhifu Gao, Zhongli Zhang, Zhigang Wen, Yujie Wang, Tao An
https://arxiv.org/abs/2510.09046

A study of 80 known pulsars at 185 MHz using MWA incoherent drift-scan observations
A systematic study of 80 known pulsars observed at 185 MHz has been conducted using archival incoherent-sum data from the Murchison Widefield Array (MWA). The dataset comprises 48 drift-scan observations from the MWA Voltage Capture System, covering approximately 30,000 square degrees of sky with sensitivities reaching about 8 mJy in the deepest regions. An optimized PRESTO-based search pipeline was deployed on the China SKA Regional Centre infrastructure. This enabled the detection of 80 known…

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 $y=0$.

Finite element analysis of a nonlinear heat Equation with damping and pumping effects
Rishabh Shukla, Wasim Akram, Manil T. Mohan
https://arxiv.org/abs/2510.10210 https://

Finite element analysis of a nonlinear heat Equation with damping and pumping effects
We study the following nonlinear heat equation with damping and pumping effects (a reaction-diffusion equation) posed on a bounded simply connected convex domain $Ω\subset \mathbb{R}^d$, $d \geq 1$ with Lipschitz boundary $\partialΩ$: $$ \frac{\partial u(t)}{\partial t} - νΔu(t) + α|u(t)|^{p-2}u(t) - \sum_{\ell=1}^M β_{\ell} |u(t)|^{q_{\ell}-2}u(t) = f(t), \quad t>0, $$ subject to homogeneous Dirichlet boundary conditions and the initial condition $u(0)=u_0$, where $2 …

🇺🇦 #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

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.}…

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

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 $0.73194$.

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…

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…

Quadratic Programming Approach for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games
Sam Ganzfried
https://arxiv.org/abs/2509.25618 https://

Quadratic Programming Approach for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games
There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer strategic-form games. While counterfactual regret minimization and fictitious play are scalable to large games and have convergence guarantees in two-player zero-sum games, they do not guarantee convergence to Nash equilibrium in multiplayer games. We present an approach for exact computat…

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.

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…

🇺🇦 #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

Sonnet 049 - XLIX
Against that time, if ever that time come,
When I shall see thee frown on my defects,
When as thy love hath cast his utmost sum,
Called to that audit by advis'd respects;
Against that time when thou shalt strangely pass,
And scarcely greet me with that sun, thine eye,
When love, converted from the thing it was,
Shall reasons find of settled gravity;
Against that time do I ensconce me here,
Within the knowledge …

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 …

🇺🇦 #NowPlaying on #KEXP's #Early
foamboy:
🎵 SUMMERING
#foamboy
#newRelease 🆕 single
https://foamboy.bandcamp.com/track/summering
https://open.spotify.com/track/600axZKBKvEHZuZnPDz0JF

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…

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…

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…

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…

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…

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…

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…

🇺🇦 #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

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…

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 …

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_…

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.

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…

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…

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.

Progress towards generalized Nash-Williams' conjecture on $K_4$-decompositions
Menglong Zhang, Gennian Ge
https://arxiv.org/abs/2510.07783 https://arxi…

Progress towards generalized Nash-Williams' conjecture on $K_4$-decompositions
A $K_4$-decomposition of a graph is a partition of its edges into $K_4$s. A fractional $K_4$-decomposition is an assignment of a nonnegative weight to each $K_4$ in a graph such that the sum of the weights of the $K_4$s containing any given edge is one. Formulating a nonlinear programming and reducing the number of variables slowly, we prove that every graph on $n$ vertices with minimum degree at least $\frac{31}{33}n$ has a fractional $K_4$-decomposition. This improves a result of Montgomery t…

A class of skew-regular quaternary Hadamard matrices
Hadi Kharaghani, Vlad Zaitsev
https://arxiv.org/abs/2510.06489 https://arxiv.org/pdf/2510.06489…

A class of skew-regular quaternary Hadamard matrices
We construct a class of skew-regular quaternary Hadamard matrices of order $1+p^2$ for every odd prime power $p$. These matrices possess a row sum of $1-pi$. Applications include the generation of Hadamard matrices of order $4(1+p^2)$ with an excess of $8p(1+p^2)$.

General Recurrence Multidimensional Zeckendorf Representations
Jiarui Cheng, Steven J. Miller, Sebastian Rodriguez-Labastida, Tianyu Shen, Alan Sun, Garrett Tresch
https://arxiv.org/abs/2510.07237

General Recurrence Multidimensional Zeckendorf Representations
We present a multidimensional generalization of Zeckendorf's Theorem (any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers) to a large family of linear recurrences. This extends work of Anderson and Bicknell-Johnson in the multi-dimensional case when the underlying recurrence is the same as the Fibonacci one. Our extension applies to linear recurrence relations defined by vectors $\vec{\mathbf{c}} = (c_1, c_2, \ldots, c_k)$ such that $c_1\geq c_2\geq\cdots \ge…

The $n^{th}$ centered moments of a large orthogonal family of automorphic $L$-functions
Vorrapan Chandee, Yoonbok Lee, Xiannan Li
https://arxiv.org/abs/2510.07647 https://

The $n^{th}$ centered moments of a large orthogonal family of automorphic $L$-functions
We obtain the $n$th centered moments of one level densities of a large orthogonal family of $L$-functions associated with holomorphic Hecke newforms of level $q$, averaged over $q\sim Q$. We verify the Katz-Sarnak conjecture for these statistics, in the range where the sum of the supports of the Fourier transforms of test functions lies in $(-4, 4)$. In so doing, we need to understand certain phantom oversized terms, which allow us to extract the right off-diagonal contributions. We further nee…

Behavior of The Extremal Bounds on the $\sigma$-Irregularity
Jasem Hamoud, Duaa Abdullah
https://arxiv.org/abs/2510.06845 https://arxiv.org/pdf/2510.06845

Behavior of The Extremal Bounds on the $σ$-Irregularity
In this paper, we establishe the extremal bounds of the topological indices -Sigma index- focusing on analyzing the sharp upper bounds and the lower bounds of the Sigma index, which is known $σ(G)=\sum_{uv\in E(G)}(d_G(u)-d_G(v))^2$. We establish precise lower and upper bounds for the Sigma index, leveraging a non-increasing degree sequence $\mathscr{D} = (d_1, d_2, \dots, d_n)$, A fundamental challenge in the study of topological indices lies in establishing precise bounds, as such findings i…

Quantum walks on finite and bounded infinite graphs
Chris Godsil, Steve Kirkland, Sarojini Mohapatra, Hermie Monterde, Hiranmoy Pal
https://arxiv.org/abs/2510.05306 https://

Quantum walks on finite and bounded infinite graphs
A weighted graph $G$ with countable vertex set is bounded if there is an upper bound on the maximum of the sum of absolute values of all edge weights incident to a vertex in $G$. In this paper, we prove a fundamental result on equitable partitions of bounded weighted graphs with twin subgraphs and use this fact to construct finite and bounded infinite graphs with pair and plus state transfer with the adjacency matrix as a Hamiltonian. We show that for each $k \ge 3$, (i) there are infinitely ma…