Tootfinder

Solving Zero-Sum Games with Fewer Matrix-Vector Products
Ishani Karmarkar, Liam O'Carroll, Aaron Sidford
https://arxiv.org/abs/2509.04426 https://arxiv…

Solving Zero-Sum Games with Fewer Matrix-Vector Products
In this paper we consider the problem of computing an $ε$-approximate Nash Equilibrium of a zero-sum game in a payoff matrix $A \in \mathbb{R}^{m \times n}$ with $O(1)$-bounded entries given access to a matrix-vector product oracle for $A$ and its transpose $A^\top$. We provide a deterministic algorithm that solves the problem using $\tilde{O}(ε^{-8/9})$-oracle queries, where $\tilde{O}(\cdot)$ hides factors polylogarithmic in $m$, $n$, and $ε^{-1}$. Our result improves upon the state-of-the…

Two-Timescale Sum-Rate Maximization for Movable Antenna Enhanced Systems
Xintai Chen, Biqian Feng, Yongpeng Wu, Derrick Wing Kwan Ng, Robert Schober
https://arxiv.org/abs/2509.04062

Two-Timescale Sum-Rate Maximization for Movable Antenna Enhanced Systems
This paper studies a novel movable antenna (MA)-enhanced multiuser multiple-input multiple-output downlink system designed to improve wireless communication performance. We aim to maximize the average achievable sum rate through two-timescale optimization exploiting instantaneous channel state information at the receiver (I-CSIR) for receive antenna position vector (APV) design and statistical channel state information at the transmitter (S-CSIT) for transmit APV and covariance matrix design. W…

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$
el Houcein el Abdalaoui
https://arxiv.org/abs/2509.04212 https://arxiv.org/pdf/…

A generalization of Littlewood's $L^α$ flat theorem, $α>0$
We establish a generalization of Littlewood's criterion on $L^α$-flatness by proving that there is no $L^α$-flat polynomials, $α>0$, within the class of analytic polynomials on the unit circle of the form $ P_n(z)=\sum_{m=1}^{n}c_m z^m, n \in {\mathbb{N}}^*,$ satisfying $$ \sum_{m=1}^{n}|c_m|^2 \leq \frac{K}{n^2} \sum_{m=1}^{n}m^2 |c_m|^2, $$ where $K$ is an absolutely constant. As a consequence, we confirm the $L^α$-Littlewood conjecture, and thereby the $L^1$-Newman an…

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.
*

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

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 …

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 …

Macaulay representation of the prolongation matrix and the SOS conjecture
Zhiwei Wang, Chenlong Yue, Xiangyu Zhou
https://arxiv.org/abs/2509.04314 https://…

Macaulay representation of the prolongation matrix and the SOS conjecture
Let $z \in \mathbb{C}^n$, and let $A(z,\bar{z})$ be a real valued diagonal bihomogeneous Hermitian polynomial such that $A(z,\bar{z})\|z\|^2$ is a sum of squares, where $\|z\|$ denotes the Euclidean norm of $z$. In this paper, we provide an estimate for the rank of the sum of squares $A(z,\bar{z})\|z\|^2$ when $A(z,\bar{z})$ is not semipositive definite. As a consequence, we confirm the SOS conjecture proposed by Ebenfelt for $2 \leq n \leq 6$ when $A(z,\bar{z})$ i…

When three experiments are better than two: Avoiding intractable correlated aleatoric uncertainty by leveraging a novel bias--variance tradeoff
Paul Scherer, Andreas Kirsch, Jake P. Taylor-King
https://arxiv.org/abs/2509.04363

When three experiments are better than two: Avoiding intractable correlated aleatoric uncertainty by leveraging a novel bias--variance tradeoff
Real-world experimental scenarios are characterized by the presence of heteroskedastic aleatoric uncertainty, and this uncertainty can be correlated in batched settings. The bias--variance tradeoff can be used to write the expected mean squared error between a model distribution and a ground-truth random variable as the sum of an epistemic uncertainty term, the bias squared, and an aleatoric uncertainty term. We leverage this relationship to propose novel active learning strategies that directl…

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…

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…

Crosslisted article(s) found for cs.DS. https://arxiv.org/list/cs.DS/new
[1/1]:
- Solving Zero-Sum Games with Fewer Matrix-Vector Products
Ishani Karmarkar, Liam O'Carroll, Aaron Sidford

Detecting Causality with Conjugation Quandles over Dihedral Groups
Zining Fan
https://arxiv.org/abs/2509.03544 https://arxiv.org/pdf/2509.03544

Detecting Causality with Conjugation Quandles over Dihedral Groups
We study whether quandle colorings can detect causality of events for links realized as skies in a $(2+1)$-dimensional globally hyperbolic spacetime $X$. Building off the Allen--Swenberg paper in which their $2$-sky link was conjectured to be causally related, they showed that the Alexander--Conway polynomial does not distinguish that link from the connected sum of two Hopf links, corresponding to two causally unrelated events. We ask whether the Alexander--Conway polynomial together with diffe…

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

“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!

Generation of Lognormal Synthetic Lyman-$\alpha$ Forest Spectra for $P_{1D}$ Analysis
Meagan Herbold, Naim G\"oksel Kara\c{c}ayl{\i}, Paul Martini
https://arxiv.org/abs/2509.04405

Generation of Lognormal Synthetic Lyman-$α$ Forest Spectra for $P_{1D}$ Analysis
The one-dimensional flux power spectrum (P1D) of the Lyman-$α$ forest probes small-scale structure in the intergalactic medium (IGM) and is therefore sensitive to a variety of cosmological and astrophysical parameters. These include the amplitude and shape of the matter power spectrum, the thermal history of the IGM, the sum of neutrino masses, and potential small-scale fluctuations due to the nature of dark matter. However, P1D is also highly sensitive to observational and instrumental system…

🤼‍♂️ 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.

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…

Hausdorff dimension of double base expansions and binary shifts with a hole
Jian Lu, Wolfgang Steiner, Yuru Zou
https://arxiv.org/abs/2509.04227 https://ar…

Hausdorff dimension of double base expansions and binary shifts with a hole
For two real bases $q_0, q_1 > 1$, a binary sequence $i_1 i_2 \cdots \in \{0,1\}^\infty$ is the $(q_0,q_1)$-expansion of the number \[ π_{q_0,q_1}(i_1 i_2 \cdots) = \sum_{k=1}^\infty \frac{i_k}{q_{i_1} \cdots q_{i_k}}. \] Let $U_{q_0,q_1}$ be the set of all real numbers having a unique $(q_0,q_1)$-expansion. When the bases are equal, i.e., $q_0 = q_1 = q$, Allaart and Kong (2019) established the continuity in $q$ of the Hausdorff dimension of the univoque set $U_{q,q}$, building on the work of…

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…

"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…

Replaced article(s) found for cs.CR. https://arxiv.org/list/cs.CR/new
[2/2]:
- Synthetic Census Data Generation via Multidimensional Multiset Sum
Cynthia Dwork, Kristjan Greenewald, Manish Raghavan

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…

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…

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.

Replaced article(s) found for cs.CY. https://arxiv.org/list/cs.CY/new
[1/1]:
- Synthetic Census Data Generation via Multidimensional Multiset Sum
Cynthia Dwork, Kristjan Greenewald, Manish Raghavan

Free-energy variations for determinantal 2D plasmas with holes
Nicolas Rougerie (UMPA-ENSL)
https://arxiv.org/abs/2510.01745 https://arxiv.org/pdf/2510.017…

Free-energy variations for determinantal 2D plasmas with holes
We study the Gibbs equilibrium of a classical 2D Coulomb gas in the determinantal case = 2. The external potential is the sum of a quadratic term and the potential generated by individual charges pinned in several extended groups. This leads to an equilibrium measure (droplet) with flat density and macroscopic holes. We consider ''correlation energy'' (free energy minus its mean-field approximation) expansions, for large particle number . Under the assumptions that the holes are sufficiently sm…

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…

Frugal forward-backward splitting methods with deviations
Yongyu Fu, Haowen Zheng, Qiao-Li Dong, Xiaolong Qin, Jing Zhao
https://arxiv.org/abs/2509.03865 https://

Frugal forward-backward splitting methods with deviations
The deviation vectors provide additional degrees of freedom and effectively enhance the flexibility of algorithms. In the literature, the iterative schemes with deviations are constructed and their convergence analyses are performed on an inefficient, algorithm-by-algorithm basis. In this paper, we address these by providing a general framework of frugal forward-backward splitting methods with deviations for finding zeros in the sum of a finite number of maximally monotone operators and cocoerc…

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^-}…

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…

Making, not Taking, the Best of N
Ammar Khairi, Daniel D'souza, Marzieh Fadaee, Julia Kreutzer
https://arxiv.org/abs/2510.00931 https://arxiv.org/pdf/2…

Making, not Taking, the Best of N
Obtaining high-quality generations in modern LLMs has largely been framed as a selection problem: identifying a single winning generation from a diverse pool of N samples, the Best-of-N (BoN). Yet, this approach is inherently zero-sum, discarding diverse and potentially useful information from the pool. Instead, we explore a collaborative setup, where all candidates can potentially contribute to the final winning generation. To this end, we propose Fusion-of-N (FusioN): a method that uses a gen…

Computing Control Lyapunov-Barrier Functions: Softmax Relaxation and Smooth Patching with Formal Guarantees
Jun Liu, Maxwell Fitzsimmons
https://arxiv.org/abs/2510.02223 https:/…

Computing Control Lyapunov-Barrier Functions: Softmax Relaxation and Smooth Patching with Formal Guarantees
We present a computational framework for synthesizing a single smooth Lyapunov function that certifies both asymptotic stability and safety. We show that the existence of a strictly compatible pair of control barrier and control Lyapunov functions (CBF-CLF) guarantees the existence of such a function on the exact safe set certified by the barrier. To maximize the certifiable safe domain while retaining differentiability, we employ a log-sum-exp (softmax) relaxation of the nonsmooth maximum barr…

A Novel Algorithm for Representing Positive Semi-Definite Polynomials as Sums of Squares with Rational Coefficients
Zhenbing Zeng, Yong Huang, Lu Yang, Yongsheng Rao
https://arxiv.org/abs/2510.01568

A Novel Algorithm for Representing Positive Semi-Definite Polynomials as Sums of Squares with Rational Coefficients
This paper presents a novel algorithm for constructing a sum-of-squares (SOS) decomposition for positive semi-definite polynomials with rational coefficients. Unlike previous methods that typically yield SOS decompositions with floating-point coefficients, our approach ensures that all coefficients in the decomposition remain rational. This is particularly useful in formal verification and symbolic computation, where exact arithmetic is required. We introduce a stepwise reduction technique that…

Symmetry analysis and new partially invariant solutions for the gas dynamics system with a special equation of state
Dilara Siraeva, Irina A. Kogan
https://arxiv.org/abs/2510.01415

Symmetry analysis and new partially invariant solutions for the gas dynamics system with a special equation of state
This paper is a contribution to the symmetry analysis of the gas dynamics system in the vein of the ''podmodeli'' (submodels) program outlined by Ovsyannikov (1994). We consider the case of the special state equation, prescribing pressure to be the sum of entropy and an arbitrary function of density. Such a system has a 12-dimensional symmetry Lie algebra. This work advances the study of its four-dimensional subalgebras, continuing the work started in Siraeva (2024). For a large subset of not p…

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.

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…

In a short blog post for the MacArthur Foundation, my colleague Veronica Thamaini and I discuss the Abstract Wikipedia proposal, one of five finalists for the ongoing 100&Change program.
A Path to a World Where Everyone Can Share in the Sum of All Knowledge
https://www.

A Path to a World Where Everyone Can Share in the Sum of All Knowledge

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.

I love little programming katas like this where the theoretical solution is kinda obvious but the implementation needs many things to wrap your head around.
Here: sum to numbers as strings (that will possibly exceed the max value of your numeric data type).
https://www.codewars.com/kata/5324945e2ece

Classification for smooth manifolds looking like $\mathbb{CP}^3\times S^7$
Wen Shen
https://arxiv.org/abs/2510.00613 https://arxiv.org/pdf/2510.00613

Classification for smooth manifolds looking like $\mathbb{CP}^3\times S^7$
In this paper, we classify simply connected closed smooth $13$-dimensional manifolds whose cohomology ring is isomorphic to that of $\mb{CP}^3\times S^7$, up to diffeomorphism, homeomorphism, and homotopy equivalence. Furthermore, if such a manifold satisfies certain conditions, either itself or its connected sum with an exotic $13$-sphere $Σ^{13}$ admits a Riemannian metric of non-negative sectional curvature. As an additional application of our classification, we classify the diagonal $S^1$-…

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.

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.

Classical feature map surrogates and metrics for quantum control landscapes
Martino Calzavara, Tommaso Calarco, Felix Motzoi
https://arxiv.org/abs/2509.25930 https://

Classical feature map surrogates and metrics for quantum control landscapes
We derive and analyze three feature map representations of parametrized quantum dynamics, which generalize variational quantum circuits. These are (i) a Lie-Fourier partial sum, (ii) a Taylor expansion, and (iii) a finite-dimensional sinc kernel regression representation. The Lie-Fourier representation is shown to have a dense spectrum with discrete peaks, that reflects control Hamiltonian properties, but that is also compressible in typically found symmetric systems. We prove boundedness in th…

""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.""

Abelian 3D TQFT gravity, ensemble holography and stabilizer states
Nikolaos Angelinos
https://arxiv.org/abs/2509.26052 https://arxiv.org/pdf/2509.26052

Abelian 3D TQFT gravity, ensemble holography and stabilizer states
We construct a model of 3D quantum gravity based on abelian topological quantum field theory (TQFT), by defining the gravitational path-integral as a sum over all 3D topologies with genus-$g$ boundary $Σ_g$. The path-integral of an abelian TQFT $\mathcal T$ on any single topology with boundary $Σ_g$ prepares a stabilizer state. This way, $\mathcal T$ partitions all these topologies into finitely many equivalence classes, where each topology within a class is associated with the same stabilize…

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…

«So, to sum it up, Kling wears his mask a bit better than DHH, but as far as I’m concerned it seems clear that both projects are run by fascists. If it walks like a fascist and quacks like a fascist… then why is Cloudflare giving them hundreds of thousands of dollars?»
I think we all know the answer to that one!
https://drewdevault.com/2025/09/24/2025-09-24-Cloudflare-and-fascists.html

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

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…

A Bouquet of Results on Maximum Range Sum: General Techniques and Hardness Reductions
Rachana Gusain, Saladi Rahul, Aditya Subramanian
https://arxiv.org/abs/2509.16008 https://

A Bouquet of Results on Maximum Range Sum: General Techniques and Hardness Reductions
We revisit the maximum range sum (MaxRS) problem: given a set $P$ of $n$ weighted points in $\mathbb{R}^d$ and a range $Q$ (typically axis-aligned $d$-box or $d$-ball), the goal is to place $Q$ to maximize the total weight of points in $P\cap Q$. We study three natural variations: (1) Dynamic MaxRS: The goal is to update the placement of a $d$-ball under point insertions and deletions. We give a randomized $(\frac{1}{2}-ε)$-approximation with update time $O_ε(\log n)$. The approximation fac…

Computing Linear Combinations of $\varphi$-Function Actions for Exponential Integrators
Awad H. Al-Mohy
https://arxiv.org/abs/2509.26475 https://arxiv.org/…

Computing Linear Combinations of $φ$-Function Actions for Exponential Integrators
We propose a matrix-free algorithm for evaluating linear combinations of $φ$-function actions, $w_i := \sum_{j=0}^{p} α_i^{\,j}\,φ_j(t_i A)v_j$ for $i=1\colon r$, arising in exponential integrators. The method combines the scaling and recovering method with a truncated Taylor series, choosing a spectral shift and a scaling parameter by minimizing a power-based objective of the shifted operator. Accuracy is user-controlled and ultimately limited by the working precision. The algorithm decoupl…

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…

Systematics on two-body mass measurements and the $\Lambda$-baryon mass
Allison Chu, Yiming Liu, Matthew Needham
https://arxiv.org/abs/2509.26130 https://a…

Systematics on two-body mass measurements and the $Λ$-baryon mass
The effect of detector-related uncertainties on the determination of the parent particle mass in two-body decays is described. Studies of the biases versus the sum and difference of the daughter particle momenta can be used to determine biases on the mass. The approach is illustrated for the case of measuring the $Λ$ hyperon mass.

Minimum Sum Coloring with Bundles in Trees and Bipartite Graphs
Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto
https://arxiv.org/abs/2509.15080

Minimum Sum Coloring with Bundles in Trees and Bipartite Graphs
The minimum sum coloring problem with bundles was introduced by Darbouy and Friggstad (SWAT 2024) as a common generalization of the minimum coloring problem and the minimum sum coloring problem. During their presentation, the following open problem was raised: whether the minimum sum coloring problem with bundles could be solved in polynomial time for trees. We answer their question in the negative by proving that the minimum sum coloring problem with bundles is NP-hard even for paths. We compl…

Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks
Nazar Emirov, Guohui Song, Qiyu Sun
https://arxiv.org/abs/2510.01511

Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks
We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration solves local subproblems around selected fusion centers and coordinates only with neighboring fusion centers. Under standard assumptions of smoothness, strong convexity, and locality on the objective function, together with polynomial growth conditions on the …

Semileptonic and nonleptonic weak decays of bottom baryons $\Omega^{(*)}_{b}$
L. Khajouei, K. Azizi
https://arxiv.org/abs/2510.01429 https://arxiv.org/pdf/…

Semileptonic and nonleptonic weak decays of bottom baryons $Ω^{(*)}_{b}$
We present an investigation into the semileptonic and nonleptonic weak decays of bottom baryons $Ω^{*}_{b}$ and $Ω_{b}$ within the framework of three-point QCD sum rules. In the semileptonic sector, the $Ω^{*}_b\rightarrowΩ_c\ell\barν_{\ell}$ and $Ω_b\rightarrowΩ^*_c\ell\barν_{\ell}$ transitions are specifically considered. Utilizing the operator product expansion up to dimension six, the responsible form factors of these decays are obtained. The acquired form factors enable us to deter…

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.

Explicit formulae for the Aicardi-Juyumaya bracket of tied links
O'Bryan C\'ardenas-Andaur, Juan Gonz\'alez-Meneses, Marithania Silvero
https://arxiv.org/abs/2510.02075

Explicit formulae for the Aicardi-Juyumaya bracket of tied links
The double bracket $\langle \langle \cdot \rangle \rangle$ (also known as the AJ-bracket) is an invariant of framed tied links that extends the Kauffman bracket of classical links. Unlike the classical setting, little is known about the structure of AJ-states (analogous to classical Kauffman states) of a given tied link diagram, and no general state-sum formula for the AJ-bracket is currently available. In this paper we analyze the AJ-states of $2$- and $3$-tied link diagrams, and provide a com…

Understanding the ratio of the partition sum to its Bethe approximation via double covers
Pascal O. Vontobel
https://arxiv.org/abs/2509.19910 https://arxiv…

Understanding the ratio of the partition sum to its Bethe approximation via double covers
For various classes of graphical models it has been observed that the ratio of the partition sum to its Bethe approximation is often close to being the square of the ratio of the partition sum to its degree-2 Bethe approximation. This is of relevance because the latter ratio can often better be analyzed and/or quantified than the former ratio. In this paper, we give some justifications for the observed relationship between these two ratios and then analyze these ratios for two classes of log-su…

The inverse of the (alternating) infinite sum of the reciprocal of the weighted sum for generalized Fibonacci sub-sequences
Yongkang Wan, Zhonghao Liang, Qunying Liao
https://arxiv.org/abs/2509.14569

The inverse of the (alternating) infinite sum of the reciprocal of the weighted sum for generalized Fibonacci sub-sequences
In this paper, for the generalized Fibonacci sequence $\left\{W_n\left(a,b,p,q\right)\right\}$, by using elementary methods and techniques, we give the asymptotic estimation values of $\left(\sum\limits_{k=n}^{\infty}\frac{1}{\sum\limits_{i=0}^{t}s_{i}W_{mk+l_i}}\right)^{-1}$ and $\left(\sum\limits_{k=n}^{\infty}\frac{\left(-1\right)^k}{\sum\limits_{i=0}^{t}s_{i}W_{mk+l_i}}\right)^{-1}$, respectively. In particular, for some special $a,b,p,q,m,t,s_i$ and $l_i\left(0\leq i\leq t \right)$, Theore…

Dequantization and Hardness of Spectral Sum Estimation
Roman Edenhofer, Atsuya Hasegawa, Fran\c{c}ois Le Gall
https://arxiv.org/abs/2509.20183 https://arxi…

Dequantization and Hardness of Spectral Sum Estimation
We give new dequantization and hardness results for estimating spectral sums of matrices, such as the log-determinant. Recent quantum algorithms have demonstrated that the logarithm of the determinant of sparse, well-conditioned, positive matrices can be approximated to $\varepsilon$-relative accuracy in time polylogarithmic in the dimension $N$, specifically in time $\mathrm{poly}(\mathrm{log}(N), s, κ, 1/\varepsilon)$, where $s$ is the sparsity and $κ$ the condition number of the input matr…

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…

Secure ISAC with Fluid Antenna Systems: Joint Precoding and Port Selection
Abdelhamid Salem, Hao Xu, Kai-Kit Wong, Chan-Byoung Chae, Yangyang Zhang
https://arxiv.org/abs/2509.26572

Secure ISAC with Fluid Antenna Systems: Joint Precoding and Port Selection
This paper presents a novel framework for enhancing physical-layer security in integrated sensing and communication (ISAC) systems by leveraging the reconfigurability of fluid antenna systems (FAS). We propose a joint precoding and port selection (JPPS) strategy that maximizes the sum secrecy rate while simultaneously ensuring reliable radar sensing. The problem is formulated using fractional programming (FP) and solved through an iterative algorithm that integrates FP transformations with succ…

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 …

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…

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.

An SoS Entropy Dichotomy via Windowed Hypercontractivity
Marko Lela
https://arxiv.org/abs/2509.24280 https://arxiv.org/pdf/2509.24280

An SoS Entropy Dichotomy via Windowed Hypercontractivity
We prove an entropy versus degree dichotomy for low-degree tests and the Sum-of-Squares (SoS) hierarchy on a calibrated window after a gadget layer. For a target distribution \(μ\) and a product-like proxy \(u\), we study the low-degree discrepancy \(Δ_k(μ,u)\), defined as the optimal distinguishing advantage of degree \(\le k\) polynomial tests. Using a bias-orthonormal Walsh basis and a test-moment equivalence on the window, we relate \(Δ_k\) (up to constants) to the squared \(\ell_2\) ma…

A Novel Framework for Honey-X Deception in Zero-Sum Games
Brendan Gould, Kyriakos Vamvoudakis
https://arxiv.org/abs/2509.20329 https://arxiv.org/pdf/2509.2…

A Novel Framework for Honey-X Deception in Zero-Sum Games
In this paper, we present a novel, game-theoretic model of deception in two-player, zero-sum games. Our framework leverages an information asymmetry: one player (the deceiver) has access to accurate payoff information, while the other (the victim) observes a modified version of these payoffs due to the deception strategy employed. The deceiver's objective is to choose a deception-action pair that optimally exploits the victim's best response to the altered payoffs, subject to a constraint on th…

Spectral theory of Schr\"odinger operators with potentials that are measures supported on ${\Bbb N}$
Oleg Safronov
https://arxiv.org/abs/2509.20320 https://

Spectral theory of Schrödinger operators with potentials that are measures supported on ${\Bbb N}$
We discuss spectral properties of the one-dimensional Schrödinger operator with a potential of the form $\sum V(n)δ(x-n)$. Our main result says that the absolutely continuous spectum of such an operator covers an interval $[α^2,β^2]$, if $V\in \ell^4$ and the Fourier series $\sum e^{2i kn}V(n)$ is a function of $k$ that is square integrable over $[α,β]$. We prove that this result is sharp by constructing examples of potentials $V\notin\ell^2$ for which the spectrum of the Schrödinger ope…

Zeta expansion for long-range interactions under periodic boundary conditions with applications to micromagnetics
Andreas A. Buchheit, Jonathan K. Busse, Torsten Ke{\ss}ler, Filipp N. Rybakov
https://arxiv.org/abs/2509.26274

Zeta expansion for long-range interactions under periodic boundary conditions with applications to micromagnetics
We address the efficient computation of power-law-based interaction potentials of homogeneous $d$-dimensional bodies with an infinite $n$-dimensional array of copies, including their higher-order derivatives. This problem forms a serious challenge in micromagnetics with periodic boundary conditions and related fields. Nowadays, it is common practice to truncate the associated infinite lattice sum to a finite number of images, introducing uncontrolled errors. We show that, for general interactin…

🇺🇦 #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

All Giant Graviton Two-Point Functions at Two-Loops
Yu Wu, Yunfeng Jiang, Chang Liu, Yang Zhang
https://arxiv.org/abs/2509.23161 https://arxiv.org/pdf/2509…

All Giant Graviton Two-Point Functions at Two-Loops
We present a comprehensive two-loop computation of correlation functions involving two maximal giant gravitons and two arbitrary $R$-charge single-trace half-BPS operators in $\mathcal{N}=4$ Super-Yang-Mills theory. By combining the partially-contracted giant graviton (PCGG) method with the $\mathcal{N}=2$ harmonic superspace formalism, we achieve significant simplifications in perturbative calculations. The resulting correlation functions encode rich CFT data, from which we derive sum rules fo…

Zero-sum turn games using Q-learning: finite computation with security guarantees
Sean Anderson, Chris Darken, Jo\~ao Hespanha
https://arxiv.org/abs/2509.13585 https://

Zero-sum turn games using Q-learning: finite computation with security guarantees
This paper addresses zero-sum ``turn'' games, in which only one player can make decisions at each state. We show that pure saddle-point state-feedback policies for turn games can be constructed from dynamic programming fixed-point equations for a single value function or Q-function. These fixed-points can be constructed using a suitable form of Q-learning. For discounted costs, convergence of this form of Q-learning can be established using classical techniques. For undiscounted costs, we provi…

The Sum Leaks More Than Its Parts: Compositional Privacy Risks and Mitigations in Multi-Agent Collaboration
Vaidehi Patil, Elias Stengel-Eskin, Mohit Bansal
https://arxiv.org/abs/2509.14284

The Sum Leaks More Than Its Parts: Compositional Privacy Risks and Mitigations in Multi-Agent Collaboration
As large language models (LLMs) become integral to multi-agent systems, new privacy risks emerge that extend beyond memorization, direct inference, or single-turn evaluations. In particular, seemingly innocuous responses, when composed across interactions, can cumulatively enable adversaries to recover sensitive information, a phenomenon we term compositional privacy leakage. We present the first systematic study of such compositional privacy leaks and possible mitigation methods in multi-agent…

Euler-type Recurrence Relation for Arbitrary Arithmetical Function
A. David christopher
https://arxiv.org/abs/2510.01277 https://arxiv.org/pdf/2510.01277…

Euler-type Recurrence Relation for Arbitrary Arithmetical Function
An interplay between the Lambert series and Euler's Pentagonal Number Theorem gives an Euler-type recurrence relation for any given arithmetical function. As consequences of this, we present Euler-type recurrence relations for some well-known arithmetic functions. Furthermore, we derive Euler-type recurrence relations for certain partition functions and sum-of-divisors functions using infinite product identities of Jacobi and Gauss.

Throttling for metric dimension and its variants
Boris Brimkov, Peter Diao, Jesse Geneson, Carolyn Reinhart, Shen-Fu Tsai, William Wang, Kyle Worley
https://arxiv.org/abs/2510.00530

Throttling for metric dimension and its variants
Metric dimension is a graph parameter that has been applied to robot navigation and finding low-dimensional vector embeddings. Throttling entails minimizing the sum of two available resources when solving certain graph problems. In this paper, we introduce throttling for metric dimension, edge metric dimension, and mixed metric dimension. In the context of vector embeddings, metric dimension throttling finds a low-dimensional, low-magnitude embedding with integer coordinates. We show that compu…

A Polylogarithmic Competitive Algorithm for Stochastic Online Sorting and TSP
Andreas Kalavas, Charalampos Platanos, Thanos Tolias
https://arxiv.org/abs/2509.26073 https://

A Polylogarithmic Competitive Algorithm for Stochastic Online Sorting and TSP
In \emph{Online Sorting}, an array of $n$ initially empty cells is given. At each time step $t$, an element $x_t \in [0,1]$ arrives and must be placed irrevocably into an empty cell without any knowledge of future arrivals. We aim to minimize the sum of absolute differences between pairs of elements placed in consecutive array cells, seeking an online placement strategy that results in a final array close to a sorted one. An interesting multidimensional generalization, a.k.a. the \emph{Online T…

Neural-Model-Augmented Hybrid NMS-OSD Decoders for Near-ML in Short Block Codes
Guangwen Li, Xiao Yu
https://arxiv.org/abs/2509.25580 https://arxiv.org/pdf…

Neural-Model-Augmented Hybrid NMS-OSD Decoders for Near-ML in Short Block Codes
This paper introduces a hybrid decoding architecture that serially couples a normalized min-sum (NMS) decoder with reinforced ordered statistics decoding (OSD) to achieve near-maximum likelihood (ML) performance for short linear block codes. The framework incorporates several key innovations: a decoding information aggregation model that employs a convolutional neural network to refine bit reliability estimates for OSD using the soft-output trajectory of the NMS decoder; an adaptive decoding pa…

Strengthening the Bridge Between Chiral Lagrangians and QCD Sum-Rules
J. Ho, Amir H. Fariborz, T. G. Steele
https://arxiv.org/abs/2509.16380 https://arxiv.…

Strengthening the Bridge Between Chiral Lagrangians and QCD Sum-Rules
Previous work has shown that mesonic fields in chiral Lagrangians can be systematically connected to quark-level operators in QCD sum rules through chiral-symmetry constrained and energy-independent scale factor matrices. This framework yields universal scale factors associated with each chiral nonet, whether composed of quark-antiquark ($q\bar{q}$) or four-quark ($qq\bar{q}\bar{q}$) operators. Building on the demonstrated scale-factor universality for the $K_0^*$ isodoublet and $a_0$ isotriple…

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/3]:
- Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimization
Constantinos Daskalakis, Ioannis Panageas

Interpreting a Sum of Third Powers by using a Geometric Assembly in Four Dimensions
Joseph Alfano (Assumption University), Emily Armstrong (University of Pittsburgh), Vincent DeNolf (University of Colorado), Jonah Sagarin (Union College)
https://arxiv.org/abs/2509.19114

Further Applications of Cubic $q$-Binomial Transformations
Alexander Berkovich, Aritram Dhar
https://arxiv.org/abs/2510.00130 https://arxiv.org/pdf/2510.00…

Further Applications of Cubic $q$-Binomial Transformations
Consider \begin{align*} G(N,M;α,β,K,q) = \sum\limits_{j\in\mathbb{Z}}(-1)^jq^{\frac{1}{2}Kj((α+β)j+α-β)}\left[\begin{matrix}M+N\\N-Kj\end{matrix}\right]_{q}. \end{align*} In this paper, we prove the non-negativity of coefficients of some cases of $G(N,M;α,β,K,q)$. For instance, for non-negative integers $n$ and $t$, we prove that \begin{align*} G\left(n,n;\frac{4}{3}+\frac{3(3^t-1)}{2},\frac{5}{3}+\frac{3(3^t-1)}{2},3^{t+1},q\right) \end{align*} and \begin{align*} G\left(n-\frac{3^t-1}{…

Hook immanantal inequalities for totally nonnegative matrices
Mark Skandera
https://arxiv.org/abs/2510.00327 https://arxiv.org/pdf/2510.00327

Hook immanantal inequalities for totally nonnegative matrices
Given a weakly decreasing positive integer sequence $λ= (λ_1,\dotsc,λ_\ell)$ summing to $n$, let $χ^λ$ denote the irreducible character of the symmetric group $S_n$ indexed by $λ$. This representation has dimension $χ^λ(e)$, where $e$ is the identity element of $S_n$. Let $\mathrm{Imm}_{χ^λ}$ denote the corresponding irreducible character immanant, the function on $n \times n$ matrices $A = (a_{i,j})$ defined by $\mathrm{Imm}_{χ^λ}(A) := \sum_{w \in S_n} χ^λ(w) a_{1,w_1} \cdots a_…

Satellite Operations and $\theta$
Rob McConkey, Luke J Seaton
https://arxiv.org/abs/2509.22939 https://arxiv.org/pdf/2509.22939

Satellite Operations and $θ$
We study the behavior of the knot invariant $θ$ under satellite operations. First, we prove that $θ$ is additive under connected sum. We then introduce a computational tool to generate $t$-twisted Whitehead doubles and apply it to explore the case of untwisted Whitehead doubles. We propose a conjecture describing the behavior of $θ$ on untwisted Whitehead doubles and verify the conjecture for the first 2977 prime knots. The pair of invariants $Θ= (Δ,θ)$ was introduced by Bar-Natan and van…

Efficient tau-pair invariant mass reconstruction with simplified matrix element techniques
Artur Kalinowski, Wiktor Matyszkiewicz
https://arxiv.org/abs/2509.26069 https://

Efficient tau-pair invariant mass reconstruction with simplified matrix element techniques
The quality of the invariant mass reconstruction of the di-τ system is crucial for searches and analyses of di-τ resonances. Due to the presence of neutrinos in the final state, the τ τ invariant mass cannot be calculated directly at hadron colliders, where the longitudinal momentum sum constraint cannot be applied. A number of approaches have been adopted to mitigate this issue. The most general one uses Matrix Element (ME) integration for likelihood estimation, followed by invariant mass …

The Service Rate Region of Hamming Codes
Priyanka Choudhary, Maheshanand Bhaintwal
https://arxiv.org/abs/2509.22898 https://arxiv.org/pdf/2509.22898…

The Service Rate Region of Hamming Codes
The service rate region of a coded distributed storage system is the set of all achievable data access requests under the capacity constraints. This paper investigates the service rate regions of systematic Hamming codes using hypergraph theory and derives bounds for the maximal achievable service rate of individual data objects. We establish upper bounds on the sum of service rates of data symbols indexed by a subset of systematic nodes in a systematic binary Hamming code, and explore the achi…

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…

Extra Radiation Cosmologies: Implications of the Hubble Tension for eV-scale Neutrinos
Helena Garc\'ia Escudero, Kevork N. Abazajian
https://arxiv.org/abs/2509.25478 https:/…

Extra Radiation Cosmologies: Implications of the Hubble Tension for eV-scale Neutrinos
We present a new analysis on sterile neutrino cosmologies using the Dark Energy Spectroscopic Instrument (DESI) second data release (DR2) baryon acoustic oscillation (BAO) measurements in combination with cosmic microwave background (CMB), CMB lensing, and supernova data. We show that BAO observables are intrinsically less sensitive to the combined effects of relativistic energy density, $N_{\rm eff}$, and the sum of neutrino masses, $Σm_ν$, which are both augmented in sterile neutrino cosmol…

Sphere intersections and incidences over finite fields
Doowon Koh, Ben Lund, Chuandong Xu, Semin Yoo
https://arxiv.org/abs/2509.25997 https://arxiv.org/pdf…

Sphere intersections and incidences over finite fields
We bound the number of incidences between points and spheres in finite vector spaces by bounding the sum of the number of points in the pairwise intersections of the spheres. We obtain new incidence bounds that are interesting when the number of spheres is not too large. Our approach also leads to an elementary proof of the Iosevich-Rudnev bound on the Erdős-Falconer distance problem in odd dimensions.

A $q$-analogue of distance matrix of bi-block graphs
Joyentanuj Das
https://arxiv.org/abs/2509.26060 https://arxiv.org/pdf/2509.26060

A $q$-analogue of distance matrix of bi-block graphs
A $q$-analogue of the distance matrix, referred to as the \emph{$q$-distance matrix}, is obtained from the distance matrix by replacing each nonzero entry $α$ with the sum $1+q+\cdots+q^{α-1}$. This notion was introduced independently by Bapat, Lal, and Pati~\cite{Ba-Lal-Pati}, and by Yan and Yeh~\cite{Yan}. A connected graph is called a \emph{bi-block graph} if each of its blocks is a complete bipartite graph. In this paper, we derive explicit formulas for the determinant and the inverse of …

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…

A sum rule for derangements
Jean-Christophe Pain
https://arxiv.org/abs/2509.14672 https://arxiv.org/pdf/2509.14672

A sum rule for derangements
We propose a sum rule for derangements. Three different proofs are provided. The first one involves integral representations and the second one relies on the Hermite identity for the integer part of the product of an integer by a real number. The third one, which, unlike the previous ones, is not based on induction, proceeds directly from a recurrence relation for the number of derangements.

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.…

On Averages of Shifted Convolutions with Applications to $GL(2)$ and $GL(3)$ Fourier Coefficients
Jiseong Kim
https://arxiv.org/abs/2509.24152 https://arxi…

On Averages of Shifted Convolutions with Applications to $GL(2)$ and $GL(3)$ Fourier Coefficients
In this paper, we study the average of shifted sum for general multiplicative functions. As applications, we prove non-trivial upper bounds for weighted averages of shifted convolutions involving $GL(2)$ and $GL(3)$ Fourier coefficients without smoothing. We apply square-root cancellation on average over short intervals for $GL(2)$ Fourier coefficients with the standard Hardy-Littlewood circle method.

Semigroup rings and algebraically independent sequences with respect to idempotents in commutative semigroups
Guoqing Wang
https://arxiv.org/abs/2509.18724 https://

Semigroup rings and algebraically independent sequences with respect to idempotents in commutative semigroups
For any finite abelian group $G$ and commutative unitary ring $R$, by $R[G]$ we denote the group algebra over $R$. Let $T=(g_1,\ldots,g_{\ell})$ be a sequence over the group $G$. We say $T$ is algebraically zero-sum free over R if $\prod\limits_{i=1}^r(X^{g_i}-a_i)\neq 0\in R[G]$ for all $a_1,\ldots,a_{\ell}\in R\setminus \{0\}$. Let $d(G,R)={\rm sup}\{|T|: T \mbox{ is an algebraically zero-sum free sequence over } R \mbox{ of terms from }G\}.$ This invariant of the group algebra $R[G…

The trigonometric polynomial on sums of two squares, an additive problem and generalisation
Olivier Ramare, GK Viswanadham
https://arxiv.org/abs/2509.23260 https://

The trigonometric polynomial on sums of two squares, an additive problem and generalisation
Let $B$ be the set of odd integers that are sums of two coprime squares. We prove that the trigonometric polynomial $S(α;N)=\sum_{b\in B,b\leq N} e(bα)$ satisfies \[ \frac{S(α; N)}{N/\sqrt{\log N}}<<_{A,A'} \frac{1}{ϕ(q)} + \sqrt{\frac{q}{N}}(\log N)^{7} +\frac{1}{(\log N)^A} \] for any $A,A'\geq 0$ and when $(a,q)=1$ and $|qα-a|\leq (\log N)^{A'}/N$. We use this estimate together with a variant of the circle method influenced by Green and Tao's Transference Principle to obtain t…

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…

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…

Improvement of Drmota-Verwee's effective Erdos-Wintner theorem for Zeckendorf expansions
Johann Verwee
https://arxiv.org/abs/2509.14974 https://arxiv.o…

Improvement of Drmota-Verwee's effective Erdos-Wintner theorem for Zeckendorf expansions
We revisit the effective Erdos-Wintner theorem for Zeckendorf expansions. Drmota and the author obtained a uniform Kolmogorov bound whose error involves $T\sum_{j>L-2h}|f(F_j)|$, which assumes absolute convergence of the linear tail $\sum_j f(F_j)$. We remove this assumption. Grouping the transfer matrices in pairs and working to second order on the logarithm of the product, after extracting the common linear phase along the dominant direction, yields a quadratic tail $T^2\sum_{j>L-2h…