Tootfinder

Turnpike properties for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
Xun Li, Fan Wu, Xin Zhang
https://arxiv.org/abs/2509.09358 h…

Turnpike properties for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
This paper investigates the long-time behavior of zero-sum stochastic linear-quadratic (SLQ) differential games within Markov regime-switching diffusion systems and establishes the turnpike property of the optimal triple. By verifying the convergence of the associated coupled differential Riccati equations (CDREs) along with their convergence rate, we show that, for a sufficiently large time horizon, the equilibrium strategy in the finite-horizon problem can be closely approximated by that of t…

Diffraction-Unlimited Tip-Enhanced Sum-Frequency Vibrational Nanoscopy
Shota Takahashi, Koichi Kumagai, Atsunori Sakurai, Tatsuto Mochizuki, Tomonori Hirano, Akihiro Morita, Toshiki Sugimoto
https://arxiv.org/abs/2509.09179

Diffraction-Unlimited Tip-Enhanced Sum-Frequency Vibrational Nanoscopy
Sum-frequency generation (SFG) is a powerful second-order nonlinear spectroscopic technique that provides detailed insights into molecular structures and absolute orientations at surfaces and interfaces. However, conventional SFG based on far-field schemes suffers from the diffraction limit of light, which inherently averages spectroscopic information over micrometer-scale regions and obscures nanoscale structural inhomogeneity. Here, we overcome this fundamental limitation by leveraging a high…

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…

Special restricted partition functions for the stable sheaf cohomology on flag varieties
Mircea Cimpoeas
https://arxiv.org/abs/2509.09418 https://arxiv.org…

Special restricted partition functions for the stable sheaf cohomology on flag varieties
Let $\mathbf a:=(a_1,\ldots,a_r)$ be a sequence of positive integers, $d\geq 2$ and $j\geq 1$, some integers. We study the functions $p_{\mathbf a,d}(n):=$ the number of integer solutions $(x_1,\dots,x_r)$ of $\sum_{i=1}^r a_ix_i=n$, with $x_i\geq 0$ and $x_i \equiv 0,1(\bmod\;d)$, for all $1\leq i\leq r$, and $p_{\mathbf a,d}(n;j):=$ the number of $(x_1,\ldots,x_r)$ as above which satisfy also the condition $\sum_{i=1}^r \left(x_i-(d-2)\left\lfloor \frac{x_i}{d} \right\rfloor\right) =j$. We …

Retrocausal capacity of a quantum channel
Kaiyuan Ji, Seth Lloyd, Mark M. Wilde
https://arxiv.org/abs/2509.08965 https://arxiv.org/pdf/2509.08965

Retrocausal capacity of a quantum channel
We study the capacity of a quantum channel for retrocausal communication, where messages are transmitted backward in time, from a sender in the future to a receiver in the past, through a noisy postselected closed timelike curve (P-CTC) represented by the channel. We completely characterize the one-shot retrocausal quantum and classical capacities of a quantum channel, and we show that the corresponding asymptotic capacities are equal to the average and sum, respectively, of the channel's max-i…

Large character sums with multiplicative coefficients
Zikang Dong, Yutong Song, Weijia Wang, Hao Zhang, Shengbo Zhao
https://arxiv.org/abs/2509.09649 https://

Large character sums with multiplicative coefficients
In this paper, we investigate large values of Dirichlet character sums with multiplicative coefficients $\sum_{n\le N}f(n)χ(n)$. We prove a new Omega result in the region $\exp((\log q)^{\frac12+δ})\le N\le\sqrt q$, where $q$ is the prime modulus.

Normalized Derivations for Milnor's Primitive Operations on the Dickson Algebra and Applications
Dang Vo Phuc
https://arxiv.org/abs/2509.08861 https://…

Normalized Derivations for Milnor's Primitive Operations on the Dickson Algebra and Applications
Our work investigates the action of primitive Milnor operations $St^{Δ_i}$ on the Dickson algebra $D_n$ over $\mathbb{F}_p$, building upon a foundational formula by Nguyen Sum [3]. Our central contribution is the introduction of a normalized operator, $δ_i$, by factoring out the ubiquitous invariant $Q_{n, 0}$. This normalization transforms $St^{Δ_i}$ into a true derivation on the localized Dickson algebra, thereby establishing an elegant differential framework. This framework yields two new…

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…

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…

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

Moduli spaces of open strings have polylogarithmic Mirzakhani volumes
Yi Huang, Ivan Telpukhovskiy
https://arxiv.org/abs/2509.09401 https://arxiv.org/pdf/2…

Moduli spaces of open strings have polylogarithmic Mirzakhani volumes
We show that the Mirzakhani volume, as introduced by Chekhov, of the moduli space of every non-contractible crowned hyperbolic surface is naturally expressible as a sum of Gaussian rational multiples of polylogarithms evaluated at $\pm1$ and $\pm\sqrt{-1}$.

Reionization optical depth and CMB-BAO tension in punctuated inflation
Zhiqi Huang
https://arxiv.org/abs/2509.09086 https://arxiv.org/pdf/2509.09086…

Reionization optical depth and CMB-BAO tension in punctuated inflation
Within the standard six-parameter Lambda cold dark matter ($Λ$CDM) model, a $2$-$3σ$ tension persists between baryon acoustic oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) and observations of the cosmic microwave background (CMB). Although this tension has often been interpreted as evidence for dynamical dark energy or a sum of neutrino masses below the established minimum, recent studies suggest it may instead originate from an underestimation of the rei…

On Kanai's conjecture for frame flows over negatively curved manifolds
Louis-Brahim Beaufort
https://arxiv.org/abs/2509.09500 https://arxiv.org/pdf/250…

On Kanai's conjecture for frame flows over negatively curved manifolds
Let $M$ be a closed, negatively curved Riemannian manifold of dimension $n \neq 4, 8$ with strictly $1/4$-pinched sectional curvature. We prove, that if the frame flow is ergodic and the sum of its unstable and stable bundles together with its flow direction is $\mathcal{C}^2$, then $M$ is homothetic to a real hyperbolic manifold. This extends to higher dimensions a previous result of Kanai in dimension 3. The proof generalises to isometric extensions of geodesic flows to a principal bundle $P$…

Chromatic Calorimetry -- A Novel Approach to Validate Energy Resolution and Particle Discrimination
Devanshi Arora
https://arxiv.org/abs/2509.09511 https://

Chromatic Calorimetry -- A Novel Approach to Validate Energy Resolution and Particle Discrimination
Chromatic calorimetry (CCAL) analyses particle detection by utilizing scintillators with distinct emission wavelengths to measure the longitudinal energy deposition of particle showers in high-energy physics, improving particle identification (PID) and energy resolution. By stacking scintillators in order of decreasing emission wavelength, CCAL enables layer-specific energy measurements, analyzed via amplitude fractions ($f_i = A_i / \sum_j A_j$) and center of gravity ($\langle z_{\text{cog}} \…

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…

Crosslisted article(s) found for physics.chem-ph. https://arxiv.org/list/physics.chem-ph/new
[1/1]:
- Diffraction-Unlimited Tip-Enhanced Sum-Frequency Vibrational Nanoscopy
Takahashi, Kumagai, Sakurai, Mochizuki, Hirano, Morita, Sugimoto

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 $\sumelements$.

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 …

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

Work statistics of sudden Quantum quenches: A random matrix theory perspective on Gaussianity and its deviations
Miguel Tierz
https://arxiv.org/abs/2509.09640 https://

Work statistics of sudden Quantum quenches: A random matrix theory perspective on Gaussianity and its deviations
We show that, for sudden quenches, the work distribution reduces to the statistics of traces of powers of Haar unitaries, which are random unitary matrices drawn uniformly from the unitary group. For translation-invariant quadratic fermionic chains with interactions extending to $m$ neighbors and periodic boundary conditions, the Loschmidt amplitude admits a unitary matrix-model / Toeplitz representation, which yields a work variable of the form $W=\sum_{r\le m} a_r\,\mathrm{Re}\,\mathrm{Tr}\,U…

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

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

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

A $\sqrt{2}$-accelerated FISTA for composite strongly convex problems
Kansei Ushiyama
https://arxiv.org/abs/2509.09295 https://arxiv.org/pdf/2509.09295

A $\sqrt{2}$-accelerated FISTA for composite strongly convex problems
In this paper, we propose a novel accelerated forward-backward splitting algorithm for minimizing convex composite functions, written as the sum of a smooth function and a (possibly) nonsmooth function. When the objective function is strongly convex, the method attains, to the best of our knowledge, the fastest known convergence rate, yielding a simultaneous linear and sublinear nonasymptotic bound. Our convergence analysis remains valid even when one of the two terms is only weakly convex (whi…

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…

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

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

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…

“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…

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…

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…

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…

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…

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 …

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.

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.
*

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…

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

Prescribed $p$-curvature problem on Riemannian manifolds with negative curvature
Jiaogen Zhang
https://arxiv.org/abs/2510.06577 https://arxiv.org/pdf/2510.…

Prescribed $p$-curvature problem on Riemannian manifolds with negative curvature
Let $(N,g)$ be a compact Riemannian manifold with negative curvature of dimension $n\geq 3$. This paper investigates the prescribed curvature problem defined by the $p$-fold sum of the modified Shouten tensor for $1\leq p\leq n$. As an application, we establish the existence of a metric $\tilde{g}$ conformal to $g$ such that \[ \mathcal{M}_{p}(\mathrm{Ric}_{\tilde{g}})=constant. \] In the case $p=1$, this resolves a well-known result of Gursky and Viaclovsky [Indiana Univ. Math. J. 52 (2003), n…

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…

Mass-Lumped Virtual Element Method with Strong Stability-Preserving Runge-Kutta Time Stepping for Two-Dimensional Parabolic Problems
Paulo Akira F. Enabe, Rodrigo Provasi
https://arxiv.org/abs/2510.06653

Mass-Lumped Virtual Element Method with Strong Stability-Preserving Runge-Kutta Time Stepping for Two-Dimensional Parabolic Problems
This paper presents a mass-lumped Virtual Element Method (VEM) with explicit Strong Stability-Preserving Runge-Kutta (SSP-RK) time integration for two-dimensional parabolic problems on general polygonal meshes. A diagonal mass matrix is constructed via row-sum operations combined with flooring to ensure uniform positivity. Stabilization terms vanish identically under row summation, so the lumped weights derive solely from the $L^2$ projector and are computable through a small polynomial system …

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

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…

Iterating Non-Aggregative Structure Compositions
Marius Bozga, Radu Iosif, Florian Zuleger
https://arxiv.org/abs/2510.06019 https://arxiv.org/pdf/2510.0601…

Iterating Non-Aggregative Structure Compositions
An aggregative composition is a binary operation obeying the principle that the whole is determined by the sum of its parts. The development of graph algebras, on which the theory of formal graph languages is built, relies on aggregative compositions that behave like disjoint union, except for a set of well-marked interface vertices from both sides, that are joined. The same style of composition has been considered in the context of relational structures, that generalize graphs an…

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…

“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!

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

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.

Noninteracting tight-binding models for Fock parafermions
Edward McCann
https://arxiv.org/abs/2510.07029 https://arxiv.org/pdf/2510.07029

Noninteracting tight-binding models for Fock parafermions
By mapping itinerant spin-$1/2$ fermions to four-state Fock parafermions, we construct noninteracting tight-binding models for Fock parafermions in one dimension. They have single-particle real energy spectra consisting of a sum of single-particle energy levels each multiplied by a parafermionic occupation number. The single-particle levels may be determined by diagonalizing a square matrix whose order scales linearly with system size. These levels are the same as those of noninteracting fermio…

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.

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.

"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…

Statistical properties of Markov shifts (part I)
Yeor Hafouta
https://arxiv.org/abs/2510.07757 https://arxiv.org/pdf/2510.07757

Statistical properties of Markov shifts (part I)
We prove central limit theorems, Berry-Esseen type theorems, almost sure invariance principles, large deviations and Livsic type regularity for partial sums of the form $S_n=\sum_{j=0}^{n-1}f_j(...,X_{j-1},X_j,X_{j+1},...)$, where $(X_j)$ is an inhomogeneous Markov chain satisfying some mixing assumptions and $f_j$ is a sequence of sufficiently regular functions. Even though the case of non-stationary chains and time dependent functions $f_j$ is more challenging, our results seem to be new alre…

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…

🤼‍♂️ 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.

A geometrical approach to neutrino oscillation parameters
Mohammad Ful Hossain Seikh
https://arxiv.org/abs/2510.06526 https://arxiv.org/pdf/2510.06526

A geometrical approach to neutrino oscillation parameters
We propose a geometric hypothesis for neutrino mixing: twice the sum of the three mixing angles equals $180^\circ$, forming a Euclidean triangle. This condition leads to a predictive relation among the mixing angles and, through trigonometric constraints, enables reconstruction of the mass-squared splittings. The hypothesis offers a phenomenological resolution to the $θ_{23}$ octant ambiguity, reproduces the known mass hierarchy patterns, and suggests a normalized geometric structure underlyin…

Robustness of Covariance Estimators with Application in Activity Detection
Hendrik Bernd Zarucha, Peter Jung, Giuseppe Caire
https://arxiv.org/abs/2510.07044 https://

Robustness of Covariance Estimators with Application in Activity Detection
The first part of this work considers a general class of covariance estimators. Each estimator of that class is generated by a real-valued function $g$ and a set of model covariance matrices $H$. If $\bf{W}$ is a potentially perturbed observation of a searched covariance matrix, then the estimator is the minimizer of the sum of $g$ applied to each eigenvalue of $\bf{W}^\frac{1}{2}\bf{Z}^{-1}\bf{W}^\frac{1}{2}$ under the constraint that $\bf{Z}$ is from $H$. It is shown that under mild condition…

Cooperative Multi-Static ISAC Networks: A Unified Design Framework for Active and Passive Sensing
Yan Yang, Zhendong Li, Jianwei Zhao, Qingqing Wu, Zhiqing Wei, Wen Chen, Weimin Jia
https://arxiv.org/abs/2510.06654

Cooperative Multi-Static ISAC Networks: A Unified Design Framework for Active and Passive Sensing
Multi-static cooperative sensing emerges as a promising technology for advancing integrated sensing and communication (ISAC), enhancing sensing accuracy and range. In this paper, we develop a unified design framework for joint active and passive sensing (JAPS). In particular, we consider a JAPSbased cooperative multi-static ISAC system for coexisting downlink (DL) and uplink (UL) communications. An optimization problem is formulated for maximizing the sum rate of both the DL and UL transmission…

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…

A Computer-Assisted Proof of the Optimal Density Bound for Pinwheel Covering
Akitoshi Kawamura, Yusuke Kobayashi
https://arxiv.org/abs/2510.06533 https://a…

A Computer-Assisted Proof of the Optimal Density Bound for Pinwheel Covering
In the covering version of the pinwheel scheduling problem, a daily task must be assigned to agents under the constraint that agent $i$ can perform the task at most once in any $a_i$-day interval. In this paper, we determine the optimal constant $α^* = 1.264\ldots {}$ such that every instance with $\sum_{i} \frac{1}{a_i} \ge α^*$ is schedulable. This resolves an open problem posed by Soejima and Kawamura (2020). Our proof combines Kawamura's (2024) techniques for the packing version with new …

Minimal Unimodal Decomposition is NP-Hard on Graphs
Mishal Assif P K, Yuliy Baryshnikov
https://arxiv.org/abs/2510.05944 https://arxiv.org/pdf/2510.05944…

Minimal Unimodal Decomposition is NP-Hard on Graphs
A function on a topological space is called unimodal if all of its super-level sets are contractible. A minimal unimodal decomposition of a function $f$ is the smallest number of unimodal functions that sum up to $f$. The problem of decomposing a given density function into its minimal unimodal components is fundamental in topological statistics. We show that finding a minimal unimodal decomposition of an edge-linear function on a graph is NP-hard. Given any $k \geq 2$, we establish the NP-hard…

A neighborhood union condition for the existence of a spanning tree without samll degree vertices
Yibo Li, Fengming Dong, Huiqing Liu
https://arxiv.org/abs/2510.07655 https://…

A neighborhood union condition for the existence of a spanning tree without samll degree vertices
For an integer k\ge2, a [2,k]-ST of a connected graph G is a spanning tree of G in which there are no vertices of degree between 2 and k. A [2,k]-ST is a natural extension of a homeomorphically irreducible spanning tree (HIST), which is a spanning tree without vertices of degree 2. In this paper, we give a neighborhood union condition for the existence of a [2,k]-ST in G. We generalize a known degree sum condition that guarantees the existence of a [2,k]-ST in G.

Replaced article(s) found for math.PR. https://arxiv.org/list/math.PR/new
[1/1]:
- H\"older estimates and weak convergences of certain weighted sum processes
Shigeki Aida, Nobuaki Naganuma

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…

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…

Approximate Bregman proximal gradient algorithm with variable metric Armijo--Wolfe line search
Kiwamu Fujiki, Shota Takahashi, Akiko Takeda
https://arxiv.org/abs/2510.06615 http…

Approximate Bregman proximal gradient algorithm with variable metric Armijo--Wolfe line search
We propose a variant of the approximate Bregman proximal gradient (ABPG) algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function. Although ABPG is known to converge globally to a stationary point even when the smooth part of the objective function lacks globally Lipschitz continuous gradients, and its iterates can often be expressed in closed form, ABPG relies on an Armijo line search to guarantee global convergence. Such reliance can slow down performanc…

Nonlinear Optical Response in Pseudo-Hermitian Systems at Steady State
S. Sajad Dabiri, Reza Asgari
https://arxiv.org/abs/2510.06580 https://arxiv.org/pdf/…

Nonlinear Optical Response in Pseudo-Hermitian Systems at Steady State
We establish a steady-state theory for nonlinear optical conductivity in pseudo-Hermitian systems. We derive compact formulas for the first and second order conductivity tensors in both the velocity and length gauges and prove their exact equivalence through generalized sum rules and Berry connection identities by formulating the nonlinear response in terms of a biorthogonal density matrix. Utilizing the formalism on parity-time symmetric two-level systems reveals nonlinear phenomena that are n…

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.

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 …

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…

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…

Improved Clifford operations in constant commutative depth
Richard Cleve, Zhiqian Ding, Luke Schaeffer
https://arxiv.org/abs/2510.04921 https://arxiv.org/p…

Improved Clifford operations in constant commutative depth
The commutative depth model allows gates that commute with each other to be performed in parallel. We show how to compute Clifford operations in constant commutative depth more efficiently than was previously known. Bravyi, Maslov, and Nam [Phys. Rev. Lett. 129:230501, 2022] showed that every element of the Clifford group (on $n$ qubits) can be computed in commutative depth 23 and size $O(n^2)$. We show that the Prefix Sum problem can be computed in commutative depth 16 and size $O(n \log n)$, …

Some Remarks on Commuting Probability
Alexander Kushkuley
https://arxiv.org/abs/2510.04458 https://arxiv.org/pdf/2510.04458

Some Remarks on Commuting Probability
We introduce a weighted sum of irreducible character ratios as an estimator for commutator probabilities. The estimator yields Frobenius formula when applied to a regular representation

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…

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…

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

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

On 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…

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 $O(1/T)$ Convergence of Alternating Gradient Descent-Ascent in Bilinear Games
Tianlong Nan, Shuvomoy Das Gupta, Garud Iyengar, Christian Kroer
https://arxiv.org/abs/2510.03855

On the $O(1/T)$ Convergence of Alternating Gradient Descent-Ascent in Bilinear Games
We study the alternating gradient descent-ascent (AltGDA) algorithm in two-player zero-sum games. Alternating methods, where players take turns to update their strategies, have long been recognized as simple and practical approaches for learning in games, exhibiting much better numerical performance than their simultaneous counterparts. However, our theoretical understanding of alternating algorithms remains limited, and results are mostly restricted to the unconstrained setting. We show that f…

Geometry of Distance Protection
Josh A. Taylor, Alejandro D. Dom\'inguez-Garc\'ia
https://arxiv.org/abs/2510.04379 https://arxiv.org/pdf/2510.04379…

Geometry of Distance Protection
Distance relays detect faults on transmission lines. They face uncertainty from the fault's location and resistance, as well as the current from the line's remote terminal. In this paper, we aggregate this uncertainty with the Minkowski sum. This allows us to explicitly model the power grid surrounding the relay's line, and in turn accommodate any mix of synchronous machines and inverter-based resources. To make the relay's task easier, inverters can inject perturbations, or auxiliary signals, …

A representation of Milnor's triple linking number by chord diagrams and doodle invariants
Ryosuke Hirata
https://arxiv.org/abs/2510.04362 https://arxi…

A representation of Milnor's triple linking number by chord diagrams and doodle invariants
From the work of X. S. Lin and Z. Wang, it follows that degree two knot invariant admits a decomposition into the sum of a Gauss diagram count and a term involving Arnold invariants. In this paper we establish an analogous description for Milnor's triple linking number - likewise of degree two - showing that it can be represented in terms of counts of certain chord diagrams together with doodle invariants.

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…

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…

Counting integral points in homogeneous spaces over function fields
Sheng Chen, Jing Liu
https://arxiv.org/abs/2510.06983 https://arxiv.org/pdf/2510.06983

Counting integral points in homogeneous spaces over function fields
We establish the asymptotic formula for the number of integral points in non-compact symmetric homogeneous spaces of semi-simple simply connected algebraic groups over global function fields, given by the sum of the products of local densities twisted by suitable Brauer elements.

Complementarity Reveals Entanglement Sharing in Sequential Quantum Measurements
Zinuo Cai, Changliang Ren
https://arxiv.org/abs/2510.02710 https://arxiv.or…

Complementarity Reveals Entanglement Sharing in Sequential Quantum Measurements
We investigate entanglement sharing in a two-qubit sequential measurement scenario using three complementary classical correlation metrics: mutual information (I), sum of conditional probabilities (S), and the Pearson correlation coefficient (C). By investigating both weak measurement and probabilistic projective measurement (PPM) strategies in unilateral and bilateral scenarios, the phenomenon of entanglement sharing is conclusively certified when multiple pairs of classical correlation metric…

Pinching Antenna Systems (PASS) for Cell-Free Communications
Haochen Li
https://arxiv.org/abs/2510.03628 https://arxiv.org/pdf/2510.03628

Pinching Antenna Systems (PASS) for Cell-Free Communications
A pinching antenna system (PASS) assisted cell-free communication system is proposed. A sum rate maximization problem under the BS power budget constraint and PA deployment constraint is formulated. To tackle the proposed non-convex optimization problem, an alternating optimization (AO) algorithm is developed. In particular, the digital beamforming sub-problem is solved using the weighted minimum mean square error (WMMSE) method, whereas the pinching beamforming sub-problem is handled via a pen…

Volume-Based Lower Bounds to the Capacity of the Gaussian Channel Under Pointwise Additive Input Constraints
Neri Merhav (Shitz), Shlomo Shamai (Shitz)
https://arxiv.org/abs/2510.04095

Volume-Based Lower Bounds to the Capacity of the Gaussian Channel Under Pointwise Additive Input Constraints
We present a family of relatively simple and unified lower bounds on the capacity of the Gaussian channel under a set of pointwise additive input constraints. Specifically, the admissible channel input vectors $\bx = (x_1, \ldots, x_n)$ must satisfy $k$ additive cost constraints of the form $\sum_{i=1}^n ϕ_j(x_i) \le n Γ_j$, $j = 1,2,\ldots,k$, which are enforced pointwise for every $\bx$, rather than merely in expectation. More generally, we also consider cost functions that depend on a slid…

Systematic analysis of the transition form factors of $B_c$ to $D$-wave charmonia and corresponding semileptonic decays
Jie Lu, Dian-Yong Chen, Guo-Liang Yu, Zhi-Gang Wang
https://arxiv.org/abs/2510.03757

Systematic analysis of the transition form factors of $B_c$ to $D$-wave charmonia and corresponding semileptonic decays
In this article, the vector, axial vector and tensor form factors of $B_c$ to $D$-wave charmonia $ψ_J$ ($J=1,2,3$) and $η_{c2}$ are analyzed within the framework of three-point QCD sum rules. With the estimated vector and axial vector form factors, we study the decay widths and branching ratios of semileptonic decays $B_c\toψ_Jl\bar{ν_l}$ and $B_c\toη_{c2}l\bar{ν_l}$. Our results indicate that the semileptonic decay branching ratios of $B_c$ to $D$-wave charmonia decreases as the total an…

Efficient Input-Constrained Impulsive Optimal Control of Linear Systems with Application to Spacecraft Relative Motion
Ethan Foss, Simone D'Amico
https://arxiv.org/abs/2510.03423

Efficient Input-Constrained Impulsive Optimal Control of Linear Systems with Application to Spacecraft Relative Motion
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta functions, are typically formulated as an optimization over a normed function space subject to integral equality constraints and can be efficiently solved for linear time-varying systems in their dual formulation. In this dual setting, the problem takes the form …

Reverse Littlewood--Offord problems with parity conditions
Lawrence Hollom, Gregory B. Sorkin
https://arxiv.org/abs/2510.05044 https://arxiv.org/pdf/2510.0…

Reverse Littlewood--Offord problems with parity conditions
We consider the probability that the random signed sum $ξ_1 v_1 + \dotsb + ξ_n v_n$ lies within a given distance $r$ of the origin, where $v_1,\dotsc,v_n \in \mathbb{R}^d$ are fixed unit vectors and $ξ_1,\dotsc,ξ_n$ are independently and uniformly distributed on $\{-1,+1\}$. In particular, our results demonstrate that, for certain values of $r$, the infimum of this probability is very sensitive to the parity of $n$. We prove that, for any $d\geq 3$, there is some $\varepsilon = \varepsilo…

Towards Secure ISAC Beamforming: How Many Dedicated Sensing Beams Are Required?
Fanghao Xia, Zesong Fei, Xinyi Wang, Nanchi Su, Zhaolin Wang, Yuanwei Liu, Jie Xu
https://arxiv.org/abs/2510.03749

Towards Secure ISAC Beamforming: How Many Dedicated Sensing Beams Are Required?
In this paper, sensing-assisted secure communication in a multi-user multi-eavesdropper integrated sensing and communication (ISAC) system is investigated. Confidential communication signals and dedicated sensing signals are jointly transmitted by a base station (BS) to simultaneously serve users and sense aerial eavesdroppers (AEs). A sum rate maximization problem is formulated under AEs' Signal-to-Interference-plus-Noise Ratio (SINR) and sensing Signal-to-Clutter-plus-Noise Ratio (SCNR) const…

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…

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…

Distribution of mixed character sums and extremal problems for Littlewood polynomials
Jonathan W. Bober, Oleksiy Klurman, Besfort Shala
https://arxiv.org/abs/2510.06161 https://…

Distribution of mixed character sums and extremal problems for Littlewood polynomials
We prove distributional results for mixed character sums \begin{equation*} \sum_{n\le x }χ(n)e(nθ), \end{equation*} for fixed $θ\in [0,1]$ and random character $χ\pmod q$, as well as for a fixed character $χ$ and randomly sampled $θ\in [0,1].$ We present various applications of our results. For example, we construct Littlewood polynomials with large Mahler measure, thus establishing a new record in the Mahler problem (1963). We also show that $L_{2k}$ norms of well-known Turyn polynomials…

Vanishing Coefficients of q^{5n r} and q^{7n r} in Certain Infinite q-series Expansions
M. P. Thejitha, Anusree Anand, S. N. Fathima
https://arxiv.org/abs/2510.05929 https://

Vanishing Coefficients of q^{5n+r} and q^{7n+r} in Certain Infinite q-series Expansions
Motivated by the recent work of several authors on vanishing coefficients of the arithmetic progression in certain $q$-series expansion, we study some variants of these $q$-series and prove some comparable results. For instance, if $\sum_{n=0}^{\infty}c_1(n)q^n=\left(\pm q^2,\pm q^3; q^5\right)_\infty^2 \left( q, q^{14}; q^{15}\right)_\infty$, then $c_1(5n+3)=0$.

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…

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

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…

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.

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…