Tootfinder

Correlations of error terms for weighted prime counting functions
Shubhrajit Bhattacharya, Greg Martin, Reginald M. Simpson
https://arxiv.org/abs/2507.13504

Correlations of error terms for weighted prime counting functions
Standard prime-number counting functions, such as $ψ(x)$, $θ(x)$, and $π(x)$, have error terms with limiting logarithmic distributions once suitably normalized. The same is true of weighted versions of those sums, like $π_r(x) = \sum_{p\le x} \frac1p$ and $π_\ell(x) = \sum_{p\le x} \log(1-\frac1p)^{-1}$, that were studied by Mertens. These limiting distributions are all identical, but passing to the limit loses information about how these error terms are correlated with one another. In t…

Her, standing in front of opened fridge and kitchen cupboard: "Help me with a counting rhyme, I can't decide what to make for dinner!"
Me: "Why can't you decide like an adult?"
Her: "My nearest dice set is too far away..."
Me: "I gave you a small travel dice set to keep in your pockets for stuff like this."
Her: "They are in my backpack, with the emergency medical supplies."
Yes, I went to get the dice.

Raiders training camp preview: Team counting on veteran linebackers https://www.reviewjournal.com/sports/raiders/raiders-training-camp-preview-team-counting-on-veteran-linebackers-3398130/

Project-connex Decompositions and Tractability of Aggregate Group-by Conjunctive Queries
Diego Figueira, Cibele Freire
https://arxiv.org/abs/2507.14101 htt…

Project-connex Decompositions and Tractability of Aggregate Group-by Conjunctive Queries
We introduce 'project-connex' tree-width as a measure of tractability for counting and aggregate conjunctive queries over semirings with 'group-by' projection (also known as 'AJAR' or 'FAQ' queries). This elementary measure allows to obtain comparable complexity bounds to the ones obtained by previous structural conditions tailored for efficient evaluation of semiring aggregate queries, enumeration algorithms of conjunctive queries, and tractability of counting answers to conjunctive queries. …

Can Current AI Models Count What We Mean, Not What They See? A Benchmark and Systematic Evaluation
Gia Khanh Nguyen, Yifeng Huang, Minh Hoai
https://arxiv.org/abs/2509.13939 htt…

Can Current AI Models Count What We Mean, Not What They See? A Benchmark and Systematic Evaluation
Visual counting is a fundamental yet challenging task, especially when users need to count objects of a specific type in complex scenes. While recent models, including class-agnostic counting models and large vision-language models (VLMs), show promise in counting tasks, their ability to perform fine-grained, intent-driven counting remains unclear. In this paper, we introduce PairTally, a benchmark dataset specifically designed to evaluate fine-grained visual counting. Each of the 681 high-reso…

Congested Clique Counting for Local Gibbs Distributions
Joshua Z. Sobel
https://arxiv.org/abs/2508.13083 https://arxiv.org/pdf/2508.13083

Congested Clique Counting for Local Gibbs Distributions
There are well established reductions between combinatorial sampling and counting problems (Jerrum, Valiant, Vazirani TCS 1986). Building off of a very recent parallel algorithm utilizing this connection (Liu, Yin, Zhang arxiv 2024), we demonstrate the first approximate counting algorithm in the CongestedClique for a wide range of problems. Most interestingly, we present an algorithm for approximating the number of $q$-colorings of a graph within $ε$-multiplicative error, when $q>αΔ$ for any…

Counting Matrices in SL3(Z) with Fixed Completely Split Character Polynomial: Preliminary Upper Bounds
Igor Rivin
https://arxiv.org/abs/2507.15129 https://…

Counting Matrices in SL3(Z) with Fixed Completely Split Character Polynomial: Preliminary Upper Bounds
We count matrices in the special linear group SL(n, Z) whose characteristic polynomials split completely over Q.

Topology-Aware Volume Fusion for Spectral Computed Tomography via Histograms and Extremum Graph
Mohit Sharma, Emma Nilsson, Martin Falk, Talha Bin Masood, Lee Jollans, Anders Persson, Tino Ebbers, Ingrid Hotz
https://arxiv.org/abs/2508.14719

Topology-Aware Volume Fusion for Spectral Computed Tomography via Histograms and Extremum Graph
Photon-Counting Computed Tomography (PCCT) is a novel imaging modality that simultaneously acquires volumetric data at multiple X-ray energy levels, generating separate volumes that capture energy-dependent attenuation properties. Attenuation refers to the reduction in X-ray intensity as it passes through different tissues or materials. This spectral information enhances tissue and material differentiation, enabling more accurate diagnosis and analysis. However, the resulting multivolume datase…

Understanding ramification of branched {$\mathbb{Z}_p$}-covers
Debanjana Kundu, Katharina Mueller
https://arxiv.org/abs/2508.15677 https://arxiv.org/pdf/25…

Understanding ramification of branched {$\mathbb{Z}_p$}-covers
We provide a combinatorial approach to counting the number of spanning trees at the $n$-th layer of a branched $\mathbb{Z}_p$-cover of a finite connected graph $\mathsf{X}$. Our method achieves in explaining how the position of the ramified vertices affects the count and hence the Iwasawa invariants. We do so by introducing the notion of segments, segmental decomposition of a graph, and number of segmental $t$-tree spanning forests.

An Exhaustive DPLL Approach to Model Counting over Integer Linear Constraints with Simplification Techniques
Mingwei Zhang, Zhenhao Gu, Liangda Fang, Cunjing Ge, Ziliang Chen, Zhao-Rong Lai, Quanlong Guan
https://arxiv.org/abs/2509.13880

An Exhaustive DPLL Approach to Model Counting over Integer Linear Constraints with Simplification Techniques
Linear constraints are one of the most fundamental constraints in fields such as computer science, operations research and optimization. Many applications reduce to the task of model counting over integer linear constraints (MCILC). In this paper, we design an exact approach to MCILC based on an exhaustive DPLL architecture. To improve the efficiency, we integrate several effective simplification techniques from mixed integer programming into the architecture. We compare our approach to state-o…

Weighted First Order Model Counting for Two-variable Logic with Axioms on Two Relations
Qipeng Kuang, V\'aclav K\r{u}la, Ond\v{r}ej Ku\v{z}elka, Yuanhong Wang, Yuyi Wang
https://arxiv.org/abs/2508.11515

Weighted First Order Model Counting for Two-variable Logic with Axioms on Two Relations
The Weighted First-Order Model Counting Problem (WFOMC) asks to compute the weighted sum of models of a given first-order logic sentence over a given domain. The boundary between fragments for which WFOMC can be computed in polynomial time relative to the domain size lies between the two-variable fragment ($\text{FO}^2$) and the three-variable fragment ($\text{FO}^3$). It is known that WFOMC for \FOthree{} is $\mathsf{\#P_1}$-hard while polynomial-time algorithms exist for computing WFOMC for $…

The Complexity of Finding and Counting Subtournaments
Simon D\"oring, Sarah Houdaigoui, Lucas Picasarri-Arrieta, Philip Wellnitz
https://arxiv.org/abs/2509.14807 https://…

The Complexity of Finding and Counting Subtournaments
We study the complexity of counting and finding small tournament patterns inside large tournaments. Given a fixed tournament $T$ of order $k$, we write ${\#}\text{IndSub}_{\text{To}}(\{T\})$ for the problem whose input is a tournament $G$ and the task is to compute the number of subtournaments of $G$ that are isomorphic to $T$. Previously, Yuster [Yus25] obtained that ${\#}\text{IndSub}_{\text{To}}(\{T\})$ is hard to compute for random tournaments $T$. We consider a new approach that uses linea…

Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants
Kaixu Zhang
https://arxiv.org/abs/2508.13464 https://arxiv.org/pdf/2508.13464

Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants
Ian Agol and Francesco Lin proved the existence of hyperbolic four-manifolds with vanishing Seiberg-Witten invariants. We prove that the number of such manifolds of volume at most $v$ is asymptotically bounded by $v^{cv}$ considered up to commensurability, which has the same form as the lower bound and upper bound of the number of hyperbolic four-manifolds of volume at most $v$ proved by Tsachik Gelander and Arie Levit.

Replaced article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Point Counting on Igusa Varieties for function fields
Paul Hamacher, Wansu Kim

New Algorithms for #2-SAT and #3-SAT
Junqiang Peng, Zimo Sheng, Mingyu Xiao
https://arxiv.org/abs/2507.14504 https://arxiv.org/pdf/25…

New Algorithms for #2-SAT and #3-SAT
The #2-SAT and #3-SAT problems involve counting the number of satisfying assignments (also called models) for instances of 2-SAT and 3-SAT, respectively. In 2010, Zhou et al. proposed an $\mathcal{O}^*(1.1892^m)$-time algorithm for #2-SAT and an efficient approach for #3-SAT, where $m$ denotes the number of clauses. In this paper, we show that the weighted versions of #2-SAT and #3-SAT can be solved in $\mathcal{O}^*(1.1082^m)$ and $\mathcal{O}^*(1.4423^m)$ time, respectively. These results dir…

Idefix-Closed Languages and Their Application in Contextual Grammars
Marvin K\"odding, Bianca Truthe
https://arxiv.org/abs/2507.15312 https://arxiv.or…

Idefix-Closed Languages and Their Application in Contextual Grammars
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate infix-, prefix-, and suffix-closed languages (referred to as idefix-closed languages) and compare such language families to some other subregular families of languages (finite, monoidal, nilpotent, combinational, (symmetric) definite, ordered, non-counting, power-separating, commutative, circular, union-free, star, and comet …

"I think when you're just counting on your voice, you actually need double the energy. I find myself acting out the scenes and being very physical while I'm recording because I think you can tell when someone is just sitting on a stool."
—Judy Greer
#acting #coaching …

Full counting statistics for twisted XXX spin chains
S. Belliard, A. Hutsalyuk
https://arxiv.org/abs/2509.13928 https://arxiv.org/pdf/2509.13928

Full counting statistics for twisted XXX spin chains
Full counting statistics for an arbitrary spin operator is considered for the twisted XXX spin one-half chain. We use the quantum inverse scattering formalism and the modified algebraic Bethe ansatz to construct an explicit formula, given by a form factor expansion.

"Stop counting sheep – and 13 more no-nonsense tips for getting back to sleep"
https://www.theguardian.com/lifeandstyle/2025/jul/04/stop-counting-sheep-and-13-more-no-nonsense-tips-for-getting-back-to-sleep…

Real-Time Beach Litter Detection and Counting: A Comparative Analysis of RT-DETR Model Variants
Miftahul Huda, Arsyiah Azahra, Putri Maulida Chairani, Dimas Rizky Ramadhani, Nabila Azhari, Ade Lailani
https://arxiv.org/abs/2508.13101

Real-Time Beach Litter Detection and Counting: A Comparative Analysis of RT-DETR Model Variants
Coastal pollution is a pressing global environmental issue, necessitating scalable and automated solutions for monitoring and management. This study investigates the efficacy of the Real-Time Detection Transformer (RT-DETR), a state-of-the-art, end-to-end object detection model, for the automated detection and counting of beach litter. A rigorous comparative analysis is conducted between two model variants, RT-DETR-Large (RT-DETR-L) and RT-DETR-Extra-Large (RT-DETR-X), trained on a publicly ava…

Distribution of integer points on determinant surfaces and a $\text{mod-}p$ analogue
Satadal Ganguly, Rachita Guria
https://arxiv.org/abs/2508.14793 https://

Distribution of integer points on determinant surfaces and a $\text{mod-}p$ analogue
We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form $xy-zw=r$, where $r$ is a non-zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables $x, y, z, w$ as well as of $r$. We also establish an asymptotic formula for counting integer solutions with smooth weights to the congruence $xy-zw \equiv 1 (\text{mod }p)$, where $p$ is a large prime, with a strong bound on the error term.

Prompt-Based One-Shot Exact Length-Controlled Generation with LLMs
Juncheng Xie, Hung-yi Lee
https://arxiv.org/abs/2508.13805 https://arxiv.org/pdf/2508.13…

Prompt-Based One-Shot Exact Length-Controlled Generation with LLMs
Controlling the length of text produced by large language models (LLMs) remains challenging: models frequently overshoot or undershoot explicit length instructions because they cannot reliably keep an internal token count. We present a prompt-based, one-shot strategy that compels an off-the-shelf LLM to generate exactly a desired number of tokens - words (English) or characters (Chinese) - without any fine-tuning or iterative sampling. The prompt appends countdown markers and explicit counting …

BGD domains in p.c.f. self-similar sets II: spectral asymptotics for Laplacians
Qingsong Gu, Hua Qiu
https://arxiv.org/abs/2507.14858 https://

BGD domains in p.c.f. self-similar sets II: spectral asymptotics for Laplacians
Let $K$ be a p.c.f. self-similar set equipped with a strongly recurrent Dirichlet form. Under a homogeneity assumption, for an open set $Ω\subset K$ whose boundary $\partial Ω$ is a graph-directed self-similar set, we prove that the eigenvalue counting function $ρ^Ω(x)$ of the Laplacian with Dirichlet or Neumann boundary conditions (Neumann only for connected $Ω$) has an explicit second term as $x\to +\infty$, beyond the dominant Weyl term. If $\partialΩ$ has a strong iterated structure, …

Remagine Ventures: 342 Israeli startups are focused on generative AI in 2025, up by 198 since May 2024, and they have collectively raised $20B to date (Elihay Vidal/CTech)
https://www.calcalistech.com/ctechnews/article/s1yl6mlulx

Mapping Israel’s $20B GenAI boom: 342 startups and counting
New Remagine Ventures report charts explosive growth and the rise of agentic AI systems.

Dutch drought still getting worse. Precipitation deficit already at 238 mm (not counting this year's headstart in March); that's double the peak in a median year and in the worst 5% of years on record.

Raiders’ Pete Carroll Offers Blunt Words on Facing Marcus Mariota https://heavy.com/sports/nfl/las-vegas-raiders/pete-carroll-response-marcus-mariota-commanders/?adt_ei=[email]

Measuring irreversibility by counting: a random coarse-graining framework
Ruicheng Bao, Naruo Ohga, Sosuke Ito
https://arxiv.org/abs/2508.11586 https://arx…

Measuring irreversibility by counting: a random coarse-graining framework
Thermodynamic irreversibility is a fundamental concept in statistical physics, yet its experimental measurement remains challenging, especially for complex systems. We introduce a novel random coarse-graining framework to identify model-free measures of irreversibility in complex many-body systems. These measures are constructed from the asymmetry of cross-correlation functions between suitably chosen observables, providing rigorous lower bounds on entropy production. For many-particle systems,…

Replaced article(s) found for q-bio.PE. https://arxiv.org/list/q-bio.PE/new
[1/1]:
- Counting rankings of tree-child networks
Qiang Zhang, Mike Steel
https://

Counting Answer Sets of Disjunctive Answer Set Programs
Mohimenul Kabir, Supratik Chakraborty, Kuldeep S Meel
https://arxiv.org/abs/2507.11655 https://

Counting Answer Sets of Disjunctive Answer Set Programs
Answer Set Programming (ASP) provides a powerful declarative paradigm for knowledge representation and reasoning. Recently, counting answer sets has emerged as an important computational problem with applications in probabilistic reasoning, network reliability analysis, and other domains. This has motivated significant research into designing efficient ASP counters. While substantial progress has been made for normal logic programs, the development of practical counters for disjunctive logic pr…

Counting Martingales for Measure and Dimension in Complexity Classes
John M. Hitchcock, Adewale Sekoni, Hadi Shafei
https://arxiv.org/abs/2508.07619 https://

Counting Martingales for Measure and Dimension in Complexity Classes
This paper makes two primary contributions. First, we introduce the concept of counting martingales and use it to define counting measures, counting dimensions, and counting strong dimensions. Second, we apply these new tools to strengthen previous circuit lower bounds. Resource-bounded measure and dimension have traditionally focused on deterministic time and space bounds. We use counting complexity classes to develop resource-bounded counting measures and dimensions. Counting martingales ar…

Coulomb branch localization, quasimaps, and surface counting in Calabi--Yau fourfolds
Duiliu-Emanuel Diaconescu, Nicolo Piazzalunga
https://arxiv.org/abs/2508.11512 https://

Coulomb branch localization, quasimaps, and surface counting in Calabi--Yau fourfolds
We present a string theoretic approach to surface counting in local Calabi--Yau fourfolds via supersymmetric localization in topologically twisted four-dimensional gauge theories. This approach is based on a spectral correspondence between PT1-stable pairs on local fourfolds and twisted quasimaps with fixed two-dimensional domain associated to the ADHM quiver, or, equivalently, ADHM sheaves. For local toric fourfolds, we derive a conjectural residue formula for the K-theoretic quasimap partitio…

Subgraph Counting under Edge Local Differential Privacy Based on Noisy Adjacency Matrix
Jintao Guo, Ying Zhou, Chao Li, Guixun Luo
https://arxiv.org/abs/2507.06508

Subgraph Counting under Edge Local Differential Privacy Based on Noisy Adjacency Matrix
When analyzing connection patterns within graphs, subgraph counting serves as an effective and fundamental approach. Edge-local differential privacy (edge-LDP) and shuffle model have been employed to achieve subgraph counting under a privacy-preserving situation. Existing algorithms are plagued by high time complexity, excessive download costs, low accuracy, or dependence on trusted third parties. To address the aforementioned challenges, we propose the Noisy Adjacency Matrix (NAM), which combi…

Almost 700 followers (not counting those following the Bluesky bridge), and I'm not sure 100 of them have ever interacted in some way.
Social media in a nutshell.

Numerical Considerations in Weighted Model Counting
Randal E. Bryant
https://arxiv.org/abs/2508.06264 https://arxiv.org/pdf/2508.06264

Numerical Considerations in Weighted Model Counting
Weighted model counting computes the sum of the rational-valued weights associated with the satisfying assignments for a Boolean formula, where the weight of an assignment is given by the product of the weights assigned to the positive and negated variables comprising the assignment. Weighted model counting finds applications across a variety of domains including probabilistic reasoning and quantitative risk assessment. Most weighted model counting programs operate by (explicitly or implicitl…

Series A, Episode 03 - Cygnus Alpha
BLAKE: [Into communicator] Jenna, it appears to have worked.
[Interior. Liberator teleport area.]
BLAKE: [V.O.] Start counting.
JENNA: Four minutes.
https://blake.torpidity.net/m/103/265 B7B4

Normalized Square Root: Sharper Matrix Factorization Bounds for Differentially Private Continual Counting
Monika Henzinger, Nikita P. Kalinin, Jalaj Upadhyay
https://arxiv.org/abs/2509.14334

Normalized Square Root: Sharper Matrix Factorization Bounds for Differentially Private Continual Counting
The factorization norms of the lower-triangular all-ones $n \times n$ matrix, $γ_2(M_{count})$ and $γ_{F}(M_{count})$, play a central role in differential privacy as they are used to give theoretical justification of the accuracy of the only known production-level private training algorithm of deep neural networks by Google. Prior to this work, the best known upper bound on $γ_2(M_{count})$ was $1 + \frac{\log n}π$ by Mathias (Linear Algebra and Applications, 1993), and the best known lower…

Counting Zeros of Complex-Valued Harmonic Functions via Rouch\'e's Theorem
Japheth Carlson
https://arxiv.org/abs/2508.06721 https://arxiv.org/pdf/2…

Counting Zeros of Complex-Valued Harmonic Functions via Rouché's Theorem
Rouché's Theorem is among the most useful results in complex analysis for counting zeros of analytic functions. Rouché's Theorem also admits a harmonic analogue for counting zeros of complex harmonic functions. This analogue has previously been applied to closed curves of simple forms, such as circles, to count zeros (e.g., \cite{Brilleslyper}). We apply the harmonic analogue of Rouché's Theorem directly on non-circular critical curves to determine the total number of zeros of a family of co…

Counting Homogeneous Einstein Metrics
Renato G. Bettiol, Hannah Friedman
https://arxiv.org/abs/2509.09830 https://arxiv.org/pdf/2509.09830

Counting Homogeneous Einstein Metrics
We present an explicit upper bound on the number of isolated homogeneous Einstein metrics on compact homogeneous spaces whose isotropy representations consist of pairwise inequivalent irreducibles. This is the BKK bound of the corresponding system of Laurent polynomials and is found combinatorially by computing the volume of a polytope. Inspired by a connection with algebraic statistics, we describe this system's BKK discriminant in terms of the principal $A$-determinant of scalar curvature. As…

To whom did my vote go?
Andrew Conway, Michelle Blom, Alexander Ek, Peter Stuckey, Vanessa Teague, Damjan Vukcevic
https://arxiv.org/abs/2509.13370 https://

To whom did my vote go?
Single Transferable Vote (STV) counting, used in several jurisdictions in Australia, is a system for choosing multiple election winners given voters' preferences among candidates. The system is complex and it is not always obvious how an individual's vote contributes to candidates' tallies across rounds of tabulation. This short paper presents a demonstration system that allows voters to enter an example vote in a past Australian STV election, and see: (i)~how that vote would have been transfer…

Noise-Robust Sound Event Detection and Counting via Language-Queried Sound Separation
Yuanjian Chen, Yang Xiao, Han Yin, Yadong Guan, Xubo Liu
https://arxiv.org/abs/2508.07176 h…

Noise-Robust Sound Event Detection and Counting via Language-Queried Sound Separation
Most sound event detection (SED) systems perform well on clean datasets but degrade significantly in noisy environments. Language-queried audio source separation (LASS) models show promise for robust SED by separating target events; existing methods require elaborate multi-stage training and lack explicit guidance for target events. To address these challenges, we introduce event appearance detection (EAD), a counting-based approach that counts event occurrences at both the clip and frame level…

Maize Seedling Detection Dataset (MSDD): A Curated High-Resolution RGB Dataset for Seedling Maize Detection and Benchmarking with YOLOv9, YOLO11, YOLOv12 and Faster-RCNN
Dewi Endah Kharismawati, Toni Kazic
https://arxiv.org/abs/2509.15181

Maize Seedling Detection Dataset (MSDD): A Curated High-Resolution RGB Dataset for Seedling Maize Detection and Benchmarking with YOLOv9, YOLO11, YOLOv12 and Faster-RCNN
Accurate maize seedling detection is crucial for precision agriculture, yet curated datasets remain scarce. We introduce MSDD, a high-quality aerial image dataset for maize seedling stand counting, with applications in early-season crop monitoring, yield prediction, and in-field management. Stand counting determines how many plants germinated, guiding timely decisions such as replanting or adjusting inputs. Traditional methods are labor-intensive and error-prone, while computer vision enables e…

Panthers counting on Ja'Tavion Sanders, TE corps to step up in 2025 https://www.espn.com/nfl/story/_/id/45695478/nfl-carolina-panthers-jatavion-sanders-tommy-tremble

Data-Driven Safety Certificates of Infinite Networks with Unknown Models and Interconnection Topologies
Mahdieh Zaker, Amy Nejati, Abolfazl Lavaei
https://arxiv.org/abs/2507.10979

Data-Driven Safety Certificates of Infinite Networks with Unknown Models and Interconnection Topologies
Infinite networks are complex interconnected systems comprising a countably infinite number of subsystems, where counting them precisely poses a significant challenge due to the seemingly endless interconnected nature of the network (e.g., counting vehicles on the road). In such scenarios, the presence of infinitely many subsystems within the network renders the existing analysis frameworks tailored for finite networks inapplicable to infinite ones. This paper is concerned with offering a data-…

Contrary to the article, counting sheep works wonderfully. But you have to use it to pace breathing (see further down in the article) and it helps to visualise the sheep, if you can.
Stop counting sheep – and 13 more no-nonsense tips for getting back to sleep | Sleep | The Guardian
https://archive.ph/wyL4J…

"I think when you're just counting on your voice, you actually need double the energy. I find myself acting out the scenes and being very physical while I'm recording because I think you can tell when someone is just sitting on a stool."
—Judy Greer
#acting #coaching …

The average genus number for pure fields of prime degree
Sambhabi Bose, Kevin J. McGown, Ishan Panpaliya, Natalie Welling, Laney Williams
https://arxiv.org/abs/2507.14317

The average genus number for pure fields of prime degree
Let $\ell\geq 5$ be prime. Let $\mathcal{F}_\ell$ be the collection of (isomorphism classes of) pure number fields $\mathbb{Q}(\sqrt[\ell]{a})$ of degree $\ell$, ordered by the absolute value of their discriminant. In 2018, Benli proved a counting theorem for $\mathcal{F}_\ell$, generalizing a previous theorem of Cohen and Morra when $\ell=3$. We prove that the proportion of pure fields of degree $\ell$ with genus number one is asymptotic to $(A_\ell \log X)^{-1}$ and that the average genus num…

Eigenvalue Distribution of Large Weighted Random Sparse Uniform $q$-Hypergraphs
Valentin Vengerovsky
https://arxiv.org/abs/2508.13297 https://arxiv.org/pdf…

Eigenvalue Distribution of Large Weighted Random Sparse Uniform $q$-Hypergraphs
We study eigenvalue distribution of the adjacency matrix $A^{(N,p,q)}$ of weighted random uniform $q$-hypergraphs $Γ= Γ_{N,p,q}$. We assume that the graphs have $N$ vertices and the average number of hyperedges attached to one vertex is $(q-1)!\cdot p$. To each edge of the graph $e_{ij}$ we assign a weight given by a random variable $a_{ij}$ with all moments finite. We consider the moments of normalized eigenvalue counting function $σ_{N,p,q}$ of $A^{(N,p,q)}$. Assuming all moments of $a$ fi…

Interleaving Logic and Counting
Johan van Benthem, Thomas Icard
https://arxiv.org/abs/2507.05219 https://arxiv.org/pdf/2507.05219

Interleaving Logic and Counting
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common linguistic usage and its extension into the broader practice of natural language plus "grassroots mathematics". We begin with a brief review of first-order logic with counting operators and cardinality comparisons. This system is known to be of high complexity, and …

Patterson-Sullivan construction of equilibrium states and weighted counting in nonpositive curvature
Weisheng Wu
https://arxiv.org/abs/2509.09924 https://a…

Patterson-Sullivan construction of equilibrium states and weighted counting in nonpositive curvature
Consider the geodesic flow on a closed rank one manifold of nonpositive curvature. For certain Hölder continuous potential, there exists a unique equilibrium state by \cite{BCFT}. In this paper, we introduce the notions of core limit set, regular radial limit set and uniformly recurrent and regular vectors, and then construct a family of Patterson-Sullivan measures on the boundary at infinity in two separate settings. Then we give an explicit construction of the above unique equilibrium state …

Per-Row Activation Counting on Real Hardware: Demystifying Performance Overheads
Jumin Kim, Seungmin Baek, Minbok Wi, Hwayong Nam, Michael Jaemin Kim, Sukhan Lee, Kyomin Sohn, Jung Ho Ahn
https://arxiv.org/abs/2507.05556

Per-Row Activation Counting on Real Hardware: Demystifying Performance Overheads
Per-Row Activation Counting (PRAC), a DRAM read disturbance mitigation method, modifies key DRAM timing parameters, reportedly causing significant performance overheads in simulator-based studies. However, given known discrepancies between simulators and real hardware, real-machine experiments are vital for accurate PRAC performance estimation. We present the first real-machine performance analysis of PRAC. After verifying timing modifications on the latest CPUs using microbenchmarks, our analy…

personally i'm not planning to migrate from github any time soon. the people who i'd've lost on ethical grounds have self-selected out long ago, i have basically no lock-in besides very heavy reliance GH Actions (which have no viable replacement besides gitlab maybe) and i'm counting on the process of corporate death to take a few years until it starts to cause actual immediate problems

Psyquandle Brackets
Sam Nelson, Natsumi Oyamaguchi
https://arxiv.org/abs/2508.13331 https://arxiv.org/pdf/2508.13331

Psyquandle Brackets
We extend the notion of biquandle brackets to the case of psyquandles, defining quantum enhancements of the psyquandle counting invariant for singular knots and pseudoknots. We provide examples to illustrate the computation of these invariants, establishing that the enhancement is proper. We compute a few toy examples, noting that the true power of this infinite family of invariants lies in more computationally expensive larger-cardinality psyquandles and infinite coefficient rings.

Counting down to zero: the final warning from a climate diplomat
https://www.theguardian.com/environment/2025/aug/26/counting-down-to-zero-the-final-warning-from-a-climate-diplomat?CMP=Share_Androi…

In celebration of #StarWars #Andor winning 4 #EMMY AWARDS (and counting)...
...I'd like to announce that we've also discovered the Rebel bass. 😁
▶️ One Hour of Dancing Mon Mothma | Andor…

Counting gauge-invariant states with matter fields and finite gauge groups
Alessandro Mariani
https://arxiv.org/abs/2509.02173 https://arxiv.org/pdf/2509.0…

Counting gauge-invariant states with matter fields and finite gauge groups
Gauge theories with finite gauge groups have applications to quantum simulation and quantum gravity. Recently, the exact number of gauge-invariant states was computed for pure gauge theories on arbitrary lattices. In this work, we generalize this counting to include the case of scalar and fermionic matter, as well as various kinds of boundary conditions. As a byproduct, we consider several related questions, such as the implementation of charge conjugation for a generic finite group. These resu…

Algorithmic Perspective on Toda's Theorem
Dror Fried, Etay Segal, Gad E. Yaron
https://arxiv.org/abs/2509.13871 https://arxiv.org/pdf/2509.13871…

Algorithmic Perspective on Toda's Theorem
Toda's Theorem is a fundamental result in computational complexity theory, whose proof relies on a reduction from a QBF problem with a constant number of quantifiers to a model counting problem. While this reduction, henceforth called Toda's reduction, is of a purely theoretical nature, the recent progress of model counting tools raises the question of whether the reduction can be utilized to an efficient algorithm for solving QBF. In this work, we address this question by looking at Toda's red…

On the dimension distortion under fractionally smooth mappings
Ryan Alvarado, Efstathios Konstantinos Chrontsios Garitsis
https://arxiv.org/abs/2509.15149 https://

On the dimension distortion under fractionally smooth mappings
We determine the extent to which continuous mappings in various Sobolev classes distort various dimensions, including the Hausdorff, the upper Minkowski (box-counting), and the upper intermediate dimensions. The intermediate and Minkowski dimension distortion results we obtain are novel already for various classes of fractionally smooth mappings between Euclidean spaces, extending the results of Hencl-Honzík (2015) and Huynh (2022) to these dimensions. In addition, our work also generalizes th…

Counting Short Trajectories in Elementary Cellular Automata using the Transfer Matrix Method
C\'edric Koller, Barbora Hudcov\'a
https://arxiv.org/abs/2508.09768 https://…

Took longer than it prob should have, but I now have a 4tb (3.6, really, but who's counting) "Fikwot" (aka Kikwot, according to my OS) NVME SSD installed in my PC. Also PC got some bonus cleaning with the 20gal air compressor.
This Meshify case from Fractal doing a great job. It's been a year since the build, but there was just some caked on surface dust. Little bit of brushing and blasts of air and the PC looks almost new again.
Reason it took longer than expe…

Remedio, which uses AI to detect risky device misconfigurations on corporate networks, raised $65M led by Bessemer, a source says at a $300M valuation (Thomas Brewster/Forbes)
https://www.forbes.com/sites/thomasbrewste

How This Israeli Hacker Bootstrapped Her AI Cyber Company To Profitability
An alum of Israel’s intelligence complex, Tal Kollender built her now $300 million-valued startup largely through word of mouth, counting Amazon and Coca-Cola as customers.

It seems that #Anubis site is down for some reason, I hope it's not because of some sort of attack.
Just today I was on my way to implement some extra protection measures for my web infrastructure and I'm counting on Anubis among other tools (I'm checking if it could be combined with #Iocaine ).

RateCount: Learning-Free Device Counting by Wi-Fi Probe Listening
Tianlang He, Zhangyu Chang, S. -H. Gary Chan
https://arxiv.org/abs/2507.03873 https://

RateCount: Learning-Free Device Counting by Wi-Fi Probe Listening
A Wi-Fi-enabled device, or simply Wi-Fi device, sporadically broadcasts probe request frames (PRFs) to discover nearby access points (APs), whether connected to an AP or not. To protect user privacy, unconnected devices often randomize their MAC addresses in the PRFs, known as MAC address randomization. While prior works have achieved accurate device counting under MAC address randomization, they typically rely on machine learning, resulting in inefficient deployment due to the time-consuming p…

"Mr. Market is counting on more TACO trade with Trump’s dissing of Canada and a score of other countries. The betting is his new deadline will come and go, or be paused, amended or ended. A Chinese government official said days ago that 47 changes his mind as often as his shoes. Seems about right. (By the way, those guys now have a lux EV that charges in five minutes. Suck that, Elon.)"
--Garth Turner

🇺🇦 Auf radioeins läuft...
Jonathan Jeremiah:
🎵 Counting Down The Days
#NowPlaying #JonathanJeremiah
https://open.spotify.com/track/4407e0DZqGA9sf8pcb0u4k

Counting primitive integral solutions to spherical generalized Fermat equations
Santiago Arango-Pi\~neros
https://arxiv.org/abs/2508.13093 https://arxiv.or…

Counting primitive integral solutions to spherical generalized Fermat equations
A solution $(x,y,z) \in \mathbb{Z}^3-\{(0,0,0)\}$ to a generalized Fermat equation \[ Ax^a + By^b + Cz^c = 0, \] is called \emph{primitive} if $\gcd(x,y,z) = 1$. By work of Beukers, we know that in the \emph{spherical} regime (that is, when the Euler characteristic $χ= \tfrac{1}{a} + \tfrac{1}{b} + \tfrac{1}{c} - 1$ is positive), if the equation has one primitive solution, then it has infinitely many. In this work, we use the method of \emph{Fermat descent}, as employed by Poonen--Schaefer--…

Arithmetics within the Linear Time Hierarchy
Chris Pollett
https://arxiv.org/abs/2508.13195 https://arxiv.org/pdf/2508.13195…

Arithmetics within the Linear Time Hierarchy
We identify fragments of the arithmetic $S_1$ that enjoy nice closure properties and have exact characterization of their definable multifunctions. To do this, in the language of $S_1$, $L_1$, starting from the formula classes, $Σ^{\mathsf b}_{i}$, which ignore sharply bounded quantifiers when determining quantifier alternations, we define new syntactic classes by counting bounded existential sharply bounded universal quantifiers blocks. Using these, we define arithmetics: $\breve{S}^{i}_{1}$,…

Strongly correlated stochastic systems
Marco Biroli
https://arxiv.org/abs/2508.12818 https://arxiv.org/pdf/2508.12818…

Strongly correlated stochastic systems
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the universal characterization of conditionally independent identically distributed variables-random variables that become independent upon conditioning on latent parameters. This structure arises naturally in systems with stochastic resetting, a mechanism that ge…

Human-AI collaboration or obedient and often clueless AI in instruct, serve, repeat dynamics?
Mohammed Saqr, Kamila Misiejuk, Sonsoles L\'opez-Pernas
https://arxiv.org/abs/2508.10919

Human-AI collaboration or obedient and often clueless AI in instruct, serve, repeat dynamics?
While research on human-AI collaboration exists, it mainly examined language learning and used traditional counting methods with little attention to evolution and dynamics of collaboration on cognitively demanding tasks. This study examines human-AI interactions while solving a complex problem. Student-AI interactions were qualitatively coded and analyzed with transition network analysis, sequence analysis and partial correlation networks as well as comparison of frequencies using chi-square an…

A Simple and Robust Protocol for Distributed Counting
Edith Cohen, Moshe Shechner, Uri Stemmer
https://arxiv.org/abs/2509.05870 https://arxiv.org/pdf/2509.…

A Simple and Robust Protocol for Distributed Counting
We revisit the distributed counting problem, where a server must continuously approximate the total number of events occurring across $k$ sites while minimizing communication. The communication complexity of this problem is known to be $Θ(\frac{k}ε\log N)$ for deterministic protocols. Huang, Yi, and Zhang (2012) showed that randomization can reduce this to $Θ(\frac{\sqrt{k}}ε\log N)$, but their analysis is restricted to the {\em oblivious setting}, where the stream of events is independent …

Private Queries with Sigma-Counting
Jun Gao, Jie Ding
https://arxiv.org/abs/2509.07018 https://arxiv.org/pdf/2509.07018

Private Queries with Sigma-Counting
Many data applications involve counting queries, where a client specifies a feasible range of variables and a database returns the corresponding item counts. A program that produces the counts of different queries often risks leaking sensitive individual-level information. A popular approach to enhance data privacy is to return a noisy version of the actual count. It is typically achieved by adding independent noise to each query and then control the total privacy budget within a period. This a…

Counting Graph Homomorphisms in Bipartite Settings
Igal Sason
https://arxiv.org/abs/2508.06977 https://arxiv.org/pdf/2508.06977

Counting Graph Homomorphisms in Bipartite Settings
This paper studies the problem of counting homomorphisms from a bipartite source graph to a bipartite target graph. An exact formula is first derived for the number of homomorphisms from a complete bipartite graph into a general bipartite graph. While exact, this formula is typically computationally intensive to evaluate. To address this, computable combinatorial lower bounds are established. When the target graph contains no 4-cycles, the lower bound simplifies and becomes exact. Two additiona…

Equiangular tight frames in real symplectic space: Zauner's conjecture and the skew Hadamard conjecture
Kean Fallon
https://arxiv.org/abs/2509.14463 https://

Equiangular tight frames in real symplectic space: Zauner's conjecture and the skew Hadamard conjecture
We introduce the notion of equiangular tight frames in real symplectic spaces and formulate a conjecture on their existence in terms of the dimension and number of vectors. Our main results shows the "symplectic Zauner's conjecture" is equivalent to the skew Hadamard conjecture. The proof involves counting subgraphs called "diamonds" in tournaments.

Dual LiDAR-Based Traffic Movement Count Estimation at a Signalized Intersection: Deployment, Data Collection, and Preliminary Analysis
Saswat Priyadarshi Nayak, Guoyuan Wu, Kanok Boriboonsomsin, Matthew Barth
https://arxiv.org/abs/2507.13073

Dual LiDAR-Based Traffic Movement Count Estimation at a Signalized Intersection: Deployment, Data Collection, and Preliminary Analysis
Traffic Movement Count (TMC) at intersections is crucial for optimizing signal timings, assessing the performance of existing traffic control measures, and proposing efficient lane configurations to minimize delays, reduce congestion, and promote safety. Traditionally, methods such as manual counting, loop detectors, pneumatic road tubes, and camera-based recognition have been used for TMC estimation. Although generally reliable, camera-based TMC estimation is prone to inaccuracies under poor l…

Replaced article(s) found for cs.CC. https://arxiv.org/list/cs.CC/new
[1/1]:
- On the complexity of unique quantum witnesses and quantum approximate counting
Anurag Anshu, Jonas Haferkamp, Yeongwoo Hwang, Quynh T. Nguyen

Counting sums of two powers
Anand Patel
https://arxiv.org/abs/2507.08337 https://arxiv.org/pdf/2507.08337

Counting sums of two powers
We generalize two well-known enumerative facts. The first, due to Clebsch, says that a general binary sextic form is expressible as the sum of a cube and a square in 40 different ways. The second, due to Zariski and later Vakil, states that a general pencil of binary 12-ics contains exactly 3762 cubes plus squares, ignoring scaling.

YOLO-Count: Differentiable Object Counting for Text-to-Image Generation
Guanning Zeng, Xiang Zhang, Zirui Wang, Haiyang Xu, Zeyuan Chen, Bingnan Li, Zhuowen Tu
https://arxiv.org/abs/2508.00728

YOLO-Count: Differentiable Object Counting for Text-to-Image Generation
We propose YOLO-Count, a differentiable open-vocabulary object counting model that tackles both general counting challenges and enables precise quantity control for text-to-image (T2I) generation. A core contribution is the 'cardinality' map, a novel regression target that accounts for variations in object size and spatial distribution. Leveraging representation alignment and a hybrid strong-weak supervision scheme, YOLO-Count bridges the gap between open-vocabulary counting and T2I generation …

Quantum Physics using Weighted Model Counting
Dirck van den Ende, Joon Hyung Lee, Alfons Laarman
https://arxiv.org/abs/2508.21288 https://arxiv.org/pdf/250…

Quantum Physics using Weighted Model Counting
Weighted model counting (WMC) has proven effective at a range of tasks within computer science, physics, and beyond. However, existing approaches for using WMC in quantum physics only target specific problem instances, lacking a general framework for expressing problems using WMC. This limits the reusability of these approaches in other applications and risks a lack of mathematical rigor on a per-instance basis. We present an approach for expressing linear algebraic problems, specifically those…

Counting the number of $2$-periodic integral points of a discrete dynamical system with applications from arithmetic statistics, IV
Brian Kintu
https://arxiv.org/abs/2507.08601

Counting the number of $2$-periodic integral points of a discrete dynamical system with applications from arithmetic statistics, IV
In this follow-up paper, we inspect a surprising relationship between the set of $2$-periodic points of a polynomial map $φ_{d, c}$ defined by $φ_{d, c}(z) = z^d + c$ for all $c, z \in \mathbb{Z}$ and the coefficient $c$, where $d>2$ is an integer. As in the previous articles, we again wish to study here counting problems that are inspired by exciting advances of Bhargava-Shankar-Tsimerman and their collaborators on $2$-torsion point-counting in arithmetic statistics, and also by Hutz's conje…

Brownian motion and orbit counting of Kleinian groups
Yanlong Hao, Beibei Liu
https://arxiv.org/abs/2508.09807 https://arxiv.org/pdf/2508.09807

Brownian motion and orbit counting of Kleinian groups
In this paper, we investigate the relationship between the divergence of Kleinian groups $Γ$ and the recurrence of simple random walks on the Schreier graph associated with $Γ$. In particular, we show that if $Γ$ is a subgroup of a lattice and is of divergence type, then the Schreier graph is recurrent. Our approach builds connections among the growth rate of the $Γ$-orbit, the volume growth rate of the quotient manifolds, and the growth rate of the Schreier graph. Using the connections, we…

Low sets for counting functions
Yaroslav Ivanashev
https://arxiv.org/abs/2507.04110 https://arxiv.org/pdf/2507.04110

Low sets for counting functions
In this paper, we characterize the classes of languages and functions that are low for counting function classes. The classes #P and GapP have their low classes exactly characterized: Low(#P) = UP $\cap$ coUP and Low(GapP) = SPP. We prove that Low(TotP) = P, Low(SpanP) = NP $\cap$ coNP, and give characterizations of low function classes for #P, GapP, TotP, and SpanP. We establish the relations between NPSVt, UPSVt, and the counting function classes. For each of the inclusions between these clas…

Counting $D_4$-field extensions by multi-invariants
Willem Hansen, Anna Zanoli
https://arxiv.org/abs/2507.12342 https://arxiv.org/pdf…

Counting $D_4$-field extensions by multi-invariants
We count the number of Galois extensions $M/\mathbb{Q}$ with fixed Galois group $\text{Gal}(M/\mathbb{Q})=D_4$ ordered by multi-invariants introduced by Gundlach. We verify the asymptotic behavior predicted by Gundlach's version of Malle's conjecture. We compare the leading constant to recent predictions by Loughran and Santens.

A Hydrodynamic Theory for Non-Equilibrium Full Counting Statistics in One-Dimensional Quantum Systems
David X. Horvath, Benjamin Doyon, Paola Ruggiero
https://arxiv.org/abs/2507.05954

A Hydrodynamic Theory for Non-Equilibrium Full Counting Statistics in One-Dimensional Quantum Systems
We study the dynamics of charge fluctuations after homogeneous quantum quenches in one-dimensional systems with ballistic transport. For short but macroscopic times where the non-trivial dynamics is largely dominated by long-range correlations, a simple expression for the associated full counting statistics can be obtained by hydrodynamic arguments. This formula links the non-equilibrium charge fluctuation after the quench to the fluctuations of the associated current after a charge-biased inho…

Linear Recurrences from Counting Schreier-Type Multisets
Hung Viet Chu, Yubo Geng, Julian King, Steven J. Miller, Garrett Tresch, Zachary Louis Vasseur
https://arxiv.org/abs/2509.05158

Linear Recurrences from Counting Schreier-Type Multisets
A nonempty set $F$ is Schreier if $\min F\ge |F|$. Bird observed that counting Schreier sets in a certain way produces the Fibonacci sequence. Since then, various connections between variants of Schreier sets and well-known sequences have been discovered. Building on these works, we prove a linear recurrence for the sequence that counts multisets $F$ with $\min F\ge p|F|$. In particular, if we let $$\mathcal{A}^{(s)}_{p, n}\ :=\ \{F\subset \{\underbrace{1, \ldots, 1}_{s}, \l…

DSGC-Net: A Dual-Stream Graph Convolutional Network for Crowd Counting via Feature Correlation Mining
Yihong Wu, Jinqiao Wei, Xionghui Zhao, Yidi Li, Shaoyi Du, Bin Ren, Nicu Sebe
https://arxiv.org/abs/2509.02261

DSGC-Net: A Dual-Stream Graph Convolutional Network for Crowd Counting via Feature Correlation Mining
Deep learning-based crowd counting methods have achieved remarkable progress in recent years. However, in complex crowd scenarios, existing models still face challenges when adapting to significant density distribution differences between regions. Additionally, the inconsistency of individual representations caused by viewpoint changes and body posture differences further limits the counting accuracy of the models. To address these challenges, we propose DSGC-Net, a Dual-Stream Graph Convolutio…

Replaced article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- Separation and Definability in Fragments of Two-Variable First-Order Logic with Counting
Louwe Kuijer, Tony Tan, Frank Wolter, Michael Zakharyaschev

Evaluating Multiple Instance Learning Strategies for Automated Sebocyte Droplet Counting
Maryam Adelipour, Gustavo Carneiro, Jeongkwon Kim
https://arxiv.org/abs/2509.04895 https…

Evaluating Multiple Instance Learning Strategies for Automated Sebocyte Droplet Counting
Sebocytes are lipid-secreting cells whose differentiation is marked by the accumulation of intracellular lipid droplets, making their quantification a key readout in sebocyte biology. Manual counting is labor-intensive and subjective, motivating automated solutions. Here, we introduce a simple attention-based multiple instance learning (MIL) framework for sebocyte image analysis. Nile Red-stained sebocyte images were annotated into 14 classes according to droplet counts, expanded via data augme…

Reverse Hurwitz counts of genus 1 curves
Michael Mueller
https://arxiv.org/abs/2509.11280 https://arxiv.org/pdf/2509.11280…

Reverse Hurwitz counts of genus 1 curves
In this paper, we study a problem that is in a sense a reversal of the Hurwitz counting problem. The Hurwitz problem asks: for a generic target -- $\mathbb P^1$ with a list of $n$ points $q_1,\dots,q_n\in \mathbb P^1$ -- and partitions $σ_1,\dots,σ_n$ of $d$, how many degree $d$ covers $C\to\mathbb P^1$ are there with specified ramification $σ_i$ over $q_i$? We ask: for a generic source -- an $r$-pointed curve $(C,p_1,\dots,p_r)$ of genus $1$ -- and partitions $μ, σ_1,\dots,σ_n$ of $d$ wi…

An Explicit Cohen-Style Threefield Identity
Lucas Perryman-Deskins
https://arxiv.org/abs/2508.12152 https://arxiv.org/pdf/2508.12152

An Explicit Cohen-Style Threefield Identity
In 1988, Andrews, Dyson, and Hickerson showed that a $q$-series $σ$ found in Ramanujan's lost notebook and related to partitions could be interpreted as counting ideals in $\mathbb{Q}(\sqrt{6})$, and found similar formulas for $σ$ in terms of ideals of $\mathbb{Q}(\sqrt{2})$ and $\mathbb{Q}(\sqrt{3})$. Cohen followed this by showing more generally that for certain triples of quadratic fields, there is abelian extension and conductor so that the ray class character theta series for all three f…

Approximate SMT Counting Beyond Discrete Domains
Arijit Shaw, Kuldeep S. Meel
https://arxiv.org/abs/2507.18612 https://arxiv.org/pdf/2507.18612

Approximate SMT Counting Beyond Discrete Domains
Satisfiability Modulo Theory (SMT) solvers have advanced automated reasoning, solving complex formulas across discrete and continuous domains. Recent progress in propositional model counting motivates extending SMT capabilities toward model counting, especially for hybrid SMT formulas. Existing approaches, like bit-blasting, are limited to discrete variables, highlighting the challenge of counting solutions projected onto the discrete domain in hybrid formulas. We introduce pact, an SMT model…

Counting w-coprime S-integers and S-integral ideals in positive characteristic
Si-Han Liu, Zhe-Cheng Liu, Jia-Yan Yao
https://arxiv.org/abs/2508.10484 https://

Counting w-coprime S-integers and S-integral ideals in positive characteristic
Let Fq be the finite field with q elements, and K an algebraic function field over with Fq as its field of constants. Let S be a finite nonempty set of prime divisors over K, and OS be the ring of integers of K attached to S. Let w greater than 1 be an integer. In this work we shall count w coprime S integers and S integral ideals, and our proofs are a combination of analytic methods and the Riemann Roch theorem and the Weil theorem for function fields in positive characteristic.

Convolutive sequences, I: Through the lens of integer partition functions
Shane Chern, Dennis Eichhorn, Shishuo Fu, James A. Sellers
https://arxiv.org/abs/2507.10965

Convolutive sequences, I: Through the lens of integer partition functions
Motivated by the convolutive behavior of the counting function for partitions with designated summands in which all parts are odd, we consider coefficient sequences $(a_n)_{n\ge 0}$ of primitive eta-products that satisfy the generic convolutive property \begin{align*} \sum_{n\ge 0} a_{mn} q^n = \left(\sum_{n\ge 0} a_n q^n\right)^m \end{align*} for a specific positive integer $m$. Given the results of an exhaustive search of the Online Encyclopedia of Integer Sequences for such sequences…

Which graph motif parameters count?
Markus Bl\"aser, Radu Curticapean, Julian D\"orfler, Christian Ikenmeyer
https://arxiv.org/abs/2507.12244 htt…

Which graph motif parameters count?
For a fixed graph H, the function #IndSub(H,*) maps graphs G to the count of induced H-copies in G; this function obviously "counts something" in that it has a combinatorial interpretation. Linear combinations of such functions are called graph motif parameters and have recently received significant attention in counting complexity after a seminal paper by Curticapean, Dell and Marx (STOC'17). We show that, among linear combinations of functions #IndSub(H,*) involving only graphs H without isol…

Counting points on a family of degree one del Pezzo surfaces
Katharine Woo
https://arxiv.org/abs/2508.09391 https://arxiv.org/pdf/2508.09391

Counting points on a family of degree one del Pezzo surfaces
We study rational points on the elliptic surface given by the equation: $$y^2 = x^3 + AxQ(u,v)^2 + BQ(u,v)^3,$$ where $A,B\in \mathbb{Z}$ satisfy that $4A^3-27B^2\neq 0$ and $Q(u,v)$ is a positive-definite quadratic form. We prove asymptotics for a special subset of the rational points, specifically those that are integral with respect to the singularity. This method utilizes Mordell's parameterization of integral points on quadratic twists on elliptic curves, which is based on a syzygy for…

CountCluster: Training-Free Object Quantity Guidance with Cross-Attention Map Clustering for Text-to-Image Generation
Joohyeon Lee, Jin-Seop Lee, Jee-Hyong Lee
https://arxiv.org/abs/2508.10710

CountCluster: Training-Free Object Quantity Guidance with Cross-Attention Map Clustering for Text-to-Image Generation
Diffusion-based text-to-image generation models have demonstrated strong performance in terms of image quality and diversity. However, they still struggle to generate images that accurately reflect the number of objects specified in the input prompt. Several approaches have been proposed that rely on either external counting modules for iterative refinement or quantity representations derived from learned tokens or latent features. However, they still have limitations in accurately reflecting t…

Secondary terms in the counting functions of quartic fields II
Arul Shankar, Jacob Tsimerman
https://arxiv.org/abs/2508.08527 https://arxiv.org/pdf/2508.08…

Secondary terms in the counting functions of quartic fields II
We determine the smoothed counts of $S_4$-quartic fields with bounded discriminant, satisfying any finite specified set of local conditions, as the sum of two main terms with a power saving error term. We also prove an analogous result for quartic rings (weighted by the number of cubic resolvents), deducing as a consequence that the Shintani zeta functions associated to the prehomogeneous vector space $\mathbb{C}^2\otimes\mathrm{Sym}^2(\mathbb{C}^3)$ have at most a simple pole at $s=5/6$.

Multimodal Mathematical Reasoning Embedded in Aerial Vehicle Imagery: Benchmarking, Analysis, and Exploration
Yue Zhou, Litong Feng, Mengcheng Lan, Xue Yang, Qingyun Li, Yiping Ke, Xue Jiang, Wayne Zhang
https://arxiv.org/abs/2509.10059

Multimodal Mathematical Reasoning Embedded in Aerial Vehicle Imagery: Benchmarking, Analysis, and Exploration
Mathematical reasoning is critical for tasks such as precise distance and area computations, trajectory estimations, and spatial analysis in unmanned aerial vehicle (UAV) based remote sensing, yet current vision-language models (VLMs) have not been adequately tested in this domain. To address this gap, we introduce AVI-Math, the first benchmark to rigorously evaluate multimodal mathematical reasoning in aerial vehicle imagery, moving beyond simple counting tasks to include domain-specific knowl…

Counting Salem numbers arising from arithmetic hyperbolic orbifolds
Michelle Chu, Plinio G. P. Murillo, Otto Romero, Lola Thompson
https://arxiv.org/abs/2508.08003 https://

Counting Salem numbers arising from arithmetic hyperbolic orbifolds
The relationship between Salem numbers and short geodesics has been fruitful in quantitative studies of arithmetic hyperbolic orbifolds, particularly in dimensions 2 and 3. In this article, we push these connections even further. The primary goals are: (1) to bound the proportion of Salem numbers of degree up to $n+1$ in the commensurability class of classical arithmetic lattices in any odd dimension $n$; (2) to improve lower bounds for the strong exponential growth of averages of multiplicitie…

Counting isomorphism classes of elliptic curves over $\mathbb{F}_q(t)$
Jun-Yong Park
https://arxiv.org/abs/2507.06754 https://arxiv.o…

Counting isomorphism classes of elliptic curves over $\mathbb{F}_q(t)$
We determine the precise number of isomorphism classes of elliptic curves over $\mathbb{F}_q(t)$ with $\text{char}(\mathbb{F}_q) = 3,2$. The key idea is to obtain the exact unweighted number of rational points on the classifying stacks $\mathcal{B} Q_{12}$, $\mathcal{B} Q_{24}$ and $\mathcal{B} Z$, where $Q_{12}$ and $Q_{24}$ denote the dicyclic groups of orders 12 and 24, respectively, and $Z$ denotes the non-reduced group scheme of order 2. This computation, inspired by the classical work of …

Counting the number of $2$-periodic $\mathcal{O}_{K}$-points of a discrete dynamical system with applications from arithmetic statistics, V
Brian Kintu
https://arxiv.org/abs/2508.16393

Counting the number of $2$-periodic $\mathcal{O}_{K}$-points of a discrete dynamical system with applications from arithmetic statistics, V
In this follow-up paper, we again inspect a surprising relationship between the set of $2$-periodic points of a polynomial map $φ_{d, c}$ defined by $φ_{d, c}(z) = z^d + c$ for all $c, z \in \mathcal{O}_{K}$ and the coefficient $c$, where $K$ is any number field of degree $n\geq 2$ and $d>2$ is an integer. As before, we again study here counting problems that are inspired by the exciting advances on $2$-torsion point-counting in arithmetic statistics and on $2$-periodic point-counting in arit…