Tootfinder

Linear groups of alternating type containing non-scalar elements with all but one eigenvalues of multiplicity 1
Alexandre Zalesski
https://arxiv.org/abs/2509.05770 https://

Linear groups of alternating type containing non-scalar elements with all but one eigenvalues of multiplicity 1
We determine the irreducible representations of alternating and symmetric groups and their universal central extensions that contain a non-scalar element with all but one eigenvalues of multiplicity 1. The ground field is algebraically closed of arbitrary characteristic.

Internal multiplicity distributions of jets from nonlinear evolution within the jet function framework
Pi Duan, Weiyao Ke, Guang-You Qin, Lei Wang
https://arxiv.org/abs/2510.04895

Internal multiplicity distributions of jets from nonlinear evolution within the jet function framework
Jets selected with high internal charged-particle multiplicity exhibit markedly different substructure patterns compared to inclusive jet samples. Such correlations motivate a systematic study of jet observables as a function of the normalized multiplicity, $ν= N_{\rm ch}/\langle N_{\rm ch}\rangle$. In this work, we develop a theoretical framework for the full charged-particle multiplicity distribution of exclusive and inclusive jets, formulated within the jet-function approach. The hard produ…

A remark on weighted average multiplicities in prime factorisation
Viktor Mirjani\'c, Daattavya Aggarwal, Challenger Mishra
https://arxiv.org/abs/2510.06993 https://

A remark on weighted average multiplicities in prime factorisation
We study a generalisation of the quality of an ABC triple that we call the weighted average multiplicity (WAM), in which the logarithmic heights of prime factors are raised to a complex exponent s. The WAM is connected to the standard ABC conjecture at s=1. We show that for real part of s less than 1, WAM is unbounded over ABC triples both for integers and polynomials. For real part greater than 1, we characterise a boundary beyond which WAM is holomorphic and bounded. In this region, we show t…

Multiplicity distributions in QCD jets and jet topics
Xiang-Pan Duan, Lin Chen, Guo-Liang Ma, Carlos A. Salgado, Bin Wu
https://arxiv.org/abs/2509.06158 https://

Multiplicity distributions in QCD jets and jet topics
We evaluate the Koba--Nielsen--Olesen (KNO) scaling functions for quark- and gluon-initiated jets by incorporating energy conservation into the Double Logarithmic Approximation (DLA). The resulting modified DLA (MDLA) expressions differ substantially from the DLA predictions and qualitatively align with the recently proposed QCD-inspired expressions, albeit with some quantitative differences. By fixing the two parameters in the MDLA expressions, we show that the inclusive charged-particle multi…

Factorial cumulants of proton multiplicity near a critical point using maximum entropy freeze-out prescription
Jamie Karthein, Maneesha Pradeep, Krishna Rajagopal, Mikhail Stephanov, Yi Yin
https://arxiv.org/abs/2510.05567

Factorial cumulants of proton multiplicity near a critical point using maximum entropy freeze-out prescription
We present the first application of the maximum-entropy freeze-out prescription to calculate factorial cumulants of proton multiplicities near the conjectured QCD critical point in thermal equilibrium. We map the Gibbs free energy of the 3D Ising model to a parameterized class of possible EoS near QCD critical point. This equilibrium baseline highlights how factorial cumulants isolate critical fluctuations by subtracting trivial self-correlations, setting the stage for future out-of-equilibrium…

Measure $0$ of the singular set for $2$-valued stationary hypercurrents
Jonas Hirsch, Luca Spolaor
https://arxiv.org/abs/2509.05544 https://arxiv.org/pdf/2…

Measure $0$ of the singular set for $2$-valued stationary hypercurrents
We prove that the singular set of a multiplicity $2$ integral hypercurrent that is stationary in the sense of varifolds has a singular set of measure zero.

Self-Image Multiplicity in a Concave Cylindrical Mirror
Thach A. Nguyen, Kaitlyn S. Yasumura, Duy V. Tran, Trung V. Phan
https://arxiv.org/abs/2510.04370 https://

Self-Image Multiplicity in a Concave Cylindrical Mirror
Concave mirrors are fundamental optical elements, yet some easily observed behaviors are rarely addressed in standard textbooks, such as the formation of multiple reflected images. Here we investigate self-imaging -- where the observer is also the observed object -- using a concave cylindrical mirror. We predict the number of self-images visible from different observation points and classify space into regions by image count. We then test these predictions with an inexpensive stainless-steel co…

Multiple solutions to a class of $p$-Laplacian Schr\"{o}dinger equations
Lin Zhang
https://arxiv.org/abs/2509.05556 https://arxiv.org/pdf/2509.05556…

Multiple solutions to a class of $p$-Laplacian Schrödinger equations
In this paper, we will prove the existence of infinitely many solutions to the following equation by utilizing the variational perturbation method \begin{equation*} -div(A(x,u)|\nabla u|^{p-2}\nabla u)+\frac{1}{p}A_{t}(x,u)|\nabla u|^{p}+V(x)|u|^{p-2}u=g(x, u), ~~ x\in\mathbb{R}^{N}, \end{equation*} where $2

Cosmic Threads: Interlinking the Stellar Initial Mass Function from Star-Birth to Galaxies
Tereza Jerabkova, Donatella Romano, Pavel Kroupa, Philippe Andr\'e, Martyna Chru\'sli\'nska, Fabio Fontanot, Andrew Hopkins, Vikrant Jadhav, Natalia Lah\'en, Yueh-Ning Lee, Alessio Mucciarelli, Stefania Salvadori, Long Wang, Zhiqiang Yan, Morten Andersen, Anna Durrant, Fabien Louvet, Mariya Lyubenova, Francesca Matteucci, Piyush Sharda, Glenn van de Ven, Alexandre Vazdekis

Cosmic Threads: Interlinking the Stellar Initial Mass Function from Star-Birth to Galaxies
The stellar initial mass function (sIMF) describes the distribution of stellar masses formed in a single star formation event in a molecular cloud clump. It is fundamental to astrophysics and cosmology, shaping our understanding of unresolved stellar populations, galactic chemical enrichment and habitable zones, and black hole growth. This White Paper reviews studies on the core mass function, stellar multiplicity, and dynamical processes affecting sIMF determinations, as well as the link betwe…

Metric version of the Zariski Multiplicity Conjecture is true for multiplicity two
A. Fernandes, Z. Jelonek, J. E. Sampaio
https://arxiv.org/abs/2509.03447 https://

Metric version of the Zariski Multiplicity Conjecture is true for multiplicity two
We prove that if two algebraic $(n-1)$-dimensional cones $P, R\subset\mathbb C^n$ are ambient homeomorphic, then their bases $B_P$ and $B_R$ have the same Euler characteristic. As an application, we show our main result: if $(X,0),(Y,0)\subset (\C^n,0)$ are germs of analytic hypersurfaces, which are ambient bi-Lipschitz equivalent and $m_0(X)=2$, then also $m_0(Y)=2.$. As another application, we also obtain a complete positive answer to the Metric Arnold-Vassiliev Problem, which says that if tw…

Upper bound on the multiplicity of rational and Du Bois singularities
Sung Gi Park
https://arxiv.org/abs/2509.21807 https://arxiv.org/pdf/2509.21807…

Upper bound on the multiplicity of rational and Du Bois singularities
This paper resolves a question of Huneke and Watanabe by proving a sharp upper bound for the multiplicity of Du Bois singularities: at a point of a $d$-dimensional variety with Du Bois singularities and embedding dimension $e$, the multiplicity is at most $\binom{e}{d}$. Additionally, the result recovers the previously known upper bound for the multiplicity of rational singularities.

Solving Skolem problem for negative indexed $k-$generalized Pell numbers
Monalisa Mohapatra, Pritam Kumar Bhoi, Gopal Krishna Panda
https://arxiv.org/abs/2509.04503 https://

Solving Skolem problem for negative indexed $k-$generalized Pell numbers
In this paper, we address the Skolem problem for the $k-$Generalized Pell numbers ($P_n^{(k)}$) extended to negative indices. We focus on identifying and bounding the indices $n<0$ for which $P_n^{(k)}=0.$ In particular, we establish that the zero multiplicity is $ χ_k = 1 + (k(k-2)/4),$ if $k$ is even and $1 + ((k - 1)^2/4)$, if $k$ is odd for all $k \in [4, 500].$

On the multiplicity of matching polynomial roots and $\theta$-critical graphs
Leyou Xu
https://arxiv.org/abs/2509.23842 https://arxiv.org/pdf/2509.23842

On the multiplicity of matching polynomial roots and $θ$-critical graphs
The matching polynomial of a graph encodes rich combinatorial information through its roots. We determine the maximum multiplicity of a non-zero matching polynomial root and characterize all graphs attaining the bound. We also generalize the result to any fixed $θ$, where the graphs attaining the bound are related to $θ$-critical graphs. Inspired by these graphs, we give a constructive answer to Godsil's question. Finally, we show the existence of $1$-critical tree of order $n$ for all $n\ge …

Lithium Abundances of Main-Sequence Stars in the Old Open Cluster NGC 188: Probes of Stellar Evolution Beyond the Solar Age
Qinghui Sun, Constantine P. Deliyannis, Bruce A. Twarog, Barbara J. Anthony-Twarog
https://arxiv.org/abs/2509.02931

Lithium Abundances of Main-Sequence Stars in the Old Open Cluster NGC 188: Probes of Stellar Evolution Beyond the Solar Age
We present lithium abundances for 119 main-sequence stars in the 6.3 Gyr open cluster NGC 188, using high-resolution, high signal-to-noise ratio spectra from WIYN/Hydra. We observe the stars over multiple nights and measure radial velocities for each night, which we combine with Gaia proper motions to identify multiplicity and cluster membership. We identify 95 single members, 14 binary members, 9 members with uncertain multiplicity, and 1 single likely member. We determine effective temperatur…

NA61/SHINE results on multiplicity and net-charge fluctuations at CERN SPS energies
Ma\'ckowiak-Paw{\l}owska
https://arxiv.org/abs/2510.00687 https://a…

NA61/SHINE results on multiplicity and net-charge fluctuations at CERN SPS energies
This contribution presents final results on the energy dependence of multiplicity and net-electric charge fluctuations in Ar+Sc interactions collected by the NA61/SHINE experiment. Fluctuations were analyzed using higher-order cumulant ratios in Ar+Sc most central collisions and compared to p+p interactions. The results consider detector bias and centrality selection in the case of Ar+Sc. The results are compared across different energies and against model predictions.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems
Fleur Hendriks, Ond\v{r}ej Roko\v{s}, Martin Do\v{s}k\'a\v{r}, Marc G. D. Geers, Vlado Menkovski
https://arxiv.org/abs/2509.03340

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems
Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models struggle to capture this multiplicity, averaging over solutions and failing to represent lower-symmetry outcomes. In this work, we propose a generative framework based on flow matching to model the full probability distribution over bifurcation outcomes. Our method enables direct sampling of multiple val…

Copula-Based Clustering of Financial Time Series via Evidence Accumulation
Andrea Mecchina, Roberta Pappad\`a, Nicola Torelli
https://arxiv.org/abs/2510.05960 https://

Copula-Based Clustering of Financial Time Series via Evidence Accumulation
Understanding the dependence structure of asset returns is fundamental in risk assessment and is particularly relevant in a portfolio diversification strategy. We propose a clustering approach where evidence accumulated in a multiplicity of classifications is achieved using classical hierarchical procedures and multiple copula-based dissimilarity measures. Assets that are grouped in the same cluster are such that their stochastic behavior is similar during risky scenarios, and riskaverse invest…

Ulrich modules over local rings of dimension two
Srikanth B. Iyengar, Linquan Ma, Mark E. Walker
https://arxiv.org/abs/2510.02698 https://arxiv.org/pdf/251…

Ulrich modules over local rings of dimension two
It is proved that Ulrich modules exist for a large class of local rings of dimension two. This complements earlier work of the authors and Ziquan Zhuang that described complete intersection domains of dimension two that admit no Ulrich modules. As an application, it is proved that, for this class of rings, the length of a nonzero module of finite projective dimension is at least the multiplicity of the local ring.

Particle momentum spectra, correlations, and maximum entropy principle in high-multiplicity collision events
S. V. Akkelin
https://arxiv.org/abs/2510.01822 https://

Particle momentum spectra, correlations, and maximum entropy principle in high-multiplicity collision events
In this paper, we utilize the maximum entropy prescription to determine a quantum state of a small collision system at the kinetic freeze-out. We derive expressions for multiplicity-selected particle momentum spectra and correlation functions by applying a fixed particle number constraint to this state. The results of our analysis may be useful for interpreting the multiplicity dependence of the particle momentum spectra and correlations in high-multiplicity $pp$ collision events at a fixed LHC…

Several sufficient conditions for projective hypersurfaces to be GIT (semi)stable
Xuancong He
https://arxiv.org/abs/2510.03695 https://arxiv.org/pdf/2510.0…

Several sufficient conditions for projective hypersurfaces to be GIT (semi)stable
In this paper, I present some sufficient conditions for projective hypersurfaces to be GIT (semi-)stable. These conditions will be presented in terms of dimension and degree of the hypersurfaces, dimension of the singular locus and multiplicities of the singular points. When singularities of the hypersurface are isolated and all have multiplicity 2, we can judge its stability via the ranks of Hessian matrices at these singular points.

Deconstruction of the anisotropic magnetic interactions from spin-entangled optical excitations in van der Waals antiferromagnets
Dipankar Jana, Swagata Acharya, Milan Orlita, Clement Faugeras, Dimitar Pashov, Mark van Schilfgaarde, Marek Potemski, Maciej Koperski
https://arxiv.org/abs/2510.03010

Deconstruction of the anisotropic magnetic interactions from spin-entangled optical excitations in van der Waals antiferromagnets
Magneto-optical excitations in antiferromagnetic d systems can originate from a multiplicity of light-spin and spin-spin interactions, as the light and spin degrees of freedom can be entangled. This is exemplified in van der Waals systems with attendant strong anisotropy between in-plane and out- of-plane directions, such as MnPS3 and NiPS3 films studied here. The rich interplay between the magnetic ordering and sub-bandgap optical transitions poses a challenge to resolve the mechanisms driving…

Kronecker Coefficients and Simultaneous Conjugacy Classes
Jyotirmoy Ganguly, Digjoy Paul, Amritanshu Prasad, K N Raghavan, Velmurugan S
https://arxiv.org/abs/2510.04497 https://…

Kronecker Coefficients and Simultaneous Conjugacy Classes
A Kronecker coefficient is the multiplicity of an irreducible representation of a finite group $G$ in a tensor product of irreducible representations. We define Kronecker Hecke algebras and use them as a tool to study Kronecker coefficients in finite groups. We show that the number of simultaneous conjugacy classes in a finite group $G$ is equal to the sum of squares of Kronecker coefficients, and the number of simultaneous conjugacy classes that are closed under elementwise inversion is the su…

Asymptotic behaviour and existence of positive solutions for mixed local nonlocal elliptic equations with Hardy potential
Shammi Malhotra, Sarika Goyal, K. Sreenadh
https://arxiv.org/abs/2510.04763

Asymptotic behaviour and existence of positive solutions for mixed local nonlocal elliptic equations with Hardy potential
We investigate the existence and multiplicity of positive solutions to the following problem driven by the superposition of the Laplacian and the fractional Laplacian with Hardy potential \begin{equation*} \left\{ \begin{aligned} -Δu + (-Δ)^s u - μ\frac{u}{|x|^2} &= λ|u|^{p-2} u + |u|^{2^*-2} u \quad \text{in } Ω\subset \mathbb{R}^N, u &= 0 \quad \text{in } \mathbb{R}^N \setminus Ω, \end{aligned} \right. \end{equation*} where $ Ω\subset \mathbb{R}^N $ is…

Comparing particle multiplicity predictions: Insights from Pythia, Herwig with the LHCb use case
Saliha Bashir, Agnieszka Ob{\l}\k{a}kowska-Mucha, Gloria Corti
https://arxiv.org/abs/2509.24567

Comparing particle multiplicity predictions: Insights from Pythia, Herwig with the LHCb use case
Monte Carlo Event Generators are tools for simulating outcomes of high-energy collisions and particle production in High Energy Physics (HEP), such as those conducted at the Large Hadron Collider (LHC). Two of the most widely used general-purpose event generators are \textsc{Pythia} and \textsc{Herwig}, both of which play a significant role in understanding particle production, the internal structure of the proton, and the underlying physics of interactions that take place at LHC. This paper em…

Replaced article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
- The Modular number, Congruence number, and Multiplicity One
Amod Agashe
https:…

Resonances for the one dimensional Schr\"odinger operator with the matrix-valued complex square-well potential
Yuri Latushkin, Alin Pogan
https://arxiv.org/abs/2509.00235 h…

Resonances for the one dimensional Schrödinger operator with the matrix-valued complex square-well potential
We study the resonances of (generally, non-selfadjoint) Schrödinger operators with matrix-valued square-well potentials. We compute explicitly the Jost function and derive complex transcendental equations for the resonances. We prove several results concerning the distribution of resonances in the complex plane. We compute the multiplicity of resonances and prove a version of the Weyl Law for the number of resonances.

M&SCheck: Towards a Checklist to Support Software Engineering Newcomers to the Modeling and Simulation Area
Luiza Martins de Freitas Cintra, Philipp Zech, Mohamad Kassab, Eliomar Ara\'ujo Lima, Sofia Larissa da Costa Paiva, Valdemar Vicente Graciano Neto
https://arxiv.org/abs/2509.25625

M&SCheck: Towards a Checklist to Support Software Engineering Newcomers to the Modeling and Simulation Area
The advent of increasingly complex and dynamic ecosystems, such as digital twins (DT), smart cities and Industry 4.0 and 5.0, has made evident the need to include modeling and simulation (M&S) in the software development life cycle. Such disruptive systems include simulation models in their own architecture (such as DT) or require the use of simulation models to represent the high degree of movement and the multiplicity of interactions that occur between the involved systems. However, when soft…

Transverse slices and Zariski's multiplicity conjecture for quasihomogeneous surfaces
Otoniel Nogueira da Silva, Manoel Messias da Silva J\'unior
https://arxiv.org/abs/2509.01634

Transverse slices and Zariski's multiplicity conjecture for quasihomogeneous surfaces
In this work, we study finitely determined, quasihomogeneous, corank 1 map germs $f$ from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^3,0)$. We introduce the notion of the $μ_{\boldsymbol{m},\boldsymbol{k}}$-minimal transverse slice of $f.$ Since this slice is a plane curve, we provide its (topological) normal form. In the irreducible case, under certain conditions, we prove that the number of characteristic exponents of the curve is upper semicontinuous. Furthermore, we show that every topologically t…

Unital Specker $\ell$-groups and boolean multispaces
Marco Abbadini, Daniele Mundici
https://arxiv.org/abs/2508.21500 https://arxiv.org/pdf/2508.21500

Unital Specker $\ell$-groups and boolean multispaces
As a topological generalization of the notion of multiset, a boolean multispace is a boolean space $X$ with a continuous function $u\colon X\to \mathbb Z_{>0}$, where $\mathbb Z_{>0}=\{1,2,\dots\}$ has the discrete topology. In this paper the category of boolean multispaces and continuous multiplicity-decreasing morphisms with respect to the divisibility order is shown to be dually equivalent to the category of unital Specker $\ell$-groups and unital $\ell$-homomorphisms. This result extends St…

Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
Igor Pak, Boris Shapiro, Ilya Smirnov, Ken-ichi Yoshida
https://arxiv.org/abs/2508.17915 https://a…

Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
We show that the Hilbert-Kunz multiplicity of the d-dimensional non-degenerate quadric hypersurface of characteristic p > 2 is a rational function of p composed from the Ehrhart polynomials of integer polytopes. In consequence, we explain and recover a result of Gessel and Monsky and prove that the Hilbert-Kunz multiplicity of quadrics of fixed characteristic is a decreasing function of dimension.

Dynamical Architectures of S-type Transiting Planets in Binaries II: A Dichotomy in Orbital Alignment of Small Planets in Close Binary Systems
Jingwen Zhang, Daniel Huber, Michael Bottom, Lauren M. Weiss, Jerry W. Xuan, Adam L. Kraus, Chih-Chun Hsu, Jason J. Wang, Fei Dai, Katelyn Horstman, Ashley Baker, Randall Bartos, Benjamin Calvin, Sylvain Cetre, Catherine A. Clark, David R. Ciardi, Jacques-Robert Delorme, Gregory W. Doppmann, Daniel Echeverri, Luke Finnerty, Michael P. Fitzgerald…

Dynamical Architectures of S-type Transiting Planets in Binaries II: A Dichotomy in Orbital Alignment of Small Planets in Close Binary Systems
Stellar multiplicity plays a crucial role in shaping planet formation and dynamical evolution. We present a survey of 54 TESS Objects of Interest (TOIs) within 300 pc that exhibit significant Hipparcos-Gaia astrometric accelerations. We identified 35 TOIs with stellar companions at projected separations between $0.1^{\prime\prime}$ to $2^{\prime\prime}$ (or $10-200$ AU). We also identified 12 TOIs that could host planetary-mass or brown dwarf companions, including 6 that are newly discovered. F…

Generalization and Power of Kocay's Lemma in Graph Reconstruction
Peter Stark
https://arxiv.org/abs/2509.02604 https://arxiv.org/pdf/2509.02604

Generalization and Power of Kocay's Lemma in Graph Reconstruction
This paper generalizes Kocay's lemma, with particular applications to graph reconstruction, as well as discussing and proving aspects around the power of these generalizations and Kocay's original lemma, with a result on the reconstruction of the multiplicity of a tree T as a subgraph of G.

System size and event shape dependence of particle-identified balance functions in proton-proton collisions at $\sqrt{s}=13$ TeV
Subash Chandra Behera, Arvind Khuntia
https://arxiv.org/abs/2508.21030

System size and event shape dependence of particle-identified balance functions in proton-proton collisions at $\sqrt{s}=13$ TeV
We investigate charge balance functions for identified hadron pairs (pions, kaons, and protons) in proton-proton (pp) collisions at $\sqrt{s}=13$~TeV, using transverse spherocity to classify event topology and charged particle multiplicity to select system size. Simulations with PYTHIA8 and EPOS-LHC reveal that balance function widths in rapidity and azimuthal angle depend on multiplicity and event shape. In PYTHIA8, widths decrease monotonically with multiplicity, consistent with local charge …

The epsilon-regularity theorem for Brakke flows near triple junctions
Salvatore Stuvard, Yoshihiro Tonegawa
https://arxiv.org/abs/2510.02969 https://arxiv.…

The epsilon-regularity theorem for Brakke flows near triple junctions
We establish the $\varepsilon$-regularity theorem for $k$-dimensional, possibly forced, Brakke flows near a static, multiplicity-one triple junction. This result provides the parabolic analogue to L. Simon's foundational work on the singular set of stationary varifolds and confirms that the regular structure of triple junctions persists under weak mean curvature flow. The regularity holds provided the flow satisfies a mild structural assumption on its 1-dimensional slices taken orthogonal to th…

Bifurcation Curve Diagrams for a Diffusive Generalized Logistic Problem with Minkowski Curvature Operator and Constant-Yield Harvesting
Shao-Yuan Huang
https://arxiv.org/abs/2510.00362

Bifurcation Curve Diagrams for a Diffusive Generalized Logistic Problem with Minkowski Curvature Operator and Constant-Yield Harvesting
This paper investigates the bifurcation diagrams of positive solutions for a one-dimensional diffusive generalized logistic boundary-value problem with the Minkowski curvature operator and constant yield harvesting. We prove that the corresponding bifurcation curves on both the (lambda, sup-norm of u)-plane and the (mu, sup-norm of u)-plane are C-shaped. Furthermore, by characterizing the bifurcation set on the (mu, lambda)-plane, we determine the exact multiplicity of positive solutions.

Odd Spoof Multiperfect Numbers Of Higher Order
L\'aszl\'o T\'oth
https://arxiv.org/abs/2510.01752 https://arxiv.org/pdf/2510.01752

Odd Spoof Multiperfect Numbers Of Higher Order
We extend our previous work on odd spoof multiperfect numbers to the case where spoof factor multiplicities exceed $2$. This leads to the identification of $11$ new integers that would be odd multiperfect numbers if one of their prime factors had higher multiplicity. An example is $181545$, which would be an odd multiperfect number if only one of its prime factors, $3$, had multiplicity $5$.

Replaced article(s) found for stat.ML. https://arxiv.org/list/stat.ML/new
[2/2]:
- Reconsidering Fairness Through Unawareness From the Perspective of Model Multiplicity
Benedikt H\"oltgen, Nuria Oliver

Hilbert-Kunz multiplicity and $F$-signature can disagree
Seungsu Lee, Suchitra Pande, Austyn Simpson
https://arxiv.org/abs/2508.19985 https://arxiv.org/pdf…

Hilbert-Kunz multiplicity and $F$-signature can disagree
We compute the $F$-signature function of the ample cone of any nontrivial ruled surface over $\mathbb{P}^1_k$ where $k$ is an algebraically closed field of prime characteristic. As an application, we construct a Noetherian $F$-finite strongly $F$-regular ring $R$ of prime characteristic admitting two maximal ideals $\mathfrak{n}_1,\mathfrak{n}_2\in \mathrm{Spec} R$ at which the Hilbert-Kunz multiplicity and $F$-signature measure different singularities; that is, $\operatorname{e}_{\operatorname…

High multiplicity and global structure of coexistence states in a predator-prey model with saturation
Kousuke Kuto, Juli\'an L\'opez-G\'omez, Eduardo Mu\~noz-Hern\'andez
https://arxiv.org/abs/2508.05714

High multiplicity and global structure of coexistence states in a predator-prey model with saturation
This paper establishes that, under the appropriate range of values of the parameters involved in the formulation of the model, a diffusive predator-prey system with saturation can have an arbitrarily large number of coexistence states for sufficiently large saturation rates. Moreover, it ascertains the global structure of the set of coexistence states in the limiting system as the saturation rate blows-up.

Hypergeometry from $\mathrm{\widehat P}$-Symmetry: Feynman Integrals in One and Two Dimensions
Gwena\"el Ferrando, Florian Loebbert, Amelie Pitters, Sven F. Stawinski
https://arxiv.org/abs/2509.16305

Hypergeometry from $\mathrm{\widehat P}$-Symmetry: Feynman Integrals in One and Two Dimensions
Feynman integrals with generic propagator powers in one and two spacetime dimensions are investigated from various perspectives. In particular, we argue that the class of track integrals at any loop order is fixed by the recently found $\mathrm{\widehat P}$-symmetries of Yangian type. All track integrals up to six external points (and four loops) are bootstrapped explicitly as well as the full family of one-loop integrals at any multiplicity. Moreover, the triangle tracks at generic loop order,…

"A 6 or a 9?": Ensemble Learning Through the Multiplicity of Performant Models and Explanations
Gianlucca Zuin, Adriano Veloso
https://arxiv.org/abs/2509.09073 https:/…

"A 6 or a 9?": Ensemble Learning Through the Multiplicity of Performant Models and Explanations
Creating models from past observations and ensuring their effectiveness on new data is the essence of machine learning. However, selecting models that generalize well remains a challenging task. Related to this topic, the Rashomon Effect refers to cases where multiple models perform similarly well for a given learning problem. This often occurs in real-world scenarios, like the manufacturing process or medical diagnosis, where diverse patterns in data lead to multiple high-performing solutions.…

Quantum Howe duality and Schur duality of type AIII
Weinan Zhang
https://arxiv.org/abs/2509.18982 https://arxiv.org/pdf/2509.18982

An adaptive procedure for detecting replicated signals with $k$-family-wise error rate control
Ninh Tran
https://arxiv.org/abs/2508.15363 https://arxiv.org…

An adaptive procedure for detecting replicated signals with $k$-family-wise error rate control
Partial conjunction (PC) hypothesis testing is widely used to assess the replicability of scientific findings across multiple comparable studies. In high-throughput meta-analyses, testing a large number of PC hypotheses with k-family-wise error rate (k-FWER) control often suffers from low statistical power due to the multiplicity burden. The state-of-the-art AdaFilter-Bon procedure by Wang et al. (2022, Ann. Stat., 50(4), 1890-1909) alleviates this problem by filtering out hypotheses unlikely t…

Lensed stars in galaxy-galaxy strong lensing -- a JWST prediction for the Cosmic Horseshoe
Sung Kei Li, Luke Weisenbach, Thomas E. Collett, Jose M. Diego, Jeremy Lim, Thomas J. Broadhurst, Alex Chow, Wolfgang J. R. Enzi, Patrick L. Kelly, Carlos R. Melo-Carneiro, Jose M. Palencia, Liliya L. R. Williams, Jiashuo Zhang
https://arxiv.org/abs/…

Lensed stars in galaxy-galaxy strong lensing -- a JWST prediction for the Cosmic Horseshoe
We explore for the first time the possibility of detecting lensed star transients in galaxy-galaxy strong lensing systems upon repeated, deep imaging using the {\it James-Webb Space Telescope} ({\it JWST}). Our calculation predicts that the extremely high recent star formation rate of $\sim 100\,M_{\odot}\textrm{yr}^{-1}$ over the last 50 Myr (not accounting for image multiplicity) in the ``Cosmic Horseshoe'' lensed system ($z = 2.381$) generates many young, bright stars, of which their large a…

Replaced article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[3/5]:
- Systemizing Multiplicity: The Curious Case of Arbitrariness in Machine Learning
Prakhar Ganesh, Afaf Taik, Golnoosh Farnadi

Stationary and stable varifolds with singularities
Camillo De Lellis, Jonas Hirsch, Luca Spolaor
https://arxiv.org/abs/2509.21508 https://arxiv.org/pdf/250…

Stationary and stable varifolds with singularities
We construct minimal $m$-dimensional immersions in $\mathbb{R}^{m+1}$, equipped with a $C^{m-1, α}$ metric, $α\in [0,1)$, with a sequence of catenoidal necks or floating disks converging to an isolated, multiplicity $2$, singular flat point.

Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery
Martin Hentschinski, Hannes Jung, Krzysztof Kutak
https://arxiv.org/abs/2509.03400 https://

Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery
We study entropy production in Deep Inelastic Scattering using Monte Carlo simulations. We show that the dominant contribution to entropy is due to soft gluons. This contribution is usually neglected in standard Monte Carlo approaches, since it does not affect hadronic spectra. However, it is relevant for entropy and multiplicity distributions, as we demonstrate with explicit calculations. We further show that, as one lowers the cutoff - i.e. includes soft gluons - thereby making the Monte Carl…

Multiplicity dependence of $\Xi_c^ $ and $\Xi_c^0$ production in pp collisions at $\sqrt{s} = 13$ TeV
ALICE Collaboration
https://arxiv.org/abs/2508.09955 https://

Multiplicity dependence of $Ξ_c^+$ and $Ξ_c^0$ production in pp collisions at $\sqrt{s} = 13$ TeV
The first measurement at midrapidity ($|y| < 0.5$) of the production yield of the strange-charm baryons $Ξ_c^+$ and $Ξ_c^0$ as a function of charged-particle multiplicity in proton-proton collisions at $\sqrt{s} = 13$ TeV with the ALICE experiment at the LHC is reported. The $Ξ_c^+$ baryon is reconstructed via the $Ξ_c^+ \rightarrow Ξ^-π^+π^+$ decay channel in the range $4 < p_{\rm T} < 12$ GeV/$c$, while the $Ξ_c^0$ baryon is reconstructed via both the $Ξ_c^0 \rightarrow Ξ^…

Neutron Skin from Conserved Charge Measurements at Collider Experiments
Gr\'egoire Pihan, Akihiko Monnai, Bj\"orn Schenke, Chun Shen
https://arxiv.org/abs/2509.21644 ht…

Neutron Skin from Conserved Charge Measurements at Collider Experiments
We propose a novel method for measuring the neutron skin of heavy nuclei using collider experiments. Specifically, we demonstrate that the neutron skin thickness of the lead nucleus can be extracted in $p$+$^{208}$Pb collisions by analyzing a double ratio: The ratio of net electric charge to net baryon number measured near the lead-going rapidity, taken for high-multiplicity events and divided by the same ratio for low-multiplicity events. We compute the expected sensitivity of the double ratio…

Radial Velocity Monitoring and Analysis of Gaia Astrometry of Selected Intermediate Mass Stars to Constrain Their Multiplicity Status
J. B\"atz, M. Mugrauer, K. -U. Michel, J. Reichert, A. Tschirschky, L. Pietsch, F. Edelmann, R. Neuh\"auser
https://arxiv.org/abs/2510.09772

Radial Velocity Monitoring and Analysis of Gaia Astrometry of Selected Intermediate Mass Stars to Constrain Their Multiplicity Status
We present new radial velocity measurements of 13 selected intermediate mass stars (2 - 6 M$_\odot$). The measurements were performed between 29 April and 6 September 2024 at the University Observatory Jena using the échelle spectrograph FLECHAS. The radial velocity of eight stars was found to be constant during our spectroscopic monitoring, namely: 17 Dra A, HD 148374, HD 169487 A, 57 Cnc, $γ$ And, HD 11031, $κ$ And, and $λ$ Cas. In contrast, the radial velocity of five stars showed signif…

On stable solutions to the Allen-Cahn equation with bounded energy density in $\mathbb{R}^4$
Enric Florit-Simon, Joaquim Serra
https://arxiv.org/abs/2509.02739 https://

On stable solutions to the Allen-Cahn equation with bounded energy density in $\mathbb{R}^4$
We show that stable solutions $u:\mathbb{R}^4\to (-1,1)$ to the Allen-Cahn equation with bounded energy density (or equivalently, with cubic energy growth) are one-dimensional. This is known to entail important geometric consequences, such as robust curvature estimates for stable phase transitions, and the multiplicity one and Morse index conjectures of Marques-Neves for Allen-Cahn approximations of minimal hypersurfaces in closed 4-manifolds.

Strong Multiplicity One for Goss Zeta and its Teichmuller Lift
Shaver Phagan
https://arxiv.org/abs/2509.14083 https://arxiv.org/pdf/2509.14083

Strong Multiplicity One for Goss Zeta and its Teichmuller Lift
Using recent results, we prove strong multiplicity one theorems for Goss zeta functions and their Teichmuller lifts.

Multiplicity Distributions and the Frontier between Soft and Hard Physics
H. R. Martins-Fontes, F. S. Navarra
https://arxiv.org/abs/2509.15056 https://arxi…

Multiplicity Distributions and the Frontier between Soft and Hard Physics
The multiplicity distributions measured in proton proton collisions at the LHC exhibit interesting new features. One of them is the appearance of substructures, such as the so-called "shoulder" at large multiplicities. The most natural interpretation of this behavior is the existence of two production mechanisms. The final result is then a superposition of two distributions. In a previous publication we assumed that the two production mechanisms are soft and semihard partonics scatterings. In t…

Persistence probabilities for fractionally integrated fractional Brownian noise
G. Molchan
https://arxiv.org/abs/2509.10265 https://arxiv.org/pdf/2509.1026…

Persistence probabilities for fractionally integrated fractional Brownian noise
The main object the study is fractionally integrated fractional Brownian noise, I(t/a,H) where a>0 is the multiplicity(not necessarily an integer) of integration, and H is the Hurst parameter . The subject of the analysis is the persistence exponent e(a,H) that determines the power-law asymptotic of probability that the process will not exceed a fixit positive level in a growing time interval (0,T). In the important cases (a=1,H) and (a=2,H=1/2) these exponents are well known. To understand the…

Bifurcation and stability of stationary shear flows of Ericksen-Leslie model for nematic liquid crystals
Weishi Liu, Majed Sofiani
https://arxiv.org/abs/2508.19125 https://

Bifurcation and stability of stationary shear flows of Ericksen-Leslie model for nematic liquid crystals
In this work, focusing on a critical case for shear flows of nematic liquid crystals, we investigate multiplicity and stability of stationary solutions via the parabolic Ericksen-Leslie system. We establish a one-to-one correspondence between the set of the stationary solutions with the set of solutions of an algebraic equation. The existence of multiple stationary solutions is established through countably many saddle-node bifurcations at critical shear speeds for the algebraic equation. We th…

Note on length and multiplicity of modules over two-dimensional regular local rings
Futoshi Hayasaka, Vijay Kodiyalam
https://arxiv.org/abs/2510.07779 https://

Note on length and multiplicity of modules over two-dimensional regular local rings
We give lower and upper bounds on the Buchsbaum-Rim multiplicity of finitely generated torsion-free modules over two-dimensional regular local rings, and conditions for them to attain the bounds. As consequences, we have formulae on the multiplicity of integrally closed modules.

The spectrum of the Steklov-Helmholtz operator
Nilima Nigam, Kshitij Patil, Weiran Sun
https://arxiv.org/abs/2509.07249 https://arxiv.org/pdf/2509.07249

The spectrum of the Steklov-Helmholtz operator
We present a wavenumber-robust strategy for computing Steklov eigenpairs of the Helmholtz operator $-Δ-μ^2$. As the wavenumber $μ\rightarrow μ_D$ from below (where $μ_D^2 $ is a Dirichlet- Laplace eigenvalue of multiplicity $\ell$), the lowest $\ell$ Steklov-Helmholtz eigenvalues diverge to $-\infty$. Computationally, the Steklov-Helmholtz eigenvalue problem becomes severely ill-conditioned when $μ\approx μ_D$. We first reformulate the problem in terms of a suitably-defined Dirichlet-t…

Replaced article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[2/2]:
- Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
Igor Pak, Boris Shapiro, Ilya Smirnov, Ken-ichi Yoshida

Discovery of the Second Y Y Dwarf Binary System: CWISEP J193518.59-154620.3
Matthew De Furio, Jacqueline Kelly Faherty, Daniella C. Bardalez Gagliuffi, Jonathan Gagn\'e, Eileen C. Gonzales, Rocio Kiman, Marc Kuchner, Federico Marocco, Sherelyn Alejandro Merchan, Melanie Rowland, Adam C. Schneider, Genaro Su\'arez, Johanna M. Vos
https://

Discovery of the Second Y+Y Dwarf Binary System: CWISEP J193518.59-154620.3
We present the discovery of a companion to the Y-dwarf, CWISEP J193518.59-154620.3, the second Y-Y dwarf binary detected to date. Y-dwarfs are the coldest known free-floating objects ($<$ 500 K) and on average represent the lowest mass objects directly formed through turbulent fragmentation of a molecular cloud. Studying their multiplicity allows us to place strong constraints on the ability to form multiple systems of planetary masses and approaching the opacity limit of fragmentation. Due to …

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations
Lidan Wang
https://arxiv.org/abs/2508.18840 https://arxiv.or…

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations
In this paper, we study the discrete fractional logarithmic Kirchhoff equation $$ \left(a+b \int_{\mathbb{Z}^d}|\nabla^s u|^{2} d μ\right) (-Δ)^s u+h(x) u=|u|^{p-2}u \log u^{2}, \quad x\in \mathbb{Z}^d, $$ where $a,\,b>0$ and $04$; then we verify the existence of ground state sign-changing solutions based on the method of Nehari manifold f…

Tropical regions of near mass-shell pentabox
A. V. Belitsky, V. A. Smirnov
https://arxiv.org/abs/2508.14298 https://arxiv.org/pdf/2508.14298

Tropical regions of near mass-shell pentabox
Coulomb branch amplitudes of maximally supersymmetric Yang-Mills theory display infrared properties different from their conformal counterparts. While the four-leg amplitude is known to very high perturbative orders, amplitudes of higher multiplicity fall into an uncharted territory starting already from two loops. The reason for this is that they are not easily amenable to traditional techniques like canonical differential equations due to the uncontrolled swelling of solutions to integration-…

The Corona-Australis star-forming region: New insights on its formation history from detailed stellar and disk analysis
Elisabetta Rigliaco, Raffaele Gratton, Valerio Nascimbeni
https://arxiv.org/abs/2508.19757

The Corona-Australis star-forming region: New insights on its formation history from detailed stellar and disk analysis
The star-forming complex of Corona Australis (CrA) is one of the closest and most isolated molecular clouds. It belongs to a chain of clusters that show age gradients with distance from the galactic plane. We aim to provide suggestions regarding its formation history by examining the stellar and disk populations, stellar multiplicity, and interstellar absorption. We made a census of stars and disks using Gaia DR3 and infrared data. Interstellar absorption in the direction of each star was deriv…

Local spin polarization of $\Lambda$ hyperons and its interaction corrections
Cong Yi, Shuo Fang, Dong-Lin Wang, Shi Pu
https://arxiv.org/abs/2509.00377 https://

Local spin polarization of $Λ$ hyperons and its interaction corrections
We have computed the second Fourier sine coefficient of the longitudinal spin polarization, $\langle P_{z} \sin 2(ϕ_{p} - Ψ_{2}) \rangle$, as a function of multiplicity or centrality in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV and in $p$+Pb collisions at $\sqrt{s_{NN}} = 8.16$ TeV using the CLVisc hydrodynamic framework. The numerical results successfully describe the data in Au+Au collisions. However, understanding the data in $p$+Pb collisions remains a puzzle. Additionally, we have re…

Study of the interaction between $\Xi$ baryons and light mesons via femtoscopy at the LHC
ALICE Collaboration
https://arxiv.org/abs/2509.24519 https://arxi…

Study of the interaction between $Ξ$ baryons and light mesons via femtoscopy at the LHC
Meson-baryon systems with strangeness content provide a unique laboratory for investigating the strong interaction and testing theoretical models of hadron structure and dynamics. In this work, the measured correlation functions for oppositely charged $Ξ-{\rm K}$ and $Ξ-π$ pairs obtained in high-multiplicity pp collisions at $\sqrt{s} = 13$ TeV at the LHC are presented. For the first time, high-precision data on the $Ξ-{\rm K}$ interaction are delivered at small relative momenta. The scatte…

Exponents of $2$-multiarrangements and Wakefield--Yuzvinsky matrices
Shota Maehara
https://arxiv.org/abs/2509.16569 https://arxiv.org/pdf/2509.16569…

Exponents of $2$-multiarrangements and Wakefield--Yuzvinsky matrices
In the theory of hyperplane arrangements, M. Wakefield and S. Yuzvinsky utilized a square matrix in their research on the exponents of $2$-dimensional multiarrangements. Using such a matrix, they showed that the exponents of $2$-dimensional multiarrangements are as close as possible in general position for any fixed balanced multiplicity. In this article, we introduce a matrix similar to that of Wakefield and Yuzvinsky and explore its further application to the exponents. In fact, exponents of …

Caccioppoli-type inequalities for the Dunkl-$A$-Laplacian and their application to nonexistence result
Athulya P, Sandeep Kumar Verma
https://arxiv.org/abs/2509.00565 https://…

Caccioppoli-type inequalities for the Dunkl-$A$-Laplacian and their application to nonexistence result
For a suitable function $A:\mathbb{R}^n\to \mathbb{R}^n$, we introduce the $A$-Laplacian in the Dunkl framework as $Δ_{k,A}(u) =\text{div}_k(A(\nabla_ku))$, where $\nabla_k$ is the Dunkl-gradient operator associated with the multiplicity function $k$ and the root system $\mathcal{R}$. We derive the local and global Caccioppoli-type inequality for an element $u$ in the Dunkl-Orlicz-Sobolev space, satisfying the Dunkl-differential inequality $$ -Δ_{k, A}(u) \geq bΦ(u)χ_{\{u>0\}}. $$ Using the…

Topological Levinson's theorem and corrections at thresholds: the full picture in a quasi-1D example
T. T. Nguyen, D. Parra, S. Richard
https://arxiv.org/abs/2509.12684 http…

Topological Levinson's theorem and corrections at thresholds: the full picture in a quasi-1D example
Various threshold effects are investigated on a discrete quasi-1D scattering system. In particular, one of these effects is to add corrections to Levinson's theorem. We explain how these corrections are due to the opening or to the closing of channels of scattering, and how these contributions can be computed as partial winding numbers on newly introduced operators. Embedded thresholds, thresholds associated with changes of spectral multiplicity, and doubly degenerate thresholds are exhibited a…

Minimal surface doublings and electrostatics for Schr\"odinger operators
Adrian Chun-Pong Chu, Daniel Stern
https://arxiv.org/abs/2509.18630 https://a…

Minimal surface doublings and electrostatics for Schrödinger operators
Twenty years ago, N. Kapouleas introduced a singular perturbation construction known as "doubling", which produces sequences of high-genus minimal surfaces converging to a given minimal surface with multiplicity two. Doubling constructions have since been implemented successfully in several settings, with deep work of Kapouleas-McGrath reducing their existence theory to the problem of finding suitable families of ansatz data on the initial minimal surface. In this paper, we introduce a variat…

Initial-state geometry and multiplicity distributions in pPb collisions
R. Terra, A. V. Giannini, F. S. Navarra
https://arxiv.org/abs/2510.12561 https://ar…

Initial-state geometry and multiplicity distributions in pPb collisions
This work investigates the possibility of accessing the initial geometric shape of the proton in proton-nucleus collisions at the LHC, in particular the configuration in which the proton is made of three quarks linked by a Y-shape gluon string, called baryon junction. This initial state spatial configuration has been used in the past to describe data on baryon rapidity distributions, diffractive $J/ψ$ production and multiplicity distributions in pp collisions. In spite of its success in explai…

Modular analogs of character formulas and multiplicities of induced representations
Patrick Allen, Preston Wake, Robin Zhang
https://arxiv.org/abs/2508.06657 https://

Modular analogs of character formulas and multiplicities of induced representations
Let $G$ be a finite group, $k$ a characteristic-$p$ field, and $π$ be a simple $k[G]$-module. We show that if $π$ is in a $p$-nilpotent block with cyclic defect group, then $π$ appears with multiplicity at most one in the socle and cosocle of induced $k[G]$-modules that are multiplicity-free in characteristic zero and satisfy some additional hypotheses. We show that this applies, in particular, to certain Deligne--Lusztig modules $π$. As an application, we prove that well-known character fo…

Exploration of vertical self-resonant bifurcations from DRO in the Earth-Moon CR3BP
Cengiz Aydin
https://arxiv.org/abs/2508.17286 https://arxiv.org/pdf/250…

Exploration of vertical self-resonant bifurcations from DRO in the Earth-Moon CR3BP
The purpose of this paper is to investigate vertical self-resonant (VSR) bifurcations from distant retrograde orbit (DRO) family in the framework of the Earth-Moon CR3BP. To this end, by using a classical corrector-predictor algorithm we compute the vertical stability of DROs and identify twelve vertical-critical DROs. We split them into three groups according to orbiting around libration points $L_i$, $i=1,2,4,5$. (i) We first analyze six VSR bifurcations of multiplicity from five to ten assoc…

Hydrodynamic effects on spin polarization along the beam direction in Au Au and p Pb collisions
Cong Yi, Xiang-Yu Wu, Jie Zhu, Shi Pu, Guang-You Qin
https://arxiv.org/abs/2509.00380

Hydrodynamic effects on spin polarization along the beam direction in Au+Au and p+Pb collisions
We investigate hydrodynamic effects on the spin polarization of $Λ$ hyperons in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV and p+Pb collisions at $\sqrt{s_{NN}} = 8.16$ TeV using the CLVisc hydrodynamic framework. We present numerical results for the second Fourier sine coefficient of the longitudinal spin polarization, $\langle P_{z} \sin 2(ϕ_{p} - Ψ_{2}) \rangle$, as a function of multiplicity (centrality) under three equilibrium scenarios: $Λ$ equilibrium, $s$-quark equilibrium, and i…

A search for Be stars in multiple systems within the solar neighborhood
V. M. Kalari, R. Salinas, C. Saez-Carvajal, R. D. Oudmaijer, S. Howell, S. Caballero-Nieves, K. Kamp, R. Matson, N. Scott, T. Cao, Z. Hartman, H. Kim
https://arxiv.org/abs/2509.19286

On the partition regularity of arithmetic progressions and linear equations in k-IP-sets
Rapha\"el Giordano
https://arxiv.org/abs/2509.17013 https://a…

On the partition regularity of arithmetic progressions and linear equations in k-IP-sets
In this paper, we provide versions of Van der Waerden's theorem and Rado's theorem for finite colorings of IP-sets and k-IP-sets. Here, by an IP-set we mean a set of integers that contains all finite sums of an infinite subset of N, and we define k-IP-sets similarly to IP-sets but allowing each summand to appear with multiplicity bounded by k - 1.

Is Repeated Bayesian Interim Analysis Consequence-Free?
Suyu Liu, Beibei Guo, Laura Thompson, Lei Nie, Ying Yuan
https://arxiv.org/abs/2508.07403 https://a…

Is Repeated Bayesian Interim Analysis Consequence-Free?
Interim analyses are commonly used in clinical trials to enable early stopping for efficacy, futility, or safety. While their impact on frequentist operating characteristics is well studied and broadly understood, the effect of repeated Bayesian interim analyses - when conducted without appropriate multiplicity adjustment - remains an area of active debate. In this article, we provide both theoretical justification and numerical evidence illustrating how such analyses affect key inferential pro…

Unboundedness of fixed point multiplicities on a K3 surface
Kenji Hashimoto, Yuta Takada
https://arxiv.org/abs/2508.18814 https://arxiv.org/pdf/2508.18814

Unboundedness of fixed point multiplicities on a K3 surface
We exhibit automorphisms of a certain K3 surface in $\mathbb{P}^1\times \mathbb{P}^1 \times \mathbb{P}^1$ with an isolated fixed point at which the induced action on the stalk of the structure sheaf is arbitrarily close to the identity. This implies that the multiplicities of these automorphisms at the fixed point can be arbitrarily large. As another application, we show that the intersection multiplicity of two isomorphic curves at a point can be arbitrarily large on this K3 surface.

Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models
Krzysztof Kutak, S\'andor L\"ok\"os
https://arxiv.org/abs/2509.07898 http…

Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models
We investigate and compare QCD dipole cascade models, the 1D Mueller dipole model, its high energy limit and its generalization that follows from studies of 1D systems with conformal symmetry. To address the ambiguity stemming from different definitions of the rapidity ranges in experimental measurements, we propose the entropy as the function of the logarithm of the average multiplicity, $S(\ln\langle n \rangle)$, as a universal observable. From the solutions of the models, we calculate both t…

$\Sigma^{ }$ production in pp collisions at $\sqrt{s} = 13$ TeV
ALICE Collaboration
https://arxiv.org/abs/2508.20808 https://arxiv.org/pdf/2508.20808

$Σ^{+}$ production in pp collisions at $\sqrt{s} = 13$ TeV
The measurement of $Σ^{+}$ production in pp collisions at $\sqrt{s} = 13$ TeV is presented. The measurement is performed at midrapidity in both minimum-bias and high-multiplicity pp collisions at $\sqrt{s} = 13$ TeV. The $Σ^{+}$ is reconstructed via its weak-decay topology in the decay channel $Σ^{+} \rightarrow {\rm p} + π^{0}$ with $π^{0} \rightarrow γ+ γ$. In a novel approach, the neutral pion is reconstructed by combining photons that convert in the detector material with photons mea…

Numerical Approximation and Bifurcation Results for an Elliptic Problem with Superlinear Subcritical Nonlinearity on the Boundary
Shalmali Bandyopadhyay, Thomas Lewis, Dustin Nichols
https://arxiv.org/abs/2509.08990

Numerical Approximation and Bifurcation Results for an Elliptic Problem with Superlinear Subcritical Nonlinearity on the Boundary
We develop numerical algorithms to approximate positive solutions of elliptic boundary value problems with superlinear subcritical nonlinearity on the boundary of the form $-Δu + u = 0$ in $Ω$ with $\frac{\partial u}{\partial η} = λf(u)$ on $\partialΩ$ as well as an extension to a corresponding system of equations. While existence, uniqueness, nonexistence, and multiplicity results for such problems are well-established, their numerical treatment presents computational challenges due to th…

Bifurcation Curves in Semipositone Problems with Geometrically Concave and Concave Nonlinearities
Shao-Yuan Huang
https://arxiv.org/abs/2510.10412 https://…

Bifurcation Curves in Semipositone Problems with Geometrically Concave and Concave Nonlinearities
In this paper, we study the exact multiplicity and bifurcation curves of positive solutions for the semipositone problem defined on the interval from minus one to one, with zero boundary conditions at both ends. The function f is twice continuously differentiable on the positive real line, and there exist two positive numbers such that f is positive between them and negative outside this range. We allow f at zero from the right to be negative infinity and provide many examples to illustrate the…

Multiplicity dependence of $\Upsilon$(nS) mean transverse momentum in proton-proton collisions
Luis Gabriel Gallegos Mari\~nez, Lizardo Valencia Palomo, Luis Cedillo Barrera
https://arxiv.org/abs/2510.07824

Multiplicity dependence of $Υ$(nS) mean transverse momentum in proton-proton collisions
Correct description of quarkonia production and kinematics are still one of the most challenging assignments for Quantum Chromodynamics. This document presents a study of the $Υ$(1S), (2S) and (3S) mean transverse momentum ($\langle p_{\mathrm{T}}^Υ \rangle$) as a function of the charged particle multiplicity ($N_{\mathrm{Track}}$) in proton-proton collisions at $\sqrt{s}$ = 7 TeV generated with Pythia 8.312 CUETP8M1 tune. The comparison to real data collected by the CMS experiment indicates …

Ledrappier-Young entropy formula for $C^1$ diffeomorphisms with dominated splitting Part 1: Unstable entropy formula and invariance principle
Shaobo Gan, Yao Tong, Jiagang Yang
https://arxiv.org/abs/2509.16981

Ledrappier-Young entropy formula for $C^1$ diffeomorphisms with dominated splitting Part 1: Unstable entropy formula and invariance principle
We study the unstable entropy of $C^1$ diffeomorphisms with dominated splittings. Our main result shows that when the zero Lyapunov exponent has multiplicity one, the center direction contributes no entropy, and the unstable entropy coincides with the metric entropy. This extends the celebrated work of Ledrappier-Young [18] for $C^2$ diffeomorphisms to the $C^1$ setting under these assumptions. In particular, our results apply to $C^1$ diffeomorphisms away from homoclinic tangencies due to [20]…

Cross talk between experimental data and simple validation of shell closure in pre-actinides
Punit Dubey, Mahima Upadhyay, Mahesh Choudhary, Namrata Singh, Sriya Paul, Shweta Singh, N. Saneesh, Mohit Kumar, Rishabh Prajapati, K. S. Golda, Akhil Jhingan, P. Sugathan, Jhilam Sadhukhan, Raghav Aggarwal, Kiran, Ajay Kumar
https://arxiv.org/ab…

Cross talk between experimental data and simple validation of shell closure in pre-actinides
Two back-to-back experiments, 28Si + 178Hf and 28Si + 186W, were intentionally conducted to validate the role of shell closure in pre-actinides by studying neutron multiplicity in compound nucleus (CN) 206Rn and 214Ra. In the first experiment, Dubey et al. [Phys. Rev. C 112, L011602 (2025)], we established the influence of the neutron shell closure. In the present work, the CN 214Ra was deliberately selected to investigate the dependence of the total neutron multiplicity (Mtotal) on the proton …

Joint reductions and mixed Buchsbaum-Rim multiplicities of modules and a joint-reduction-number-zero theorem
Daniel Katz, Vijay Kodiyalam, J. K. Verma
https://arxiv.org/abs/2508.07437

Joint reductions and mixed Buchsbaum-Rim multiplicities of modules and a joint-reduction-number-zero theorem
We offer new definitions of joint reductions and mixed Buchsbaum-Rim multiplicity for certain collections of modules over a Noetherian local ring and illustrate their application to give two different proofs of a joint-reduction-number-zero theorem for integrally closed modules over two-dimensional regular local rings. We also relate the mixed Buchsbaum-Rim multiplicity of modules to the Euler-Poincaré characteristic of a natural Koszul complex and relate it to the mixed Buchsbaum-Rim multipli…

Exploring parameter dependence of heavy-flavor dynamics in small collision systems
Grace Pang
https://arxiv.org/abs/2509.23081 https://arxiv.org/pdf/2509.2…

Exploring parameter dependence of heavy-flavor dynamics in small collision systems
Observations from high-multiplicity proton-lead ($p$-Pb) collisions indicate that small systems may exhibit collective behavior in both heavy and light hadrons. This work investigates the roles of initial- and final-state interactions in shaping the nuclear modification factor and elliptic flow of $D$ mesons measured in $p$-Pb collisions. Initial-state effects, including the Cronin and shadowing effects, are considered in the heavy-quark initial conditions, while final-state interactions are si…

Search for emerging jets in $pp$ collisions at $\sqrt{s} = 13$ TeV with the ATLAS experiment
ATLAS Collaboration
https://arxiv.org/abs/2510.12347 https://a…

Search for emerging jets in $pp$ collisions at $\sqrt{s} = 13$ TeV with the ATLAS experiment
A search is presented for emerging jets using 140 fb$^{-1}$ of proton-proton collision data at $\sqrt{s} = 13$ TeV, collected by the ATLAS experiment between 2015 and 2018. The search looks for the existence of a dark sector with symmetries similar to those in quantum chromodynamics. This dark sector is populated with dark quarks, which undergo showering similar to quarks in the Standard Model, leading to a high multiplicity of long-lived dark hadrons within a dark jet. These dark hadrons subse…

Three more proofs of two congruences for Merca's partition function
Fabrizio Zanello
https://arxiv.org/abs/2509.09833 https://arxiv.org/pdf/2509.09833

Three more proofs of two congruences for Merca's partition function
In this note, we provide three new, very short proofs of two interesting congruences for Merca's partition function $a(n)$, which enumerates integer partitions where the odd parts have multiplicity at most 2. These modulo 2 congruences were first shown elementarily by Sellers. We then frame $a(n)$ into the much broader context of eta-quotients, and suggest how to comprehensively describe its parity behavior. In particular, extensive computations suggest that $a(n)$ is odd precisely 25\% of the …

A high fraction of close massive binary stars at low metallicity
H. Sana, T. Shenar, J. Bodensteiner, N. Britavskiy, N. Langer, D. J. Lennon, L. Mahy, I. Mandel, S. E. de Mink, L. R. Patrick, J. I. Villasenor, M. Dirickx, M. Abdul-Masih, L. A. Almeida, F. Backs, S. R. Berlanas, M. Bernini-Peron, D. M. Bowman, V. A. Bronner, P. A. Crowther, K. Deshmukh, C. J. Evans, M. Fabry, M. Gieles, A. Gilkis, G. Gonzalez-Tora, G. Grafener, Y. Gotberg, C. Hawcroft, V. Henault-Brunet, A. Herrero, G. …

A high fraction of close massive binary stars at low metallicity
At high metallicity, a majority of massive stars have at least one close stellar companion. The evolution of such binaries is subject to strong interaction processes, heavily impacting the characteristics of their life-ending supernova and compact remnants. For the low-metallicity environments of high-redshift galaxies constraints on the multiplicity properties of massive stars over the separation range leading to binary interaction are crucially missing. Here we show that the presence of massi…

The Gross-Zagier formula on singular moduli for Shimura curves
Andrew Phillips
https://arxiv.org/abs/2509.11553 https://arxiv.org/pdf/2509.11553

The Gross-Zagier formula on singular moduli for Shimura curves
The Gross-Zagier formula on singular moduli can be seen as a calculation of the intersection multiplicity of two CM divisors on the integral model of a modular curve. We prove a generalization of this result to a Shimura curve.

Strong Gelfand Pairs of the Dihedral and Dicyclic Groups
Joseph E. Marrow
https://arxiv.org/abs/2508.10756 https://arxiv.org/pdf/2508.10756

Strong Gelfand Pairs of the Dihedral and Dicyclic Groups
A strong Gelfand pair $(G, H)$ is a finite group $G$ and a subgroup $H$ where every irreducible character of $H$ induces to a multiplicity-free character of $G$. We determine the strong Gelfand pairs of the dihedral groups $D_{2n}$ and the dicyclic groups $Dic_{4n}$ for all $n$.

Expanding the Landscape of Exotic Muon Decays
Admir Greljo, Ajdin Palavri\'c, Mirsad Tunja, Jure Zupan
https://arxiv.org/abs/2510.08674 https://arxiv.o…

Expanding the Landscape of Exotic Muon Decays
We chart new-physics models that produce exotic, high-multiplicity muon decays featuring prompt or displaced $e^+e^-$ pairs and/or photons, with or without missing energy, such as $μ\to 5e$, $μ\to 7e$, etc. Starting from an effective-field-theory perspective, we estimate the reach on the ultraviolet scale and identify conditions under which lower-multiplicity modes are suppressed or occur at comparable rates. We then construct explicit realizations in minimal dark-sector models with light, fe…

Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two
Rylan Gajek-Leonard, Antonio Lei
https://arxiv.org/abs/2508.11007 https://

Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two
Fix an odd prime $p$ and let $f$ be a non-ordinary eigen-cuspform of weight $k$ and level coprime to $p$. Assuming $p>k-1$, we compute asymptotic formulas for the Iwasawa invariants of the Mazur-Tate elements attached to $f$ in terms of the corresponding invariants of the signed $p$-adic $L$-functions. By combining this with a version of mod $p$ multiplicity one, we also obtain descriptions of the $λ$-invariants of Mazur-Tate elements attached to certain higher weight modular forms with Serre …

Steady states of FitzHugh-Nagumo-type systems with sign-changing coefficients
Jo\~ao Marcos do \'O, Evelina Shamarova, Victor V. Silva
https://arxiv.org/abs/2508.14854 https…

Steady states of FitzHugh-Nagumo-type systems with sign-changing coefficients
We establish existence and multiplicity results for steady-state solutions of spatially heterogeneous FitzHugh-Nagumo-type systems, extending the existing theory from constant to variable coefficients that may change sign. Specifically, we study the system Specifically, we study the system $-Δu + a(x)v = f(x,u)$ in $\mathbb{R}^N$, $-Δv + b(x)v = c(x)u$ in $\mathbb{R}^N$, where $N \geqslant 3$, the coefficients $a,b,c : \mathbb{R}^N \to \mathbb{R}$ are $L^\infty_{\mathrm{loc}}$-functions…

Generalized Rank via Minimal Subposet
Thomas Br\"ustle, Justin Desrochers, Samuel Leblanc
https://arxiv.org/abs/2510.10837 https://arxiv.org/pdf/2510.…

Generalized Rank via Minimal Subposet
Let $\mathcal{C}$ be a small, connected category with finite hom-sets. We show that if the embedding of a connected subcategory $\mathcal{J}$ is both initial and final, then the restriction of any $\mathcal{C}$-module along $\mathcal{J}$ preserves the generalized rank-or equivalently, the multiplicity of the ``entire" interval modules for $\mathcal{C}$ and $\mathcal{J}$. Conversely, we prove that this property characterizes initial and final embeddings when both $\mathcal{C}$ and $\mathcal{J}$ …

Unveiling stealth SUSY in the low missing energy terrain at the LHC
Justin I. Alvarez, Marvin M Flores
https://arxiv.org/abs/2509.16501 https://arxiv.org/p…

Unveiling stealth SUSY in the low missing energy terrain at the LHC
Using a set of missing energy-independent selection criteria involving large-radius jet multiplicity and angular separation among the final states, we extend the discovery potential of the stealth SUSY squark-pair production in the low missing transverse energy (ETmiss) parameter space, thereby complementing existing ATLAS and CMS searches that are sensitive in the high ETmiss regime. With these kinematic cuts, the estimated sensitivity was extended to squark masses up to 2500 GeV for a bino ma…

Baselines for Abelian Charge Fluctuations in Nuclear Collisions:Theory and Comparison with Experimental Data
Bengt Friman, Krzysztof Redlich, Anar Rustamov
https://arxiv.org/abs/2508.18879

Baselines for Abelian Charge Fluctuations in Nuclear Collisions:Theory and Comparison with Experimental Data
We investigate fluctuations in the canonical ensemble of an Abelian charge, such as baryon number. Our focus is on cumulants and factorial cumulants of baryon and antibaryon multiplicity distributions, including their sum and difference, in both the full phase space and subsystems. In particular, we establish a correlation between net-baryon number fluctuations within a subsystem, which is pertinent for fluctuation analyses in nucleus-nucleus collisions, and fluctuations of baryon and antibaryo…

Saddle solution to the complex Ginzburg-Landau system in three dimensions
Michele Caselli, Nicola Picenni
https://arxiv.org/abs/2509.13935 https://arxiv.or…

Saddle solution to the complex Ginzburg-Landau system in three dimensions
We construct an entire saddle solution to the non-magnetic complex Ginzburg-Landau system in three dimensions, whose zero set is the union of two perpendicular, intersecting lines, and whose blow-downs concentrate on these lines with multiplicity one.

Scaling behaviour of charged particles generated in Xe$-$Xe collisions at $\sqrt{s_{\rm{NN}}}$ = 5.44 TeV using the AMPT model
Zarina Banoo, Ramni Gupta, Salman K. Malik, Fakhar Ul Haider, Balwan Singh, Sheetal Sharma
https://arxiv.org/abs/2508.12796

Scaling behaviour of charged particles generated in Xe$-$Xe collisions at $\sqrt{s_{\rm{NN}}}$ = 5.44 TeV using the AMPT model
The spatial configurations of particles produced in the kinematic phase space during a heavy-ion collision reflect the characteristics of the system created in the collision. The scaling behaviour of the multiplicity fluctuations is studied for the charged particles generated in Xe--Xe collisions at $\sqrt{s_{\rm{NN}}}$ = 5.44 TeV using the String Melting (SM) mode of the AMPT (A Multi-Phase Transport) model. The scaling behaviour of the normalized factorial moments ($F_\text{q}$) give signific…

Normalized solutions for fractional Choquard equation with critical growth on bounded domain
Divya Goel, Asmita Rai
https://arxiv.org/abs/2509.07618 https://

Normalized solutions for fractional Choquard equation with critical growth on bounded domain
In this work, we establish the multiplicity of positive solutions for the following critical fractional Choquard equation with a perturbation on the star-shaped bounded domain $$ \left\{ \begin{array}{lr} (-Δ)^s u = λu +α|u|^{p-2}u+ \left( \int\limits_Ω \frac{|u(y)|^{2^{*}_{μ,s}}}{|x-y|^ μ}\, dy\right) |u|^{2^{*}_{μ,s}-2}u\; \text{in} \; Ω,\\ u>0\; \text{in}\; Ω,\; \\ u = 0\; \text{in} \; \mathbb{R}^{N}\backslashΩ, \\ \int_Ω|u|^2 dx…

FASTColor -- Full-color Amplitude Surrogate Toolkit for QCD
Javier Mari\~no Villadamigo, Rikkert Frederix, Tilman Plehn, Timea Vitos, Ramon Winterhalder
https://arxiv.org/abs/2509.07068

FASTColor -- Full-color Amplitude Surrogate Toolkit for QCD
High-multiplicity events remain a bottleneck for LHC simulations due to their computational cost. We present a ML-surrogate approach to accelerate matrix element reweighting from leading-color (LC) to full-color (FC) accuracy, building on recent advancements in LC event generation. Comparing a variety of modern network architectures for representative QCD processes, we achieve speed-up of around a factor two over the current LC-to-FC baseline. We also show how transformers learn and exploit und…