Tootfinder

from my link log —
Practical seed recovery for the PCG pseudo-random number generator.
https://tosc.iacr.org/index.php/ToSC/article/view/8700
saved 2025-10-15

OCTOPUS: A Versatile, User-Friendly, and Extensible Public Code for General-Relativistic Ray-Tracing in Spherically Symmetric and Static Spacetimes
Shiyang Hu, Shijie Tan, Dan Li, Lina Zhang, Chen Deng, Wenfu Cao
https://arxiv.org/abs/2510.12585

OCTOPUS: A Versatile, User-Friendly, and Extensible Public Code for General-Relativistic Ray-Tracing in Spherically Symmetric and Static Spacetimes
This paper presents OCTOPUS, a relativistic ray-tracing algorithm developed within a Fortran-based, OpenMP-accelerated framework, designed for asymptotically flat, spherically symmetric curved spacetimes. The code efficiently and accurately computes key relativistic features -- including the black hole event horizon, photon rings, critical curves, and innermost stable circular orbits -- and simulates black hole shadows, redshift factor distributions, accretion disk images, toroidal images, as w…

Optimal $L^2$ error estimation for the unfitted interface finite element method based on the non-symmetric Nitsche's methods
Gang Chen, Chaoran Liu, Yangwen Zhang
https://arxiv.org/abs/2510.12151

Optimal $L^2$ error estimation for the unfitted interface finite element method based on the non-symmetric Nitsche's methods
This paper establishes optimal error estimates in the $L^2$ for the non-symmetric Nitsche method in an unfitted interface finite element setting. Extending our earlier work, we give a complete analysis for the Poisson interface model and, by formulating a tailored dual problem that restores adjoint consistency, derive the desired bounds.

A Symmetric-Key Cryptosystem Based on the Burnside Ring of a Compact Lie Group
Ziad Ghanem
https://arxiv.org/abs/2510.10901 https://arxiv.org/pdf/2510.1090…

A Symmetric-Key Cryptosystem Based on the Burnside Ring of a Compact Lie Group
Classical linear ciphers, such as the Hill cipher, operate on fixed, finite-dimensional modules and are therefore vulnerable to straightforward known-plaintext attacks that recover the key as a fully determined linear operator. We propose a symmetric-key cryptosystem whose linear action takes place instead in the Burnside ring $A(G)$ of a compact Lie group $G$, with emphasis on the case $G=O(2)$. The secret key consists of (i) a compact Lie group $G$; (ii) a secret total ordering of the subgrou…

A family of three maximally symmetric boost-invariant flows in relativistic hydrodynamics
Sa\v{s}o Grozdanov
https://arxiv.org/abs/2510.10769 https://arxiv…

A family of three maximally symmetric boost-invariant flows in relativistic hydrodynamics
I discuss the constructions of boost-invariant dissipative conformal hydrodynamic flows by elaborating on the geometric procedure by Gubser and Yarom, which starts from a static, maximally symmetric flow on dS$_3\times\mathbb{R}$. Three foliations of dS$_3$ preserve three-dimensional non-Abelian isometry groups, namely, the flat ISO(2)-invariant, the spherical (closed) SO(3)-invariant, and the hyperbolic (open) SO(2,1)-invariant slicings. I show that the fluids that preserve these symmetries, a…

Transition Matrices between Plethystic Bases of Polysymmetric Functions via Bijective Methods
Aditya Khanna
https://arxiv.org/abs/2510.12723 https://arxiv.…

Transition Matrices between Plethystic Bases of Polysymmetric Functions via Bijective Methods
Many identities involving symmetric functions can be proved through bijective manipulations of tableaux. In this paper, we prove identities involving polysymmetric functions through bijections and sign-reversing involutions. In their paper titled "Polysymmetric functions and motivic measures of configuration spaces", Asvin G and Andrew O'Desky introduced the algebra of polysymmetric functions (PSym) which can be defined as the tensor product of copies of the symmetric functions algebra (Sym) wh…

Quantum variance for cubic moment of Hecke--Maass cusp forms and Eisenstein series
Bingrong Huang, Liangxun Li
https://arxiv.org/abs/2510.12322 https://arx…

Quantum variance for cubic moment of Hecke--Maass cusp forms and Eisenstein series
In this paper, we give the upper bounds on the variance for cubic moment of Hecke--Maass cusp forms and Eisenstein series respectively. For the cusp form case, the bound comes from a large sieve inequality for symmetric cubes. We also give some nontrivial bounds for higher moments of symmetric cube $L$-functions. For the Eisenstein series case, the upper bound comes from Lindelöf-on-average type bounds for various $L$-functions. In particular, we establish the sharp upper bounds for the fourth…

Mirror symmetric polynomials orthogonal on the unit circle
Alexei Zhedanov
https://arxiv.org/abs/2510.10447 https://arxiv.org/pdf/2510.10447

Mirror symmetric polynomials orthogonal on the unit circle
We introduce and study a special family of polynomials orthogonal on the unit circle (OPUC). These OPUC satisfy a mirror symmetry property of their Verblunsky coefficients. Several equivalent conditions for the OPUC to be mirror symmetric are presented. Corresponding unitary CMV matrices satisfy simple algebraic relations similar to relations for persymmetric tridiagonal matrices. We present three explicit examples of mirror symmetric OPUC.

GKLO representations of twisted Yangians in type $\mathsf{AI}$ and quantizations of symmetric quotients of the affine Grassmannian
Robin Bartlett, Tomasz Przezdziecki, Lukas Tappeiner
https://arxiv.org/abs/2510.12706

GKLO representations of twisted Yangians in type $\mathsf{AI}$ and quantizations of symmetric quotients of the affine Grassmannian
We construct an analogue of Gerasimov-Kharchev-Lebedev-Oblezin (GKLO) representations for twisted Yangians of type $\mathsf{AI}$, using the recently found current presentation of these algebras due to Lu, Wang and Zhang. These new representations allow us to define interesting truncations of twisted Yangians, which, in the spirit of Ciccoli-Drinfeld-Gavarini quantum duality, reflect the Poisson geometry of homogeneous spaces. As our main result, we prove that a truncated twisted Yangian quantiz…

Symmetric Persistent Tensors and their Hessian
Masoud Gharahi, Giorgio Ottaviani
https://arxiv.org/abs/2510.07404 https://arxiv.org/pdf/2510.07404

Symmetric Persistent Tensors and their Hessian
Persistent tensors, introduced in [Quantum 8 (2024), 1238], and inspired by quantum information theory, form a recursively defined class of tensors that remain stable under the substitution method and thereby yield nontrivial lower bounds on tensor rank. In this work, we investigate the symmetric case-namely, symmetric persistent tensors, or equivalently, persistent polynomials. We establish that a symmetric tensor in $\mathrm{Sym}^n \mathbb{C}^d$ is persistent if the determinant of its Hessian…

The Levi-Civita products of Leibniz algebras with nondegenerate skew-symmetric 2-cocycles
Quan Zhao, Guilai Liu
https://arxiv.org/abs/2510.10949 https://ar…

The Levi-Civita products of Leibniz algebras with nondegenerate skew-symmetric 2-cocycles
This paper studies the associated Levi-Civita products of a Leibniz algebra with a nondegenerate skew-symmetric $2$-cocycle. Such products form into the notion of an anti-pre-Leibniz algebra, which is characterized as a Leibniz-admissible algebra which renders a representation of the sub-adjacent Leibniz algebra through the negative multiplication operators. Such a characterization serves as the converse side of the role that pre-Liebniz algebras play in the splitting theory of Leibniz algebras…

A Cascade of Systems and the Product of Their $\theta$-Symmetric Scaled Relative Graphs
Xiaokan Yang, Ding Zhang, Wei Chen, Li Qiu
https://arxiv.org/abs/2510.06583 https://

A Cascade of Systems and the Product of Their $θ$-Symmetric Scaled Relative Graphs
In this paper, we utilize a variant of the scaled relative graph (SRG), referred to as the $θ$-symmetric SRG, to develop a graphical stability criterion for the feedback interconnection of a cascade of systems. A crucial submultiplicative property of $θ$-symmetric SRG is established, enabling it to handle cyclic interconnections for which conventional graph separation methods are not applicable. By integrating both gain and refined phase information, the $θ$-symmetric SRG provides a unified …

Inhomogeneous branching trees with symmetric and asymmetric offspring and their genealogies
Frederik M. Andersen, Marc A. Suchard, Carsten Wiuf, Samir Bhatt
https://arxiv.org/abs/2510.07921

Inhomogeneous branching trees with symmetric and asymmetric offspring and their genealogies
We define symmetric and asymmetric branching trees, a class of processes particularly suited for modeling genealogies of inhomogeneous populations where individuals may reproduce throughout life. In this framework, a broad class of Crump-Mode-Jagers processes can be constructed as (a)symmetric Sevast'yanov processes, which count the branches of the tree. Analogous definitions yield reduced (a)symmetric Sevast'yanov processes, which restrict attention to branches that lead to extant progeny. We …

Symmetric Lorentzian Polynomials
Tracy Chin, Daniel Qin
https://arxiv.org/abs/2510.07819 https://arxiv.org/pdf/2510.07819

Symmetric Lorentzian Polynomials
We study the class of Lorentzian symmetric polynomials and Lorentzian symmetric functions, which are defined to be symmetric functions for which every truncation of variables is Lorentzian. Similar to the space of Lorentzian polynomials, we show that the space of Lorentzian symmetric polynomials is homeomorphic to a closed Euclidean ball. Our main result is a reduction scheme that significantly reduces the complexity of testing for Lorentzianity. Using this method, we provide explicit semialgeb…

Universal properties of Delannoy categories
Kevin Coulembier, Nate Harman, Andrew Snowden
https://arxiv.org/abs/2510.10317 https://arxiv.org/pdf/2510.10317…

Universal properties of Delannoy categories
Recently, the second and third authors introduced a new symmetric tensor category $\underline{\mathrm{Perm}}(G, μ)$ associated to an oligomorphic group $G$ with a measure $μ$. When $G$ is the group of order preserving self-bijections of the real line there are four such measures, and the resulting tensor categories are called the Delannoy categories. The first Delannoy category is semi-simple, and was studied in detail by Harman, Snowden, and Snyder. We give universal properties for all four …

A minimal and universal representation of fermionic wavefunctions (fermions = bosons one)
Liang Fu
https://arxiv.org/abs/2510.11431 https://arxiv.org/pdf…

A minimal and universal representation of fermionic wavefunctions (fermions = bosons + one)
Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science. In this work, we introduce a universal and exact representation of continuous antisymmetric functions by lifting them to continuous symmetric functions defined on an enlarged space. Building on this lifting, we obtain a \emph{parity-graded representation} of fermionic wavefunctions, expressed in terms of symmetric feature variables that encode particle configuration and ant…

Quantumness and its hierarchies in PT-symmetric down-conversion models
Jan Pe\v{r}ina Jr., Karol Bartkiewicz, Grzegorz Chimczak, Anna Kowalewska-Kudlaszyk, Adam Miranowicz, Joanna K. Kalaga, Wies{\l}aw Leonski
https://arxiv.org/abs/2510.06171

Quantumness and its hierarchies in PT-symmetric down-conversion models
We investigate the hierarchy of quantum correlations in a quadratic bosonic parity-time-symmetric system (PTSS) featuring distinct dissipation and amplification channels. The hierarchy includes global nonclassicality, entanglement, asymmetric quantum steering, and Bell nonlocality. We elucidate the interplay between the system physical nonlinearity -- which serves as a source of quantumness -- and the specific dynamics of bosonic PTSSs, which are qualitatively influenced by their damping and am…

Theoretical filters for shift-symmetric Horndeski gravities
Athanasios Bakopoulos, Christos Charmousis, Nikos Chatzifotis, Theodoros Nakas
https://arxiv.org/abs/2510.09547 https…

Theoretical filters for shift-symmetric Horndeski gravities
We investigate the structure of nontrivial maximally symmetric vacua and compact-object solutions in shift-symmetric scalar-tensor theories. Focusing on Horndeski gravity, we derive consistency conditions directly from the field equations to identify the subclasses that admit Minkowski and de Sitter vacua with a nontrivial scalar field. In doing so, we obtain a filtering mechanism that operates independently of observational data. In this context, we introduce the notion of stealth vacua, where…

A semi-symmetric metric connection, perfect fluid space-time and phantom barrier
Miroslav Maksimovi\'c, Milan Zlatanovi\'c, Marija Najdanovi\'c
https://arxiv.org/abs/2510.00849

A semi-symmetric metric connection, perfect fluid space-time and phantom barrier
We consider a concircularly semi-symmetric metric connection and its application. The Ricci tensors with respect to the concircularly semi-symmetric metric connection are symmetric, and they are used to define Einstein type manifolds. In this way, conditions under which a pseudo-Riemannian manifold is quasi-Einstein are obtained. On a Lorentzian manifold, a concircularly semi-symmetric metric connection with a unit timelike generator becomes a semi-symmetric metric $P$-connection, and a Lorentz…

An elementary derivation of 3-cycles for a quadratic map
Arpad Benyi, Ioan Casu
https://arxiv.org/abs/2510.12558 https://arxiv.org/pdf/2510.12558

An elementary derivation of 3-cycles for a quadratic map
We present an elementary derivation of the period-three cycles for the real quadratic map $x\mapsto x^2+c$, a fundamental model in one-dimensional discrete dynamics. Using symmetric polynomials, we obtain a complete algebraic characterization of 3-cycles and determine explicit conditions for their existence and stability, without reliance on computer algebra. Through conjugacy with the logistic map, we recover the classical threshold values of the logistic parameter corresponding to the emergen…

Symmetric Rule-Based Achlioptas Processes for Random $k$-SAT
Arnab Chatterjee
https://arxiv.org/abs/2510.07870 https://arxiv.org/pdf/2510.07870

Symmetric Rule-Based Achlioptas Processes for Random $k$-SAT
Inspired by the "power-of-two-choices" model from random graphs, we investigate the possibility of limited choices of online clause choices that could shift the satisfiability threshold in random $k$-SAT.Here, we introduce an assignment symmetric, non-adaptive, topology-oblivious online rule called \emph{MIDDLE-HEAVY}, that prioritizes balanced sign profile clauses.Upon applying a biased $2$-SAT projection and a two-type branching process certificate, we derive closed-form expressions for the s…

An extended and extremely thin gravitational arc from a lensed compact symmetric object at redshift 2.059
J. P. McKean, C. Spingola, D. M. Powell, S. Vegetti
https://arxiv.org/abs/2510.07386

An extended and extremely thin gravitational arc from a lensed compact symmetric object at redshift 2.059
Compact symmetric objects (CSOs) are thought to be short-lived radio sources with two lobes of emission that are separated by less than a kpc in projection. However, studies of such systems at high redshift is challenging due to the limited resolution of present-day telescopes, and can be biased to the most luminous objects. Here we report imaging of a gravitationally lensed CSO at a redshift of 2.059 using very long baseline interferometry at 1.7 GHz. The data are imaged using Bayesian forward…

Reconstruction of tensor categories of type $G_2$
Lilit Martirosyan, Hans Wenzl
https://arxiv.org/abs/2510.09922 https://arxiv.org/pdf/2510.09922

Reconstruction of tensor categories of type $G_2$
We prove that any non-symmetric ribbon tensor category $\mathcal{C}$ with the fusion rules of the compact group of type $G_2$ needs to be equivalent to the representation category of the corresponding Drinfeld-Jimbo quantum group for $q$ not a root of unity. We also prove an analogous result for the corresponding finite fusion tensor categories.

Dirac neutrino and dark matter in left-right symmetric models
Shohei Okawa, Yuji Omura, Keyun Wu
https://arxiv.org/abs/2510.04549 https://arxiv.org/pdf/251…

Dirac neutrino and dark matter in left-right symmetric models
We study neutrino mass generation and dark matter in a left-right symmetric model. The model is based on an $SU(3)_c\times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ gauge theory with a softly broken parity symmetry. Masses of the charged leptons and neutrinos are generated radiatively at one-loop and three-loop level respectively, through their interactions with newly introduced neutral fermion and scalar particles. A mass hierarchy of those new particles is required to reproduce the observed p…

Fair Assignment of Indivisible Chores to Asymmetric Agents
Masoud Seddighin, Saeed Seddighin
https://arxiv.org/abs/2510.10698 https://arxiv.org/pdf/2510.10…

Fair Assignment of Indivisible Chores to Asymmetric Agents
We consider the problem of assigning indivisible chores to agents with different entitlements in the maximin share value (\MMS) context. While constant-\MMS\ allocations/assignments are guaranteed to exist for both goods and chores in the symmetric setting, the situation becomes much more complex when agents have different entitlements. For the allocation of indivisible goods, it has been proven that an $n$-\WMMS\ (weighted \MMS) guarantee is the best one can hope for. For indivisible chores, h…

Symmetric Division of Linear Ordinary Differential Operators
Lixin Du, Manuel Kauers
https://arxiv.org/abs/2510.01436 https://arxiv.org/pdf/2510.01436

Symmetric Division of Linear Ordinary Differential Operators
The symmetric product of two ordinary linear differential operators $L_1,L_2$ is an operator whose solution set contains the product $f_1f_2$ of any solution $f_1$ of $L_1$ and any solution $f_2$ of~$L_2$. It is well known how to compute the symmetric product of two given operators $L_1,L_2$. In this paper we consider the corresponding division problem: given a symmetric product $L$ and one of its factors, what can we say about the other factors?

Ukraine to turn tables in "first symmetric winter" as its drones overwhelm Russian air defenses - Euromaidan Press
https://euromaidanpress.com/2025/11/25/ukraine-to-turn-tables-in-first-symmetric-winter-as-its-drones-overwhelm-russian-air-defenses/

A million-solar-mass object detected at a cosmological distance using #GravitationalImaging / An extended and extremely thin gravitational arc from a lensed compact symmetric object at redshift of 2.059: https://www.nature.com/articles/s41550-025-02651-2 / https://academic.oup.com/mnrasl/article/544/1/L24/8262431?login=false -> Astronomers ‘image’ a mysterious dark object in the distant Universe: https://jive.eu/news/new-nature-astronomy-and-mnras-letters-astronomers-image-mysterious-dark-object-distant

Form uniqueness for graphs with weakly spherically symmetric ends
Luis Hernandez, Sean Ku, Jun Masamune, Genevieve Romanelli, Rados{\l}aw K. Wojciechowski
https://arxiv.org/abs/2509.22967

Form uniqueness for graphs with weakly spherically symmetric ends
We give characterizations for the failure of form uniqueness on weakly spherically symmetric graphs. The first characterization is in terms of the graph structure, the second involves the capacity of a Cauchy boundary. We also discuss the stability of form uniqueness and give characterizations for graphs which, following the removal of a set, consist of a disjoint union of weakly spherically symmetric graphs.

TWIN: Two window inspection for online change point detection
Patrick Bastian, Tim Kutta
https://arxiv.org/abs/2510.11348 https://arxiv.org/pdf/2510.11348

TWIN: Two window inspection for online change point detection
We propose a new class of sequential change point tests, both for changes in the mean parameter and in the overall distribution function. The methodology builds on a two-window inspection scheme (TWIN), which aggregates data into symmetric samples and applies strong weighting to enhance statistical performance. The detector yields logarithmic rather than polynomial detection delays, representing a substantial reduction compared to state-of-the-art alternatives. Delays remain short, even for lat…

Symmetric monoidal extensions and graph cobordisms between finite sets
Andrea Bianchi
https://arxiv.org/abs/2509.22575 https://arxiv.org/pdf/2509.22575

Symmetric monoidal extensions and graph cobordisms between finite sets
Given a symmetric monoidal $(\infty,n)$-category $\mathcal{C}$ and a space $X$, we address the problem of explicitly describing the symmetric monoidal $(\infty,n)$-category freely obtained from $\mathcal{C}$ by adjoining $X$ new $n$-morphisms with prescribed sources and targets. We develop an apparatus of tools that allow one to detect in concrete situations such a free symmetric monoidal extension. As motivating application, we introduce a symmetric monoidal $(\infty,2)$-category ${\mathbb{G}\…

$\omega$-Lie bialgebras and $\omega$-Yang-Baxter equation
Yining Sun, Zeyu Hao, Ziyi Zhang, Liangyun Chen
https://arxiv.org/abs/2510.09630 https://arxiv.or…

$ω$-Lie bialgebras and $ω$-Yang-Baxter equation
In this paper, we introduce the definition of multiplicative $ω$-Lie bialgebra, which is equivalent to the Manin triples and matched pairs. We also study the $ω$-Yang-Baxter equation and Yang-Baxter $ω$-Lie bialgebra. The skew-symmetric solutions of the $ω$-Yang-Baxter equation can be used to construct Yang-Baxter $ω$-Lie bialgebra. We further introduce the concept of the $ω$-$\mathcal{O}$-operator, which can be constructed from a left-symmetric algebras, and based on the $ω$-$\mathcal{O…

dHPR: A Distributed Halpern Peaceman--Rachford Method for Non-smooth Distributed Optimization Problems
Zhangcheng Feng, Defeng Sun, Yancheng Yuan, Guojun Zhang
https://arxiv.org/abs/2511.10069 https://arxiv.org/pdf/2511.10069 https://arxiv.org/html/2511.10069
arXiv:2511.10069v1 Announce Type: new
Abstract: This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$ iteration complexity regarding Karush--Kuhn--Tucker residual. By leveraging the symmetric Gauss--Seidel decomposition, the dHPR effectively decouples the linear operators in the objective functions and consensus constraints while maintaining parallelizability and avoiding additional large proximal terms, leading to a decentralized implementation with provably fast convergence. The superior performance of dHPR is demonstrated through comprehensive numerical experiments on distributed LASSO, group LASSO, and $L_1$-regularized logistic regression problems.
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High-order, Compact, and Symmetric Finite Difference Methods for a $d$-Dimensional Hypercube
Qiwei Feng, Bin Han, Michelle Michelle, Jiwoon Sim
https://arxiv.org/abs/2510.03927 …

High-order, Compact, and Symmetric Finite Difference Methods for a $d$-Dimensional Hypercube
This paper presents compact, symmetric, and high-order finite difference methods (FDMs) for the variable Poisson equation on a $d$-dimensional hypercube. Our scheme produces a symmetric linear system: an important property that does not immediately hold for a high-order FDM. Since the model problem is coercive, the linear system is in fact symmetric positive definite, and consequently many fast solvers are applicable. Furthermore, the symmetry combined with the minimum support of the stencil ke…

The $\mathbb{A}^1$-Euler characteristic of symmetric powers
Louisa F. Br\"oring, Jesse Pajwani, Anna M. Viergever
https://arxiv.org/abs/2510.06922 https://

The $\mathbb{A}^1$-Euler characteristic of symmetric powers
The $\mathbb{A}^1$-Euler characteristic is a refinement in algebraic geometry of the classical topological Euler characteristic, which can be constructed using motivic homotopy theory. This invariant is a quadratic form rather than an integer, which carries a lot of information, but is difficult to compute in practice. In this survey, we discuss a conjectural way for computing the $\mathbb{A}^1$-Euler characteristic of the symmetric powers of a variety in terms of the $\mathbb{A}^1$-Euler chara…

An investigation into the combined effect of steady and pulsatile flow within a wavy channel filled with an anisotropic porous medium
Sanchita Pramanik, Timir Karmakar
https://arxiv.org/abs/2510.08729 …

An investigation into the combined effect of steady and pulsatile flow within a wavy channel filled with an anisotropic porous medium
We provide an analytical solution to examine the impact of steady and pulsatile flow in a symmetric wavy channel filled with an anisotropic porous medium. The flow inside the wavy channel with a porous substrate is governed by the Darcy-Brinkman equation. We used the perturbation approach to ascertain the solution to the problem, assuming that the ratio between the channel width and the wavelength is very small (i.e., $δ^2 \ll 1$). We solved the problem up to $O(δ^2)$ by assuming $λ^2 δ^2 \…

Grand-Canonical Symmetric Orbifold Theories
Lior Benizri
https://arxiv.org/abs/2510.03132 https://arxiv.org/pdf/2510.03132…

Grand-Canonical Symmetric Orbifold Theories
In this letter, we study grand-canonical symmetric orbifolds of conformal field theories on the sphere. We show that a consistent operator product expansion can be defined, provided the Hilbert space is taken to be the direct sum of symmetric orbifolds of all degrees. This Hilbert space contains a tower of central operators of conformal dimension zero, one of which represents the central charge of the Virasoro algebra. Our construction thus provides a conformal field theory interpretation of th…

Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
Sami Raatikainen, Syksy Rasanen, Eemeli Tomberg
https://arxiv.org/abs/2510.09303

Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
We study stochastic effects in viable ultra-slow-roll inflation models that produce primordial black holes. We consider asteroid, solar, and supermassive black hole seed masses. In each case, we simulate $10^8$ patches of the universe that may collapse into PBHs. In every patch, we follow $4\times10^4$ momentum shells to construct its spherically symmetric profile from first principles, without introducing a window function. We include the effects of critical collapse and the radiation era tran…

Cutting along a symmetric quadrilateral to construct an embedded flexible dodecahedron
Elvar Atlason
https://arxiv.org/abs/2510.06897 https://arxiv.org/pdf…

Cutting along a symmetric quadrilateral to construct an embedded flexible dodecahedron
Until recently, the simplest known flexible polyhedron was Steffen's polyhedron on nine vertices. However, in 2024, an embedded flexible polyhedron on eight vertices was announced. It attains the known lower bound for the number of vertices, showing that the simplest embedded flexible polyhedron has eight vertices. We introduce a method for making new flexible polyhedral surfaces from old ones. This general method applies to the above minimal example, giving another proof of its flexibility. We…

Combinatorial equivalence of separable elements in types $A$ and $B$
Yong Liao, Yuping Yang, Houyi Yu
https://arxiv.org/abs/2510.12046 https://arxiv.org/pd…

Combinatorial equivalence of separable elements in types $A$ and $B$
We study the combinatorial equivalence of separable elements in types $A$ and $B$. A bijection is constructed from the set of separable permutations in the symmetric group $S_{n+1}$ to the set of separable signed permutations in the hyperoctahedral group $B_n$. This bijection preserves descent statistics and induces a poset isomorphism under the left weak order. As a consequence, separable signed permutations are enumerated by the large Schröder numbers, and their descent polynomials are shown…

Simultaneously Determining Regional Heterogeneity and Connection Directionality from Neural Activity and Symmetric Connection
Jiawen Chang, Zhuda Yang, Changsong Zhou
https://arxiv.org/abs/2510.04110

Simultaneously Determining Regional Heterogeneity and Connection Directionality from Neural Activity and Symmetric Connection
The spatiotemporal patterns of neural dynamics are jointly shaped by directed structural interactions and heterogeneous intrinsic features of the neural components. Despite well-developed methods for estimating directionality in network connections from network of homogeneous nodes, how local heterogeneity impacts on directionality estimation remains poorly understood. In particular, the role of excitatory-inhibitory interactions in shaping network directionality and how these interactions shou…

Irreducible restrictions of spin representations of symmetric and alternating groups
Alexander Kleshchev, Lucia Morotti, Pham Huu Tiep
https://arxiv.org/abs/2510.08223 https://

Irreducible restrictions of spin representations of symmetric and alternating groups
Let $\mathbb{F}$ be an algebraically closed field and $G$ be an almost quasi-simple group. An important problem in representation theory is to classify the subgroups $H

Commutators of n-cycles in the symmetric group
Philipp Bader
https://arxiv.org/abs/2509.22749 https://arxiv.org/pdf/2509.22749

Commutators of n-cycles in the symmetric group
We show that for $n \ge 6$ every even permutation on $n$ symbols is the commutator of two $n$-cycles. More precisely, let $S_n$ be the symmetric group and $A_n$ the alternating group. Let $C(n) \subset S_n$ denote the conjugacy class of $n$-cycles and $[\cdot, \cdot]$ be the commutator of two permutations. We prove: The map $C(n) \times C(n) \to A_n, \ (τ, π) \mapsto [τ, π]$ is surjective for all $n \ge 6$.

$p$-retract Rationality and Norm One Tori
Kazuki Sato
https://arxiv.org/abs/2510.10027 https://arxiv.org/pdf/2510.10027

$p$-retract Rationality and Norm One Tori
We study whether the norm one torus associated with a finite separable non-Galois field extension $K/k$ is $p$-retract rational over $k$ for a prime $p$, focusing on the case where the Galois group of the Galois closure of $K/k$ is either the symmetric or the alternating group.

Symmetric L\'evy flights in semi-infinite domain
Barnali Pyne, Kiran M. Kolwankar
https://arxiv.org/abs/2509.23282 https://arxiv.org/pdf/2509.23282

Symmetric Lévy flights in semi-infinite domain
We study symmetric Lévy flights in a semi-infinite domain $[0,\infty)$ with a reflecting and absorbing boundary at 0. To this end, we use the fractional differential equation that governs the Lévy process. Incorporating the boundary conditions in Lévy flights has been an open and tricky question, as the long jumps can lead to the Lévy flights leaping over the boundary. We, for the first time, incorporate reflecting and absorbing boundary conditions for Lévy flights and solve the fractional…

${\mathrm G}_2$-structures with parallel skew-symmetric torsion
Andrei Moroianu, Uwe Semmelmann
https://arxiv.org/abs/2510.02899 https://arxiv.org/pdf/2510…

${\mathrm G}_2$-structures with parallel skew-symmetric torsion
We classify $7$-dimensional Riemannian manifolds carrying a metric connection with parallel skew-symmetric torsion whose holonomy is contained in $\mathrm{G}_2$, up to naturally reductive homogeneous spaces and nearly parallel $\mathrm{G}_2$-structures. This extends and completes the classification initiated by Th. Friedrich in the cocalibrated case. Incidentally, we also obtain the list of $\mathrm{SU}(3)$ geometries with parallel skew-symmetric torsion, up to naturally reductive homogeneous s…

confession: for several years i had assumed, unquestioningly, that "SMP Minecraft" is for "symmetric multiplayer"

Reversible computations are computations
Cl\'ement Aubert, Jean Krivine
https://arxiv.org/abs/2510.06585 https://arxiv.org/pdf/2510.06585

Reversible computations are computations
Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this simple requirement is equally relevant when the occurrence of an event is invertible. We propose a conservative extension of causal models for concurrency that accommodates reversible computations. We first model reversible computations using a symmetric res…

Post-Quantum Security of Block Cipher Constructions
Gorjan Alagic, Chen Bai, Christian Majenz, Kaiyan Shi
https://arxiv.org/abs/2510.08725 https://arxiv.or…

Post-Quantum Security of Block Cipher Constructions
Block ciphers are versatile cryptographic ingredients that are used in a wide range of applications ranging from secure Internet communications to disk encryption. While post-quantum security of public-key cryptography has received significant attention, the case of symmetric-key cryptography (and block ciphers in particular) remains a largely unexplored topic. In this work, we set the foundations for a theory of post-quantum security for block ciphers and associated constructions. Leveraging o…

Spectral properties of a Non-Hermitian extension of the diluted Wishart ensemble
Isaac P\'erez Castillo, Edgar Guzm\'an-Gonz\'alez
https://arxiv.org/abs/2510.10758 h…

Spectral properties of a Non-Hermitian extension of the diluted Wishart ensemble
We develop a theoretical framework based on the cavity and replica methods to analyze the spectral properties of sparse asymmetric correlation matrices of the form $\boldsymbol{F} = (\boldsymbol{X}\boldsymbol{Y}^\top + ω\boldsymbol{Y}\boldsymbol{X}^\top)/2T$, where $\boldsymbol{X}$ and $\boldsymbol{Y}$ are adjacency matrices of weighted Erdős--Rényi random graphs. We examine how the spectral density evolves as the asymmetry parameter $ω$ varies from $0 < ω< 1$ (nearly symmetric matrices) t…

Fixed Points and Stochastic Meritocracies: A Long-Term Perspective
Gaurab Pokharel, Diptangshu Sen, Sanmay Das, Juba Ziani
https://arxiv.org/abs/2510.07478 https://

Fixed Points and Stochastic Meritocracies: A Long-Term Perspective
We study group fairness in the context of feedback loops induced by meritocratic selection into programs that themselves confer additional advantage, like college admissions. We introduce a novel stylized inter-generational model for the setting and analyze it in situations where there are no underlying differences between two populations. We show that, when the benefit of the program (or the harm of not getting into it) is completely symmetric, disparities between the two populations will even…

Optimal monophasic, asymmetric electric field pulses for selective transcranial magnetic stimulation (TMS) with minimised power and coil heating
Ke Ma, Andrey Vlasov, Zeynep B. Simsek, Jinshui Zhang, Yiru Li, Boshuo Wang, David L. K. Murphy, Jessica Y. Choi, Maya E. Clinton, Noreen Bukhari-Parlakturk, Angel V. Peterchev, Stephan M. Goetz
https://

Optimal monophasic, asymmetric electric field pulses for selective transcranial magnetic stimulation (TMS) with minimised power and coil heating
Transcranial magnetic stimulation (TMS) with asymmetric electric field pulses, such as monophasic, offers directional selectivity for neural activation but requires excessive energy. Previous pulse shape optimisation has been limited to symmetric pulses or heavily constrained variations of conventional waveforms without achieving general optimality in energy efficiency or neural selectivity. We implemented an optimisation framework that incorporates neuron model activation constraints and flexi…

Exploring the Origin of Anisotropy in Small Systems: From Symmetric (O O) to Asymmetric (d Au) Collisions
Zhengxi Yan (for the STAR Collaboration)
https://arxiv.org/abs/2510.03454

Exploring the Origin of Anisotropy in Small Systems: From Symmetric (O+O) to Asymmetric (d+Au) Collisions
This contribution reports STAR measurements of azimuthal anisotropies in produced particle distributions of the d+Au and $^{16}$O+$^{16}$O collisions at $\sqrt{s_{NN}} = 200$ GeV, probing the origin of collectivity in small systems. We test the hydrodynamic response of the produced medium by comparing these systems with vastly different initial geometries. The measured elliptic ($v_2$) and triangular ($v_3$) anisotropies, and their event-by-event fluctuations, scale robustly with initial-state …

Automatic Model Extraction of the Match Standard in Symmetric--Reciprocal--Match Calibration
Ziad Hatab, Michael Ernst Gadringer, Arash Arsanjani, Wolfgang Boesch
https://arxiv.org/abs/2509.18426

Replaced article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- LS-category and sequential topological complexity of symmetric products
Ekansh Jauhari

The Theory of Topo-Symmetric Extensions of Topological Groups
Es-said En-naoui
https://arxiv.org/abs/2510.00018 https://arxiv.org/pdf/2510.00018

The Theory of Topo-Symmetric Extensions of Topological Groups
We introduce the notion of \emph{topo-symmetric extensions} of topological groups, a new generalization of classical group extensions that incorporates both topological and symmetry constraints. We define morphisms between such extensions, construct the associated groupoid, and develop classification results in terms of adapted cohomology. Several new invariants are introduced, including dimension, stabilizer, and density invariants, which characterize the fine structure of these extensions. Ap…

Counterdiabatic driving at Rydberg excitation for symmetric $C_Z$ gates with ultracold neutral atoms
I. I. Beterov, K. V. Kozenko, P. Xu, I. I. Ryabtsev
https://arxiv.org/abs/2510.04766

Counterdiabatic driving at Rydberg excitation for symmetric $C_Z$ gates with ultracold neutral atoms
We extend the scheme of neutral atom Rydberg $C_Z$ gate based on double sequence of adiabatic pulses applied symmetrically to both atoms using counterdiabatic driving in the regime of Rydberg blockade. This provides substantial reducing of quantum gate operation times (at least five times) compared to previously proposed adiabatic schemes, which is important for high-fidelity entanglement due to finite Rydberg lifetimes. We analyzed schemes of adiabatic rapid passage with counterdiabatic drivin…

Cocycle weighted infinitesimal bialgebras and pre-Lie algebras on rooted trees
Lo\"ic Foissy (LMPA), Yunzhou Xie (NJUST), Dawei Zhang (NJUST), Yi Zhang (NJUST)
https://arxiv.org/abs/2510.12239

Cocycle weighted infinitesimal bialgebras and pre-Lie algebras on rooted trees
The concept of weighted infinitesimal bialgebras provides an algebraic framework for understanding the non-homogeneous associative Yang-Baxter equation. In this paper, we endow the space of decorated planar rooted forests with a two-parameters family of coproducts, making it into a weighted infinitesimal bialgebra. A combinatorial characterization of the coproducts is given via the notion of forest biideals. Furthermore, by constructing a bilinear symmetric form and introducing a new grafting o…

On the monodromy conjecture for determinantal varieties
Yifan Chen, Huaiqing Zuo
https://arxiv.org/abs/2510.11425 https://arxiv.org/pdf/2510.11425

On the monodromy conjecture for determinantal varieties
This paper presents a proof of the monodromy conjecture for determinantal varieties. Our strategy centers on an in-depth analysis of monodromy zeta functions, leveraging a generalized A'Campo formula, an examination of multiple contact loci, and the exploitation of the intrinsic symmetric structures inherent to these varieties. Keywords. monodromy conjecture, determinantal varieties, monodromy zeta function.

Spinon Mediation of Witness-Spin Dynamics and Ground State in Herbertsmithite
Hiroto Takahashi, Jack Murphy, Mitikorn Wood-Thanan, Pascal Puphal, Miguel Angel Sanchez-Martinez, Fabian Jerzembeck, Chun-Chih Hsu, Jonathan Ward, Masahiko Isobe, Yosuke Matsumoto, Hidenori Takagi, Stephen J. Blundell, Michael R. Norman, Felix Flicker, J. C. S\'eamus Davis
https:…

Spinon Mediation of Witness-Spin Dynamics and Ground State in Herbertsmithite
The kagome lattice of spin-1/2 Cu atoms in herbertsmithite (ZnCu3(OH)6Cl2) may sustain a quantum spin liquid (QSL) state with spinon quasiparticles. Each kagome plane is separated from its homologues by a layer of spinless Zn atoms. Providentially, however, some spin-1/2 Cu atoms substitute randomly onto these inter-kagome Zn sites. We reconceptualize these 'impurity' atoms as quantum 'witness-spins', an exceptional new interrogative of the conjectured Z2-gauge-symmetric QSL state. Thus we intr…

Cosmological implications of LRS Bianchi type-I cosmological model in $f(T)$ gravity
Shivangi Rathore, S. Surendra Singh
https://arxiv.org/abs/2510.10428 https://

Cosmological implications of LRS Bianchi type-I cosmological model in $f(T)$ gravity
We perform the dynamical system analysis of the Locally Rotationally Symmetric (LRS) Bianchi type-I cosmological model in f(T) gravity in the presence of energy interaction . A cosmologically viable form of $f(T)$ is chosen (where $T$ is the torsion scalar in teleparallelism) in the background of homogenous and anisotropic. For our model, we take $f(T) = T+ζT^{2}$ where $ζ$ is a constant. The evolution equations are reduced to the autonomous system of differential equations by suitable transf…

Instances of models of double-categorical theories
Kevin Carlson, Evan Patterson
https://arxiv.org/abs/2510.08861 https://arxiv.org/pdf/2510.08861

Instances of models of double-categorical theories
We contribute a chapter in common to categorical database theory and to the study of higher morphisms between double categories. The common thread here is the notion of instance, or right module, which we generalize from functors from a plain category into Set to the models of a (cartesian) double theory. This provides a concept of instance for such objects as a category equipped with a monad, or a (symmetric) multicategory, recovering the multifunctors into Set in the latter case. We also show…

Optimal $L^2$ Error Estimates for Non-symmetric Nitsche's Methods
Gang Chen, Chaoran Liu, Yangwen Zhang
https://arxiv.org/abs/2510.05597 https://arxiv.…

Optimal $L^2$ Error Estimates for Non-symmetric Nitsche's Methods
We establish optimal $L^2$-error estimates for the non-symmetric Nitsche method. Existing analyses yield only suboptimal $L^2$ convergence, in contrast to consistently optimal numerical results. We resolve this discrepancy by introducing a specially constructed dual problem that restores adjoint consistency. Our analysis covers both super-penalty and penalty-free variants on quasi-uniform meshes, as well as the practically important case on general shape-regular meshes without quasi-uniformity.…

Almost symmetric submanifolds
Claudio Gorodski, Carlos Olmos
https://arxiv.org/abs/2509.23301 https://arxiv.org/pdf/2509.23301

Almost symmetric submanifolds
We introduce the class of almost symmetric submanifolds of Euclidean space, a close relative of symmetric submanifolds and (contact) sub-Riemannian symmetric spaces, and prove a number of results about their structure and classification. In particular, we show that their cohomogeneity is at most one.

Non-Euclidean Crystallographic Rigidity
Jack Esson, Eleftherios Kastis, Bernd Schulze
https://arxiv.org/abs/2510.08128 https://arxiv.org/pdf/2510.08128

Non-Euclidean Crystallographic Rigidity
This paper establishes combinatorial characterisations of forced-symmetric and forced-periodic rigidity (under a fixed lattice) of bar-joint frameworks in non-Euclidean normed planes. In $\ell_q$-planes for $q\in(1,\infty)\backslash\{2\}$, we prove characterisations for periodic rigidity and finite reflectionally-symmetric rigidity. We also characterise symmetric rigidity in this space with respect to the orientation-reversing wallpaper group $\mathbb{Z}^2\rtimes\mathcal{C}_s$, otherwise known …

Symmetric quantum walks on Hamming graphs and their limit distributions
Robert C. Griffiths, Shuhei Mano
https://arxiv.org/abs/2509.26243 https://arxiv.org…

Symmetric quantum walks on Hamming graphs and their limit distributions
We study a class of symmetric quantum walks on Hamming graphs, where the distance between vertices specifies the transition probability. A special model is the simple quantum walk on the hypercube, which has been discussed in the literature. Eigenvalues of the unitary operator of the quantum walks are zeros of certain self-reciprocal polynomials. We obtain a spectral representation of the wave vector, where our systematic treatment relies on the coin space isomorphic to the state space and the …

The Herzog-Sch\"onheim conjecture for simple and symmetric groups
M. Garonzi, L. Margolis
https://arxiv.org/abs/2509.25118 https://arxiv.org/pdf/2509.…

The Herzog-Schönheim conjecture for simple and symmetric groups
The Herzog-Schönheim conjecture states that if $H_1, \ldots, H_k$ are subgroups of a group $G$ and $x_1, \ldots, x_k$ are elements of $G$ such that $H_1x_1, \ldots, H_kx_k$ is a partition of $G$ into cosets, then two of these subgroups must have the same index. We prove this conjecture for simple groups and for symmetric groups.

A symmetric biderivation structure on polynomial algebras and a class of modules over the special Jordan algebra $H_n(K)$ of symmetric matrices
Yangjie Yin, Gang Han
https://arxiv.org/abs/2509.25867

A symmetric biderivation structure on polynomial algebras and a class of modules over the special Jordan algebra $H_n(K)$ of symmetric matrices
There exists a biderivation structure on the polynomial algebra $\mathscr{A}[n] = K[x_1,\dots,x_n],$ where $K$ is a field with $\operatorname{char}(K)\ne 2$, defined by $f \circ h = \sum_{i=1}^n \frac{\partial f}{\partial x_i}\,\frac{\partial h}{\partial x_i}.$ Let $\mathscr{A}_k[n]$ denote the subspace of homogeneous polynomials of degree $k$. Then $(\mathscr{A}_2[n],\circ)$ is a Jordan algebra, isomorphic to the special Jordan algebra $H_n(K)$ of $n\times n$ symmetric matrices. Each $\mathscr…

On RoCK blocks of double covers of symmetric and alternating groups and the refined Brou\'e conjecture
Yucong Du, Xin Huang
https://arxiv.org/abs/2510.02147 https://

On RoCK blocks of double covers of symmetric and alternating groups and the refined Broué conjecture
Recently, Kleshchev and Livesey proved the existence of RoCK $p$-blocks for double covers of symmetric and alternating groups over large enough coefficient rings. They proved that RoCK blocks of double covers are Morita equivalent to standard ``local" blocks via bimodules with endopermutation source. Based on this, Kleshchev and Livesey proved that these RoCK blocks are splendidly Rickard equivalent to their Brauer correspondents. The analogous result for blocks of symmetric groups, a theorem o…

Microlensing of non-singular black holes at finite size: a ray tracing approach
Jens Boos, Hao Hu
https://arxiv.org/abs/2510.10282 https://arxiv.org/pdf/25…

Microlensing of non-singular black holes at finite size: a ray tracing approach
We study the gravitational microlensing of various static and spherically symmetric non-singular black holes (and horizonless, non-singular compact objects of similar size). For pointlike sources we extend the parametrized post-Newtonian lensing framework to fourth order, whereas for extended sources we develop a ray tracing approach via a simple radiative transfer model. Modelling non-relativistic proper motion of the lens in front of a background star we record the apparent brightness as a fu…

On partitions associated with elementary symmetric polynomials
Cristina Ballantine, Shaheen Nazir, Bridget Eileen Tenner, Karlee Westrem, Chenchen Zhao
https://arxiv.org/abs/2510.01100

On partitions associated with elementary symmetric polynomials
The elementary symmetric partition function is a map on the set of partitions. It sends a partition lambda to the partition whose parts are the summands in the evaluation of the elementary symmetric function on the parts of lambda. These elementary symmetric partition functions have been studied before, and are related to plethysm. In this note, we study properties of the elementary symmetric partition functions, particularly related to injectivity and the number of parts appearing in their ima…

Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm
Thomas Bake, Erin Carson, Yuxin Ma
https://arxiv.org/abs/2510.11379 https://

Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm
The preconditioned conjugate gradient (PCG) algorithm is one of the most popular algorithms for solving large-scale linear systems Ax = b, where A is a symmetric positive definite matrix. Rather than computing residuals directly, it updates the residual vectors recursively. Current analyses of the conjugate gradient (CG) algorithm in finite precision typically assume that the norm of the recursively updated residual goes orders of magnitude below the machine precision, focusing mainly on boundi…

An algebra modality admitting countably many deriving transformations
Jean-Baptiste Vienney
https://arxiv.org/abs/2510.03953 https://arxiv.org/pdf/2510.039…

An algebra modality admitting countably many deriving transformations
A differential category is an additive symmetric monoidal category, that is, a symmetric monoidal category enriched over commutative monoids, with an algebra modality, axiomatizing smooth functions, and a deriving transformation on this algebra modality, axiomatizing differentiation. Lemay proved that a comonoidal algebra modality has at most one deriving transformation, thus differentiation is unique in models of differential linear logic. It was then an open problem whether this result extend…

A New Supersymmetry Index for Symmetric Orbifold CFTs
Marcel R. R. Hughes, Masaki Shigemori
https://arxiv.org/abs/2509.19425 https://arxiv.org/pdf/2509.194…

A New Supersymmetry Index for Symmetric Orbifold CFTs
We propose a new supersymmetry index for symmetric orbifold CFTs in the setup of the AdS$_3$/CFT$_2$ correspondence. In a novel formulation for symmetric orbifold CFTs based on the Schur-Weyl duality, we show how this index naturally emerges and its protection follows from the detailed nature of exactly marginal operators in these theories. This index is a one-parameter generalization of the standard index and gives more fine-grained information about the structure of microstates than previousl…

Symmetric Spaces with Rectangular Unit Lattices, Revisited
Jost-Hinrich Eschenburg, Ernst Heintze, Peter Quast
https://arxiv.org/abs/2509.16166 https://arx…

Symmetric Spaces with Rectangular Unit Lattices, Revisited
We give a new proof of a theorem of Loos stating that a Riemannian symmetric space X with rectangular unit lattice is a symmetric R-space. For this we construct explicitly an isometric extrinsically symmetric embedding of X in a Euclidean space which reveals X as a standardly embedded symmetric R-space. We further determine the root systems, Euclidean root data, fundamental groups and eigenvalues of the Laplacian of symmetric spaces with rectangular unit lattice in a direct way.

Time-reversal positivity
Zhong-Chao Wei
https://arxiv.org/abs/2510.06226 https://arxiv.org/pdf/2510.06226

Time-reversal positivity
We propose a new analytical tool called time-reversal positivity. It is an analogue of the Majorana reflection positivity in time-reversal symmetric case. This new time-reversal positivity can fully explain the relationship between time-reversal symmetry and the sign-free property in quantum Monte Carlo simulations. Using a cone-theoretical method, we show the ground state uniqueness for the time-reversal symmetric non-hermitian Hubbard model.

Geometric Construction of Quiver Tensor Products
Daigo Ito, John S. Nolan
https://arxiv.org/abs/2510.05277 https://arxiv.org/pdf/2510.05277

Geometric Construction of Quiver Tensor Products
By a classic theorem of Beilinson, the perfect derived category $\operatorname{Perf}(\mathbb{P}^n)$ of projective space is equivalent to the category of derived representations of a certain quiver with relations. The vertex-wise tensor product of quiver representations corresponds to a symmetric monoidal structure $\otimes_{\mathsf{Q}}$ on $\operatorname{Perf}(\mathbb{P}^n)$. We prove that, for a certain choice of equivalence, the symmetric monoidal structure $\otimes_{\mathsf{Q}}$ may be descr…

Scalar-Tensor Symmetric Teleparallel Gravity: Reconstruct the Cosmological History with a Steep Potential
Ghulam Murtaza, Avik De, Andronikos Paliathanasis
https://arxiv.org/abs/2510.03042

Scalar-Tensor Symmetric Teleparallel Gravity: Reconstruct the Cosmological History with a Steep Potential
Within the framework of scalar-non-metricity gravity, we introduce a steep potential together with a power-law coupling function and investigate whether the acceleration phases of the universe can be consistently described by this model. In the symmetric teleparallel formulation, and under a Friedmann--Lemaître--Robertson--Walker background, three distinct branches of the connection arise, leading to three different cosmological scenarios. We perform a detailed dynamical analysis of these mode…

Inverse Monoid Topological Quantum Field Theories and Open-Closed Grand Canonical Symmetric Orbifolds
Jan Troost
https://arxiv.org/abs/2510.02782 https://a…

Inverse Monoid Topological Quantum Field Theories and Open-Closed Grand Canonical Symmetric Orbifolds
We present an open-closed topological quantum field theory for inverse monoids which generalizes the theory of principle fiber bundles with finite gauge group over Riemann surfaces with boundary. The theory is constructed using the isomorphism between the semisimple inverse monoid algebra and a matrix algebra which lies at the heart of monoid structure and representation theory. An example that we study in detail is the Ivanov-Kerov monoid of partial permutations. We review motivations from str…

Coherence for Pseudo Commutative Monads
Diego Manco
https://arxiv.org/abs/2509.15101 https://arxiv.org/pdf/2509.15101…

Coherence for Pseudo Commutative Monads
We prove that the free algebra functor associated to a symmetric, pseudo commutative 2-monad, from the underlying symmetric monoidal 2-category to the 2-category of algebras and pseudo maps over the 2-monad can be enhanced to a multifunctor. Furthermore, we prove that this multifunctor is pseudo symmetric. Our proof implies coherence results for both symmetric and non-symmetric pseudo commutative 2-monads conjectured by Hyland and Power.

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

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

Entanglement distillation on symmetric two-qutrit entangled states of rank five
Zihua Song, Lin Chen, Yongge Wang
https://arxiv.org/abs/2509.21258 https://…

Entanglement distillation on symmetric two-qutrit entangled states of rank five
Entanglement distillation is a key step in quantum information, both theoretically and practically. It has been proven that non-positive-partial transpose (NPT) entangled states of rank at most four is 1-distillable under local operation and classical communications. In this paper we investigate the distillation of a more complex family of NPT entangled states, namely a family of symmetric two-qutrit states $\r$ of rank five with given eigenvectors. We explicitly construct five families of such…

Pinnacles for Complex Reflection Groups
Aaron Burnham-Schmidt, Nicolle Gonz\'alez
https://arxiv.org/abs/2510.03580 https://arxiv.org/pdf/2510.03580

Pinnacles for Complex Reflection Groups
We study, characterize, and enumerate the admissible pinnacle sets of nonexceptional complex reflection groups $G(m,p,n)$, which include all generalized symmetric groups $\mathbb{Z}_m \wr S_n$ as special cases. This generalizes the work of Davis--Nelson--Petersen--Tenner for symmetric groups $S_n$ and González--Harris--Rojas Kirby--Smit Vega Garcia--Tenner for signed symmetric groups $\mathbb{Z}_2 \wr S_n$. As a consequence, we prove a conjecture of González--Harris--Rojas Kirby--Smit Vega Ga…

Asymptotically flat black holes with a singular Cauchy horizon and a spacelike singularity
Maxime Van de Moortel
https://arxiv.org/abs/2510.07431 https://a…

Asymptotically flat black holes with a singular Cauchy horizon and a spacelike singularity
In our recent work [Van de Moortel, The coexistence of null and spacelike singularities inside spherically symmetric black holes], we analyzed the transition between null and spacelike singularities in spherically symmetric dynamical black holes and demonstrated that the spacelike portion is described by a Kasner metric with positive varying exponents that degenerate to $(1,0,0)$ near the null-spacelike transition. In the present paper, we provide examples of global spacetimes satisfying the as…

Strong cohomological integrality for symmetric stacks
Lucien Hennecart, Tasuki Kinjo
https://arxiv.org/abs/2509.21298 https://arxiv.org/pdf/2509.21298

Strong cohomological integrality for symmetric stacks
We prove a strong form of the cohomological integrality theorem, decomposing the cohomology of smooth symmetric stacks as the cohomological Hall induction of the intersection cohomology of the good moduli spaces of stacks of graded points. This generalizes the previous result by the second author together with Bu--Davison--Ibáñez Nuñez--Pădurariu to non-orthogonal stacks, and confirms a conjecture of the first author that the algebraic BPS cohomology of the quotient stack of a symmetric rep…

Symmetric Killing tensors on almost abelian Lie groups
Renan Berto-Cuevas, Viviana del Barco, Andrei Moroianu
https://arxiv.org/abs/2509.26195 https://arxi…

Symmetric Killing tensors on almost abelian Lie groups
In this work we provide a complete characterization of left-invariant symmetric Killing tensors on almost abelian Lie groups endowed with a left-invariant Riemannian metric. We show in particular that all such tensors are decomposable, in the sense that they can be expressed as a polynomial in the Killing vector fields and the Riemannian metric.

Combinatorial proofs of Petrie Pieri rule and Plethystic Pieri rule
Saintan Wu, Sen-Peng Eu, Kuo-Han Ku, Yu-Sheng Shih
https://arxiv.org/abs/2509.16872 https://

Combinatorial proofs of Petrie Pieri rule and Plethystic Pieri rule
Petrie symmetric functions $G(k,n)$, also known as truncated homogeneous symmetric functions or modular complete symmetric functions, form a class of symmetric functions interpolating between the elementary symmetric functions $e_n$ and the homogeneous symmetric functions $h_n$. Analogous to the Pieri rule for $s_μh_n$ and the dual Pieri rule for $s_μe_n$, Grinberg showed that the Schur coefficients for the ``Pieri rule'' of $s_μG(k,n)$ can be determined by the determinant $\pet_k(λ,μ)$ of…

A Geometric View on Crossing-Symmetric Dispersion Relations
Joan Elias Miro, Andrea Guerrieri, Mehmet Asim Gumus, Ahmadullah Zahed
https://arxiv.org/abs/2509.14170 https://

A Geometric View on Crossing-Symmetric Dispersion Relations
We introduce a general framework for constructing dispersion relations using crossing-symmetric variables, leading to infinitely many distinct representations of the 2-to-2 scattering amplitude of identical scalars. Classical formulations such as the Auberson-Khuri crossing-symmetric dispersion relations (CSDRs), the Mahoux-Roy-Wanders relations, and the local CSDR, as well as fixed-t dispersion relations emerge as special cases. Within this setting we re-derive the null constraints from a geom…

Generation of C-band entangled photon pairs by biexciton-exciton cascade from symmetric InAs/InP quantum dots
Anna Musia{\l}, Maja Wasiluk, Katarzyna Roszak, Micha{\l} Gawe{\l}czyk, Wojciech Rudno-Rudzi\'nski, Pawe{\l} Wyborski, Johann P. Reithmaier, Mohamed Benyoucef, Grzegorz S\k{e}k
https://arxiv.org/abs/2509.24500

Generation of C-band entangled photon pairs by biexciton-exciton cascade from symmetric InAs/InP quantum dots
Hereby, we study the generation of pairs of polarization-entangled photons at telecom C-band by biexciton-exciton cascade from non-resonantly excited epitaxial InAs/InP quantum dots (QDs). It is realized without external tuning of the fine structure splitting (FSS), which does not exceed 10 $μ$eV in as-grown nanostructures, due to their high in-plane symmetry. Excitonic complexes are identified by means of excitation power-dependent and polarization-resolved magneto)microphotoluminescence. The…

Closing paths to cycles in symmetric graphs
Martin Milani\v{c}, {\DJ}or{\dj}e Mitrovi\'c
https://arxiv.org/abs/2510.05404 https://arxiv.org/pdf/2510.05…

Closing paths to cycles in symmetric graphs
It was shown by Beisegel, Chudnovsky, Gurvich, Milanič, and Servatius in 2022 that every induced $2$-edge path in a vertex-transitive graph closes to an induced cycle. Similar results were obtained for 3-edge paths closing to cycles in edge-transitive graphs, where the cycle can be assumed to be induced if the path is induced. Motivated by these results, we consider the following problem: For a given class of graphs, determine all integers $\ell\geq 0$ such that for every graph in the class, e…

Spectral equivalence of unsymmetric kernel matrices and applications
Tizian Wenzel, Armin Iske
https://arxiv.org/abs/2509.24561 https://arxiv.org/pdf/2509.…

Spectral equivalence of unsymmetric kernel matrices and applications
Symmetric kernel matrices are a well researched topic in the literature of kernel based approximation. In particular stability properties in terms of lower bounds on the smallest eigenvalue of such symmetric kernel matrices are thoroughly investigated, as they play a fundamental role in theory and practice. In this work, we focus on unsymmetric kernel matrices and derive stability properties under small shifts by establishing a spectral equivalence to their unshifted, symmetric versions. This e…

First eigenvalue and nodal domains of the drift Laplacian on symmetric self-shrinkers in $\mathbb{R}^3$
Elham Matinpour
https://arxiv.org/abs/2509.25617 https://

First eigenvalue and nodal domains of the drift Laplacian on symmetric self-shrinkers in $\mathbb{R}^3$
Consider $\mathbb{R}^3$ equipped with the Euclidean metric and the Gaussian measure. Let $Σ$ be a complete embedded self-shrinker in $\mathbb{R}^3$ with the induced metric and weighted measure, and let $λ_1$ denote the first eigenvalue of the drift Laplacian in the weighted $L^2$ space. Inspired by Choe and Soret's estimate of the first eigenvalue of the Laplacian on symmetric minimal surfaces in $\mathbb{S}^3$, we prove that $λ_1$= 1/2 for self-shrinkers invariant under the dihedral group $…

Noncommutative Bianchi I and III Cosmology Models: Radiation Era Dynamics and gamma Estimation
G. Oliveira-Neto, Y. Soncco Apaza
https://arxiv.org/abs/2510.08796 https://…

Noncommutative Bianchi I and III Cosmology Models: Radiation Era Dynamics and gamma Estimation
Understanding the early evolution of the universe requires models that incorporate possible quantum and anisotropic effects in its dynamics. In this work, we analyze the dynamical evolution of locally rotationally symmetric anisotropic cosmological models of Bianchi type I (flat curvature) and Bianchi type III (open curvature) within a noncommutative phase space framework characterized by a deformation parameter gamma. Using a Hamiltonian formulation based on Schutz formalism for a perfect radi…

Bidifferentials, Lagrangian projections and the Virasoro extension
Eduard Looijenga
https://arxiv.org/abs/2510.08208 https://arxiv.org/pdf/2510.08208

Bidifferentials, Lagrangian projections and the Virasoro extension
Let $C$ be a smooth projective curve over an algebraically closed field $k$ of characteristic zero. We prove that a Lagrangian supplement of $H^0(C, Ω_C)$ in the de Rham cohomology group $H^1_{dR}(C)$ determines and is determined by a particular type of symmetric bidifferential on $C^2$ (its polar divisor must be twice the diagonal and have biresidue one along it). When $k$ is the complex field, a natural choice of such supplement is $H^{0,1}(C)$ and we show that this corresponds with the bidi…

Equal knapsack identities between symmetric group character degrees
David J. Hemmer, Armin Straub, Karlee J. Westrem
https://arxiv.org/abs/2510.00301 https://

Equal knapsack identities between symmetric group character degrees
We prove a series of ``knapsack'' type equalities for irreducible character degrees of symmetric groups. That is, we find disjoint subsets of the partitions of $n$ so that the two corresponding character-degree sums are equal. Our main result refines our recent description of the Riordan numbers as the sum of all character degrees $f^λ$ where $λ$ is a partition of $n$ into three parts of the same parity. In particular, the sum of the ``fat-hook'' degrees $f^{(k,k,1^{n-2k})}+f^{(k+1,k+1,1^{n-2…

Motivic Classes of Isotropic Degeneracy Loci and Symmetric Orbit Closures
Minyoung Jeon
https://arxiv.org/abs/2509.24348 https://arxiv.org/pdf/2509.24348…

Motivic Classes of Isotropic Degeneracy Loci and Symmetric Orbit Closures
We provide explicit formulas for computing the motivic Chern and Hirzebruch classes of degeneracy loci, especially those coming from the symplectic and odd orthogonal Grassmannians. The Chern--Schwartz--MacPherson classes, K-theory classes, and Cappell--Shaneson L-classes arise as specializations of the motivic Chern and Hirzebruch classes. Our result is the analogue of the result of Anderson--Chen--Tarasca for the degeneracy loci from the ordinary Grassmannians. As applications, we obtain the …

Light deflection in axially symmetric stationary spacetimes filled with a moving medium
Christian Pfeifer, Barbora Bezd\v{e}kov\'a, Oleg Yu. Tsupko
https://arxiv.org/abs/2510.01326

Light deflection in axially symmetric stationary spacetimes filled with a moving medium
The deflection of light rays near gravitating objects can be influenced not only by gravity itself but also by the surrounding medium. Analytical studies of such effects are possible within the geometrical optics approximation, where the medium introduces additional light bending due to refraction. These studies typically assume a cold non-magnetized plasma, for which light propagation is independent of the medium's velocity. In this paper, we extend the analysis to the general case of dispersi…

Hopf algebra maps taking chromatic symmetric functions to their graph complements
Shao Yuan Lin, Laura Pierson
https://arxiv.org/abs/2509.16318 https://arx…

Hopf algebra maps taking chromatic symmetric functions to their graph complements
Cho and van Willigenburg (arXiv:1508.07670) and Alinaeifard, Wang, and van Willgenburg (arXiv:2010.00147) introduce multiplicative chromatic bases for the ring $Λ$ of symmetric functions, consisting of the chromatic symmetric functions (CSFs) of a sequence of connected graphs $G_1,G_2,\dots$ such that $G_n$ has total weight $n$, together with the CSFs of their disjoint unions. In arXiv:1707.04058, Tsujie introduces an alternative ring structure $\widetildeΛ$ on the vector space $Λ$ that make…

Symmetry of the refined $q,t$-Catalan polynomials for $\vec{k}$-Dyck paths
Menghao Qu, Yingrui Zhang
https://arxiv.org/abs/2510.08196 https://arxiv.org/pdf…

Symmetry of the refined $q,t$-Catalan polynomials for $\vec{k}$-Dyck paths
Pappe, Paul, and Schilling introduced two combinatorial statistics, depth and ddinv, associated with classical Dyck paths, and proved that the distributions of (area, depth) and (dinv, ddinv) are $q,t$-symmetric by constructing an involution on plane trees. They also provided a new formula for the original $q,t$-Catalan polynomials $C_{n}(q,t)$. We observe that depth is a slight modification of bounce, which was defined by the filling algorithm and ranking algorithm of Xin and the second author…

A bijection between symmetric plane partitions and quasi transpose complementary plane partitions
Takuya Inoue
https://arxiv.org/abs/2509.17064 https://arx…

A bijection between symmetric plane partitions and quasi transpose complementary plane partitions
We resolve the explicit bijection problem between symmetric plane partitions (SPPs) and quasi transpose complementary plane partitions (QTCPPs), introduced by Schreier-Aigner, who proved their equinumerosity. First, we relate this problem to Proctor's parallel equinumerosities for SPPs, even SPPs, staircase plane partitions, and parity staircase plane partitions, by constructing several bijections, one of which is based on the jeu de taquin algorithm. As a result, we reduce the task to construc…