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Impact of Heterogeneity on Scalar Flux Variance Relations Across Diverse Ecosystems
Tyler Waterman, Ivana Stiperski, Laura Torres-Rojas, Marc Calaf
https://arxiv.org/abs/2509.18385

Complexity of Activity Patterns in a Bio-Inspired Hopfield-Type Network in Different Topologies
Marco Cafiso, Paolo Paradisi
https://arxiv.org/abs/2509.18758 https://

Reduced Density Matrix Functional Theory And A Reduced Formulation Of Density Functional Theory
H{\aa}kon Richard Fredheim, Simen Kvaal
https://arxiv.org/abs/2510.12242 https://…

Reduced Density Matrix Functional Theory And A Reduced Formulation Of Density Functional Theory
A mathematical framework for reduced density matrix functional theory (RDMFT) is proposed. The work is inspired by and generalizes the work by E.H.~Lieb [E.H. Lieb, Int. J. Quant. Chem. 24(1983), pp.243--277] on density-functional theory (DFT). We introduce a Banach space for density matrices with finite kinetic energy. The dual space is a rich class of single-particle potentials, i.e., Hermitian forms. The ground state energy of an $N$-fermion system with external forces given by any such Herm…

From points to complexes: a concept of unexpectedness for simplicial complexes
Thiago Holleben
https://arxiv.org/abs/2510.10884 https://arxiv.org/pdf/2510.…

From points to complexes: a concept of unexpectedness for simplicial complexes
In 2018, Cook, Harbourne, Migliore and Nagel introduced the concept of unexpected hypersurfaces, which connects the study of Lefschetz properties of artinian algebras defined by powers of linear forms, to a family of interpolation problems. In this paper, inspired by the theory of unexpected hypersurfaces, we introduce the concept of unexpected systems of parameters for squarefree monomial ideals. Similarly to the setting of points, we show that the existence of an unexpected system of paramete…

An introduction to representations of p-adic groups
Jessica Fintzen
https://arxiv.org/abs/2510.08692 https://arxiv.org/pdf/2510.08692

An introduction to representations of p-adic groups
An explicit understanding of the (category of all smooth, complex) representations of p-adic groups provides an important tool not just within representation theory. It also has applications to number theory and other areas, and, in particular, it enables progress on various different forms of the Langlands program. In this write-up of the author's ECM 2024 colloquium-style talk, we will introduce p-adic groups and explain how the category of representations of p-adic groups decomposes into sub…

Infinite-dimensional Lagrange-Dirac systems with boundary energy flow II: Field theories with bundle-valued forms
Fran\c{c}ois Gay-Balmaz, \'Alvaro Rodr\'iguez Abella, Hiroaki Yoshimura
https://arxiv.org/abs/2511.05687 https://arxiv.org/pdf/2511.05687 https://arxiv.org/html/2511.05687
arXiv:2511.05687v1 Announce Type: new
Abstract: Part I of this paper introduced the infinite dimensional Lagrange--Dirac theory for physical systems on the space of differential forms over a smooth manifold with boundary. This approach is particularly well-suited for systems involving energy exchange through the boundary, as it is built upon a restricted dual space -a vector subspace of the topological dual of the configuration space- that captures information about both the interior dynamics and boundary interactions. Consequently, the resulting dynamical equations naturally incorporate boundary energy flow. In this second part, the theory is extended to encompass vector-bundle-valued differential forms and non-Abelian gauge theories. To account for two commonly used forms of energy flux and boundary power densities, we introduce two distinct but equivalent formulations of the restricted dual. The results are derived from both geometric and variational viewpoints and are illustrated through applications to matter and gauge field theories. The interaction between gauge and matter fields is also addressed, along with the associated boundary conditions, applied to the case of the Yang-Mills-Higgs equations.
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Global forms of $\mathcal{N}=4$ theories and non-minimal Seiberg-Witten solutions
Robert Moscrop
https://arxiv.org/abs/2510.02055 https://arxiv.org/pdf/251…

Global forms of $\mathcal{N}=4$ theories and non-minimal Seiberg-Witten solutions
To each four dimensional $\mathcal{N}\geq 2$ supersymmetric quantum field theory, one can associate an algebraic completely integrable (ACI) system that encodes the low energy dynamics of theory. In this paper we explicitly derive the appropriate ACI systems for the global forms of $\mathcal{N}=4$ super Yang-Mills (sYM) using isogenies of polarised abelian varieties. In doing so, we relate the complex moduli of the resulting varieties to the exactly marginal coupling of the theory, thus allowin…

A family of Hecke eigenforms for Drinfeld modular forms of arbitrary rank
O\u{g}uz Gezmi\c{s}, \"Ozge \"Ulkem
https://arxiv.org/abs/2509.20895 https://

A family of Hecke eigenforms for Drinfeld modular forms of arbitrary rank
We aim to provide a family of Drinfeld-Hecke eigenforms given in terms of a determinant of twisted Eisenstein series. Our main tool is the theory of vectorial Drinfeld modular forms, previously introduced by Pellarin [18] and extensively studied by Pellarin [19] as well as in his joint work with Perkins [20] in the rank two setting. We will develop this theory in the present paper for the arbitrary rank setting by using a particular representation.

A General Theory of Emergent Linearity in Complex Dynamical Systems: The Role of Spatial Averaging and Vanishing Correlations
Sabbir Ahmed, Hafiz Fareed Ahmed, Erfan Nozari
https://arxiv.org/abs/2509.25589

A General Theory of Emergent Linearity in Complex Dynamical Systems: The Role of Spatial Averaging and Vanishing Correlations
Various natural and engineered systems, from urban traffic flow to the human brain, have been described by large-scale networked dynamical systems. Despite their vast differences, these systems are often similar in being comprised of numerous microscopic subsystems with complex nonlinear dynamics and interactions that give rise to diverse emergent macroscopic behaviors. As such, a long-standing question across various fields has been to understand why and how various forms of macroscopic behavi…

Projected Holstein-Primakoff boson representation of quantum spins for spin wave theory
Ke Liu, Fangyu Xiong, Fa Wang
https://arxiv.org/abs/2509.26607 https://

Projected Holstein-Primakoff boson representation of quantum spins for spin wave theory
The Holstein-Primakoff boson representation of quantum spins and associated large-$S$ expansion have been the standard framework for describing the spin wave excitations in magnetically order phases of quantum spin systems. However, we will show that the omission of projection operators and normal-ordering in this representation can produce incorrect magnon hamiltonians for finite $S$. We will present the exact normal-ordered forms of the finite-$S$ projection operators and projected Holstein-P…

Fine-Grained Classification Of Detecting Dominating Patterns
Jonathan Dransfeld, Marvin K\"unnemann, Mirza Redzic
https://arxiv.org/abs/2509.22332 https://

Fine-Grained Classification Of Detecting Dominating Patterns
We consider the following generalization of dominating sets: Let $G$ be a host graph and $P$ be a pattern graph $P$. A dominating $P$-pattern in $G$ is a subset $S$ of vertices in $G$ that (1) forms a dominating set in $G$ \emph{and} (2) induces a subgraph isomorphic to $P$. The graph theory literature studies the properties of dominating $P$-patterns for various patterns $P$, including cliques, matchings, independent sets, cycles and paths. Previous work (Kunnemann, Redzic 2024) obtains algori…

Summation Formulas for Harmonic Maass Forms
Nikolaos Diamantis, Joshua Pimm
https://arxiv.org/abs/2509.22607 https://arxiv.org/pdf/2509.22607

Summation Formulas for Harmonic Maass Forms
In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such forms without any restrictions on their growth. We deduce a summation formula for the partition function. We further employ the same theory to derive a result on classical modular forms, namely, a summation formula and the asymptotics of a Riesz sum attached …

Building an AdS/BCFT Josephson junction within Horndeski gravity
Fabiano F. Santos, Henrique Boschi-Filho
https://arxiv.org/abs/2510.07165 https://arxiv.or…

Building an AdS/BCFT Josephson junction within Horndeski gravity
This work explores the constriction and normal Josephson junctions of superconductors within Horndeski's gravitational theory framework. Through a single scalar field of this theory, we provide a dual holographic description via the AdS/BCFT correspondence. We identify a critical temperature below which a charged condensate forms through a second-order phase transition in constriction and normal junctions. Our findings reveal that the condensate comprises pairs of quasiparticles. The junctions …

Towards A Universally Transferable Acceleration Method for Density Functional Theory
Zhe Liu, Yuyan Ni, Zhichen Pu, Qiming Sun, Siyuan Liu, Wen Yan
https://arxiv.org/abs/2509.25724

Towards A Universally Transferable Acceleration Method for Density Functional Theory
Recently, sophisticated deep learning-based approaches have been developed for generating efficient initial guesses to accelerate the convergence of density functional theory (DFT) calculations. While the actual initial guesses are often density matrices (DM), quantities that can convert into density matrices also qualify as alternative forms of initial guesses. Hence, existing works mostly rely on the prediction of the Hamiltonian matrix for obtaining high-quality initial guesses. However, the…

Analyzing {\alpha}-divergence in Gaussian Rate-Distortion-Perception Theory
Martha V. Sourla, Giuseppe Serra, Photios A. Stavrou, Marios Kountouris
https://arxiv.org/abs/2509.19572

Analyzing α-divergence in Gaussian Rate-Distortion-Perception Theory
The problem of estimating the information rate distortion perception function (RDPF), which is a relevant information-theoretic quantity in goal-oriented lossy compression and semantic information reconstruction, is investigated here. Specifically, we study the RDPF tradeoff for Gaussian sources subject to a mean-squared error (MSE) distortion and a perception measure that belongs to the family of α divergences. Assuming a jointly Gaussian RDPF, which forms a convex optimization problem, we ch…

Arithmetic Properties of Partitions with 1 colored Even Parts and r colored Odd Parts
M. P. Thejitha, S. N. Fathima
https://arxiv.org/abs/2509.24324 https://

Arithmetic Properties of Partitions with 1 colored Even Parts and r colored Odd Parts
Recently, Hirschhorn and Sellers defined the partition function a_r(n), which counts the number of partitions of n wherein even parts come in only one color, while the odd parts may appear in one of r-colors for fixed r greater than or equal to 1. In this paper, we employ an identity of Newman to derive infinite families of congruences modulo 5 for a_3(n), and use arithmetic theory of modular forms to prove congruences modulo 3 and modulo 5 for a_5(n).

Lorentz Covariance of the $4d$ Nonlinear Higher-Spin Equations via BRST
O. A. Gelfond, M. A. Vasiliev
https://arxiv.org/abs/2509.22852 https://arxiv.org/pd…

Lorentz Covariance of the $4d$ Nonlinear Higher-Spin Equations via BRST
We propose a BRST extension of the higher-spin gauge theory in $AdS_4$ with the BRST operator associated with the local Lorentz symmetry. Our construction supports manifest local Lorentz covariance and is applicable both to any homotopy scheme of the perturbative analysis including the recently proposed differential homotopy and to the variety of further extended higher-spin models in $AdS_3$ and $AdS_4$ with higher differential forms and Coxeter higher-spin algebras.

Evaluation of lattice sums via telescoping over topographs
Nikita Kalinin
https://arxiv.org/abs/2510.02082 https://arxiv.org/pdf/2510.02082

Evaluation of lattice sums via telescoping over topographs
Topographs, introduced by Conway in 1997, are infinite trivalent planar trees used to visualize the values of binary quadratic forms. In this work, we study series whose terms are indexed by the vertices of a topograph and show that they can be evaluated using telescoping sums over its edges. Our technique provides arithmetic proofs for modular graph function identities arising in string theory, yields alternative derivations of Hurwitz-style class number formulas, and provides a unified fram…

Crosslisted article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- Modular analogs of character formulas and minimal lifts of modular forms
Patrick B. Allen, Preston Wake

Replaced article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
- Diagonal cycles and anticyclotomic Iwasawa theory of modular forms
Francesc Castella, Kim Tuan Do

Modularity from $q$-series
Ken Ono
https://arxiv.org/abs/2509.20316 https://arxiv.org/pdf/2509.20316

Modularity from $q$-series
In 1975, G. E. Andrews challenged the community to provide a proof that takes the summatory forms of the Rogers--Ramanujan $q$-series as input and directly establishes their modularity. This question is important because many different $q$-series appearing in combinatorics, representation theory, and physics often seem to be mysteriously modular, yet there is no general test to confirm this directly from the exotic $q$-series expressions. In this note, solve this general problem using $q$-serie…