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Twisted Conjugacy Growth of the Generalised Heisenberg Groups
Lukas Vandeputte
https://arxiv.org/abs/2509.02231 https://arxiv.org/pdf/2509.02231

Twisted Conjugacy Growth of the Generalised Heisenberg Groups
We determine the twisted conjugacy growth function for automorphisms on generalised Heisenberg groups. In particular we demonstrate for these groups that up to a natural equivalence this function is either given by $n^k$ or $n^k\ln(n)$ for some constant $k$. We give a precise description for which of these functions we obtain in terms of dimensions and ranks on the upper and lower central series. In particular we obtain that the twisted conjugacy growth is always bounded by the conjugacy growth.

Intrinsic Heisenberg-type lower bounds on spacelike hypersurfaces in general relativity
Thomas Sch\"urmann
https://arxiv.org/abs/2510.01628 https://ar…

Intrinsic Heisenberg-type lower bounds on spacelike hypersurfaces in general relativity
We prove a coordinate- and foliation-independent Heisenberg-type lower bound for quantum states strictly localized in geodesic balls of radius $r$ on spacelike hypersurfaces of arbitrary spacetimes (with matter and a cosmological constant). The estimate depends only on the induced Riemannian geometry of the slice; it is independent of the lapse, shift, and extrinsic curvature, and controls the canonical momentum variance/uncertainty $σ_p$ by the first Dirichlet eigenvalue of the Laplace-Beltra…

Realism and the Inequivalence of the Two Quantum Pictures
Charles Alexandre B\'edard
https://arxiv.org/abs/2510.02138 https://arxiv.org/pdf/2510.02138

Realism and the Inequivalence of the Two Quantum Pictures
The standard claim that the Schrödinger and Heisenberg pictures of quantum mechanics are equivalent rests on the fact that they yield identical empirical predictions. This equivalence therefore assumes the instrumentalist worldview in which theories serve only as tools for prediction. Under scientific realism, by contrast, theories aim to describe reality. Whereas the Schrödinger picture posits a time-evolving wave function, the Heisenberg picture posits so-called descriptors, time-evolving g…

Restricted Central Extensions of Restricted Heisenberg Lie Superalgebras
Yong Yang
https://arxiv.org/abs/2509.00426 https://arxiv.org/pdf/2509.00426…

Restricted Central Extensions of Restricted Heisenberg Lie Superalgebras
Restricted Heisenberg Lie superalgebras are studied over an algebraically closed field F of characteristic p > 2. We use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 2-cohomology spaces. As an application, the corresponding restricted one-dimensional central extensions are described.

The Finite-Temperature Behavior of a Triangular Heisenberg Antiferromagnet
Cecilie Glittum, Olav F. Sylju{\aa}sen
https://arxiv.org/abs/2510.02042 https://…

The Finite-Temperature Behavior of a Triangular Heisenberg Antiferromagnet
We investigate the classical antiferromagnetic Heisenberg model on the triangular lattice with up to third-nearest neighbor couplings using nematic bond theory. This approach allows us to compute the free energy and the neutron scattering static structure factor at finite temperatures. We map out the phase diagram with a particular emphasis on finite-temperature phase transitions that break lattice rotational symmetries, spiral spin liquids and the broad specific heat hump that is ubiquitous in…

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AttentionDep: Domain-Aware Attention for Explainable Depression Severity Assessment
Yusif Ibrahimov, Tarique Anwar, Tommy Yuan, Turan Mutallimov, Elgun Hasanov
https://arxiv.org/abs/2510.00706

AttentionDep: Domain-Aware Attention for Explainable Depression Severity Assessment
In today's interconnected society, social media platforms provide a window into individuals' thoughts, emotions, and mental states. This paper explores the use of platforms like Facebook, X (formerly Twitter), and Reddit for depression severity detection. We propose AttentionDep, a domain-aware attention model that drives explainable depression severity estimation by fusing contextual and domain knowledge. Posts are encoded hierarchically using unigrams and bigrams, with attention mechanisms hi…

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On the Restricted Cohomology of Twisted Heisenberg Lie Superalgebras
Yong Yang
https://arxiv.org/abs/2509.03016 https://arxiv.org/pdf/2509.03016

On the Restricted Cohomology of Twisted Heisenberg Lie Superalgebras
Restricted twisted Heisenberg Lie superalgebras are studied over an algebraically closed field F of characteristic p > 0. We determine the restricted structures and use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 2-cohomology spaces. As an application, the corresponding restricted one-dimensional central extensions are classified and described.