Tootfinder

Understanding Online Polarization Through Human-Agent Interaction in a Synthetic LLM-Based Social Network
Tim Donkers, J\"urgen Ziegler
https://arxiv.org/abs/2506.15866

Understanding Online Polarization Through Human-Agent Interaction in a Synthetic LLM-Based Social Network
The rise of social media has fundamentally transformed how people engage in public discourse and form opinions. While these platforms offer unprecedented opportunities for democratic engagement, they have been implicated in increasing social polarization and the formation of ideological echo chambers. Previous research has primarily relied on observational studies of social media data or theoretical modeling approaches, leaving a significant gap in our understanding of how individuals respond t…

Capturing Misalignment
Pierfrancesco Guarino, Gabriel Ziegler
https://arxiv.org/abs/2506.17176 https://arxiv.org/pdf/2506.17176

Capturing Misalignment
We introduce and formalize misalignment, a phenomenon of interactive environments perceived from an analyst's perspective where an agent holds beliefs about another agent's beliefs that do not correspond to the actual beliefs of the latter. We demonstrate that standard frameworks, such as type structures, fail to capture misalignment, necessitating new tools to analyze this phenomenon. To this end, we characterize misalignment through non-belief-closed state spaces and introduce agent-dependent…

Classification of exact structures using the Ziegler spectrum
Julia Sauter
https://arxiv.org/abs/2506.02304 https://arxiv.org/pdf/250…

Classification of exact structures using the Ziegler spectrum
Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the additive category has weak cokernels, this topological space is an open subset of the Ziegler spectrum and this is a result of Kevin Schlegel. We also look at some module categories of rings where the Ziegler spectrum is known and calculate the global dimensi…

Trade Pitch Has Raiders $25 Million Defender Reunite With Dave Ziegler https://heavy.com/sports/nfl/las-vegas-raiders/tyree-wilson-titans-trade-rumors/?adt_ei=[email]

Second-Order Parameterizations for the Complexity Theory of Integrable Functions
Aras Bacho, Martin Ziegler
https://arxiv.org/abs/2506.11210 https://

Second-Order Parameterizations for the Complexity Theory of Integrable Functions
We develop a unified second-order parameterized complexity theory for spaces of integrable functions. This generalizes the well-established case of second-order parameterized complexity theory for spaces of continuous functions. Specifically we prove the mutual linear equivalence of three natural parameterizations of the space $\Lrm{p}$ of $p$-integrable complex functions on the real unit interval: (binary) $\Lrm{p}$-modulus, rate of convergence of Fourier series, and rate of approximation by s…

The Chow Ring of the 2-Sylow Subgroup of $\mathrm{GL}(4,2)$
Alexander Ziegler
https://arxiv.org/abs/2506.06512 https://arxiv.org/pdf/…

The Chow Ring of the 2-Sylow Subgroup of $\mathrm{GL}(4,2)$
This paper provides a computation of the mod 2 Chow ring of the motivic étale classifying space of the finite group $\mathrm{Syl}_2(\mathrm{GL}(4,2))$. It outlines a general computation strategy, adapted from work by Burt Totaro, that has been largely automated by the author. This strategy can be used to compute more examples of Chow rings of motivic étale classifying spaces quickly.

Self-gravity in thin protoplanetary discs: 1. The smoothing-length approximation versus the exact self-gravity kernel
S. Rendon Restrepo, T. Rometsch, U. Ziegler, O. Gressel
https://arxiv.org/abs/2506.10812

Self-gravity in thin protoplanetary discs: 1. The smoothing-length approximation versus the exact self-gravity kernel
Planet-forming discs often contain structures like spiral arms, typically linked to the disc's gravitational forces. In 2D models, an ad hoc softening prescription is commonly used for self-gravity, but this overlooks the vertical structure's impact, suppresses the Newtonian nature of gravity at short distances and doesn't respect Newton's third law. To address these issues, associated with a Plummer potential approximation, we developed an exact self-gravity kernel for thin, hydrostatically …

This https://arxiv.org/abs/2503.10524 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the computation of the vanishing locus of a finitely presented functor
We discuss invariants which are helpful for the computation of the vanishing locus of a finitely presented functor $\mathcal{G}$, i.e., the set of points in the Ziegler spectrum on which $\mathcal{G}$ vanishes. These invariants are: the rank of $\mathcal{G}$, the supports of its co- and contravariant defect, and the class of $\mathcal{G}$ in the Grothendieck group of the category of finitely presented functors. We show that these invariants determine the vanishing locus in the case of a finitel…

What Pareto-Efficiency Adjustments Cannot Fix
Josue Ortega, Gabriel Ziegler, R. Pablo Arribillaga, Geng Zhao
https://arxiv.org/abs/2506.11660 https://

What Pareto-Efficiency Adjustments Cannot Fix
The Deferred Acceptance (DA) algorithm is stable and strategy-proof, but can produce outcomes that are Pareto-inefficient for students, and thus several alternative mechanisms have been proposed to correct this inefficiency. However, we show that these mechanisms cannot correct DA's rank-inefficiency and inequality, because these shortcomings can arise even in cases where DA is Pareto-efficient. We also examine students' segregation in settings with advantaged and marginalized students. We pr…

The TOI-1117 Multi-planetary System: 3 sub-Neptunes, 1 in both the Neptunian Desert and Radius Valley
Isobel S. Lockley, David J. Armstrong, Jorge Fern\'andez Fern\'andez, Sarah Millholland, Henrik Knierim, Elisa Delgado Mena, Sergio Sousa, Karen A. Collins, Cristilyn N. Watkins, Steve B. Howell, Vardan Adibekyan, Ravit Helled, Carl Ziegler, Daniel Bayliss, C\'esar Brice\~no, Amadeo Castro-Gonz\'alez, Catherine A. Clark, Kevin I. Collins, Jessie L. Christiansen, Kaiming…

The TOI-1117 Multi-planetary System: 3 sub-Neptunes, 1 in both the Neptunian Desert and Radius Valley
We present the discovery of three sub-Neptune planets around TOI-1117, a Sun-like star with mass $0.97\pm0.02M_{\odot}$, radius $1.05\pm0.03R_{\odot}$, age $4.42\pm1.50$ Gyr and effective temperature $5635\pm62$ K. Light curves from TESS and LCOGT show a transiting sub-Neptune with a $2.23$ day period, mass $M_b=8.90_{-0.96}^{+0.95}M_{\oplus}$ and radius $R_b=2.46_{-0.12}^{+0.13}R_{\oplus}$. This is a rare 'hot Neptune' that falls within the parameter spaces known as the 'Neptunian Desert' and …