Tootfinder

Absolute Calibration of Cluster Mira Variables to Provide a New Anchor for the Hubble Constant Determination
Anupam Bhardwaj, Noriyuki Matsunaga, Caroline D. Huang, Adam G. Riess, Marina Rejkuba
https://arxiv.org/abs/2507.10658

Absolute Calibration of Cluster Mira Variables to Provide a New Anchor for the Hubble Constant Determination
Mira variables in globular clusters can provide an accurate and precise absolute calibration of their period-luminosity relations (PLRs) to independently anchor the cosmic distance scale and determine the Hubble constant. We present homogeneous near-infrared ($JHK_s$) time-series photometric observations of a sample of 55 candidate long-period variables in 18 globular clusters covering a wide metallicity range ($-1.7 < \textrm{[Fe/H]} < -0.1$ dex). The Gaia proper motions, long-period variabili…

A locally constrained inverse Hessian quotient flow in de Sitter space
Kuicheng Ma
https://arxiv.org/abs/2507.11149 https://arxiv.org…

A locally constrained inverse Hessian quotient flow in de Sitter space
In this paper, an Alexandrov-Fenchel inequality is established for closed $2$-convex spacelike hypersurface in de Sitter space by investigating the behavior of the locally constrained inverse curvature flow \begin{align} \frac{\partial }{\partial t}x=\bigg(u-\frac{λ'E_1}{E_2}\bigg)ν,\nonumber \end{align} which provides a partial answer to the conjecture raised by Hu and Li in \cite{HL}.

Galaxies at the edges: a complete census of MACS J0416.1-2403 cluster
Rossella Ragusa, Maurizio D'Addona, Amata Mercurio, Marcella Longhetti, Marisa Girardi, Marianna Annunziatella, Nicolas Estrada, Claudio Grillo, Angela Iovino, Giula Rodighiero, Piero Rosati, Benedetta Vulcani, Giuseppe Angora, Hans Bohringer, Massimo Brescia, Gabriel Bartosch Caminha, Gayoung Chon, Fedor Getman, Aniello Grado, Marco Gullieuszik, Luca Limatola, Alessia Moretti, Luisa Pecoraro

Galaxies at the edges: a complete census of MACS J0416.1-2403 cluster
Numerous studies have established that the environment influences the physical properties of a galaxy. While gas inflows supply the fuel for SF, high density and temperature conditions suppress SF activity through various quenching processes. Investigations into large scale structures, such as filaments and overdense regions in the cluster outskirts, have focused on the low z. To move to intermediate z and explore galaxy pathways combined with environmental effects, it is crucial to join wide f…

Clustering of large deviations events in heavy-tailed moving average processes: the catastrophe principle in the short-memory case
Jiaqi Wang, Gennady Samorodnitsky
https://arxiv.org/abs/2506.10256

Clustering of large deviations events in heavy-tailed moving average processes: the catastrophe principle in the short-memory case
How do large deviation events in a stationary process cluster? The answer depends not only on the type of large deviations, but also on the length of memory in the process. Somewhat unexpectedly, it may also depend on the tails of the process. In this paper we work in the context of large deviations for partial sums in moving average processes with short memory and regularly varying tails. We show that the structure of the large deviation cluster in this case markedly differs from the correspon…

Witnessing and guiding sets of tangles
Annegret Seibt
https://arxiv.org/abs/2507.04394 https://arxiv.org/pdf/2507.04394

Witnessing and guiding sets of tangles
Tangles o er a way to indirectly but precisely capture cluster-like though possibly fuzzy substructures in discrete data. In this paper, we analyze witnessing and guiding sets of tangles that can help to find proper cluster candidates for given tangles. We show that every k-tangle has a witnessing set whose size is bounded in an exponential function in k which improves a result of Grohe and Schweizer. Further, we generalize a result of Diestel, Elbracht and Jacobs by providing a characterizatio…

Shifting from Ranking to Set Selection for Retrieval Augmented Generation
Dahyun Lee, Yongrae Jo, Haeju Park, Moontae Lee
https://arxiv.org/abs/2507.06838 …

Shifting from Ranking to Set Selection for Retrieval Augmented Generation
Retrieval in Retrieval-Augmented Generation(RAG) must ensure that retrieved passages are not only individually relevant but also collectively form a comprehensive set. Existing approaches primarily rerank top-k passages based on their individual relevance, often failing to meet the information needs of complex queries in multi-hop question answering. In this work, we propose a set-wise passage selection approach and introduce SETR, which explicitly identifies the information requirements of a q…

The Complexity of the Set of Validities of a Theory
Denis Hirschfeldt, Henry Towsner, Scott Weinstein
https://arxiv.org/abs/2506.08901 https://

The Complexity of the Set of Validities of a Theory
We study the collection of first-order logical schemata all of whose instances are theorems of a given theory $T$; we call these the validities of $T$ ($\mathsf{V}(T)$). It is easy to see that if $T$ is a decidable theory, then $\mathsf{V}(T)$ is distinct from the set of valid formulas of first-order logic as customarily understood. We provide a complete model-theoretic characterization of the complexity, in the sense of Turing degree, of $\mathsf{V}(T)$ for decidable theories $T$, and answer a…

Hierarchical Lexical Graph for Enhanced Multi-Hop Retrieval
Abdellah Ghassel, Ian Robinson, Gabriel Tanase, Hal Cooper, Bryan Thompson, Zhen Han, Vassilis N. Ioannidis, Soji Adeshina, Huzefa Rangwala
https://arxiv.org/abs/2506.08074

Hierarchical Lexical Graph for Enhanced Multi-Hop Retrieval
Retrieval-Augmented Generation (RAG) grounds large language models in external evidence, yet it still falters when answers must be pieced together across semantically distant documents. We close this gap with the Hierarchical Lexical Graph (HLG), a three-tier index that (i) traces every atomic proposition to its source, (ii) clusters propositions into latent topics, and (iii) links entities and relations to expose cross-document paths. On top of HLG we build two complementary, plug-and-play ret…

The UK local election results so far are fairly grim. People are understandably cross with #Labour, they have put themselves in an awkward position where they have effectively promised not to raise any of the maIn sources of tax when demands on the treasury are rising.
The Reform party cannot be the answer. They are a collection of easy answers to problems where there are no easy answers. …

A collection of results relating the geometry of plane domains and the exit time of planar Brownian motion, II
Greg Markowsky, Clayton McDonald
https://arxiv.org/abs/2506.09364

A collection of results relating the geometry of plane domains and the exit time of planar Brownian motion, II
This paper is the sequel to another with the same name (Buttigieg et al., Comput. Methods Funct. Theory, 2023), and is concerned with results of the same type. We deduce a result on the moments of the exit time of Brownian motion from domains whose boundary curve is replaced by a dashed line, and from domains arising from a periodic tiling of the plane. We also give a construction of a type of domain which is similar to a wedge domain, but the behaviour of whose exit time moments answer several…