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Ich wusste es! #ichWussteEs CDU-Scholz ist schuld.

Ich wusste es! #ichWussteEs CDU-Scholz ist schuld.

Tietze extension does not always work in constructive mathematics if closed sets are defined as sequentially closed sets
Shun Ding, Yang Wan, Luofei Wang, Siqi Xiao
https://arxiv.org/abs/2508.11635

Tietze extension does not always work in constructive mathematics if closed sets are defined as sequentially closed sets
We prove that Tietze Extension does not always exist in constructive mathematics if closed sets on which the function we are extending are defined as sequentially closed sets. Firstly, we take a discrete metric space as our topological space. Now all sets open and sequentially closed. Then, we form an unextendible algorithmic function transforming positive integers to 0 and 1, looking at the preimages of these values as our sequentially closed sets. Then we show that if the Tietze theorem concl…

The electron temperature distribution and the high ionization just behind the shock in the Cygnus Loop
Masahiro Ichihashi, Aya Bamba, Dai Tateishi, Kouichi Hagino, Satoru Katsuda, Hiroyuki Uchida, Hiromasa Suzuki, Ryo Yamazaki, Yutaka Ohira
https://arxiv.org/abs/2509.10346

The electron temperature distribution and the high ionization just behind the shock in the Cygnus Loop
The physical processes behind astrophysical collisionless shocks, such as thermal relaxation and ionization after shock passage, remain poorly understood. To investigate these processes, we analyze the northeastern region of the Cygnus Loop with XMM-Newton. The electron temperature is found to increase towards the interior of the remnant ranging from 0.15-0.19 keV energy range within a spatial scale of 6 arcmin (or 1.27 pc at a distance of 725 pc) from the shock front. This can be explained wel…

MK2 at PBIG Competition: A Prompt Generation Solution
Yuzheng Xu, Tosho Hirasawa, Seiya Kawano, Shota Kato, Tadashi Kozuno
https://arxiv.org/abs/2507.08335

MK2 at PBIG Competition: A Prompt Generation Solution
The Patent-Based Idea Generation task asks systems to turn real patents into product ideas viable within three years. We propose MK2, a prompt-centric pipeline: Gemini 2.5 drafts and iteratively edits a prompt, grafting useful fragments from weaker outputs; GPT-4.1 then uses this prompt to create one idea per patent, and an Elo loop judged by Qwen3-8B selects the best prompt-all without extra training data. Across three domains, two evaluator types, and six criteria, MK2 topped the automatic le…

CLF-RL: Control Lyapunov Function Guided Reinforcement Learning
Kejun Li, Zachary Olkin, Yisong Yue, Aaron D. Ames
https://arxiv.org/abs/2508.09354 https://

CLF-RL: Control Lyapunov Function Guided Reinforcement Learning
Reinforcement learning (RL) has shown promise in generating robust locomotion policies for bipedal robots, but often suffers from tedious reward design and sensitivity to poorly shaped objectives. In this work, we propose a structured reward shaping framework that leverages model-based trajectory generation and control Lyapunov functions (CLFs) to guide policy learning. We explore two model-based planners for generating reference trajectories: a reduced-order linear inverted pendulum (LIP) mode…

DS@GT at CheckThat! 2025: Exploring Retrieval and Reranking Pipelines for Scientific Claim Source Retrieval on Social Media Discourse
Jeanette Schofield, Shuyu Tian, Hoang Thanh Thanh Truong, Maximilian Heil
https://arxiv.org/abs/2507.06563

DS@GT at CheckThat! 2025: Exploring Retrieval and Reranking Pipelines for Scientific Claim Source Retrieval on Social Media Discourse
Social media users often make scientific claims without citing where these claims come from, generating a need to verify these claims. This paper details work done by the DS@GT team for CLEF 2025 CheckThat! Lab Task 4b Scientific Claim Source Retrieval which seeks to find relevant scientific papers based on implicit references in tweets. Our team explored 6 different data augmentation techniques, 7 different retrieval and reranking pipelines, and finetuned a bi-encoder. Achieving an MRR@5 of 0.…