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On $2$-connected graphs avoiding cycles of length $0$ modulo $4$
Hojin Chu, Boram Park, Homoon Ryu
https://arxiv.org/abs/2507.12798 https://

On $2$-connected graphs avoiding cycles of length $0$ modulo $4$
For two integers $k$ and $\ell$, an $(\ell \text{ mod }k)$-cycle means a cycle of length $m$ such that $m\equiv \ell\pmod{k}$. In 1977, Bollobás proved a conjecture of Burr and Erdős by showing that if $\ell$ is even or $k$ is odd, then every $n$-vertex graph containing no $(\ell \text{ mod }k)$-cycles has at most a linear number of edges in terms of $n$. Since then, determining the exact extremal bounds for graphs without $(\ell \text{ mod }k)$-cycles has emerged as an interesting question i…

Complex three-dimensional rearing environments amplify compensatory plasticity following early blindness https://www.biorxiv.org/content/10.1101/2025.05.02.651847v1 "underscoring the role of experience in directing compensatory plasticity following early sensory loss.&q…

Complex three-dimensional rearing environments amplify compensatory plasticity following early blindness
The neocortex has a remarkable capacity to alter its functional organization and connectivity in response to sensory loss, particularly if this loss occurs early in life. A key question is whether this cross-modal reorganization is driven by sensory deprivation itself or through enhanced use of the spared senses. We investigated how different rearing environments shape neural responses in primary somatosensory cortex (S1) of short-tailed opossums ( Monodelphis domestica) , following elimination…

K2-18b Does Not Meet The Standards of Evidence For Life
Kevin B. Stevenson, Jacob Lustig-Yaeger, E. M. May, Ravi K. Kopparapu, Thomas J. Fauchez, Jacob Haqq-Misra, Mary Anne Limbach, Edward W. Schwieterman, Kristin S. Sotzen, Shang-Min Tsai
https://arxiv.org/abs/2508.05961

K2-18b Does Not Meet The Standards of Evidence For Life
K2-18b, a temperate sub-Neptune, has garnered significant attention due to claims of possible biosignatures in its atmosphere. Low-confidence detections of dimethyl sulfide (DMS) and/or dimethyl disulfide (DMDS) have sparked considerable debate, primarily around arguments that their absorption features are not uniquely identifiable. Here, we consider a different question from the astrobiology standards of evidence framework: Have we detected an authentic signal? To answer this, we analyzed prev…

Characterizing Equivalence of Logically Constrained Terms via Existentially Constrained Terms (Full Version)
Kanta Takahata, Jonas Sch\"opf, Naoki Nishida, Takahito Aoto
https://arxiv.org/abs/2505.21986

Characterizing Equivalence of Logically Constrained Terms via Existentially Constrained Terms (Full Version)
Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained term rewriting. A fundamental question on constrained terms arising there is how to characterize equivalence between them. However, in the current literature only limited progress has been made on this. In this paper, we provide several sound and complete so…