Search:
Match:
2 results
Research Paper#Knot Theory, 3-Manifold Topology, Instanton Homology🔬 ResearchAnalyzed: Jan 3, 2026 16:46

Instanton Homology and Fibered Knots: 2-Torsion and Alexander Polynomial

Published:Dec 30, 2025 13:14
1 min read
ArXiv

Analysis

This paper investigates the properties of instanton homology, a powerful tool in 3-manifold topology, focusing on its behavior in the presence of fibered knots. The main result establishes the existence of 2-torsion in the instanton homology of fibered knots (excluding a specific case), providing new insights into the structure of these objects. The paper also connects instanton homology to the Alexander polynomial and Heegaard Floer theory, highlighting its relevance to other areas of knot theory and 3-manifold topology. The technical approach involves sutured instanton theory, allowing for comparisons between different coefficient fields.
Reference

“The paper proves that the unreduced singular instanton homology has 2-torsion for any null-homologous fibered knot (except for a specific case) and provides a formula for calculating it.”

PermalinkArXiv
Paper#Medical Imaging🔬 ResearchAnalyzed: Jan 3, 2026 15:59

MRI-to-CT Synthesis for Pediatric Cranial Evaluation

Published:Dec 29, 2025 23:09
1 min read
ArXiv

Analysis

This paper addresses a critical clinical need by developing a deep learning framework to synthesize CT scans from MRI data in pediatric patients. This is significant because it allows for the assessment of cranial development and suture ossification without the use of ionizing radiation, which is particularly important for children. The ability to segment cranial bones and sutures from the synthesized CTs further enhances the clinical utility of this approach. The high structural similarity and Dice coefficients reported suggest the method is effective and could potentially revolutionize how pediatric cranial conditions are evaluated.
Reference

“sCTs achieved 99% structural similarity and a Frechet inception distance of 1.01 relative to real CTs. Skull segmentation attained an average Dice coefficient of 85% across seven cranial bones, and sutures achieved 80% Dice.”

PermalinkArXiv