Department de Química , Universitat de les Illes Balears, Carretera de Valldemossa km 7.5 , 07122 Palma de Mallorca , Baleares , Spain.
Published: October 2018
AI Article Synopsis
Article Abstract
Conventional approaches to the synthesis of molecular knots and links mostly rely on metal templation. We present here an alternative strategy that uses the hydrophobic effect to drive the formation of complex interlocked structures in water. We designed an aqueous dynamic combinatorial system that can generate knots and links. In this system, the self-assembly of a topologically complex macrocycle is thermodynamically favored only if an optimum packing of all its components minimizes the hydrophobic surface area in contact with water. Therefore, the size, geometry, and rigidity of the initial building blocks can be exploited to control the formation of a specific topology. We illustrate the validity of this concept with the syntheses of a Hopf link, a Solomon link, and a trefoil knot. This latter molecule, whose self-assembly is templated by halides, binds iodide with high affinity in water. Overall, this work brings a fresh perspective on the synthesis of topologically complex molecules: Solvophobic effects can be intentionally harnessed to direct the efficient and selective self-assembly of knots and links.
By braiding non-Abelian anyons it is possible to realize fault-tolerant quantum algorithms through the computation of Jones polynomials. So far, this has been an experimentally formidable task. In this Letter, a photonic quantum system employing two-photon correlations and nondissipative imaginary-time evolution is utilized to simulate two inequivalent braiding operations of Majorana zero modes.
Ordered media often support vortex structures with intriguing topological properties. Here, we investigate non-Abelian vortices in tetrahedral order using the mathematical formalism of colored links. Due to the generality of our methods, the results apply to all physical systems governed by tetrahedral order, such as the cyclic phase of spin-2 Bose-Einstein condensates and the tetrahedratic phase of bent-core nematic liquid crystals.
A subtle interplay between the flexibility of the 2,2'-bipyridyl-based diamine and the denticity of the coordination domain formed upon self-assembly enabled the formation of four distinct topologies stabilised by [Ag···Ag]2+ pairs. The reactions utilising 2,6-diformylpyridine resulted in the formation of silver(I)-stabilised molecular tweezer, trefoil knot, and Solomon link. The 1,8-naphthyridine-based dialdehyde promoted the formation of [2]catenanes and trefoil knot, demonstrating very close AgI···AgI distances.
The study focuses on the complex development of teeth in vertebrates, utilizing advanced genomic techniques to explore how teeth are formed and organized over time and space.
It identifies twelve spatial compartments and seventeen unique cell clusters that play crucial roles in tooth development, revealing that most lineage species appear earlier in the tooth bud than previously thought.
The research uncovers a new mode of tooth tissue arrangement and highlights the interplay between mechanical signals and biochemical processes in driving tooth formation, while also linking genes to tooth abnormalities.
- Topological data analysis has gained traction in data science, but traditional knot theory struggles with practical use due to localization and quantization issues.
- The introduction of knot data analysis (KDA) integrates curve segmentation and multiscale analysis into the Gauss link integral (mGLI), enabling a better understanding of global and local topological structures in data.
- By combining mGLI with machine learning techniques, KDA outperforms existing methods on 13 complex biological datasets, paving the way for a new research area called "knot deep learning."
