The investigation of molecular chirality within interlocked molecules is an appealing research area however, the synthesis of optically active interlocked molecules poses considerable challenges. In this study, we combined chiral spiroborate formation with the chiral recognition of secondary ammonium ions by a borate-containing crown macrocycle to synthesise optically active pseudo[2]rotaxanes from an achiral bis-catechol, chiral amines and boric acid. We examined how the chiral centres in amines influence the stereoselectivity of pseudo[2]rotaxanes under kinetic and thermodynamic conditions. Because the reversible borate-forming reaction creates a dynamic covalent bond between B and O, it facilitates the stereoselective formation of optically active pseudo[2]rotaxanes, achieving a diastereoselectivity of up to 40 : 1. After isolating the pseudo[2]rotaxanes, X-ray crystallography, circular dichroism spectroscopy and density functional theory calculations were used to reveal their absolute configuration.
A group of temperate grassland plant species, referred to as the 'Mansen elements,' is found in Japan and extensively distributed in the grasslands of continental East Asia. It has been considered that these species are remnants of once-expanded grasslands in Japan during a colder geological era. However, the detailed phylogeographic history, including migration age and distributional changes within Japan for these species, remains unresolved. To elucidate the phylogeographic history of the Mansen elements, we investigated the genetic structure and phylogeny of the populations ofPulsatilla cernua, one of the Mansen elements, using single-nucleotide polymorphisms (SNPs) obtained from multiplexed inter-simple sequence repeat genotyping by sequencing (MIG-seq). The phylogenetic analysis indicates a continental origin and migration route via the Korean Peninsula for P. cernua. The DIYABC and the genetic structure analyses suggest that the divergence between the continental and Japanese populations occurred the late stage of the Last Glacial Period (LGP). Although the estimated divergence time is not fully constrained, it is suggested that an initial expansion in Japan occurred before the Last Glacial Maximum (LGM). This once-expanded distribution area was subsequently fragmented during the coldest climate, followed by a secondary expansion after the LGP. This represents the first documented instance among the Mansen element species in which secondary range expansion brought fragmented populations into secondary contact.
When a (non-)Abelian gauge field acquires an isotropic background configuration during inflation, strong gravitational waves (GWs) with parity-violating polarization, known as chiral GWs, can be produced in addition to the intrinsic unpolarized GWs. However, previous studies have analyzed individual models, leaving the generality of this phenomenon unclear. To perform a model-independent analysis, we construct an effective field theory (EFT) of chiral GWs by extending the EFT of inflation and incorporating gauge fields. The resulting action unifies inflationary models with a SU(2) gauge field, such as chromo-natural inflation and gauge-flation, and ones with a triplet of U(1) gauge fields, systematically encompassing all possible GW production mechanisms consistent with the symmetry breaking induced by the gauge field background. We find that chiral GWs are generically and inevitably produced, provided that the effective energy density of the background gauge field is positive and the gauge kinetic function is not fine-tuned to a specific time dependence. This EFT offers a useful foundation for future phenomenological studies as well as for deepening our theoretical understanding of chiral GWs.
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of continuous functions on the shift space contains two disjoint subsets: one is a dense $G_\delta $ set for which all maximizing measures have 'relatively small' entropy; the other is the set of functions having uncountably many, fully supported ergodic maximizing measures with 'relatively large' entropy. This result generalizes and unifies the results of Morris [Discrete Contin. Dyn. Syst. 27 (2010), 383-388] and Shinoda [Nonlinearity 31 (2018), 2192-2200] on symbolic dynamics, and applies to a wide class of intrinsically ergodic non-Markov symbolic dynamics without the Bowen specification property, including any transitive piecewise monotonic interval map, some coded shifts, and multidimensional $\beta $ -transformations. Along with these examples of application, we provide an example of an intrinsically ergodic subshift with positive obstruction entropy to specification.
We study the crossing matrix of a braid and introduce a polynomial invariant for braid systems that is invariant under Hurwitz equivalence. As an application to the study of surface braids and surface links, we also define an invariant that can be used as an indicator of the necessity of Euler fusion or fission between braid systems.
