Dynamics of social group competition: modeling the decline of religious affiliation

When social groups compete for members, the resulting dynamics may be understandable with mathematical models. We demonstrate that a simple ordinary differential equation (ODE) model is a good fit for religious shift by comparing it to a new international data set tracking religious nonaffiliation. We then generalize the model to include the possibility of nontrivial social interaction networks and examine the limiting case of a continuous system. Analytical and numerical predictions of this generalized system, which is robust to polarizing perturbations, match those of the original ODE model and justify its agreement with real-world data. The resulting predictions highlight possible causes of social shift and suggest future lines of research in both physics and sociology.     

A Visible‐Light‐Mediated Radical Smiles Rearrangement and its Application to the Synthesis of a Difluoro‐Substituted Spirocyclic ORL‐1 Antagonist

A visible‐light‐mediated radical Smiles rearrangement has been developed to address the challenging synthesis of the gem‐difluoro group present in an opioid receptor‐like 1 (ORL‐1) antagonist that is currently in development for the treatment of depression and/or obesity. This method enables the direct and efficient introduction of the difluoroethanol motif into a range of aryl and heteroaryl systems, representing a new disconnection for the synthesis of this versatile moiety. When applied to the target compound, the photochemical step could be conducted on 15 g scale using industrially relevant [Ru(bpy)₃Cl₂] catalyst loadings of 0.01 mol %. This transformation is part of an overall five‐step route to the antagonist that compares favorably to the current synthetic sequence and demonstrates, in this specific case, a clear strategic benefit of photocatalysis.     

Facile Synthesis and Properties of 2‐λ5‐Phosphaquinolines and 2‐λ5‐Phosphaquinolin‐2‐ones

Treatment of 2‐ethynylanilines with P(OPh)₃ gives either 2,2‐diphenoxy‐2‐λ⁵‐phosphaquinolines or 2‐phenoxy‐2‐λ⁵‐phosphaquinolin‐2‐ones under transition‐metal‐free conditions. This reaction offers access to an underexplored heterocycle, which opens up the study of the fundamental nature of the N?P^V double bond and its potential for delocalization within a cyclic π‐electron system. This heterocycle can serve as a carbostyril mimic, with application as a bioisostere for pharmaceuticals based on the 2‐quinolinone scaffold. It also holds promise as a new fluorophore, since initial screening reveals quantum yields upwards of 40 %, Stokes shifts of 50–150 nm, and emission wavelengths of 380–540 nm. The phosphaquinolin‐2‐ones possess one of the strongest solution‐state dimerization constants for a D–A system (130 M ^?1) owing to the close proximity of a strong acceptor (P?O) and a strong donor (phosphonamidate N? H), which suggests that they might hold promise as new hydrogen‐bonding hosts for optoelectronic sensing.