Exact relaxations of non-convex variational problems

Here, we solve non-convex, variational problems given in the form

Stereoselective one-pot synthesis of oxazolines

Treatment of alkenes with NBS, a nitrile, NaHCO3 and water in the presence of Cu(OTf)2 or Zn(OTf)2 is reported to furnish oxazolines in one pot and good yields. The reaction is equally applicable to chalcones.     

Deacylative 1,6-addition of Bestmann-Ohira reagent to p-quinone methides for the synthesis of α-diazo-β-diarylphosphonates and cis-stilbenyl phosphonates

The role of Bestmann-Ohira Reagent (BOR) as a conjugate addition partner is reported for the first time. Deacylation of BOR in the presence of ethanolic KOH and 1,6-addition of the resulting diazophosphonate anion to p-quinone methides (PQMs) provides β-disubstituted α-diazophosphonates in good to excellent yields in most cases. Such 1,6-adducts further undergo Rh-catalyzed elimination of the diazo group and 1,2-migration of the phenolic group to afford cis-stilbenylphosphonates with high E-selectivity. The migration of the phenolic group presumably takes place via a spirocyclopropane intermediate derived from the Rh-carbenoid.     

Dynamics of Coordinate Ascent Variational Inference: A Case Study in 2D Ising Models

Variational algorithms have gained prominence over the past two decades as a scalable computational environment for Bayesian inference. In this article, we explore tools from the dynamical systems literature to study the convergence of coordinate ascent algorithms for mean field variational inference. Focusing on the Ising model defined on two nodes, we fully characterize the dynamics of the sequential coordinate ascent algorithm and its parallel version. We observe that in the regime where the objective function is convex, both the algorithms are stable and exhibit convergence to the unique fixed point. Our analyses reveal interesting discordances between these two versions of the algorithm in the region when the objective function is non-convex. In fact, the parallel version exhibits a periodic oscillatory behavior which is absent in the sequential version. Drawing intuition from the Markov chain Monte Carlo literature, we empirically show that a parameter expansion of the Ising model, popularly called the Edward–Sokal coupling, leads to an enlargement of the regime of convergence to the global optima.     

Unitary tridiagonalization inM(4, ⫳)

A question of interest in linear algebra is whether alln xn complex matrices can be unitarily tridiagonalized. The answer for alln ≠ 4 (affirmative or negative) has been known for a while, whereas the casen = 4 seems to have remained open. In this paper we settle then = 4 case in the affirmative. Some machinery from complex algebraic geometry needs to be used.     

Interference due to coherence swapping

We propose a method called ‘coherence swapping’ which enables us to create superposition of a particle in two distinct paths, which is fed with initially incoherent, independent radiation. This phenomenon is also present for the charged particles, and can be used to swap the effect of flux line due to the Aharonov-Bohm effect. We propose an optical version of experimental set-up to test the coherence swapping. The phenomenon, which is simpler than entanglement swapping or teleportation, raises some fundamental questions about the true nature of wave-particle duality, and also opens up the possibility of studying the quantum erasure from a new angle.     

Combining Traceless Directing Groups with Hybridization Control of Radical Reactivity: From Skipped Enynes to Defect‐Free Hexagonal Frameworks

This work discloses the first general solution for converting oligoalkynes into polyaromatic polycyclic systems free of pentagonal defects. The efficiency and selectivity of this cascade originate from the combination of the Bu₃Sn‐mediated TDG (traceless directing group) cascade transformations of skipped alkynes where the reactivity of the key radical precursor is tempered by hybridization effects. This approach ensures that the final structure consists of only six‐membered rings. Practical implementation of this strategy is readily accomplished by incorporation of a suitably‐substituted alkene as a final unit in the domino transformation. This strategy opens a new avenue for the controlled preparation of polyaromatic ribbons. The resulting ester functionality can be used for an additional Friedel–Crafts ring closure which effectively anneals two extra cycles with distinct electronic features to the extended aromatic system formed by the radical cascade.