Flexible and Efficient Inference with Particles for the Variational Gaussian Approximation

Variational inference is a powerful framework, used to approximate intractable posteriors through variational distributions. The de facto standard is to rely on Gaussian variational families, which come with numerous advantages: they are easy to sample from, simple to parametrize, and many expectations are known in closed-form or readily computed by quadrature. In this paper, we view the Gaussian variational approximation problem through the lens of gradient flows. We introduce a flexible and efficient algorithm based on a linear flow leading to a particle-based approximation. We prove that, with a sufficient number of particles, our algorithm converges linearly to the exact solution for Gaussian targets, and a low-rank approximation otherwise. In addition to the theoretical analysis, we show, on a set of synthetic and real-world high-dimensional problems, that our algorithm outperforms existing methods with Gaussian targets while performing on a par with non-Gaussian targets.     

The Mixmaster Universe in a generalized uncertainty principle framework

The Bianchi IX cosmological model is analyzed in a generalized uncertainty principle framework. The Arnowitt–Deser–Misner reduction of the dynamics is performed and a time-coordinate, namely the volume of the Universe, naturally arises. Such a variable is treated in the ordinary way while the anisotropies (the physical degrees of freedom) are described by a deformed Heisenberg algebra. The analysis of the model (passing through Bianchi I and II) is performed at classical level by studying the modifications induced on the symplectic geometry by the deformed algebra. We show that the Universe cannot isotropize because of the deformed Kasner dynamics, the triangular allowed domain is asymptotically stationary with respect to the particle (Universe) and its bounces against the walls are not interrupted by the deformed effects. Furthermore, no reflection law can be in general obtained since the Bianchi II model is no longer analytically integrable. This way, the deformed Mixmaster Universe can be still considered as a chaotic system.     

An X-ray Crystallographic Study of 1,4-Di[(<Emphasis Type="Italic">E</Emphasis>)-2-(<Emphasis Type="Italic">p</Emphasis>-tolyl)-1-diazenyl]piperazine

Abstract  

The crystal structure of methyl 1,4-di[(E)-2-(p-tolyl)-1-diazenyl]piperazine (4) has been determined by single crystal X-ray diffraction analysis. The bis-triazene (4) adopts a normal chair conformation in the piperazine ring, with puckering parameters : φ₂ = −29(5)°, Q_T = 0.534(2) ? and θ₂ = 177.0(2)°. The crystal structure of 4 is compared with the structure of the triazene (2a) and the closely related bis-triazenes (3 and 5a). The piperazine ring of 2a and 4 adopt a typical chair conformation, whereas the piperazine ring of 3 adopts an unusual pseudo-boat conformation. Crystal data: 4 C₁₈H₂₂N₆, triclinic, space group P[`1] P\overline{1} , a = 6.8925(2) ?, b = 7.8574(3) ?, c = 16.8856(8) ?, α = 103.103(2)°, β = 90.528(2)°, γ = 101.776(2)° and V = 870.44 (6) ?³, for Z = 2.     

Bell-type inequalities to detect true n-body nonseparability

We analyze the structure of correlations among more than two quantum systems. We introduce a classification of correlations based on the concept of nonseparability, which is different a priori from the concept of entanglement. Generalizing a result of Svetlichny [Phys. Rev. D 35, 3066 (1987)] on three-particle correlations, we find an inequality for n-particle correlations that holds under the most general separability condition and that is violated by some quantum-mechanical states.     

Proposal for energy-time entanglement of quasiparticles in a solid-state device

We present a proposal for the experimental observation of energy-time entanglement of quasiparticles in mesoscopic physics. This type of entanglement arises whenever correlated particles are produced at the same time and this time is uncertain in the sense of quantum uncertainty, as has been largely used in photonics. We discuss its feasibility for electron-hole pairs. In particular, we argue that junctions between materials in which electrons and holes, respectively, propagate ballistically and behave as "entanglers" for energy-time entanglement when irradiated with a continuous laser.     

The calculation of London coefficients by the variation-perturbation method

The London coefficients for the dispersion interaction between LiLi, BeBe and LiBe are calculated by the variation-perturbation method using the whole atomic hamiltonian as H₀ and the Hartree-Fock approximation for the upper turbed wavefunction ?₀. A single excited valence configuration with optimized orbital exponents gives accurate results for Li, whereas comparable accuracy for Be is obtained when part of the valence correlation energy in the ground as well as in the excited state is accounted for through a limited configuration interaction.     

Dissipation-driven phase transition in two-dimensional Josephson arrays

We analyze the interplay of dissipative and quantum effects in the proximity of a quantum phase transition. The prototypical system is a resistively shunted two-dimensional Josephson junction array, studied by means of an advanced Fourier path-integral Monte Carlo algorithm. The reentrant superconducting-to-normal phase transition driven by quantum fluctuations, recently discovered in the limit of infinite shunt resistance, persists for moderate dissipation strength but disappears in the limit of small resistance. For large quantum coupling our numerical results show that, beyond a critical dissipation strength, the superconducting phase is always stabilized at sufficiently low temperature. Our phase diagram explains recent experimental findings.     

A straightforward enantioselective route to dialkyl sulfoxides based upon two carbon-for-carbon substitution reactions on the sulfinyl group

Benzyl p-bromophenyl sulfoxide 1 was obtained on a multigram scale and in an enantiomerically pure form by an enantioselective catalytic oxidation, using tert-butyl hydroperoxide in the presence of chiral titanium complexes. Some mechanistic and stereochemical features of interest were studied in this process. Compound 1 was then subjected to two different substitution reactions with Grignard reagents, which caused two sequentially stereocontrolled carbon-for-carbon displacements, leading to chiral nonracemic dialkyl sulfoxides.