Sampling the Variational Posterior with Local Refinement

Variational inference is an optimization-based method for approximating the posterior distribution of the parameters in Bayesian probabilistic models. A key challenge of variational inference is to approximate the posterior with a distribution that is computationally tractable yet sufficiently expressive. We propose a novel method for generating samples from a highly flexible variational approximation. The method starts with a coarse initial approximation and generates samples by refining it in selected, local regions. This allows the samples to capture dependencies and multi-modality in the posterior, even when these are absent from the initial approximation. We demonstrate theoretically that our method always improves the quality of the approximation (as measured by the evidence lower bound). In experiments, our method consistently outperforms recent variational inference methods in terms of log-likelihood and ELBO across three example tasks: the Eight-Schools example (an inference task in a hierarchical model), training a ResNet-20 (Bayesian inference in a large neural network), and the Mushroom task (posterior sampling in a contextual bandit problem).     

Enhancement of the SPR Effect in an Optical Fiber Device Utilizing a Thin Ag Layer and a 3092A Liquid Crystal Mixture

This paper is a continuation of previous work and shows the enhancement of the surface plasmon resonance effect in a tapered optical fiber device. The study investigated liquid crystal cells containing a tapered optical fiber covered with a silver nanolayer, surrounded by a low refractive index liquid crystal in terms of the properties of light propagation in the taper structure. Silver films with a thickness of d = 10 nm were deposited on the tapered waist area. Measurements were performed at room temperature; liquid crystal steering voltage U from 0 to 200 V, with and without any amplitude modulation with a frequency of f = 5 Hz, and the wavelength λ ranged from 550 to 1200 nm. A significant influence of the initial arrangement of liquid crystals molecules on light propagation was observed. Three types of liquid crystal cells—orthogonal, parallel, and twist—were considered. During the measurements, resonant peaks were obtained—the position of which can also be controlled by the type of liquid crystal cells and the steering voltage. Based on the obtained results, the best parameters, such as highest peak’s width reduction, and the highest SNR value were received for twisted cells. In addition, the present work was compared with the previous work and showed the possibility of improving properties of the manufactured probes, and consequently, the surface plasmon resonance effect. In the presented paper, the novelty is mainly focused on the used materials as well as suitable changes in applied technological parameters. In contrast to gold, silver is characterized by different optic and dielectric properties, e.g., refractive index, extension coefficient, and permittivity, which results in changes in the light propagation and the SPR wavelengths.     

Characterization of tri-o-methylcellulose by one- and two-dimensional NMR methods

Tri-O-methylcellulose was prepared from partially O-methylated cellulose and its chemical shifts (¹H and ¹³C), and proton coupling constants were assigned using the following NMR methods: (1) One-dimensional ¹H and ¹³C spectra of the title compound were used to assign functional groups and to compare with literature data; (2) double quantum filtered proton–proton correlation spectroscopy (¹H, ¹H DQF-COSY) was used to assign the chemical shifts of the network of 7 protons in the anhydroglucose portion of the repeat unit; (3) the heteronuclear single-quantum coherence (HSQC) spectrum was used to establish connectivities between the bonded protons and carbons; (4) the heteronuclear multiple-bond correlation (HMBC) spectrum was used to connect the hydrogens of the methyl ethers to their respective sugar carbons; (5) the combination of HSQC and HMBC spectra was used to assign the ¹³C shifts of the methyl ethers; (6) all spectra were used in combination to verify the assigned chemical shifts; (7) first-order proton coupling constants data (J_H,H in Hz) were obtained from the resolution-enhanced proton spectra. The NMR spectra of tri-O-methylcellulose and other cellulose ethers do not resemble the spectra of similarly substituted cellobioses. Although the ¹H and ¹³C shifts and coupling constants of 2,3,6-tri-O-methylcellulose closely resemble those of methyl tetra-O-methyl-β-D -glucoside, there are differences with regard to the chemical shifts and the order of appearances of the resonating nuclei of the methyl ether appendages and the proton at position 4 in the pyranose ring. H4 in tri-O-methylcellulose is deshielded by the acetal system comprising the β-1→4 linkage, and it resonates downfield. H4 in the permethylated glucoside is not as deshielded by the equitorial O-methyl group at C4, and it resonates upfield. The order of appearance of the ¹H and ¹³C resonances in the spectra of the tri-O-methylcellulose repeat unit (from upfield to downfield) are H2 < H3 < H5 < H6a < H3a < H2a < pro R H6B < H4 < pro S H6A ≪ H1 and C6a < C3a < C2a < C6 < C5 < C4 < C2 < C3 ≪ C1, respectively. Close examination of the pyranose ring coupling constants of the repeat unit in tri-O-methylcellulose supports the ⁴C₁ arrangement of the glucopyranose ring. Examination of the proton coupling constants about the C5-C6 bond (J_5,6A and J_5,6B) in the nuclear Overhauser effect difference spectra revealed that the C6 O-methyl group is predominantly in the gauche gauche conformation about the C5-C6 bond for the polymer in solution. © 1999 John Wiley & Sons, Inc.* J Polym Sci A: Polym Chem 37: 4019–4032, 1999     

Herstellung von 6,14-Ethenomorphinan-Derivaten

Zusammenfassung Dihydronorthevinon (2b) wurde aus Dihydrothevinon (2a) mit Azodicarbonsäurediethylester (DEAD) hergestellt und zu einigen neuen N-substituierten Dihydronorthevinon-Derivaten (2c–2g) umgesetzt. Es wurdenGrignard-Reaktionen dieser Verbindungen mit Methylmagnesiumiodid bzw.tert-Butylmagnesiumchlorid durchgeführt. O-Demethylierungen von3a–3j ergaben die entsprechenden N-substituierten Buprenorphin- bzw. Diprenorphin-Analoga4a–4j.

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Preparation of 6,14-ethenomorphinan derivatives

Summary Dihydronorthevinone (2b) was prepared from dihydrothevinone (2a) with diethyl azodicarboxylate (DEAD) and transformed into a number of new N-substituted dihydronorthevinone derivatives (2c–2g).Grignard reactions of the new compounds with methylmagnesium iodide andtert-butyl-magnesium chloride were studied. O-Demethylation of3a–3j resulted in the corresponding N-substituted buprenorphine and diprenorphine analogs4a–4j.

     

Random quantum operations

We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Φ associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of Φ and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state.     

Locking entanglement with a single qubit

We study the loss of entanglement of a bipartite state subjected to discarding or measurement of one qubit. Examining behavior of different entanglement measures, we find that entanglement of formation, entanglement cost, logarithmic negativity, and one-way distillable entanglement are lockable measures in that they can decrease arbitrarily after measuring one qubit. We prove that any convex and asymptotically noncontinuous measure is lockable. As a consequence, all the convex-roof measures can be locked. The relative entropy of entanglement is shown to be a nonlockable measure.     

Cross-metathesis reaction of vinyl sulfones and sulfoxides

Cross-metathesis reactions of α,β-unsaturated sulfones and sulfoxides in the presence of molybdenum and ruthenium pre-catalysts were tested. A selective metahesis reaction was achieved between functionalized terminal olefins and vinyl sulfones by using the ‘second generation’ ruthenium catalysts 1c-h while the highly active Schrock catalyst 1b was found to be functional group incompatible with vinyl sulfones. The cross-metathesis products were isolated in good yields with an excellent (E)-selectivity. Both the molybdenum and ruthenium-based complexes were, however, incompatible with α,β- and β,γ-unsaturated sulfoxides.     

The inclusion-exclusion principle for <Emphasis Type=Italic>IF</Emphasis>-events

The inclusion-exclusion principle is one of the basic theorems in combinatorics. In this paper the inclusion-exclusion principle for IF-sets on generalized probability measures is studied. The basic theorems are proved.     

Scaling laws of complex band random matrices

We study a model of complex band random matrices capable of describing the transitions between three different ensembles of Hermitian matrices: Gaussian orthogonal, Gaussian unitary and Poissonian. Analyzing numerical data we observe new scaling relations based on the generalized localization length of eigenvectors. We show that during transitions between canonical ensembles of random matrices the changes of statistical properties of eigenvalues and eigenvectors are correlated.     

Enhancement of a 24.77-nm line emitted by the plasma of a boron nitride capillary discharge irradiated by a high-intensity ultrashort laser pulse

Investigations of plasma produced by a boron nitride capillary discharge irradiated with a guided 20-TW Ti: sapphire laser pulse at a peak intensity of 4 x 10(18) W/cm2 are presented. The guided laser radiation in the plasma channel generated He-like ions that, subject to suitable plasma temperature, recombined into Li-like nitrogen ions. Intense radiation at a wavelength of 24.77 nm was observed, indicating possible lasing at the 3d(5/2) - 2p(3/2) transition in Li-like nitrogen.