Sub-linear convergence of a stochastic proximal iteration method in Hilbert space

Computational Optimization and Applications - We consider a stochastic version of the proximal point algorithm for convex optimization problems posed on a Hilbert space. A typical application of...     

Sparse Partially Collapsed MCMC for Parallel Inference in Topic Models

Topic models, and more specifically the class of latent Dirichlet allocation (LDA), are widely used for probabilistic modeling of text. Markov chain Monte Carlo (MCMC) sampling from the posterior distribution is typically performed using a collapsed Gibbs sampler. We propose a parallel sparse partially collapsed Gibbs sampler and compare its speed and efficiency to state-of-the-art samplers for topic models on five well-known text corpora of differing sizes and properties. In particular, we propose and compare two different strategies for sampling the parameter block with latent topic indicators. The experiments show that the increase in statistical inefficiency from only partial collapsing is smaller than commonly assumed, and can be more than compensated by the speedup from parallelization and sparsity on larger corpora. We also prove that the partially collapsed samplers scale well with the size of the corpus. The proposed algorithm is fast, efficient, exact, and can be used in more modeling situations than the ordinary collapsed sampler. Supplementary materials for this article are available online.     

Three-dimensional spiral waves in an excitable reaction system: initiation and dynamics of scroll rings and scroll ring pairs

We report experimental results on spiral and scroll waves in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. The propagating concentration waves are detected by two-dimensional photometry and optical tomography. Wave pulses can disappear in front-to-front and front-to-back collisions. This anomaly causes the nucleation of vortices from collisions of three nonrotating waves. In three-dimensional systems, these vortices are scroll rings that rotate around initially circular filaments. Depending on reactant concentrations, the filaments shrink or expand indicating positive and negative filament tensions, respectively. Shrinkage results in vortex annihilation. Expansion is accompanied by filament buckling and bending, which is interpreted as developing Winfree turbulence. We also describe the initiation of scroll ring pairs in four-wave collisions. The two filaments are stacked on top of each other and their motion suggests filament repulsion.     

Favorskii-type rearrangement of α-chloro ketimines

The first examples of the Favorskii-type rearrangement of α-monochloro ketimines are reported. The regiospecific opening of the intermediate cyclopropylideneamines parallels the opening of cyclopropanones under Favorskii-conditions.     

On the exchange of cyanide with acetonitrile. A test of theoretical calculations

- The theoretically predicted formation of an adduct between cyanide and anhydrous acetonitrile was tested experimentally; no evidence for such a complex was found. The previously reported radioactivity loss in the reactions of cyanide - ¹⁴C in acetonitrile solutions was possibly due to protonation and loss of hydrogen cyanide, since no exchange between cyanide and acetonitrile was evidenced within the sensitivity limits of ¹³C labelling. Potassium cyanide and carbonate in the presence of 18-crown-6 ether catalyze the H/D exchange between acetonitrile and trideuteroacetonitrile.     

The Endomorphism Monoid of the Random Graph has Uncountably Many Ideals

In this note we prove that the monoid End(R) of all endomorphisms of the random graph R is not simple. On the contrary, the lattice of ideals of End(R) embeds the poset of all subsets of , the set of natural numbers.     

Spectrophotometric determination of chloride in plants

This indirect spectrophotometric determination of chloride in plants is based on displacement of thiocyanate from mercury(II) thiocyanate. Thiocyanate is extracted into nitrobenzene as tris(l,10-phenanthroline)iron(II) thiocyanate for measurement at 516 nm. Accuracy and precision are similar to those of the Volhard method but only about 2–200 mg samples are needed.     

Emission spectroscopic and ODMR studies of the lowest excited triplet state of dichlorophenylborane

The triplet state T₁ of dichlorophenylborane (PhBCl₂) has been investigated by optical emission and ODMR spectroscopic methods in order to study the influence of substituents with mesomeric and inductive effects. The zero-field splitting (ZFS) parameters D and E, the selective kinetic rates of radiative and non-radiative deactivation of the triplet sublevels and the phosphorescence spectrum were measured. From the small value of D = 0.1201 cm^?1 a considerable charge transfer admixture to the ³L_a state of benzene has to be assumed. The ratio of the radiative rates shows a distortion of the molecule. Further a heavy atom effect of the chlorine atoms on the in-plane rates of the deactivation of T₁ can be observed.