On solving integral equations using Markov chain Monte Carlo methods

In this paper, we propose an original approach to the solution of Fredholm equations of the second kind. We interpret the standard Von Neumann expansion of the solution as an expectation with respect to a probability distribution defined on a union of subspaces of variable dimension. Based on this representation, it is possible to use trans-dimensional Markov chain Monte Carlo (MCMC) methods such as Reversible Jump MCMC to approximate the solution numerically. This can be an attractive alternative to standard Sequential Importance Sampling (SIS) methods routinely used in this context. To motivate our approach, we sketch an application to value function estimation for a Markov decision process. Two computational examples are also provided.     

Reconstruction of physics objects at the Circular Electron Positron Collider with Arbor

After the Higgs discovery, precise measurements of the Higgs properties and the electroweak observables become vital for the experimental particle physics. A powerful Higgs/Z factory, the Circular Electron Positron Collider (CEPC) is proposed. The Particle Flow oriented detector design is proposed to the CEPC and a Particle Flow algorithm, Arbor is optimized accordingly. We summarize the physics object reconstruction performance of the Particle Flow oriented detector design with Arbor algorithm and conclude that this combination fulfills the physics requirement of CEPC.     

Tackling N-Alkyl Imines with 3d Metal Catalysis: Highly Enantioselective Iron-Catalyzed Synthesis of α-Chiral Amines

A readily activated iron alkyl precatalyst effectively catalyzes the highly enantioselective hydroboration of N-alkyl imines. Employing a chiral bis(oxazolinylmethylidene)isoindoline pincer ligand, the asymmetric reduction of various acyclic N-alkyl imines provided the corresponding α-chiral amines in excellent yields and with up to >99 % ee. The applicability of this base metal catalytic system was further demonstrated with the synthesis of the pharmaceuticals Fendiline and Tecalcet.     

Directed Gas Phase Formation of Silene (H2SiCH2)

The silene molecule (H₂SiCH₂; X¹A₁) has been synthesized under single collision conditions via the bimolecular gas phase reaction of ground state methylidyne radicals (CH) with silane (SiH₄). Exploiting crossed molecular beams experiments augmented by high-level electronic structure calculations, the elementary reaction commenced on the doublet surface through a barrierless insertion of the methylidyne radical into a silicon-hydrogen bond forming the silylmethyl (CH₂SiH₃; X²A′) complex followed by hydrogen migration to the methylsilyl radical (SiH₂CH₃; X²A′). Both silylmethyl and methylsilyl intermediates undergo unimolecular hydrogen loss to silene (H₂SiCH₂; X¹A₁). The exploration of the elementary reaction of methylidyne with silane delivers a unique view at the widely uncharted reaction dynamics and isomerization processes of the carbon–silicon system in the gas phase, which are noticeably different from those of the isovalent carbon system thus contributing to our knowledge on carbon silicon bond couplings at the molecular level.     

Linearizability of d-webs, d ≥ 4, on two-dimensional manifolds

We find d − 2 relative differential invariants for a d-web, d ≥ 4, on a two-dimensional manifold and prove that their vanishing is necessary and sufficient for a d-web to be linearizable. If one writes the above invariants in terms of web functions f(x, y) and g ₄(x, y),..., g _d (x, y), then necessary and sufficient conditions for the linearizabilty of a d-web are two PDEs of the fourth order with respect to f and g ₄, and d − 4 PDEs of the second order with respect to f and g ₄,..., g _d . For d = 4, this result confirms Blaschke’s conjecture on the nature of conditions for the linearizabilty of a 4-web. We also give the Mathematica codes for testing 4- and d-webs (d > 4) for linearizability and examples of their usage.     

Biodegradable and Biocompatible Silatrane Polymers

In this study, new biodegradable and biocompatible amphiphilic polymers were obtained by modifying the peripheral hydroxyl groups of branched polyethers and polyesters with organosilicon substituents. The structures of the synthesized polymers were confirmed by NMR and GPC. Organosilicon moieties of the polymers were formed by silatranes and trimethylsilyl blocks and displayed hydrophilic and hydrophobic properties, respectively. The effect of the ratio of hydrophilic to hydrophobic organosilicon structures on the surface activity and biological activity of macromolecules was studied, together with the effect on these activities of the macromolecules’ molecular weight and chemical structure. In particular, the critical micelle concentrations were determined, the effect of the structure of the polymers on their wetting with aqueous solutions on glass and parafilm was described, and the aggregation stability of emulsions was studied. Finally, the effect of the polymer structures on their antifungal activity and seed germination stimulation was examined.     

Natural products from medicinal plants: non-alkaloidal natural constituents of the Thalictrum species

Thalictrum is an important plant genus that is widely used in traditional medicine. In this review considerable attention has been given to triterpenoid saponins in connection with their specific distribution in the Thalictrum genus and with their biological activity. All other non-alkaloid compounds isolated from the Thalictrum genus are also reviewed; these metabolites are discussed in relation to their structural features and to their role in the plants.     

Interactions of multicationic bis(guanidiniocarbonylpyrrole) receptors with double-stranded nucleic acids: syntheses, binding studies, and atomic force microscopy imaging

Compounds 1-3, composed of two guanidiniocarbonylpyrrole moieties linked by oligoamide bridges and differing in number and type of basic groups, were prepared. The sites and degree of protonation of 1-3 depend strongly on the pH value. The interactions of these compounds with several double-stranded (ds) DNA and dsRNA were investigated by means of UV/Vis and CD spectroscopy as well as isothermal titration microcalorimetry (ITC). These studies revealed that the binding of 1-3 to the polynucleotides is driven by three factors, the presence of aliphatic amino groups, the protonation state of the compounds, and the steric properties of the polynucleotide binding site, that is, the shape and structure of their grooves. The results obtained by all applied methods consistently indicated that receptors 1-3 bind to the minor groove of DNA, but, by contrast, to the major groove of RNA. Additionally, it was shown by atomic force microscopy (AFM) imaging that upon interaction of compound 2 with calf thymus (ct) DNA induced aggregation of the DNA occurs, leading to pronounced changes in its secondary structure.