Crown reductions for the Minimum Weighted Vertex Cover problem

The paper studies crown reductions for the Minimum Weighted Vertex Cover problem introduced recently in the unweighted case by Fellows et al. [Blow-Ups, Win/Win's and crown rules: some new directions in FPT, in: Proceedings of the 29th International Workshop on Graph Theoretic Concepts in Computer Science (WG’03), Lecture notes in computer science, vol. 2880, 2003, pp. 1-12, Kernelization algorithms for the vertex cover problem: theory and experiments, in: Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX), New Orleans, Louisiana, January 2004, pp. 62-69]. We describe in detail a close relation of crown reductions to Nemhauser and Trotter reductions that are based on the linear programming relaxation of the problem. We introduce and study the so-called strong crown reductions, suitable for finding (or counting) all minimum vertex covers, or finding a minimum vertex cover under some additional constraints. It is described how crown decompositions and strong crown decompositions suitable for such problems can be computed in polynomial time. For weighted König-Egerváry graphs (G,w) we observe that the set of vertices belonging to all minimum vertex covers, and the set of vertices belonging to no minimum vertex covers, can be efficiently computed.Further, for some specific classes of graphs, simple algorithms for the MIN-VC problem with a constant approximation factor r<2 are provided. On the other hand, we conclude that for the regular graphs, or for the Hamiltonian connected graphs, the problem is as hard to approximate as for general graphs.It is demonstrated how the results about strong crown reductions can be used to achieve a linear size problem kernel for some related vertex cover problems.     

Small camera as a handheld colorimetric tool in the analytical chemistry

Recently, there is an effort to introduce new types of analytical procedures and handheld assays to provide simple and reliable equipment for the field and household analyses. Development of diagnostic tools for self-diagnosis is another challenge in analytical chemistry. Digital cameras are widely available and cheap, hence they could be the sensor platform for construction of analytical and diagnostic methods. In general, good availability of cameras integrated into smartphones can be easily converted into an analytical tool. This review relates to the use of digital camera in analytical chemistry and there are introduced the facts how digital data can be processed and what the limits of digital photography are. Recent papers in this issue and discussion of development in camera based assays is also provided here.     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

K3TaF8 from laboratory X‐ray powder data

The crystal structure of tripotassium octafluoridotantalate, K₃TaF₈, determined from laboratory powder diffraction data by the simulated annealing method and refined by total energy minimization in the solid state, is built from discrete potassium cations, fluoride anions and monocapped trigonal–prismatic [TaF₇]²⁻ ions. All six atoms in the asymmetric unit are in special positions of the P6₃mc space group: the Ta and one F atom in the 2b (3m) sites, the K and two F atoms in the 6c (m) sites, and one F atom in the 2a (3m) site. The structure consists of face‐sharing K₆ octahedra with a fluoride anion at the center of each octahedron, forming chains of composition [FK₃]²⁺ running along [001] with isolated [TaF₇]²⁻ trigonal prisms in between. The structure of the title compound is different from the reported structure of Na₃TaF₈ and represents a new structure type.     

Regioisomeric analysis of triacylglycerols using silver-ion liquid chromatography-atmospheric pressure chemical ionization mass spectrometry: comparison of five different mass analyzers

Silver-ion high-performance liquid chromatography (HPLC) coupled to atmospheric pressure chemical ionization mass spectrometry (APCI-MS) is used for the regioisomeric analysis of triacylglycerols (TGs). Standard mixtures of TG regioisomers are prepared by the randomization reaction from 8 mono-acid TG standards (tripalmitin, tristearin, triarachidin, triolein, trielaidin, trilinolein, trilinolenin and tri-gamma-linolenin). In total, 32 different regioisomeric doublets and 11 triplets are synthesized, separated by silver-ion HPLC using three serial coupled chromatographic columns giving a total length of 75cm. The retention of TGs increases strongly with the double bond (DB) number and slightly for regioisomers having more DBs in sn-1/3 positions. DB positional isomers (linolenic vs. γ-linolenic acids) are also separated and their reverse retention order in two different mobile phases is demonstrated. APCI mass spectra of all separated regioisomers are measured on five different mass spectrometers: single quadrupole LC/MSD (Agilent Technologies), triple quadrupole API 3000 (AB SCIEX), ion trap Esquire 3000 (Bruker Daltonics), quadrupole time-of-flight micrOTOF-Q (Bruker Daltonics) and LTQ Orbitrap XL (Thermo Fisher Scientific). The effect of different types of mass analyzer on the ratio of [M+H-R(i)COOH](+) fragment ions in APCI mass spectra is lower compared to the effect of the number of DBs, their position on the acyl chain and the regiospecific distribution of acyl chains on the glycerol skeleton. Presented data on [M+H-R(i)COOH](+) ratios measured on five different mass analyzers can be used for the direct regioisomeric determination in natural and biological samples.     

Trap-assisted tunnelling current in MIM structures

A new model is presented of current transport in Metal Insulator Metal (MIM) structures by quantum mechanical tunnelling. In addition to direct tunnelling through an insulating layer, tunnelling via defects present in the insulating layer plays an important role. Examples of the influence of the material and thickness of the insulating layer, energy distribution of traps, and metal work functions are also provided.     

TiO2 thick films supported on reticulated macroporous Al2O3 foams and their photoactivity in phenol mineralization

TiO₂ thick films deposited on macroporous reticulated Al₂O₃ foams with pore size of 10 ppi and 15 ppi were prepared using dip coating from slurries of Aeroxide^® P25 nanopowder and precipitated titania. All prepared films have sufficiently good adhesion to the surface of the substrate also in case of strongly cracked films. No measurable release of deposited TiO₂ after repeated photocatalytic cycles was observed. The photocatalytic activity was characterized as the rate of mineralization of aqueous phenol solution under irradiation of UVA light by TOC technique. The best activity was obtained with Aeroxide^® P25 coated Al₂O₃ foam with the pore size of 10 ppi, annealed at 600 °C. The optimal annealing temperature for preparation of films from precipitated titania could be determined at 700 °C. Films prepared by sol-gel deposition technique were considerably thinner compared to coatings made of suspensions and their photocatalytic activity was significantly smaller.     

Sufficient Stochastic Maximum Principle for Discounted Control Problem

In this article, the sufficient Pontryagin’s maximum principle for infinite horizon discounted stochastic control problem is established. The sufficiency is ensured by an additional assumption of concavity of the Hamiltonian function. Throughout the paper, it is assumed that the control domain \(U\) is a convex bounded set and the control may enter the diffusion term of the state equation. The general results are applied to the controlled stochastic logistic equation of population dynamics.