Minimizing the number of transitions with respect to observation equivalence

Labeled transition systems (lts) provide an operational semantics for many specification languages. In order to abstract unrelevant details of lts's, manybehavioural equivalences have been defined; here observation equivalence is considered. We are interested in the following problem:Given a finite lts, which is the minimal observation equivalent lts corresponding to it? It is well known that the number of states of an lts can be minimized by applying arelational coarsest partition algorithm. However, the obtained lts is not unique (up to the renaming of the states): for an lts there may exist several observation equivalent lts's which have the minimal number of states but varying number of transitions. In this paper we show how the number of transitions can be minimized, obtaining a unique lts.     

The kink of cellular automaton rule 18 performs a random walk

We give an exact characterization of the movement of a single kink in the elementary cellular automaton Rule 18. It is a random walk with independent increments as well as independent delay times. Its statistical parameters are computed to confirm the earlier simulation results by Grassberger.     

Electronic spectroscopy of C2 in solid rare gas matrixes

Electronic spectroscopy of the C(2) molecule is investigated in Ar, Kr, and Xe matrixes in the 150-500 nm range. In the Ar matrix, the D ((1)Sigma(u)(+)) <-- ((1)Sigma(g)(+)) Mulliken band near 240 nm is the sole absorption in the UV range, whereas in the Kr matrix additional bands in the 188-209 nm range are assigned to the Kr(n)()(+)C(2)(-) <-- Kr(n)()C(2) charge-transfer absorptions. Because of the formation of a bound C(2)Xe species, the spectral observations in the Xe matrix differ dramatically from the lighter rare gases: the Mulliken band is absent and new bands appear near 300 and 423 nm. The latter is assigned to the forbidden B'((1)Sigma(g)(+)) <-- X ((1)Sigma(g)(+)) transition, but the origin of the former remains unclear. The spectral assignments are aided by electronic structure calculations at the MCSCF, CCSD(T), and BCCD(T) levels of theory and correlation consistent basis sets. A significant presence of multireference character of the C(2)Xe system was noted and a linear ground-state structure is predicted. The computational results contradict previous density functional studies on the same system.     

Chiral discrimination of β‐3‐homo‐amino acids using the kinetic method

Chiral discrimination of seven enantiomeric pairs of β‐3‐homo‐amino acids was studied by using the kinetic method and trimeric metal‐bound complexes, with natural and unnatural α‐amino acids as chiral reference compounds and divalent metal ions (Cu²⁺ and Ni²⁺) as the center ions. The β‐3‐homo‐amino acids were selected for this study because, first of all, chiral discrimination of β‐amino acids has not been extensively studied by mass spectrometry. Moreover, these β‐3‐homo‐amino acids studied have different aromatic side chains. Thus, the emphasis was to study the effect of the side chain (electron density of the phenyl ring, as well as the difference between phenyl and benzyl side chains) for the chiral discrimination. The results showed that by the proper choice of a metal ion and a chiral reference compound, all seven enantiomeric pairs of β‐3‐homo‐amino acids could be differentiated. Moreover, it was noted that the β‐3‐homo‐amino acids with benzyl side chains provided higher enantioselectivity than the corresponding phenyl ones. However, increasing or decreasing the electron density of the aromatic ring by different substituents in both the phenyl and benzyl side chains had practically no role for chiral discrimination of β‐3‐homo‐amino acids studied. When copper was used as the central metal, the phenyl side chain containing reference molecules (S)‐2‐amino‐2‐phenylacetic acid (L ‐Phg) and (S)‐2‐amino‐2‐(4‐hydroxyphenyl)‐acetic acid (L ‐4′‐OHPhg) gave rise to an additional copper‐reduced dimeric fragment ion, [Cu^I(ref)(A)]⁺. The inclusion of this ion improved noticeably the enantioselectivity values obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Assessment of labelled products with different radioanalytical methods: study on 18F-fluorination reaction of 4-[18F]fluoro-N-[2-[1-(2-methoxyphenyl)-1-piperazinyl]ethyl-N-2-pyridinyl-benzamide (p-[18F]MPPF)

The serotonin receptor 5-HT_1A ligand 4-[¹⁸F]fluoro-N-[2-[1-(2-methoxyphenyl)-1-piperazinyl]ethyl-N-2-pyridinyl-benzamide (p-[¹⁸F]MPPF) was produced by a simplified method of Le Bars et al. Traditional oil bath heating was compared to microwave heating. Various radioanalytical methods, radio-Thin Layer Chromatography (TLC), High Pressure Liquid Chromatography (HPLC) and Mass Spectrometry (MS), were compared in the evaluation of the labelled product(s). The crude reaction mixture consisted of p-[¹⁸F]MPPF and 2–4 radioactive by-products eluting after the product fraction, and the reverse-phase HPLC method failed occasionally to separate p-[¹⁸F]MPPF from the radioactive by-product with close retention time. The heating method had no significant effect on the composition of labelled by-products. In LC-(ESI)-MS analysis of p-[¹⁸F]MPPF the labelled product was identified with m/z ratio of 435 ([M + H⁺]). The other HPLC fractions were measured to have following m/z ratios: (1) 327; 349; (675) (2) 402; 407/408; (791) and (3) 436, suggesting different kind of decomposition of the labelled product and/or the inactive precursor. The ion trap mass spectrometer was sufficient for the qualitative analysis of p-[¹⁸F]MPPF. However, differentiation of by-products arising from the decomposition of p-[¹⁸F]MPPF or from its precursor p-MPPNO₂ proved to be challenging.     

The dynamics of defect ensembles in one-dimensional cellular automata

We investigate the dynamics of ensembles of diffusive defects in one-dimensional deterministic cellular automata. The work builds on earlier results on individual random walks in cellular automata. Here we give a natural condition guaranteeing diffusive behavior also in the presence of other defects. Simple branching and birth mechanisms are introduced and prototype classes of cellular automata exhibiting weakly interacting walks capable of annihilation and coalescence are studied. Their equilibrium behavior is also characterized. The design principles of cellular automata with desired diffusive interaction properties become transparent from this analysis.     

Measuring turbulence energy with PIV in a backward-facing step flow

Turbulence energy is estimated in a backward-facing step flow with three-component (3C, stereo) particle image velocimetry (PIV). Estimates of turbulence energy transport equation for convection, turbulence transport, turbulence production, viscous diffusion, and viscous dissipation in addition to Reynolds stresses are computed directly from PIV data. Almost all the turbulence energy terms in the backward-facing step case can be measured with 3C PIV, except the pressure-transport term, which is obtained by difference of the other turbulence energy terms. The effect of the velocity spatial sampling resolution in derivative estimations is investigated with four two-dimensional PIV measurement sets. This sampling resolution information is used to calibrate the turbulence energies estimated by 3C PIV measurements. The focus of this study is on the separated shear layer of the backward-facing step. The measurements with 3C PIV are carried out in a turbulent water flow at Reynolds number of about 15,000, based on the step height h and the inlet streamwise maximum mean velocity U₀. The expansion ratio (ER) is 1.5. Turbulence energy budget profiles in locations x/h=4, x/h=6, and x/h=10 are compared with DNS data of a turbulent flow. The shapes of profiles agree well with each other. Different ERs between the PIV case (1.5) and the DNS case (1.2) cause higher values for the turbulence energies measured by PIV than the energies by DNS when x/h=10 is approached. PIV results also show that the turbulence energy level in these experiments is generally higher than that of the DNS data.     

Characterisation of proanthocyanidin aglycones and glycosides from rose hips by high-performance liquid chromatography-mass spectrometry, and their rapid quantification together with vitamin C

Fifteen individual proanthocyanidin aglycones and 19 glycosides, together with a complex mixture of chromatographically non-separated tetra- to octameric proanthocyanidin glycosides were detected--the non-separated glycosides being novel natural products--and characterised from dog rose hips using high-performance liquid chromatography-electrospray ionisation mass spectrometry (HPLC-ESI-MS). Along with these phenolics, a 50% aqueous ethanol extract of rose hips was found to contain high levels of Vitamin C. A simple and rapid HPLC method assisted by diode array detection for the estimation of the total concentration of proanthocyanidin aglycones and glycosides, as well as Vitamin C, in rose hip extracts was developed.     

Dense Packing on Uniform Lattices

We study the Hard Core Model on the graphs G obtained from Archimedean tilings i.e. configurations in {0,1} ^G with the nearest neighbor 1’s forbidden. Our particular aim in choosing these graphs is to obtain insight to the geometry of the densest packings in a uniform discrete set-up. We establish density bounds, optimal configurations reaching them in all cases, and introduce a probabilistic cellular automaton that generates the legal configurations. Its rule involves a parameter which can be naturally characterized as packing pressure. It can have a critical value but from packing point of view just as interesting are the noncritical cases. These phenomena are related to the exponential size of the set of densest packings and more specifically whether these packings are maximally symmetric, simple laminated or essentially random packings. Research partially supported by The Finnish Academy of Science and Letters.