On the correlation structure of some random point processes on the line

The correlation structure of some remarkable point processes on the one-dimensional real line is investigated. More specifically, focus is on translation invariant determinantal, permanental and/or renewal point processes. In some cases, anomalous (non-Poissonian) fluctuations for the number of points in a large window can be observed. This may be read from the total correlation function of the point process. We try to understand when and why this occurs and what are the anomalous behaviors to be expected.From examples, it is shown that determinantal (fermion) point processes can be super-homogeneous (the number variance grows slower than the number mean) and even hyper-uniform (when variance growth saturates).Renewal point processes with bounded spacings variance are essentially Poissonian (the number variance grows like the number mean as in Poisson models).Under certain conditions, permanental (boson) point processes can be sub-homogeneous or critical (in the sense that the number variance grows faster than the number mean).We give several detailed examples illustrating these properties of interest together with unexpected behaviors.     

Synthesis of pulvinones via tandem Dieckmann condensation-alkoxide β-elimination

A series of pulvinones were prepared in three steps from a common precursor, methyl 3-phenylglycidate. This compound was readily converted to several diesters containing an ether function. Then, treatment of these compounds with lithium hexamethyldisilazide afforded the corresponding pulvinones, via tandem Dieckmann condensation-alkoxide β-elimination. The use of a 2,2,2-trifluoroethyl ether instead of a methyl ether facilitated the β-elimination and led to better yields of product.     

Efficient Large-Scale Preparation of Phenyl 3-Pyridazinyl Ketone1

A convenient approach to phenyl 3-pyridazinyl ketone 4 permitting economical large scale preparation is proposed. Commercially available 3,6-dichloropyridazine 1 serves as the starting material in the three-step process.     

A Convenient Synthesis of 2H-Pyran-2-one Derivatives

A simple procedure for the synthesis of 2H-pyran-2-ones 1 is described: selective Wittig olefination of keto aldehydes at the aldehyde group followed by a cyclization in acidic medium.     

Thermal analysis of the ω nanophase transformation from the metastable β Ti–12Mo alloy

In this study, the thermal analysis of the ω nanophase transformation from a quenched metastable β Ti–12Mo alloy composition (mass%) was investigated by electrical resistivity and dilatometry measurements. The activation energy was observed to be 121 ± 20 kJ mol⁻¹ (from resistivity measurements) and 114 ± 12 kJ mol⁻¹ (from dilatometry measurements) during the early stage of the transformation process. The kinetic of the ω nanophase transformation was modelized by using the classical Johnson–Mehl–Avrami (JMA) theory and a modified Avrami (MA) analysis. An Avrami exponent close to 1.5 was found at the early stage of the transformation suggesting a pure growth mechanism from pre-existing nucleation sites. Nevertheless, it was observed a decrease of the Avrami exponent to 0.5 at higher transformed fraction demonstrating a dimension loss in the growth mechanism due to the existence of the high misfit strain at the interface β/ω.     

Topological Complexity of the Relative Closure of a Semi-Pfaffian Couple

Gabrielov introduced the notion of relative closure of a Pfaffian couple as an alternative construction of the o-minimal structure generated by Khovanskii’s Pfaffian functions. In this paper, we use the notion of format (or complexity) of a Pfaffian couple to derive explicit upper bounds for the homology of its relative closure. We consider both the singular and the Borel–Moore homology theories.     

Role of the Protein Cavity in Phytochrome Chromoprotein Assembly and Double-bond Isomerization: A Comparison with Model Compounds

Difference patterns of ¹³C NMR chemicals shifts for the protonation of a free model compound in organic solution, as reported in the literature (M. Stanek, K. Grubmayr [1998] Chem. Eur. J. 4 , 1653–1659), were compared with changes in the protonation state occurring during holophytochrome assembly from phycocyanobilin (PCB) and the apoprotein. Both processes induce identical changes in the NMR signals, indicating that the assembly process is linked to protonation of the chromophore, yielding a cationic cofactor in a heterogeneous, quasi-liquid protein environment. The identity of both difference patterns implies that the protonation of a model compound in solution causes a partial stretching of the geometry of the macrocycle as found in the protein. In fact, the similarity of the difference pattern within the bilin family for identical chemical transformations represents a basis for future theoretical analysis. On the other hand, the change of the ¹³C NMR chemical shift pattern upon the Pr → Pfr photoisomerization is very different to that of the free model compound upon ZZZ → ZZE photoisomerization. Hence, the character of the double-bond isomerization in phytochrome is essentially different from that of a classical photoinduced double-bond isomerization, emphasizing the role of the protein environment in the modulation of this light-induced process.