Catastrophes in the multi-fractal dynamics of social-economic systems

In the present paper, the concept of multi-fractal dynamics is developed. The problem concerning catastrophes in this dynamics is studied in detail. In the framework of the concept of fractal curve as a thick curve, it is proved that the cell approach to measuring the fractal dimension D is equivalent to measuring the dependence of the length L of the line on the scope δ. The introduction of a fractal scale of temperatures T ^f is suggested.     

Synthesis of asymmetrical bis(arene) iron complexes

Visible light irradiation of the [(η-C₆H₇)Fe(η-C₆H₆)]⁺ cation (1) in CH₂Cl₂ in the presence of alkyl-substituted benzenes results in arene exchange forming the [(η⁵-C₆H₇)Fe(η-C₆R₆)]⁺ cations (2a–d: C₆R₆ is toluene, p-xylene, mesitylene, and durene). The mixed bis(arene) [(η-C₆H₆)Fe(η-C₆R₆)]²⁺ iron complexes (3a–d) were synthesized by hydride ion abstraction from 2a–d by [Ph₃C]⁺. Dedicated to Academician G. A. Abakumov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1864–1865, September, 2007.     

Synthesis and rearrangements of aminosubstituted ferra- and ruthenatricarbaboranes

A room-temperature reaction between the [7-tBuNH-nido-7,8,9-C3B8H10]- anion (1a) and [Cp*RuCl]4 leads to the ruthenatricarbollide [1-Cp*-12-tBuNH-1,2,4,12-RuC3B8H10] (2) (yield 85%). Analogously, the room-temperature photochemical reaction of 1a with [CpFe(C6H6)]PF6 gives the previously reported iron complex [1-Cp-12-tBuNH-1,2,4,12-FeC3B8H10] (3) (yield 82%). Both reactions are associated with extensive polyhedral rearrangement, which occurs under very mild conditions and brings the carbon atoms to positions of maximum separation within the framework. Compounds 2 and 3 were also surprisingly obtained via complexation of the isomeric [8-tBuNH-nido-7,8,9-C3B8H10]- (1b) anion. Complex 2 rearranges further to [1-Cp*-10-tBuNH-1,2,4,10-RuC3B8H10] (4) upon refluxing in xylene (145 degrees C). Density functional theory calculations at the B3LYP/SDD level were used to estimate relative stabilities of these metallacarborane isomers. Compounds 2 and 4, along with the 11-vertex closo compounds [1-Cp*-1,2,3,10-RuC3B7H10] (5) and [1-Cp*-10-tBuNH-1,2,3,10-RuC3B7H9] (6), were also isolated from the reaction between [Cp*RuCl2]2 and 1a in boiling xylene. The structure of 2 was established by an X-ray diffraction study, and the constitution of all compounds was determined unambiguously by multinuclear NMR spectroscopy, mass spectrometry, and elemental analyses.     

Selective Ruthenium Labeling of the Tryptophan Residue in the Bee Venom Peptide Melittin

Melittin is a membrane‐active peptide from bee venom with promising antimicrobial and anticancer activity. Herein we report on a simple and selective method for labeling of the tryptophan residue in melittin by the organometallic fragment [(C₅H₅)Ru]⁺ in aqueous solution and in air. Ruthenium coordination does not disturb the secondary structure of the peptide (as verified by 2D NMR spectroscopy), but changes the pattern of its intermolecular interactions resulting in an 11‐fold decrease of hemolytic activity. The high stability of the organometallic conjugate allowed the establishment of the biodistribution of the labeled melittin in mice by inductively coupled plasma MS analysis of ruthenium.     

Signal recovery by the generalized Kotel’nikiov series

The problem of the test signal recovery is urgent during the monitoring of the current state of a dynamical system. Such a signal is usually wideband with respect to frequency, has steep leading and trailing edges, and a short duration in the time domain. Under actual conditions, it should be recovered from a small sample of readouts (measurements) at the system output. In this paper, we propose a method of the signal recovery by the generalized Kotel’nikov series for the subsequent estimation of its parameters in the time and frequency domains. The method is more efficient than the existing signal-recovery methods. Its efficiency is confirmed by the quantitative-analysis results. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 8, pp. 712–717, August 2006.     

A description of autostable models

Models that are uniformly autostable in various senses are studied. The general criterion of autostability is cited, and we argue that it cannot be transposed into a general sufficient condition of autostability. We establish model-theoretic criteria of autostability in degree 0′, both for the whole class of recursive models and some of its main subclasses. Supported by RFFR grant No. 096-01-01525. Translated fromAlgebra i Logika, Vol. 36, No. 1, pp. 26–36, January–February, 1997.     

π-complexes of monoanionic carborane ligand [9-(Me2S)-7,8-C2B9H10]− with [η-C5R5Fe]+ (R=H, Me) and [η-C4Me4Co]+ cationic fragments

Compounds (η-C₅R₅)Fe[η-9-(Me₂S)-7,8-C₂B₉H₁₀] (R=H, Me) and (η-C₄Me₄)Co[η-9-(Me₂S)-7,8-C₂B₉H₁₀] were synthesized by the reactions of Na[9-(Me₂S)-7,8-C₂B₉H₁₀] with complexes [(η-C₅H₅)Fe(MeCN)₃]PF₆, [(η-C₅Me₅)Fe(MeCN)₃]BF₄, and [(η-C₄Me₄)Co(MeCN)₃]PF₆, respectively. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 177–179, January, 1999.     

(Indenyl)iridacarborane (η<Superscript>5</Superscript>-indenyl)Ir(η-7,8-C<Subscript>2</Subscript>B<Subscript>9</Subscript>H<Subscript>11</Subscript>): synthesis,structure, and bonding

A reaction of iodide [(η⁵-indenyl)IrI₂]_n (1) with thallium dicarbollide Tl[Tl(η-7,8-C₂B₉H₁₁)] leads to (indenyl)iridacarborane (η⁵-indenyl)Ir(η-7,8-C₂B₉H₁₁) (2) in 32% yield. The X-ray diffraction study showed that in the structure of 2, the five-membered rings C₅ and C₂B₃ have a cisoid conformation, in which the bridgehead carbon atoms of the indenyl ligand are arranged opposite to the carborane cage carbon atoms. The DFT calculations showed that the Ir—indenyl bond in compound 2 is weaker than the Ir—Cp bond in the complex (η-7,8-C₂B₉H₁₁)IrCp.     

Efficient delivery of Cre-recombinase to neurons in vivo and stable transduction of neurons using adeno-associated and lentiviral vectors

Background

As development proceeds the human embryo attains an ever more complex three dimensional (3D) structure. Analyzing the gene expression patterns that underlie these changes and interpreting their significance depends on identifying the anatomical structures to which they map and following these patterns in developing 3D structures over time. The difficulty of this task greatly increases as more gene expression patterns are added, particularly in organs with complex 3D structures such as the brain. Optical Projection Tomography (OPT) is a new technology which has been developed for rapidly generating digital 3D models of intact specimens. We have assessed the resolution of unstained neuronal structures within a Carnegie Stage (CS)17 OPT model and tested its use as a framework onto which anatomical structures can be defined and gene expression data mapped.

Results

Resolution of the OPT models was assessed by comparison of digital sections with physical sections stained, either with haematoxylin and eosin (H&E) or by immunocytochemistry for GAP43 or PAX6, to identify specific anatomical features. Despite the 3D models being of unstained tissue, peripheral nervous system structures from the trigeminal ganglion (~300 μm by ~150 μm) to the rootlets of cranial nerve XII (~20 μm in diameter) were clearly identifiable, as were structures in the developing neural tube such as the zona limitans intrathalamica (core is ~30 μm thick). Fourteen anatomical domains have been identified and visualised within the CS17 model. Two 3D gene expression domains, known to be defined by Pax6 expression in the mouse, were clearly visible when PAX6 data from 2D sections were mapped to the CS17 model. The feasibility of applying the OPT technology to all stages from CS12 to CS23, which encompasses the major period of organogenesis for the human developing central nervous system, was successfully demonstrated.

Conclusion

In the CS17 model considerable detail is visible within the developing nervous system at a minimum resolution of ~20 μm and 3D anatomical and gene expression domains can be defined and visualised successfully. The OPT models and accompanying technologies for manipulating them provide a powerful approach to visualising and analysing gene expression and morphology during early human brain development.