Analysis of a Recurrence Related to Critical Nonhomogeneous Branching Processes

Abstract

Some classes of controlled branching processes (with nonhomo-geneous migration or with nonhomo-geneous state-dependent immigration) lead in the critical case to a recurrence for the extinction probabilities. Under some additional conditions it is known that this recurrence depends on some parameter β and converges for 0 < β < 1. Now we show that the recurrence does converge for all positive values of the parameter β, which leads to an extension of some limit theorems for the corresponding branching processes. We also give a generalization of the recurrence and an asymptotic analysis of its behavior.     

Magnetically gated microelectrodes

Microelectrodes fabricated in the center of single-coil microelectromagnetic traps are described. Magnetic particles are then used to reversibly gate transport of an electroactive species to the surface of the electrode or as a means to produce an ON/OFF bioelectrocatalytic glucose sensor.     

Efficient disc on pillar substrates for surface enhanced Raman spectroscopy

In this work, geometrical optimizations of Ag disc on pillar (DOP) hybrid plasmonic nanostructures were conducted and allowed us to achieve reproducible average enhancement factors of 1 × 10(9) and greater.     

A fluorescence quenching study of the complexation of salicylic acid mono- and dianions with the copper(II) ion in aqueous solutions

Fluorescence quenching of the anions of sodium salicylate and sulfosalicylic acid by the Cu²⁺ ion in water has been studied. The Stern-Volmer (SV) curves for all salicylic acid derivatives are concave. Using the modified Stern-Volmer equation, the values of the SV constant K = 1420 ± 70 and 470 ± 20 l/mol were obtained for salicylic (SA) and sulfosalicylic acid (sulfo-SA), respectively. It has been concluded that static quenching (complexation) takes place. The proportions of fluorescing available for quenching were determined to be 0.53 ± 0.02 and 0.66 ± 0.03 for SA and sulfo-SA, respectively. Tentative qualitative interpretation of the difference in the complex formation constants between sodium salicylate and sulfosalicylic acid is given in terms of the concept of difference in the accessibility of the quenching sites of salicylate ions to copper ions owing to the difference in the magnitude of interaction with water molecules.     

On lattice points in polyhedral cross-sections

(a) We prove that the convex hull of anyk ^d +1 points of ad-dimensional lattice containsk+1 collinear lattice points. (b) For a convex polyhedron we consider the numbers of its lattice points in consecutive parallel lattice hyperplanes (levels). We prove that if a polyhedron spans no more than 2 ^d−1 levels, then this string of numbers may be arbitrary. On the other hand, we give an example of a string of 2 ^d−1+1 numbers to which no convex polyhedron corresponds inR ^d .     

Coupled oscillators with power-law interaction and their fractional dynamics analogues

A one-dimensional chain of coupled oscillators with the long-range power-law interactions is considered. Equations of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order α, when 0 < α < 2. The evolution of soliton-like and breather-like structures is obtained numerically and compared for two types of simulations: using the chain of oscillators and using the continuous medium equation with the fractional derivative.     

Local Analysis of Heterogeneous Intracellular Transport: Slow and Fast Moving Endosomes

Trajectories of endosomes inside living eukaryotic cells are highly heterogeneous in space and time and diffuse anomalously due to a combination of viscoelasticity, caging, aggregation and active transport. Some of the trajectories display switching between persistent and anti-persistent motion, while others jiggle around in one position for the whole measurement time. By splitting the ensemble of endosome trajectories into slow moving subdiffusive and fast moving superdiffusive endosomes, we analyzed them separately. The mean squared displacements and velocity auto-correlation functions confirm the effectiveness of the splitting methods. Applying the local analysis, we show that both ensembles are characterized by a spectrum of local anomalous exponents and local generalized diffusion coefficients. Slow and fast endosomes have exponential distributions of local anomalous exponents and power law distributions of generalized diffusion coefficients. This suggests that heterogeneous fractional Brownian motion is an appropriate model for both fast and slow moving endosomes. This article is part of a Special Issue entitled: “Recent Advances In Single-Particle Tracking: Experiment and Analysis” edited by Janusz Szwabiński and Aleksander Weron.     

Room‐Temperature Insulating Ferromagnetic (Ni,Co)1+2xTi1−xO3 Thin Films

Insulating uniaxial room‐temperature ferromagnets are a prerequisite for commonplace spin wave‐based devices, the obstacle in contemporary ferromagnets being the coupling of ferromagnetism with large conductivity. It is shown that the uniaxial A_{1 + 2x}Ti⁴⁺_{1 ? x}O₃ (ATO), A = Ni²⁺,Co²⁺, and 0.6 < x ≤ 1, thin films are electrically insulating ferromagnets already at room temperature. The octahedra network of the ATO and the corundum and ilmenite structures are the same yet different octahedra‐filling proved to be a route to switch from the antiferromagnetic to ferromagnetic regime. Octahedra can continuously be filled up to x = 1, or vacated (?0.24 < x < 0) in the ATO structure. TiO‐layers, which separate the ferromagnetic (Ni,Co)O‐layers and intermediate the antiferromagnetic coupling between the ferromagnetic layers in the NiTiO₃ and CoTiO₃ ilmenites, can continuously be replaced by (Ni,Co)O‐layers to convert the ATO‐films to ferromagnetic insulator with abundant direct cation interactions.     

Migration of poly-L-lysine through a lipid bilayer

When a giant vesicle, composed of neutral and anionic lipid (90:10 mol %), comes into contact with various poly-l-lysines (MW 500-29 300), ropelike structures form within the vesicle interior. By using fluorescence lipids and epi-fluorescence microscopy, we have shown that both neutral and anionic lipids are constituents of the ropes. Evidence that the ropes are also comprised of poly-l-lysine comes from two experiments: (a) direct microinjection of poly(acrylic acid) into rope-containing vesicles causes the ropes to contract into small particles, an observation consistent with a polycation/polyanion interaction; and (b) direct microinjection of fluorescein isothiocyanate (a compound that covalently labels poly-l-lysine with a fluorescent moiety) into rope-containing vesicles leads to fluorescent ropes. The results may be explained by a model in which poly-l-lysine binds to the vesicle exterior, forms a domain, and enters the vesicle through defects or at the domain boundary. The model helps explain the ability of poly-l-lysine to mediate the permeation of a cancer drug, doxorubicine, into the vesicle interior.     

Highly efficient modification of DNA polymerase β under conditions of direct and sensitized activation of photoreactive DNAs. Modification of cell extract proteins

dUTP and dCTP derivatives containing a 4-azido-2,3,5,6-tetrafluorobenzylideneaminooxy group were incorporated into the 3′-end of the DNA primer within complexes with the DNA-matrix as analogs of natural dTTP by virtue of catalytic activity of DNA polymerase β or endogenous DNA polymerases of the cell extract. The photoreactive DNAs synthesized in situ were used for affinity modification of DNA polymerase β and DNA-binding proteins of the cell extract. For the photoreactive DNA based on these analogs, the efficiency of formation of covalent adducts with DNA polymerase β under the highest degree of DNA complexation with the enzyme was determined. The yield of covalent DNA adducts with the enzyme was 28–47%, depending on the type of the analog. The effect of the sequence of the DNA template near the localization of the photoreactive group on the redistribution of covalent cross-links between the possible targets was demonstrated. A possibility of increasing the efficiency of DNA polymerase β modification in the presence of a substantial excess of photoreactive DNA using a sensitizer, a dUTP derivative containing a pyrene residue, was studied. When photoreactive DNA containing a 2,3,5,6-tetrafluoro-4-azidobenzoyl (FAB) group was used, about 60% of DNA polymerase β was covalently attached to DNA. Photoreactive dNTP analogs ensuring a high level of protein modification in the cell extract were found. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1273–1283, May, 2005.