On the law of the iterated logarithm for the discrepancy of 〈n k x〉

By a well known result of Philipp (1975), the discrepancy D _N (ω) of the sequence (n _k ω) _k≥1 mod 1 satisfies the law of the iterated logarithm under the Hadamard gap condition n _{k + 1}/n _k ≥ q > 1 (k = 1, 2, …). Recently Berkes, Philipp and Tichy (2006) showed that this result remains valid, under Diophantine conditions on (n _k ), for subexpenentially growing (n _k ), but in general the behavior of (n _k ω) becomes very complicated in the subexponential case. Using a different norming factor depending on the density properties of the sequence (n _k ), in this paper we prove a law of the iterated logarithm for the discrepancy D _N (ω) for subexponentially growing (n _k ) without number theoretic assumptions. C. Aistleitner, Research supported by FWF grant S9603-N13. I. Berkes, Research supported by FWF grant S9603-N13 and OTKA grants K 61052 and K 67961. Authors’ addresses: C. Aistleitner, Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria; I. Berkes, Institute of Statistics, Graz University of Technology, Steyrergasse 17/IV, 8010 Graz, Austria     

Metabolic network dynamics in open chaotic flow

We have analyzed the dynamics of metabolically coupled replicators in open chaotic flows. Replicators contribute to a common metabolism producing energy-rich monomers necessary for replication. The flow and the biological processes take place on a rectangular grid. There can be at most one molecule on each grid cell, and replication can occur only at localities where all the necessary replicators (metabolic enzymes) are present within a certain neighborhood distance. Due to this finite metabolic neighborhood size and imperfect mixing along the fractal filaments produced by the flow, replicators can coexist in this fluid system, even though coexistence is impossible in the mean-field approximation of the model. We have shown numerically that coexistence mainly depends on the metabolic neighborhood size, the kinetic parameters, and the number of replicators coupled through metabolism. Selfish parasite replicators cannot destroy the system of coexisting metabolic replicators, but they frequently remain persistent in the system. (c) 2002 American Institute of Physics.     

Modeling the active site of cytochrome oxidase: synthesis and characterization of a cross-linked histidine-phenol

A cross-linked histidine-phenol compound was synthesized as a chemical analogue of the active site of cytochrome c oxidase. The structure of the cross-linked compound (compound 1) was verified by IR, (1)H and (13)C NMR, mass spectrometry, and single-crystal X-ray analysis. Spectrophotometric titrations indicated that the pK(a) of the phenolic proton on compound 1 (8.34) was lower than the pK(a) of tyrosine (10.1) or of p-cresol (10.2). This decrease in pK(a) is consistent with the hypothesis that a cross-linked histidine-tyrosine may facilitate proton delivery to the binuclear site in cytochrome c oxidase. Time-resolved optical absorption spectra of compound 1 at room temperature, generated by excitation at 266 nm in the presence and absence of dioxygen, indicated a species with absorption maxima at approximately 330 and approximately 500 nm, which we assign to the phenoxyl radical of compound 1. The electron paramagnetic resonance (EPR) spectra of compound 1, obtained after UV photolysis, confirmed the generation of a paramagnetic species at low temperature. Because the cross-linked compound lacks beta-methylene protons, the EPR line shape was dramatically altered when compared to that of the tyrosyl radical. However, simulation of the EPR line shape and measurement of the isotropic g value was consistent with a small coupling to the imidazole nitrogen and with little spin density perturbation in the phenoxyl ring. The ground-state Fourier transform infrared (FT-IR) spectrum of compound 1 showed that addition of the imidazole ring perturbs the frequency of the tyrosine ring stretching vibrations. The difference FT-IR spectrum, associated with the oxidation of the cross-linked compound, detected significant perturbations of the phenoxyl radical vibrational bands. We postulate that phenol oxidation produces a small delocalization of spin density onto the imidazole nitrogen of compound 1, which may explain its unique optical spectral properties.     

Precipitate pattern formation in fluctuating media

Simulation of the Liesegang pattern formation in low concentration gradient is presented using concentration perturbation in a deterministic model. The precipitation process is based on ion-product supersaturation theory (Ostwald's model). In the classical experiments with high initial concentration gradients, appearance time and locations of the band formation are well reproducible. Decreasing initial concentration gradients results in a more stochastic pattern structure; this means that the reproducibility of the experiments becomes worse. The presented model and the results of the simulations exhibit the same trend, which were demonstrated and investigated experimentally by Kai et al.     

Why do grain boundaries exhibit finite facet lengths?

Uniform finite facets are frequently observed at grain boundaries (GBs) and are usually attributed to equilibrium stabilization by GB stress. We report calculations for an aluminum twin GB using density functional theory, the embedded-atom method, and continuum elasticity theory. These methods show that GB stress is much too small to stabilize finite facets, suggesting that the usual explanation is incorrect.     

Localized error bursts in estimating the state of spatiotemporal chaos

We consider the problem of estimating the current state of an evolving spatiotemporally chaotic system from noisy observations of the system state and a model of the system dynamics. Using a simple scheme for state estimation, we show the possible occurrence of temporally and spatially intermittent large bursts in the estimation error. We discuss the similarity of these bursts with those occurring at the bubbling transition in the synchronization of low dimensional chaotic dynamical systems. We characterize the spatial and temporal behavior of the bursts and investigate how the behavior changes as we vary the number and location of the observations.     

A Global Review on Short Peptides: Frontiers and Perspectives

Peptides are fragments of proteins that carry out biological functions. They act as signaling entities via all domains of life and interfere with protein-protein interactions, which are indispensable in bio-processes. Short peptides include fundamental molecular information for a prelude to the symphony of life. They have aroused considerable interest due to their unique features and great promise in innovative bio-therapies. This work focusing on the current state-of-the-art short peptide-based therapeutical developments is the first global review written by researchers from all continents, as a celebration of 100 years of peptide therapeutics since the commencement of insulin therapy in the 1920s. Peptide “drugs” initially played only the role of hormone analogs to balance disorders. Nowadays, they achieve numerous biomedical tasks, can cross membranes, or reach intracellular targets. The role of peptides in bio-processes can hardly be mimicked by other chemical substances. The article is divided into independent sections, which are related to either the progress in short peptide-based theranostics or the problems posing challenge to bio-medicine. In particular, the SWOT analysis of short peptides, their relevance in therapies of diverse diseases, improvements in (bio)synthesis platforms, advanced nano-supramolecular technologies, aptamers, altered peptide ligands and in silico methodologies to overcome peptide limitations, modern smart bio-functional materials, vaccines, and drug/gene-targeted delivery systems are discussed.     

The hydrolysis of unsubstituted N-acylhomoserine lactones to their homoserine metabolites. Analytical approaches using ultra performance liquid chromatography

Derivatives of N-acylhomoserine lactones (HSLs) with different alkanoyl side chains occur as quorum or diffusion sensing molecules in gram-negative bacteria and their quantitative chemical analysis became important as a possible way to follow regulation processes of their pathogenicity towards plants and animals. The lactone-ring of HSLs is chemically and biologically not stable: the corresponding serines can be formed in alkaline conditions and these may presumably behave inactive for the biological system. A fast and MS compatible liquid chromatographic method applying high pressure (ultra performance liquid chromatography) with diode array detection was optimized for the rapid quantitative determination of HSLs and their corresponding hydrolysis products. The technique was used to follow and model the hydrolysis reactions of HSLs as function of pH under controlled conditions. Moreover, the method could be triggered to allow a confirmation in the assignment of the potential HSLs in real samples by analysis of the real samples before and after hydrolysis. Quantitative performance characteristics and the character of the hydrolysis reaction were studied as well. The optimized method was successfully applied to a bacterial culture supernatant real sample containing HSLs.