Entropy conditions for subsequences of random variables with applications to empirical processes

We introduce new entropy concepts measuring the size of a given class of increasing sequences of positive integers. Under the assumption that the entropy function of is not too large, many strong limit theorems will continue to hold uniformly over all sequences in . We demonstrate this fact by extending the Chung-Smirnov law of the iterated logarithm on empirical distribution functions for independent identically distributed random variables as well as for stationary strongly mixing sequences to hold uniformly over all sequences in . We prove a similar result for sequences (n _k ω) mod 1 where the sequence (n _k ) of real numbers satisfies a Hadamard gap condition. Authors’ addresses: István Berkes, Department of Statistics, Technical University Graz, Steyrergasse 17/IV, A-8010 Graz, Austria; Walter Philipp, Department of Statistics, University of Illinois, 725 S. Wright Street, Champaign, IL 61820, USA; Robert F. Tichy, Department of Analysis and Computational Number Theory, Technical University Graz, Steyrergasse 30, A-8010 Graz, Austria     

On the inner structure and topology of clusters in two-component lipid bilayers. Comparison of monomer and dimer Ising models

It has been shown on model and biological systems that membrane clusters can affect in-plane membrane reactions and can control biochemical reaction cascades. Clusters of two-component phospholipid bilayers have been simulated by two Ising-type lattice models: the monomer and the dimer model. In each model the plane of one layer of the bilayer is represented by a triangular lattice, each site of which is occupied by an acyl chain of either a component 1 or a component 2 lipid molecule. The dimer model assumes that pairs of acyl chains (lipid molecules) are permanently connected, forming dimers on the lattice, while in the case of the monomer model this covalent connection between acyl chains is ignored. Phase diagrams of two-component phospholipid bilayers were successfully calculated by both models. In this work, we use Monte Carlo techniques to calculate thermodynamic averages of global and local characteristics of the largest component 2 cluster (such as outer/inner perimeter, percolation, minimal linear size, and local density) and compare the results obtained by the two models. A new method is developed to characterize the inner structure of the clusters. Each point of a cluster is classified based on its shortest distance (or depth) from the cluster's outer perimeter. Then local cluster properties, such as density, are calculated as a function of the depth. The depth analysis reveals that toward the cluster interior the average density usually decreases in midsize clusters and remains constant in very large clusters. On the basis of the simulations the following typical cluster topologies are identified at different cluster sizes and cooperativity parameter values: (i) branch-like, (ii) circular, (iii) band-like, and (iv) planar.We did not find qualitative differences between the cluster structures in the dimer and monomer model. However, at the same cluster size and cooperativity parameter value the cluster of the dimer model is more compact. The cluster properties of the dimer model are different from that of the monomer model because of the lower mixing entropy and higher formation energy of an elementary inner island.     

Patterns of the ferrocyanide-iodate-sulfite reaction revisited: the role of immobilized carboxylic functions

We experimentally demonstrate that the standing lamella reaction-diffusion patterns initially observed 17 years ago in a gel-filled open spatial reactor operated with the ferrocyanide-iodate-sulfite bistable reaction requires an upper critical concentration of low-mobility species with weak acid functional groups, a parameter that was overlooked at the time and had made observations difficult to reproduce. The present approach enables the control of the space scale separation between activatory and inhibitory processes. It makes the wealth of exotic pattern dynamics observed earlier easier to reproduce and understand. This contribution should considerably revive the interest in this reaction and boost the search for the control of reaction-diffusion patterns in other bistable systems.     

Didepside Formation by the Nonreducing Polyketide Synthase Preu6 of Preussia isomera Requires Interaction of Starter Acyl Transferase and Thioesterase Domains

Orsellinic acid (OA) derivatives are produced by filamentous fungi using nonreducing polyketide synthases (nrPKSs). The chain-releasing thioesterase (TE) domains of such nrPKSs were proposed to also catalyze dimerization to yield didepsides, such as lecanoric acid. Here, we use combinatorial domain exchanges, domain dissections and reconstitutions to reveal that the TE domain of the lecanoric acid synthase Preu6 of Preussia isomera must collaborate with the starter acyl transferase (SAT) domain from the same nrPKS. We show that artificial SAT-TE fusion proteins are highly effective catalysts and reprogram the ketide homologation chassis to form didepsides. We also demonstrate that dissected SAT and TE domains of Preu6 physically interact, and SAT and TE domains of OA-synthesizing nrPKSs may co-evolve. Our work highlights an unexpected domain–domain interaction in nrPKSs that must be considered for the combinatorial biosynthesis of unnatural didepsides, depsidones, and diphenyl ethers.     

OPLC Comparison of Methods for Aqueous Extraction of Sennae folium and Tiliae flos Plant Samples

JPC – Journal of Planar Chromatography – Modern TLC - A new, simplified open-vessel microwave extraction (OVME) method has been used to prepare aqueous extracts of Sennae folium and...     

Fully On-Line Hyphenation of an Experimental OPLC Separation Unit with Diode-Array Detection and Mass-Spectrometry (OPLC-DAD-MS) for Analysis of Xanthine Compounds

JPC – Journal of Planar Chromatography – Modern TLC - The newly developed experimental OPLC separation unit 100 (OSU 100) has been used for fully on-line multiple hyphenation using the...     

Molecular complexation and binding studied by electrophoretic NMR spectroscopy

Electrophoretic mobilities obtained on a molecularly selective manner by electrophoretic NMR can be used to provide a quantitative characterization of the composition and stoichiometry of molecular complexes. This is demonstrated in complexes formed by uncharged cyclodextrins which attain an electrophoretic mobility upon inclusion of charged surfactants.     

Influence of oxidative injury and monitoring of blood plasma by DSC on breast cancer patients

Damage caused by oxidative stress is involved in many types of diseases, including breast cancer. Our aim was to detect the oxidative stress parameters and blood plasma changes with differential scanning calorimetry (DSC) in breast cancer patients. The study included 40 adult breast cancer women who were grouped according to tumor diameter, regional lymph node metastases, proliferative activity, receptor status and postoperative chemotherapy. To monitor oxidative stress, malondialdehyde, oxygen free radicals (OFRs), activity of myeloperoxidase (MPO), superoxide dismutase (SOD) and catalase (CAT) were measured. Denaturation of plasma components was detected in Setaram Micro DSC-II calorimeter. The total production of OFRs, the MPO activity and lipidperoxidation were significantly increased in each breast cancer patients considering the tumor size, the metastatic lymph nodes, the proliferation activity and receptor status compared with healthy controls (p < 0.05). These pro-oxidants were slightly elevated without chemotherapy, but their values were increased significantly in chemotherapy-receiving group. The activity of SOD and CAT was significantly decreased in all groups, and in regard to the chemotherapy, they were changed significantly parallel to the severity of disease. Regarding to both the increased tumor diameter and the increased number of affected lymph nodes, DSC measurements showed a strong relationship between the maximum excess heat capacity (C_pmax) of the blood plasma and the severity of disease. The study demonstrated that oxidative stress is implicated in breast carcinoma and chemotherapy aggravates these changes which confirmed the plasma DSC measurements also.     

Skorokhod embeddings for two-sided Markov chains

Let \((X_n :n\in \mathbb {Z})\) be a two-sided recurrent Markov chain with fixed initial state \(X_0\) and let \(\nu \) be a probability measure on its state space. We give a necessary and sufficient criterion for the existence of a non-randomized time T such that \((X_{T+n} :n\in \mathbb {Z})\) has the law of the same Markov chain with initial distribution \(\nu \). In the case when our criterion is satisfied we give an explicit solution, which is also a stopping time, and study its moment properties. We show that this solution minimizes the expectation of \(\psi (T)\) in the class of all non-negative solutions, simultaneously for all non-negative concave functions \(\psi \).