De Rham Cohomology and Hodge Decomposition For Quantum Groups

Let be one of the N²-dimensionalbicovariant first order differential calculi for the quantumgroups GL_q(N), SL_q(N), SO_q(N), or Sp_q(N), where q is a transcendentalcomplex number and z is a regular parameter. It is shown thatthe de Rham cohomology of Woronowicz' external algebra coincides with the de Rham cohomologiesof its left-coinvariant, its right-coinvariant and its (two-sided)coinvariant subcomplexes. In the cases GL_q(N) and SL_q(N) thecohomology ring is isomorphic to the coinvariant external algebra and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in thesecases. The main technical tool is the spectral decompositionof the quantum Laplace-Beltrami operator. 2000 MathematicalSubject Classification: 46L87, 58A12, 81R50.     

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.     

Adaptive microphone array for unknown desired speaker's transfer function

The main drawback of minimum variance distortionless response (MVDR) beamformer is the cancellation of the desired speech signal and its degradation in multi-path wave propagation environment. To make the adaptive algorithm robust against room reverberation and to prevent desired signal cancellation an estimation of unknown desired speaker's transfer function was proposed. The estimation is based on the signal and the interference covariance matrices. The estimated transfer function is then applied to the MVDR beamformer. The proposed algorithm was tested on a simulated room with reverberation. The results showed better quality of the restored speech compared to some typical adaptive algorithms.     

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.