Plancherel Inversion as Unified Approach to Wavelet Transforms and Wigner functions

We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The wavelet transform of a signal is an $L^2$-function on an appropriately chosen group, while the Wigner function is defined on a coadjoint orbit of the group and serves as an alternative characterization of the signal, which is often used in practical applications. The Plancherel transform maps $L^2$-functions on a group unitarily to fields of Hilbert-Schmidt operators, indexed by unitary irreducible representations of the group. The wavelet transform can essentiallly be looked upon as restricted inverse Plancherel transform, while Wigner functions are modified Fourier transforms of inverse Plancherel transforms, usually restricted to a subset of the unitary dual of the group. Some known results both on Wigner functions and wavelet transforms, appearing in the literature from very different perspectives, are naturally unified within our approach. Explicit computations on a number of groups illustrate the theory.Comment: 41 page

How microorganisms use hydrophobicity and what does this mean for human needs?

Cell surface hydrophobicity (CSH) plays a crucial role in the attachment to, or detachment from the surfaces. The influence of CSH on adhesion of microorganisms to biotic and abiotic surfaces in medicine as well as in bioremediation and fermentation industry has both negative and positive aspects. Hydrophobic microorganisms cause the damage of surfaces by biofilm formation; on the other hand, they can readily accumulate on organic pollutants and decompose them. Hydrophilic microorganisms also play a considerable role in removing organic wastes from the environment because of their high resistance to hydrophobic chemicals. Despite the many studies on the environmental and metabolic factors affecting cell surface hydrophobicity (CSH), the knowledge of this subject is still scanty and is in most cases limited to observing the impact of hydrophobicity on adhesion, aggregation or flocculation. The future of research seems to lie in finding a way to managing the microbial adhesion process, perhaps by steering cell hydrophobicity

Detection of inhibitors of Candida albicans Cdr transporters using a diS-C3(3) fluorescence

Candida albicans is a major cause of opportunistic and life-threatening, systemic fungal infections. Hence new antifungal agents, as well as new methods to treat fungal infections, are still needed. The application of inhibitors of drug-efflux pumps may increase the susceptibility of C. albicans to drugs. We developed a new fluorescence method that allows the in vivo activity evaluation of compounds inhibiting of C. albicans transporters. We show that the potentiometric dye 3,3′-dipropylthiacarbocyanine iodide diS-C3(3) is pumped out by both Cdr1 and Cdr2 transporters. The fluorescence labeling with diS-C3(3) enables a real-time observation of the activity of C. albicans Cdr1 and Cdr2 transporters. We demonstrate that enniatin A and beauvericin show different specificities toward these transporters. Enniatin A inhibits diS-C3(3) efflux by Cdr1 while beauvericin inhibits both Cdr1p and Cdr2p

Antiadhesive activity of the biosurfactant pseudofactin II secreted by the Arctic bacterium Pseudomonas fluorescens BD5

<p>Abstract</p> <p>Background</p> <p>Pseudofactin II is a recently identified biosurfactant secreted by <it>Pseudomonas fluorescens </it>BD5, the strain obtained from freshwater from the Arctic Archipelago of Svalbard. Pseudofactin II is a novel compound identified as cyclic lipopeptide with a palmitic acid connected to the terminal amino group of eighth amino acid in peptide moiety. The C-terminal carboxylic group of the last amino acid forms a lactone with the hydroxyl of Thr3.</p> <p>Adhesion is the first stage of biofilm formation and the best moment for the action of antiadhesive and anti-biofilm compounds. Adsorption of biosurfactants to a surface e.g. glass, polystyrene, silicone modifies its hydrophobicity, interfering with the microbial adhesion and desorption processes. In this study the role and applications of pseudofactin II as a antiadhesive compound has been investigated from medicinal and therapeutic perspectives.</p> <p>Results</p> <p>Pseudofactin II lowered the adhesion to three types of surfaces (glass, polystyrene and silicone) of bacterial strains of five species: <it>Escherichia coli, Enterococcus faecalis, Enterococcus hirae, Staphylococcus epidermidis, Proteus mirabilis </it>and two <it>Candida albicans </it>strains. Pretreatment of a polystyrene surface with 0.5 mg/ml pseudofactin II inhibited bacterial adhesion by 36-90% and that of <it>C. albicans </it>by 92-99%. The same concentration of pseudofactin II dislodged 26-70% of preexisting biofilms grown on previously untreated surfaces. Pseudofactin II also caused a marked inhibition of the initial adhesion of <it>E. faecalis, E. coli, E. hirae </it>and <it>C. albicans </it>strains to silicone urethral catheters. The highest concentration tested (0.5 mg/ml) caused a total growth inhibition of <it>S. epidermidis</it>, partial (18-37%) inhibition of other bacteria and 8-9% inhibition of <it>C. albicans </it>growth.</p> <p>Conclusion</p> <p>Pseudofactin II showed antiadhesive activity against several pathogenic microorganisms which are potential biofilm formers on catheters, implants and internal prostheses. Up to 99% prevention could be achieved by 0.5 mg/ml pseudofactin II. In addition, pseudofactin II dispersed preformed biofilms. Pseudofactin II can be used as a disinfectant or surface coating agent against microbial colonization of different surfaces, e.g. implants or urethral catheters.</p

Wigner functions for a class of semidirect product groups

We define and construct Wigner functions for the class of semidirect product groups [Special characters omitted.] whose linear part H ✹ GL ( n , [Special characters omitted.] ) is a closed Lie subgroup of GL ( n , [Special characters omitted.] ) admitting at least one open and free orbit in [Special characters omitted.] . Such groups are classified up to conjugacy in dim n = 3 and in dim n = 4 under the further requirement that they possess a semisimple ideal. The general construction is based on three main requirements: (i) the exponential map exp : [Special characters omitted.] [arrow right] G has a dense image in G , with complement of (left or right) Haar measure zero; (ii) the group admits a square-integrable representation; (iii) the Lebesgue measure d X * in the dual of the Lie algebra can be decomposed as [Special characters omitted.] , [Special characters omitted.] where [Special characters omitted.] denotes a coadjoint orbit parametrized by an index [Special characters omitted.] , [Special characters omitted.] is a measure on the parameter space, [Special characters omitted.] is a positive function on that orbit and [Special characters omitted.] is the invariant measure under the coadjoint action of G . We discuss in detail all these elements in the case of semidirect product groups [Special characters omitted.] of the kind described above and give an explicit form of the generalized Wigner function related to them. Cases of special interest are those for which the domain of the generalized Wigner function can be endowed with the structure of phase space: a sufficient condition for this to be is given in terms of purely geometrical properties of the coadjoint orbits. Relevant examples are discussed with emphasis on the case of the quaternionic group as a 4-dimensional wavelet group; this is a natural non-abelian extension of the known notions of wavelet groups in 1 and 2 dimensions which have extensive applications in signal analysi

Blocking and dislocation of Candida albicans Cdr1p transporter bystyrylquinolines

Styrylquinolines are a novel group of quinoline drugs that are known to have p53-independent antiproliferative activity and antiviral properties. This study evaluated the antifungal activity of these drugs more deeply, particularly their activity modulation towards Cdr1p, the main multidrug transporter of Candida albicans. Styrylquinolines were found to have antifungal activity and to work synergistically with fluconazole. Additionally, they decreased the extracellular concentration of rhodamine 6G in ABC-transporter-expressing cells. The cellular localization of GFP-tagged Cdr1p was assessed by epifluorescent microscopy. Styrylquinolines induce expression of Cdr1p, as confirmed by Western blotting. Three of four drugs tested caused the partial delocalization of transport protein to the cytoplasm. These results show the first evidence that styrylquinolines decrease the activity of ABC multidrug transporters in C. albicans

Numerical study of drift influence on diffusion transport through the hybrid membrane

Sodium alginate membranes filled with iron oxide nanoparticles consist of a mixture of organic and inorganic phases. This design offers the possibility to combine the polymer’s easy processability and superior separation performance. For a better understanding of the mechanisms of mixture separation, we analyze the diffusion motion of a particle in the hybrid membrane environment. We model structures of two-dimensional heterogenic membranes, which resemble real membrane structures, and then we simulate a random walk on them. We investigate how the additional action of drift changes the motion properties of the diffusing particles through the polymeric membrane filled with inorganic powder. We test the effect of two parameters: the distribution of obstacles (filling) in the membrane and the value of drift on the nature of diffusion. It appears that the synergy between drift, the diffusion, and the membrane structure affect the occurrence of the superdiffusive and subdiffusive character of particle motion as measured by the time-averaged mean square displacement. An important point is the observation that the strong drift supports subdiffusive motion as it increases the chances of particle trapping. Moreover, there exists the optimal value of drift, for which the transport through a membrane speeds up and does not cause trapping

Design of polymer membrane morphology with prescribed structure and diffusion properties

We study the possibility of using numerical modelling in the process of design a membrane of prescribed morphology and transport properties. We started from a real example of the cross-section of alginate membrane cross-linked by glutaraldehyde containing 25 wt% magnetite particles and searched for a numerical model that will resemble its morphological properties like amount of polymer matrix, sizes of polymer matrix domains, fractal dimension and others. Two different methods of generating models of such were proposed. After choosing the best models based on its morphological similarities to the real membrane, we study their transport properties in terms of Brownian diffusion. We showed that there is a good agreement of diffusion type and diffusion constant between the models and the real membrane

Genes and structure of selected cytokines involved in pathogenesis of psoriasis.

Psoriasis is a common skin disease involving 1-4% of human population worldwide, of strong genetic background. The following cytokines are directly involved in psoriasis: TNF, IL-1, IL-2, IL-6, IL-7, IL-8, IL-15, IL-18, IL-19, IL-20, IL-23 whereas IL-4, IL-10, IL-12 as well as IL-11, IL-17 and IFN-gamma are rather indirectly engaged. This work is a review of some genetic factors and structure of selected cytokines and receptors and their genes location