Coarse embeddings of metric spaces into Banach spaces

There are several characterizations of coarse embeddability of locally finite metric spaces into a Hilbert space. In this note we give such characterizations for general metric spaces. By applying these results to the spaces , we get their coarse embeddability into a Hilbert space for . This together with a theorem by Banach and Mazur yields that coarse embeddability into and into are equivalent when . A theorem by G.Yu and the above allow us to extend to , , the range of spaces, coarse embeddings into which is guaranteed for a finitely generated group to satisfy the Novikov Conjecture.

     

Coarse Embedding into Uniformly Convex Banach Spaces

In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach spaces can be preserved under taking the union of the metric spaces under certain conditions. As an application, for a group G strongly relatively hyperbolic to a subgroup H,the author proves that B(n) = {g ∈ G | |g|S∪H≤ n} admits a coarse embedding into a uniformly convex Banach space if H does.     

Adsorption of DNA onto anionic lipid surfaces

Currently self-assembled DNA delivery systems composed of DNA multivalent cations and anionic lipids are considered to be promising tools for gene therapy. These systems become an alternative to traditional cationic lipid–DNA complexes because of their low cytotoxicity lipids. However, currently these nonviral gene delivery methods exhibit low transfection efficiencies. This feature is in large part due to the poorly understood DNA complexation mechanisms at the molecular level. It is well-known that the adsorption of DNA onto like charged lipid surfaces requires the presence of multivalent cations that act as bridges between DNA and anionic lipids. Unfortunately, the molecular mechanisms behind such adsorption phenomenon still remain unclear. Accordingly a historical background of experimental evidence related to adsorption and complexation of DNA onto anionic lipid surfaces mediated by different multivalent cations is firstly reviewed. Next, recent experiments aimed to characterise the interfacial adsorption of DNA onto a model anionic phospholipid monolayer mediated by Ca^2 + (including AFM images) are discussed. Afterwards, modelling studies of DNA adsorption onto charged surfaces are summarised before presenting preliminary results obtained from both CG and all-atomic MD computer simulations. Our results allow us to establish the optimal conditions for cation-mediated adsorption of DNA onto negatively charged surfaces. Moreover, atomistic simulations provide an excellent framework to understand the interaction between DNA and anionic lipids in the presence of divalent cations. Accordingly,our simulation results in conjunction go beyond the macroscopic picture in which DNA is stuck to anionic membranes by using multivalent cations that form glue layers between them. Structural aspects of the DNA adsorption and molecular binding between the different charged groups from DNA and lipids in the presenceof divalent cations are reported in the last part of the study. Although this research work is far from biomedical applications, we truly believe that scientific advances in this line will assist, at least in part, in the rationaldesign and development of optimal carrier systems for genes and applicable to other drugs.     

A new irradiated quartz for beta source calibration

For luminescence dating to be an accurate absolute dating technique it is very important that we are able to deliver absolutely known radiation doses in the laboratory. This is normally done using a radiation source (alpha, beta, X-ray) calibrated against an absolutely known reference source. Many laboratories have used the various different batches of Risø calibration quartz for the calibration of beta and X-ray sources, but these have been largely undescribed. Here we describe in detail the preparation and luminescence characteristics of a new quartz standard, based on a North Sea beach sand collected from south-western Denmark (Rømø). Two grain sizes (4–11 μm and 180–250 μm) have been examined in detail. These were pre-treated (annealed, dosed and annealed again) to sensitise and stabilise the luminescence signals before being given an absolutely known gamma dose from a point ¹³⁷Cs source in scatter-free geometry. The luminescence characteristics are described; the very intense blue-light stimulated signal is dominated by the fast OSL component and the IR-stimulated signal is negligible. The material is shown to be suitable for measurement using SAR, and the dose recovery ratio is indistinguishable from unity with a standard deviation of <2% for multi-grain aliquots. The material is also shown to be suitable for single-grain calibration, with >80% of the grains giving a useful signal. Although there is an unexplained dispersion in our calibration data of ∼3% (which we cannot attribute to instrument variability), we nevertheless conclude that this material is very suitable for transferring absolute known doses from a standardised gamma source to in-built irradiation sources.     

A gap 1 cardinal transfer theorem

We extend the gap 1 cardinal transfer theorem (κ ⁺, κ ) → (λ ⁺, λ ) to any language of cardinality ≤λ, where λ is a regular cardinal. This transfer theorem has been proved by Chang under GCH for countable languages and by Silver in some cases for bigger languages (also under GCH). We assume the existence of a coarse (λ, 1)‐morass instead of GCH. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

IBIsCO: a molecular dynamics simulation package for coarse-grained simulation

IBIsCO is a parallel molecular dynamics simulation package developed specially for coarse-grained simulations with numerical potentials derived by the iterative Boltzmann inversion (IBI) method (Reith et al., J Comput Chem 2003, 24, 1624). In addition to common features of molecular dynamics programs, the techniques of dissipative particle dynamics (Groot and Warren, J Chem Phys 1997, 107, 4423) and Lowe-Andersen dynamics (Lowe, Europhys Lett 1999, 47, 145) are implemented, which can be used both as thermostats and as sources of friction to compensate the loss of degrees of freedom by coarse-graining. The reverse nonequilibrium molecular dynamics simulation method (Müller-Plathe, Phys Rev E 1999, 59, 4894) for the calculation of viscosities is also implemented. Details of the algorithms, functionalities, implementation, user interfaces, and file formats are described. The code is parallelized using PE_MPI on PowerPC architecture. The execution time scales satisfactorily with the number of processors.     

Design of equalized holographic ROADMs for application in CWDM METRO networks

In this paper a design for an equalized holographic ROADM (Reconfigurable Optical Add-Drop Multiplexer) is done. This device can address several wavelengths at the input to different output fibers, according to the holograms stored in a SLM (Spatial Light Modulator), where all the outputs are equalized in power. All combinations of the input wavelengths are possible at the different output fibers.These type of ROADMs are designed for application in CWDM (Coarse Wavelength Division Multiplexing) networks, where the distance between the different wavelength allow the use of DML (Direct Modulation Lasers) without cooling, reducing the cost and the tolerances of the network components. Application in METRO networks and its interconnection with some PON (Passive Optical Network), as a part of the access to the subscriber, is reviewed.     

Expressions for forces and torques in molecular simulations using rigid bodies

Expressions for intermolecular forces and torques, derived from pair potentials between rigid non-spherical units, are presented. The aim is to give compact and clear expressions, which are easily generalized, and which minimize the risk of error in writing molecular dynamics simulation programs. It is anticipated that these expressions will be useful in the simulation of liquid crystalline systems, and in coarse-grained modelling of macromolecules.