A geometric view of cryptographic equation solving

This paper considers the geometric properties of the Relinearisation algorithm and of the XL algorithm used in cryptology for equation solving. We give a formal description of each algorithm in terms of projective geometry, making particular use of the Veronese variety. We establish the fundamental geometrical connection between the two algorithms and show how both algorithms can be viewed as being equivalent to the problem of finding a matrix of low rank in the linear span of a collection of matrices, a problem sometimes known as the MinRank problem. Furthermore, we generalise the XL algorithm to a geometrically invariant algorithm, which we term the GeometricXL algorithm. The GeometricXL algorithm is a technique which can solve certain equation systems that are not easily soluble by the XL algorithm or by Groebner basis methods

Aggregation of amyloid Aβ(1-40) peptide in perdeuterated 2,2,2-trifluoroethanol caused by ultrasound sonication

Ultrasound sonication of protein and peptide solutions is routinely used in biochemical, biophysical, pharmaceutical and medical sciences to facilitate and accelerate dissolution of macromolecules in both aqueous and organic solvents. However, the impact of ultrasound waves on folding/unfolding of treated proteins, in particular, on aggregation kinetics of amyloidogenic peptides and proteins is not understood. In this work, effects of ultrasound sonication on the misfolding and aggregation behavior of the Alzheimer's Aβ (1-40)-peptide is studied by pulsed-field gradient (PFG) spin-echo diffusion NMR and UV circular dichroism (CD) spectroscopy. Upon simple dissolution of Aβ(1-40) in perdeuterated trifluoroethanol, CF3-CD2-OD (TFE-d3), the peptide is present in the solution as a stable monomer adopting α-helical secondary structural motifs. The self-diffusion coefficient of Aβ(1 -40) monomers in TFE-d3 was measured as 1.35 × 10-10 m2 s-1, reflecting its monomeric character. However, upon ultrasonic sonication for less than 5 min, considerable populations of Aβ molecules (ca 40%) form large aggregates as reflected in diffusion coefficients smaller than 4.0 × 10-13 m2 s-1. Sonication for longer times (up to 40 min in total) effectively reduces the fraction of these aggregates in 1H PFG NMR spectra to ca 25%. Additionally, absorption below 230 nm increased significantly upon sonication treatment, an observation, which also clearly confirms the ongoing aggregation process of Aβ(1-40) in TFE-d3. Surprisingly, upon ultrasound sonication only small changes in the peptide secondary structure were detected by CD: the peptide molecules mainly adopt α-helical motifs in both monomers and aggregates formed upon sonication. Copyright © 2010 John Wiley & Sons, Ltd

Lateral diffusion in equimolar mixtures of natural sphingomyelins with dioleoylphosphatidylcholine

Cellular membranes of mammals are composed of a complex assembly of diverse phospholipids. Sphingomyelin (SM) and phosphatidylcholine (PC) are important lipids of eukaryotic cellular membranes and neuronal tissues, and presumably participate in the formation of membrane domains, known as "rafts," through intermolecular interaction and lateral microphase decomposition. In these two-dimensional membrane systems, lateral diffusion of lipids is an essential dynamic factor, which might even be indicative of lipid phase separation process. Here, we used pulsed field gradient nuclear magnetic resonance to study lateral diffusion of lipid components in macroscopically oriented bilayers composed of equimolar mixtures of natural SMs of egg yolk, bovine brain, bovine milk and dipalmitoylphosphatidylcholine (DPPC) with dioleoylphosphatidylcholine (DOPC). In addition, differential scanning calorimetry was used as a complementary technique to characterize the phase state of the lipid bilayers. In fully liquid bilayers, the lateral diffusion coefficients in both DOPC/DPPC and DOPC/SM systems exhibit mean values of the pure bilayers. For DOPC/SM bilayer system, this behavior can be explained by a model where most SM molecules form short-lived lateral domains with preferential SM-SM interactions occurring within them. However, for bilayers in the presence of their low-temperature gel phase, lateral diffusion becomes complicated and cannot simply be understood solely by a simple change in the liquid phase decomposition. © 2012 Elsevier Inc

Diffusion and aggregation of Alzheimer's Aβ1-40 peptide in aqueous trifluoroethanol solutions as studied by pulsed field gradient NMR

Pulsed field gradient nuclear magnetic resonance technique was applied to measure the self-diffusion coefficient of Aβ1-40 peptide in trifluoroethanol (TFE) and mixed solvent TFE-water (D2O) buffer (pD 7.8) at 293 K. The data were analyzed on the basis of the Stokes model and the hard-sphere approach was used to estimate self-diffusion coefficients. It was found that the extent of the Aβ1-40 aggregation in TFE solutions depends on the concentration of the peptide and the sample preparation protocol. After soft mixing, i.e., without any additional mechanical pretreatment of the peptide, the peptide is present in the monomeric form in TFE solutions. However, the additional water-bath sonication of the sample during the dissolution of Aβ1-40 in TFE enforces oligomerization of the peptide with the size of aggregates ranging from tetra- to hexamers. An increase of D2O in the mixed TFE-D2O solvent of up to 75% leads to the aggregation of the larger part of the peptide. However, the components of self-diffusion coefficients related to low-mass Aβ1-40 oligomers (dimers and trimers) were not observed in the diffusion decay curves. The most probable explanation is that dimers and trimers are not the principal intermediate species in the aggregation of Aβ1-40 peptide. © Springer-Verlag 2005

Reflection of photons and azimuthal distribution of photoelectrons in a cylindrical beam pipe

In a cryogenic proton accelerator, such as the LHC, the creation of an electron cloud and generated heat loads resulting from electron bombardment are strongly dependent on the azimuthal distribution of created photoelectrons. In this context, photon reflection and photoelectron yield measurements have been performed using a beam line on the VEPP-2M storage ring. Six electrodes, covering the complete vacuum chamber perimeter, were mounted such that they could be suitably biased, and while one electrode was irradiated with synchrotron radiation the resulting electron current of all others could be measured. A detailed description of the experimental apparatus and the results of the measurements of photon reflection and the azimuthal distribution of generated photoelectrons are presented

Quality assurance of the Brewer UV measurements in Finland

International audienceThe quality assurance of the two Brewer spectrophotometers of the Finnish Meteorological Institute is discussed in this paper. The complete data processing chain from raw signal to high quality spectra is presented. The quality assurance includes daily maintenance, laboratory characterizations, calculation of long term spectral responsivity, data processing and quality assessment. The cosine correction of the measurements is based on a new method, and included in the data processing software. The results showed that the actual cosine correction factor of the Finnish Brewers can vary between 1.08?1.13 and 1.08?1.12, respectively, depending on the sky radiance distribution and wavelength. The temperature characterization showed a linear temperature dependence between the internal temperature and the photon counts per cycle, and a temperature correction was used for correcting the measurements. The long term spectral responsivity was calculated using time series of several lamps using two slightly different methods. The long term spectral responsivity was scaled to the irradiance scale of the Helsinki University of Technology (HUT) for the whole measurement time periods 1990?2006 and 1995?2006 for Sodankylä and Jokioinen, respectively. Both Brewers have participated in many international spectroradiometer comparisons, and have shown good stability. The differences between the Brewers and the portable reference spectroradiometer QASUME have been within 5% during 2002?2007

Beam Vacuum Interconnects for the LHC Cold Arcs

The design of the beam vacuum interconnect is described in this paper. Features include a novel RF bridge design to maximise lateral flexibility during cryostat Cold arcs of the LHC will consist of twin aperture dipole, quadrupole and corrector magnets in cryostats, operating at 1.9 K. Beam vacuum chambers, along with all connecting elements require flexible 'interconnects' between adjacent cryostats to allow for thermal and mechanical offsets foreseen during machine operation and alignment. In addition, the beam vacuum chambers contain perforated beam screens to intercept beam induced heat loads at an intermediate temperature. These must also be connected with low impedance RF bridges in the interconnect zones.alignment and so-called 'nested' bellows to minimise the required length of the assembly

Quality assurance of the Brewer spectral UV measurements in Finland

The quality assurance of the two Brewer spectrophotometers of the Finnish Meteorological Institute is discussed in this paper. The complete data processing chain from raw signal to high quality spectra is presented. The quality assurance includes daily maintenance, laboratory characterizations, calculation of long-term spectral responsivity, data processing and quality assessment. The cosine correction of the measurements is based on a new method, and is included in the data processing software. The results showed that the actual cosine correction factor of the two Finnish Brewers can vary between 1.08–1.13 and 1.08–1.12, respectively, depending on the sky radiance distribution and wavelength. The temperature characterization showed a linear temperature dependence between the instruments' internal temperature and the photon counts per cycle, and a temperature correction was used for correcting the measurements. The long-term spectral responsivity was calculated using the time series of several lamps using two slightly different methods. The long-term spectral responsivity was scaled to the irradiance scale of the Helsinki University of Technology (HUT) for the whole of the measurement time-periods 1990–2006 and 1995–2006 for Sodankylä and Jokioinen, respectively. Both Brewers have participated in many international spectroradiometer comparisons, and have shown good stability. The differences between the Brewers and the portable reference spectroradiometer QASUME have been within 5% during 2002–2007

Electron Cloud: Observations with LHC-Type Beams in the SPS

In August 1999, strong pressure increases were observed in the SPS in the presence of the new LHC-type beams. This paper reports on observations of the electron cloud phenomenon and the related pressure increase as a function of parameters such as the number of protons per bunch, the number of bunches per batch, the shape of the vacuum chamber and the electron current collected on pick-ups. Results of the observed clean-up, "beam scrubbing" will be presented as well as the consequences of the e-cloud phenomenon on the SPS operation with the LHC nominal beam intensity