Fixed-Size Quadruples for a New, Hardware-Oriented Representation of the 4D Clifford Algebra

Clifford algebra (geometric algebra) offers a natural and intuitive way to model geometry in fields as robotics, machine vision and computer graphics. This paper proposes a new representation based on fixed-size elements (quadruples) of 4D Clifford algebra and demonstrates that this choice leads to an algorithmic simplification which in turn leads to a simpler and more compact hardware implementation of the algebraic operations. In order to prove the advantages of the new, quadruple-based representation over the classical representation based on homogeneous elements, a coprocessing core supporting the new fixed-size Clifford operands, namely Quad-CliffoSor (Quadruple-based Clifford coprocesSor) was designed and prototyped on an FPGA board. Test results show the potential to achieve a 23× speedup for Clifford products and a 33× speedup for Clifford sums and differences compared to the same operations executed by a software library running on a general-purpose processor.     

Group theoretic characterizations of Buekenhout–Metz unitals in $\mathop{\mathrm{PG}}(2,q^{2})$

Let G be the group of projectivities stabilizing a unital \(\mathcal{U}\) in \(\mathop{\mathrm{PG}}(2,q^{2})\) and let A,B be two distinct points of \(\mathcal{U}\). In this paper we prove that, if G has an elation group of order q with center A and a group of projectivities stabilizing both A and B of order a divisor of q?1 greater than \(2(\sqrt{q}-1)\), then \(\mathcal{U}\) is an ovoidal Buekenhout–Metz unital. From this result two group theoretic characterizations of orthogonal Buekenhout–Metz unitals are given.     

icoshift: An effective tool for the alignment of chromatographic data

The Interval Correlation Optimised Shifting algorithm (icoshift) has recently been introduced for the alignment of nuclear magnetic resonance spectra. The method is based on an insertion/deletion model to shift intervals of spectra/chromatograms and relies on an efficient Fast Fourier Transform based computation core that allows the alignment of large data sets in a few seconds on a standard personal computer. The potential of this programme for the alignment of chromatographic data is outlined with focus on the model used for the correction function. The efficacy of the algorithm is demonstrated on a chromatographic data set with 45 chromatograms of 64,000 data points. Computation time is significantly reduced compared to the Correlation Optimised Warping (COW) algorithm, which is widely used for the alignment of chromatographic signals. Moreover, icoshift proved to perform better than COW in terms of quality of the alignment (viz. of simplicity and peak factor), but without the need for computationally expensive optimisations of the warping meta-parameters required by COW. Principal component analysis (PCA) is used to show how a significant reduction on data complexity was achieved, improving the ability to highlight chemical differences amongst the samples.     

Fabrication of single crystal CuGaS2 nanorods by X-ray irradiation

CuGaS(2) nanorods were synthesized by irradiating the precursor solution with intense X-rays. The products are single crystal nanorods with preferential [220] growth and a uniform size distribution. We also report on the photoresponse of drop-cast films of these nanorods.     

Understanding the role of carbamate reactivity in fatty acid amide hydrolase inhibition by QM/MM mechanistic modelling

QM/MM modelling of FAAH inactivation by O-biphenyl-3-yl carbamates identifies the deprotonation of Ser241 as the key reaction step, explaining why FAAH is insensitive to the electron-donor effect of conjugated substituents; this may aid design of new inhibitors with improved selectivity and in vivo potency.     

Enantio and diastereoselective addition of phenylacetylene to racemic α-chloroketones

In this report, we have presented the first diastereoselective addition of phenylacetylene to chiral racemic chloroketones. The addition is controlled by the reactivity of the chloroketones that allowed the stereoselective reaction to be performed at -20 °C. Chiral racemic chloroketones are used in the reaction. By carefully controlling the temperature and the reaction time we were able to isolate the corresponding products in moderate yields and with good, simple and predictable facial stereoselection. Our reaction is a rare example of the use of chiral ketones in an enantioselective alkynylation reaction and opens new perspectives for the formation of chiral quaternary stereocenters.     

HMGB1–Carbenoxolone Interactions: Dynamics Insights from Combined Nuclear Magnetic Resonance and Molecular Dynamics

The interplay of protein dynamics and molecular recognition is of fundamental importance in biological processes. Atomic‐resolution insights into these phenomena may provide new opportunities for drug discovery. Herein, we have combined NMR relaxation experiments and residual dipolar coupling (RDC) measurements with molecular dynamics (MD) simulations to study the effects of the anti‐inflammatory drug carbenoxolone (CBNX) on the conformational properties and on the internal dynamics of a subdomain (box A) of high‐mobility group B protein (HMGB1). ¹⁵N relaxation data show that CBNX binding enhances the fast pico‐ to nanosecond motions of a loop and partially removes the internal motional anisotropy of the first two helices of box A. Dipolar wave analysis of amide RDC data shows that ligand binding induces helical distortions. In parallel, increased mobility of the loop upon ligand binding is highlighted by the essential dynamics analysis (EDA) of MD simulations. Moreover, simulations detect two possible orientations for CBNX, which induces two possible conformations of helix H3, one being similar to the free form and the second one causing a partial helical distortion. Finally, we introduce a new approach for the analysis of the internal coordination of protein residues that is consistent with experimental data and allows us to pinpoint which substructures of box A are dynamically affected by CBNX. The observations reported here may be useful for understanding the role of protein dynamics in binding at atomic resolution.     

Remarks on the solution of extended Stokes' problems

The analytical solutions of first and second Stokes' problems are discussed, for infinite and finite-depth flows of a Newtonian fluid in planar geometries. Problems arising from the motion of the wall as a whole (one-dimensional flows) as well as of only one half of the wall (two-dimensional) are solved and the wall stresses are evaluated.The solutions are written in real form. In many cases, they improve the ones in literature, leading to simpler mathematical forms of velocities and stresses. The numerical computation of the solutions is performed by using recurrence relations and elementary integrals, in order to avoid the evaluation of integrals of rapidly oscillating functions.The main physical features of the solutions are also discussed. In particular, the steady-state solutions of the second Stokes' problems are analyzed by separating their “in phase” and “in quadrature” components, with respect to the wall motion. By using this approach, stagnation points have been found in infinite-depth flows.     

Contact mechanics of microscopically rough surfaces with graded elasticity

The well-known Greenwood and Williamson contact theory for microscopically homogeneous rough surfaces is generalized by considering functionally graded elastic rough surfaces. In particular, two distinct cases giving rise to a non-constant Young’s modulus with depth are considered: (I) an initially plane layered (or graded) solid which is non-uniformly eroded, so that the final product is a rough surface with asperities having an elastic modulus depending on the height; (II) an initially homogeneous rough surface which receives a surface treatment or a chemical degradation which modify the elastic properties of the asperities as a function of the depth from the exposed surface. These Functionally Graded Surfaces (FGS) can be observed both in biological systems and in mechanical components. The effects of graded elasticity on the relationship between real contact area versus applied load, and on the plasticity index are quantified and illustrated with numerical examples. It will be shown that the contact response may differ up to one order of magnitude with respect to that of a homogeneous surface. Comparison between Case I and Case II also shows that, for special surface properties, the two types of grading can provide the same mechanical response.