3,793 research outputs found
Spherical harmonics coeffcients for ligand-based virtual screening of cyclooxygenase inhibitors
Background: Molecular descriptors are essential for many applications in computational chemistry, such as ligand-based similarity searching. Spherical harmonics have previously been suggested as comprehensive descriptors of molecular structure and properties. We investigate a spherical harmonics descriptor for shape-based virtual screening. Methodology/Principal Findings: We introduce and validate a partially rotation-invariant three-dimensional molecular shape descriptor based on the norm of spherical harmonics expansion coefficients. Using this molecular representation, we parameterize molecular surfaces, i.e., isosurfaces of spatial molecular property distributions. We validate the shape descriptor in a comprehensive retrospective virtual screening experiment. In a prospective study, we virtually screen a large compound library for cyclooxygenase inhibitors, using a self-organizing map as a pre-filter and the shape descriptor for candidate prioritization. Conclusions/Significance: 12 compounds were tested in vitro for direct enzyme inhibition and in a whole blood assay. Active compounds containing a triazole scaffold were identified as direct cyclooxygenase-1 inhibitors. This outcome corroborates the usefulness of spherical harmonics for representation of molecular shape in virtual screening of large compound collections. The combination of pharmacophore and shape-based filtering of screening candidates proved to be a straightforward approach to finding novel bioactive chemotypes with minimal experimental effort
Switching quantum reference frames in the N-body problem and the absence of global relational perspectives
Given the importance of quantum reference systems to both quantum and
gravitational physics, it is pertinent to develop a systematic method for
switching between the descriptions of physics relative to different choices of
quantum reference systems, which is valid in both fields. Here, we continue
with such a unifying approach, begun in arxiv:1809.00556, whose key ingredients
is a gravity-inspired symmetry principle, which enforces physics to be
relational and leads, thanks to gauge related redundancies, to a
perspective-neutral structure which contains all frame choices at once and via
which frame perspectives can be consistently switched. Formulated in the
language of constrained systems, the perspective-neutral structure turns out to
be the constraint surface classically and the gauge invariant Hilbert space in
the Dirac quantized theory. By contrast, a perspective relative to a specific
frame corresponds to a gauge choice and the associated reduced phase and
Hilbert space. Quantum reference frame switches thereby amount to a symmetry
transformation. In the quantum theory, they require a transformation that takes
one from the Dirac to a reduced quantum theory and we show that it amounts to a
trivialization of the constraints and a subsequent projection onto the
classical gauge fixing conditions. We illustrate this method in the relational
-body problem with rotational and translational symmetry. This model is
particularly interesting because it features the Gribov problem so that
globally valid gauge fixing conditions are impossible which, in turn, implies
also that globally valid relational frame perspectives are absent in both the
classical and quantum theory. These challenges notwithstanding, we exhibit how
one can systematically construct the quantum reference frame transformations
for the three-body problem.Comment: 22 pages, plus appendice
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Shape descriptors for mode-shape recognition and model updating
The most widely used method for comparing mode shapes from finite elements and experimental measurements is the Modal Assurance Criterion (MAC), which returns a single numerical value and carries no explicit information on shape features. New techniques, based on image processing (IP) and pattern recognition (PR) are described in this paper. The Zernike moment descriptor (ZMD), Fourier descriptor (FD), and wavelet descriptor (WD), presented in this article, are the most popular shape descriptors having properties that include efficiency of expression, robustness to noise, invariance to geometric transformation and rotation, separation of local and global shape features and computational efficiency. The comparison of mode shapes is readily achieved by assembling the shape features of each mode shape into multi-dimensional shape feature vectors (SFVs) and determining the distances separating them. © 2009 IOP Publishing Ltd
Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
We formulate hydrodynamic equations and spectrally accurate numerical methods
for investigating the role of geometry in flows within two-dimensional fluid
interfaces. To achieve numerical approximations having high precision and level
of symmetry for radial manifold shapes, we develop spectral Galerkin methods
based on hyperinterpolation with Lebedev quadratures for -projection to
spherical harmonics. We demonstrate our methods by investigating hydrodynamic
responses as the surface geometry is varied. Relative to the case of a sphere,
we find significant changes can occur in the observed hydrodynamic flow
responses as exhibited by quantitative and topological transitions in the
structure of the flow. We present numerical results based on the
Rayleigh-Dissipation principle to gain further insights into these flow
responses. We investigate the roles played by the geometry especially
concerning the positive and negative Gaussian curvature of the interface. We
provide general approaches for taking geometric effects into account for
investigations of hydrodynamic phenomena within curved fluid interfaces.Comment: 14 figure
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