21,007 research outputs found
Assessment of atomic charge models for gas-phase computations on polypeptides
The concept of the atomic charge is extensively used to model the electrostatic properties of proteins. Atomic charges are not only the basis for the electrostatic energy term in biomolecular force fields but are also derived from quantum mechanical computations on protein fragments to get more insight into their electronic structure. Unfortunately there are many atomic charge schemes which lead to significantly different results, and it is not trivial to determine which scheme is most suitable for biomolecular studies. Therefore, we present an extensive methodological benchmark using a selection of atomic charge schemes [Mulliken, natural, restrained electrostatic potential, Hirshfeld-I, electronegativity equalization method (EEM), and split-charge equilibration (SQE)] applied to two sets of penta-alanine conformers. Our analysis clearly shows that Hirshfeld-I charges offer the best compromise between transferability (robustness with respect to conformational changes) and the ability to reproduce electrostatic properties of the penta-alanine. The benchmark also considers two charge equilibration models (EEM and SQE), which both clearly fail to describe the locally charged moieties in the zwitterionic form of penta-alanine. This issue is analyzed in detail because charge equilibration models are computationally much more attractive than the Hirshfeld-I scheme. Based on the latter analysis, a straightforward extension of the SQE model is proposed, SQE+Q0, that is suitable to describe biological systems bearing many locally charged functional groups
Monodromy invariants in symplectic topology
This text is a set of lecture notes for a series of four talks given at
I.P.A.M., Los Angeles, on March 18-20, 2003. The first lecture provides a quick
overview of symplectic topology and its main tools: symplectic manifolds,
almost-complex structures, pseudo-holomorphic curves, Gromov-Witten invariants
and Floer homology. The second and third lectures focus on symplectic Lefschetz
pencils: existence (following Donaldson), monodromy, and applications to
symplectic topology, in particular the connection to Gromov-Witten invariants
of symplectic 4-manifolds (following Smith) and to Fukaya categories (following
Seidel). In the last lecture, we offer an alternative description of symplectic
4-manifolds by viewing them as branched covers of the complex projective plane;
the corresponding monodromy invariants and their potential applications are
discussed.Comment: 42 pages, notes of lectures given at IPAM, Los Angele
Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models
We conjecture that a non-flat -real-dimensional compact Calabi-Yau
manifold, such as a quintic hypersurface with D=6, or a K3 manifold with D=4,
has locally length minimizing closed geodesics, and that the number of these
with length less than L grows asymptotically as L^{D}. We also outline the
physical arguments behind this conjecture, which involve the claim that all
states in a nonlinear sigma model can be identified as "momentum" and "winding"
states in the large volume limit.Comment: minor corrections, 43 pages, to appear in frontiers in mathematical
physics. Frontiers in Physics, Dec 16, 201
A Data Science Course for Undergraduates: Thinking with Data
Data science is an emerging interdisciplinary field that combines elements of
mathematics, statistics, computer science, and knowledge in a particular
application domain for the purpose of extracting meaningful information from
the increasingly sophisticated array of data available in many settings. These
data tend to be non-traditional, in the sense that they are often live, large,
complex, and/or messy. A first course in statistics at the undergraduate level
typically introduces students with a variety of techniques to analyze small,
neat, and clean data sets. However, whether they pursue more formal training in
statistics or not, many of these students will end up working with data that is
considerably more complex, and will need facility with statistical computing
techniques. More importantly, these students require a framework for thinking
structurally about data. We describe an undergraduate course in a liberal arts
environment that provides students with the tools necessary to apply data
science. The course emphasizes modern, practical, and useful skills that cover
the full data analysis spectrum, from asking an interesting question to
acquiring, managing, manipulating, processing, querying, analyzing, and
visualizing data, as well communicating findings in written, graphical, and
oral forms.Comment: 21 pages total including supplementary material
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