78,885 research outputs found
Mapping Properties of Co-existentially Closed Continua
A continuous surjection between compacta is called co-existential if it is the second of two maps whose composition is a standard ultracopower projection. A continuum is called co-existentially closed if it is only a co-existential image of other continua. This notion is not only an exact dual of Abraham Robinson\u27s existentially closed structures in model theory, it also parallels the definition of other classes of continua defined by what kinds of continuous images they can be. In this paper we continue our study of co-existentially closed continua, especially how they (and related continua) behave in certain mapping situations
A physically meaningful method for the comparison of potential energy functions
In the study of the conformational behavior of complex systems, such as
proteins, several related statistical measures are commonly used to compare two
different potential energy functions. Among them, the Pearson's correlation
coefficient r has no units and allows only semi-quantitative statements to be
made. Those that do have units of energy and whose value may be compared to a
physically relevant scale, such as the root mean square deviation (RMSD), the
mean error of the energies (ER), the standard deviation of the error (SDER) or
the mean absolute error (AER), overestimate the distance between potentials.
Moreover, their precise statistical meaning is far from clear. In this article,
a new measure of the distance between potential energy functions is defined
which overcomes the aforementioned difficulties. In addition, its precise
physical meaning is discussed, the important issue of its additivity is
investigated and some possible applications are proposed. Finally, two of these
applications are illustrated with practical examples: the study of the van der
Waals energy, as implemented in CHARMM, in the Trp-Cage protein (PDB code 1L2Y)
and the comparison of different levels of the theory in the ab initio study of
the Ramachandran map of the model peptide HCO-L-Ala-NH2.Comment: 30 pages, 7 figures, LaTeX, BibTeX. v2: A misspelling in the author's
name has been corrected. v3: A new application of the method has been added
at the end of section 9 and minor modifications have also been made in other
sections. v4: Journal reference and minor corrections adde
Ginsparg-Wilson-Luscher Symmetry and Ultralocality
Important recent discoveries suggest that Ginsparg-Wilson-Luscher (GWL)
symmetry has analogous dynamical consequences for the theory on the lattice as
chiral symmetry does in the continuum. While it is well known that inherent
property of lattice chiral symmetry is fermion doubling, we show here that
inherent property of GWL symmetry is that the infinitesimal symmetry
transformation couples fermionic degrees of freedom at arbitrarily large
lattice distances (non-ultralocality). The consequences of this result for
ultralocality of symmetric actions are discussed.Comment: 18 pages, LATEX. For clarity changed to infinitesimal
transformations, typos corrected, explicit hypothesis adde
Newtonian Quantum Gravity
Puts forward a complete scenario for interpreting nonlinear field theories
highlighting the role played by gravitational self--energy in enabling a
consistent revival of the Schroedinger approach to unifying micro and macro
physics.Comment: 38 pages, RevTex. Uses epsf. Five "tar.gz" compressed PostScipt
figures included separatel
- …