28,837 research outputs found

### Effects of local mutations in quadratic iterations

We introduce mutations in replication systems, in which the intact copying
mechanism is performed by discrete iterations of a complex quadratic map. More
specifically, we consider a "correct" function acting on the complex plane
(representing the space of genes to be copied). A "mutation" is a different
("erroneous") map acting on a complex locus of given radius r around a mutation
focal point. The effect of the mutation is interpolated radially to eventually
recover the original map when reaching an outer radius R. We call the resulting
map a "mutated" map.
In the theoretical framework of mutated iterations, we study how a mutation
(replication error) affects the temporal evolution of the system, on both a
local and global scale (from cell diffetentiation to tumor formation). We use
the Julia set of the system to quantify simultaneously the long-term behavior
of the entire space under mutated maps. We analyze how the position, timing and
size of the mutation can alter the topology of the Julia set, hence the
system's long-term evolution, its progression into disease, but also its
ability to recover or heal. In the context of genetics, mutated iterations may
help shed some light on aspects such as the importance of location, size and
type of mutation when evaluating a system's prognosis, and of customizing
intervention.Comment: 15 pages, 15 figures, 7 reference

### A Thermal Gradient Approach for the Quasi-Harmonic Approximation and its Application to Improved Treatment of Anisotropic Expansion

We present a novel approach to efficiently implement thermal expansion in the
quasi-harmonic approximation (QHA) for both isotropic and more importantly,
anisotropic expansion. In this approach, we rapidly determine a crystal's
equilibrium volume and shape at a given temperature by integrating along the
gradient of expansion from zero Kelvin up to the desired temperature. We
compare our approach to previous isotropic methods that rely on a brute-force
grid search to determine the free energy minimum, which is infeasible to carry
out for anisotropic expansion, as well as quasi-anisotropic approaches that
take into account the contributions to anisotropic expansion from the lattice
energy. We compare these methods for experimentally known polymorphs of
piracetam and resorcinol and show that both isotropic methods agree to within
error up to 300 K. Using the Gr\"{u}neisen parameter causes up to 0.04 kcal/mol
deviation in the Gibbs free energy, but for polymorph free energy differences
there is a cancellation in error with all isotropic methods within 0.025
kcal/mol at 300 K.
Anisotropic expansion allows the crystals to relax into lattice geometries
0.01-0.23 kcal/mol lower in energy at 300 K relative to isotropic expansion.
For polymorph free energy differences all QHA methods produced results within
0.02 kcal/mol of each other for resorcinol and 0.12 kcal/mol for piracetam, the
two molecules tested here, demonstrating a cancellation of error for isotropic
methods.
We also find that when expanding in more than a single volume variable, there
is a non-negligible rate of failure of the basic approximations of QHA.
Specifically, while expanding into new harmonic modes as the box vectors are
increased, the system often falls into alternate, structurally distinct
harmonic modes unrelated by continuous deformation from the original harmonic
mode.Comment: 38 pages, including 9 pages supporting informatio

### The Visibility of Galactic Bars and Spiral Structure At High Redshifts

We investigate the visibility of galactic bars and spiral structure in the
distant Universe by artificially redshifting 101 B-band CCD images of local
spiral galaxies from the Ohio State University Bright Spiral Galaxy Survey. Our
artificially redshifted images correspond to Hubble Space Telescope I-band
observations of the local galaxy sample seen at z=0.7, with integration times
matching those of both the very deep Northern Hubble Deep Field data, and the
much shallower Flanking Field observations. The expected visibility of galactic
bars is probed in two ways: (1) using traditional visual classification, and
(2) by charting the changing shape of the galaxy distribution in "Hubble
space", a quantitative two-parameter description of galactic structure that
maps closely on to Hubble's original tuning fork. Both analyses suggest that
over 2/3 of strongly barred luminous local spirals i.e. objects classified as
SB in the Third Reference Catalog) would still be classified as strongly barred
at z=0.7 in the Hubble Deep Field data. Under the same conditions, most weakly
barred spirals (classified SAB in the Third Reference Catalog) would be
classified as regular spirals. The corresponding visibility of spiral structure
is assessed visually, by comparing luminosity classifications for the
artificially redshifted sample with the corresponding luminosity
classifications from the Revised Shapley Ames Catalog. We find that for
exposures times similar to that of the Hubble Deep Field spiral structure
should be detectable in most luminous low-inclination spiral galaxies at z=0.7
in which it is present. [ABRIDGED]Comment: Accepted for publication in The Astronomical Journa

### Noncommutative theories and general coordinate transformations

We study the class of noncommutative theories in $d$ dimensions whose spatial
coordinates $(x_i)_{i=1}^d$ can be obtained by performing a smooth change of
variables on $(y_i)_{i=1}^d$, the coordinates of a standard noncommutative
theory, which satisfy the relation $[y_i, y_j] = i \theta_{ij}$, with a
constant $\theta_{ij}$ tensor. The $x_i$ variables verify a commutation
relation which is, in general, space-dependent. We study the main properties of
this special kind of noncommutative theory and show explicitly that, in two
dimensions, any theory with a space-dependent commutation relation can be
mapped to another where that $\theta_{ij}$ is constant.Comment: 21 pages, no figures, LaTeX. v2: section 5 added, typos corrected.
Version to appear in Physical Review

### Transit Node Routing Reconsidered

Transit Node Routing (TNR) is a fast and exact distance oracle for road
networks. We show several new results for TNR. First, we give a surprisingly
simple implementation fully based on Contraction Hierarchies that speeds up
preprocessing by an order of magnitude approaching the time for just finding a
CH (which alone has two orders of magnitude larger query time). We also develop
a very effective purely graph theoretical locality filter without any
compromise in query times. Finally, we show that a specialization to the online
many-to-one (or one-to-many) shortest path further speeds up query time by an
order of magnitude. This variant even has better query time than the fastest
known previous methods which need much more space.Comment: 19 pages, submitted to SEA'201

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