4,204 research outputs found
Locating regions in a sequence under density constraints
Several biological problems require the identification of regions in a
sequence where some feature occurs within a target density range: examples
including the location of GC-rich regions, identification of CpG islands, and
sequence matching. Mathematically, this corresponds to searching a string of 0s
and 1s for a substring whose relative proportion of 1s lies between given lower
and upper bounds. We consider the algorithmic problem of locating the longest
such substring, as well as other related problems (such as finding the shortest
substring or a maximal set of disjoint substrings). For locating the longest
such substring, we develop an algorithm that runs in O(n) time, improving upon
the previous best-known O(n log n) result. For the related problems we develop
O(n log log n) algorithms, again improving upon the best-known O(n log n)
results. Practical testing verifies that our new algorithms enjoy significantly
smaller time and memory footprints, and can process sequences that are orders
of magnitude longer as a result.Comment: 17 pages, 8 figures; v2: minor revisions, additional explanations; to
appear in SIAM Journal on Computin
Role of Charged Gauge Fields in Generating Magnetic Seed Fields in Bubble Collisions during the Cosmological Electroweak Phase Transition
We calculate the magnetic field generated during bubble collisions in a
first-order electroweak phase transition that may occur for some choices of
parameters in the minimal supersymmetric Standard Model. We show that for
sufficiently gentle collisions, where the Higgs field is relatively unperturbed
in the bubble overlap region, the equations of motion can be linearized so that
in the absence of fermions the charged W fields are the source of the
electromagnetic current for generating the seed fields. Solutions of the
equations of motion for the charged gauge fields and Maxwell's equations for
the magnetic field in O(1,2) space-time symmetry are expressed in closed form
by applying boundary conditions at the time of collision. Our results indicate
that the magnetic fields generated by charged fields in the collision
are comparable to those found in previous work. The magnetic fields so produced
could seed galactic and extra-galactic magnetic fields observed today.Comment: 15 Pages, 7 Figure
Band-to-band transitions, selection rules, effective mass and exciton binding energy parameters in monoclinic \beta-Ga2O3
We employ an eigen polarization model including the description of direction
dependent excitonic effects for rendering critical point structures within the
dielectric function tensor of monoclinic \beta-Ga2O3 yielding a comprehensive
analysis of generalized ellipsometry data obtained from 0.75 eV--9 eV. The
eigen polarization model permits complete description of the dielectric
response, and we obtain single-electron and excitonic band-to-band transition
anisotropic critical point structure model parameters including their
polarization eigenvectors within the monoclinic lattice. We compare our
experimental analysis with results from density functional theory calculations
performed using a recently proposed Gaussian-attenuation-Perdue-Burke-Ernzerhof
hybrid density functional, and we present and discuss the order of the
fundamental direct band-to-band transitions and their polarization selection
rules, the electron and hole effective mass parameters for the three lowest
band-to-band transitions, and their exciton binding energy parameters, in
excellent agreement with our experimental results. We find that the effective
masses for holes are highly anisotropic and correlate with the selection rules
for the fundamental band-to-band transitions, where the observed transitions
are polarized closely in the direction of the lowest hole effective mass for
the valence band participating in the transition
Effective Polarisability Models
Theories for the effective polarisability of a small particle in a medium are
presented using different levels of approximation: we consider the virtual
cavity, real cavity and the hard-sphere models as well as a continuous
interpolation of the latter two. We present the respective hard-sphere and
cavity radii as obtained from density-functional simulations as well as the
resulting effective polarisabilities at discrete Matsubara frequencies. This
enables us to account for macroscopic media in van der Waals interactions
between molecules in water and their Casimir-Polder interaction with an
interface
Solving the TTC 2011 Compiler Optimization Task with metatools
The authors' "metatools" are a collection of tools for generic programming.
This includes generating Java sources from mathematically well-founded
specifications, as well as the creation of strictly typed document object
models for XML encoded texts. In this context, almost every computer-internal
structure is treated as a "model", and every computation is a kind of model
transformation.
This concept differs significantly from "classical model transformation"
executed by specialized tools and languages. Therefore it seemed promising to
the organizers of the TTC 2011, as well as to the authors, to apply metatools
to one of the challenges, namely to the "compiler optimization task". This is a
report on the resulting experiences.Comment: In Proceedings TTC 2011, arXiv:1111.440
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