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 $W^{\pm}$ 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