Three-dimensional imaging of direct-written photonic structures

Third harmonic generation microscopy has been used to analyze the morphology of photonic structures created using the femtosecond laser direct-write technique. Three dimensional waveguide arrays and waveguide-Bragg gratings written in fused-silica and doped phosphate glass were investigated. A sensorless adaptive optical system was used to correct the optical aberrations occurring in the sample and microscope system, which had a lateral resolution of less than 500 nm. This non-destructive testing method creates volume reconstructions of photonic devices and reveals details invisible to other linear microscopy and index profilometry techniques.Comment: 8 pages, 3 color figures, 2 hyper-linked animation

LRM-Trees: Compressed Indices, Adaptive Sorting, and Compressed Permutations

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them. We describe how they yield many other convenient results in a variety of areas, from data structures to algorithms: some compressed succinct indices for range minimum queries; a new adaptive sorting algorithm; and a compressed succinct data structure for permutations supporting direct and indirect application in time all the shortest as the permutation is compressible.Comment: 13 pages, 1 figur

Simulation of the growth of the 3D Rayleigh-Taylor instability in Supernova Remnants using an expanding reference frame

Context: The Rayleigh-Taylor instabilities generated by the deceleration of a supernova remnant during the ejecta-dominated phase are known to produce finger-like structures in the matter distribution which modify the geometry of the remnant. The morphology of supernova remnants is also expected to be modified when efficient particle acceleration occurs at their shocks. Aims: The impact of the Rayleigh-Taylor instabilities from the ejecta-dominated to the Sedov-Taylor phase is investigated over one octant of the supernova remnant. We also study the effect of efficient particle acceleration at the forward shock on the growth of the Rayleigh-Taylor instabilities. Methods: We modified the Adaptive Mesh Refinement code RAMSES to study with hydrodynamic numerical simulations the evolution of supernova remnants in the framework of an expanding reference frame. The adiabatic index of a relativistic gas between the forward shock and the contact discontinuity mimics the presence of accelerated particles. Results: The great advantage of the super-comoving coordinate system adopted here is that it minimizes numerical diffusion at the contact discontinuity, since it is stationary with respect to the grid. We propose an accurate expression for the growth of the Rayleigh-Taylor structures that connects smoothly the early growth to the asymptotic self-similar behaviour. Conclusions: The development of the Rayleigh-Taylor structures is affected, although not drastically, if the blast wave is dominated by cosmic rays. The amount of ejecta that makes it into the shocked interstellar medium is smaller in the latter case. If acceleration occurs at both shocks the extent of the Rayleigh-Taylor structures is similar but the reverse shock is strongly perturbed.Comment: 15 pages, 12 figures, accepted for publication in Astronomy and Astrophysics with minor editorial changes. Version with full resolution images can be found at http://www.lpl.arizona.edu/~ffrasche/~12692.pd

Comparison of Five Spatio-Temporal Satellite Image Fusion Models over Landscapes with Various Spatial Heterogeneity and Temporal Variation

In recent years, many spatial and temporal satellite image fusion (STIF) methods have been developed to solve the problems of trade-off between spatial and temporal resolution of satellite sensors. This study, for the first time, conducted both scene-level and local-level comparison of five state-of-art STIF methods from four categories over landscapes with various spatial heterogeneity and temporal variation. The five STIF methods include the spatial and temporal adaptive reflectance fusion model (STARFM) and Fit-FC model from the weight function-based category, an unmixing-based data fusion (UBDF) method from the unmixing-based category, the one-pair learning method from the learning-based category, and the Flexible Spatiotemporal DAta Fusion (FSDAF) method from hybrid category. The relationship between the performances of the STIF methods and scene-level and local-level landscape heterogeneity index (LHI) and temporal variation index (TVI) were analyzed. Our results showed that (1) the FSDAF model was most robust regardless of variations in LHI and TVI at both scene level and local level, while it was less computationally efficient than the other models except for one-pair learning; (2) Fit-FC had the highest computing efficiency. It was accurate in predicting reflectance but less accurate than FSDAF and one-pair learning in capturing image structures; (3) One-pair learning had advantages in prediction of large-area land cover change with the capability of preserving image structures. However, it was the least computational efficient model; (4) STARFM was good at predicting phenological change, while it was not suitable for applications of land cover type change; (5) UBDF is not recommended for cases with strong temporal changes or abrupt changes. These findings could provide guidelines for users to select appropriate STIF method for their own applications

Algorithms and Data Structures for Multi-Adaptive Time-Stepping

Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the multi-adaptive methods allow individual and adaptive time steps to be used for different components or in different regions of space. We present algorithms for efficient multi-adaptive time-stepping, including the recursive construction of time slabs and adaptive time step selection. We also present data structures for efficient storage and interpolation of the multi-adaptive solution. The efficiency of the proposed algorithms and data structures is demonstrated for a series of benchmark problems.Comment: ACM Transactions on Mathematical Software 35(3), 24 pages (2008

An open and parallel multiresolution framework using block-based adaptive grids

A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and explicit time integration. Grid refinement and coarsening are triggered by multiresolution analysis, i.e. thresholding of wavelet coefficients, which allow controlling the precision of the adaptive approximation of the solution with respect to uniform grid computations. The implementation of the scheme is fully parallel using MPI with a hybrid data structure. Load balancing relies on space filling curves techniques. Validation tests for 2D advection equations allow to assess the precision and performance of the developed code. Computations of the compressible Navier-Stokes equations for a temporally developing 2D mixing layer illustrate the properties of the code for nonlinear multi-scale problems. The code is open source

RLZAP: Relative Lempel-Ziv with Adaptive Pointers

Relative Lempel-Ziv (RLZ) is a popular algorithm for compressing databases of genomes from individuals of the same species when fast random access is desired. With Kuruppu et al.'s (SPIRE 2010) original implementation, a reference genome is selected and then the other genomes are greedily parsed into phrases exactly matching substrings of the reference. Deorowicz and Grabowski (Bioinformatics, 2011) pointed out that letting each phrase end with a mismatch character usually gives better compression because many of the differences between individuals' genomes are single-nucleotide substitutions. Ferrada et al. (SPIRE 2014) then pointed out that also using relative pointers and run-length compressing them usually gives even better compression. In this paper we generalize Ferrada et al.'s idea to handle well also short insertions, deletions and multi-character substitutions. We show experimentally that our generalization achieves better compression than Ferrada et al.'s implementation with comparable random-access times

Time lower bounds for nonadaptive turnstile streaming algorithms

We say a turnstile streaming algorithm is "non-adaptive" if, during updates, the memory cells written and read depend only on the index being updated and random coins tossed at the beginning of the stream (and not on the memory contents of the algorithm). Memory cells read during queries may be decided upon adaptively. All known turnstile streaming algorithms in the literature are non-adaptive. We prove the first non-trivial update time lower bounds for both randomized and deterministic turnstile streaming algorithms, which hold when the algorithms are non-adaptive. While there has been abundant success in proving space lower bounds, there have been no non-trivial update time lower bounds in the turnstile model. Our lower bounds hold against classically studied problems such as heavy hitters, point query, entropy estimation, and moment estimation. In some cases of deterministic algorithms, our lower bounds nearly match known upper bounds