We present an approach to hierarchically encode the topology of functions over triangulated surfaces. Its Morse-Smale complex, a well known structure in computational topology, describes the topology of a function. Fo...
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We present an approach to hierarchically encode the topology of functions over triangulated surfaces. Its Morse-Smale complex, a well known structure in computational topology, describes the topology of a function. Following concepts of Morse theory, a Morse-Smale complex (and therefore a function's topology) can be simplified by successively canceling pairs of critical points. We demonstrate how cancellations can be effectively encoded to produce a highly adaptive topology-based multi-resolution representation of a given function. Contrary to the approach, we avoid encoding the complete complex in a traditional mesh hierarchy. Instead, the information is split into a new structure we call a cancellation forest and a traditional dependency graph. The combination of this new structure with a traditional mesh hierarchy proofs to be significantly more flexible than the one previously reported. In particular, we can create hierarchies that are guaranteed to be of logarithmic height.
We introduce TLHaar, an n-bit to n-bit reversible trans-form similar to the S-transform, TLHaar uses lookup tables that approximate the S-transform, but reorder the co-efficients so they fit into n bits. TLHaar is sui...
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We introduce TLHaar, an n-bit to n-bit reversible trans-form similar to the S-transform, TLHaar uses lookup tables that approximate the S-transform, but reorder the co-efficients so they fit into n bits. TLHaar is suited for loss-less compression in fixed-width channels, such as digital video channels and graphics hardware frame buffers. Tests indicate that when the incoming image data has lines or hard edges TLHaar coefficients compress better than S-transform coefficients. For other types of image data TL-Haar coefficients compress up to 2.5% worse than those of the S-transform, depending on the data and the compression method used.
SCIRun is a general purpose problem solving environment that seeks to integrate the steps of preparing, executing, and visualizing simulations of physical and biological systems. The implementation of SCIRun is by mea...
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SCIRun is a general purpose problem solving environment that seeks to integrate the steps of preparing, executing, and visualizing simulations of physical and biological systems. The implementation of SCIRun is by means of an interactive dataflow network consisting of modules and data pipes exposed as a visual programming language. SCIRun also contains specific modules for bioelectric field simulations and visualizations and the combination of SCIRun with this package is known as BioPSE (***/software/biopse). This software has been in the public domain since 2000 and in that time we have developed strategies for software development, engineering, testing, documentation, and training. We have also continued to expand the scope of the SCIRun/BioPSE package not only through our own codes but by constructing bridges to other systems, both open source and proprietary. We have also created a repository for relevant sample networks and datasets with the aim of allowing diverse groups to test and evaluate algorithms using identical data and to share their results with the community for comparison of performance and accuracy. We present here a summary of the software system and describe specific experiences and conclusions with regard to creating and managing a large open source software project carried out within a university setting.
We introduce the piecewise-linear Haar (PLHaar) transform, a reversible n-bit to n-bit transform that is based on the Haar wavelet transform. PLHaar is continuous, while all current n-bit to n-bit methods are not, and...
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We introduce the piecewise-linear Haar (PLHaar) transform, a reversible n-bit to n-bit transform that is based on the Haar wavelet transform. PLHaar is continuous, while all current n-bit to n-bit methods are not, and is therefore uniquely usable with both lossy and lossless methods (e.g. image compression). PLHaar has both integer and continuous (i.e. non-discrete) forms. By keeping the coefficients to n bits PLHaar is particularly suited for use in hardware environments where channel width is limited, such as digital video channels and graphics hardware.
Adaptive mesh refinement (AMR) is a technique used in numerical simulations to automatically refine (or de-refine) certain regions of the physical domain in a finite difference calculation. AMR data consists of nested...
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Adaptive mesh refinement (AMR) is a technique used in numerical simulations to automatically refine (or de-refine) certain regions of the physical domain in a finite difference calculation. AMR data consists of nested hierarchies of data grids. As AMR visualization is still a relatively unexplored topic, our work is motivated by the need to perform efficient visualization of large AMR data sets. We present a software algorithm for parallel direct volume rendering of AMR data using a cell-projection technique on several different parallel platforms. Our algorithm can use one of several different distribution methods, and we present performance results for each of these alternative approaches. By partitioning an AMR data set into blocks of constant resolution and estimating rendering costs of individual blocks using an application specific benchmark, it is possible to achieve even load balancing.
A computer simulation model of electrodeposition of polymer chains on an impenetrable wall is used to evaluate the power-law scaling exponents ( νx(y)) for the longitudinal and transverse spread, Rgx(y)∼Lcνx(y); we...
A computer simulation model of electrodeposition of polymer chains on an impenetrable wall is used to evaluate the power-law scaling exponents ( νx(y)) for the longitudinal and transverse spread, Rgx(y)∼Lcνx(y); we find that the exponents νx(y) depend on the field strength, i.e., they are nonuniversal. A conformational crossover is observed for the transverse spread from the bulk with νy≃1/3–2/3 to the wall with νy≃2/3–1. A similar crossover also occurs for the longitudinal component of Rg but with an opposite trend, i.e., magnitude of νx is larger in bulk than at the wall.
The conformations of interacting polymer chains driven by a biased field in heterogeneous media are studied using Monte Carlo simulations in three dimensions. In addition to excluded volume, a nearest-neighbor interac...
The conformations of interacting polymer chains driven by a biased field in heterogeneous media are studied using Monte Carlo simulations in three dimensions. In addition to excluded volume, a nearest-neighbor interaction is considered with polymer-polymer repulsion and polymer-solvent attraction. Two types of heterogeneous media are considered: (i) a homogeneous-annealed system consisting of mobile polymer chains and solvents and (ii) quenched porous media, generated by adding a random distribution of quenched barriers. Effects of polymer concentration (p), bias (B), temperature (T), and porosity (ps) on the magnitude of the radius of gyration (Rg) of the chains and its scaling with the chain length (Lc) are studied. In an annealed system, we observe a crossover in power-law variation of the radius of gyration with the chain length, Rg∼Lcγ, from an extended conformation with γ≃0.7 at low bias (B=0.2), low p, and high T to a collapsed conformation with γ∼0.20-0.31 at high bias (B⩾0.5) and low T. In a quenched porous medium, we observe a somewhat lower value of the power-law exponent, γ∼0.60-0.70, from its annealed value at high T and low bias. At low temperatures, in contrast, the magnitude of γ∼0.39-0.47 is enhanced with respect to its annealed value. Various nonlinear responses of Rg to bias are observed in different ranges of B, Lc, ps, and T. In particular, we find that the response is nonmonotonic at low temperatures (T≃0.1) in the annealed system and at high temperatures (T≃100.0) in a porous medium with a relatively high barrier concentration (pb⩾0.3).
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