Visibility preserving terrain simplification— an experimental study

The terrain surface simplification problem has been studied extensively, as it has important applications in geographic information systems and computer graphics. The goal is to obtain a new surface that is combinatorially as simple as possible, while maintaining a prescribed degree of similarity with the original input surface. Generally, the approximation error is measured with respect to distance (e.g., Hausdorff) from the original or with respect to visual similarity. In this paper, we propose a new method of simplifying terrain surfaces, designed specifically to maximize a new measure of quality based on preserving inter-point visibility relationships. Our work is motivated by various problems of terrain analysis that rely on inter-point visibility relationships, such as optimal antenna placement.

We have implemented our new method and give experimental evidence of its effectiveness in simplifying terrains according to our quality measure. We experimentally compare its performance with that of other leading simplification methods.     

Marrow infarction in sickle cell anemia: correlation with marrow type and distribution by MRI

Ischemic necrosis of bone is believed to occur exclusively in areas of predominantly fatty marrow. Sickle cell disease is unusual in that marrow infarction occurs in areas of active hematopoiesis. MR images of long bone obtained in ten patients with sickle cell anemia (SCA) were analyzed to correlate the distribution and appearance of marrow infarction with the type of marrow. While the hematopoietic marrow predominated in metaphyseal and diaphyseal regions of femurs and tibias, the fatty or mixed marrow was the most common pattern in epiphyses. Infarcts occurred in fatty as well as hematopoietic marrow. Marrow infarcts were isointense or minimally hyperintense on T1 weighted images with the hematopoietic marrow and therefore difficult to detect. On T2 weighted images, the infarcts showed very high signal. T2 weighted images are essential for detection of marrow infarction. Soft tissue changes seen as low signal on T1 and high signal on T2, may be secondary to intramuscular injections of analgesics or muscle ischemia occurring during sickle crisis.     

New Similarity Measures between Polylines with Applications to Morphing and Polygon Sweeping

   Abstract. We introduce two new related metrics, the geodesic width and the link width , for measuring the ``distance' between two nonintersecting polylines in the plane. If the two polylines have n vertices in total, we present algorithms to compute the geodesic width of the two polylines in O(n <sup>2</sup> log n) time using O(n <sup>2</sup> ) space and the link width in O(n <sup>3</sup> log n) time using O(n <sup>2</sup> ) working space where n is the total number of edges of the polylines. Our computation of these metrics relies on two closely related combinatorial strutures: the shortest-path diagram and the link diagram of a simple polygon. The shortest-path (resp., link) diagram encodes the Euclidean (resp., link) shortest path distance between all pairs of points on the boundary of the polygon. We use these algorithms to solve two problems: • Compute a continuous transformation that ``morphs' one polyline into another polyline. Our morphing strategies ensure that each point on a polyline moves as little as necessary during the morphing, that every intermediate polyline is also simple and disjoint to any other intermediate polyline, and that no portion of the polylines to be morphed is stretched or compressed by more than a user-defined parameter during the entire morphing. We present an algorithm that computes the geodesic width of the two polylines and utilizes it to construct a corresponding morphing strategy in O(n ² log ² n) time using O(n ² ) space. We also give an O(nlog n) time algorithm to compute a 2-approximation of the geodesic width and a corresponding morphing scheme. • Locate a continuously moving target using a group of guards moving inside a simple polygon. The guards always determine a simple polygonal chain within the polygon, with consecutive guards along the chain being mutually visible. We compute a strategy that sweeps such a chain of guards through the polygon in order to locate a target. We compute in O(n ³ ) time and O(n ² ) working space the minimum number r ^* of guards needed to sweep an n -vertex polygon. We also give an approximation algorithm, using O(n log n) time and O(n) space, to compute an integer r such that max(r - 16, 2)≤ r ^* ≤ r and P can be swept with a chain of r guards.     

On the plus construction forBGL ℤ\left[ {\tfrac{1}{2}} \right] at the prime 2at the prime 2

The author was supported by a NSF grant and by an American Mathematical Society Centennial Research Fellowship     

Rheological properties of diblock copolymer/layered‐silicate nanocomposites

The melt‐state viscoelastic properties of nanocomposites prepared with a symmetrical polystyrene–polyisoprene block copolymer and organically modified layered silicates are examined. Nanocomposites based on three thermodynamically equivalent organically modified layered silicates, primarily differing in lateral disk diameter (d), are studied with small‐amplitude oscillatory shear. The effects of the domain structure of the ordered block copolymer and the mesoscale dispersion of the layered silicates on the rheological properties are examined via a comparison of data for the nanocomposites in the ordered and disordered states of the block copolymer. Hybrids prepared with 5 wt % organically modified fluorohectorite (d ～ 10 μm) and montmorillonite (d ～ 1 μm) demonstrate a notable decrease in the frequency dependence of the moduli at low frequencies and a significant enhancement in the complex viscosity at low frequencies in the disordered state. This behavior is understood in terms of the development of a percolated layered‐silicate network structure. However, the viscoelastic properties in the disordered state with 5 wt % organically modified laponite (d ～ 30 nm) and in the ordered state of the block copolymer for all layered silicates demonstrate only minor changes from those observed for the unfilled polymer. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1434–1443, 2002     

Synthesis of ThCr2Si2-type arsenides from Bi flux

LaCo(2)As(2) can be synthesized as pure crystalline material by annealing a mixture of elements in Bi flux. The reaction, however, is accompanied by the incorporation of a small quantity of Bi into the structure and the formation of vacancies in the Co sublattice, which lead to substantial changes in structural and magnetic properties of the material.     

Connecting theory with experiment to understand the initial nucleation steps of heteropolyoxometalate clusters

A complimentary combination of Density Functional Theory (DFT) methodology and Electrospray Ionization-Mass Spectrometry (ESI-MS) has been utilized to increase our limited understanding of the first nucleation steps in the formation of the [XM(12)O(40)](n-) Keggin polyoxometalates (POMs) (where addenda metal atom M = W or Mo, and the heteroatom X = P or As). We postulate that the first key steps of nucleation into discrete, high nuclearity heteropolyanions proceed via the formation of isodinuclear species (e.g. [M(2)O(7)](2-)), which undergo successive steps of protonation and water condensation to form a heterotrinuclear fragment, which acts as a template for the constituent parts required for subsequent aggregation and formation of the plenary Keggin heteropolyanion. The stability of calculated structures of the numerous postulated intermediates has been analysed and discussed in detail, and these results complemented using experimental mass spectrometry, using an assembly (reaction solution analysis) and disassembly (fragmentation of single crystals) approach. Overall, no significant differences between the Keggin POMs were found when changing the addenda metal atom (W or Mo) or the heteroatom (P or As); although small differences among the lowest-energy structures were detected.