Computing Approximate Shortest Paths on Convex Polytopes

The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algorithm for computing approximate shortest paths on a convex polyhedral surface. Given a convex polyhedral surface P in \reals ³ , two points s, t ∈ P , and a parameter \eps > 0 , it computes a path between s and t on P whose length is at most (1+\eps) times the length of the shortest path between those points. It constructs in time O(n/\sqrt \eps ) a graph of size O(1/\eps ⁴ ) , computes a shortest path on this graph, and projects the path onto the surface in O(n/\eps) time, where n is the number of vertices of P . In the postprocessing step we have added a heuristic that considerably improves the quality of the resulting path. Received July 25, 2000; revised June 6, 2001.     

Improved Algorithms for Uniform Partitions of Points

We consider the following one- and two-dimensional bucketing problems: Given a set S of n points in \reals ¹ or \reals ² and a positive integer b , distribute the points of S into b equal-size buckets so that the maximum number of points in a bucket is minimized. Suppose at most (n/b) + Δ points lie in each bucket in an optimal solution. We present algorithms whose time complexities depend on b and Δ . No prior knowledge of Δ is necessary for our algorithms. For the one-dimensional problem, we give a deterministic algorithm that achieves a running time of O(b ⁴ (Δ ² +log n) + n) . For the two-dimensional problem, we present a Monte Carlo algorithm that runs in subquadratic time for small values of b and Δ . The previous algorithms, by Asano and Tokuyama [1], searched the entire parameterized space and required Ω ( n ² ) time in the worst case even for constant values of b and Δ . We also present a subquadratic algorithm for the special case of the two-dimensional problem when b=2 .     

Synthesis and Physical Properties of (Cu,M)Ba2Ca3Cu4Oz (M=C,Mg,Ni,Al,Zn,Tl)

We have synthesized the single phase samples of Cu _x C _0.1 Ba ₂ Ca ₃ Cu ₄ O _z (x=0.20.9). Transport and magnetic measurements and iodometric titration analysis were carried out for these materials. From these results we discuss the correlation between T _c , the Hall number, copper valence and oxygen content. The effect of the substituted M ions on T _c in (CuC, M)-l234 (M=Ni,Zn,Al,TI,Mg) is also discussed. We propose a unique selective carrier-doping mechanism in (Cu,C)- and (CuC,Mg)-1234 systems.     

Piezoelectric effect in renal calculi

The piezoelectric effect is investigated for the first time in renal calculi in vitro. The kidney stones are shaped from solid samples as well as from stones crushed into powder and pressed into tablets. Presence of alpha quartz in the renal calculi is investigated by an X-ray technique and the presence of this constituent also helps to explain the piezoelectric effect in the renal calculi. The dielectric and piezoelectric parameters are studied in detail.     

Design of a notch filter with improved performance

The frequency response of a constrained notch filter (CNF) of Rao and Kung or Nehorai becomes ideal as the polecontraction factor α approaches unity while the transient duration approaches infinity. However, for practically useful values of α the phase and magnitude distortions so caused can reduce the allpass nature of the CNFs (i.e. the transparency property) and cause large errors. In this paper we define a measure for the transparency misadjustment and propose two suboptimal methods of minimizing these distortions. One of these methods is based on increasing the filter order by a strategic pole/zero placement. We present a closed-form solution for this method. In the second method we increase the order by manipulating the error filter associated with the standard CNF; the coefficients of the resulting filter are determined directly. an important feature of these methods is the significant improvement in the transient performance.     

Regulation of periodontal ligament cell functions by interleukin-1beta

Periodontal ligament (PDL) cells maintain the attachment of the tooth to alveolar bone. These cells reside at a site in which they are challenged frequently by bacterial products and proinflammatory cytokines, such as interleukin-1beta (IL-1beta), during infections. In our initial studies we observed that IL-1beta down-regulates the osteoblast-like characteristics of PDL cells in vitro. Therefore, we examined the functional significance of the loss of the PDL cell's osteoblast-like characteristics during inflammation. In this report we show that, during inflammation, IL-1beta can modulate the phenotypic characteristics of PDL cells to a more functionally significant lipopolysaccharide (LPS)-responsive phenotype. In a healthy periodontium PDL cells exhibit an osteoblast-like phenotype and are unresponsive to gram-negative bacterial LPS. Treatment of PDL cells with IL-1beta inhibits the expression of their osteoblast-like characteristics, as assessed by the failure to express transforming growth factor beta1 (TGF-beta1) and proteins associated with mineralization, such as alkaline phosphatase and osteocalcin. As a consequence of this IL-1beta-induced phenotypic change, PDL cells become responsive to LPS and synthesize proinflammatory cytokines. The IL-1beta-induced phenotypic changes in PDL cells were transient, as removal of IL-1beta from PDL cell cultures resulted in reacquisition of their osteoblast-like characteristics and lack of LPS responsiveness. The IL-1beta-induced phenotypic changes occurred at concentrations that are frequently observed in tissue exudates during periodontal inflammation (0.05 to 5 ng/ml). The results suggest that, during inflammation in vivo, IL-1beta may modulate PDL cell functions, allowing PDL cells to participate directly in the disease process by assuming LPS responsiveness at the expense of their normal structural properties and functions.     

Rotationplasty as a limb salvage procedure for malignant bone tumours

We report two patients with severe haemophilia A, factor VIII < 2 u dL-1, diagnosed at birth, through isolated bleeding in the adrenal gland (case 1) and through a haematoma in the liver (case 2). In these two clinical cases, the vital emergency, with haemorrhagic shock, required early diagnosis of the hereditary coagulation defect. Generally at birth, any unexplained bleeding should prompt screening for haemophilia. In the newborn period, the PTT is inadequate for many reasons and the laboratory evaluation must include factor VIII and IX levels.