The patient, a 45-year-old male, was referred to the rheumatology clinic due to diffuse joint pain on the wrists and knees. The patient was diagnosed with liver cirrhosis and severe hepatopulmonary syndrome. Physical examination showed swelling of the knees and wrists (arthritis) and clubbing. The X-rays requested showed periosteal thickening observed continuously, in a diaphysometaphysiary loc...

Let U(n, g) and B(n, g) be the set of unicyclic graphs and bicyclic graphs on n vertices with girth g, respectively. Let B1(n, g) be the subclass of B(n, g) consisting of all bicyclic graphs with two edge-disjoint cycles and B2(n, g) = B(n, g)\B1(n, g). This paper determines the unique graph with the maximal signless Laplacian spectral radius among all graphs in U(n, g) and B(n, g), respectivel...

Let r and w be a fixed positive numbers, w < r. In a bold drawing of a graph, every vertex is represented by a disk of radius r, and every edge by a narrow rectangle of width w. We solve a problem of van Kreveld [K09] by showing that every graph admits a bold drawing in which the region occupied by the union of the disks and rectangles representing the vertices and edges does not contain any di...

We present analytical and computational models used to investigate the dependence of etch resolution on pulse duration, tool radius, and etched feature aspect ratio in electrochemical machining with ultrashort voltage pulses. Our results predict that, for the high aspect ratio system in which the effect of trench top and bottom edges can be ignored, the increase of etch resolution with pulse le...

We show that the neighbor-joining algorithm is a robust quartet method for constructing trees from distances. This leads to a new performance guarantee that contains Atteson’s optimal radius bound as a special case and explains many cases where neighbor-joining is successful even when Atteson’s criterion is not satisfied. We also provide a proof for Atteson’s conjecture on the optimal edge radi...

Let P ⊆ R be a set of n points, each with an associated radius rp > 0. This induces a directed graph on P with an edge from p to q if and only if q lies in the ball with radius rp around p. We show that for d = 1 there is a data structure that answers reachability queries (given two vertices, is there a directed path between them?) in time O(1) using O(n) space and O(n log n) preprocessing time...

It is shown that for any fixed c ≥ 3 and r, the maximum possible chromatic number of a graph on n vertices in which every subgraph of radius at most r is c-colorable is Θ̃ ( n 1 r+1 ) : it is O ( (n/ logn) 1 r+1 ) and Ω ( n 1 r+1 / logn ) . The proof is based on a careful analysis of the local and global colorability of random graphs and implies, in particular, that a random n-vertex graph with ...