Many touchings force many crossings

Crossings between Curves with Many Tangencies

Let A and B be two families of two-way infinite x-monotone curves, no three of which pass through the same point. Assume that every curve in A lies above every curve in B and that there are m pairs of curves, one from A and the other from B, that are tangent to each other. Then the number of proper crossings among the members of A∪B is at least (1/2− o(1))m lnm. This bound is almost tight.

Linear-time algorithms for geometric graphs with sublinearly many crossings

We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an iterated logarithmic factor. Specific problems we study include Voronoi diagrams and single-source shortest paths. Our algorithms all run in linear time in the ...

Adiabatic evolution for systems with infinitely many eigenvalue crossings

many drops make a lake

the desire and drive for excellence in any endeavor in life requires an effort from the individual; in addition it requires a constellation of features around such individuals that help them to become successful. for surgeons, it is the operating room staff, the administrative and medical assistants and our residents and fellows. however, perhaps the most important contribution to a physician’s...

Publication Ethics: Many Facets, Collaboration Required

Sir, the recent publication on “Publication Ethics” is very interesting (1). The article by Fazly Bazzaz and Sadeghi demonstrated many interesting cases                   of misconducts. Indeed, the misconducts can be seen  in many ways. As mentioned in the present publication, both author and editor can perform publication misconducts. Nevertheless, the problem has many more facets. Sometimes,...