Suppose that for a set H of n unknown hyperplanes in the Euclidean d-dimensional space, a line probe is available which reports the set of intersection points of a query line with the hyperplanes. Under this model, this paper investigates the complexity to nd a generic line for H and further to determine the hyperplanes in H. This problem arises in factoring the u-resultant to solve systems of ...

We study the Kertész line of the q–state Potts model at (inverse) temperature β, in presence of an external magnetic field h. This line separates two regions of the phase diagram according to the existence or not of an infinite cluster in the Fortuin-Kasteleyn representation of the model. It is known that the Kertész line hK(β) coincides with the line of first order phase transition for small f...

A diagnostic of a power law distribution is that a log-log plot of frequency against rank yields a (nearly) straight line. For instance, Zipf (1935) plotted word token counts in a variety of texts against the inverse rank of each distinct word type and showed that typically such plots approximate a straight line. The characteristic ‘Zipf curve’ of word frequency against rank deviates from this ...

A spectroscopic analysis of the DAB white dwarf PG 1115+166 is presented. The observed hydrogen and helium line profiles are shown to be incompatible with model spectra calculated under the assumption of homogeneous or stratified chemical compositions. In contrast, an excellent fit to the optical spectrum of PG 1115+166 can be achieved if the object is interpreted as an unresolved double degene...

An important class of planar straight-line drawings of graphs are convex drawings, in which all the faces are drawn as convex polygons. A planar graph is said to be convex planar if it admits a convex drawing. We give a new combinatorial characterization of convex planar graphs based on the decomposition of a biconnected graph into its triconnected components. We then consider the problem of te...

We study the complexity of determining a winning committee under Chamberlin-Courant voting rule when voters' preferences are single-crossing on line, or, more generally, tree. For Skowron et al. (2015) describe an O(n^2mk) algorithm (where n, m, k number voters, candidates and size, respectively); we show that simple tweak improves time to O(nmk). then improve this bound for k=Ω(log n) by reduc...

This problem comes in two distinct avors In query mode preprocessing is allowed and q is a query to be an swered on line In o line mode we are given the array A and a set of d rectangles q qm and we must com pute the m sums A qi Partial sum is a special case of the classical orthogonal range searching problem Given n weighted points in d space and a query d rectangle q compute the cumulative we...