Corners are important image features whose detection has proved elusive since they are associated with the locations of multiple edge orientation. In this paper, we explicitly model the multiple orientations by using a mixture model based on von Mises edge-direction distributions. In order to infer the parameters of the mixture model, a bank of Gabor filters is employed. The resulting mixture m...

We discuss interplays between log-concave functions and log-concave sequences. We prove a Bernstein-type theorem, which characterizes the Laplace transform of logconcave measures on the half-line in terms of log-concavity of the alternating Taylor coefficients. We establish concavity inequalities for sequences inspired by the PrékopaLeindler and the Walkup theorems. One of our main tools is a s...

In this paper we devise an optimal deterministic algorithm for routing -relations on-line on an -input/output multibutterfly. The algorithm, which is obtained by generalizing the circuit-switching techniques of [3], routes any -relation with messages of bits, in log steps in the bit model, and in log log communication steps in the word model. Unlike other recently developed algorithms, our algo...

Here we propose an efficient algorithm for computing the smallest enclosing circle whose center is constrained to lie on a query line segment. Our algorithm preprocesses a given set of n points P = {p1, p2, . . . , pn} such that for any query line or line segment L, it efficiently locates a point c′ on L that minimizes the maximum distance among the points in P from c′. Roy et al. [11] has prop...

We show an arithmetic generalization of the recent work of Lazarsfeld–Mustaţǎ which uses Okounkov bodies to study linear series of line bundles. As applications, we derive a log-concavity inequality on volumes of arithmetic line bundles and an arithmetic Fujita approximation theorem for big line bundles.

When young children attempt to locate the positions of numerals on a number line, the positions are often logarithmically rather than linearly distributed. This finding has been taken as evidence that the children represent numbers on a mental number line that is logarithmically calibrated. This article reports a statistical simulation showing that log-like positioning is a consequence of 2 fac...

We present a data structure for efficient axis-aligned orthogonal range search on a set of n lines in a bounded plane. The algorithm requires O(log n+ k) time in the worst case to find all lines intersecting an axis aligned query rectangle R, where k is the number of lines in range. O(n + λ) space is required for the data structure used by the algorithm, where λ is the number of intersection po...

The network discovery (verification) problem asks for a minimum subset Q ⊆ V of queries in an undirected graph G = (V,E) such that these queries discover all edges and non-edges of the graph. This is motivated by the common approach of combining local measurements in order to obtain maps of the Internet or other dynamically growing networks. In the distance query model, a query at node q return...

Zipf (1949) already noted that the linear relationship that he observed between log frequency and log rank is strongest in the middle range: both very high and very low frequency items tend to deviate from the log-log regression line. In this paper the causes for such deviations are investigated and a more detailed statistical model is offered. The subgeometric mean property of frequency counts...

In his third notebook, Ramanujan claims that ∫ ∞ 0 cos(nx) x2 + 1 log xdx+ π 2 ∫ ∞ 0 sin(nx) x2 + 1 dx = 0. In a following cryptic line, which only became visible in a recent reproduction of Ramanujan’s notebooks, Ramanujan indicates that a similar relation exists if log x were replaced by log x in the first integral and log x were inserted in the integrand of the second integral. One of the go...