Abstract Signomial Programming (SP) has proven to be a powerful tool for engineering design optimization, striking balance between the computational efficiency of Geometric (GP) and extensibility more general methods optimization. While techniques exist fitting GP compatible models data, no have been proposed that take advantage increased modeling flexibility available in SP. Here, new Differen...

This paper’s origins are in two papers: One by Colesanti and Fragalà studying the surface area measure of a log-concave function, one Cordero-Erausquin Klartag regarding moment convex function. These notions same, this paper we continue same construction as well its generalization. In first half prove variation formula for integral functions under minimal optimal conditions. We also explain why...

We present an algorithm which computes the convex hull of a set of n spheres in dimension d in time O(n d d 2 e + n log n). It is worst-case optimal in three dimensions and in even dimensions. The same method can also be used to compute the convex hull of a set of n homothetic convex objects of IE d. If the complexity of each object is constant, the time needed in the worst case is O(n d d 2 e ...

We consider the planar convex hull range query problem. Let P be a set of points in the plane. We preprocess these points into a data structure such that given an orthogonal range query, we can report the convex hull of the points in the range in O(log n + h) time, where h is the size of the output. The data structure uses O(n log n) space. This improves the previous bound of O(log n+h) time an...

The Largest Empty Circle problem seeks the largest circle centered within the convex hull of a set P of n points in R2 and devoid of points from P . In this paper, we introduce a query version of this well-studied problem. In our query version, we are required to preprocess P so that when given a query line Q, we can quickly compute the largest empty circle centered at some point on Q and withi...

Let H denote the discrete Heisenberg group, equipped with a word metric dW associated to some finite symmetric generating set. We show that if (X, ‖ ·‖) is a p-convex Banach space then for any Lipschitz function f : H→ X there exist x, y ∈ H with dW (x, y) arbitrarily large and ‖f(x)− f(y)‖ dW (x, y) . ( log log dW (x, y) log dW (x, y) )1/p . (1) We also show that any embedding into X of a ball...

Consider a non-negative function f : R → R+ such that ∫ f dγn = 1, where γn is the ndimensional Gaussian measure. If f is semi-log-convex, i.e. if there exists a number β ≥ 1 such that for all x ∈ R, the eigenvalues of ∇ log f(x) are at least −β, then f satisfies an improved form of Markov’s inequality: For all α ≥ e, γn ( {x ∈ R : f(x) > α} ) ≤ 1 α · Cβ(log logα) 4 √ logα , where C is a univer...

Log-Brunn-Minkowski inequality was conjectured by Boröczky, Lutwak, Yang and Zhang [7], and it states that a certain strengthening of the classical Brunn-Minkowski inequality is admissible in the case of symmetric convex sets. It was recently shown by Nayar, Zvavitch, the second and the third authors [27], that Log-Brunn-Minkowski inequality implies a certain dimensional Brunn-Minkowski inequal...

We show that O(n) exchanging flips suffice to transform any edge-labelled pointed pseudo-triangulation into any other with the same set of labels. By using insertion, deletion and exchanging flips, we can transform any edge-labelled pseudo-triangulation into any other with O(n log c+h log h) flips, where c is the number of convex layers and h is the number of points on the convex hull.