Today’s state-of-the-art visual object detection systems are based on three key components: 1) sophisticated features (to encode various visual invariances), 2) a powerful classifier (to build a discriminative object class model), and 3) lots of data (to use in largescale hard-negative mining). While conventional wisdom tends to attribute the success of such methods to the ability of the classi...

Numerous studies of the interaction between buyers and sellers in a market can be found in the rapidly developing research literature on electronic commerce (EC). This interaction usually takes the form of a transaction process, in which goods or services are exchanged between customers and suppliers. (See Figure 1.) This process may involve none, one or several intermediaries or middlemen, dep...

Let a, b and c be positive integers and consider a hexagon with side lengths a,b,c,a,b,c whose angles are 120◦ (see Figure 1). The subject of our interest is rhombus tilings of such a hexagon using rhombi with all sides of length 1 and angles 60◦ and 120◦. Figure 2 shows an example of a rhombus tiling of a hexagon with a = 3, b = 5 and c = 4. A first natural question to be asked is how many rho...

Theorem 1. Let (S2, g) be the two dimensional sphere with a metric of class C1,1 whose Gaussian curvature satisfies 0 ≤ K ≤ 1. Then any simple closed geodesic γ on (S2, g) has length at least 2π. If the length of γ is 2π, then (S2, g) is isometric to the standard round sphere (S2, g0) and γ is a great circle on (S2, g0) or (S 2, g) is isometric to a circular cylinder of circumference 2π capped ...

In this paper we consider homogenization of oscillating free boundary velocities in periodic media, with general initial data. We prove that there is a unique and stable effective free boundary velocity in the homogenization limit. 0 Introduction Consider a compact set K ⊂ IR with smooth boundary ∂K. Suppose that a bounded domain Ω contains K and let Ω0 = Ω − K and Γ0 = ∂Ω. We also assume that ...

1. CONSTRUCTIONS IN GEOMETRY. The study of methods that accomplish trisections is vast and extends back in time approximately 2300 years. My own favorite method of trisection from the Ancients is due to Archimedes, who performed a “neusis” between a circle and line. Basically a neusis (or use of a marked ruler) allows the marking of points on constructed objects of unit distance apart using a r...

The theory of stable pairs in the derived category yields an enumerative geometry of curves in 3-folds. We evaluate the equivariant vertex for stable pairs on toric 3-folds in terms of weighted box counting. In the toric Calabi-Yau case, the result simplifies to a new form of pure box counting. The conjectural equivalence with the DT vertex predicts remarkable identities. The equivariant vertex...

Our contribution in this work is a new measure of similarity between surface points based on a spin-image surface representation that allows efficient identification of corresponding points between two surfaces. We represent a molecular surface as a collection of two-dimensional (2D) spin images associated to Connolly's points [1]. Given a surface point P with normal n, its associated spin imag...

Data is everywhere, notably in this information explosion era. Beyond the first-order summary of a sample by its average value or its median, the bell-shaped Gaussian (or normal) curve has long been observed in the histograms of many data samples since the early history of probability, statistics and related fields. The Gaussian distribution, known commonly under the name of Law of Frequency of...

Before we discuss the details of the Bayesian detection, let us take a quick tour about the overall framework to detect (or classify) an object in practice. In the Bayesian setting, we model observations as random samples drawn from some probability distributions. The classification process usually involves extracting features from the observations, and a decision rule that satisfies certain op...