We experimentally realize "hybrid" entanglement swapping between discrete-variable (DV) and continuous-variable (CV) optical systems. DV two-mode entanglement as obtainable from a single photon split at a beam splitter is robustly transferred by means of efficient CV entanglement and operations, using sources of squeezed light and homodyne detections. The DV entanglement after the swapping is v...

Let V be a set of points in R. Define a linear functional L on the space of polynomials, Lf = ∑ x∈V f(x)ρ(x), where ρ is a nonzero function on V . The structure of discrete orthogonal polynomials of several variables with respect to the bilinear form 〈f, g〉 = L(fg) is studied. For a given V , the subspace of polynomials that will generate orthogonal polynomials on V is identified. One result sh...

Suppose a city’s traffic engineering department monitors a certain intersection during a one-hour period in the middle of the day. Many characteristics might be of interest to the observers, including the number of vehicles that enter the intersection, the largest number of vehicles in the left turn lane during a signal cycle, the speed of the fastest vehicle going through the intersection, the...

A prominent issue in statistics education is the sometimes large disparity between the theoretical and the computational coursework. discreteRV is an R package for manipulation of discrete random variables which uses clean and familiar syntax similar to the mathematical notation in introductory probability courses. The package offers functions that are simple enough for users with little experi...

Large-scale computational models have become common tools for analyzing complex manmade systems. However, when coupled with optimization or uncertainty quantification methods in order to conduct extensive model exploration and analysis, the computational expense quickly becomes intractable. Furthermore, these models may have both continuous and discrete parameters. One common approach to mitiga...

We describe five types of results concerning information and concentration of discrete random variables, and relationships between them. These results are motivated by their counterparts in the continuous case. The results we consider are information theoretic approaches to Poisson approximation, the maximum entropy property of the Poisson distribution, discrete concentration (Poincaré and loga...

Both the simulation research and software communities have been interested in optimization via simulation (OvS), by which we mean maximizing or minimizing the expected value of some output of a stochastic simulation. Continuous-decision-variable OvS, and gradient estimation to support it, has been an active research area with significant advances. However, the decision variables in many operati...