Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science

Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in data science. The group consisted of 25 undergraduate faculty from a variety of institutions in the United States, primarily from the disciplines of mathematics, statistics, and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in data science

On the Passage of Gaussian Beams through Cusps in Ray Paths

Gaussian beams are asymptotic solutions to hyperbolic partial differentiable equations which propagate along null bicharacteristic curves in phase space. To build gaussian beams, one constructs a phase and an amplitude by using data along a specific null bicharacteristic. The current construction assumes that the ray path a beam follows in position space is smooth. In this work, we extend the construction to the case in which the ray path has cusps and deduce the phase shift that occurs when a beam passes through these cusps. We also present a new formula for the phase of a gaussian beam

On the Passage of Gaussian Beams through Cusps in Ray Paths

Gaussian beams are asymptotic solutions to hyperbolic partial differentiable equations which propagate along null bicharacteristic curves in phase space. To build gaussian beams, one constructs a phase and an amplitude by using data along a specific null bicharacteristic. The current construction assumes that the ray path a beam follows in position space is smooth. In this work, we extend the construction to the case in which the ray path has cusps and deduce the phase shift that occurs when a beam passes through these cusps. We also present a new formula for the phase of a gaussian beam

Temporal Reasoning with Kinodynamic Networks

Temporal reasoning is central to Artificial Intelligence (AI) and many of its applications. However, the existing algorithmic frameworks for temporal reasoning are not expressive enough to be applicable to robots with complex kinodynamic constraints typically described using differential equations. For example, while minimum and maximum velocity constraints can be encoded in Simple Temporal Networks (STNs), higher-order kinodynamic constraints cannot be represented in existing frameworks. In this paper, we present a novel framework for temporal reasoning called Kinodynamic Networks (KDNs). KDNs combine elements of existing temporal reasoning frameworks with the idea of Bernstein polynomials. The velocity profiles of robots are represented using Bernstein polynomials; and dynamic constraints on these velocity profiles can be converted to linear constraints on the to-be-determined coefficients of their Bernstein polynomials. We study KDNs for their attractive theoretical properties and apply them to the Multi-Agent Path Finding (MAPF) problem with higher-order kinodynamic constraints. We show that our approach is not only scalable but also yields smooth velocity profiles for all robots that can be executed by their controllers