Path integral formulationThe path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization.
Mode choiceMode choice analysis is the third step in the conventional four-step transportation forecasting model of transportation planning, following trip distribution and preceding route assignment. From origin-destination table inputs provided by trip distribution, mode choice analysis allows the modeler to determine probabilities that travelers will use a certain mode of transport. These probabilities are called the modal share, and can be used to produce an estimate of the amount of trips taken using each feasible mode.
Route assignmentRoute assignment, route choice, or traffic assignment concerns the selection of routes (alternatively called paths) between origins and destinations in transportation networks. It is the fourth step in the conventional transportation forecasting model, following trip generation, trip distribution, and mode choice. The zonal interchange analysis of trip distribution provides origin-destination trip tables. Mode choice analysis tells which travelers will use which mode.
GPS tracking unitA GPS tracking unit, geotracking unit, satellite tracking unit, or simply tracker is a navigation device normally on a vehicle, asset, person or animal that uses satellite navigation to determine its movement and determine its WGS84 UTM geographic position (geotracking) to determine its location. Satellite tracking devices may send special satellite signals that are processed by a receiver. Locations are stored in the tracking unit or transmitted to an Internet-connected device using the cellular network (GSM/GPRS/CDMA/LTE or SMS), radio, or satellite modem embedded in the unit or WiFi work worldwide.
Trip distributionTrip distribution (or destination choice or zonal interchange analysis) is the second component (after trip generation, but before mode choice and route assignment) in the traditional four-step transportation forecasting model. This step matches tripmakers’ origins and destinations to develop a “trip table”, a matrix that displays the number of trips going from each origin to each destination. Historically, this component has been the least developed component of the transportation planning model.
Location-based serviceA location-based service (LBS) is a general term denoting software services which use geographic data and information to provide services or information to users. LBS can be used in a variety of contexts, such as health, indoor object search, entertainment, work, personal life, etc. Commonly used examples of location based services include navigation software, social networking services, location-based advertising, and tracking systems. LBS can also include mobile commerce when taking the form of coupons or advertising directed at customers based on their current location.
Matching (graph theory)In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In other words, a subset of the edges is a matching if each vertex appears in at most one edge of that matching. Finding a matching in a bipartite graph can be treated as a network flow problem. Given a graph G = (V, E), a matching M in G is a set of pairwise non-adjacent edges, none of which are loops; that is, no two edges share common vertices.
Wheeler's delayed-choice experimentWheeler's delayed-choice experiment describes a family of thought experiments in quantum physics proposed by John Archibald Wheeler, with the most prominent among them appearing in 1978 and 1984. These experiments are attempts to decide whether light somehow "senses" the experimental apparatus in the double-slit experiment it travels through, adjusting its behavior to fit by assuming an appropriate determinate state, or whether light remains in an indeterminate state, exhibiting both wave-like and particle-like behavior until measured.
Nonlinear dimensionality reductionNonlinear dimensionality reduction, also known as manifold learning, refers to various related techniques that aim to project high-dimensional data onto lower-dimensional latent manifolds, with the goal of either visualizing the data in the low-dimensional space, or learning the mapping (either from the high-dimensional space to the low-dimensional embedding or vice versa) itself. The techniques described below can be understood as generalizations of linear decomposition methods used for dimensionality reduction, such as singular value decomposition and principal component analysis.
Shortest path problemIn graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment.
