Agent-based modelAn agent-based model (ABM) is a computational model for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) in order to understand the behavior of a system and what governs its outcomes. It combines elements of game theory, complex systems, emergence, computational sociology, multi-agent systems, and evolutionary programming. Monte Carlo methods are used to understand the stochasticity of these models.
Urban historyUrban history is a field of history that examines the historical nature of cities and towns, and the process of urbanization. The approach is often multidisciplinary, crossing boundaries into fields like social history, architectural history, urban sociology, urban geography, business history, and archaeology. Urbanization and industrialization were popular themes for 20th-century historians, often tied to an implicit model of modernization, or the transformation of rural traditional societies.
Sustainable urbanismSustainable urbanism is both the study of cities and the practices to build them (urbanism), that focuses on promoting their long term viability by reducing consumption, waste and harmful impacts on people and place while enhancing the overall well-being of both people and place. Well-being includes the physical, ecological, economic, social, health and equity factors, among others, that comprise cities and their populations.
Axiom of choiceIn mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty. Informally put, the axiom of choice says that given any collection of sets, each containing at least one element, it is possible to construct a new set by arbitrarily choosing one element from each set, even if the collection is infinite. Formally, it states that for every indexed family of nonempty sets, there exists an indexed set such that for every .
Traffic lightTraffic lights, traffic signals, or stoplights – also known as robots in South Africa – are signalling devices positioned at road intersections, pedestrian crossings, and other locations in order to control the flow of traffic. Traffic lights consist normally of three signals, transmitting meaningful information to road users through colours and symbols including arrows and bicycles. The regular traffic light colours are red, yellow (also known as amber), and green arranged vertically or horizontally in that order.
Dimensionality reductionDimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with).
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.
Curse of dimensionalityThe curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming. Dimensionally cursed phenomena occur in domains such as numerical analysis, sampling, combinatorics, machine learning, data mining and databases.
Urban heat islandAn urban heat island (UHI) is an urban area that is significantly warmer than its surrounding rural areas due to human activities. The temperature difference is usually larger at night than during the day, and is most apparent when winds are weak. UHI is most noticeable during the summer and winter. The main cause of the UHI effect is from the modification of land surfaces. A study has shown that heat islands can be affected by proximity to different types of land cover, so that proximity to barren land causes urban land to become hotter and proximity to vegetation makes it cooler.
SequenceIn mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position.
Urban forestAn urban forest is a forest, or a collection of trees, that grow within a city, town or a suburb. In a wider sense, it may include any kind of woody plant vegetation growing in and around human settlements. As opposed to a forest park, whose ecosystems are also inherited from wilderness leftovers, urban forests often lack amenities like public bathrooms, paved paths, or sometimes clear borders which are distinct features of parks. Care and management of urban forests is called urban forestry.
Zermelo–Fraenkel set theoryIn set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.
