Component (graph theory)In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting of the whole graph. Components are sometimes called connected components. The number of components in a given graph is an important graph invariant, and is closely related to invariants of matroids, topological spaces, and matrices.
Subspace topologyIn topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology). Given a topological space and a subset of , the subspace topology on is defined by That is, a subset of is open in the subspace topology if and only if it is the intersection of with an open set in .
Social networkA social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for analyzing the structure of whole social entities as well as a variety of theories explaining the patterns observed in these structures. The study of these structures uses social network analysis to identify local and global patterns, locate influential entities, and examine network dynamics.
Product topologyIn topology and related areas of mathematics, a product space is the Cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more natural-seeming, topology called the box topology, which can also be given to a product space and which agrees with the product topology when the product is over only finitely many spaces.
Complex systemA complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and ultimately the entire universe.
Network theoryIn mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the nodes or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components. Network theory has applications in many disciplines, including statistical physics, particle physics, computer science, electrical engineering, biology, archaeology, linguistics, economics, finance, operations research, climatology, ecology, public health, sociology, psychology, and neuroscience.
Initial topologyIn general topology and related areas of mathematics, the initial topology (or induced topology or weak topology or limit topology or projective topology) on a set with respect to a family of functions on is the coarsest topology on that makes those functions continuous. The subspace topology and product topology constructions are both special cases of initial topologies. Indeed, the initial topology construction can be viewed as a generalization of these.
ForecastingForecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual results creating a variance actual analysis. Prediction is a similar but more general term. Forecasting might refer to specific formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods or the process of prediction and resolution itself.
Structured data analysis (statistics)Structured data analysis is the statistical data analysis of structured data. This can arise either in the form of an a priori structure such as multiple-choice questionnaires or in situations with the need to search for structure that fits the given data, either exactly or approximately. This structure can then be used for making comparisons, predictions, manipulations etc. Algebraic data analysis Bayesian analysis Cluster analysis Combinatorial data analysis Formal concept analysis Functional data analysi
Anomaly detectionIn data analysis, anomaly detection (also referred to as outlier detection and sometimes as novelty detection) is generally understood to be the identification of rare items, events or observations which deviate significantly from the majority of the data and do not conform to a well defined notion of normal behaviour. Such examples may arouse suspicions of being generated by a different mechanism, or appear inconsistent with the remainder of that set of data.
Dynamic network analysisDynamic network analysis (DNA) is an emergent scientific field that brings together traditional social network analysis (SNA), link analysis (LA), social simulation and multi-agent systems (MAS) within network science and network theory. Dynamic networks are a function of time (modeled as a subset of the real numbers) to a set of graphs; for each time point there is a graph. This is akin to the definition of dynamical systems, in which the function is from time to an ambient space, where instead of ambient space time is translated to relationships between pairs of vertices.
Economic forecastingEconomic forecasting is the process of making predictions about the economy. Forecasts can be carried out at a high level of aggregation—for example for GDP, inflation, unemployment or the fiscal deficit—or at a more disaggregated level, for specific sectors of the economy or even specific firms. Economic forecasting is a measure to find out the future prosperity of a pattern of investment and is the key activity in economic analysis.
