OscillationOscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms.
Connectivity (graph theory)In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network. In an undirected graph G, two vertices u and v are called connected if G contains a path from u to v.
Kuramoto modelThe Kuramoto model (or Kuramoto–Daido model), first proposed by Yoshiki Kuramoto, is a mathematical model used in describing synchronization. More specifically, it is a model for the behavior of a large set of coupled oscillators. Its formulation was motivated by the behavior of systems of chemical and biological oscillators, and it has found widespread applications in areas such as neuroscience and oscillating flame dynamics. Kuramoto was quite surprised when the behavior of some physical systems, namely coupled arrays of Josephson junctions, followed his model.
Social dynamicsSocial dynamics (or sociodynamics) is the study of the behavior of groups that results from the interactions of individual group members as well to the study of the relationship between individual interactions and group level behaviors. The field of social dynamics brings together ideas from economics, sociology, social psychology, and other disciplines, and is a sub-field of complex adaptive systems or complexity science. The fundamental assumption of the field is that individuals are influenced by one another's behavior.
Academic degreeAn academic degree is a qualification awarded to a student upon successful completion of a course of study in higher education, usually at a college or university. These institutions often offer degrees at various levels, usually divided into undergraduate and postgraduate degrees. The most common undergraduate degree is the bachelor's degree, although some educational systems offer lower level undergraduate degrees such as associate and foundation degrees. Common postgraduate degrees include master's degrees and doctorates.
K-vertex-connected graphIn graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed. The vertex-connectivity, or just connectivity, of a graph is the largest k for which the graph is k-vertex-connected. A graph (other than a complete graph) has connectivity k if k is the size of the smallest subset of vertices such that the graph becomes disconnected if you delete them.
K-edge-connected graphIn graph theory, a connected graph is k-edge-connected if it remains connected whenever fewer than k edges are removed. The edge-connectivity of a graph is the largest k for which the graph is k-edge-connected. Edge connectivity and the enumeration of k-edge-connected graphs was studied by Camille Jordan in 1869. Let be an arbitrary graph. If the subgraph is connected for all where , then G is said to be k-edge-connected. The edge connectivity of is the maximum value k such that G is k-edge-connected.
Graph propertyIn graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations such as particular labellings or drawings of the graph. While graph drawing and graph representation are valid topics in graph theory, in order to focus only on the abstract structure of graphs, a graph property is defined to be a property preserved under all possible isomorphisms of a graph. In other words, it is a property of the graph itself, not of a specific drawing or representation of the graph.
Injection lockingInjection locking and injection pulling are the frequency effects that can occur when a harmonic oscillator is disturbed by a second oscillator operating at a nearby frequency. When the coupling is strong enough and the frequencies near enough, the second oscillator can capture the first oscillator, causing it to have essentially identical frequency as the second. This is injection locking. When the second oscillator merely disturbs the first but does not capture it, the effect is called injection pulling.
Bachelor's degreeA bachelor's degree (from Middle Latin baccalaureus) or baccalaureate (from Modern Latin baccalaureatus) is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six years (depending on institution and academic discipline). The two most common bachelor's degrees are the Bachelor of Arts (BA) and the Bachelor of Science (BS or BSc).