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.
Statistical classificationIn statistics, classification is the problem of identifying which of a set of categories (sub-populations) an observation (or observations) belongs to. Examples are assigning a given email to the "spam" or "non-spam" class, and assigning a diagnosis to a given patient based on observed characteristics of the patient (sex, blood pressure, presence or absence of certain symptoms, etc.). Often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features.
ConnectomicsConnectomics is the production and study of connectomes: comprehensive maps of connections within an organism's nervous system. More generally, it can be thought of as the study of neuronal wiring diagrams with a focus on how structural connectivity, individual synapses, cellular morphology, and cellular ultrastructure contribute to the make up of a network. The nervous system is a network made of billions of connections and these connections are responsible for our thoughts, emotions, actions, memories, function and dysfunction.
Brain–computer interfaceA brain–computer interface (BCI), sometimes called a brain–machine interface (BMI) or smartbrain, is a direct communication pathway between the brain's electrical activity and an external device, most commonly a computer or robotic limb. BCIs are often directed at researching, mapping, assisting, augmenting, or repairing human cognitive or sensory-motor functions. They are often conceptualized as a human–machine interface that skips the intermediary component of the physical movement of body parts, although they also raise the possibility of the erasure of the discreteness of brain and machine.
Brain connectivity estimatorsBrain connectivity estimators represent patterns of links in the brain. Connectivity can be considered at different levels of the brain's organisation: from neurons, to neural assemblies and brain structures. Brain connectivity involves different concepts such as: neuroanatomical or structural connectivity (pattern of anatomical links), functional connectivity (usually understood as statistical dependencies) and effective connectivity (referring to causal interactions).
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.
Neural decodingNeural decoding is a neuroscience field concerned with the hypothetical reconstruction of sensory and other stimuli from information that has already been encoded and represented in the brain by networks of neurons. Reconstruction refers to the ability of the researcher to predict what sensory stimuli the subject is receiving based purely on neuron action potentials. Therefore, the main goal of neural decoding is to characterize how the electrical activity of neurons elicit activity and responses in the brain.
Symmetric graphIn the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u_1—v_1 and u_2—v_2 of G, there is an automorphism such that and In other words, a graph is symmetric if its automorphism group acts transitively on ordered pairs of adjacent vertices (that is, upon edges considered as having a direction). Such a graph is sometimes also called 1-arc-transitive or flag-transitive. By definition (ignoring u_1 and u_2), a symmetric graph without isolated vertices must also be vertex-transitive.
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.
Lobes of the brainThe lobes of the brain are the major identifiable zones of the cerebral cortex, and they comprise the surface of each hemisphere of the cerebrum. The two hemispheres are roughly symmetrical in structure, and are connected by the corpus callosum. They traditionally have been divided into four lobes, but are today considered as having six lobes each. The lobes are large areas that are anatomically distinguishable, and are also functionally distinct to some degree.
