Ricci curvatureIn differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or pseudo-Euclidean space. The Ricci tensor can be characterized by measurement of how a shape is deformed as one moves along geodesics in the space.
InvertebrateInvertebrates are a paraphyletic group of animals that neither possess nor develop a vertebral column (commonly known as a backbone or spine), derived from the notochord. This is a grouping including all animals apart from the chordate subphylum Vertebrata. Familiar examples of invertebrates include arthropods, mollusks, annelids, echinoderms and cnidarians. The majority of animal species are invertebrates; one estimate puts the figure at 97%. Many invertebrate taxa have a greater number and variety of species than the entire subphylum of Vertebrata.
Common octopusThe common octopus (Octopus vulgaris) is a mollusc belonging to the class Cephalopoda. Octopus vulgaris is one of the most studied of all octopus species, and also one of the most intelligent. It ranges from the eastern Atlantic, extends from the Mediterranean Sea and the southern coast of England, to the southern coast of South Africa. It also occurs off the Azores, Canary Islands, and Cape Verde Islands. The species is also common in the Western Atlantic. Octopus vulgaris grows to in mantle length with arms up to long.
Online machine learningIn computer science, online machine learning is a method of machine learning in which data becomes available in a sequential order and is used to update the best predictor for future data at each step, as opposed to batch learning techniques which generate the best predictor by learning on the entire training data set at once. Online learning is a common technique used in areas of machine learning where it is computationally infeasible to train over the entire dataset, requiring the need of out-of-core algorithms.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Blue-ringed octopusBlue-ringed octopuses, comprising the genus Hapalochlaena, are four extremely venomous species of octopus that are found in tide pools and coral reefs in the Pacific and Indian oceans, from Japan to Australia. They can be identified by their yellowish skin and characteristic blue and black rings that change color dramatically when the animal is threatened. They eat small crustaceans, including crabs, hermit crabs, shrimp and other small sea animals. They are one of the world's most venomous marine animals.
Measure-preserving dynamical systemIn mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservative systems. They provide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from classical mechanics (in particular, most non-dissipative systems) as well as systems in thermodynamic equilibrium.
Robot kinematicsIn robotics, robot kinematics applies geometry to the study of the movement of multi-degree of freedom kinematic chains that form the structure of robotic systems. The emphasis on geometry means that the links of the robot are modeled as rigid bodies and its joints are assumed to provide pure rotation or translation. Robot kinematics studies the relationship between the dimensions and connectivity of kinematic chains and the position, velocity and acceleration of each of the links in the robotic system, in order to plan and control movement and to compute actuator forces and torques.
Supervised learningSupervised learning (SL) is a paradigm in machine learning where input objects (for example, a vector of predictor variables) and a desired output value (also known as human-labeled supervisory signal) train a model. The training data is processed, building a function that maps new data on expected output values. An optimal scenario will allow for the algorithm to correctly determine output values for unseen instances. This requires the learning algorithm to generalize from the training data to unseen situations in a "reasonable" way (see inductive bias).
Marine larval ecologyMarine larval ecology is the study of the factors influencing dispersing larvae, which many marine invertebrates and fishes have. Marine animals with a larva typically release many larvae into the water column, where the larvae develop before metamorphosing into adults. Marine larvae can disperse over long distances, although determining the actual distance is challenging, because of their size and the lack of a good tracking method. Knowing dispersal distances is important for managing fisheries, effectively designing marine reserves, and controlling invasive species.
