Decision problemIn computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers x and y, does x evenly divide y?". The answer is either 'yes' or 'no' depending upon the values of x and y. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem.
Differential formIn mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For instance, the expression f(x) dx is an example of a 1-form, and can be integrated over an interval [a, b] contained in the domain of f: Similarly, the expression f(x, y, z) dx ∧ dy + g(x, y, z) dz ∧ dx + h(x, y, z) dy ∧ dz is a 2-form that can be integrated over a surface S: The symbol ∧ denotes the exterior product, sometimes called the wedge product, of two differential forms.
Conjugate gradient methodIn mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition. Large sparse systems often arise when numerically solving partial differential equations or optimization problems.
Computational anatomyComputational anatomy is an interdisciplinary field of biology focused on quantitative investigation and modelling of anatomical shapes variability. It involves the development and application of mathematical, statistical and data-analytical methods for modelling and simulation of biological structures. The field is broadly defined and includes foundations in anatomy, applied mathematics and pure mathematics, machine learning, computational mechanics, computational science, biological imaging, neuroscience, physics, probability, and statistics; it also has strong connections with fluid mechanics and geometric mechanics.
Procrustes analysisIn statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name Procrustes (Προκρούστης) refers to a bandit from Greek mythology who made his victims fit his bed either by stretching their limbs or cutting them off. In mathematics: an orthogonal Procrustes problem is a method which can be used to find out the optimal rotation and/or reflection (i.e., the optimal orthogonal linear transformation) for the Procrustes Superimposition (PS) of an object with respect to another.
Ordered geometryOrdered geometry is a form of geometry featuring the concept of intermediacy (or "betweenness") but, like projective geometry, omitting the basic notion of measurement. Ordered geometry is a fundamental geometry forming a common framework for affine, Euclidean, absolute, and hyperbolic geometry (but not for projective geometry). Moritz Pasch first defined a geometry without reference to measurement in 1882. His axioms were improved upon by Peano (1889), Hilbert (1899), and Veblen (1904).
SailingSailing employs the wind—acting on sails, wingsails or kites—to propel a craft on the surface of the water (sailing ship, sailboat, raft, windsurfer, or kitesurfer), on ice (iceboat) or on land (land yacht) over a chosen course, which is often part of a larger plan of navigation. From prehistory until the second half of the 19th century, sailing craft were the primary means of maritime trade and transportation; exploration across the seas and oceans was reliant on sail for anything other than the shortest distances.
Dinghy sailingDinghy sailing is the activity of sailing small boats by using five essential controls: the sails the foils (i.e. the daggerboard or centreboard and rudder and sometimes lifting foils as found on the Moth) the trim (forward/rear angle of the boat in the water) side-to-side balance of the dinghy by hiking or movement of the crew, particularly in windy weather ("move fast or swim") the choice of route (in terms of existing and anticipated wind shifts, possible obstacles, other water traffic, currents, tides etc.
Boat racingBoat racing is a sport in which boats, or other types of watercraft, race on water. Boat racing powered by oars is recorded as having occurred in ancient Egypt, and it is likely that people have engaged in races involving boats and other water-borne craft for as long as such watercraft have existed. A regatta is a series of boat races. The term comes from the Venetian language, with regata meaning "contest, contention for mastery"(from regatare ("compete, haggle, sell at retail"), possibly from ''recatare') and typically describes racing events of rowed or sailed water craft, although some powerboat race series are also called regattas.
Hamiltonian path problemIn the mathematical field of graph theory the Hamiltonian path problem and the Hamiltonian cycle problem are problems of determining whether a Hamiltonian path (a path in an undirected or directed graph that visits each vertex exactly once) or a Hamiltonian cycle exists in a given graph (whether directed or undirected). Both problems are NP-complete.
