Green's theoremIn vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C. It is the two-dimensional special case of Stokes' theorem. Let C be a positively oriented, piecewise smooth, simple closed curve in a plane, and let D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D and have continuous partial derivatives there, then where the path of integration along C is anticlockwise.
Net forceIn mechanics, the net force is the sum of all the forces acting on an object. For example, if two forces are acting upon an object in opposite directions, and one force is greater than the other, the forces can be replaced with a single force that is the difference of the greater and smaller force. That force is the net force. When forces act upon an object, they change its acceleration. The net force is the combined effect of all the forces on the object's acceleration, as described by Newton's second law of motion.
Precision and recallIn pattern recognition, information retrieval, object detection and classification (machine learning), precision and recall are performance metrics that apply to data retrieved from a collection, corpus or sample space. Precision (also called positive predictive value) is the fraction of relevant instances among the retrieved instances. Written as a formula:. Recall (also known as sensitivity) is the fraction of relevant instances that were retrieved. Written as a formula: . Both precision and recall are therefore based on relevance.
CentroidIn mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. The same definition extends to any object in n-dimensional Euclidean space. In geometry, one often assumes uniform mass density, in which case the barycenter or center of mass coincides with the centroid. Informally, it can be understood as the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin.
TheoremIn mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic.
Sensitivity and specificitySensitivity and specificity mathematically describe the accuracy of a test that reports the presence or absence of a condition. If individuals who have the condition are considered "positive" and those who do not are considered "negative", then sensitivity is a measure of how well a test can identify true positives and specificity is a measure of how well a test can identify true negatives: Sensitivity (true positive rate) is the probability of a positive test result, conditioned on the individual truly being positive.
Binary classificationBinary classification is the task of classifying the elements of a set into two groups (each called class) on the basis of a classification rule. Typical binary classification problems include: Medical testing to determine if a patient has certain disease or not; Quality control in industry, deciding whether a specification has been met; In information retrieval, deciding whether a page should be in the result set of a search or not. Binary classification is dichotomization applied to a practical situation.
Pythagorean theoremIn mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation: The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.
Triangle centerIn geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example, the centroid, circumcenter, incenter and orthocenter were familiar to the ancient Greeks, and can be obtained by simple constructions. Each of these classical centers has the property that it is invariant (more precisely equivariant) under similarity transformations.
Evaluation of binary classifiersThe evaluation of binary classifiers compares two methods of assigning a binary attribute, one of which is usually a standard method and the other is being investigated. There are many metrics that can be used to measure the performance of a classifier or predictor; different fields have different preferences for specific metrics due to different goals. For example, in medicine sensitivity and specificity are often used, while in computer science precision and recall are preferred.
AvicennaIbn Sina (ابن سینا; 980 – June 1037 CE), commonly known in the West as Avicenna (ˌævɪˈsɛnə,_ˌɑːvɪ-), was the preeminent philosopher and physician of the Muslim world, flourishing during the Islamic Golden Age, serving in the courts of various Iranian rulers. He is often described as the father of early modern medicine. His philosophy was of the Muslim Peripatetic school derived from Aristotelianism.
WeightIn science and engineering, the weight of an object is the force acting on the object due to acceleration or gravity. Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar quantity, the magnitude of the gravitational force. Yet others define it as the magnitude of the reaction force exerted on a body by mechanisms that counteract the effects of gravity: the weight is the quantity that is measured by, for example, a spring scale.
