In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from elementary algebra. In propositional logic, distribution refers to two valid rules of replacement. The rules allow one to reformulate conjunctions and disjunctions within logical proofs.
For example, in arithmetic:
In the left-hand side of the first equation, the 2 multiplies the sum of 1 and 3; on the right-hand side, it multiplies the 1 and the 3 individually, with the products added afterwards. Because these give the same final answer (8), it is said that multiplication by 2 distributes over addition of 1 and 3. Since one could have put any real numbers in place of 2, 1, and 3 above, and still have obtained a true equation, we say that multiplication of real numbers distributes over addition of real numbers.
Given a set S and two binary operators ∗ and + on S, we say that the operation:
∗ is left-distributive over + if, given any elements x, y, and z of S,
In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference. Examples are found in experiments whose sample space is non-numerical, where the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution can be specified by a probability mass function; and experiments with sample spaces encoded by continuous random variables, where the distribution can be specified by a probability density function. More complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures.
In applied probability, a probability distribution can be specified in a number of different ways, often chosen for mathematical convenience:
In mathematics and computer science, a history monoid is a way of representing the histories of concurrently running computer processes as a collection of strings, each string representing the individual history of a process. The history monoid provides a set of synchronization primitives (such as locks, mutexes or thread joins) for providing rendezvous points between a set of independently executing processes or threads.
History monoids occur in the theory of concurrent computation, and provide a low-level mathematical foundation for process calculi, such as CSP the language of communicating sequential processes, or CCS, the calculus of communicating systems. History monoids were first presented by M.W. Shields.
History monoids are isomorphic to trace monoids (free partially commutative monoids) and to the monoid of dependency graphs. As such, they are free objects and are universal. The history monoid is a type of semi-abelian categorical product in the category of monoids.
In mathematics and computer science, an algorithm (i/ˈælɡərɪðəm/ AL-gə-ri-dhəm) is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning.
The words 'algorithm' and 'algorism' come from the name al-Khwārizmī. Al-Khwārizmī (Persian: خوارزمي, c. 780-850) was a Persian mathematician, astronomer, geographer, and scholar.
An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.
A medical algorithm is any computation, formula, statistical survey, nomogram, or look-up table, useful in healthcare. Medical algorithms include decision tree approaches to healthcare treatment (e.g., if symptoms A, B, and C are evident, then use treatment X) and also less clear-cut tools aimed at reducing or defining uncertainty.
Medical algorithms are part of a broader field which is usually fit under the aims of medical informatics and medical decision making. Medical decisions occur in several areas of medical activity including medical test selection, diagnosis, therapy and prognosis, and automatic control of medical equipment.
In relation to logic-based and artificial neural network-based clinical decision support system, which are also computer applications to the medical decision making field, algorithms are less complex in architecture, data structure and user interface. Medical algorithms are not necessarily implemented using digital computers. In fact, many of them can be represented on paper, in the form of diagrams, nomographs, etc.
Algorithm is the first studio album from My Heart to Fear. Solid State Records released the album on July 9, 2013.
Awarding the album three stars from Alternative Press, Jason Schreurs writes, "As is the case with the bulk of this musical style, the vocals bring it back down to a near-mediocre level." Bradley Zorgdrager, rating the album a five out of ten for Exclaim!, says, "Unfortunately, a lack of inspiration causes the songs to come undone, as many of the parts sound only like a means to get to the next." Giving the album four stars at About.com, Todd Lyons states, "everything binds together into one masterful meditation." Tim Dodderidge, indicating in a 8.5 out of ten review by Mind Equals Blown, writes, "From start to finish, My Heart to Fear’s debut full-length is an energetic, ferocious, cathartic and inspiring metal album."
Kevin Hoskins, giving the album three and a half stars for Jesus Freak Hideout, describes, "this is just metal done well ... but any hardcore fan will be digging this release all summer long." Awarding the album four and a half stars from HM Magazine, Sean Huncherick states, "One good thing about Algorithm is that the band realizes they don’t need to constantly play as fast as they can." Brody B., rating the album four star at Indie Vision Music, writes, "With a few minor tweaks here and there that could have made songs feel more fleshed out I would have had a hard time finding fault with this debut record."