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Functional Decomposition
In mathematics, functional decomposition is the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed (i.e., recomposed) from those parts by function composition. This process of decomposition may be undertaken to gain insight into the identity of the constituent components which may reflect individual physical processes of interest. Also functional decomposition may result in a compressed representation of the global function, a task which is feasible only when the constituent processes possess a certain level of ''modularity'' (i.e., independence or non-interaction). between the components are critical to the function of the collection. All interactions may not be , but possibly deduced through repetitive , synthesis, validation and verification of composite behavior. Basic mathematical definition For a multivariate function y = f(x_1,x_2,\dots,x_n), functional decomposition generally refers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anti-realism
In analytic philosophy, anti-realism is a position which encompasses many varieties such as metaphysical, mathematical, semantic, scientific, moral and epistemic. The term was first articulated by British philosopher Michael Dummett in an argument against a form of realism Dummett saw as 'colorless reductionism'. In anti-realism, the truth of a statement rests on its demonstrability through internal logic mechanisms, such as the context principle or intuitionistic logic, in direct opposition to the realist notion that the truth of a statement rests on its correspondence to an external, independent reality. In anti-realism, this external reality is hypothetical and is not assumed. Anti-realism in its most general sense can be understood as being in contrast to a ''generic realism'', which holds that distinctive objects of a subject-matter exist and have properties independent of one's beliefs and conceptual schemes. The ways in which anti-realism rejects these type of claims ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Equation Modeling
Structural equation modeling (SEM) is a label for a diverse set of methods used by scientists in both experimental and observational research across the sciences, business, and other fields. It is used most in the social and behavioral sciences. A definition of SEM is difficult without reference to highly technical language, but a good starting place is the name itself. SEM involves the construction of a ''model'', to represent how various aspects of an observable or theoretical phenomenon are thought to be causally structurally related to one another. The ''structural'' aspect of the model implies theoretical associations between variables that represent the phenomenon under investigation. The postulated causal structuring is often depicted with arrows representing causal connections between variables (as in Figures 1 and 2) but these causal connections can be equivalently represented as equations. The causal structures imply that specific patterns of connections should appe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Networks
A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms can perform inference and learning in Bayesian networks. Bayesian networks that model sequences of variables (''e.g.'' speech signals or protein sequences) are called dynamic Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called influence diagrams. Graphical mode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensional Definition
In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term. Intensional definition An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. In the case of nouns, this is equivalent to specifying the properties that an object needs to have in order to be counted as a referent of the term. For example, an intensional definition of the word "bachelor" is "unmarried man". This definition is valid because being an unmarried man is both a necessary condition and a sufficient condition for being a bachelor: it is necessary because one cannot be a bachelor without being an unmarried man, and it is sufficient because any unmarried man is a bachelor.Cook, Roy T. "Intensional Definition". In ''A Dictionary of Philosophical Logic''. Edinburgh: Edinburgh University Press, 2009. 155. This ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accident (philosophy)
An accident (Greek ), in metaphysics and philosophy, is a property that the entity or substance has contingently, without which the substance can still retain its identity. An accident does not affect its essence. It does not mean an "accident" as used in common speech, a chance incident, normally harmful. Examples of accidents are color, taste, movement, and stagnation. Accident is contrasted with essence: a designation for the property or set of properties that make an entity or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity. Aristotle made a distinction between the essential and accidental properties of a thing. Thomas Aquinas and other Catholic theologians have employed the Aristotelian concepts of substance and accident in articulating the theology of the Eucharist, particularly the transubstantiation of bread and wine into body and blood. In this example, the bread and wine are considered accidents, since at trans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Property (philosophy)
In logic and philosophy (especially metaphysics), a property is a characteristic of an Object (philosophy), object; a red object is said to have the property of redness. The property may be considered a form of object in its own right, able to possess other properties. A property, however, differs from individual objects in that it may be instantiation principle, instantiated, and often in more than one object. It differs from the logical/mathematical concept of class (set theory), class by not having any concept of extensionality, and from the philosophical concept of class (philosophy), class in that a property is considered to be distinct from the objects which possess it. Understanding how different individual entities (or particulars) can in some sense have some of the same properties is the basis of the problem of universals. Terms and usage A property is any member of a class of entities that are capable of being attributed to objects. Terms similar to ''property'' include ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Essence
Essence ( la, essentia) is a polysemic term, used in philosophy and theology as a designation for the property or set of properties that make an entity or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity. Essence is contrasted with accident: a property that the entity or substance has contingently, without which the substance can still retain its identity. The concept originates rigorously with Aristotle (although it can also be found in Plato), who used the Greek expression ''to ti ên einai'' (τὸ τί ἦν εἶναι, literally meaning "the what it was to be" and corresponding to the scholastic term quiddity) or sometimes the shorter phrase ''to ti esti'' (τὸ τί ἐστι, literally meaning "the what it is" and corresponding to the scholastic term haecceity) for the same idea. This phrase presented such difficulties for its Latin translators that they coined the word ''essentia'' (English "essence") to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Porphyry (philosopher)
Porphyry of Tyre (; grc-gre, Πορφύριος, ''Porphýrios''; ar, فُرْفُورِيُوس, ''Furfūriyūs''; – ) was a Neoplatonic philosopher born in Tyre, Roman Phoenicia during Roman rule. He edited and published ''The Enneads'', the only collection of the work of Plotinus, his teacher. His commentary on Euclid's ''Elements'' was used as a source by Pappus of Alexandria. He wrote original works in the Greek language on a wide variety of topics, ranging from music theory to Homer to vegetarianism. His ''Isagoge'', or ''Introduction'', an introduction to logic and philosophy, was the standard textbook on logic throughout the Middle Ages in its Latin and Arabic translations. Porphyry was, and still is, also well-known for his anti-Christian polemics. Through works such as ''Philosophy from Oracles'' and ''Against the Christians'' (which was banned by Constantine the Great), he was involved in a controversy with early Christians. Biography The ''Suda'' (a 10th- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotelianism
Aristotelianism ( ) is a philosophical tradition inspired by the work of Aristotle, usually characterized by deductive logic and an analytic inductive method in the study of natural philosophy and metaphysics. It covers the treatment of the social sciences under a system of natural law. It answers why-questions by a scheme of four causes, including purpose or teleology, and emphasizes virtue ethics. Aristotle and his school wrote tractates on physics, biology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, and government. Any school of thought that takes one of Aristotle's distinctive positions as its starting point can be considered "Aristotelian" in the widest sense. This means that different Aristotelian theories (e.g. in ethics or in ontology) may not have much in common as far as their actual content is concerned besides their shared reference to Aristotle. In Aristotle's time, philosophy included natur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Philosophers
Ancient Greek philosophy arose in the 6th century BC, marking the end of the Greek Dark Ages. Greek philosophy continued throughout the Hellenistic period and the period in which Greece and most Greek-inhabited lands were part of the Roman Empire. Philosophy was used to make sense of the world using reason. It dealt with a wide variety of subjects, including astronomy, epistemology, mathematics, political philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric and aesthetics. Greek philosophy has influenced much of Western culture since its inception. Alfred North Whitehead once noted: "The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato". Clear, unbroken lines of influence lead from ancient Greek and Hellenistic philosophers to Roman philosophy, Early Islamic philosophy, Medieval Scholasticism, the European Renaissance and the Age of Enlightenment. Greek philosophy was influenced to some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
