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Diagrammatic Expansion Of The Luttinger–Ward Functional
A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word ''graph'' is sometimes used as a synonym for diagram. Overview The term "diagram" in its commonly used sense can have a general or specific meaning: * ''visual information device'' : Like the term "illustration", "diagram" is used as a collective term standing for the whole class of technical genres, including graphs, technical drawings and tables. * ''specific kind of visual display'' : This is the genre that shows qualitative data with shapes that are connected by lines, arrows, or other visual links. In science the term is used in both ways. For example, Anderson (1997) stated more generally: "diagrams are pictorial, yet abstract, representat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Depiction
Depiction is reference conveyed through pictures. A picture refers to its object through a non-linguistic two-dimensional scheme, and is distinct from writing or notation. A depictive two-dimensional scheme is called a picture plane and may be constructed according to descriptive geometry, where they are usually divided between ''projections'' (orthogonal and various oblique angles) and ''perspectives'' (according to number of vanishing points). Pictures are made with various materials and techniques, such as painting, drawing, or prints (including photography and movies) mosaics, tapestries, stained glass, and collages of unusual and disparate elements. Occasionally, picture-like features may be recognised in simple inkblots, accidental stains, peculiar clouds or a glimpse of the moon, but these are special cases, and it is controversial whether they count as genuine instances of depiction. Similarly, sculpture and theatrical performances are sometimes said to depict, but this req ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by computer graphics hardware. It is a vast and recently developed area of computer science. The phrase was coined in 1960 by computer graphics researchers Verne Hudson and William Fetter of Boeing. It is often abbreviated as CG, or typically in the context of film as computer generated imagery (CGI). The non-artistic aspects of computer graphics are the subject of computer science research. Some topics in computer graphics include user interface design, sprite graphics, rendering, ray tracing, geometry processing, computer animation, vector graphics, 3D modeling, shaders, GPU design, implicit surfaces, visualization, scientific c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homomorphism
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word ''homomorphism'' comes from the Ancient Greek language: () meaning "same" and () meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German meaning "similar" to meaning "same". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925). Homomorphisms of vector spaces are also called linear maps, and their study is the subject of linear algebra. The concept of homomorphism has been generalized, under the name of morphism, to many other structures that either do not have an underlying set, or are not algebraic. This generalization is the starting point of category theory. A homomorphism may also be an isomorphism, an endomorphism, an automorphism, etc. (see below). Each of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isomorphism
In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word isomorphism is derived from the Ancient Greek: ἴσος ''isos'' "equal", and μορφή ''morphe'' "form" or "shape". The interest in isomorphisms lies in the fact that two isomorphic objects have the same properties (excluding further information such as additional structure or names of objects). Thus isomorphic structures cannot be distinguished from the point of view of structure only, and may be identified. In mathematical jargon, one says that two objects are . An automorphism is an isomorphism from a structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if there is only one isomorphism between the two structures (as it is the case for solutions of a univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Sanders Peirce
Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for thirty years, Peirce made major contributions to logic, a subject that, for him, encompassed much of what is now called epistemology and the philosophy of science. He saw logic as the formal branch of semiotics, of which he is a founder, which foreshadowed the debate among logical positivists and proponents of philosophy of language that dominated 20th-century Western philosophy. Additionally, he defined the concept of abductive reasoning, as well as rigorously formulated mathematical induction and deductive reasoning. As early as 1886, he saw that logic gate, logical operations could be carried out by electrical switching circuits. The same idea was used decades later to produce digital computers. See Also In 1934, the philosopher Paul W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Similarity
The structural similarity index measure (SSIM) is a method for predicting the perceived quality of digital television and cinematic pictures, as well as other kinds of digital images and videos. SSIM is used for measuring the similarity between two images. The SSIM index is a full reference metric; in other words, the measurement or prediction of image quality is based on an initial uncompressed or distortion-free image as reference. SSIM is a perception-based model that considers image degradation as ''perceived change in structural information'', while also incorporating important perceptual phenomena, including both luminance masking and contrast masking terms. The difference with other techniques such as MSE or PSNR is that these approaches estimate ''absolute errors''. Structural information is the idea that the pixels have strong inter-dependencies especially when they are spatially close. These dependencies carry important information about the structure of the objects i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagrammatology
Diagrammatology is the academic study of diagrams. It studies fundamental role played by the diagram in the communication and creation of knowledge. Diagrammatology is not only an interdisciplinary subject, but pan-historical and cross-cultural. Overview The term diagrammatology is often used synonymously with diagrammatics, however diagrammatics tends to be more common place within the fields of Mathematics (especially logic), the sciences and technology. In contrast, diagrammatology is currently the term of choice for the arts and humanities, where it is closely associated with Charles Sanders Peirce's work on diagrammatic reasoning. In the introduction to his seminal 2011 work "Diagrammatology", Frederik Stjernfelt describes the reasoning behind his use of the term: "As a substitute for the neologism of 'diagrammatology', the title might equally have well have been 'diagrammatical reasoning'. But two things argued against such a choice: (1) a book with that title already ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arrow
An arrow is a fin-stabilized projectile launched by a bow. A typical arrow usually consists of a long, stiff, straight shaft with a weighty (and usually sharp and pointed) arrowhead attached to the front end, multiple fin-like stabilizers called fletchings mounted near the rear, and a slot at the rear end called a nock for engaging the bowstring. A container or bag carrying additional arrows for convenient reloading is called a quiver. The use of bows and arrows by humans predates recorded history and is common to most cultures. A craftsman who makes arrows is a fletcher, and one that makes arrowheads is an arrowsmith.Paterson ''Encyclopaedia of Archery'' p. 56 History The oldest evidence of likely arrowheads, dating to c. 64,000 years ago, were found in Sibudu Cave, current South Africa.Backwell L, d'Errico F, Wadley L.(2008). Middle Stone Age bone tools from the Howiesons Poort layers, Sibudu Cave, South Africa. Journal of Archaeological Science, 35:1566–1580. Backwe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line
Line most often refers to: * Line (geometry), object with zero thickness and curvature that stretches to infinity * Telephone line, a single-user circuit on a telephone communication system Line, lines, The Line, or LINE may also refer to: Arts, entertainment, and media Films * ''Lines'' (film), a 2016 Greek film * ''The Line'' (2017 film) * ''The Line'' (2009 film) * ''The Line'', a 2009 independent film by Nancy Schwartzman Podcasts * ''The Line'' (podcast), 2021 by Dan Taberski Literature * Line (comics), a term to describe a subset of comic book series by a publisher * ''Line'' (play), by Israel Horovitz, 1967 * Line (poetry), the fundamental unit of poetic composition * "Lines" (poem), an 1837 poem by Emily Brontë * ''The Line'' (memoir), by Arch and Martin Flanagan * ''The Line'' (play), by Timberlake Wertenbaker, 2009 Music Albums * ''Lines'' (The Walker Brothers album), 1976 * ''Lines'' (Pandelis Karayorgis album), 1995 * ''Lines'' (Unthanks album), 201 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantitative Data
Quantitative research is a research strategy that focuses on quantifying the collection and analysis of data. It is formed from a deductive approach where emphasis is placed on the testing of theory, shaped by empiricist and positivist philosophies. Associated with the natural, applied, formal, and social sciences this research strategy promotes the objective empirical investigation of observable phenomena to test and understand relationships. This is done through a range of quantifying methods and techniques, reflecting on its broad utilization as a research strategy across differing academic disciplines. The objective of quantitative research is to develop and employ mathematical models, theories, and hypotheses pertaining to phenomena. The process of measurement is central to quantitative research because it provides the fundamental connection between empirical observation and mathematical expression of quantitative relationships. Quantitative data is any data that is in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Content Format
A content format is an encoded format for converting a specific type of data to displayable information. Content formats are used in recording and transmission to prepare data for observation or interpretation. This includes both analog and digitized content. Content formats may be recorded and read by either natural or manufactured tools and mechanisms. In addition to converting data to information, a content format may include the encryption and/or scrambling of that information. Multiple content formats may be contained within a single section of a storage medium (e.g. track, disk sector, computer file, document, page, column) or transmitted via a single channel (e.g. wire, carrier wave) of a transmission medium. With multimedia, multiple tracks containing multiple content formats are presented simultaneously. Content formats may either be recorded in secondary signal processing methods such as a software container format (e.g. digital audio, digital video) or recorded i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
