Unfolding (album)
Unfolding may refer to: Mathematics * Unfolding (functions), of a manifold * Unfolding (geometry), of a polyhedron * Deconvolution Other uses * Unfolding (DSP implementation) * Unfolding (music), in Schenkerian analysis * ''Unfolding'' (sculpture), by Bernhard Heiliger located near Milwaukee, Wisconsin, United States * Equilibrium unfolding, in biochemistry See also * Unfold (other) * Unfoldment (other) Unfoldment may refer to: * Implicate and explicate order Implicate order and explicate order are ontological concepts for quantum theory coined by theoretical physicist David Bohm during the early 1980s. They are used to describe two different fra ...

Unfolding (functions)
In mathematics, an unfolding of a smooth real-valued function ''ƒ'' on a smooth manifold, is a certain family of functions that includes ''ƒ''. Definition Let M be a smooth manifold and consider a smooth mapping f : M \to \mathbb. Let us assume that for given x_0 \in M and y_0 \in \mathbb we have f(x_0) = y_0 . Let N be a smooth k-dimensional manifold, and consider the family of mappings (parameterised by N) given by F : M \times N \to \mathbb . We say that F is a k-parameter unfolding of f if F(x,0) = f(x) for all x. In other words the functions f : M \to \mathbb and F : M \times \ \to \mathbb are the same: the function f is contained in, or is unfolded by, the family F. Example Let f : \mathbb^2 \to \mathbb be given by f(x,y) = x^2 + y^5. An example of an unfolding of f would be F : \mathbb^2 \times \mathbb^3 \to \mathbb given by :F((x,y),(a,b,c)) = x^2 + y^5 + ay + by^2 + cy^3. As is the case with unfoldings, x and y are called variables, and a, b, an ...
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Unfolding (geometry)
In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for physical models of polyhedra to be constructed from material such as thin cardboard. An early instance of polyhedral nets appears in the works of Albrecht Dürer, whose 1525 book ''A Course in the Art of Measurement with Compass and Ruler'' (''Unterweysung der Messung mit dem Zyrkel und Rychtscheyd '') included nets for the Platonic solids and several of the Archimedean solids. These constructions were first called nets in 1543 by Augustin Hirschvogel. Existence and uniqueness Many different nets can exist for a given polyhedron, depending on the choices of which edges are joined and which are separated. The edges that are cut from a convex polyhedron to form a net must form a spanning tree of ...
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Deconvolution
In mathematics, deconvolution is the operation inverse to convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution method with a certain degree of accuracy. Due to the measurement error of the recorded signal or image, it can be demonstrated that the worse the SNR, the worse the reversing of a filter will be; hence, inverting a filter is not always a good solution as the error amplifies. Deconvolution offers a solution to this problem. The foundations for deconvolution and time-series analysis were largely laid by Norbert Wiener of the Massachusetts Institute of Technology in his book ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'' (1949). The book was based on work Wiener had done during World War II but that had been classified at the time. Some of the early attempts to apply these theories were in the fields of ...
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Unfolding (DSP Implementation)
Unfolding is a transformation technique of duplicating the functional blocks to increase the throughput of the DSP program in such a way that preserves its functional behavior at its outputs. Unfolding was first proposed by Keshab K. Parhi and David G. Messerschmitt in 1989.K.K. Parhi, and D.G. Messerschmitt, "Static Rate-Optimal Scheduling of Iterative Data Flow Programs via Optimum Unfolding," IEEE Trans. on Computers, Vol. 40(2), February 1991, pp. 178-195, https://doi.org/10.1109/12.73588 Unfolding in general program is as known as Loop unrolling. Unfolding has applications in designing high-speed and low-power ASIC architectures. One application is to unfold the program to reveal hidden concurrency so that the program can be scheduled to a smaller iteration period, thus increasing the throughput of the implementation. Another application is parallel processing in word level or bit level. Therefore these transformed circuit could increase the throughput and decrease the power ...
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Unfolding (music)
In Schenkerian analysis, unfolding (German: '' Ausfaltung'') or compound melody is the implication of more than one melody or line by a single voice through skipping back and forth between the notes of the two melodies. In music cognition, the phenomenon is also known as melodic fission. The term "compound melody" may have its origin in Walter Piston's ''Counterpoint'' (New York, Norton, 1947), under the form "compound melodic line" (London edition, 1947, p. 23). In the context of Schenkerian analysis, it appears among others in Forte & Gilbert, ''Introduction to Schenkerian Analysis'' (1982), Chapter 3, pp. 67-80. Manfred Bukofzer, ''Music in the Baroque Era'', New York, Norton, 1947, had spoken of "implied polyphony". Unfolding is "a prolongation by means of the unfolding of intervals horizontally." Though the notes skipped between, those heard, may be considered near the foreground, the dyads, those implied, are in the middle or background. Middleground dyads are "unfold ...
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Unfolding (sculpture)
''Unfolding'' is a public art work by artist Bernhard Heiliger located at the Lynden Sculpture Garden near Milwaukee, Wisconsin Wisconsin () is a state in the upper Midwestern United States. Wisconsin is the 25th-largest state by total area and the 20th-most populous. It is bordered by Minnesota to the west, Iowa to the southwest, Illinois to the south, Lake M .... The sculpture has an abstract form; it is installed on the patio. References Outdoor sculptures in Milwaukee 1968 sculptures Bronze sculptures in Wisconsin Abstract sculptures in Wisconsin 1968 establishments in Wisconsin {{Public-art-stub ...
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Equilibrium Unfolding
In biochemistry, equilibrium unfolding is the process of unfolding a protein or RNA molecule by gradually changing its environment, such as by changing the temperature or pressure, pH, adding chemical denaturants, or applying force as with an atomic force microscope tip. If the equilibrium was maintained at all steps, the process theoretically should be reversible during equilibrium folding. Equilibrium unfolding can be used to determine the thermodynamic stability of the protein or RNA structure, i.e. free energy difference between the folded and unfolded states. Theoretical background In its simplest form, equilibrium unfolding assumes that the molecule may belong to only two thermodynamic states, the ''folded state'' (typically denoted ''N'' for "native" state) and the unfolded state (typically denoted ''U''). This "all-or-none" model of protein folding was first proposed by Tim Anson in 1945, but is believed to hold only for small, single structural domains of protei ...
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Unfold (other)
Unfold may refer to: Science * Unfoldable cardinal, in mathematics * Unfold (higher-order function), in computer science a family of anamorphism functions * Unfoldment (other), in spirituality and physics * Unfolded protein response, in biochemistry * Equilibrium unfolding, in biochemistry * Unfolded state (denatured protein), in biochemistry * Maximum variance unfolding (semidefinite embedding), in computer science Music * ''Unfold'' (Marié Digby album), 2008 * ''Unfold'' (John O'Callaghan album), 2011 * ''Unfold'' (The Necks album), 2017 * "Unfold" (Porter Robinson song), 2021 * "Unfold", a song by De La Soul from the 2016 album '' And the Anonymous Nobody...'' See also * Fold (other) Fold, folding or foldable may refer to: Arts, entertainment, and media * ''Fold'' (album), the debut release by Australian rock band Epicure *Fold (poker), in the game of poker, to discard one's hand and forfeit interest in the current pot *Above ...