Because conceptual separability is the undisputed law of the land, infringement is more likely to be found than under a more stringent test such as literal separability.
|
|
The Supreme Court recently considered separability of creativity from functionality in Star Athletica v.
|
|
Here's a news flash: In today's world, work and life are intertwined beyond separability.
|
|
Obviously the rule of separability in copyright will not decide all of these questions.
|
|
To answer, we need to look back at how separability was previously applied to copyright claims.
|
|
Justice Ruth Bader Ginsburg concurred in the majority decisions but said she would not have applied a "separability" test.
|
|
Copyright law, including the separability rule, has always sought to draw that line between copying that is permissible and copying that is not.
|
|
Overall, ZeroFox determined that the abundant use of hashtags is in itself a bad sign: "We found high separability between the number of hashtags in scam posts as compared to benign posts, meaning the number of hashtags was a powerful predictor to determine whether a post was a scam or not," the company said in its report.
|
|
In the low-dimensional (2 X 2 and 2 X 3) cases, the Peres-Horodecki criterion is actually a necessary and sufficient condition for separability. Other separability criteria include (but not limited to) the range criterion, reduction criterion, and those based on uncertainty relations. See Ref. for a review of separability criteria in discrete variable systems.
|
|
In practice N is fixed and one is interested in approximate separability between time series components. A number of indicators of approximate separability can be used, see Golyandina et al. (2001, Ch. 1). The window length L determines the resolution of the method: larger values of L provide more refined decomposition into elementary components and therefore better separability.
|
|
A reflexive Banach space is separable if and only if its continuous dual is separable. This follows from the fact that for every normed space Y, separability of the continuous dual implies separability .Theorem 1.12.11 and Corollary 1.12.
|
|
We see that the problem quickly becomes intractable, even for low dimensions. Thus more sophisticated formulations are required. The separability problem is a subject of current research. A separability criterion is a necessary condition a state must satisfy to be separable.
|
|
In the multipartite case there is no simple necessary and sufficient condition for separability like the one given by the PPT criterion for the 2\otimes2 and 2\otimes3 cases. However, many separability criteria used in the bipartite setting can be generalized to the multipartite case.
|
|
The definition of separability can also be stated for other index sets and state spaces,, p. 22 such as in the case of random fields, where the index set as well as the state space can be n-dimensional Euclidean space. The concept of separability of a stochastic process was introduced by Joseph Doob,. The underlying idea of separability is to make a countable set of points of the index set determine the properties of the stochastic process.
|
|
Rau, Alan Scott; Separability in the United States Supreme Court; October 24, 2006; retrieved September 27, 2008.
|
|
In this paper, Leinaas et al. also give a numerical approach to test for separability in the general case.
|
|
The multi-surface method (MSM) is a form of decision making using the concept of piecewise-linear separability of datasets to categorize data.
|
|
It is not, however, optimized for class separability. However, it has been used to quantify the distance between two or more classes by calculating center of mass for each class in principal component space and reporting Euclidean distance between center of mass of two or more classes. The linear discriminant analysis is an alternative which is optimized for class separability.
|
|
Title VII established the separability of the act, affirming that the rest of the act shall go unaffected if one provision is found invalid.
|
|
D. Pa. Feb. 13, 1995). Architectural designs registered as architectural works under § 102(a)(8), however, are not evaluated under the separability test.See H.R. Rep.
|
|
Any stochastic process with a countable index set already meets the separability conditions, so discrete-time stochastic processes are always separable. A theorem by Doob, sometimes known as Doob's separability theorem, says that any real-valued continuous-time stochastic process has a separable modification. Versions of this theorem also exist for more general stochastic processes with index sets and state spaces other than the real line.
|
|
L. 1, at 39, 2007; retrieved September 26, 2008. Richard Reuben of Missouri law school, a longtime critic of mandatory arbitration, calls Prima Paint's adoption of the separability doctrine "a perhaps unparalleled display of judicial sophistry". He fears it can have negative consequences for society as a whole: "By denying citizens the right to a day in court, arbitration imposed through mandatory processes and separability fosters cynicism and distrust in the rule of law, undermining its legitimacy." Defenders of the decision and separability have said that it is necessary for arbitration clauses to have any force, otherwise parties would be able to avoid them too easily by filing suits on any number of grounds.
|
|
In mathematics in complex analysis, the concept of holomorphic separability is a measure of the richness of the set of holomorphic functions on a complex manifold or complex-analytic space.
|
|
If a reservoir has fading memory and input separability, with help of a readout, it can be proven the liquid state machine is a universal function approximator using Stone-Weierstrass theorem.
|
|
A is separable if it is a projective module over A^e; thus, the A^e-projective dimension of A, sometimes called the bidimension of A, measures the failure of separability.
|
|
In quantum mechanics, in particular quantum information, the Range criterion is a necessary condition that a state must satisfy in order to be separable. In other words, it is a separability criterion.
|
|
Arora, Ge, Halpern, Mimno, Moitra, Sontag, Wu, & Zhu (2013) give a polynomial time algorithm for exact NMF that works for the case where one of the factors W satisfies a separability condition.
|
|
His work included foundational papers in both pure and applied mathematics, celestial mechanics (notably on the three-body problem), analytic mechanics (the Levi-Civita separability conditions in the Hamilton–Jacobi equation) and hydrodynamics.
|
|
For example, separability is assumed when constructing and studying random fields, where the collection of random variables is now indexed by sets other than the real line such as n-dimensional Euclidean space.
|
|
This is sometimes called the "Luzin separability principle" (though it was implicit in the proof of Suslin's theorem). Analytic sets are always Lebesgue measurable (indeed, universally measurable) and have the property of Baire and the perfect set property.
|
|
Laurie Jeanne Butler (born 1959) is an American physical chemist known for her experimental work testing the Born–Oppenheimer approximation on separability of nuclear and electron motions. She is a professor emeritus of chemistry at the University of Chicago.
|
|
In quantum mechanics, negativity is a measure of quantum entanglement which is easy to compute. It is a measure deriving from the PPT criterion for separability. It has shown to be an entanglement monotone and hence a proper measure of entanglement.
|
|
On the other hand, if the original elements are not required, the work will be protectable without regard to physical or conceptual separability of the elements. As a result, "the aesthetically pleasing overall shape of an architectural work (can) be protected".
|
|
For the construction of such a stochastic process, it is assumed that the sample functions of the stochastic process belong to some suitable function space, which is usually the Skorokhod space consisting of all right- continuous functions with left limits. This approach is now more used than the separability assumption, but such a stochastic process based on this approach will be automatically separable. Although less used, the separability assumption is considered more general because every stochastic process has a separable version. It is also used when it is not possible to construct a stochastic process in a Skorokhod space.
|
|
The separability problem is a concept from the field of social choice theory that describes the situation where two or more issues up for vote on a ballot either are, or are perceived as, related. The separability problem commonly manifests itself most intensely in referendums and in voting on multiple charges before juries or panels of judges, where simultaneous voting is employed. Some or all voters view the approval or disapproval of one issue dependent on the approval or disapproval of another. The voters have no information on the outcome of related issues, so they simply cast their first preference votes.
|
|
Examine the case where an image of size X\times Y is being passed through a separable filter of size J\times K. The image itself is not separable. If the result is calculated using the direct convolution approach without exploiting the separability of the filter, this will require approximately XYJK multiplications and additions. If the separability of the filter is taken into account, the filtering can be performed in two steps. The first step will have XYJ multiplications and additions and the second step will have XYK, resulting in a total of XYJ+XYK or XY(J+K) multiplications and additions.
|
|
The trade-off of optimal accuracy between the resulting copies has been studied in quantum circuits,A. T. Rezakhani, S. Siadatnejad, and A. H. Ghaderi. Separability in Asymmetric Phase-Covariant Cloning (First submitted on 2 December 2003). Physics Letters A 336 (4), 278.
|
|
Many of the results obtained in this collaboration were included in his DSc thesis "Schurity and separability of association schemes", that was defended in 2004. Starting in 2005, he was a leading researcher in St. Petersburg Department Mathematical Institute of Russian Academy of Sciences.
|
|
A metric space is separable space if it has a countable dense subset. Typical examples are the real numbers or any Euclidean space. For metric spaces (but not for general topological spaces) separability is equivalent to second-countability and also to the Lindelöf property.
|
|
Testing for separability in the general case is an NP-hard problem. Leinaas et. al. formulated an iterative, probabilistic algorithm for testing if a given state is separable. When the algorithm is successful, it gives an explicit, random, representation of the given state as a separable state.
|
|
How to be an ecological economist. Ecological Economics 66(1):1-7. Preprint. Ecological economists have questioned fundamental mainstream economic approaches such as cost-benefit analysis, and the separability of economic values from scientific research, contending that economics is unavoidably normative, i.e. prescriptive, rather than positive or descriptive.
|
|
The same argument is used by , in order to prove the non separability of the space of bounded sequences, and also . This example can be obviously extended to higher dimensions, and since it involves only local properties, it implies that the same property is true also for BV_{loc}.
|
|
Sevag Gharibian, Strong NP-Hardness of the Quantum Separability Problem, Quantum Information and Computation, Vol. 10, No. 3&4, pp. 343-360, 2010. arXiv:0810.4507. Some appreciation for this difficulty can be obtained if one attempts to solve the problem by employing the direct brute force approach, for a fixed dimension.
|
|
The Court did not consider whether the designs in the case actually met copyright restriction's threshold of originality. Thomas rejected arguments from Varsity and the United States that separability analysis was unneeded,Star Athletica, slip op. at 4-6. but also did away with all the lower court tests used previously.
|
|
Prima Paint Corp. v. Flood & Conklin Mfg. Co., 388 U.S. 395 (1967), is a United States Supreme Court decision that established what has become known as the "separability principle" in contracts with arbitration clauses.McDougall, Andrew de Lotbiniére and Ioannou, Leon; , Mealey's International Arbitration Report; March 2006; retrieved September 4, 2008.
|
|
As this formalism was developed at a semiempirical quantum level, it enables also the complete separability of these components. The SEEB formalism was extended to describe protein-ligand interactions using a pair-wise potential.Exact and Effective Pair-Wise Potential for Protein- Ligand Interactions Obtained from a Semiempirical Energy Partition. Int J Mol Sci.
|
|
Similar to row-column decomposition, the helix transform computes the multidimensional convolution by incorporating one-dimensional convolutional properties and operators. Instead of using the separability of signals, however, it maps the Cartesian coordinate space to a helical coordinate space allowing for a mapping from a multidimensional space to a one-dimensional space.
|
|
The board is made up of four square panels, each comprising 12 x 12 movement spaces. The mountains and rough terrain are scattered throughout the board space. The separability of the four panels allows a variety of board layouts, as each may be freely turned to change the landscape of the board.
|
|
1, cited at Ware, Stephen; , 8 Nevada Law Journal 107, 117, 2007. Stephen Ware of Kansas calls on Congress to repeal the separability doctrine and require that courts be permitted to compel arbitration only after they have heard and rejected any challenges to the validity of the contract itself: "The separability doctrine separates arbitration law from an important part of contract law — the defenses to enforcement — and thus fails to provide the right to litigate with the protection of those defenses."Ware, 121., "[T]he Buckeye decision forces the lower courts to either continue the search for a workable rule or accept the undermining of the moral foundations of contract law," says Timothy Hall of the University of Louisville's Louis D. Brandeis School of Law.
|
|
The algorithm assumes that the topic matrix satisfies a separability condition that is often found to hold in these settings. Hassani, Iranmanesh and Mansouri (2019) proposed a feature agglomeration method for term-document matrices which operates using NMF. The algorithm reduces the term-document matrix into a smaller matrix more suitable for text clustering.
|
|
In 1927, Bohr drew attention to a consequence of non-separability. The evolution of the system, as determined by the Schrödinger equation, does not display particle trajectories through space–time. It is possible to extract trajectory information from such evolution, but not simultaneously to extract energy–momentum information. This incompatibility is expressed in the Heisenberg uncertainty principle.
|
|
In quantum information theory, the reduction criterion is a necessary condition a mixed state must satisfy in order for it to be separable. In other words, the reduction criterion is a separability criterion. It was first proved and independently formulated in 1999. Violation of the reduction criterion is closely related to the distillability of the state in question.
|
|
Star Athletica, LLC v. Varsity Brands, Inc., 580 U.S. ___ (2017), was a Supreme Court of the United States case in which the Court decided under what circumstances aesthetic elements of "useful articles" can be restricted by copyright law. The Court created a two-prong "separability" test, granting copyrightability on conditions of separate identification and independent existence.
|
|
A reality exists independent of our ability to observe it. :2. Objects are located at distinct points in spacetime and have their own independent, real existence. In other words, he believed in separability and locality. :3. Although at a superficial level, quantum events may appear random, at some ultimate level, strict causality underlies all processes in nature.
|
|
The problem of deciding whether a state is separable in general is sometimes called the separability problem in quantum information theory. It is considered to be a difficult problem. It has been shown to be NP-hard.Gurvits, L., Classical deterministic complexity of Edmonds’ problem and quantum entanglement, in Proceedings of the 35th ACM Symposium on Theory of Computing, ACM Press, New York, 2003.
|
|
Some critics of the referendum attack the use of closed questions. A difficulty called the separability problem can plague a referendum on two or more issues. If one issue is in fact, or in perception, related to another on the ballot, the imposed simultaneous voting of first preference on each issue can result in an outcome which is displeasing to most.
|
|
For example, the finite element method may be recast as a multigrid method. In these cases, multigrid methods are among the fastest solution techniques known today. In contrast to other methods, multigrid methods are general in that they can treat arbitrary regions and boundary conditions. They do not depend on the separability of the equations or other special properties of the equation.
|
|
In multirate filters, the number of coefficients by taking advantage of its bandwidth limits, where the input signal is downsampled (e.g. to its critical frequency), and upsampled after filtering. Another issue related to computational complexity is separability, that is, if and how a filter can be written as a convolution of two or more simpler filters. In particular, this issue is of importance for multidimensional filters, e.g.
|
|
The scheduling of receivers with different spatial signatures allows good separability. Diversity coding techniques are used when there is no channel knowledge at the transmitter. In diversity methods, a single stream (unlike multiple streams in spatial multiplexing) is transmitted, but the signal is coded using techniques called space-time coding. The signal is emitted from each of the transmit antennas with full or near orthogonal coding.
|
|
Those who approached from a consumer-rights standpoint were not as solicitous. Texas arbitration expert Alan Scott Rau called Scalia's phrasing "sloppy and unguarded", noting it failed to recognize that some challenges to a contract that the law reserves for courts, such as capacity and forgery, necessarily include the arbitration clause.Rau, Alan Scott; Alan Scott "Separability" in the United States Supreme Court, 2006 Stockholm Int'l Arb. Rev.
|
|
TOT states should be separated from FOK (feeling of knowing) states. FOK, in contrast, is the feeling that one will be able to recognize - from a list of items - an item that is currently inaccessible. There are still currently opposing articles of the separability of the process underlying these concepts. However, there is some evidence that TOTs and FOKs draw on different parts of the brain.
|
|
In an older definition, P(X) was considered separable if each of its irreducible factors in K[X] is separable in the modern definition.N. Jacobson, Basic Algebra I, p. 233 In this definition, separability depended on the field K, for example, any polynomial over a perfect field would have been considered separable. This definition, although it can be convenient for Galois theory, is no longer in use.
|
|
Every algebraic extension of a field of characteristic zero is separable, and every algebraic extension of a finite field is separable.Isaacs, Theorem 18.11, p. 281 It follows that most extensions that are considered in mathematics are separable. Nevertheless, the concept of separability is important, as the existence of inseparable extensions is the main obstacle for extending many theorems proved in characteristic zero to non-zero characteristic.
|
|
The Peres–Horodecki criterion is a necessary condition, for the joint density matrix \rho of two quantum mechanical systems A and B, to be separable. It is also called the PPT criterion, for positive partial transpose. In the 2x2 and 2x3 dimensional cases the condition is also sufficient. It is used to decide the separability of mixed states, where the Schmidt decomposition does not apply.
|
|
The two kinds of information have to be extracted on different occasions, because of the non-separability of the wave function representation. In Bohr's thinking, space–time visualizability meant trajectory information. Again, in Bohr's thinking, 'causality' referred to energy–momentum transfer; in his view, lack of energy–momentum knowledge meant lack of 'causality' knowledge. Therefore Bohr thought that knowledge respectively of 'causality' and of space–time visualizability were incompatible but complementary.
|
|
A voting system is consistent if, whenever the electorate is divided (arbitrarily) into several parts and elections in those parts garner the same result, then an election of the entire electorate also garners that result. Smith calls this property separability and Woodall calls it convexity. It has been proven a ranked voting system is "consistent if and only if it is a scoring function", i.e. a positional voting system.
|
|
R. Rep. No. 735, at 6949-50 (1990) Thus, for example, individual elements that are driven by function are not copyrightable, including the presence of doors and windows or those elements required by building codes. Accordingly, architectural designs must be analyzed to determine the scope of their functionality. Architectural designs registered as pictorial, graphic, or sculptural works under § 102(a)(5) are evaluated for functionality under the separability test.
|
|
Ryszard Horodecki (born 30 September 1943) is a Polish physicist and a professor of University of Gdańsk. He contributed largely to the field of quantum informatics. In his most widely cited paper, 'Separability of Mixed States: Necessary and Sufficient Conditions' written together with his sons, Michał and Paweł, he proposed the idea currently known as the Peres-Horodecki criterion. With over 12,000 citations, he is considered to be one of the leading Polish physicists .
|
|
In these cases, multigrid methods are among the fastest solution techniques known today. In contrast to other methods, multigrid methods are general in that they can treat arbitrary regions and boundary conditions. They do not depend on the separability of the equations or other special properties of the equation. They have also been widely used for more-complicated non-symmetric and nonlinear systems of equations, like the Lamé equations of elasticity or the Navier-Stokes equations.
|
|
It is used to measure the separability of classes in classification and it is considered to be more reliable than the Mahalanobis distance, as the Mahalanobis distance is a particular case of the Bhattacharyya distance when the standard deviations of the two classes are the same. Consequently, when two classes have similar means but different standard deviations, the Mahalanobis distance would tend to zero, whereas the Bhattacharyya distance grows depending on the difference between the standard deviations.
|
|
After a thesis in mathematical logic, his early work was in field theory and valuation theory. He wrote on valuation rings and Witt vectors, and separability in infinite field extensions. He started writing on group extensions in 1942, and in 1943 began his research on what are now called Eilenberg–MacLane spaces K(G,n), having a single non-trivial homotopy group G in dimension n. This work opened the way to group cohomology in general.
|
|
In 2016 he was awarded the Jeffery–Williams Prize and the CRM-Fields-PIMS Prize. In 2016 Wise was awarded a Guggenheim Fellowship. He was elected a Fellow of the Royal Society of Canada (FRSC) in 2014 and a Fellow of the Royal Society (FRS) in 2018. For the theory of special cube complexes and his establishment of subgroup separability for a wide class of groups, Daniel Wise together with Ian Agol was awarded in 2013 the Oswald Veblen Prize in Geometry.
|
|
Fee is a Pentecostal; nevertheless, he has disagreed with some long held and deeply cherished Pentecostal beliefs. Specifically, he has questioned article 7 of the Assemblies of God Statement of Fundamental Truths, which articulates a classical Pentecostal understanding of baptism in the Holy Spirit as subsequent to and separate from Christian conversion. In "Baptism in the Holy Spirit: The Issue of Separability and Subsequence", Fee writes that there is little biblical evidence to prove the traditional Pentecostal doctrinal position.Gordon D Fee.
|
|
Many studies have used the AIDS system to determine the optimal allocation of expenditure among broad commodity groups, i.e., at high levels of commodity aggregation. In addition, the AIDS system has been used as a brand demand system to determine optimal consumption rates for each brand using product category spending and brand prices alone. Assuming weak separability of consumer preferences, the optimal allocation of expenditure among the brands of a given product category can be determined independently of the allocation of expenditure within other product categories.
|
|
The Maxover algorithm (Wendemuth, 1995) is "robust" in the sense that it will converge regardless of (prior) knowledge of linear separability of the data set. In the linearly separable case, it will solve the training problem – if desired, even with optimal stability (maximum margin between the classes). For non-separable data sets, it will return a solution with a small number of misclassifications. In all cases, the algorithm gradually approaches the solution in the course of learning, without memorizing previous states and without stochastic jumps.
|
|
From the one-to-one correspondence between positive maps and entanglement witnesses, we have that a state ρ is entangled if and only if there exists a positive map Φ such that :(I \otimes \Phi)(\rho) is not positive. Therefore, if ρ is separable, then for all positive map Φ, :(I \otimes \Phi)(\rho) \geq 0. Thus every positive, but not completely positive, map Φ gives rise to a necessary condition for separability in this way. The reduction criterion is a particular example of this.
|
|
Varsity Brands, Inc., No. 15-866, 580 U.S. ___ (2017), slip op. at 1 (Ginsburg, J., concurring in judgment) Because the Copyright Act of 1976 provided copyright claimants "the right to reproduce the work in or on any kind of article, whether useful or otherwise," the claimant of a pictorial, graphical, or sculptural work's copyright could restrict others from reproducing the work's elements on their separate useful articles. According to her, there was no need for the court to address the separability analysis issue at all.
|
|
In quantum chemistry, size consistency and size extensivity are concepts relating to how the behaviour of quantum chemistry calculations changes with size. Size consistency (or strict separability) is a property that guarantees the consistency of the energy behaviour when interaction between the involved molecular system is nullified (for example, by distance). Size-extensivity, introduced by Bartlett, is a more mathematically formal characteristic which refers to the correct (linear) scaling of a method with the number of electrons. Let A and B be two non-interacting systems.
|
|
Alabama (1940) concluded that the separability of constitutional and unconstitutional applications of statutes may not apply if their effect is to leave a statute capable of having many unconstitutional applications. Roth v. United States (1957) stated that obscene speech and writings are not protected under the constitution. Dean Milk Co. v. City of Madison, Wisconsin (1951) showed that a State’s power to restrict or prevent the distribution of obscene materials is not free from constitutional restrictions to any form of exercise of that power.
|
|
Arcidiacono, along with Robert A. Miller and John Bailey Jones, is the co-developer of using the Expectation–maximization algorithm and conditional choice probabilities (CCPs) to simplify the maximum likelihood estimation of structural econometric models. These methods allow a researcher to estimate the structural parameters of an economic model in stages because of additive separability in the objective function. Additionally, CCPs allow the researcher to estimate the structural parameters without having to fully solve the agent's dynamic decision problem. Both approaches result in substantial computational gains.
|
|
Exactly what features of either were actually restricted was left up to debate because the registration's description could diverge almost entirely from the lawsuit's filing, so Fromer and McKenna contended it would be impossible to know what the copyright holder considered restricted before they described it in a lawsuit, let alone before the second party begins the desired copying. Moreover, in the absence of that description, they said it was impossible to perform a separability analysis and determine if the feature was even copyrightable at all before active litigation.
|
|
Brief of United States as Amicus Curiae, Star Athletica, LLC v. Varsity Brands, Inc., No. 15-866, 580 U.S. ___ (2017) Star Athletica had conceded this because it was an abstract painting, not a design for a dress, but the United States said that the painting would cover the entire dress surface--no different than the Varsity designs, they claimed. The government also argued that, in applying the requested conceptual separability analysis, what mattered was that a uniform stripped of the design "remain[ed] similarly useful" when compared to the original.
|
|
Star Athletica, slip op. at 8-11. After applying this test to the cheerleading uniforms, the Court ruled in Varsity's favor that the designs were separable from the useful article and could be copyrighted.Star Athletica, slip op. at 10. The separability analysis started with the admittedly permissive first requirement, identifying the designs as separately identifiable "pictoral, graphical, or sculptural works." The design needed to be able to exist independently, and Thomas concluded that the design did when it appeared in other media, such as the two-dimensional drawings submitted to the Copyright Office.
|
|
The Supreme Court was the source of a number of concepts in the field, including fair use, the idea- expression divide, the useful articles or separability doctrine, and the uncopyrightability of federal documents. This list is a list solely of United States Supreme Court decisions about applying copyright law. Not all Supreme Court decisions are ultimately influential and, as in other fields, not all important decisions are made at the Supreme Court level. Many federal courts issue rulings that are significant or come to be influential, but those are outside the scope of this list.
|
|
She gained an M.Sc. in mathematics at University of Warsaw, Faculty of Mathematics, Physics and Chemistry in 1956. She held position at Institute of Mathematics PAS until 1972. She received her Ph.D. in 1965 in the area of discriminant analysis ("Power of Test, and Separability of Hypothesis in Statistical Design of Experiments"). Her habilitation thesis, titled "Trend Estimation Problems in Time Series Analysis", was accepted in 1973. In 1967/8 she was visiting researcher in University of Wales (Great Britain), and in 1971/2 in University of Montreal.
|
|
"Baptism in the Holy Spirit: The Issue of Separability and Subsequence," Pneuma: The Journal of the Society of Pentecostal Studies 7:2 (Fall 1985), p. 88. On the other hand, he maintains that "the Pentecostal experience itself can be defended on exegetical grounds as a thoroughly biblical phenomenon".Fee (1985), "Baptism in the Holy Spirit", 91. Fee believes that in the early church, the Pentecostal experience was an expected part of conversion: Fee believes the Spirit's empowerment is a necessary element in the life of the Church that has too often been neglected.
|
|
In quantum mechanics, a product state, or simply separable state, is a special type of separable state in which there are neither classical nor quantum correlations. Precisely, it is a joint state of two systems which can be expressed as : \rho = \rho_1 \otimes \rho_2 , where \rho_1 and \rho_2 are states of the respective systems. This is a more restrictive condition than mere separability, : \rho = \sum_k p_k \rho^k_1 \otimes \rho^k_2 . Category:Quantum mechanics One property of the product state is that in terms of entropy, : S(\rho) = S(\rho_1) + S(\rho_2).
|
|
In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of points as being colored red. These two sets are linearly separable if there exists at least one line in the plane with all of the blue points on one side of the line and all the red points on the other side. This idea immediately generalizes to higher-dimensional Euclidean spaces if the line is replaced by a hyperplane.
|
|
The primary differences between these and backplates are the lack of a rigid plate and possible non-separability of the softpack and harness. The relatively low density of the softpack usually necessitates more ballast weight. A minimalist form of softpack harness is a set of webbing straps much like that of the backplate, but with a webbing strap instead of the plate. This strap may be formed by stitching or threading through sliders a double layer of webbing with slots between the layers which the cambands pass through, and the wing is sandwiched between harness and cylinder.
|
|
At the same time, considerations of construction of such an element receded: the theorem becomes an existence theorem. The following theorem of Artin then takes the place of the classical primitive element theorem. ;Theorem Let E/F be a finite degree field extension. Then E=F(\alpha) for some element \alpha\in E if and only if there exist only finitely many intermediate fields K with E\supseteq K\supseteq F. A corollary to the theorem is then the primitive element theorem in the more traditional sense (where separability was usually tacitly assumed): ;Corollary Let E/F be a finite degree separable extension.
|
|
There's also some uncertainty over how this case law may impact the copyrightability of another class of useful articles: food. Top chefs had been seeking this for years before Star Athletica, some taking the step of prohibiting their customers from taking photographs of the food in the name of supposed copyright restriction. The pre-Star Athletica interpretation of separability allowed one to argue the copyrightability of food as a sculpture with artistic features that didn't contribute to its purpose as a consumable. James P. Flynn of Epstein Becker & Green wondered if Star Athletica might have changed the fate of served food.
|
|
The Institute spoke highly of "geek fashion," including cosplay, as a burgeoning part of the industry rife with copyrightable expression. The United States government also supported Varsity. In part, the government claimed that the question of a proper separability analysis was unnecessary because, in creating the designs as drawings, Varsity had received a copyright for them and reserved the exclusive ability to reproduce that design however they chose in any medium. They pointed to a concession from Star Athletica that if, hypothetically, Varsity controlled The Starry Night, Varsity would be able to restrict the printing of the painting on dresses.
|
|
Coffin wrote for the panel that although the agreement was governed by Swiss law, the scope of the arbitration clause was within the court's jurisdiction. The Federal Arbitration Act preempted Puerto Rican law on the subject, which, he noted, Soler tacitly acknowledged by arguing that the Puerto Rico Dealers' Act (PRDA) was implicitly incorporated into the agreement, since it explicitly incorporated savings and separability clauses from the distributorship agreement that violated the PRDA. He called this argument "tortured", since neither was actually incorporated into the sales procedure agreement as Soler claimed. Nor was the arbitration clause limited to contractual claims.Mitsubishi Motors I, at 159.
|
|
These linear inequalities can be selected in the standard (Fisher's) form of the linear discriminant for a rich family of probability distribution. In particular, such theorems are proven for log- concave distributions including multidimensional normal distribution (the proof is based on the concentration inequalities for log-concave measuresGuédon, O., Milman, E. (2011) Interpolating thin-shell and sharp large-deviation estimates for isotropic log-concave measures, Geom. Funct. Anal. 21 (5), 1043–1068.) and for product measures on a multidimensional cube (this is proven using Talagrand's concentration inequality for product probability spaces). Data separability by classical linear discriminants simplifies the problem of error correction for artificial intelligence systems in high dimension.
|
|
One approach for avoiding mathematical construction issues of stochastic processes, proposed by Joseph Doob, is to assume that the stochastic process is separable. Separability ensures that infinite-dimensional distributions determine the properties of sample functions by requiring that sample functions are essentially determined by their values on a dense countable set of points in the index set. Furthermore, if a stochastic process is separable, then functionals of an uncountable number of points of the index set are measurable and their probabilities can be studied. Another approach is possible, originally developed by Anatoliy Skorokhod and Andrei Kolmogorov, for a continuous-time stochastic process with any metric space as its state space.
|
|
He feared it would put legal matters in the hands of arbitrators with little or no legal understanding of it nor duty to follow the law. In subsequent cases concerning the FAA, the Court has reaffirmed the separability principle and held that the FAA and this reading of it apply to arbitrable contracts under state law, even in cases where the contract is alleged to be illegal or state law provides for administrative dispute resolution. This has been seen as expanding the use of arbitration in contracts in the later 20th century, not only those between businesses but between businesses and consumers as well.
|
|
"We must weigh the concerns of American Safety against a strong belief in the efficacy of arbitral procedures for the resolution of international commercial disputes and an equal commitment to the enforcement of freely negotiated choice-of- forum clauses."Mitsubishi Motors II, at 628–631. "[W]e confess to some skepticism of certain aspects of the American Safety doctrine," Blackmun wrote. Where the First Circuit had expressed concern that the underlying contract may have been adhesive, he said that suspicion was too narrow a ground to defeat the arbitration clause, especially since the Court's Prima Paint separability doctrine had held that the validity of the arbitration clause itself could be attacked in court.
|
|
The new report, published September 29, 2017, reminded that useful articles and, more specifically, clothing articles were not copyrightable. Regarding two-dimensional visual designs applied to useful articles, the Compendium reduced its 2014 discussion of the copyrightability of various kinds of design on various kinds of useful article to one section in the 2017 guide that quoted Star Athleticas two step separability test. There was a note indicating that the Office was "developing updated guidance" on the matter to be included in a future version of the report. The Office released a draft of the new edition of the Compendium on March 15, 2019, including new material that specifically addressed Star Athletica.
|
|
Individuals are more likely to attribute their emotions to their exchange partners or groups when the task can only be completed with one or more partners, when the task requires interdependent (nonseparable) contributions, and when there is a shared sense of responsibility for the success or failure of the exchange. The mode of exchange determines the features of the exchange task and influences the attribution of the emotion produced The mode of exchange (productive, negotiated, reciprocal, or generalized) provides a description of the exchange task. The task features are defined by the degree of interdependence (separability of tasks) and shared responsibility between partners to complete the task. These features influence the strength of the emotion felt.
|
|
William Moore "Terence" Gorman (17 June 1923 – 12 January 2003) was an Irish economist and academic. He was predominantly a theorist and is most famous for his work on aggregation and separability of goods, and in this context he developed his famous Gorman polar form. Gorman's career saw him a professor at such schools as Oxford, London School of Economics, Johns Hopkins, and Stanford, and he was honoured with the Presidency of the Econometric Society in 1972. His work was often highly technical and theoretical in nature, which made him incomprehensible to many of his contemporaries, but his keen eye for applications has given his work a lasting influence on modern economics.
|
|
The engineer's report is a critical document in the assessment process because it contains the detailed supporting basis for levying the assessment. This includes a detailed supporting basis for compliance with the substantive requirements for assessments such as presence of special benefits, proper apportionment of special benefits between parcels, separability of general benefits from special benefits, proper assessment of parcels owned by public agencies, detailed cost information, and the manner of calculating assessments upon specific parcels. In a legal challenge concerning the validity of an assessment, the courts typically refer to the engineer's report to determine whether the assessment complies with Proposition 218. Proposition 218 does not require the engineer's report be mailed to property owners as part of the assessment notification process.
|
|
EPR paradox illustration Roy's research was principally based on pion dynamics and hadron interactions. His work on axiomatic quantum field theory assisted him to develop an exact integral equation which later came to be known as Roy's equations, and many scientists opined that the equation helped in pion–pion data analysis. He furthered the studies of Andre Martin on high-energy bounds and the observations of John Stewart Bell regarding Einstein-Podolsky-Rosen paradox; his work on the former resulted in the development of Roy-Singh bounds (unitarity bounds on high-energy cross sections) and the studies on the latter evolved into Roy-Singh multiparticle Bell inequalities and Auberson-Mahoux-Roy-Singh Bell inequalities. He developed the theme further by proposing Roy's multipartite separability inequalities.
|
|
In algebraic geometry, the term branched covering is used to describe morphisms f from an algebraic variety V to another one W, the two dimensions being the same, and the typical fibre of f being of dimension 0. In that case, there will be an open set W' of W (for the Zariski topology) that is dense in W, such that the restriction of f to W' (from V' = f^{-1}(W') to W', that is) is unramified. Depending on the context, we can take this as local homeomorphism for the strong topology, over the complex numbers, or as an étale morphism in general (under some slightly stronger hypotheses, on flatness and separability). Generically, then, such a morphism resembles a covering space in the topological sense.
|
|
Indeed, this condition is necessary since the multiplication mapping \mu : A \otimes_K A \rightarrow A arising in the definition above is a A-A-bimodule epimorphism, which is split as an A-K- bimodule map by the right inverse mapping A \rightarrow A \otimes_K A given by a \mapsto a \otimes 1 . The converse can be proven by a judicious use of the separability idempotent (similarly to the proof of Maschke's theorem, applying its components within and without the splitting maps). Equivalently, the relative Hochschild cohomology groups H^n(R,S;M) of (R,S) in any coefficient bimodule M is zero for n > 0. Examples of separable extensions are many including first separable algebras where R = separable algebra and S = 1 times the ground field.
|
|
Co., the U.S. Supreme Court established the "separability principle", under which enforceability of a contract must be challenged in arbitration before any court action, unless the arbitration clause itself has been challenged. Some jurisdictions exclude or restrict the possibility of arbitration for reasons of the protection of weaker members of the public, e.g. consumers. For example, German law excludes disputes over the rental of living space from any form of arbitration,Section 1030 subsection 2 Zivilprozessordnung while arbitration agreements with consumers are only considered valid if they are signed,To be correct: A certain form, as defined by statute, of an electronic signature using a chip card and a PIN code is also sufficient and if the signed document does not bear any other content than the arbitration agreement.Section 1031 subesction 5 of the Zivilprozessordnung.
|
|
The outcomes of these decision-making polls are often displeasing to a majority of voters merely because simultaneous voting denied them the information on outcomes of individual issues or the opportunity to express preferences of outcomes of related issues. The solution to the separability problem for referendums would be set-wise voting, where the voter can express preferences for outcomes of related issues, as this process needs to be done at a particular time. For matters before juries or judicial panels, either set-wise or sequential voting can be employed to mitigate this problem, as all votes need not be cast in one instance. If sequential voting were employed, the outcome of every vote tally on an issue would be announced before a vote on the next issue would be taken.
|
|
Hiley later pointed out that Eddington attributed to a particle not a metaphysical existence but a structural existence as an idempotent of an algebra, similarly as in process philosophy an object is a system which continuously transforms onto itself. With their approach based on algebraic idempotents, Bohm and Hiley "incorporate Bohr's notion of ‘wholeness’ and d'Espagnat's concept of ‘non-separability’ in a very basic way". In 1981, Bohm and Hiley introduced the "characteristic matrix", a non-Hermitian extension of the density matrix. The Wigner and Moyal transformation of the characteristic matrix yields a complex function, for which the dynamics can be described in terms of a (generalized) Liouville equation with the aid of a matrix operating in phase space, leading to eigenvalues that can be identified with stationary states of motion.
|
|
Those whose practice involves arbitrating disputes that are international in scope have credited it with bringing U.S. arbitration law closer to European norms, helping American companies compete and making the U.S. a viable venue for arbitration. In several papers, Alan Scott Rau of the University of Texas law school has gone to a greater extent than Fortas did in grounding Prima Paint and the separability doctrine. He notes that challenges to the arbitration clause are often inseparable from the underlying claim, and that some public policy objectives may be better served by allowing the case to be heard by an arbitrator first. Conversely, he also notes that some challenges to a contract's formation necessarily include a challenge to the arbitration clause in any event, contrary to some recent lower-court decisions.
|
|
A ring homomorphism (of unital, but not necessarily commutative rings) :K \to A is called separable (or a separable extension) if the multiplication map :\mu : A \otimes_K A \to A, a \otimes b \mapsto ab admits a section :\sigma: A \to A \otimes_K A by means of a homomorphism σ of A-A-bimodules. Such a section σ is determined by its value :p := \sigma(1) = \sum a_i \otimes b_i σ(1). The condition that σ is a section of μ is equivalent to :\sum a_i b_i = 1 and the condition to be an homomorphism of A-A-bimodules is equivalent to the following requirement for any a in A: :\sum a a_i \otimes b_i = \sum a_i \otimes b_i a. Such an element p is called a separability idempotent, since it satisfies p^2 = p.
|
|
Richard Healey offered a modal interpretation and used it to present a model account of the puzzling correlations which portrays them as resulting from the operation of a process that violates both spatial and spatiotemporal separability. He argued that, on this interpretation, the nonseparability of the process is a consequence of physical property holism; and that the resulting account yields genuine understanding of how the correlations come about without any violation of relativity theory or Local Action. Subsequent work by Clifton, Dickson and Myrvold cast doubt on whether the account can be squared with relativity theory’s requirement of Lorentz invariance but leaves no doubt of an spatially entangled holism in the theory. Paul Davies and John Gribbin further observe that Wheeler's delayed choice experiment shows how the quantum world displays a sort of holism in time as well as space.
|
|
Shortly after making his famous "God does not play dice" comment, Einstein attempted to formulate a deterministic counter proposal to quantum mechanics, presenting a paper at a meeting of the Academy of Sciences in Berlin, on 5 May 1927, titled "Bestimmt Schrödinger's Wellenmechanik die Bewegung eines Systems vollständig oder nur im Sinne der Statistik?" ("Does Schrödinger's wave mechanics determine the motion of a system completely or only in the statistical sense?").The Collected Papers of Albert Einstein, Volume 15: The Berlin Years: Writings & Correspondence, June 1925-May 1927 (English Translation Supplement), p. 512Albert Einstein Archives reel 2, item 100 However, as the paper was being prepared for publication in the academy's journal, Einstein decided to withdraw it, possibly because he discovered that, contrary to his intention, it implied non-separability of entangled systems, which he regarded as absurd.
|
|
Mann called Thomas's dismissal of the opposing arguments "half-hearted" and predicted scholarly debate of the separability test's shift in copyright law to last a long time. Professors Jeanne C. Fromer and Mark P. McKenna were critical of the ambiguity of the decision because the three major stages of litigation resulted in three different majority decisions on three different grounds, with more divergent opinions among the dissents and concurrence. Because the courts allowed Varsity to define extremely narrow copyright restrictions in the registration then sue others like Star Athletica with general descriptions in court filings, they were concerned that this disconnect in requirements would lead to more controversial lawsuits, even outside the realm of useful articles. After all, a model car could be copyrighted as a sculpture, a drawing of that model could be copyrighted, and the claimant could use features of either equally to file copyright claims.
|
|
Prima Paint established in federal jurisprudence what became known as the "separability" or "severability" principle in contracts with arbitration clauses, under which a legal fiction is created that the clause itself constitutes a contract separate from the underlying, or "container", contract. This is similar to the principle of compétence compétence in international arbitration, under which the arbitrator or arbitrators are presumed competent to decide the limits of their own jurisdiction. Starting in the mid-1980s, the Court has greatly expanded the reach of Prima Paint in later cases. Since some of these have applied to the expanded use of arbitration clauses in contracts of adhesion between companies and consumers, some consumer advocates and legal scholars have criticized the decision as the inadvertent opening wedge of an assault on the right to litigate, and a weakening of state contract law and the Erie Railroad principle of deference to state common law.
|
|
Prima Paint attracted little analysis and commentary in its time, but as it became the foundation for the Court's expansion of the scope of the Arbitration Act and its subsequent application to contracts between consumers and businesses as well as among businesses, its reasoning has been the subject of more legal papers. Critics have reiterated Black's concerns in focusing on how the later decisions have exposed fundamental flaws in Prima Paint, while defenders have found them to reinforce its fundamental soundness. Labor lawyer Zeb-Michael Curtin of the Minneapolis firm Dorsey & Whitney says the Court "muddied the clear language of [the FAA]" and "enabled results contrary to the intentions of the framers of the FAA" by embracing the separability doctrine. Richard Barnes of the University of Mississippi has argued that, contrary to Fortas's assertions, Prima Paint and its progeny have created fundamental problems with the Erie Railroad doctrine.
|
|
Polygraphic Co., where the court, with only Harold Hitz Burton dissenting, had refused to allow a federal court to decide whether an arbitration clause was valid simply because one party to the dispute had moved to another state than the one in which the contract was originally executed.. In 1959 the Second Circuit Court of Appeals suggested that the FAA applied to state court actions as well, when it ruled that disputes over not just the execution but the contract itself were arbitrable. In the 1967 Prima Paint case the Court had opened the door to more widespread use of arbitration when it adopted the separability principle, compelling arbitration of a claim that a contract had been fraudulently induced. That held that any challenge to the validity of a contract with an arbitration clause must be heard by the arbitrator first unless the challenge is to the arbitration clause itself. It creates a legal fiction that two separate contracts exist.
|
|
In statistics, fixed-effect Poisson models are used for static panel data when the outcome variable is count data. Hausman, Hall, and Griliches pioneered the method in the mid 1980s. Their outcome of interest was the number of patents filed by firms, where they wanted to develop methods to control for the firm fixed effects.Hausman, J. A., B. H. Hall, and Z. Griliches (1984): "Econometric Models for Count Data with an Application to the Patents-R&D; Relationship." Econometrica (46), pp. 909–938 Linear panel data models use the linear additivity of the fixed effects to difference them out and circumvent the incidental parameter problem. Even though Poisson models are inherently nonlinear, the use of the linear index and the exponential link function lead to multiplicative separability, more specifically Cameron, C. A. and P. K. Trivedi (2015) "Count Panel Data," Oxford Handbook of Panel Data, ed. by B. Baltagi, Oxford University Press, pp. 233–256 : E[yit ∨ xi1... xiT, ci ] = m(xit, ci, b0 ) = exp(ci \+ xit b0 ) = ai exp(xit b0 ) = μti (1) This formula looks very similar to the standard Poisson premultiplied by the term ai.
|
|