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Configurable topological photonic polycrystal based on a synthetic hybrid dimension. [PDF]
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Densities of degeneracies and near-degeneracies
Physical Review A, 1993The eigenvalues of a quantum system depending on two parameters become degenerate at isolated points in the parameter space, which are called diabolical points because of their double-cone structure. Varying one parameter produces near-degeneracies termed avoided crossings. Some results on the density of these objects in parameter space can be obtained
, Wilkinson, , Austin
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SIAM Journal on Scientific and Statistical Computing, 1984
The paper surveys some of the more commonly used methods for approximating the rank of a matrix X, with particular attention to the effects of errors. It is supposed that X itself cannot be observed and only a perturbed matrix \(X=X+E\) is given.
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The paper surveys some of the more commonly used methods for approximating the rank of a matrix X, with particular attention to the effects of errors. It is supposed that X itself cannot be observed and only a perturbed matrix \(X=X+E\) is given.
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International Journal of Mathematics, 1996
Let \(X_r\) be the degeneracy locus of rank \(r\) of a morphism \(\varphi\) of vector bundles over a smooth irreducible variety \(X\), and \({\mathcal I}_{X_r}\) the ideal sheaf of \(X_r\). We quote from the author's introduction: Our aim is to study the cohomology of \({\mathcal I}_{X_r}\). In particular we want to know if \(H^1 ({\mathcal I}_{X_r})=0\
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Let \(X_r\) be the degeneracy locus of rank \(r\) of a morphism \(\varphi\) of vector bundles over a smooth irreducible variety \(X\), and \({\mathcal I}_{X_r}\) the ideal sheaf of \(X_r\). We quote from the author's introduction: Our aim is to study the cohomology of \({\mathcal I}_{X_r}\). In particular we want to know if \(H^1 ({\mathcal I}_{X_r})=0\
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Interdimensional degeneracies, near degeneracies, and their applications
The Journal of Chemical Physics, 1986Recently developed approximation methods for quantum mechanical problems which treat the spatial dimension D as an expansion parameter offer approximations to energy levels at arbitrary D. Rather than simply being a detour to the D=3 case, there is physical interest in nonphysical values of D due to degeneracies between states in different dimensions ...
D. J. Doren, D. R. Herschbach
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DARTS with Degeneracy Correction
2023The neural architecture search (NAS) is characterized by a wide search space and a time consuming objective function. Many papers have dealt with the reduction of the cost of the objective function assessment. Among them, there is DARTS paper [1] that proposes to transform the original discrete problem into a continuous one.
Lacharme, Guillaume +3 more
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Twisted Cubic: Degeneracy Degree and Relationship with General Degeneracy
2010Fundamental matrix, drawing geometric relationship between two images, plays an important role in 3-dimensional computer vision. Degenerate configurations of space points and two camera optical centers affect stability of computation for fundamental matrix.
Tian Lan, Yihong Wu 0002, Zhanyi Hu
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Journal of the Operational Research Society, 1992
Summary: Two projected gradient algorithms for linear programming are discussed. The first uses a conventional enough steepest edge approach, and implements a version of Wolfe's method for resolving any problems of degeneracy. The second makes use of a steepest descent direction which is calculated by solving a linear least squares problem subject to ...
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Summary: Two projected gradient algorithms for linear programming are discussed. The first uses a conventional enough steepest edge approach, and implements a version of Wolfe's method for resolving any problems of degeneracy. The second makes use of a steepest descent direction which is calculated by solving a linear least squares problem subject to ...
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Annals of Operations Research, 1993
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