A principal component analysis of cosmic microwave background (CMB) anisotropy measurements is used to investigate degeneracies among cosmological parameters. The results show that a degeneracy with tensor modes – the ‘tensor degeneracy’ – dominates uncertainties in estimates of the baryon and cold dark matter densities, ωb = Ωbh , ωc = Ωch , from an analysis of CMB anisotropies alone. The prin...

Spin-polarized electronic and transport properties of Armchair GraphdiyneNanoribbons (A-GDYNR) with single vacancy (SV), two types of configurations fordouble vacancy (DV1, DV2) and multi vacancy (MV) defects are studied by nonequilibriumGreen’s function (NEGF) combined with density functional theory (DFT).The results demonstrate that the A-GDYNR with the SV has the lowe...

Compared with direct-gap semiconductors, the valley degeneracy of silicon and germanium opens up new channels for spin relaxation that counteract the spin degeneracy of the inversion-symmetric system. Here the symmetries of the electron-phonon interaction for silicon and germanium are identified and the resulting spin lifetimes are calculated. Room-temperature spin lifetimes of electrons in sil...

Abstract – Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network’s adjacency matrix provides an understanding to the origins of occurrence of high multiplicities in the networks spectra. We find that the eigenvectors associated with the degenerate eigenvalues shed light on the structures contributing to the degeneracy. Since t...

We consider sequential decision problems over an infinite horizon. The forecast or solution horizon approach to solving such problems requires that the optimal initial decision be unique. We show that multiple optimal initial decisions can exist in general and refer to their existence as degeneracy. We then present a conceptual cost perturbation algorithm for resolving degeneracy and identifyin...

In global supersymmetric Wess-Zumino models with minimal Kähler potentials, F-type supersymmetry breaking always yields instability or continuous degeneracy of non-supersymmetric vacua. As a generalization of the original O’Raifeartaigh’s result, the existence of instability or degeneracy is true to any higher order corrections at tree level for models even with non-renormalizable superpotentia...

Weak gravitational lensing is considered to be one of the most powerful tools to study the mass and the mass distribution of galaxy clusters. However, weak lensing mass reconstructions are plagued by the so-called mass-sheet degeneracy – the surface mass density κ of the cluster can be determined only up to a degeneracy transformation κ → κ′ = λκ+(1−λ), where λ is an arbitrary constant. This tr...

By extending the constant-acceleration analysis of Smith, Mao, & Paczy´nski to include jerk, I show that microlens parallax measurements are subject to a four-fold discrete degeneracy. The new degeneracy is characterized by a projected velocity˜v j = −(3/4) csc β ec (cos 2 ψ sin 2 β ec + sin 2 ψ) 3/2 v ⊕ , where β ec is the ecliptic latitude, ψ is the phase of the Earth's orbit relative to oppo...

Weak gravitational lensing is considered to be one of the most powerful tools to study the mass and the mass distribution of galaxy clusters. However, weak lensing mass reconstructions are plagued by the so-called mass-sheet degeneracy – the surface mass density κ of the cluster can be determined only up to a degeneracy transformation κ → κ′ = λκ+ (1− λ), where λ is an arbitrary constant. This ...

A k-box B = (R1, R2, . . . , Rk), where each Ri is a closed interval on the real line, is defined to be the Cartesian product R1 × R2 × · · · × Rk. If each Ri is a unit length interval, we call B a k-cube. Boxicity of a graph G, denoted as box(G), is the minimum integer k such that G is an intersection graph of k-boxes. Similarly, the cubicity of G, denoted as cub(G), is the minimum integer k s...