We introduce a general formulation for dimension reduction and coefficient estimation in the multivariate linear model. We argue that many of the existing methods that are commonly used in practice can be formulated in this framework and have various restrictions. We continue to propose a new...

In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result, we then propose penalty decomposition methods for...

We study entanglement, purity and fidelity in the anisotropy (1/2,1) mixed-spin Heisenberg chain. We find that negativity, as a measure of entanglement, displays a dip at the SU(2) isotropic point of the system, which is in contrast to the peak appearance of concurrence in the spin-1/2 XXZ...

By using the concept of negativity, we investigate entanglement in (12,1) mixed-spin Heisenberg systems. We obtain the analytical results of entanglement in small isotropic Heisenberg clusters with only nearest-neighbor (NN) interactions up to four spins and in the four-spin Heisenberg model...

We obtain an exact expression of the negativity for SU(2)-invariant bipartite spin-(1,s) states via the partial time reversal method. Studies of thermal states show that the threshold temperature of entanglement may be arbitrary high when s is sufficient large, indicating that the entanglement...

In this paper, we first propose a constrained optimization reformulation to the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$L_{1/2}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>L</mi> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </msub> </math> </EquationSource> </InlineEquation> regularization problem. The constrained problem is to minimize a smooth function subject to some quadratic constraints and nonnegative constraints. A good property of the constrained...</equationsource></equationsource></inlineequation>

Four organic dyes (XS10–13) employing carbazole unit as electron donor and N,N-dimethylarylamine moieties as electron-donating groups were designed and synthesized for nanocrystalline TiO2 dye-sensitized solar cells. The electron-donating groups of dimethylarylamine increase the electron...

We study pairwise entanglements in spin-half and spin-one Heisenberg chains with an open boundary condition, respectively. We find out that the ground-state and the first-excited-state entanglements are equal for the three-site spin-one chain. When the number of sites L3, the concurrences and...