37,051 research outputs found

    One-Bit Compressed Sensing by Greedy Algorithms

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    Sign truncated matching pursuit (STrMP) algorithm is presented in this paper. STrMP is a new greedy algorithm for the recovery of sparse signals from the sign measurement, which combines the principle of consistent reconstruction with orthogonal matching pursuit (OMP). The main part of STrMP is as concise as OMP and hence STrMP is simple to implement. In contrast to previous greedy algorithms for one-bit compressed sensing, STrMP only need to solve a convex and unconstraint subproblem at each iteration. Numerical experiments show that STrMP is fast and accurate for one-bit compressed sensing compared with other algorithms.Comment: 16 pages, 7 figure

    Differential Geometrical Formulation of Gauge Theory of Gravity

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    Differential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantum gauge theory of gravity which is proposed in the references hep-th/0109145 and hep-th/0112062 is formulated completely in the framework of traditional quantum field theory. In order to study the relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curved space, it is important to find the differential geometric formulation of quantum gauge theory of gravity. We first give out the correspondence between quantum gauge theory of gravity and differential geometry. Then we give out differential geometric formulation of quantum gauge theory of gravity.Comment: 10 pages, no figur

    The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation

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    The paper is to reveal the direct links between the well known Sylvester equation in matrix theory and some integrable systems. Using the Sylvester equation KM+MK=rsT\boldsymbol{K} \boldsymbol{M}+\boldsymbol{M} \boldsymbol{K}=\boldsymbol{r}\, \boldsymbol{s}^{T} we introduce a scalar function S(i,j)=sTKj(I+M)1KirS^{(i,j)}=\boldsymbol{s}^{T}\, \boldsymbol{K}^j(\boldsymbol{I}+\boldsymbol{M})^{-1}\boldsymbol{K}^i\boldsymbol{r} which is defined as same as in discrete case. S(i,j)S^{(i,j)} satisfy some recurrence relations which can be viewed as discrete equations and play indispensable roles in deriving continuous integrable equations. By imposing dispersion relations on r\boldsymbol{r} and s\boldsymbol{s}, we find the Korteweg-de Vries equation, modified Korteweg-de Vries equation, Schwarzian Korteweg-de Vries equation and sine-Gordon equation can be expressed by some discrete equations of S(i,j)S^{(i,j)} defined on certain points. Some special matrices are used to solve the Sylvester equation and prove symmetry property S(i,j)=S(i,j)S^{(i,j)}=S^{(i,j)}. The solution M\boldsymbol{M} provides τ\tau function by τ=I+M\tau=|\boldsymbol{I}+\boldsymbol{M}|. We hope our results can not only unify the Cauchy matrix approach in both continuous and discrete cases, but also bring more links for integrable systems and variety of areas where the Sylvester equation appears frequently.Comment: 23 page

    Detecting edge degeneracy in interacting topological insulators through entanglement entropy

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    The existence of degenerate or gapless edge states is a characteristic feature of topological insulators, but is difficult to detect in the presence of interactons. We propose a new method to obtain the degeneracy of the edge states from the perspective of entanglement entropy, which is very useful to identify interacting topological states. Employing the determinant quantum Monte Carlo technique, we investigate the interaction effect on two representative models of fermionic topological insulators in one and two dimensions, respectively. In the two topologically nontrivial phases, the edge degeneracies are reduced by interactions but remain to be nontrivial.Comment: 6 pages, 4 figure