37,051 research outputs found

### One-Bit Compressed Sensing by Greedy Algorithms

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

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

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 $\boldsymbol{K} \boldsymbol{M}+\boldsymbol{M}
\boldsymbol{K}=\boldsymbol{r}\, \boldsymbol{s}^{T}$ we introduce a scalar
function $S^{(i,j)}=\boldsymbol{s}^{T}\,
\boldsymbol{K}^j(\boldsymbol{I}+\boldsymbol{M})^{-1}\boldsymbol{K}^i\boldsymbol{r}$
which is defined as same as in discrete case. $S^{(i,j)}$ 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 $\boldsymbol{r}$ and $\boldsymbol{s}$, 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 $S^{(i,j)}$ defined on certain points. Some special
matrices are used to solve the Sylvester equation and prove symmetry property
$S^{(i,j)}=S^{(i,j)}$. The solution $\boldsymbol{M}$ provides $\tau$ function
by $\tau=|\boldsymbol{I}+\boldsymbol{M}|$. 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

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

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