Single-input and single-output (SISO) controller reduction based on the L1L_1-norm

This paper proposes a new method to solve the controller-reduction problem based on the $L_1$-norm. This method uses a reduced-order closed-loop system to deduce reduced-order controllers. The problem of obtaining the required lower-order closed-loop system was formulated as an $L_1$-norm optimization, and the conditions were provided for guaranteeing the internal stability and the existence of lower-order controllers from the obtained reduced-order closed-loop system. In addition, the particle swarm optimization and sequence linear programming were adopted to solve the resultant $L_1$-norm optimization. Two numerical examples demonstrated the effectiveness of the proposed method

On Source Density Evolution of Gamma-ray Bursts

Recent optical afterglow observations of gamma-ray bursts indicate a setting and distance scale that many relate to star-formation regions. In this paper, we use $$ and a set of artificial trigger thresholds to probe several potential GRB source density evolutionary scenarios. In particular, we compare a uniform subset of BATSE 4B data to cosmological scenarios where GRBs evolve as the comoving density, the star formation rate, the QSO rate, and the SN Type Ic rate. Standard candle bursts with power-law spectra and a universe without vacuum energy were assumed. Our results significantly favor a comoving density model, implying that GRB source density evolution is weaker than expected in these evolutionary scenarios. GRB density might still follow star-formation rates given proper concurrent GRB luminosity evolution, significant beaming, significant error in standard candle assumptions, or were a significant modification of star formation rate estimates to occur.Comment: 12 pages, 4 figures, accepted by Ap

Spectroscopic signatures of the Larkin-Ovchinnikov state in the conductance characteristics of a normal-metal/superconductor junction

Using a discrete-lattice approach, we calculate the conductance spectra between a normal metal and an s-wave Larkin-Ovchinnikov (LO) superconductor, with the junction interface oriented {\em along} the direction of the order-parameter (OP) modulation. The OP sign reversal across one single nodal line can induce a sizable number of zero-energy Andreev bound states around the nodal line, and a hybridized midgap-states band is formed amid a momentum-dependent gap as a result of the periodic array of nodal lines in the LO state. This band-in-gap structure and its anisotropic properties give rise to distinctive features in both the point-contact and tunneling spectra as compared with the BCS and Fulde-Ferrell cases. These spectroscopic features can serve as distinguishing signatures of the LO state.Comment: 8 pages, 5 figures; version as publishe

SNE: Signed Network Embedding

Several network embedding models have been developed for unsigned networks. However, these models based on skip-gram cannot be applied to signed networks because they can only deal with one type of link. In this paper, we present our signed network embedding model called SNE. Our SNE adopts the log-bilinear model, uses node representations of all nodes along a given path, and further incorporates two signed-type vectors to capture the positive or negative relationship of each edge along the path. We conduct two experiments, node classification and link prediction, on both directed and undirected signed networks and compare with four baselines including a matrix factorization method and three state-of-the-art unsigned network embedding models. The experimental results demonstrate the effectiveness of our signed network embedding.Comment: To appear in PAKDD 201

The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential

As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces for hard potential when the solution is a small perturbation of a global equilibrium