Maximizing spectral radii of uniform hypergraphs with few edges

In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs, linear or power unicyclic hypergraphs with given girth, linear or power bicyclic hypergraphs, respectively

Degree correlation effect of bipartite network on personalized recommendation

In this paper, by introducing a new user similarity index base on the diffusion process, we propose a modified collaborative filtering (MCF) algorithm, which has remarkably higher accuracy than the standard collaborative filtering. In the proposed algorithm, the degree correlation between users and objects is taken into account and embedded into the similarity index by a tunable parameter. The numerical simulation on a benchmark data set shows that the algorithmic accuracy of the MCF, measured by the average ranking score, is further improved by 18.19% in the optimal case. In addition, two significant criteria of algorithmic performance, diversity and popularity, are also taken into account. Numerical results show that the presented algorithm can provide more diverse and less popular recommendations, for example, when the recommendation list contains 10 objects, the diversity, measured by the hamming distance, is improved by 21.90%.Comment: 9 pages, 3 figure

Teleportation of an arbitrary multipartite state via photonic Faraday rotation

We propose a practical scheme for deterministically teleporting an arbitrary multipartite state, either product or entangled, using Faraday rotation of the photonic polarization. Our scheme, based on the input-output process of single-photon pulses regarding cavities, works in low-Q cavities and only involves virtual excitation of the atoms, which is insensitive to both cavity decay and atomic spontaneous emission. Besides, the Bell-state measurement is accomplished by the Faraday rotation plus product-state measurements, which could much relax the experimental difficulty to realize the Bell-state measurement by the CNOT operation.Comment: 11 pages, 2 figures

VLBA 24 and 43 GHz observations of massive binary black hole candidate PKS 1155+251

PKS 1155+251 is a radio-loud quasar source at z=0.203. Observations using very long baseline interferometry (VLBI) at ~2, 5, 8 and 15 GHz show that the structure of the radio source is quite complicated on parsec scales and that the outer hot spots are apparently undergoing a significant contraction. Because these results cannot be fully explained based on the compact symmetric object (CSO) scenario with a radio core located between the northern and southern complexes, we made observations with the Very Long Baseline Array (VLBA) at 24 and 43 GHz to search for compact substructures and alternative interpretations. The results show that the radio core revealed in the previous VLBI observations remains compact with a flat spectrum in our sub-milli-arcsecond--resolution images; the northern lobe emission becomes faint at 24 GHz and is mostly resolving out at 43 GHz; the southern complex is more bright but has been resolved into the brightest southern-end (S1) and jet or tail alike components westwards. Explaining the southern components aligned westward with a standard CSO scenario alone remains a challenge. As for the flatter spectral index of the southern-end component S1 between 24 and 43 GHz in our observations and the significant 15 GHz VLBA flux variability of S1, an alternative scenario is that the southern complex may be powered by a secondary black hole residing at S1. But more sensitive and high-resolution VLBI monitoring is required to discriminate the CSO and the binary black hole scenarios.Comment: 7 pages, 3 figures, accepted by MNRA