Binomial Difference Ideal and Toric Difference Variety

In this paper, the concepts of binomial difference ideals and toric difference varieties are defined and their properties are proved. Two canonical representations for Laurent binomial difference ideals are given using the reduced Groebner basis of Z[x]-lattices and regular and coherent difference ascending chains, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, perfect, and toric are given in terms of their support lattices which are Z[x]-lattices. The reflexive, well-mixed, and perfect closures of a Laurent binomial difference ideal are shown to be binomial. Four equivalent definitions for toric difference varieties are presented. Finally, algorithms are given to check whether a given Laurent binomial difference ideal I is reflexive, prime, well-mixed, perfect, or toric, and in the negative case, to compute the reflexive, well-mixed, and perfect closures of I. An algorithm is given to decompose a finitely generated perfect binomial difference ideal as the intersection of reflexive prime binomial difference ideals.Comment: 72 page

Design of Reconfigurable Intelligent Surface-Aided Cross-Media Communications

A novel reconfigurable intelligent surface (RIS)-aided hybrid reflection/transmitter design is proposed for achieving information exchange in cross-media communications. In pursuit of the balance between energy efficiency and low-cost implementations, the cloud-management transmission protocol is adopted in the integrated multi-media system. Specifically, the messages of devices using heterogeneous propagation media, are firstly transmitted to the medium-matched AP, with the aid of the RIS-based dual-hop transmission. After the operation of intermediate frequency conversion, the access point (AP) uploads the received signals to the cloud for further demodulating and decoding process. Based on time division multiple access (TDMA), the cloud is able to distinguish the downlink data transmitted to different devices and transforms them into the input of the RIS controller via the dedicated control channel. Thereby, the RIS can passively reflect the incident carrier back into the original receiver with the exchanged information during the preallocated slots, following the idea of an index modulation-based transmitter. Moreover, the iterative optimization algorithm is utilized for optimizing the RIS phase, transmit rate and time allocation jointly in the delay-constrained cross-media communication model. Our simulation results demonstrate that the proposed RIS-based scheme can improve the end-to-end throughput than that of the AP-based transmission, the equal time allocation, the random and the discrete phase adjustment benchmarks

Lower Bound of Concurrence Based on Positive Maps

We study the concurrence of arbitrary dimensional bipartite quantum systems. An explicit analytical lower bound of concurrence is obtained, which detects entanglement for some quantum states better than some well-known separability criteria, and improves the lower bounds such as from the PPT, realignment criteria and the Breuer's entanglement witness.Comment: 8 pages, 1 figur

Probing nuclear symmetry energy at high densities using pion, kaon, eta and photon productions in heavy-ion collisions

The high-density behavior of nuclear symmetry energy is among the most uncertain properties of dense neutron-rich matter. Its accurate determination has significant ramifications in understanding not only the reaction dynamics of heavy-ion reactions especially those induced by radioactive beams but also many interesting phenomena in astrophysics, such as the explosion mechanism of supernova and the properties of neutron stars. The heavy-ion physics community has devoted much effort during the last few years to constrain the high-density symmetry using various probes. In particular, the pion-/pion+ ratio has been most extensively studied both theoretically and experimentally. All models have consistently predicted qualitatively that the pion-/pion+ ratio is a sensitive probe of the high-density symmetry energy especially with beam energies near the pion production threshold. However, the predicted values of the pion-/pion+ ratio are still quite model dependent mostly because of the complexity of modeling pion production and reabsorption dynamics in heavy-ion collisions, leading to currently still controversial conclusions regarding the high-density behavior of nuclear symmetry energy from comparing various model calculations with available experimental data. As more pion-/pion+ data become available and a deeper understanding about the pion dynamics in heavy-ion reactions is obtained, more penetrating probes, such as the kaon+/kaon0 ratio, eta meson and high energy photons are also being investigated or planned at several facilities. Here, we review some of our recent contributions to the community effort of constraining the high-density behavior of nuclear symmetry energy in heavy-ion collisions. In addition, the status of some worldwide experiments for studying the high-density symmetry energy, including the HIRFL-CSR external target experiment (CEE) are briefly introduced.Comment: 10 pages, 10 figures, Contribution to the Topical Issue on Nuclear Symmetry Energy in EPJA Special Volum