On Homology Roses and the D(2)-problem

For a commutative ring $R$ with a unit, an $R$-homology rose is a topological space whose homology groups with $R$-coefficients agree with those of a bouquet of cirlces. In this paper, we study some special properties of covering spaces and fundamental groups of $R$-homology roses, from which we obtain some result supporting the Carlsson conjecture on free $(Z_p)^r$ actions. In addition, for a group $G$ and a field $F$, we define an integer called the $F$-gap of $G$, which is an obstruction for $G$ to be realized as the fundamental group of a 2-dimensional $F$-homology rose. Furthermore, we discuss how to search candidates of the counterexamples of Wall's D(2)-problem among $F$-homology roses and $F$-acyclic spaces.Comment: 26 pages, no figure; some new results are added to the previous versio

Exploiting Device-to-Device Communications in Joint Scheduling of Access and Backhaul for mmWave Small Cells

With the explosive growth of mobile data demand, there has been an increasing interest in deploying small cells of higher frequency bands underlying the conventional homogeneous macrocell network, which is usually referred to as heterogeneous cellular networks, to significantly boost the overall network capacity. With vast amounts of spectrum available in the millimeter wave (mmWave) band, small cells at mmWave frequencies are able to provide multi-gigabit access data rates, while the wireless backhaul in the mmWave band is emerging as a cost-effective solution to provide high backhaul capacity to connect access points (APs) of the small cells. In order to operate the mobile network optimally, it is necessary to jointly design the radio access and backhaul networks. Meanwhile, direct transmissions between devices should also be considered to improve system performance and enhance the user experience. In this paper, we propose a joint transmission scheduling scheme for the radio access and backhaul of small cells in the mmWave band, termed D2DMAC, where a path selection criterion is designed to enable device-to-device transmissions for performance improvement. In D2DMAC, a concurrent transmission scheduling algorithm is proposed to fully exploit spatial reuse in mmWave networks. Through extensive simulations under various traffic patterns and user deployments, we demonstrate D2DMAC achieves near-optimal performance in some cases, and outperforms other protocols significantly in terms of delay and throughput. Furthermore, we also analyze the impact of path selection on the performance improvement of D2DMAC under different selected parameters.Comment: 16 pages, 26 figures, a journal paper, Accepted by IEEE JSAC Special Issue on Recent Advances in Heterogeneous Network

Modeling Spacing Distribution of Queuing Vehicles in Front of a Signalized Junction Using Random-Matrix Theory

Modeling of headway/spacing between two consecutive vehicles has many applications in traffic flow theory and transport practice. Most known approaches only study the vehicles running on freeways. In this paper, we propose a model to explain the spacing distribution of queuing vehicles in front of a signalized junction based on random-matrix theory. We show that the recently measured spacing distribution data well fit the spacing distribution of a Gaussian symplectic ensemble (GSE). These results are also compared with the spacing distribution observed for car parking problem. Why vehicle-stationary-queuing and vehicle-parking have different spacing distributions (GSE vs GUE) seems to lie in the difference of driving patterns

Evidence of the side jump mechanism in the anomalous Hall effect in paramagnets

Persistent confusion has existed between the intrinsic (Berry curvature) and the side jump mechanisms of anomalous Hall effect (AHE) in ferromagnets. We provide unambiguous identification of the side jump mechanism, in addition to the skew scattering contribution in epitaxial paramagnetic Ni$_{34}$Cu$_{66}$ thin films, in which the intrinsic contribution is by definition excluded. Furthermore, the temperature dependence of the AHE further reveals that the side jump mechanism is dominated by the elastic scattering