Estimating the number of communities is one of the fundamental problems in community detection. We re-examine the Bayesian paradigm for stochastic block models (SBMs) and propose a "corrected ...Bayesian information criterion" (CBIC), to determine the number of communities and show that the proposed criterion is consistent under mild conditions as the size of the network and the number of communities go to infinity. The CBIC outperforms those used in Wang and Bickel and Saldana, Yu, and Feng which tend to underestimate and overestimate the number of communities, respectively. The results are further extended to degree corrected SBMs. Numerical studies demonstrate our theoretical results.
We propose a new secure transmission scheme in the multi-input multi-output multi-eavesdropper wiretap channel. In this channel, the N A -antenna transmitter adopts transmit antenna selection (TAS) ...to choose the antenna that maximizes the instantaneous signal-to-noise ratio (SNR) at the receiver to transmit, while the NB-antenna receiver and the N E -antenna eavesdropper adopt maximal-ratio combining (MRC) to combine the received signals. We focus on the practical scenario where the channel state information (CSI) during the TAS process is outdated. In this scenario, we propose a new transmission scheme to prevent the detrimental effect of the outdated CSI on the wiretap codes design at the transmitter. To thoroughly assess the secrecy performance achieved by the proposed scheme, we derive new closed-form expressions for the exact secrecy outage probability and the probability of non-zero secrecy capacity for arbitrary SNRs. We also derive new compact expressions for the asymptotic secrecy outage probability at high SNRs. Notably, in the analysis, we take spatial correlation at the receiver into consideration. Apart from the advantage of our scheme over the conventional TAS/MRC scheme, we demonstrate that the outdated TAS reduces the secrecy diversity order from N A N B to N B . We also demonstrate that antenna correlation improves the secrecy performance at low SNR but deteriorates the secrecy performance at medium and high SNRs, by affecting the secrecy array gain only.
The stochastic block model is widely used for detecting community structures in network data. How to test the goodness of fit of the model is one of the fundamental problems and has gained growing ...interests in recent years. In this article, we propose a novel goodness-of-fit test based on the maximum entry of the centered and rescaled adjacency matrix for the stochastic block model. One noticeable advantage of the proposed test is that the number of communities can be allowed to grow linearly with the number of nodes ignoring a logarithmic factor. We prove that the null distribution of the test statistic converges in distribution to a Gumbel distribution, and we show that both the number of communities and the membership vector can be tested via the proposed method. Furthermore, we show that the proposed test has asymptotic power guarantee against a class of alternatives. We also demonstrate that the proposed method can be extended to the degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.
Supplementary materials
for this article are available online.
Physical layer security is a promising technique to ensure the confidentiality of short-packet communications, since no additional channel uses are needed. Motivated by the fact of finite coding ...blocklength in short-packet communications, we attempt to investigate the problem of how many the channel uses utilized for channel training should be allocated to perform secure communications. Based on the finite blocklength information theory, we derive a closed-form expression to approximate the average achievable secrecy throughput. To gain more insights, we also present the asymptotic average secrecy throughput under two special cases, i.e., high signal-to-noise ratio (SNR) and infinite blocklength. Moreover, we determine the optimal channel training length to maximize the average secrecy throughput under the reliability constraint and given blocklength. Numerical results are provided to validate the analysis and demonstrate that the performance gain achieved by the optimal channel training length is remarkable, relative to other benchmark schemes.
We design new secure on-off transmission schemes in wiretap channels with outdated channel state information (CSI). In our design, we consider not only the outdated CSI from the legitimate receiver ...but two distinct scenarios as well, depending on whether the outdated CSI from the eavesdropper is known at the transmitter. Under this consideration, our schemes exploit useful knowledge contained in the available outdated CSI, and based on this, the transmitter decides on whether to transmit or not. We derive new closed-form expressions for the transmission probability, the connection outage probability, the secrecy outage probability, and the reliable and secure transmission probability to characterize the achievable performance. Based on these results, we present the optimal solutions that maximize the secrecy throughput under dual connection and secrecy outage constraints. Our analytical and numerical results offer detailed insights into the design of the wiretap coding parameters and the imposed outage constraints. We further show that allowing more freedom on the codeword transmission rate enables a larger feasible region of the dual outage constraints by exploiting the tradeoff between reliability and security.
We design a novel artificial-noise-aided secure ON-OFF transmission scheme in a wiretap channel. We consider a practical scenario, where the multi-antenna transmitter only obtains partial channel ...knowledge from the single-antenna receiver through limited training and feedback but has no channel knowledge about the single-antenna eavesdropper. In the design, we first propose a three-period block transmission protocol to capture the practical training and quantization features. We then characterize the statistics of the received signal-to-noise ratios at the receiver and the eavesdropper. Under the secrecy outage constraint, we exploit the ON-OFF scheme to perform secure transmission and derive a closed-form expression for the secrecy throughput. Moreover, we investigate the optimization problem of maximizing the secrecy throughput by proposing an iterative algorithm to determine the optimal power allocation between the information signal and artificial noise, as well as the optimal codeword transmission rate. Furthermore, we define the net secrecy throughput (NST), which takes the signaling overhead into account and address the problem of optimally allocating the block resource to the training and feedback overhead. Numerical results clearly demonstrate how the optimal signaling overhead changes with the number of transmit antennas, and there exists an optimal number of antennas that maximizes the NST.
Due to the complexity and uncertainty of decision-making, probabilistic linguistic term sets (PLTSs) are currently important tools for qualitative evaluation of decision-makers. The asymmetry of ...evaluation information can easily lead to the loss of subjective preference information for decision-makers, and the existing operation of decision-maker evaluation information fusion operators is difficult to solve this problem. To solve such problems, this paper proposes some new operational methods for PLTSs based on Dombi T-conorm and T-norm. Considering the interrelationships between the input independent variables of PLTSs, the probabilistic linguistic weighted Dombi Bonferroni mean Power average (PLWDBMPA) operators are extended and the properties of these aggregation operators are proposed. Secondly, the PLWDBMPA operator is used to fuse the evaluation information of decision-makers, avoiding the loss of decision information as much as possible. This paper uses social media platforms and web crawler technology to obtain online comments from users on decision-making to obtain the public’s attitude towards decision events. TF-IDF and Word2Vec are used to calculate the weight of alternatives on each attribute. Under traditional group decision-making methods and integrating the wisdom of the public, a novel multi-attribute group decision-making method based on TODIM method is proposed. Finally, the case study of Turkey earthquake shelter selection proves this method is scientific and effective. Meanwhile, the superiority of this method was further verified through comparisons with the PL-TOPSIS, PLWA, SPOTIS and PROMETHEE method.
Lithium metal anodes have long been considered as “holy grail” in the field of energy storage batteries, but dendrite growth and large volume changes hinder their practical applications. Herein, a ...facile and eco‐friendly CF4 plasma treatment is employed for the surface modification of Li anodes, and an artificial layer consisting of LiF and Li2C2 is fabricated for the first time. Experimental results and theoretical calculations reveal that the high adsorption energy of LiF and low Li+ diffusion barriers in Li2C2 induce uniform nucleation and planar growth of Li, guaranteeing a stable and dendrite‐free Li structure during the repeated plating/stripping process of cycling. Symmetric cells using CF4 plasma‐treated Li operate stably for more than 6500 h (at 2 mA cm−2 and 1 mAh cm−2) or 950 h (at 1 mA cm−2 and 10 mAh cm−2). When paired with a LiFePO4 cathode, full batteries deliver a high reversible capacity of 136 mAh g−1 (at 1 C) with considerable cycling stability (97.2% capacity retention over 200 cycles) and rate performance (116 mAh g−1 up to 5 C). This powerful application of plasma technology toward novel LiF‐Li2C2 artificial layers provide new routes for constructing environment‐friendly and high‐performance energy storage devices.
An artificial layer consisting of LiF and Li2C2 is fabricated by a facile and eco‐friendly CF4 plasma treatment for the first time. The symmetric cells using the CF4 plasma‐treated Li can operate stably for more than 6500 h with an overpotential of 50 mV.
Due to the EV (Electric Vehicles) charging stations are characterized by weak damping and low inertia, the EV with a high degree of uncertainty can easily have an impact on the stability of the ...charging station system. Therefore, this paper proposes an optimization control method to improve the system inertia effect based on the fractional order impedance model of the charging station. This paper presents a study on establishing a fractional impedance model for charging stations, using the deviation between theoretical impedance spectra and actual measurements as a criterion. The goal is to enhance system inertia and optimize the parameters of the fractional-order controller to improve the supporting capacity of the charging station system and enhance its dynamic response. Initially, considering the fractional characteristics of the EV load, a fractional impedance model of the charging station is established. The analysis demonstrates that the fractional-order capacitor provides inertia to the system, enhancing its inertia support capability. In addition, a virtual inertia control strategy based on fractional-order PID (FOPID) is designed. Finally, an improved particle swarm optimization algorithm is utilized to optimize the control parameters. Through experimental verification under different operating conditions, it has been demonstrated that the fractional-order control strategy can achieve a dynamic response time of approximately 0.025s and limit the voltage deviation within 5%. Furthermore, the rotational inertia can rapidly increase to the maximum value satisfying the objective function within 0.05s. The results indicate that this control method effectively suppresses the DC voltage and power oscillations in the distribution grid.
Helvella bachu, a prized edible and medicinal fungus, is primarily found in the forests of Populus euphratica, an ancient and endangered species crucial to desert riparian ecosystems. Despite ...extensive efforts, the isolation of pure cultures and cultivation of fruiting bodies of H. bachu have remained elusive. While some species within the Helvella genus have been confirmed as ectomycorrhizal fungi, others have been considered either saprotrophic or mycorrhizal. By integrating field observations of H. bachu habitat, macro- and micro-anatomical examination of plant root tips, and molecular data from fruiting bodies, mycorrhizae, and host plants, it has been confirmed that H. bachu forms ectomycorrhizal associations with Populus trees. The mycorrhiza of H. bachu displays a light earth color with a curved smooth cylindrical shape. It features a thick mantle and the presence of a Hartig net, accompanied by a small amount of epitaxy mycelia. Morphological observation of the root tips requires meticulous handling, and the paraffin section technique has yielded noteworthy results. Host plants encompass four Populus species, including P. euphratica, P. pruinosa, P. nigra, and P. alba var. pyramidalis (synonym Populus bolleana). A conservation area was established within the young P. euphratica forest at Tarim University, resulting in a 14.75% increase in the quantity of fruiting bodies during the second year. Establishing a conservation area and in situ propagation of H. bachu holds economic and ecological implications. This study will contribute to the conservation of resources related to H. bachu and P. euphratica.
PDF
