Accurate gradient computations at interfaces using finite element methods

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea from \cite{wheeler1974galerkin}. For 2D interface problems, the idea is to introduce a small tube near the interface and introduce the gradient as part of unknowns, which is similar to a mixed finite element method, except only at the interface. Thus the computational cost is just slightly higher than the standard finite element method. We present rigorous one dimensional analysis, which show second order convergence order for both of the solution and the gradient in 1D. For two dimensional problems, we present numerical results and observe second order convergence for the solution, and super-convergence for the gradient at the interface

PoFEL: Energy-efficient Consensus for Blockchain-based Hierarchical Federated Learning

Facilitated by mobile edge computing, client-edge-cloud hierarchical federated learning (HFL) enables communication-efficient model training in a widespread area but also incurs additional security and privacy challenges from intermediate model aggregations and remains the single point of failure issue. To tackle these challenges, we propose a blockchain-based HFL (BHFL) system that operates a permissioned blockchain among edge servers for model aggregation without the need for a centralized cloud server. The employment of blockchain, however, introduces additional overhead. To enable a compact and efficient workflow, we design a novel lightweight consensus algorithm, named Proof of Federated Edge Learning (PoFEL), to recycle the energy consumed for local model training. Specifically, the leader node is selected by evaluating the intermediate FEL models from all edge servers instead of other energy-wasting but meaningless calculations. This design thus improves the system efficiency compared with traditional BHFL frameworks. To prevent model plagiarism and bribery voting during the consensus process, we propose Hash-based Commitment and Digital Signature (HCDS) and Bayesian Truth Serum-based Voting (BTSV) schemes. Finally, we devise an incentive mechanism to motivate continuous contributions from clients to the learning task. Experimental results demonstrate that our proposed BHFL system with the corresponding consensus protocol and incentive mechanism achieves effectiveness, low computational cost, and fairness

DuPont Model and Product Profitability Analysis Based on Activity-based Costing and Economic Value Added

Although DuPont analysis is widely used it is not easy to provide accurate performance information based on DuPont profitability analysis, which is established on the basis of traditional accounting earnings. Since Activity-based Costing (ABC) and Economic Value Added (EVA) are advanced approaches to costing activities and estimating economic profit of a firm, DuPont analysis using ABC and EVA information can be more appropriate in understanding Return on Equity (ROE). In this paper we set up an improved EVA-ABC based DuPont analysis system as well as its relative indices. Then it is applied to traditional profitability analysis to get a better performance measurement. The results show that the improved system can reduce the negative impacts of accounting principles and objectively reflect the operating performance of the enterprise. It also provides more accurate information for decision makers. Keywords: DuPont Analysis; Activity-based Costing; Economic Value Added; Profitability Analysi

LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear p-Laplace Diffusion

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinear p-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods in W1,p(Ω), Itô formula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays

Enhancing Automatic Modulation Recognition through Robust Global Feature Extraction

Automatic Modulation Recognition (AMR) plays a crucial role in wireless communication systems. Deep learning AMR strategies have achieved tremendous success in recent years. Modulated signals exhibit long temporal dependencies, and extracting global features is crucial in identifying modulation schemes. Traditionally, human experts analyze patterns in constellation diagrams to classify modulation schemes. Classical convolutional-based networks, due to their limited receptive fields, excel at extracting local features but struggle to capture global relationships. To address this limitation, we introduce a novel hybrid deep framework named TLDNN, which incorporates the architectures of the transformer and long short-term memory (LSTM). We utilize the self-attention mechanism of the transformer to model the global correlations in signal sequences while employing LSTM to enhance the capture of temporal dependencies. To mitigate the impact like RF fingerprint features and channel characteristics on model generalization, we propose data augmentation strategies known as segment substitution (SS) to enhance the model's robustness to modulation-related features. Experimental results on widely-used datasets demonstrate that our method achieves state-of-the-art performance and exhibits significant advantages in terms of complexity. Our proposed framework serves as a foundational backbone that can be extended to different datasets. We have verified the effectiveness of our augmentation approach in enhancing the generalization of the models, particularly in few-shot scenarios. Code is available at \url{https://github.com/AMR-Master/TLDNN}.Comment: submitted to IEEE Transactions on Vehicular Technology, 14 pages, 11 figure

Deep Learning for Hybrid Beamforming with Finite Feedback in GSM Aided mmWave MIMO Systems

Hybrid beamforming is widely recognized as an important technique for millimeter wave (mmWave) multiple input multiple output (MIMO) systems. Generalized spatial modulation (GSM) is further introduced to improve the spectrum efficiency. However, most of the existing works on beamforming assume the perfect channel state information (CSI), which is unrealistic in practical systems. In this paper, joint optimization of downlink pilot training, channel estimation, CSI feedback, and hybrid beamforming is considered in GSM aided frequency division duplexing (FDD) mmWave MIMO systems. With the help of deep learning, the GSM hybrid beamformers are designed via unsupervised learning in an end-to-end way. Experiments show that the proposed multi-resolution network named GsmEFBNet can reach a better achievable rate with fewer feedback bits compared with the conventional algorithm.Comment: 4 pages, 4 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notic