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

Straggler Mitigation and Latency Optimization in Blockchain-based Hierarchical Federated Learning

Cloud-edge-device hierarchical federated learning (HFL) has been recently proposed to achieve communication-efficient and privacy-preserving distributed learning. However, there exist several critical challenges, such as the single point of failure and potential stragglers in both edge servers and local devices. To resolve these issues, we propose a decentralized and straggler-tolerant blockchain-based HFL (BHFL) framework. Specifically, a Raft-based consortium blockchain is deployed on edge servers to provide a distributed and trusted computing environment for global model aggregation in BHFL. To mitigate the influence of stragglers on learning, we propose a novel aggregation method, HieAvg, which utilizes the historical weights of stragglers to estimate the missing submissions. Furthermore, we optimize the overall latency of BHFL by jointly considering the constraints of global model convergence and blockchain consensus delay. Theoretical analysis and experimental evaluation show that our proposed BHFL based on HieAvg can converge in the presence of stragglers, which performs better than the traditional methods even when the loss function is non-convex and the data on local devices are non-independent and identically distributed (non-IID)

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