Voltage fluctuations are common disturbances in power grids. Initially, it is necessary to selectively identify individual sources of voltage fluctuations to take actions to minimize the effects of voltage fluctuations. Selective identification of disturbing loads is possible by using a signal chain consisting of demodulation, decomposition, and assessment of the propagation of component signals. The accuracy of such an approach is closely related to the applied decomposition method. The paper presents a new method for decomposition by approximation with pulse waves. The proposed method allows for an correct identification of selected parameters, that is, the frequency of changes in the operating state of individual sources of voltage fluctuations and the amplitude of voltage changes caused by them. The article presents results from numerical simulation studies and laboratory experimental studies, based on which the estimation errors of the indicated parameters were determined by the proposed decomposition method and other empirical decomposition methods available in the literature. The real states that occur in power grids were recreated in the research. The metrological interpretation of the results obtained from the numerical simulation and experimental research is discussed.
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Machine learned partial differential equation (PDE) solvers trade the reliability of standard numerical methods for potential gains in accuracy and/or speed. The only way for a solver to guarantee that it outputs the exact solution is to use a convergent method in the limit that the grid spacing $\Delta x$ and timestep $\Delta t$ approach zero. Machine learned solvers, which learn to update the solution at large $\Delta x$ and/or $\Delta t$, can never guarantee perfect accuracy. Some amount of error is inevitable, so the question becomes: how do we constrain machine learned solvers to give us the sorts of errors that we are willing to tolerate? In this paper, we design more reliable machine learned PDE solvers by preserving discrete analogues of the continuous invariants of the underlying PDE. Examples of such invariants include conservation of mass, conservation of energy, the second law of thermodynamics, and/or non-negative density. Our key insight is simple: to preserve invariants, at each timestep apply an error-correcting algorithm to the update rule. Though this strategy is different from how standard solvers preserve invariants, it is necessary to retain the flexibility that allows machine learned solvers to be accurate at large $\Delta x$ and/or $\Delta t$. This strategy can be applied to any autoregressive solver for any time-dependent PDE in arbitrary geometries with arbitrary boundary conditions. Although this strategy is very general, the specific error-correcting algorithms need to be tailored to the invariants of the underlying equations as well as to the solution representation and time-stepping scheme of the solver. The error-correcting algorithms we introduce have two key properties. First, by preserving the right invariants they guarantee numerical stability. Second, in closed or periodic systems they do so without degrading the accuracy of an already-accurate solver.
In this paper, an efficient ensemble domain decomposition algorithm is proposed for fast solving the fully-mixed random Stokes-Darcy model with the physically realistic Beavers-Joseph (BJ) interface conditions. We utilize the Monte Carlo method for the coupled model with random inputs to derive some deterministic Stokes-Darcy numerical models and use the idea of the ensemble to realize the fast computation of multiple problems. One remarkable feature of the algorithm is that multiple linear systems share a common coefficient matrix in each deterministic numerical model, which significantly reduces the computational cost and achieves comparable accuracy with the traditional methods. Moreover, by domain decomposition, we can decouple the Stokes-Darcy system into two smaller sub-physics problems naturally. Both mesh-dependent and mesh-independent convergence rates of the algorithm are rigorously derived by choosing suitable Robin parameters. Optimized Robin parameters are derived and analyzed to accelerate the convergence of the proposed algorithm. Especially, for small hydraulic conductivity in practice, the almost optimal geometric convergence can be obtained by finite element discretization. Finally, two groups of numerical experiments are conducted to validate and illustrate the exclusive features of the proposed algorithm.
While deep neural networks have facilitated significant advancements in the field of speech enhancement, most existing methods are developed following either empirical or relatively blind criteria, lacking adequate guidelines in pipeline design. Inspired by Taylor's theorem, we propose a general unfolding framework for both single- and multi-channel speech enhancement tasks. Concretely, we formulate the complex spectrum recovery into the spectral magnitude mapping in the neighborhood space of the noisy mixture, in which an unknown sparse term is introduced and applied for phase modification in advance. Based on that, the mapping function is decomposed into the superimposition of the 0th-order and high-order polynomials in Taylor's series, where the former coarsely removes the interference in the magnitude domain and the latter progressively complements the remaining spectral detail in the complex spectrum domain. In addition, we study the relation between adjacent order terms and reveal that each high-order term can be recursively estimated with its lower-order term, and each high-order term is then proposed to evaluate using a surrogate function with trainable weights so that the whole system can be trained in an end-to-end manner. Given that the proposed framework is devised based on Taylor's theorem, it possesses improved internal flexibility. Extensive experiments are conducted on WSJ0-SI84, DNS-Challenge, Voicebank+Demand, spatialized Librispeech, and L3DAS22 multi-channel speech enhancement challenge datasets. Quantitative results show that the proposed approach yields competitive performance over existing top-performing approaches in terms of multiple objective metrics.
Time-Sensitive Networking (TSN) is an enhancement of Ethernet which provides various mechanisms for real-time communication. Time-triggered (TT) traffic represents periodic data streams with strict real-time requirements. Amongst others, TSN supports scheduled transmission of TT streams, i.e., the transmission of their frames by end stations is coordinated in such a way that none or very little queuing delay occurs in intermediate nodes. TSN supports multiple priority queues per egress port. The TAS uses so-called gates to explicitly allow and block these queues for transmission on a short periodic timescale. The TAS is utilized to protect scheduled traffic from other traffic to minimize its queuing delay. In this work, we consider scheduling in TSN which comprises the computation of periodic transmission instants at end stations and the periodic opening and closing of queue gates. In this paper, we first give a brief overview of TSN features and standards. We state the TSN scheduling problem and explain common extensions which also include optimization problems. We review scheduling and optimization methods that have been used in this context. Then, the contribution of currently available research work is surveyed. We extract and compile optimization objectives, solved problem instances, and evaluation results. Research domains are identified, and specific contributions are analyzed. Finally, we discuss potential research directions and open problems.
The aim of this paper is twofold. First, we prove $L^p$ estimates for a regularized Green's function in three dimensions. We then establish new estimates for the discrete Green's function and obtain some positivity results. In particular, we prove that the discrete Green's functions with singularity in the interior of the domain cannot be bounded uniformly with respect of the mesh parameter $h$. Actually, we show that at the singularity the discrete Green's function is of order $h^{-1}$, which is consistent with the behavior of the continuous Green's function. In addition, we also show that the discrete Green's function is positive and decays exponentially away from the singularity. We also provide numerically persistent negative values of the discrete Green's function on Delaunay meshes which then implies a discrete Harnack inequality cannot be established for unstructured finite element discretizations.
This paper proposes novel inferential procedures for the network Granger causality in high-dimensional vector autoregressive models. In particular, we offer two multiple testing procedures designed to control discovered networks' false discovery rate (FDR). The first procedure is based on the limiting normal distribution of the $t$-statistics constructed by the debiased lasso estimator. The second procedure is based on the bootstrap distributions of the $t$-statistics made by imposing the null hypotheses. Their theoretical properties, including FDR control and power guarantee, are investigated. The finite sample evidence suggests that both procedures can successfully control the FDR while maintaining high power. Finally, the proposed methods are applied to discovering the network Granger causality in a large number of macroeconomic variables and regional house prices in the UK.
A recent line of works, initiated by Russo and Xu, has shown that the generalization error of a learning algorithm can be upper bounded by information measures. In most of the relevant works, the convergence rate of the expected generalization error is in the form of $O(\sqrt{\lambda/n})$ where $\lambda$ is some information-theoretic quantities such as the mutual information or conditional mutual information between the data and the learned hypothesis. However, such a learning rate is typically considered to be ``slow", compared to a ``fast rate" of $O(\lambda/n)$ in many learning scenarios. In this work, we first show that the square root does not necessarily imply a slow rate, and a fast rate result can still be obtained using this bound under appropriate assumptions. Furthermore, we identify the critical conditions needed for the fast rate generalization error, which we call the $(\eta,c)$-central condition. Under this condition, we give information-theoretic bounds on the generalization error and excess risk, with a fast convergence rate for specific learning algorithms such as empirical risk minimization and its regularized version. Finally, several analytical examples are given to show the effectiveness of the bounds.
Existing analysis of AdaGrad and other adaptive methods for smooth convex optimization is typically for functions with bounded domain diameter. In unconstrained problems, previous works guarantee an asymptotic convergence rate without an explicit constant factor that holds true for the entire function class. Furthermore, in the stochastic setting, only a modified version of AdaGrad, different from the one commonly used in practice, in which the latest gradient is not used to update the stepsize, has been analyzed. Our paper aims at bridging these gaps and developing a deeper understanding of AdaGrad and its variants in the standard setting of smooth convex functions as well as the more general setting of quasar convex functions. First, we demonstrate new techniques to explicitly bound the convergence rate of the vanilla AdaGrad for unconstrained problems in both deterministic and stochastic settings. Second, we propose a variant of AdaGrad for which we can show the convergence of the last iterate, instead of the average iterate. Finally, we give new accelerated adaptive algorithms and their convergence guarantee in the deterministic setting with explicit dependency on the problem parameters, improving upon the asymptotic rate shown in previous works.
Synthetic control is a causal inference tool used to estimate the treatment effects of an intervention by creating synthetic counterfactual data. This approach combines measurements from other similar observations (i.e., donor pool ) to predict a counterfactual time series of interest (i.e., target unit) by analyzing the relationship between the target and the donor pool before the intervention. As synthetic control tools are increasingly applied to sensitive or proprietary data, formal privacy protections are often required. In this work, we provide the first algorithms for differentially private synthetic control with explicit error bounds. Our approach builds upon tools from non-private synthetic control and differentially private empirical risk minimization. We provide upper and lower bounds on the sensitivity of the synthetic control query and provide explicit error bounds on the accuracy of our private synthetic control algorithms. We show that our algorithms produce accurate predictions for the target unit, and that the cost of privacy is small. Finally, we empirically evaluate the performance of our algorithm, and show favorable performance in a variety of parameter regimes, as well as providing guidance to practitioners for hyperparameter tuning.
When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.
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