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1. Traffic Rate Network Tomography via Moment Generating Function Matching

   Ephraim, Yariv; Coblenz, Joshua; Mark, Brian L.; Lev-Ari, Hanoch (March 2022, Conference on Information Sciences and Systems)

   Network tomography aims at estimating source-destination traffic rates from link traffic measurements. This inverse problem was formulated by Vardi in 1996 for independent Poisson traffic over networks operating under deterministic as well as random routing regimes. Vardi used a second-order moment matching approach to estimate the rates where a solution for the resulting linear matrix equation was obtained using an iterative minimum I-divergence procedure. Vardi’s second-order moment matching approach was recently extended to higher order cumulant matching approach with the goal of improving the rank of the system of linear equations. In this paper we go one step further and develop a moment generating function matching approach for rate estimation, and seek a least squares as well as an iterative minimum I-divergence solution of the resulting linear equations. We also specialize this approach to a characteristic function matching approach which exhibits some advantages. These follow from the fact that the characteristic function matching approach results in fewer conflicting equations involving the empirical estimates. We demonstrate that the new approach outperforms the cumulant matching approach while being conceptually simpler. 

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2. Subset selection for improved parameter estimation in on-line identification of a synchronous generator

   https://doi.org/10.1109/59.744536  

   Burth, M.; Verghese, G.C.; Velez-Reyes, M. (June 1999, IEEE Transactions on Power Systems)

   This paper examines subset selection for nonlinear least squares parameter estimation, and applies the methodology to a test system previously studied in the power system literature, involving the on-line identification of a synchronous generator model with many parameters. Subset selection partitions the parameters into well-conditioned and ill-conditioned subsets. We show for the test system that fixing the ill-conditioned parameters to prior estimates (even if these prior estimates are substantially in error), and estimating only the remaining parameters, significantly improves the performance of the estimation algorithm and greatly enhances the quality of the estimated parameters. It is shown that attempts to estimate all of the model parameters, as done in the original work with this test system, can yield extremely unreliable results. 

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3. A Kaczmarz Algorithm for Solving Tree Based Distributed Systems of Equations

   https://doi.org/10.1007/978-3-030-69637-5_20  

   Hegde, Chinmay; Keinert, Fritz; Weber, Eric S. (February 2021, Applied and numerical harmonic analysis)

   The Kaczmarz algorithm is an iterative method for solving systems of linear equations. We introduce a modified Kaczmarz algorithm for solving systems of linear equations in a distributed environment, i.e., the equations within the system are distributed over multiple nodes within a network. The modification we introduce is designed for a network with a tree structure that allows for passage of solution estimates between the nodes in the network. We prove that the modified algorithm converges under no additional assumptions on the equations. We demonstrate that the algorithm converges to the solution, or the solution of minimal norm, when the system is consistent. We also demonstrate that in the case of an inconsistent system of equations, the modified relaxed Kaczmarz algorithm converges to a weighted least squares solution as the relaxation parameter approaches 0. 

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4. Mantle Wavespeed and Discontinuity Structure Below East Africa: Implications for Cenozoic Hotspot Tectonism and the Development of the Turkana Depression

   https://doi.org/10.1029/2022GC010775  

   Boyce, A.; Kounoudis, R.; Bastow, I. D.; Cottaar, S.; Ebinger, C. J.; Ogden, C. S. (August 2023, Geochemistry, Geophysics, Geosystems)

   Abstract Ethiopia's Cenozoic flood basalt magmatism, uplift, and rifting have been attributed to one or more mantle plumes. The Nubian plate, however, has drifted 500–1,000 km north since initial magmatism at ∼45 Ma, having developed above mantle that now underlies the northern Tanzania craton and the low‐lying Turkana Depression. Unfortunately, our knowledge of mantle wavespeed structure and mantle transition zone (MTZ) topography below these regions is poorest, due to a historical lack of seismograph stations. The same data gap means we lack constraints on lithospheric structure in and around the NW–SE trending Mesozoic Anza rift. We exploit data from new seismograph networks in the Turkana Depression and neighboring northern Uganda to develop AFRP22, a new African absolute P‐wavespeed tomographic model that resolves whole mantle structure along the entire East African rift system. We also map MTZ thickness using Ps receiver functions. East Africa's thinnest MTZ (∼25 km thinning) underlies the northwest Turkana Depression. AFRP22 reveals a co‐located, previously unrecognized, slow wavespeed plume tail, extending from the MTZ, deep into the lower mantle. This plume may thus have contributed, along with the African Superplume, to the development of the 45–30 Ma flood basalt province that preceded extension. Pervasive sub‐lithospheric slow wavespeeds imply that Turkana's present‐day low elevation is explained best by Mesozoic and Cenozoic‐age crustal thinning. At ∼100 km depth, AFRP22 illuminates a fast wavespeed SE Ethiopian plateau. In addition to governing the northernmost limit of Mesozoic Anza rifting, the refractory nature of this lithospheric block likely minimized Cenozoic flood basalt magmatism there. 

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5. Graph Convolutional Networks for Power System State Estimation

   Q. Yang, A. Sadeghi (January 2020, Proceedings of IEEE Smartgridcom Conference)

   null (Ed.)

   Power system state estimation (PSSE) aims at finding the voltage magnitudes and angles at all generation and load buses, using meter readings and other available information. PSSE is often formulated as a nonconvex and nonlinear least-squares (NLS) cost function, which is traditionally solved by the Gauss-Newton method. However, Gauss-Newton iterations for minimizing nonconvex problems are sensitive to the initialization, and they can diverge. In this context, we advocate a deep neural network (DNN) based “trainable regularizer” to incorporate prior information for accurate and reliable state estimation. The resulting regularized NLS does not admit a neat closed form solution. To handle this, a novel end-to-end DNN is constructed subsequently by unrolling a Gauss-Newton-type solver which alternates between least-squares loss and the regularization term. Our DNN architecture can further offer a suite of advantages, e.g., accommodating network topology via graph neural networks based prior. Numerical tests using real load data on the IEEE 118-bus benchmark system showcase the improved estimation performance of the proposed scheme compared with state-of-the-art alternatives. Interestingly, our results suggest that a simple feed forward network based prior implicitly exploits the topology information hidden in data. 

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