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1. Sample Complexity Bound for Evaluating the Robust Observer’s Performance under Coprime Factors Uncertainty

   Sabau, Serban; Zhang, Yifei; Ukil, Sourav Kumar (June 2023, Proceedings of Machine Learning Research)

   Lawrence, N (Ed.)

   This paper addresses the end-to-end sample complexity bound for learning in closed loop the state estimator-based robust H2 controller for an unknown (possibly unstable) Linear Time Invariant (LTI) system, when given a fixed state-feedback gain. We build on the results from Ding et al. (1994) to bridge the gap between the parameterization of all state-estimators and the celebrated Youla parameterization. Refitting the expression of the relevant closed loop allows for the optimal linear observer problem given a fixed state feedback gain to be recast as a convex problem in the Youla parameter. The robust synthesis procedure is performed by considering bounded additive model uncertainty on the coprime factors of the plant, such that a min-max optimization problem is formulated for the robust H2 controller via an observer approach. The closed-loop identification scheme follows Zhang et al. (2021), where the nominal model of the true plant is identified by constructing a Hankel-like matrix from a single time-series of noisy, finite length input-output data by using the ordinary least squares algorithm from Sarkar et al. (2020). Finally, a H∞ bound on the estimated model error is provided, as the robust synthesis procedure requires bounded additive uncertainty on the coprime factors of the model. Reference Zhang et al. (2022b) is the extended version of this paper. 

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2. Ring graphs and Goldberg's bound on chromatic index

   https://doi.org/10.1002/jgt.22494  

   Cao, Yan; Chen, Guantao; He, Shushan; Jing, Guangming (August 2019, Journal of Graph Theory)

   Abstract Let be a multigraph with maximum degree and chromatic index . If is bipartite then . Otherwise, by a theorem of Goldberg, , where denotes the odd girth of . Stiebitz, Scheide, Toft, and Favrholdt in their book conjectured that if then contains as a subgraph a ring graph with the same chromatic index. Vizing's characterization of graphs with chromatic index attaining the Shannon's bound showed the above conjecture holds for . Stiebitz et al verified the conjecture for graphs with and . McDonald proved the conjecture when is divisible by . In this paper, we show that the chromatic index condition alone is not sufficient to give the conclusion in the conjecture. On the positive side, we show that the conjecture holds for every with , and the maximum degree condition is best possible. This positive result leans on the positive resolution of the Goldberg‐Seymour conjecture. 

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3. Intertidal foraging by gentoo penguins in a macroalgal raft

   https://doi.org/10.1017/S095410201900052X  

   McClintock, James B.; Amsler, Charles D.; Amsler, Margaret O.; Fraser, William R. (February 2020, Antarctic Science)

   Foraging strategies in gentoo penguins ( Pygoscelis papua ) have been well studied (e.g. Croxall et al. 1988, Robinson & Hindell 1996, Lescroël et al. 2004, Takahashi et al. 2008, Xavier et al. 2017). The general consensus is this largest member of the three pygoscelid penguins displays both nearshore benthic and pelagic foraging tactics to consume combinations of crustaceans and fish. In a recent study, Carpenter-Kling et al. (2017) reported that gentoos at sub-Antarctic Marion Island displayed a novel foraging strategy that consisted of alternating typical lengthy foraging trips with much shorter nearshore afternoon trips. They suggest the latter foraging behaviour may be a response to suboptimal feeding conditions caused by local environmental change. This novel discovery reinforces the fact that, despite considerable study, not all foraging tactics in penguins have been documented. In this paper, we describe what we believe to be, yet another undocumented foraging tactic employed by gentoos. 

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4. A Study of Privacy Preservation in Average Consensus Algorithm via Deterministic Obfuscation Signals

   https://doi.org/10.1109/TCNS.2023.3290114  

   Rezazadeh, Navid; Kia, Solmaz S. (March 2024, IEEE Transactions on Control of Network Systems)

   This article is a study on the use of additive obfuscation signals to keep the reference values of the agents in the continuous-time Laplacian average consensus algorithm private from eavesdroppers. Obfuscation signals are perturbations that agents add to their local dynamics and their transmitted-out messages to conceal their private reference values. An eavesdropper is an agent inside or outside the network that has access to some subset of the interagent communication messages, and its knowledge set also includes the network topology. Rather than focusing on using a zero-sum and vanishing additive signal, our work determines the necessary and sufficient conditions that define the set of admissible obfuscation signals that do not perturb the convergence point of the algorithm from the average of the reference values of the agents. Of theoretical interest, our results show that this class includes nonvanishing signals as well. Given this broader class of admissible obfuscation signals, we define a deterministic notion of privacy preservation. In this definition, privacy preservation for an agent means that neither the private reference value nor a finite set of values to which the private reference value of the agent belongs to can be obtained. Then, we evaluate the agents’ privacy against eavesdroppers with different knowledge sets. 

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5. Impacts of Limited Model Resolution on the Representation of Mountain Wave and Secondary Gravity Wave Dynamics in Local and Global Models. 1: Mountain Waves in the Stratosphere and Mesosphere

   https://doi.org/10.1029/2021JD035990  

   Fritts, David C.; Lund, Adam C.; Lund, Thomas S.; Yudin, Valery (May 2022, Journal of Geophysical Research: Atmospheres)

   Abstract Long‐term efforts have sought to extend global model resolution to smaller scales enabling more accurate descriptions of gravity wave (GW) sources and responses, given their major roles in coupling and variability throughout the atmosphere. Such studies reveal significant improvements accompanying increasing resolution, but no guidance on what is sufficient to approximate reality. We take the opposite approach, using a finite‐volume model solving the Navier‐Stokes equations exactly. The reference simulation addresses mountain wave (MW) generation and responses over the Southern Andes described using isotropic 500 m, central resolution by Fritts et al. (2021),https://doi.org/10.1175/JAS-D-20-0207.1and Lund et al. (2020),https://doi.org/10.1175/JAS-D-19-0356.1. Reductions of horizontal resolution to 1 and 2 km result in (a) systematic increases in initial MW breaking altitudes, (b) weaker, larger‐scale generation of secondary GWs and acoustic waves accompanying these dynamics, and (c) significantly weaker and less extended responses in the mesosphere in latitude and longitude. Horizontal resolution of 4 km largely suppresses instabilities, but allows weak, sustained mean‐flow interactions. Responses for 8 km resolution are very weak and fail to capture any aspects of the high‐resolution responses. The chosen mean winds allow efficient MW penetration into the mesosphere and lower thermosphere, hence only exhibit strong pseudo‐momentum deposition and mean wind decelerations at higher altitudes. A companion paper by Fritts et al. (2022),https://doi.org/10.1029/2021JD036035explores the impacts of decreasing resolution on responses in the thermosphere. 

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