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1. Dynamic Modeling, Analysis, and Design Synthesis of a Reduced Complexity Quadruped with a Serpentine Robotic Tail

   https://doi.org/10.1093/icb/icab083  

   Liu, Yujiong; Ben-Tzvi, Pinhas (May 2021, Integrative and Comparative Biology)

   Synopsis Serpentine tail structures are widely observed in the animal kingdom and are thought to help animals to handle various motion tasks. Developing serpentine robotic tails and using them on legged robots has been an attractive idea for robotics. This article presents the theoretical analysis for such a robotic system that consists of a reduced complexity quadruped and a serpentine robotic tail. Dynamic model and motion controller are formulated first. Simulations are then conducted to analyze the tail’s performance on the airborne righting and maneuvering tasks of the quadruped. Using the established simulation environment, systematic analyses on critical design parameters, namely, the tail mounting point, tail length, torso center of mass (COM) location, tail–torso mass ratio, and the power consumption distribution, are performed. The results show that the tail length and the mass ratio influence the maneuvering angle the most while the COM location affects the landing stability the most. Based on these design guidelines, for the current robot design, the optimal tail parameters are determined as a length of two times as long as the torso length and a weight of 0.09 times as heavy as the torso weight. 

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2. Heavy-Tailed Density Estimation

   https://doi.org/10.1080/01621459.2022.2104727  

   Tokdar, Surya T.; Jiang, Sheng; Cunningham, Erika L. (September 2022, Journal of the American Statistical Association)

   A novel statistical method is proposed and investigated for estimating a heavy tailed density under mildsmoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem ofsparse information in the tail of the distribution getting washed away by unrelated features of a hefty bulk.The proposed Bayesian method avoids this problem by incorporating smoothness and tail regularizationthrough a carefully specified semiparametric prior distribution, and is able to consistently estimate boththe density function and its tail index at near minimax optimal rates of contraction. A joint, likelihood drivenestimation of the bulk and the tail is shown to help improve uncertainty assessment in estimating the tailindex parameter and offer more accurate and reliable estimates of the high tail quantiles compared tothresholding methods. Supplementary materials for this article are available online. 

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3. COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependence

   https://doi.org/10.24963/ijcai.2022/462  

   McDonald, Andrew; Tan, Pang-Ning; Luo, Lifeng (July 2022, Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence)

   Normalizing flows—a popular class of deep generative models—often fail to represent extreme phenomena observed in real-world processes. In particular, existing normalizing flow architectures struggle to model multivariate extremes, characterized by heavy-tailed marginal distributions and asymmetric tail dependence among variables. In light of this shortcoming, we propose COMET (COpula Multivariate ExTreme) Flows, which decompose the process of modeling a joint distribution into two parts: (i) modeling its marginal distributions, and (ii) modeling its copula distribution. COMET Flows capture heavy-tailed marginal distributions by combining a parametric tail belief at extreme quantiles of the marginals with an empirical kernel density function at mid-quantiles. In addition, COMET Flows capture asymmetric tail dependence among multivariate extremes by viewing such dependence as inducing a low-dimensional manifold structure in feature space. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of COMET flows in capturing both heavy-tailed marginals and asymmetric tail dependence compared to other state-of-the-art baseline architectures. All code is available at https://github.com/andrewmcdonald27/COMETFlows. 

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4. Tail-Limited Phase-Type Burstiness Bounds for Network Traffic

   https://doi.org/10.1109/CISS.2019.8692817  

   Boroujeny, Massieh Kordi; Mark, Brian L.; Ephraim, Yariv (March 2019, 2019 53rd Annual Conference on Information Sciences and Systems (CISS))

   The bursty nature of network traffic makes it difficult to characterize accurately, and may give rise to heavy-tailed queue distributions within the network. Building on prior work in stochastic network calculus, we propose traffic burstiness bounds based on the class of phase-type distributions and develop an approach to estimate the parameter of such bounds using the expectation-maximization (EM) algorithm. By limiting the tail of the burstiness bound, our approach achieves a better fit of the phase-type distribution to the empirical data from heavy-tailed traffic. The proposed tail-limited phase-type burstiness bounds fall within the framework for stochastic network calculus based on generalized stochastically bounded burstiness. We demonstrate the effectiveness of the proposed methodology with a numerical example involving a heavy-tailed M/G/1 queue. 

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5. Spatial patterns of extreme precipitation and their changes under ~ 2 °C global warming: a large-ensemble study of the western USA

   https://doi.org/10.1007/s00382-022-06214-3  

   Rupp, David E; Hawkins, Linnia R; Li, Sihan; Koszuta, Matthew; Siler, Nicholas (October 2022, Climate Dynamics)

   Extreme precipitation events are expected to increase in magnitude in response to global warming, but the magnitude of the forced response may vary considerably across distances of ~ 100 km or less. To examine the spatial variability of extreme precipitation and its sensitivity to global warming with high statistical certainty, we use a large (16,980 years), initial-condition ensemble of dynamically downscaled global climate model simulations. Under approximately 2 °C of global warming above a recent baseline period, we find large variability in the change (0 to > 60%) of the magnitude of very rare events (from 10 to 1000-year return period values of annual maxima of daily precipitation) across the western United States. Western (and predominantly windward) slopes of coastal ranges, the Cascades, and the Sierra Nevada typically show smaller increases in extreme precipitation than eastern slopes and bordering valleys and plateaus, but this pattern is less evident in the continental interior. Using the generalized extreme value shape parameter to characterize the tail of the precipitation distribution (light to heavy tail), we find that heavy tails dominate across the study region, but light tails are common on the western slopes of mountain ranges. The majority of the region shows a tendency toward heavier tails under warming, though some regions, such as plateaus of eastern Oregon and Washington, and the crest of the Sierra Nevada, show a lightening of tails. Spatially, changes in long return-period precipitation amounts appear to partially result from changes in the shape of the tail of the distribution. 

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