In our daily lives, we rely heavily on our visual and auditory channels to receive information from others. In the case of impairment, or when large amounts of information are already transmitted visually or aurally, alternative methods of communication are needed. A haptic language offers the potential to provide information to a user when visual and auditory channels are unavailable. Previously created haptic languages include deconstructing acoustic signals into features and displaying them through a haptic device, and haptic adaptations of Braille or Morse code; however, these approaches are unintuitive, slow at presenting language, or require a large surface area. We propose using a multi-sensory haptic device called MISSIVE, which can be worn on the upper arm and is capable of producing brief cues, sufficient in quantity to encode the full English phoneme set. We evaluated our approach by teaching subjects a subset of 23 phonemes, and demonstrated an 86% accuracy in a 50 word identification task after 100 minutes of training.

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Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a least squares space-time control volume scheme, we circumvent issues particularly related to imposition of boundary conditions and conservation while reducing solution regularity requirements. Additionally, connections to classical finite volume methods allows application of biases toward entropy solutions and total variation diminishing properties. For inverse problems, we may impose further thermodynamic biases, allowing us to fit shock hydrodynamics models to molecular simulation of rarefied gases and metals. The resulting data-driven equations of state may be incorporated into traditional shock hydrodynamics codes.

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Deep operator learning has emerged as a promising tool for reduced-order modelling and PDE model discovery. Leveraging the expressive power of deep neural networks, especially in high dimensions, such methods learn the mapping between functional state variables. While proposed methods have assumed noise only in the dependent variables, experimental and numerical data for operator learning typically exhibit noise in the independent variables as well, since both variables represent signals that are subject to measurement error. In regression on scalar data, failure to account for noisy independent variables can lead to biased parameter estimates. With noisy independent variables, linear models fitted via ordinary least squares (OLS) will show attenuation bias, wherein the slope will be underestimated. In this work, we derive an analogue of attenuation bias for linear operator regression with white noise in both the independent and dependent variables, showing that the norm upper bound of the operator learned via OLS decreases with increasing noise in the independent variable. In the nonlinear setting, we computationally demonstrate underprediction of the action of the Burgers operator in the presence of noise in the independent variable. We propose errorin-variables (EiV) models for two operator regression methods, MOR-Physics and DeepONet, and demonstrate that these new models reduce bias in the presence of noisy independent variables for a variety of operator learning problems. Considering the Burgers operator in 1D and 2D, we demonstrate that EiV operator learning robustly recovers operators in high-noise regimes that defeat OLS operator learning. We also introduce an EiV model for time-evolving PDE discovery and show that OLS and EiV perform similarly in learning the Kuramoto-Sivashinsky evolution operator from corrupted data, suggesting that the effect of bias in OLS operator learning depends on the regularity of the target operator.

The 2016 United States presidential election has been characterized as a period of extreme divisiveness that was exacerbated on social media by the influence of fake news, trolls, and social bots. However, the extent to which the public became more polarized in response to these influences over the course of the election is not well understood. In this paper we propose IdeoTrace, a framework for (i) jointly estimating the ideology of social media users and news websites and (ii) tracing changes in user ideology over time. We apply this framework to the last two months of the election period for a group of 47508 Twitter users and demonstrate that both liberal and conservative users became more polarized over time.

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