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Hybrid dynamical systems are ubiquitous as practical robotic applications often involve both continuous states and discrete switchings. Safety is a primary concern for hybrid robotic systems. Existing safety-critical control approaches for hybrid systems are either computationally inefficient, detrimental to system performance, or limited to small-scale systems. To amend these drawbacks, in this paper, we propose a learningenabled approach to construct local Control Barrier Functions (CBFs) to guarantee the safety of a wide class of nonlinear hybrid dynamical systems. The end result is a safe neural CBFbased switching controller. Our approach is computationally efficient, minimally invasive to any reference controller, and applicable to large-scale systems. We empirically evaluate our framework and demonstrate its efficacy and flexibility through two robotic examples including a high-dimensional autonomous racing case, against other CBF-based approaches and model predictive control.

We use Markov categories to develop generalizations of the theory of Markov chains and hidden Markov models in an abstract setting. This comprises characterizations of hidden Markov models in terms of local and global conditional independences as well as existing algorithms for Bayesian filtering and smoothing applicable in all Markov categories with conditionals. We show that these algorithms specialize to existing ones such as the Kalman filter, forward-backward algorithm, and the Rauch-Tung-Striebel smoother when instantiated in appropriate Markov categories. Under slightly stronger assumptions, we also prove that the sequence of outputs of the Bayes filter is itself a Markov chain with a concrete formula for its transition maps. There are two main features of this categorical framework. The first is its generality, as it can be used in any Markov category with conditionals. In particular, it provides a systematic unified account of hidden Markov models and algorithms for filtering and smoothing in discrete probability, Gaussian probability, measure-theoretic probability, possibilistic nondeterminism and others at the same time. The second feature is the intuitive visual representation of information flow in these algorithms in terms of string diagrams.

Biometric authentication prospered because of its convenient use and security. Early generations of biometric mechanisms suffer from spoofing attacks. Recently, unobservable physiological signals (e.g., Electroencephalogram, Photoplethysmogram, Electrocardiogram) as biometrics offer a potential remedy to this problem. In particular, Photoplethysmogram (PPG) measures the change in blood flow of the human body by an optical method. Clinically, researchers commonly use PPG signals to obtain patients' blood oxygen saturation, heart rate, and other information to assist in diagnosing heart-related diseases. Since PPG signals contain a wealth of individual cardiac information, researchers have begun to explore their potential in cyber security applications. The unique advantages (simple acquisition, difficult to steal, and live detection) of the PPG signal allow it to improve the security and usability of the authentication in various aspects. However, the research on PPG-based authentication is still in its infancy. The lack of systematization hinders new research in this field. We conduct a comprehensive study of PPG-based authentication and discuss these applications' limitations before pointing out future research directions.

Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to MLE become significantly limited when dealing with grouped loss severity data, with only a handful of methods like least squares, minimum Hellinger distance, and optimal bounded influence function available. This paper introduces a novel robust estimation technique, the Method of Truncated Moments (MTuM), specifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of MTuM is established by employing the central limit theorem and validating them through a comprehensive simulation study.

We present an experimental validation of a recently proposed optimization technique for reservoir computing, using an optoelectronic setup. Reservoir computing is a robust framework for signal processing applications, and the development of efficient optimization approaches remains a key challenge. The technique we address leverages solely a delayed version of the input signal to identify the optimal operational region of the reservoir, simplifying the traditionally time-consuming task of hyperparameter tuning. We verify the effectiveness of this approach on different benchmark tasks and reservoir operating conditions.

Researchers commonly use difference-in-differences (DiD) designs to evaluate public policy interventions. While established methodologies exist for estimating effects in the context of binary interventions, policies often result in varied exposures across regions implementing the policy. Yet, existing approaches for incorporating continuous exposures face substantial limitations in addressing confounding variables associated with intervention status, exposure levels, and outcome trends. These limitations significantly constrain policymakers' ability to fully comprehend policy impacts and design future interventions. In this study, we propose innovative estimators for causal effect curves within the DiD framework, accounting for multiple sources of confounding. Our approach accommodates misspecification of a subset of treatment, exposure, and outcome models while avoiding any parametric assumptions on the effect curve. We present the statistical properties of the proposed methods and illustrate their application through simulations and a study investigating the diverse effects of a nutritional excise tax.

Recognizing visual entities in a natural language sentence and arranging them in a 2D spatial layout require a compositional understanding of language and space. This task of layout prediction is valuable in text-to-image synthesis as it allows localized and controlled in-painting of the image. In this comparative study it is shown that we can predict layouts from language representations that implicitly or explicitly encode sentence syntax, if the sentences mention similar entity-relationships to the ones seen during training. To test compositional understanding, we collect a test set of grammatically correct sentences and layouts describing compositions of entities and relations that unlikely have been seen during training. Performance on this test set substantially drops, showing that current models rely on correlations in the training data and have difficulties in understanding the structure of the input sentences. We propose a novel structural loss function that better enforces the syntactic structure of the input sentence and show large performance gains in the task of 2D spatial layout prediction conditioned on text. The loss has the potential to be used in other generation tasks where a tree-like structure underlies the conditioning modality. Code, trained models and the USCOCO evaluation set will be made available via github.

This paper presents a novel operational matrix method to accelerate the training of fractional Physics-Informed Neural Networks (fPINNs). Our approach involves a non-uniform discretization of the fractional Caputo operator, facilitating swift computation of fractional derivatives within Caputo-type fractional differential problems with $0<\alpha<1$. In this methodology, the operational matrix is precomputed, and during the training phase, automatic differentiation is replaced with a matrix-vector product. While our methodology is compatible with any network, we particularly highlight its successful implementation in PINNs, emphasizing the enhanced accuracy achieved when utilizing the Legendre Neural Block (LNB) architecture. LNB incorporates Legendre polynomials into the PINN structure, providing a significant boost in accuracy. The effectiveness of our proposed method is validated across diverse differential equations, including Delay Differential Equations (DDEs) and Systems of Differential Algebraic Equations (DAEs). To demonstrate its versatility, we extend the application of the method to systems of differential equations, specifically addressing nonlinear Pantograph fractional-order DDEs/DAEs. The results are supported by a comprehensive analysis of numerical outcomes.

A new method of detecting adversarial attacks is proposed for an ensemble of Deep Neural Networks (DNNs) solving two-class pattern recognition problems. The ensemble is combined using Walsh coefficients which are capable of approximating Boolean functions and thereby controlling the complexity of the ensemble decision boundary. The hypothesis in this paper is that decision boundaries with high curvature allow adversarial perturbations to be found, but change the curvature of the decision boundary, which is then approximated in a different way by Walsh coefficients compared to the clean images. By observing the difference in Walsh coefficient approximation between clean and adversarial images, it is shown experimentally that transferability of attack may be used for detection. Furthermore, approximating the decision boundary may aid in understanding the learning and transferability properties of DNNs. While the experiments here use images, the proposed approach of modelling two-class ensemble decision boundaries could in principle be applied to any application area. Code for approximating Boolean functions using Walsh coefficients: //doi.org/10.24433/CO.3695905.v1

We propose a novel approach to multimodal sentiment analysis using deep neural networks combining visual analysis and natural language processing. Our goal is different than the standard sentiment analysis goal of predicting whether a sentence expresses positive or negative sentiment; instead, we aim to infer the latent emotional state of the user. Thus, we focus on predicting the emotion word tags attached by users to their Tumblr posts, treating these as "self-reported emotions." We demonstrate that our multimodal model combining both text and image features outperforms separate models based solely on either images or text. Our model's results are interpretable, automatically yielding sensible word lists associated with emotions. We explore the structure of emotions implied by our model and compare it to what has been posited in the psychology literature, and validate our model on a set of images that have been used in psychology studies. Finally, our work also provides a useful tool for the growing academic study of images - both photographs and memes - on social networks.