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In this paper, tools to study forward invariance properties with robustness to disturbances, referred to as robust forward invariance, are proposed for hybrid dynamical systems modeled as hybrid inclusions. Hybrid inclusions are given in terms of differential and difference inclusions with state and disturbance constraints, for whose definition only four objects are required. The proposed robust forward invariance notions allow for the diverse type of solutions to such systems (with and without disturbances), including solutions that have persistent flows and jumps, that are Zeno, and that stop to exist after finite amount of (hybrid) time. Sufficient conditions for sets to enjoy such properties are presented. These conditions are given in terms of the objects defining the hybrid inclusions and the set to be rendered robust forward invariant. In addition, as special cases, these conditions are exploited to state results on nominal forward invariance for hybrid systems without disturbances. Furthermore, results that provide conditions to render the sublevel sets of Lyapunov-like functions forward invariant are established. Analysis of a controlled inverter system is presented as an application of our results. Academic examples are given throughout this paper to illustrate the main ideas.

Purpose: This study introduces a framework to produce very short versions of the MacArthur-Bates Communicative Development Inventories (CDIs) by combining the Bayesian-inspired approach introduced by Mayor and Mani (2019) with an item response theory-based computerized adaptive testing that adapts to the ability of each child, in line with Makransky et al. (2016). Method: We evaluated the performance of our approach--dynamically selecting maximally informative words from the CDI and combining parental response with prior vocabulary data--by conducting real-data simulations using four CDI versions having varying sample sizes on Wordbank--the online repository of digitalized CDIs: American English (a very large data set), Danish (a large data set), Beijing Mandarin (a medium-sized data set), and Italian (a small data set). Results: Real-data simulations revealed that correlations exceeding 0.95 with full CDI administrations were reached with as few as 15 test items, with high levels of reliability, even when languages (e.g., Italian) possessed few digitalized administrations on Wordbank. Conclusions: The current approach establishes a generic framework that produces very short (less than 20 items) adaptive early vocabulary assessments--hence considerably reducing their administration time. This approach appears to be robust even when CDIs have smaller samples in online repositories, for example, with around 50 samples per month-age.

This paper proposes a general framework for analyzing continuous-Time systems controlled by event-Triggered algorithms. Closed-loop systems resulting from using both static and dynamic output (or state) feedback laws that are implemented via asynchronous event-Triggered techniques are modeled as hybrid systems given in terms of hybrid inclusions and studied using recently developed tools for robust stability. Properties of the proposed models, including stability of compact sets, robustness, and Zeno behavior of solutions are addressed. The framework and results are illustrated in several event-Triggered strategies available in the literature.

Forward invariance with robustness to disturbances for hybrid dynamical systems modeled by hybrid inclusions with state-dependent conditions enabling flows and jumps is studied. In particular, we study forward invariance notions that apply to systems with hybrid inputs and disturbances with nonlinear dynamics, for which not every solution is unique or may exist for arbitrary long hybrid time. Given state-feedback laws, notions of robust forward invariance of sets for closed-loop system are introduced. Sufficient conditions in terms of the objects defining the system are presented. One result using Lyapunov-based conditions removes the usual Lipschitz constraint on continuous dynamics. A bouncing ball example is given to illustrate major results.

Early vocabularies in most languages tend to contain more nouns than verbs. Yet, the strength of this noun bias hasbeen observed to vary across languages and cultures. Two main hypotheses have aimed at explaining such variations; eitherthat the relative importance of nouns vs. verbs is language- specific, or that socio-cultural influences shape early vocabularystructures. The present study compares the relative distribution of verbs and nouns, in English, between two groups of bilingualinfants and toddlers; Malay-English and Mandarin- English. We found that early English lexicons of Mandarin- Englishbilinguals contained more verbs than in the English lexicon of Malay-English bilinguals, in both comprehension and production.We discuss the potential role of socio-cultural influences on the vocabulary structure in young users of a language.

We present results for forward invariance-based control of hybrid dynamical systems via static feedback. Using recent results on forward invariance for hybrid systems without inputs, we present conditions on the state-feedback laws to induce forward invariance of a set for hybrid systems with inputs. In addition, we propose a notion of control Lyapunov function (CLF) that is suitable for the study of forward invariance of sublevel sets. Conditions that guarantee the existence of CLF-based feedback laws inducing forward invariance of sublevel sets are established. Examples are given to illustrate the results.

With the rapid growth of energy storage capacitors in advanced power systems, the pursuit of lightweight devices is gradually gaining importance despite the urgent need for device miniaturization. To reduce the mass of dielectric energy storage materials, certain light metal elements, such as potassium (K) and sodium (Na), offer promising prospects for achieving low material density. However, the intrinsic formation of point defects, including alkali metal vacancies and oxygen vacancies (Schottky defects), is inevitable during high-temperature sintering because of the volatilization of alkali metal oxides. These defects can lead to high conductivity under high electric fields, thereby deteriorating energy storage performance (ESP). In this work, we focus on a potassium-rich composition, K2La0.75Gd0.25Nb5O15, which is characterized by a tetragonal tungsten bronze (TTB) structure, to investigate the impact of volatile point defects. Different types of defects were designed by changing the K2O content, and energy storage properties were investigated. Based on leakage current measurements, impedance spectra, and DFT calculation results, it could be concluded that K–O defects with a shallow energy level cause conduction loss, thereby influencing polarization and ESP. Consequently, a high recoverable energy storage density (Wrec) of 5.02 J cm−3 and an energy efficiency of 85.6% were simultaneously achieved for the composition with the lowest defect content. This work reveals a mechanism in which volatile defects dominate conduction behavior and relevant ESP, stresses the significance of suppressing alkaline Schottky defects, and provides a feasible solution to developing lightweight dielectric energy storage materials. [ABSTRACT FROM AUTHOR]