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When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. These time discretizations preserve the monotonicity…
This paper presents the first scientific application of local time-stepping (LTS) schemes in the Model for Prediction Across Scales-Ocean (MPAS-O). We use LTS schemes in a single-layer, global ocean model that predicts the storm surge…
Synchronization problems of continuous and discrete singularly perturbed systems are studied in this paper with singular perturbations and time scales (SPaTS) technique. The dynamics of leader and followers are decomposed into pure-slow and…
This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $\tau(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a…
Synthesis of models and strategies is a very important problem in software engineering. The main element here is checking the satisfiability of formulae expressing the specification of a system to be implemented. This paper puts forward a…
The steady-state approximation (hereafter abbreviated as SSA) consists in setting $dy/dt=0$, where $y$ denotes the concentration of a short-lived intermediate subject to first-order decay with a rate constant $k$. The sole reason for…
Accurate prediction of the transmission of epidemic diseases such as COVID-19 is crucial for implementing effective mitigation measures. In this work, we develop a tensor method to predict the evolution of epidemic trends for many regions…
Currently, pre-trained language models (PLMs) do not cope well with the distribution shift problem, resulting in models trained on the training set failing in real test scenarios. To address this problem, the test-time adaptation (TTA)…
Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…
The directional state transition tensor (DSTT) reduces the complexity of state transition tensor (STT) by aligning the STT terms in sensitive directions only, which provides comparable accuracy in orbital uncertainty propagation. The DSTT…
Continual Test-Time Adaptation (CTTA) enables pre-trained models to adapt to continuously evolving domains. Existing methods have improved robustness but typically rely on fixed or batch-level thresholds, which cannot account for varying…
This paper presents a novel method for stability analysis of a wide class of linear, time-delay systems (TDS), including retarded non-neutral ones, as well as those incorporating incommensurate and distributed delays. The proposed method is…
Simulated annealing (SA) is a kind of relaxation method for finding equilibria of Hamiltonian systems. A set of evolution equations is solved with SA, which is derived from the original Hamiltonian system so that the energy of the system…
Increasing penetration of renewable energy introduces significant uncertainty into power systems. Traditional simulation-based verification methods may not be applicable due to the unknown-but-bounded feature of the uncertainty sets.…
This paper investigates the stability of a class of differential systems time-changed by $E_{t}$ which is the inverse of a $\beta$-stable subordinator. In order to explore stability, a time-changed Gronwall's inequality and a generalized…
In this work, we address the issue of controller synthesis for a control-affine nonlinear system to meet prescribed time reach-avoid-stay specifications. Our goal is to improve upon previous methods based on spatiotemporal tubes (STTs) by…
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are…
Stochastic Structural Stability Theory (S3T) provides analytical methods for understanding the emergence and equilibration of jets from the turbulence in planetary atmospheres based on the dynamics of the statistical mean state of the…
This paper deals with the convergence time analysis of a class of fixed-time stable systems with the aim to provide a new non-conservative upper bound for its settling time. Our contribution is fourfold. First, we revisit the well-known…
Point-supervised Temporal Action Localization (PTAL) adopts a lightly frame-annotated paradigm (\textit{i.e.}, labeling only a single frame per action instance) to train a model to effectively locate action instances within untrimmed…