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Continual learning with vision-language models like CLIP offers a pathway toward scalable machine learning systems by leveraging its transferable representations. Existing CLIP-based methods adapt the pre-trained image encoder by adding…
We propose a method for designing two-dimensional limit-cycle oscillators with prescribed periodic trajectories and phase response properties based on the phase reduction theory, which gives a concise description of weakly-perturbed…
Video anomaly detection is a subject of great interest across industrial and academic domains due to its crucial role in computer vision applications. However, the inherent unpredictability of anomalies and the scarcity of anomaly samples…
Proportional-Integral-Derivative (PID) control has been the workhorse of control technology for about a century. Yet to this day, designing and tuning PID controllers relies mostly on either tabulated rules (Ziegler-Nichols) or on classical…
We present a high-order conservative, positivity-preserving, and non-oscillatory scheme for solving the Vlasov equation. The scheme attains formal fifth-order accuracy through a convex combination of positive and non-oscillatory polynomials…
We unravel the linear stability properties of an otherwise stagnant ultrathin non-wetting liquid film of thickness $h_o$ coating a spherical substrate of radius $R$. The configuration is known to be unstable due to the competition of the…
Vision-language models (VLMs) such as CLIP demonstrate strong generalization in zero-shot classification but remain highly vulnerable to adversarial perturbations. Existing methods primarily focus on adversarial fine-tuning or prompt…
The identification of high-dimensional nonlinear dynamical systems via the Volterra series has significant potential, but has been severely hindered by the curse of dimensionality. Tensor Network (TN) methods such as the Modified…
In this paper, we investigate and prove the nonlinear stability of viscous shock wave solutions of a scalar viscous conservation law, using the methods developed for general systems of conservation laws by Howard, Mascia, Zumbrun and…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
Extending results of Oh and Zumbrun in dimensions $d\ge 3$, we establish nonlinear stability and asymptotic behavior of spatially-periodic traveling-wave solutions of viscous systems of conservation laws in critical dimensions $d=1,2$,…
We study existence and stability of steady solutions of the isentropic compressible Navier-Stokes equations on a finite interval with non characteristic boundary conditions, for general not necessarily small-amplitude data. We show that…
This paper proposes a sliding mode controller with smooth control effort for a class of nonlinear plants. The proposed controller is created by allowing some constant parameters of the earlier smooth sliding control (SSC) to vary as a…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
Optimization-based (OB) alternatives to traditional flux limiters couch preservation of properties such as local bounds and maximum principles into optimization problems, which impose these properties through inequality constraints. In this…
The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter $\lambda$. Despite that the adaptive ISTA is…
In this paper, Van der pol equation has been analyzed for stability and bifurcation phenomena with and without forcing component. Analytical solution of the Van der pol equation using Method of Multiple Scales (MMS) is compared with…
A general, compact way of achieving second-order in finite-volume numerical methods is to perform a MUSCL-like, piecewise linear reconstruction of flow properties at each cell interface. To avoid the surge of spurious oscillations in the…
Simultaneous Localization and Mapping (SLAM) using 3D LiDAR has emerged as a cornerstone for autonomous navigation in robotics. While feature-based SLAM systems have achieved impressive results by leveraging edge and planar structures, they…
Open-loop stable limit cycles are foundational to legged robotics, providing inherent self-stabilization that minimizes the need for computationally intensive feedback-based gait correction. While previous methods have primarily targeted…