相关论文: Local and global robustness at steady state

Understanding the spatial arrangement and nature of real-world objects is of paramount importance to many complex engineering tasks, including autonomous navigation. Deep learning has revolutionized state-of-the-art performance for tasks in…

Recently, deep residual networks have been successfully applied in many computer vision and natural language processing tasks, pushing the state-of-the-art performance with deeper and wider architectures. In this work, we interpret deep…

We investigate the nonlocal version of the Abels-Garcke-Gr\"{u}n (AGG) system, which describes the motion of a mixture of two viscous incompressible fluids. This consists of the incompressible Navier-Stokes-Cahn-Hilliard system…

The location of roots of the characteristic equation of a linear delay differential equation (DDE) determines the stability of the linear DDE. However, by its transcendency, there is no general criterion on the contained parameters for the…

Review of implicit methods of integrating system of stiff ordinary differential equations is presented. Defines and graphically presents absolute stability region for Gears methods (backward differentiation formula) used to solve system of…

A key property for systems subject to uncertainty in their operating environment is robustness, ensuring that unmodelled, but bounded, disturbances have only a proportionally bounded effect upon the behaviours of the system. Inspired by…

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…

Certifiable local robustness, which rigorously precludes small-norm adversarial examples, has received significant attention as a means of addressing security concerns in deep learning. However, for some classification problems, local…

Controllability scores provide control-theoretic centrality measures that quantify the relative importance of state nodes in networked dynamical systems. We establish a structural connection between finite-time controllability scoring and…

In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…

This paper proves that the episodic learning environment of every finite-horizon decision task has a unique steady state under any behavior policy, and that the marginal distribution of the agent's input indeed converges to the steady-state…

An abstract framework for constructing stable decompositions of the spaces corresponding to general symmetric positive definite problems into "local" subspaces and a global "coarse" space is developed. Particular applications of this…

Online contention resolution scheme (OCRS) is a powerful technique for online decision making, which--in the case of matroids--given a matroid and a prior distribution of active elements, selects a subset of active elements that satisfies…

For a class of generalized Hubbard models, we determine the maximal stability region for the superconducting eta-pairing ground state. We exploit the Optimized Ground State (OGS) approach and the Lanczos diagonalization procedure to derive…

We consider stability and network capacity in discrete time queueing systems. Relationships between four common notions of stability are described. Specifically, we consider rate stability, mean rate stability, steady state stability, and…

We study adversarial perturbations when the instances are uniformly distributed over $\{0,1\}^n$. We study both "inherent" bounds that apply to any problem and any classifier for such a problem as well as bounds that apply to specific…

Self-organized criticality (SOC) reveals a mechanism by which a system is autonomously evolved to be in a critical state without needing parameter tuning. Whereas various biological systems are found to be in critical states and the…

In this note, we connect two different topics from linear algebra and numerical analysis: hypocoercivity of semi-dissipative matrices and strong stability for explicit Runge--Kutta schemes. Linear autonomous ODE systems with a non-coercive…

We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph…

The Turing completeness of continuous Chemical Reaction Networks (CRNs) states that any computable real function can be computed by a continuous CRN on a finite set of molecular species, possibly restricted to elementary reactions, i.e.…