Related papers: Upper limits on the robustness of Turing models an…
This paper concerns the well-posedness and uniform stabilization of the Petrovsky-Wave Nonlinear coupled system with strong damping. Existence of global weak solutions for this problem is established by using the Galerkin method. Meanwhile,…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…
Leveraging algorithmic stability to derive sharp generalization bounds is a classic and powerful approach in learning theory. Since Vapnik and Chervonenkis [1974] first formalized the idea for analyzing SVMs, it has been utilized to study…
The increased integration of intermittent and decentralised forms of power production has eroded the stability margins of power grids and made it more challenging to ensure reliable and secure power transmission. Reliable grid operation…
We present a unified framework for the analysis of space-time methods based on Galerkin-type time discretizations for parabolic and hyperbolic problems. Crucially, the stability analysis relies on a suitable choice of test functions to…
We study linear stability of exponential periodic solutions of a system of singular amplitude equations associated with convective Turing bifurcation in the presence of conservation laws, as arises in modern biomorphology models, binary…
The lower and the upper irredundance numbers of a graph $G$, denoted $ir(G)$ and $IR(G)$ respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a…
We consider the Tur\'an-type problem of bounding the size of a set $M \subseteq \mathbb{F}_2^n$ that does not contain a linear copy of a given fixed set $N \subseteq \mathbb{F}_2^k$, where $n$ is large compared to $k$. An Erd\H{o}s-Stone…
The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is…
In this paper, we derive the limit of experiments for one parameter Ising models on dense regular graphs. In particular, we show that the limiting experiment is Gaussian in the low temperature regime, non Gaussian in the critical regime,…
Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range…
This paper investigates the stability properties of discrete-time multilinear dynamical systems via tensor spectral theory. In particular, if the dynamic tensor of a multilinear dynamical system is orthogonally decomposable (odeco), we can…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…
Perturbing a deterministic $n$-dimensional matrix with small Gaussian noise is a cornerstone of smoothed analysis of algorithms [Spielman and Teng, JACM 2004], as it reduces the condition number of the input to $O(n)$, and with it the…
This paper provides a computer-assisted proof for the Turing instability induced by heterogeneous nonlocality in reaction-diffusion systems. Due to the heterogeneity and nonlocality, the linear Fourier analysis gives rise to…
In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equations. The unknown solution is expanded into an orthogonal…
This paper deals with the robust stability analysis of linear systems, subject to time-varying parameters. The Parameter Dependent Lyapunov Function are considered, assuming that the temporal derivative of the parameters are bounded. Some…
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…
The past thirteen years have seen the development of many algorithms for approximating matrix functions in O(N) time, where N is the basis size. These O(N) algorithms rely on assumptions about the spatial locality of the matrix function;…