Related papers: Analysis and Predictability for Tipping Points wit…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science and control problems. Yet, practically valuable results are rare in this area. This paper develops a…
By means of a linear scaling of the variables we convert a singular bifurcation equation in $\R^n$ into an equivalent equation to which the classical implicit function theorem can be directly applied. This allows to deduce the existence of…
Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little…
A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the…
While LLMs have seen substantial improvement in reasoning capabilities, they also sometimes overthink, generating unnecessary reasoning steps, particularly under uncertainty, given ill-posed or ambiguous queries. We introduce statistically…
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
A variation in the environment of a system, such as the temperature, the concentration of a chemical solution or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point,…
Temporal logic rules are often used in control and robotics to provide structured, human-interpretable descriptions of trajectory data. These rules have numerous applications including safety validation using formal methods, constraining…
The strategy of early stopping is a regularization technique based on choosing a stopping time for an iterative algorithm. Focusing on non-parametric regression in a reproducing kernel Hilbert space, we analyze the early stopping strategy…
Recent theories suggest that Neural Scaling Laws arise whenever the task is linearly decomposed into power-law distributed units. Alternatively, scaling laws also emerge when data exhibit a hierarchically compositional structure, as is…
A deterministic dynamical system that slowly passes through a generic fold-type (saddle-node) bifurcation can be reduced to one-dimensional dynamics close to the bifurcation because of the centre manifold theorem. It is often tacitly…
The understanding and prediction of sudden changes in flow patterns is of paramount importance in the analysis of geophysical flows as these rare events relate to critical phenomena such as atmospheric blocking, the weakening of the Gulf…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
This paper addresses the problem of robust stabilization for linear hyperbolic Partial Differential Equations (PDEs) with Markov-jumping parameter uncertainty. We consider a 2 x 2 heterogeneous hyperbolic PDE and propose a control law using…
The identification and classification of transitions in topological and microstructural regimes in pattern-forming processes are critical for understanding and fabricating microstructurally precise novel materials in many application…
Decision rules offer a rich and tractable framework for solving certain classes of multistage adaptive optimization problems. Recent literature has shown the promise of using linear and nonlinear decision rules in which wait-and-see…
Stationary points or derivative zero crossings of a regression function correspond to points where a trend reverses, making their estimation scientifically important. Existing approaches to uncertainty quantification for stationary points…
We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in non-stationary time series. In contrast to the…
Variational inference is a very efficient and popular heuristic used in various forms in the context of latent variable models. It's closely related to Expectation Maximization (EM), and is applied when exact EM is computationally…
Tipping points characterize situations where a regulated system may experience a sudden and irreversible change and are generally associated with a random state of the system below which the change materializes. In this paper, we study a…