Related papers: Analysis and Predictability for Tipping Points wit…

Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…

In this paper the problem of retrospective change-point detection and estimation in multivariate linear models is considered. The lower bounds for the error of change-point estimation are proved in different cases (one change-point:…

Binary discrimination between well-defined signal and background datasets is a problem of fundamental importance in particle physics. With detailed event simulation and the advent of extensive deep learning tools, identification of the…

Treatment policy estimands are frequently favored by regulators, as they assess the effect of treatment assignment regardless of post-randomization events. Despite best efforts, missing data due to study discontinuation cannot be fully…

Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…

Scaling laws aim to accurately predict model performance across different scales. Existing scaling-law studies almost exclusively rely on cross-entropy as the evaluation metric. However, cross-entropy provides only a partial view of…

We develop a general criterion about coarsening for a class of nonlinear evolution equations describing one dimensional pattern-forming systems. This criterion allows one to discriminate between the situation where a coarsening process…

Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…

We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of…

In the present work, a simple algorithm for stabilizing an unknown linear time-invariant system is proposed, assuming only that this system is stabilizable. The suggested algorithm is based on first performing a partial identification of…

When the steady states at infinity become unstable through a pattern forming bifurcation, a travelling wave may bifurcate into a modulated front which is time-periodic in a moving frame. This scenario has been studied by B.Sandstede and…

An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…

This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…

The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…

We study a sequential estimation problem for an unknown reward in the presence of a random horizon. The reward takes one of two predetermined values which can be inferred from the drift of a Wiener process, which serves as a signal. The…

Abrupt shifts in ecosystems, brains, markets, and climate are often diagnosed as signs of approaching a tipping point, i.e. a critical bifurcation where stability is lost. Here we reveal a broader and more deceptive mechanism:…

We consider causal inference in dynamic settings where treatment is assigned by thresholding a state variable that can change over time. There is a large literature on regression-discontinuity methods building on the fact that, in the…

The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize…

In this paper we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains. The existence of an orthonormal basis of eigenfunctions is established making use of weak T-coercivity theory. All…

We develop an early-warning signal for bifurcations of one-dimensional random difference equations with additive bounded noise, based on the asymptotic behaviour of the stationary density near a boundary of its support. We demonstrate the…