Related papers: Prediction of long term stability by extrapolation

Many astrophysical applications require efficient yet reliable forecasts of stellar evolution tracks. One example is population synthesis, which generates forward predictions of models for comparison with observations. The majority of…

We consider planar systems of predator-prey models with small predator death rate $\epsilon>0$. Using geometric singular perturbation theory and Floquet theory, we derive characteristic functions that determines the location and the…

We consider the simple random walk on supercritical percolation clusters in the multidimensional cubic lattice. In this model, a quenched large deviation principle holds for the position of the random walk. Its rate function depends on the…

Almost every numerical task can be cast as extrapolation with respect to the fidelity or tolerance parameters of a consistent numerical method. This perspective enables probabilistic uncertainty quantification and optimal experimental…

Survival analysis is the problem of estimating probability distributions for future event times, which can be seen as a problem in uncertainty quantification. Although there are fundamental theories on strictly proper scoring rules for…

We prove stability bounds for Stokes-like virtual element spaces in two and three dimensions. Such bounds are also instrumental in deriving optimal interpolation estimates. Furthermore, we develop some numerical tests in order to…

Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…

In some randomized clinical trials, patients may die before the measurements of their outcomes. Even though randomization generates comparable treatment and control groups, the remaining survivors often differ significantly in background…

Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…

We calculate the survival probability of an immobile target surrounded by a sea of uncorrelated diffusive or subdiffusive evanescent traps, i.e., traps that disappear in the course of their motion. Our calculation is based on a fractional…

We define extrapolation as any type of statistical inference on a conditional function (e.g., a conditional expectation or conditional quantile) evaluated outside of the support of the conditioning variable. This type of extrapolation…

A dual formulation for the problem of determining absolute performance limitations on overshoot, undershoot, maximum amplitude and fluctuation minimization for continuous-time feedback systems is constructed. Determining, for example, the…

In order to understand the phenomenon of longevity in biological world, the relationship between the potential of longevity and the structural complexity of an organism is analyzed. I. The potential of longevity is the maximum lifespan of…

We calculate the survival probability of a diffusing test particle in an environment of diffusing particles that undergo coagulation at rate lambda_c and annihilation at rate lambda_a. The test particle dies at rate lambda' on coming into…

We develop a new paradigm for finding bifurcations of solutions of nonlinear problems, which is based on the detection of extreme values of new type of variational functional associated with the considering problem. The variational…

Within a concept of the fractional diffusion equation and subordination, the paper examines the influence of a competition between long waiting times and long jumps on the escape from the potential well. Applying analytical arguments and…

We derive a new fluctuation-dissipation relation for non-equilibrium systems with long-term memory. We show how this relation allows one to access new experimental information regarding active forces in living cells that cannot otherwise be…

We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…

We provide a thorough study of stability of the 1-D continuity equation, which models many physical conservation laws. In our system-theoretic perspective, the velocity is considered to be an input. An additional input appears in the…

Extreme events represent a challenge to natural as well as man-made systems. For critical infrastructure like power grids, we need to understand their resilience against large disturbances. Recently, new measures of the resilience of…