Related papers: Sensitivity Parameter and Time Variations of Funda…

Sensitivity to initial conditions is usually associated with chaotic dynamics and strange attractors. However, even systems with (quasi)periodic dynamics can exhibit it. In this context we report on the fractal properties of the isochrons…

Global sensitivity analysis (GSA) is frequently used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical…

In statistical process control, procedures are applied that require relatively strict conditions for their use. If such assumptions are violated, these methods become inefficient, leading to increased incidence of false signals. Therefore,…

It is commonly argued that an undesirable feature of a theoretical or phenomenological model is that salient observables are sensitive to values of parameters in the model. But in what sense is it undesirable to have such 'fine-tuning' of…

We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…

Nearly all statistical analyses that inform policy-making are based on imperfect data. As examples, the data may suffer from measurement errors, missing values, sample selection bias, or record linkage errors. Analysts have to decide how to…

Various classes of exotic singularity models have been studied as possible mimic models for the observed recent acceleration of the universe. Here we further study one of these classes and, under the assumption that they are…

Fine-tuning pre-trained models has been ubiquitously proven to be effective in a wide range of NLP tasks. However, fine-tuning the whole model is parameter inefficient as it always yields an entirely new model for each task. Currently, many…

The Random Parameters model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we…

We argue that the vulnerability of model parameters is of crucial value to the study of model robustness and generalization but little research has been devoted to understanding this matter. In this work, we propose an indicator to measure…

Comparisons between the redshifts of spectral lines from cosmologically-distant galaxies can be used to probe temporal changes in low-energy fundamental constants like the fine structure constant and the proton-electron mass ratio. In this…

The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…

In causal inference, sensitivity models assess how unmeasured confounders could alter causal analyses, but the sensitivity parameter -- which quantifies the degree of unmeasured confounding -- is often difficult to interpret. For this…

Cosmological parameter estimation from forthcoming experiments promise to reach much greater precision than current constraints. As statistical errors shrink, the required control over systematic errors increases. Therefore, models or…

This paper studies the robustness of observability of a linear time-invariant system under sensor failures from a computational perspective. To be precise, the problem of determining the minimum number of sensors whose removal can destroy…

Uncertainty quantification is a set of techniques that measure confidence in language models. They can be used, for example, to detect hallucinations or alert users to review uncertain predictions. To be useful, these confidence scores must…

Phononic crystals have been widely employed in many engineering fields, which is due to their unique feature of frequency band gaps. For example, their capability to filter out the incoming elastic waves, which include seismic waves, will…

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…

Causal discovery problems use a set of observations to deduce causality between variables in the real world, typically to answer questions about biological or physical systems. These observations are often recorded at regular time…

The variance of an arbitrary pointer observable is considered for the general case that a complex weak value is measured using a complex valued pointer state. For the typical cases where the pointer observable is either its position or…