Related papers: A directional uncertainty principle for periodic f…
Mode shape information play the essential role in deciding the spatial pattern of vibratory response of a structure. The uncertainty quantification of mode shape, i.e., predicting mode shape variation when the structure is subjected to…
We are interested to the multifractal analysis of inhomogeneous Bernoulli products which are also known as coin tossing measures. We give conditions ensuring the validity of the multifractal formalism for such measures. On another hand, we…
We are interested to the multifractal analysis of inhomogeneous Bernoulli products which are also known as coin tossing measures. We give conditions ensuring the validity of the multifractal formalism for such measures. On another hand, we…
In this paper, modulating functions-based method is proposed for estimating space-time dependent unknowns in one-dimensional partial differential equations. The proposed method simplified the problem into a system of algebraic equations…
We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure…
The directional subdifferential of the value function gives an estimate on how much the optimal value changes under a perturbation in a certain direction. In this paper we derive upper estimates for the directional limiting and singular…
Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…
Common statistical measures of uncertainty such as $p$-values and confidence intervals quantify the uncertainty due to sampling, that is, the uncertainty due to not observing the full population. However, sampling is not the only source of…
Particulate matter data now include various particle sizes, which often manifest as a collection of curves observed sequentially over time. When considering 51 distinct particle sizes, these curves form a high-dimensional functional time…
Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…
We define a generalized likelihood function based on uncertainty measures and show that maximizing such a likelihood function for different measures induces different types of classifiers. In the probabilistic framework, we obtain…
In this paper the uncertainty principle is found via characteristics of continuous and nowhere differentiable functions. We prove that any physical system that has a continuous and nowhere differentiable position function is subject to an…
Existing variational mesh functionals often suffer from strong nonlinearity or dependence on empirical parameters.We propose a new variational functional for adaptive moving mesh generation that enforces equidistribution and alignment…
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
Trajectory prediction seeks to forecast the future motion of dynamic entities, such as vehicles and pedestrians, given a temporal horizon of historical movement data and environmental context. A central challenge in this domain is the…
New position uncertainty (delocalization) measures for a particle on the circle are proposed and illustrated on several examples, where the previous measures (based on 2pi-periodic position operators) appear to be unsatisfactory. The new…
Unimodal univariate distributions can be characterized as piecewise convex-concave cumulative distribution functions. In this note we transfer this shape constraint characterization to the quantile function. We show that this…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to…