Related papers: Uncertain Data in Initial Boundary Value Problems:…
Consider a Conservation Law and a Hamilton-Jacobi equation with a ux/Hamiltonian depending also on the space variable. We characterize rst the attainable set of the two equations and, second, the set of initial data evolving at a prescribed…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
In many use cases the execution time of tasks is unknown and can be chosen by the designer to increase or decrease the application features depending on the availability of processing capacity. If the application has real-time constraints,…
Probabilities of Causation play a fundamental role in decision making in law, health care and public policy. Nevertheless, their point identification is challenging, requiring strong assumptions such as monotonicity. In the absence of such…
Decadal climate predictions, which are initialized with observed conditions, are characterized by two main sources of uncertainties--internal and model variabilities. Using an ensemble of climate model simulations from the CMIP5 decadal…
We investigate the initial conditions problem for multifield inflation. In these scenarios the pre-inflationary dynamics can be chaotic, increasing the sensitivity of the onset of inflation to the initial data even in the homogeneous limit.…
The uncertainty principle is a cornerstone of modern physics, and its implications have a fundamental impact on theoretical and applied quantum mechanics. The aim of this thesis is to study and apply the uncertainty relations between time…
There are many scenarios where short- and long-term causal effects of an intervention are different. For example, low-quality ads may increase short-term ad clicks but decrease the long-term revenue via reduced clicks. This work, therefore,…
Data-driven sequential decision has found a wide range of applications in modern operations management, such as dynamic pricing, inventory control, and assortment optimization. Most existing research on data-driven sequential decision…
A smooth function of the second moments of $N$ continuous variables gives rise to an uncertainty relation if it is bounded from below. We present a method to systematically derive such bounds by generalizing an approach applied previously…
Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this…
Applications extracting data from crowdsourcing platforms must deal with the uncertainty of crowd answers in two different ways: first, by deriving estimates of the correct value from the answers; second, by choosing crowd questions whose…
Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…
This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [4]. In that paper, the authors established new global-in-time existence results for admissible solutions of nonlinear…
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coefficients. By combining the energy method with the coercivity…
In many fields$\unicode{x2013}$including genomics, epidemiology, natural language processing, social and behavioral sciences, and economics$\unicode{x2013}$it is increasingly important to address causal questions in the context of factor…
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…
This paper looks at effects, due to the boundary, on inference in logistic regression. It shows that first -- and, indeed, higher -- order asymptotic results are not uniform across the model. Near the boundary, effects such as high…