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Optimizing the design of complex systems requires navigating interdependent decisions, heterogeneous components, and multiple objectives. Our monotone theory of co-design offers a compositional framework for addressing this challenge,…
The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…
Several concrete examples in quantum information are discussed to demonstrate the importance of proper modeling that relates the mathematical description to real-world applications. In particular, it is shown that some commonly accepted…
In the framework of data envelopment analysis, we review directional models \citep{Chambers1996, Chambers1998, Briec1997} and show that they are inadequate when inputs and outputs are improved simultaneously under constant returns to scale.…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
To date, most probabilistic reasoning systems have relied on a fixed belief network constructed at design time. The network is used by an application program as a representation of (in)dependencies in the domain. Probabilistic inference…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
Proteins exist as a dynamic ensemble of multiple conformations, and these motions are often crucial for their functions. However, current structure prediction methods predominantly yield a single conformation, overlooking the conformational…
Introduction: Computational modeling has rapidly advanced over the last decades, especially to predict molecular properties for chemistry, material science and drug design. Recently, machine learning techniques have emerged as a powerful…
Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed…
Recently, a framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been proposed in the literature. In this paper we develop novel tools that can be used within this framework and…
This paper studies the identification, estimation, and hypothesis testing problem in complete and incomplete economic models with testable assumptions. Testable assumptions ($A$) give strong and interpretable empirical content to the models…
A central push in operations models over the last decade has been the incorporation of models of customer choice. Real world implementations of many of these models face the formidable stumbling block of simply identifying the `right' model…
Non-probabilistic convex model utilizes a convex set to quantify the uncertainty domain of uncertain-but-bounded parameters, which is very effective for structural uncertainty analysis with limited or poor-quality experimental data. To…
Uncertainty quantification (UQ) is the process of systematically determining and characterizing the degree of confidence in computational model predictions. In the context of systems biology, especially with dynamic models, UQ is crucial…
Conformal prediction is a powerful framework for distribution-free uncertainty quantification. The standard approach to conformal prediction relies on comparing the ranks of prediction scores: under exchangeability, the rank of a future…
Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-temporal data.…
We extend conformal prediction methodology beyond the case of exchangeable data. In particular, we show that a weighted version of conformal prediction can be used to compute distribution-free prediction intervals for problems in which the…
In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based…
Economists often estimate economic models on data and use the point estimates as a stand-in for the truth when studying the model's implications for optimal decision-making. This practice ignores model ambiguity, exposes the decision…