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Reuse of data in adaptive workflows poses challenges regarding overfitting and the statistical validity of results. Previous work has demonstrated that interacting with data via differentially private algorithms can mitigate overfitting,…

Statistical physics is used to investigate independent component analysis with polynomial contrast functions. While the replica method fails, an adapted cavity approach yields valid results. The learning curves, obtained in a suitable…

To put static program analysis at the fingertips of the software developer, we propose a framework for interactive abstract interpretation. While providing sound analysis results, abstract interpretation in general can be quite costly. To…

In recent years, dynamic languages, such as JavaScript or Python, have been increasingly used in a wide range of fields and applications. Their tricky and misunderstood behaviors pose a hard challenge for static analysis of these…

Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…

Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…

We propose a new static program analysis called program behavior analysis. The analysis aims to calculate possible symbolic expressions for every variable at each program point. We design a new lattice, transfer function, and widening…

Statistical physics courses typically employ abstract language that describes objects too small to be seen, making the topic challenging for students to understand. In this work, we introduce a simple experiment that allows conceptualizing…

We consider the problem of computing numerical invariants of programs, for instance bounds on the values of numerical program variables. More specifically, we study the problem of performing static analysis by abstract interpretation using…

We consider the problem of discretizing evolution operators of linear delay equations with the aim of approximating their spectra, which is useful in investigating the stability properties of (nonlinear) equations via the principle of…

The design and implementation of precise static analyzers for significant fragments of modern imperative languages like C, C++, Java and Python is a challenging problem. In this paper, we consider a core imperative language that has several…

We introduce a modified version of the Whitney extension operators for collections of functions from a closed subset of $\mathbb{R}^n$ into scales of Banach spaces with smoothing operators. We prove an extension theorem for collections…

We are used to thinking of an operator acting once, twice, and so on. However, an operator acting integer times can be consistently analytic continued to an operator acting complex times. Applications: (s,r) diagrams and an extension of…

Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…

Variable sharing is a fundamental property in the static analysis of logic programs, since it is instrumental for ensuring correctness and increasing precision while inferring many useful program properties. Such properties include modes,…

Certain linear matrix operators arise naturally in systems analysis and design problems involving cascade interconnections of linear time-invariant systems, including problems of stabilization, estimation, and model order reduction. We…

Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…

We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…

Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…

Finite renormalization freedom in locally covariant quantum field theories on curved spacetime is known to be tightly constrained, under certain standard hypotheses, to the same terms as in flat spacetime up to finitely many curvature…