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We derive sharp approximation error bounds for inverse block Toeplitz matrices associated with multivariate long-memory stationary processes. The error bounds are evaluated for both column and row sums. These results are used to prove the…
Factorial series played a major role in Stirling's classic book "Methodus Differentialis" (1730), but now only a few specialists still use them. This article wants to show that this neglect is unjustified, and that factorial series are…
Systems modeled by partial differential equations (PDEs) are at least as ubiquitous as systems that are by nature finite-dimensional and modeled by ordinary differential equations (ODEs). And yet, systematic and readily usable…
Deep learning models have grown increasingly popular in time series applications. However, the large quantity of newly proposed architectures, together with often contradictory empirical results, makes it difficult to assess which…
We propose a Bayesian inference approach for a class of latent Markov models. These models are widely used for the analysis of longitudinal categorical data, when the interest is in studying the evolution of an individual unobservable…
Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from…
In this paper, we consider the problem of invariant set computation for black-box switched linear systems using merely a finite set of observations of system trajectories. In particular, this paper focuses on polyhedral invariant sets. We…
In recent years, the transformer has established itself as a workhorse in many applications ranging from natural language processing to reinforcement learning. Similarly, Bayesian deep learning has become the gold-standard for uncertainty…
Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
We investigate the use of a functional analytical version of the Backus-Gilbert Method as a reconstruction strategy to get specific information about the solution of linear and slightly non-linear systems with Frech\'et derivable operators.…
Replicator equations (RE) are among the basic tools in mathematical theory of selection and evolution. We develop a method for reducing a wide class of the RE, which in general are systems of differential equations in Banach space to escort…
In many real-world application, e.g., speech recognition or sleep stage classification, data are captured over the course of time, constituting a Time-Series. Time-Series often contain temporal dependencies that cause two otherwise…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
The present paper studies so-called deep image prior (DIP) techniques in the context of ill-posed inverse problems. DIP networks have been recently introduced for applications in image processing; also first experimental results for…
Matrix Lie groups provide a language for describing motion in such fields as robotics, computer vision, and graphics. When using these tools, we are often faced with turning infinite-series expressions into more compact finite series (e.g.,…
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…
We study the analyticity of bounded solutions of systems of analytic state-dependent delay differential equations. We obtain the analyticity of solutions by transforming the system of state-dependent delay equations into an abstract…