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The Transformer architecture has revolutionized artificial intelligence, yet a principled theoretical understanding of its internal mechanisms remains elusive. This paper introduces a novel analytical framework that reconceptualizes the…
Subgraph matching in logic circuits is foundational for numerous Electronic Design Automation (EDA) applications, including datapath optimization, arithmetic verification, and hardware trojan detection. However, existing techniques rely…
Accurate protein structural ensembles can be determined with metainference, a Bayesian inference method that integrates experimental information with prior knowledge of the system and deals with all sources of uncertainty and errors as well…
Structural identifiability analysis determines whether the parameters of a mechanistic ordinary differential equation (ODE) model can be uniquely recovered from ideal observations and is therefore a fundamental prerequisite for reliable…
We discuss the use of symmetries for analysing the structural identifiability and observability of control systems. Special emphasis is put on the role of discrete symmetries, in contrast to the more commonly studied continuous or Lie…
The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of DAE's system Jacobian is derived; this pattern implies a fine block-triangular form…
Accurate plasma state reconstruction will be crucial for the success of ITER and future fusion plants, but the harsh conditions of a burning plasma will make diagnostic operation more challenging than in current machines. Integrated data…
The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…
The question of finding solutions to given implicit differential equations (IDE) has been answered by several authors in the last few years, using different approaches, in an algebraic and also a geometric setting. Many of those results…
The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral…
This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the…
We outline recent developments in artificial intelligence (AI) and machine learning (ML) techniques for integrative structural biology of intrinsically disordered proteins (IDP) ensembles. IDPs challenge the traditional protein…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…
A novel framework for Bayesian structural model updating is presented in this study. The proposed method utilizes the surrogate unimodal encoders of a multimodal variational autoencoder (VAE). The method facilitates an approximation of the…
A new semi-supervised machine learning method for the discovery of structure-spectrum relationships is developed and demonstrated using the specific example of interpreting X-ray absorption near-edge structure (XANES) spectra. This method…
The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…
Artificial Intelligence for Theorem Proving has given rise to a plethora of benchmarks and methodologies, particularly in Interactive Theorem Proving (ITP). Research in the area is fragmented, with a diverse set of approaches being spread…
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…