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Measurement incompatibility, or joint measurability, is a cornerstone of quantum theory and a useful resource. For finite-dimensional systems, quantifying this resource and establishing universal bounds valid for all measurements is a…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers…
Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including graph mining, machine learning, and network science. By…
The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…
After defining non-Gaussian L\'evy processes for two-sided time, stochastic differential equations with such L\'evy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in…
We study the topology of singularities of $c$-optimal semicouplings in unequal dimension. Our main results describe homotopy-reductions from a source space $(X,\sigma)$ onto the singularities $Z_j$, $j\geq 0$ of $c$-optimal semicouplings…
The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. We propose a novel, direct geometric method to identify subsets of phase space that…
The present lack of a stable method to compare persistent homology groups with torsion is a relevant problem in current research about Persistent Homology and its applications in Pattern Recognition. In this paper we introduce a…
The anomaly of a discrete symmetry is defined as the Jacobian of the path-integral measure. Assuming that the anomaly at low energies is cancelled by the Green-Schwarz (GS) mechanism at a fundamental scale, we investigate possible Kac-Moody…
Wavelet phase is a critical parameter in seismic processing, where zero-phase wavelets are essential for maximizing temporal resolution and ensuring accurate interpretation of subsurface structures. In practice, however, the seismic wavelet…
The path-integral control, which stems from the stochastic Hamilton-Jacobi-Bellman equation, is one of the methods to control stochastic nonlinear systems. This paper gives a new insight into nonlinear stochastic optimal control problems…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
In multi-objective optimization, the set of optimal trade-offs -- the Pareto front -- often contains regions that are extremely steep or flat. The Pareto optimal points in these regions are typically of limited interest for decision-making,…
We propose Geometric Pareto Control (GPC), a framework overcoming barriers of reinforcement learning in cyber-physical systems where governing physics is known. Reinforcement learning confronts barriers in safety-critical applications:…
Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of…
This paper proposes a new methodology for deriving a point-based dimensionally homogeneous Jacobian, intended for performance evaluation and optimization of parallel manipulators with mixed degrees of freedom. Optimal manipulator often rely…
We introduce the notion of geometric pseudo-quantisation based on geometric quantisation with a weakened curvature condition. We show how such a structure arises naturally from simple deformations of the symplectic structure and pullbacks…
Future e-mobility calls for efficient electrical machines. For different areas of operation, these machines have to satisfy certain desired properties that often depend on their design. Here we investigate the use of multipatch Isogeometric…
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…