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We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the Output Function Evaluation…
We introduce Ordinal Synchronization ($OS$) as a new measure to quantify synchronization between dynamical systems. $OS$ is calculated from the extraction of the ordinal patterns related to two time series, their transformation into…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
We propose and present a concept of Topological Distance (TD), obtained from the integration of trace distance over the generalized Brillouin zone, in order to characterize the topological transitions of non-Hermitian systems. Specifically,…
Destriping is a classical problem in remote sensing image processing. Although considerable effort has been made to remove stripes, few of the existing methods can eliminate stripe noise with arbitrary orientations. This situation makes the…
In solids, crystal field splitting refers to the lifting of atomic orbital degeneracy by the surrounding ions through the static electric field. Similarly, we show that the degenerated $d$ orbitals, which were derived in the harmonic…
The Backlund Transform, first developed in the context of differential geometry, has been classically used to obtain multi-soliton states in completely integrable infinite dimensional dynamical systems. It has recently been used to study…
Contex. Stellar spectra synthesis is essential for the characterization of potential planetary hosts. In addition, comprehensive stellar variability calculations with fast radiative transfer are needed to disentangle planetary transits from…
We propose an orthogonal series density estimator for complex surveys, where samples are neither independent nor identically distributed. The proposed estimator is proved to be design-unbiased and asymptotically design-consistent. The…
Topological physics desires stable methods to measure the polarization singularities in optical vector fields. Here a periodic plasmonic metasurface is proposed to perform divergence computation of vectorial paraxial beams. We design such…
Out-of-distribution (OOD) detection is essential to prevent anomalous inputs from causing a model to fail during deployment. While improved OOD detection methods have emerged, they often rely on the final layer outputs and require a full…
Metric mean dimension is a geometric invariant of dynamical systems with infinite topological entropy. We relate this concept with the fractal structure of the phase space and the H\"older regularity of the map. Afterwards we improve our…
Out-of-time-ordered correlators (OTOCs) have been proposed as a tool to witness quantum information scrambling in many-body system dynamics. These correlators can be understood as averages over nonclassical multi-time quasi-probability…
We recall the definition of the $\epsilon$-distortion complexity of a set defined in \cite{bcc} and the results obtained in this paper for Cantor sets of the interval defined by iterated function systems. We state an analogous definition…
Reliable pose estimation in previously unseen environments is a fundamental capability of autonomous systems. Existing LiDAR odometry methods typically employ point-, surfel-, or NDT-based map representations, which are distinct from the…
We introduce sliced optimal transport dataset distance (s-OTDD), a model-agnostic, embedding-agnostic approach for dataset comparison that requires no training, is robust to variations in the number of classes, and can handle disjoint label…
This paper proposes an ordered sequence detection (OSD) for digital pulse interval modulation (DPIM) in optical wireless communications. Leveraging the sparsity of DPIM sequences, OSD shows comparable performance to the optimal maximum…
The pair separations statistical methods devised to detect the topology of the universe rely on the accurate knowledge of the three-dimensional positions of the cosmic sources. The determination of these positions, however, involves…
Circular-harmonic spectra are a compact representation of local image features in two dimensions. It is well known that the computational complexity of such transforms is greatly reduced when polar separability is exploited in steerable…
Radar odometry estimation has emerged as a critical technique in the field of autonomous navigation, providing robust and reliable motion estimation under various environmental conditions. Despite its potential, the complex nature of radar…