Related papers: Geometric signals
Approaches to signal representation and coding theory have traditionally focused on how to best represent signals using parsimonious representations that incur the lowest possible distortion. Classical examples include linear and non-linear…
The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…
In this work we have proposed a rigorous mathematical definition for the one dimensional time domain electrophysiological signals and established its relationship with two of the three Dirichlet's conditions. We have argues that any such…
Learning is a fundamental characteristic of living systems, enabling them to comprehend their environments and make informed decisions. These decision-making processes are inherently influenced by available information about their…
In this paper we develop a new technique to model joint distributions of signals. Our technique is based on quantum mechanical conjugate variables. We show that the transition probability of quantum states leads to a distance function on…
We define a morphic subshift as a subshift generated by the image of a substitution subshift by another substitution. In other words, it is the subshift associated with a ultimately periodic directive sequence. We present an efficient…
For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition…
This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing…
We investigate the use of models from the theory of regularity structures as features in machine learning tasks. A model is a polynomial function of a space-time signal designed to well-approximate solutions to partial differential…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
Multivariate signals, which are measured simultaneously over time and acquired by sensor networks, are becoming increasingly common. The emerging field of graph signal processing (GSP) promises to analyse spectral characteristics of these…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
Following Cand\`es, Romberg and Tao (IEEE Transactions on Information Theory 20,2 (2006) 489-509) a signal is represented as a function x defined on the cyclic group G = Z / NZ, and assuming that it is carried by a set S consisting of T…
With inspiration from the K\"ahler geometry, we introduce a metric structure on the energy class, $\mathcal{E}_{1,m}$, of $m$-subharmonic functions with bounded energy and show that it is complete. After studying how the metric convergence…
A general definition of the curves and geodesics associated with a given connection on a quantized manifold is given. In the particular case of the functional quantization we define geodesics in the same way as in the classical case and we…
Superoscillating signals are band--limited signals that oscillate in some region faster their largest Fourier component. While such signals have many scientific and technological applications, their actual use is hampered by the fact that…
We study the propagator of the wave equation on a closed Riemannian manifold $M$. We propose a geometric approach to the construction of the propagator as a single oscillatory integral global both in space and in time with a distinguished…