Related papers: Discrete Time Elastic Vector Spaces
Time warping function provides a mathematical representation to measure phase variability in functional data. Recent studies have developed various approaches to estimate optimal warping between functions and provide non-Euclidean models.…
The Empirical Mode Decomposition (EMD) provides a tool to characterize time series in terms of its implicit components oscillating at different time-scales. We apply this decomposition to intraday time series of the following three…
We propose novel quadratic performance tests for linear discrete-time impulsive systems based on viewing these systems as feedback interconnections of some non-impulsive linear system with an impulsive operator. In order to systematically…
We propose an approach to formally specifying the behavioral properties of systems that rely on a perception model for interactions with the physical world. The key idea is to introduce embeddings -- mathematical representations of a…
The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. Their value comes with the ability to extract meaningful patterns that are of economic,…
We show that a one-dimensional chain of trapped ions can be engineered to produce a quantum mechanical system with discrete scale invariance and fractal-like time dependence. By discrete scale invariance we mean a system that replicates…
We study the applicability of the time-dependent variational principle in matrix product state manifolds for the long time description of quantum interacting systems. By studying integrable and nonintegrable systems for which the long time…
Temporal metamaterials are artificial materials whose electromagnetic properties change over time. In analogy with spatial media and metamaterials, where their properties change smoothly or abruptly over space, temporal metamaterials can…
Understanding the temporal evolution of sets of vectors is a fundamental challenge across various domains, including ecology, crime analysis, and linguistics. For instance, ecosystem structures evolve due to interactions among plants,…
Multivariate time series present challenges to standard machine learning techniques, as they are often unlabeled, high dimensional, noisy, and contain missing data. To address this, we propose T-Rep, a self-supervised method to learn time…
The availability of multidimensional economic datasets has grown significantly in recent years. An example is bilateral trade values across goods among countries, comprising three dimensions -- importing countries, exporting countries, and…
A scheme is discussed for embedding n-dimensional, Riemannian manifolds in an (n+1)-dimensional Einstein space. Criteria for embedding a given manifold in a spacetime that represents a solution to Einstein's equations sourced by a massless…
A temporal network -- a collection of snapshots recording the evolution of a network whose links appear and disappear dynamically -- can be interpreted as a trajectory in graph space. In order to characterize the complex dynamics of such…
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous…
The prevalence of wearable sensors (e.g., smart wristband) is creating unprecedented opportunities to not only inform health and wellness states of individuals, but also assess and infer personal attributes, including demographic and…
By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time…
We consider the general problem of modeling temporal data with long-range dependencies, wherein new observations are fully or partially predictable based on temporally-distant, past observations. A sufficiently powerful temporal model…
Characteristic functions that are radially symmetric have a dual interpretation, as they can be used as the isotropic correlation functions of spatial random fields. Extensions of isotropic correlation functions from balls into…
In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space $\mathbb{R}^d$. The problem has been extensively studied…
There has been recent interest in identifying entanglement as the fundamental concept from which space may emerge. We note that the particular way that a Hilbert space is decomposed into tensor factors is important in what the resulting…