Related papers: Discrete Time Elastic Vector Spaces
In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…
The aim of this paper is to study the spatial behaviour of the solutions to the boundary-final value problems associated with the linear theory of elastic materials with voids. More precisely the present study is devoted to porous materials…
We consider the problem of analyzing multivariate time series collected on multiple subjects, with the goal of identifying groups of subjects exhibiting similar trends in their recorded measurements over time as well as time-varying groups…
Spatiotemporal metasurfaces offer unique opportunities for wave manipulation, however, their practical realization is often constrained by the requirement for in-plane spatial modulation, which necessitates a large number of time-varying…
This article proposes and studies warped-linear models for time series classification. The proposed models are time-warp invariant analogues of linear models. Their construction is in line with time series averaging and extensions of…
The merit of projecting data onto linear subspaces is well known from, e.g., dimension reduction. One key aspect of subspace projections, the maximum preservation of variance (principal component analysis), has been thoroughly researched…
This paper defines Massey-type products for a homotopy inner product on an $A_\infty$ algebra, called Massey inner products. We include an explicit description of ordinary Massey products for $A_\infty$ algebras, and for $A_\infty$ modules,…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
We introduce a unified machine-learning framework designed to conveniently tackle the temporal evolution of alloy microstructures under the influence of an elastic field. This approach allows for the simultaneous extraction of elastic…
Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the…
Data-driven and deep learning approaches have demonstrated to have the potential of replacing classical constitutive models for complex materials. Yet, the necessity of structuring constitutive models with an incremental formulation has…
In this paper, we introduce restricted products for families of locally convex spaces and formulate criteria ensuring that mappings into such products are continuous or smooth. As a special case, can define restricted products of weighted…
Generative modeling offers a promising solution to data scarcity and privacy challenges in time series analysis. However, the structural complexity of time series, characterized by multi-scale temporal patterns and heterogeneous components,…
Embedding theorems have continued to be a topic of interest in the general theory of relativity since these help connect the classical theory to higher-dimensional manifolds. This paper deals with spacetimes of embedding class one, i.e.,…
We introduce the Vector Fitting algorithm for the creation of reduced-order models from the sampled response of a linear time-invariant system. This data-driven approach to reduction is particularly useful when the system under modeling is…
The ability to design and fabricate materials with tailored mechanical properties, combined with immunity to damage, is a frontier of materials engineering. For example, materials which are characterized by elastic properties that depend on…
The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions…
Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In…
Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as…
Given a pair of multivariate time-series data of the same length and dimensions, an approach is proposed to select variables and time intervals where the two series are significantly different. In applications where one time series is an…