Related papers: Entropic and algebraic transcript-based tools in t…

Entropy metrics are nonlinear measures to quantify the complexity of time series. Among them, permutation entropy is a common metric due to its robustness and fast computation. Multivariate entropy metrics techniques are needed to analyse…

Time series and signals are attracting more attention across statistics, machine learning and pattern recognition as it appears widely in the industry especially in sensor and IoT related research and applications, but few advances has been…

For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…

We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…

Time series interpretation aims to provide an explanation of what is observed in terms of its underlying processes. The present work is based on the assumption that the common classification-based approaches to time series interpretation…

Designing distributed systems to have predictable performance under high load is difficult because of resource exhaustion, non-linearity, and stochastic behaviour. Timeliness, i.e., delivering results within defined time bounds, is a…

A time series is uniquely represented by its geometric shape, which also carries information. A time series can be modelled as the trajectory of a particle moving in a force field with one degree of freedom. The force acting on the particle…

In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…

A new symbolic representation of time series, called ABBA, is introduced. It is based on an adaptive polygonal chain approximation of the time series into a sequence of tuples, followed by a mean-based clustering to obtain the symbolic…

In the last years, algebraic tools have been proven useful in phylogenetic reconstruction and model selection through the study of phylogenetic invariants. However, up to now, the models studied from an algebraic viewpoint are either too…

The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric…

We propose a tree ensemble method, referred to as time series forest (TSF), for time series classification. TSF employs a combination of the entropy gain and a distance measure, referred to as the Entrance (entropy and distance) gain, for…

This paper proposes a framework dedicated to the construction of what we call discrete elastic inner product allowing one to embed sets of non-uniformly sampled multivariate time series or sequences of varying lengths into inner product…

We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides…

In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the…

In this work, we introduce metrics to evaluate the use of simplified time series in the context of interpretability of a TSC -- a Time Series Classifier. Such simplifications are important because time series data, in contrast to text and…

We investigate the performance of entropy estimation methods, based either on block entropies or compression approaches, in the case of bidimensional sequences. We introduce a validation dataset made of images produced by a large number of…

The recently introduced concept of timelike entanglement entropy has sparked a lot of interest. Unlike the traditional spacelike entanglement entropy, timelike entanglement entropy involves tracing over a timelike subsystem. In this work,…

Signals can be interpreted as composed of a rapidly varying component modulated by a slower varying envelope. Identifying this envelope is an essential operation in signal processing, with applications in areas ranging from seismology to…

We propose algebraic protocols that enable the definition of protocol templates and session types analogous to the definition of domain-specific types with algebraic datatypes. Parameterized algebraic protocols subsume all regular as well…