Related papers: Ordinal Patterns in the Duffing Oscillator: Analyz…
We derive the exact bifurcation diagram of the Duffing oscillator with parametric noise thanks to the analytical study of the associated Lyapunov exponent. When the fixed point is unstable for the underlying deterministic dynamics, we show…
The dynamics of cellular pattern formation is crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in…
We showcase the utility of the Lagrangian descriptors method in qualitatively understanding the underlying dynamical behavior of dynamical systems governed by fractional-order differential equations. In particular, we use the Lagrangian…
Unordered feature sets are a nonstandard data structure that traditional neural networks are incapable of addressing in a principled manner. Providing a concatenation of features in an arbitrary order may lead to the learning of spurious…
This report addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state…
A random phase property establishing a link between quasi-one-dimensional random Schroedinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system…
A time series is a collection of measurements in chronological order. Discovering patterns from time series is useful in many domains, such as stock analysis, disease detection, and weather forecast. To discover patterns, existing methods…
Algebraic representations of time series are symbolic representations whose symbols belong to a finite group. Precisely, the framework of the present paper is the analysis of coupled time series in algebraic representations and, more…
In Ordinal Classification tasks, items have to be assigned to classes that have a relative ordering, such as positive, neutral, negative in sentiment analysis. Remarkably, the most popular evaluation metrics for ordinal classification tasks…
Street networks may be planned according to clear organizing principles or they may evolve organically through accretion, but their configurations and orientations help define a city's spatial logic and order. Measures of entropy reveal a…
In this paper, we find the existence of critical features hidden in Deep NeuralNetworks (DNNs), which are imperceptible but can actually dominate the outputof DNNs. We call these features dominant patterns. As the name suggests, for a…
Temporal set prediction involves forecasting the elements that will appear in the next set, given a sequence of prior sets, each containing a variable number of elements. Existing methods often rely on intricate architectures with…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
Learning of interpretable classification models has been attracting much attention for the last few years. Discovery of succinct and contrasting patterns that can highlight the differences between the two classes is very important. Such…
The experiments conducted by various scientific groups indicate that, in dense two-dimensional systems of elongated particles subjected to vibration, the pattern formation is possible. Computer simulations have evidenced that the random…
Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We…
In a setting where $m$ items need to be partitioned among $n$ agents, we evaluate the performance of mechanisms that take as input each agent's \emph{ordinal preferences}, i.e., their ranking of the items from most- to least-preferred. The…
In the case of ergodicity much of the structure of a one-dimensional time-discrete dynamical system is already determined by its ordinal structure. We generally discuss this phenomenon by considering the distribution of ordinal patterns,…