Related papers: Smoothing Strange Attractors Using Splines
Transformers are designed for discrete tokens, yet many real-world signals are continuous processes observed through noisy sampling. Discrete tokenizations (raw values, patches, finite differences) can be brittle in low signal-to-noise…
Observing the internal state of the whole system using a small number of sensor nodes is important in analysis of complex networks. Here, we study the problem of determining the minimum number of sensor nodes to discriminate attractors…
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…
A method is proposed to generate an optimal fit of a number of connected linear trend segments onto time-series data. To be able to efficiently handle many lines, the method employs a stochastic search procedure to determine optimal…
We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform…
Exponential smoothers are a simple and memory efficient way to compute running averages of time series. Here we define and describe practical properties of exponential smoothers for signals observed at constant and variable intervals.
Time series forecasting is an active research topic in academia as well as industry. Although we see an increasing amount of adoptions of machine learning methods in solving some of those forecasting challenges, statistical methods remain…
Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time…
In many fields of application, dynamic processes that evolve through time are well described by systems of ordinary differential equations (ODEs). The analytical solution of the ODEs is often not available and different methods have been…
We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…
Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing splines is significant when the sample size $n$ is large. When the number of predictors $d\geq2$, the computational…
In this work we propose an objective function to guide the search for a state space reconstruction of a dynamical system from a time series of measurements. This statistics can be evaluated on any reconstructed attractor, thereby allowing a…
Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic…
Large samples have been generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyze such large samples due to expensive computational costs. In particular,…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
We integrate smoothing B-splines into a standard differentiable vector graphics (DiffVG) pipeline through linear mapping, and show how this can be used to generate smooth and arbitrarily long paths within image-based deep learning systems.…
In simulation technology, computationally expensive objective functions are often replaced by cheap surrogates, which can be obtained by interpolation. Full grid interpolation methods suffer from the so-called curse of dimensionality,…
We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis. Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the…
The analysis of nonlinear dynamics is an important issue in numerous fields of science. In this study, we propose a new method to analyze the time series data using persistent homology (PH). The key idea is the application of PH to the…
Using a particle model of Physarum displaying emer- gent morphological adaptation behaviour we demonstrate how a minimal approach to collective material computation may be used to transform and summarise properties of spatially represented…