Related papers: Diagnosing Heterogeneous Dynamics in Single Molecu…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
Single-cell trajectory analysis aims to reconstruct the biological developmental processes of cells as they evolve over time, leveraging temporal correlations in gene expression. During cellular development, gene expression patterns…
A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic…
The aim of this work is the numerical homogenization of a parabolic problem with several time and spatial scales using the heterogeneous multiscale method. We replace the actual cell problem with an alternate one, using Dirichlet boundary…
This work presents a purely data-driven, wavelet-based framework for modal identification and reduced-order modeling of mechanical systems with assumed linear dynamics characterized by closely spaced modes with classical or non-classical…
This work develops techniques for the sequential detection and location estimation of transient changes in the volatility (standard deviation) of time series data. In particular, we introduce a class of change detection algorithms based on…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…
Over recent years, super-resolution and single-molecule imaging methods have delivered unprecedented details on the nanoscale organization and dynamics of individual molecules in different contexts. Yet, visualizing single-molecule…
In complex plasmas, the behavior of freely floating micrometer sized particles is studied. The particles can be directly visualized and recorded by digital video cameras. To analyze the dynamics of single particles, reliable algorithms are…
We focus on the biological problem of tracking organelles as they move through cells. In the past, most intracellular movements were recorded manually, however, the results are too incomplete to capture the full complexity of organelle…
It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…
Warm dense matter systems created in the laboratory are highly dynamical. In such cases electron dynamics is often needed to accurately simulate the evolution and properties of the system. Large systems force one to make simple…
Background. Emerging technologies now allow for mass spectrometry based profiling of up to thousands of small molecule metabolites (metabolomics) in an increasing number of biosamples. While offering great promise for revealing insight into…
Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…
Time series are ubiquitous in many applications that involve forecasting, classification and causal inference tasks, such as healthcare, finance, audio signal processing and climate sciences. Still, large, high-quality time series datasets…
The interactions between climate and the environment are highly complex. Due to this complexity, process-based models are often preferred to estimate the net magnitude and directionality of interactions in the Earth System. However, these…