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Insomnia affects a vast population of the world and can have a wide range of causes. Existing treatments for insomnia have been linked with many side effects like headaches, dizziness, etc. As such, there is a clear need for improved…
Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range of tools and techniques for time series analysis already exist, the increasing…
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
Sequence modeling faces challenges in capturing long-range dependencies across diverse tasks. Recent linear and transformer-based forecasters have shown superior performance in time series forecasting. However, they are constrained by their…
Objective: In recent years, the functional connectivity of the human brain has been studied with graph theoretical tools. One such approach is community detection which is fundamental for uncovering the localized networks. Existing methods…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
Biological systems are driven by intricate interactions among the complex array of molecules that comprise the cell. Many methods have been developed to reconstruct network models of those interactions. These methods often draw on large…
Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…
The electroencephalographic (EEG) data intracerebrally recorded from 20 epileptic humans with different brain origins of focal epilepsies or types of seizures, ages and sexes are investigated (nearly 700 million data). Multi channel…
We propose an empirical approach centered on the spectral dynamics of weights -- the behavior of singular values and vectors during optimization -- to unify and clarify several phenomena in deep learning. We identify a consistent bias in…
While Deep Learning (DL) is often considered the state-of-the art for Artificial Intelligence-based medical decision support, it remains sparsely implemented in clinical practice and poorly trusted by clinicians due to insufficient…
Observations made in continuous time are often irregular and contain the missing values across different channels. One approach to handle the missing data is imputing it using splines, by fitting the piecewise polynomials to the observed…
Discrete time trawl processes constitute a large class of time series parameterized by a trawl sequence (a j) j$\in$N and defined though a sequence of independent and identically distributed (i.i.d.) copies of a continuous time process…
The observational ubiquity of inverse power law spectra (IPL) in complex phenomena entails theory for dynamic fractal phenomena capturing their fractal dimension, dynamics, and statistics. These and other properties are consequences of the…
Although much of the focus of statistical works on networks has been on static networks, multiple networks are currently becoming more common among network data sets. Usually, a number of network data sets, which share some form of…
Network data is a major object data type that has been widely collected or derived from common sources such as brain imaging. Such data contains numeric, topological, and geometrical information, and may be necessarily considered in certain…
The brain is a high-dimensional directional network system consisting of many regions as network nodes that influence each other. The directional influence from one region to another is referred to as directional connectivity. Epilepsy is a…
The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…
A coupled map is suggested to investigate various spatial or temporal designs in biology: Several cells (or tissues) in an organ are considered as connected to each other in terms of some molecular diffusions or electrical potential…