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The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
We proposed a new statistical dependency measure called Copula Dependency Coefficient(CDC) for two sets of variables based on copula. It is robust to outliers, easy to implement, powerful and appropriate to high-dimensional variables. These…
Finding the model that best describes a high-dimensional dataset is a daunting task, even more so if one aims to consider all possible high-order patterns of the data, going beyond pairwise models. For binary data, we show that this task…
To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world and scale-free topologies. The random net is the most…
Although there is no doubt that multi-parameter persistent homology is a useful tool to analyse multi-variate data, efficient ways to compute these modules are still lacking in the available topological data analysis toolboxes. Other issues…
This paper introduces a new technique to measure the feature dependency of neural network models. The motivation is to better understand a model by querying whether it is using information from human-understandable features, e.g.,…
High-throughput methods for yielding the set of connections in a neural system, the connectome, are now being developed. This tutorial describes ways to analyze the topological and spatial organization of the connectome at the macroscopic…
Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
In this article, a general family of bivariate distributions is used to model competing risks data with dependent factors. The general structure of competing risks data considered here includes ties. A comprehensive inferential framework…
Currently, knowledge discovery in databases is an essential step to identify valid, novel and useful patterns for decision making. There are many real-world scenarios, such as bankruptcy prediction, option pricing or medical diagnosis,…
Individual differences in human intelligence can be modeled and predicted from in vivo neurobiological connectivity. Many established modeling frameworks for predicting intelligence, however, discard higher-order information about…
We propose a novel approach for modeling multivariate longitudinal data in the presence of unobserved heterogeneity for the analysis of the Health and Retirement Study (HRS) data. Our proposal can be cast within the framework of linear…
Many complex systems often contain interactions between more than two nodes, known as higher-order interactions, which can change the structure of these systems in significant ways. Researchers often assume that all interactions paint a…
This work proposes the application of independent component analysis to the problem of ranking different alternatives by considering criteria that are not necessarily statistically independent. In this case, the observed data (the criteria…
Conditional mutual information is important in the selection and interpretation of graphical models. Its empirical version is well known as a generalised likelihood ratio test and that it may be represented as a difference in entropy. We…
Independence screening methods such as the two sample $t$-test and the marginal correlation based ranking are among the most widely used techniques for variable selection in ultrahigh dimensional data sets. In this short note, simple…
We introduce two novel concepts, topological difference and topological correlation, that offer a new perspective on the discriminative power of multiparameter persistence. The former quantifies the discrepancy between multiparameter and…