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Beta regression models are a suitable choice for continuous response variables on the unity interval. Random effects add further flexibility to the models and accommodate data structures such as hierarchical, repeated measures and…
A semi-algebraic set is a subset of $\mathbb{R}^n$ defined by a finite collection of polynomial equations and inequalities. In this paper, we investigate the problem of determining whether two points in such a set belong to the same…
Real bipartite networks combine degree-constrained random mixing with structured, locality-like rules. We introduce a statistical filter that benchmarks node-level bipartite clustering against degree-preserving randomizations to classify…
Recently, persistent homology has had tremendous success in biomolecular data analysis. It works by examining the topological relationship or connectivity of a group of atoms in a molecule at a variety of scales, then rendering a family of…
We introduce a segmentation algorithm to probe temporal organization of heterogeneities in human heartbeat interval time series. We find that the lengths of segments with different local values of heart rates follow a power-law…
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…
A natural way of handling imbalanced data is to attempt to equalise the class frequencies and train the classifier of choice on balanced data. For two-class imbalanced problems, the classification success is typically measured by the…
The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the…
A method of ``algebraic estimates'' is developed, and used to study the stability properties of integrals of the form \int_B|f(z)|^{-\d}dV, under small deformations of the function f. The estimates are described in terms of a stratification…
Cells can often choose among several stably heritable phenotypes. Examples are the expression of genes in eukaryotic cells where long chromosomal regions can adopt persistent and heritable silenced or active states, that may be associated…
Benchmark rankings are routinely used to justify scientific claims about method quality in gene regulatory network (GRN) inference, yet the stability of these rankings under plausible evaluation protocol choices is rarely examined. We…
$n$-gram profiles have been successfully and widely used to analyse long sequences of potentially differing lengths for clustering or classification. Mainly, machine learning algorithms have been used for this purpose but, despite their…
In this article, we investigate the properties of the EBIC in variable selection for generalized linear models with non-canonical links and diverging number of parameters in ultra-high dimensional feature space. The selection consistency of…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
This paper discusses variance estimation in sequential Monte Carlo methods, alternatively termed particle filters. The variance estimator that we propose is a natural modification of that suggested by H. P. Chan and T. L. Lai [A general…
We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
In the genomic era, the identification of gene signatures associated with disease is of significant interest. Such signatures are often used to predict clinical outcomes in new patients and aid clinical decision-making. However, recent…
In this work, we present a generalization of extended persistent homology to filtrations of graded sub-groups by defining relative homology in this setting. Our work provides a more comprehensive and flexible approach to get an algebraic…
One of the primary areas of interest in applied algebraic topology is persistent homology, and, more specifically, the persistence diagram. Persistence diagrams have also become objects of interest in topological data analysis. However,…