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Root cause analysis of anomalies aims to identify how and why a sample deviates from the normal process. Existing methods primarily focus on telling which features are responsible, ignoring that anomalies can arise through two fundamentally…

Machine learning models are primarily judged by predictive performance, especially in applied settings. Once a model reaches high accuracy, its explanation is often assumed to be correct and trustworthy. This assumption raises an overlooked…

A new model is suggested and used to mimic various spatial or temporal designs in biological or non biological formations where the focus is on the normal or irregular electrical signals coming from human heart (ECG) or brain (EEG). The…

We investigate stability of a new class of heteroclinic cycles that we call heteroclinic cycles of type Y. The cycles can be regarded as a generalisation of heteroclinic cycles of type Z introduced in [Podvigina, Nonlinearity 25, 2012]. The…

Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world…

The emergence of and transitions between distinct phenotypes in isogenic cells can be attributed to the intricate interplay of epigenetic marks, external signals, and gene regulatory elements. These elements include chromatin remodelers,…

This paper introduces diagnostic tests for the nature of lack of fit in ordinary differential equation models (ODEs) proposed for data. We present a hierarchy of three possible sources of lack of fit: unaccounted-for stochastic variation,…

Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…

The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to…

Although there are many methods for functional data analysis (FDA), little emphasis is put on characterizing variability among volatilities of individual functions. In particular, certain individuals exhibit erratic swings in their…

Gynandromorphs are creatures where at least two different body sections are a different sex. Bilateral gynandromorphs are half male and half female. Here we develop a theory of gynandromorph ontogeny based on developmental control networks.…

Uncertainty, characterised by randomness and stochasticity, is ubiquitous in applications of evolutionary game theory across various fields, including biology, economics and social sciences. The uncertainty may arise from various sources…

Mixed-effect models are flexible tools for researchers in a myriad of fields, but that flexibility comes at the cost of complexity and if users are not careful in how their model is specified, they could be making faulty inferences from…

We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate…

Non-normality can underlie pulse dynamics in many engineering contexts. However, its role in pulses generated in biomolecular contexts is generally unclear. Here, we address this issue using the mathematical tools of linear algebra and…

Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take…

Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…

We propose a new method to define anomaly scores and apply this to particle physics collider events. Anomalies can be either rare, meaning that these events are a minority in the normal dataset, or different, meaning they have values that…

Mechanistic growth models play a major role in bioprocess engineering, design, and control. Their reasonable predictive power and their high level of interpretability make them an essential tool for computer aided engineering methods.…