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We consider the dynamics of bodies with "active" microstructure described by vector-valued phase fields. For waves with time-varying amplitude, the associated evolution equation involves a matrix that can be non-normal, depending on the…
We present a framework for generating multiple imputations for continuous data when the missing data mechanism is unknown. Imputations are generated from more than one imputation model in order to incorporate uncertainty regarding the…
Cellular response to a perturbation is the result of a dynamic system of biological variables linked in a complex network. A major challenge in drug and disease studies is identifying the key factors of a biological network that are…
Frequency modulation by perturbation is the essential trait that differentiates limit cycle oscillators from phase oscillators. We studied networks of identical limit cycle oscillators whose frequencies are modulated sensitively by the…
Neuron models built from experimental data have successfully predicted observed voltage oscillations within and beyond training range. A tantalising prospect is the possibility of estimating the unobserved dynamics of ion channels which is…
Electroencephalography (EEG) monitors ---by either intrusive or noninvasive electrodes--- time and frequency variations and spectral content of voltage fluctuations or waves, known as brain rhythms, which in some way uncover activity during…
In recent times whole-genome gene expression analysis has turned out to be a highly important tool to study the coordinated function of a very large number of genes within their corresponding cellular environment, especially in relation to…
Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale…
The timing of human labor is among the most critical determinants of neonatal survival, yet the mechanisms that govern the transition from uterine quiescence to coordinated contractions remain elusive. Here we present a dynamical-systems…
Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…
Currently we routinely develop a complex neuronal network to explain observed but often paradoxical phenomena based upon biological recordings. Here we present a general approach to demonstrate how to mathematically tackle such a complex…
Globally-constrained classical fields provide a unexplored framework for modeling quantum phenomena, including apparent particle-like behavior. By allowing controllable constraints on unknown past fields, these models are retrocausal but…
The rupture of a medium under stress typifies breakdown phenomena. More generally, the latter encompass the dynamics of systems of many interacting elements governed by the interplay of a driving force with a pinning disorder, resulting in…
Accelerator-based neutrino oscillation experiments have the potential to revolutionise our understanding of fundamental physics, offering an opportunity to characterise charge-parity violation in the lepton section, to determine the…
Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…
The oscillation model has been proposed as a theoretical framework for describing user dynamics in online social networks. This model can model the user dynamics generated by a particular network structure and allow its causal relationships…
Previous menstrual health literature highlights a variety of signals not included in existing menstrual trackers because they are either difficult to gather or are not typically associated with menstrual health. Since it has become…
Determining mechanistic models of gene regulation, especially underlying phenotypic variation, is a central goal of both mathematical biology and modern evolutionary biology. However, several challenges, involving both common…