Related papers: A Novel Use of Pseudospectra in Mathematical Biolo…
A four-dimensional mathematical model of the hypothalamus-pituitary-adrenal (HPA) axis is investigated, incorporating the influence of the GR concentration and general feedback functions. The inclusion of distributed time delays provides a…
This paper analyzes a four-dimensional model of the hypothalamic-pituitary-adrenal (HPA) axis that includes the influence of the glucocorticoid receptor in the pituitary. Due to the spatial separation between the hypothalamus, pituitary and…
This paper generalizes the existing minimal model of the hypothalamic-pituitary-adrenal (HPA) axis in a realistic way, by including memory terms: distributed time delays, on one hand and fractional-order derivatives, on the other hand. The…
The pseudospectra of a linear time-invariant system are the sets in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound.…
Understanding disease progression at the molecular pathway level usually requires capturing both structural dependencies between pathways and the temporal dynamics of disease evolution. In this work, we solve the former challenge by…
The pseudospectrum of a linear time-invariant system is the set in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound.…
The thyroid gland, in conjunction with the pituitary and the hypothalamus, forms a regulated system due to their mutual influence through released hormones. The equilibrium point of this system, commonly referred to as the "set point", is…
Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…
Computing pseudospectra of non-normal matrices is essential for understanding the stability and transient behavior of dynamical systems. Such analysis is critical in applications including fluid dynamics, control systems, and differential…
Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…
Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay…
Topological data analysis (TDA) approaches are becoming increasingly popular for studying the dependence patterns in multivariate time series data. In particular, various dependence patterns in brain networks may be linked to specific tasks…
We consider a model system of two coupled Hopfield neurons, which is described by delay differential equations taking into account the finite signal propagation and processing times. When the delay exceeds a critical value, a limit cycle…
Delay differential equations (DDEs) are widely used in mathematical modeling to describe physical and biological systems. Delays can impact model dynamics, resulting in oscillatory behavior. In physiological systems, this instability may…
Angle-resolved photoemission spectra are calculated microscopically for the two-dimensional attractive Hubbard model. A system of self-consistent T-matrix equations are solved numerically in the real-time domain. The single-particle…
Prenatal stress (PS) impacts early postnatal behavioural and cognitive development. This process of 'fetal programming' is mediated by the effects of the prenatal experience on the developing hypothalamic-pituitary-adrenal (HPA) axis and…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…
We present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model. There are two monotone nonlinearities in the model: one…
The spiking properties of a subcritical Hopf oscillator with a time delayed nonlinear feedback is investigated. Finite time delay is found to significantly affect both the statistics and the fine structure of the spiking behavior. These…
Motivated by the recent advances in modelling the pseudo-Hermitian Hamiltonian (pHH) systems using superconducting qubits we analyze their quantum dynamics subject to a small time-dependent perturbation. In particular, We develop the linear…