Related papers: Disease Is a Spectral Perturbation
A $2n\times 2n$ real matrix $A$ is said to be a Hamiltonian matrix if $A^{T}J+JA=0$, where $J=\left( \begin{array}{cc} 0 & I_{n} \\ -I_{n} & 0\\ \end{array} \right)$. Hamiltonian matrices appear in many areas of applications, such as linear…
Today, despite decades of developments in medicine and the growing interest in precision healthcare, vast majority of diagnoses happen once patients begin to show noticeable signs of illness. Early indication and detection of diseases,…
With the wide application of electronic health records (EHR) in healthcare facilities, health event prediction with deep learning has gained more and more attention. A common feature of EHR data used for deep-learning-based predictions is…
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…
The Hypothalamic-Pituitary-Adrenal (HPA) axis is a major neuroendocrine system, and its dysregulation is implicated in various diseases. This system also presents interesting mathematical challenges for modeling. We consider a nonlinear…
We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…
Continuous biomarkers are common for disease screening and diagnosis. To reach a dichotomous clinical decision, a threshold would be imposed to distinguish subjects with disease from non-diseased individuals. Among various performance…
Disease in the brain is often associated with subtle, spatially diffuse, or complex tissue changes that may lie beneath the level of gross visual inspection, even on magnetic resonance imaging (MRI). Unfortunately, current computer-assisted…
Statistical inference for stochastic block models typically relies on the spectrum of the normalized adjacency matrix $\A^*$. In practice, the true probability matrix $\mathbf{B}$ is unknown and must be replaced by a plug-in estimator…
We illuminate the influence of transition mutations and disorder on charge localization and transfer along B-DNA sequences. Homopolymers are the best for charge transfer (cf. Refs.~ \cite{LVBMS:2018, MLTS:2019}). Hence, we consider as…
Parkinson's disease (PD) belongs to the class of neurodegenerative disorders that affect the central nervous system. It is usually defined as the gradual loss of dopaminergic neurons in the substantia nigra pars compacta, which causes both…
A procedure for calculation of rotation-vibration states of medium sized molecules is presented. It combines the advantages of variational calculations and perturbation theory. The vibrational problem is solved by diagonalizing a…
Perturbation theory is used systematically to investigate the symmetries of the Dirac Hamiltonian and their breaking in atomic nuclei. Using the perturbation corrections to the single-particle energies and wave functions, the link between…
Using ultrashort laser pulses, it has become possible to probe the dynamics of long-range order in solids on microscopic timescales. In the conventional description of symmetry-broken phases within time-dependent Ginzburg-Landau theory, the…
Intense debate in the Neurology community before 2010 culminated in hypothetical models of Alzheimer's disease progression: a pathophysiological cascade of biomarkers, each dynamic for only a segment of the full disease timeline. Inspired…
Non-Hermitian (NH) Hamiltonians can be used to describe dissipative systems, and are currently intensively studied in the context of topology. A salient difference between Hermitian and NH models is the breakdown of the conventional…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
Cosmological perturbation theory is an example of a gauge theory, where gauge transformations correspond to changes in the space-time coordinate system. To determine physical quantities, one is free to introduce gauge conditions (\ie to…
By using the self-consistent Born approximation, we investigate disorder effect induced by the short-range impurities on the band-gap in two-dimensional Dirac systems with the higher order terms in momentum. Starting from the…
We study a perturbed Floquet Hamiltonian $K+\beta V$ depending on a coupling constant $\beta$. The spectrum $\sigma(K)$ is assumed to be pure point and dense. We pick up an eigen-value, namely $0\in\sigma(K)$, and show the existence of a…