Related papers: Disease Is a Spectral Perturbation
Alzheimer's disease (AD) is characterized by progressive microstructural deterioration in brain tissue, yet conventional imaging and histopathology often lack the sensitivity needed to detect subtle early-stage changes. Here, we present a…
Perturbation theory with respect to the kinetic energy of the heavy component of a two-component quantum system is introduced. An effective Hamiltonian that is accurate to second order in the inverse heavy mass is derived. It contains a new…
We consider a classically chaotic system that is described by an Hamiltonian $H(Q,P;x)$ where x is a constant parameter. Our main interest is in the case of a gas-particle inside a cavity, where $x$ controls a deformation of the boundary or…
Estimating a covariance matrix is central to high-dimensional data analysis. Empirical analyses of high-dimensional biomedical data, including genomics, proteomics, microbiome, and neuroimaging, among others, consistently reveal strong…
Metabonomics, the measure of the fingerprint of biochemical perturbations caused by disease, drugs or toxins, recently has become a major focus of research in various areas especially indications of drug toxicity. Two types of technology…
To what extent do individual eigenstates encode information of their underlying Hamiltonian, and how does this depend on their spectral position? For many-body quantum systems, this issue is widely understood in terms of the differing…
Pathological brain appearances may be so heterogeneous as to be intelligible only as anomalies, defined by their deviation from normality rather than any specific pathological characteristic. Amongst the hardest tasks in medical imaging,…
Volume change measures derived from longitudinal MRI (e.g. hippocampal atrophy) are a well-studied biomarker of disease progression in Alzheimer's Disease (AD) and are used in clinical trials to track the therapeutic efficacy of…
The numerical cost of variational methods suggests using perturbative approaches to determine the electronic structure of molecular systems. In this work, a sequential construction of effective Hamiltonians drives the definition of…
The distinction between "healthy" and "unhealthy" patients is commonly based on single, discrete values taken at an isolated point in time (e.g., blood pressure or core temperature). Perhaps a more robust and insightful diagnosis can be…
The preclinical stage of many neurodegenerative diseases can span decades before symptoms become apparent. Understanding the sequence of preclinical biomarker changes provides a critical opportunity for early diagnosis and effective…
We study quenched disorder in strongly correlated systems via holography, focusing on the thermodynamic effects of mild electric disorder. Disorder is introduced through a random potential which is assumed to self-average on macroscopic…
We provide a perturbative expansion for the empirical spectral distribution of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent…
The metabolic process in a cell is modeled with the use of the Fourier transformation. The histograms of the invariant measures of chaotic attractors are constructed. In particular, a scenario of adaptation of the metabolic process under a…
Alzheimer's disease (AD) is a multifactorial neurodegenerative disorder characterized by progressive cognitive decline and widespread epigenetic dysregulation in the brain. DNA methylation, as a stable yet dynamic epigenetic modification,…
We present first-order perturbation analysis of a simple eigenvalue and the corresponding right and left eigenvectors of a general square matrix, not assumed to be Hermitian or normal. The eigenvalue result is well known to a broad…
This paper is devoted to study measure solutions $\mu_t^h$ to perturbed nonlinear structured population models where $t$ denotes time and $h$ controlls the size of perturbation. We address differentiability of the map $h \mapsto \mu_t^h$.…
Disentangling pathological changes from physiological aging in 3D medical shapes is crucial for developing interpretable biomarkers and patient stratification. However, this separation is challenging when diagnosis labels are limited or…
Alzheimer's disease is a progressive, debilitating neurodegenerative disease that affects 50 million people globally. Despite this substantial health burden, available treatments for the disease are limited and its fundamental causes remain…
Complex diseases are caused by a multitude of factors that may differ between patients. As a result, hypothesis tests comparing all patients to all healthy controls can detect many significant variables with inconsequential effect sizes. A…