Related papers: Disease Is a Spectral Perturbation
We study two spiked models of random matrices under general frameworks corresponding respectively to additive deformation of random symmetric matrices and multiplicative perturbation of random covariance matrices. In both cases, the…
In this study, we executed a genomic analysis with the objective of selecting a set of genes (possibly small) that would help in the detection and classification of samples from patients affected by Parkinson Disease. We performed a…
The metabolic wiring of patient cells is altered drastically in many diseases, including cancer. Understanding the nature of such changes may pave the way for new therapeutic opportunities, as well as the development of personalized…
We develop a perturbative approach for calculating, within the quasistatic approximation, the shift of surface resonances in response to a deformation of a dielectric volume. Our strategy is based on the conversion of the homogeneous system…
With the increase in the use of deep learning for computer-aided diagnosis in medical images, the criticism of the black-box nature of the deep learning models is also on the rise. The medical community needs interpretable models for both…
Quantifying the level of atomic disorder within materials is critical to understanding how evolving local structural environments dictate performance and durability. Here, we leverage graph neural networks to define a physically…
People are living longer than ever before, and with this arises new complications and challenges for humanity. Among the most pressing of these challenges is of understanding the role of aging in the development of dementia. This paper is…
It is shown that, for a Hamiltonian with a band structure, the half width of local spectral density of states, or strength function, is closely related to the width of the nonperturbative (NPT) parts of energy eigenfunctions. In the…
In the field of health-care and bio-medical research, understanding the relationship between the symptoms of diseases is crucial for early diagnosis and determining hidden relationships between diseases. The study aimed to understand the…
Individualized treatment rules, cornerstones of precision medicine, inform patient treatment decisions with the goal of optimizing patient outcomes. These rules are generally unknown functions of patients' pre-treatment covariates, meaning…
The mutations of a complex systemic disease like cancer can be modeled as stuck-at faults in the Boolean system paradigm. For a class of multiple faults, the fault identification is exceptionally significant under the incomplete access of…
This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly…
A new approach is applied to the 1D Anderson model by making use of a two-dimensional Hamiltonian map. For a weak disorder this approach allows for a simple derivation of correct expressions for the localization length both at the center…
We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and appropriate projections of the corresponding eigenvectors of…
We develop a field-theoretic framework, called radiant field theory, to calculate the distribution of transmission eigenvalues for coherent wave propagation in disordered media. At its core is a self-consistent transport equation for a…
The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty domain D of physical values of parameters. This means that for these parameters, H may be called crypto-Hermitian, i.e., made Hermitian via an {\it ad hoc} choice of…
Normative modeling is an emerging and promising approach to effectively study disorder heterogeneity in individual participants. In this study, we propose a novel normative modeling method by combining conditional variational autoencoder…
Degeneracies in the energy spectra of physical systems are commonly considered to be either of accidental character or induced by symmetries of the Hamiltonian. We develop an approach to explain degeneracies by tracing them back to…
Treatment switching is a common occurrence in the management of Multiple Sclerosis (MS), where patients transition across various disease-modifying therapies (DMTs) due to heterogeneous treatment responses, differences in disease…
Estimating eigenvectors and low-dimensional subspaces is of central importance for numerous problems in statistics, computer science, and applied mathematics. This paper characterizes the behavior of perturbed eigenvectors for a range of…