Related papers: Disease Is a Spectral Perturbation
We describe the implications of permutation symmetry for the state space and dynamics of quantum mechanical systems of matrices of general size $N$. We solve the general 11- parameter permutation invariant quantum matrix harmonic oscillator…
Background: Type 2 diabetes mellitus (T2DM) is increasingly recognised as a systemic disease characterised by coordinated dysfunction across metabolic, renal, lipid, and inflammatory pathways. Existing clinical assessments often fail to…
Systems with an effectively non-Hermitian Hamiltonian display an enhanced sensitivity to parametric and dynamic perturbations, which arises from the nonorthogonality of their eigenstates. This enhanced sensitivity can be quantified by the…
Histopathology is a reflection of the molecular changes and provides prognostic phenotypes representing the disease progression. In this study, we introduced feature scores generated from hematoxylin and eosin histology images based on deep…
We draw attention to the fact that a Hermitian matrix is always diagonalizable and has real discrete spectrum whereas the Hermitian Schr{\"o}dinger Hamiltonian: $H=p^2/2\mu+V(x)$, may not be so. For instance when $V(x)=x, x^3, -x^2$, $H$…
Medical data range from genomic sequences and retinal photographs to structured laboratory results and unstructured clinical narratives. Although these modalities appear disparate, many encode convergent information about a single…
Parkinsons disease (PD) alters cortical neural dynamics, yet reliable non-invasive electrophysiological biomarkers remain elusive. This study examined whether interpretable EEG features capturing complementary aspects of neural dynamics can…
A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha, with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay as…
Head and neck cancer (HNC) patients who undergo radiotherapy (RT) may experience anatomical changes during treatment, compromising the validity of the initial treatment plan, necessitating replanning. However, replanning disrupts clinical…
We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices, using an adaptative active subspace. We consider a hamiltonian which depends on external adjustable or adiabatic parameters,…
Huntington disease (HD) is a fatal autosomal dominant neurocognitive disorder that causes cognitive disturbances, neuropsychiatric symptoms, and impaired motor abilities (e.g., gait, speech, voice). Due to its progressive nature, HD…
Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the…
Hamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz [Phys. Rev. A 67, 033407 (2003)], we define mechanism via pathways of…
A goal of clinical researchers is to understand the progression of a disease through a set of biomarkers. Researchers often conduct observational studies, where they collect numerous samples from selected subjects throughout multiple years.…
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…
The vibrational behavior of molecules serves as a crucial fingerprint of their structure, chemical state, and surrounding environment. Neutron vibrational spectroscopy provides comprehensive measurements of vibrational modes without…
We consider Hamiltonians of models describing non-relativistic quantum mechanical matter coupled to a relativistic field of bosons. If the free Hamiltonian has an eigenvalue, we show that this eigenvalue persists also for nonzero coupling.…
Progressive neurodegenerative diseases, including Alzheimer's disease (AD), multiple sclerosis (MS), Parkinson's disease (PD), and amyotrophic lateral sclerosis (ALS), exhibit complex, nonlinear trajectories that challenge deterministic…
Hypertension is a medical condition that is well-established as a risk factor for many major diseases. For example, it can cause alterations in the cardiac structure and function over time that can lead to heart related morbidity and…