Related papers: Disease Is a Spectral Perturbation
Early disease detection and prevention methods based on effective interventions are gaining attention. Machine learning technology has enabled precise disease prediction by capturing individual differences in multivariate data. Progress in…
Background: Huntington's disease (HD) is a rare, genetically determined brain disorder that limits the life of the patient, although early prognosis of HD can substantially improve the patient's quality of life. Current HD prognosis methods…
Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…
Eigenvalue and eigenvector perturbation theory is a fundamental topic in several disciplines, including numerical linear algebra, quantum physics, and related fields. The central problem is to understand how the eigenvalues and eigenvectors…
Using a non-Hermitian Hamiltonian approach to open systems, we study the interplay of disorder and superradiance in a one- and three-dimensional Anderson model. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian, a…
The use of the hyperspherical harmonic (HH) basis in the description of bound states in an $A$-body system composed by identical particles is normally preceded by a symmetrization procedure in which the statistic of the system is taken into…
For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and…
We explore the influence of an arbitrary external potential perturbation V on the spectral properties of a weakly disordered conductor. In the framework of a statistical field theory of a nonlinear sigma-model type we find, depending on the…
Huntington's disease (HD) is an autosomal dominant neurodegenerative disorder characterized by motor dysfunction, psychiatric disturbances, and cognitive decline. The onset of HD is marked by severe motor impairment, which may be predicted…
In this text, based on elementary computations, we provide a perturbative expansion of the coordinates of the eigenvectors of a Hermitian matrix of large size perturbed by a random matrix with small operator norm whose entries in the…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive…
Cellular response to a perturbation is the result of a dynamic system of biological variables linked in a complex network. A major challenge in drug and disease studies is identifying the key factors of a biological network that are…
Using a non-Hermitian Hamiltonian approach to open systems, we study the interplay of disorder and superradiance in a one-dimensional Anderson model. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian, a transition to a…
Disease progression models infer group-level temporal trajectories of change in patients' features as a chronic degenerative condition plays out. They provide unique insight into disease biology and staging systems with individual-level…
We study the level-statistics of a disordered system undergoing the Anderson type metal-insulator transition. The disordered Hamiltonian is a sparse random matrix in the site representation and the statistics is obtained by taking an…
The spectroscopic properties of an open quantum system are determined by the eigenvalues and eigenfunctions of an effective Hamiltonian H consisting of the Hamiltonian H_0 of the corresponding closed system and a non-Hermitian correction…
Predictive or treatment selection biomarkers are usually evaluated in a subgroup or regression analysis with focus on the treatment-by-marker interaction. Under a potential outcome framework (Huang, Gilbert and Janes [Biometrics 68 (2012)…
The knowledge of cell molecular mechanisms implicated in human diseases is expanding and should be converted into guidelines for deciphering pathological cell signaling and suggesting appropriate treatment. The basic assumption is that…
We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective…
In this paper, we examine disorder (i.e. static imperfections in manufacture) for the fixed-Hamiltonian evolution protocol of quantum state transfer. We improve the performance by optimising the choice of Hamiltonian, and by implementing an…