Related papers: Disease Is a Spectral Perturbation
We investigate the statistical properties of the scattering matrix $S$ describing the electron transport through quasi-one dimensional disordered systems. For weak disorder (metallic regime), the energy dependence of the phase shifts of $S$…
Ultrafast disordering observed after photo-excitation challenges the conventional picture of photo-induced transitions where symmetry-breaking takes place along a single collective coordinate. We propose that key spectroscopic signatures of…
Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for…
Normative modelling is an emerging method for understanding the underlying heterogeneity within brain disorders like Alzheimer Disease (AD) by quantifying how each patient deviates from the expected normative pattern that has been learned…
Disease-modifying treatments are currently assessed in neurodegenerative diseases. Huntington's Disease represents a unique opportunity to design automatic sub-clinical markers, even in premanifest gene carriers. We investigated phonatory…
A generalization of Brillouin-Wigner perturbation theory is applied numerically to the Wigner Band Random Matrix model. The perturbation theory tells that a perturbed energy eigenstate can be divided into a perturbative part and a…
Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed…
The statistical properties of a Hamiltonian $H_0$ perturbed by a localized scatterer are considered. We prove that when $H_0$ describes a bounded chaotic motion, the universal part of the spectral statistics are not changed by the…
Searching for biomarkers has been a chief pursuit of the field of psychiatry. Toward this end, studies have catalogued candidate resting-state biomarkers in nearly all forms of mental disorder. However, it is becoming increasingly clear…
One of the biggest challenges in the field of biomedical imaging is the comprehension and the exploitation of the photon scattering through disordered media. Many studies have pursued the solution to this puzzle, achieving light-focusing…
Parkinsons disease (PD) is considered one of the most frequent neurological diseases in the world. There is a need to study the early and efficient biomarkers of Parkinsons, such as changes in structural disorders like DNA and chromatin,…
This paper introduces a novel decomposition framework to explain heterogeneity in causal effects observed across different studies, considering both observational and randomized settings. We present a formal decomposition of between-study…
Clinical decision-making is a feedback system where risk estimates influence treatment, which in turn changes disease trajectories, and both shape clinicians' measurement practices. Static prediction often fails clinically: models trained…
A new and intuitive perturbative approach to time-dependent quantum mechanics problems is presented, which is useful in situations where the evolution of the Hamiltonian is slow. The state of a system which starts in an instantaneous…
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…
There are many experimental data indicating the correlations of the changes in high level of organization of chromatin in human cells and changes in the state of the whole organism related to disease, state of tiredness or aging. In our…
We study a classically chaotic system which is described by a Hamiltonian $H(Q,P;x)$ where $(Q,P)$ are the canonical coordinates of a particle in a 2D well, and $x$ is a parameter. By changing $x$ we can deform the `shape' of the well. The…
High Frequency Oscillations (HFOs), rapid bursts of brain activity above 80 Hz, have emerged as a highly specific biomarker for epileptogenic tissue. Recent evidence suggests that HFOs are also present in Alzheimer's Disease (AD),…
To characterize atypical brain dynamics under diseases, prevalent studies investigate functional magnetic resonance imaging (fMRI). However, most of the existing analyses compress rich spatial-temporal information as the brain functional…
Neurodegeneration as measured through magnetic resonance imaging (MRI) is recognized as a potential biomarker for diagnosing Alzheimer's disease (AD), but is generally considered less specific than amyloid or tau based biomarkers. Due to a…