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We study the contact process with stirring on $\mathbb{Z}^d$. In this process, particles occupy vertices of $\mathbb{Z}^d$; each particle dies with rate 1 and generates a new particle at a randomly chosen neighboring vertex with rate…
We consider nucleation of amyloid fibrils in the case when the process occurs by the mechanism of direct polymerization of practically fully extended protein segments, i.e. beta-strands, into beta-sheets. Applying the classical nucleation…
Alzheimer's disease (AD) is a progressive neurodegenerative disorder that severely impairs survival and quality of life. While anti-amyloid beta (Abeta) therapies can slow disease progression, their efficacy depends on personalized dosing…
Three major biomarkers: beta-amyloid (A), pathologic tau (T), and neurodegeneration (N), are recognized as valid proxies for neuropathologic changes of Alzheimer's disease. While there are extensive studies on cerebrospinal fluids…
Alzheimer's disease (AD) persists as a paramount challenge in neurological research, characterized by the pathological hallmarks of amyloid-$\beta$ (A$\beta$) plaques and neurofibrillary tangles composed of hyperphosphorylated tau. This…
The presence of diffuse Focal Axonal Swellings (FAS) is a hallmark cellular feature in many neurodegenerative diseases and traumatic brain injury. Among other things, the FAS have a significant impact on spike-train encodings that propagate…
For effective treatment of Alzheimer disease (AD), it is important to identify subjects who are most likely to exhibit rapid cognitive decline. Herein, we developed a novel framework based on a deep convolutional neural network which can…
As a follow-up tutorial article of [29], in this paper, we will introduce the basic compositional units of the human brain, which will further illustrate the cell-level bio-structure of the brain. On average, the human brain contains about…
Neuroinflammation immediately follows the onset of ischemic stroke. During this process, microglial cells are activated in and recruited to the tissue surrounding the irreversibly injured infarct core, referred to as the penumbra.…
Atherosclerosis, a chronic lesion of vascular wall, remains a leading cause of death and loss of life years. Classical hypotheses for atherosclerosis are long-standing mainly to explain atherogenesis. Unfortunately, these hypotheses may not…
We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability is purely determined by the number of…
The motor neuron disease amyotrophic lateral sclerosis (ALS) typically begins with localized muscle weakness. Progressive, widespread paralysis often follows over a few years. Does the disease begin with local changes in a small piece of…
Purpose: This study investigates whether a machine-learning-based system can predict the rate of cognitive decline in mildly cognitively impaired patients by processing only the clinical and imaging data collected at the initial visit.…
We study the frog model with death on the biregular tree $\mathbb{T}_{d_1,d_2}$. Initially, there is a random number of awake and sleeping particles located on the vertices of the tree. Each awake particle moves as a discrete-time…
Alzheimer's disease (AD) is associated with local (e.g. brain tissue atrophy) and global brain changes (loss of cerebral connectivity), which can be detected by high-resolution structural magnetic resonance imaging. Conventionally, these…
Lead is a naturally-occurring element. It has been known to man for a long time, and it is one of the longest established poisons. The current consensus is that no level of lead exposure should be deemed "safe." New evidence regarding the…
This paper addresses the question of the brain's critical dynamics after an injury such as a stroke. It is hypothesized that the healthy brain operates near a phase transition (critical point), which provides optimal conditions for…
Predicting whether someone with mild cognitive impairment (MCI) will progress to Alzheimer's disease (AD) is crucial in the early stages of neurodegeneration. This uncertainty limits enrollment in clinical trials and delays urgent…
Alzheimer's disease (AD) is characterized by complex and largely unknown progression dynamics affecting the brain's morphology. Although the disease evolution spans decades, to date we cannot rely on long-term data to model the pathological…
Structural MRI-to-amyloid PET synthesis has been proposed as a non-invasive alternative for amyloid assessment in Alzheimer's disease (AD). However, reported performance of identical models varies widely across studies, and increasingly…