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We prove the existence of a phase transition for a stochastic model of interacting neurons. The spiking activity of each neuron is represented by a point process having rate $1 $ whenever its membrane potential is larger than a threshold…
We study distributed plurality consensus among $n$ nodes, each of which initially holds one of $k$ opinions. The goal is to eventually agree on the initially dominant opinion. We consider an asynchronous communication model in which each…
Memristors have been suggested as neuromorphic computing elements. Spike-time dependent plasticity and the Hodgkin-Huxley model of the neuron have both been modelled effectively by memristor theory. The d.c. response of the memristor is a…
Health concerns associated with the advent of nanotechnologies have risen sharply when it was found that particles of nanoscopic dimensions reach the cell lumina. Plasma and organelle lipid membranes, which are exposed to both the incoming…
Amyloid-$\beta$ (A$\beta$) plaques in conjunction with hyperphosphorylated tau proteins in the form of neurofibrillary tangles are the two neuropathological hallmarks of Alzheimer's disease. It is well-known that the identification of…
In 2018, Ferrari et al. wrote a paper called "Phase Transition for Infinite Systems of Spiking Neurons" in which they introduced a continuous time stochastic model of interacting neurons. This model has a parameter $\gamma$, corresponding…
Recent Alzheimer's disease (AD) patient studies have focused on retinal analysis, as the retina is the only part of the central nervous system which can be imaged non-invasively by optical methods. However as this is a relatively new…
Elderly ICU patients with coexisting diabetes mellitus and heart failure experience markedly elevated short-term mortality, yet few predictive models are tailored to this high-risk group. Diabetes mellitus affects nearly 30% of U.S. adults…
Alzheimer's disease (AD) is a progressive neurodegenerative disorder leading to cognitive decline. [$^{18}$F]-Fluorodeoxyglucose positron emission tomography ([$^{18}$F]-FDG PET) is used to monitor brain metabolism, aiding in the diagnosis…
Neutron stars can be destroyed by black holes at their center accreting material and eventually swallowing the entire star. Here we note that the accretion model adopted in the literature, based on Bondi accretion or variations thereof, is…
The influx of calcium ions into the dendritic spines through the N-metyl-D-aspartate (NMDA) channels is believed to be the primary trigger for various forms of synaptic plasticity. In this paper, the authors calculate analytically the mean…
Alzheimer's disease is a progressive form of dementia that results in problems with memory, thinking, and behavior. It often starts with abnormal aggregation and deposition of beta amyloid and tau, followed by neuronal damage such as…
A simulation model for the spread and control of lesions in the brain is constructed using a planar network (graph) representation for the Central Nervous System (CNS). The model is inspired by the lesion structures observed in the case of…
We consider irreversible second-layer nucleation that occurs when two adatoms on a terrace meet. We solve the problem analytically in one dimension for zero and infinite step-edge barriers, and numerically for any value of the barriers in…
Ballistic annihilation is an interacting system in which particles placed throughout the real line move at preassigned velocities and annihilate upon colliding. The longstanding conjecture that in the symmetric three-velocity setting there…
Nowadays, a lot of scientific efforts are concentrated on the diagnosis of Alzheimer's Disease (AD) applying deep learning methods to neuroimaging data. Even for 2017, there were published more than a hundred papers dedicated to AD…
Analyzing kinetic experiments on protein aggregation using integrated rate laws has led to numerous advances in our understanding of the fundamental chemical mechanisms behind amyloidogenic disorders such as Alzheimer's and Parkinson's…
We propose a topological framework to study the evolution of Alzheimer's disease, the most common neurodegenerative disease. The modeling of this disease starts with the representation of the brain connectivity as a graph and the seeding of…
INTRODUCTION: Quantification of amyloid plaques (A), neurofibrillary tangles (T2), and neurodegeneration (N) using PET and MRI is critical for Alzheimer's disease (AD) diagnosis and prognosis. Existing pipelines face limitations regarding…
We study possible relations between the structure of the connectome, white matter connecting different regions of brain, and Alzheimer disease. Regression models in covariates including age, gender and disease status for the extent of white…