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Alzheimer's Disease (AD) is the most widespread neurodegenerative disease, affecting over 50 million people across the world. While its progression cannot be stopped, early and accurate diagnostic testing can drastically improve quality of…
We consider a system consisting of two delay differential equations with a large parameter, modeling the association of a pair of neurooscillators. The unknown functions describe the changes in the normalized membrane potentials of neurons…
Studying the relationship between neuroanatomy and cognitive decline due to Alzheimer's has been a major research focus in the last decade. However, to infer cause-effect relationships rather than simple associations from observational…
The formation of amyloid fibrils comprising amyloid $\beta$ (A$\beta$) peptides is associated with the pathology of Alzheimer's disease. In this study, we theoretically investigated the A$\beta$ structure at the fibril end using the density…
Alzheimer's disease (AD) is an irreversible neurode generative disease of the brain.The disease may causes memory loss, difficulty communicating and disorientation. For the diagnosis of Alzheimer's disease, a series of scales are often…
Alzheimer's disease (AD) causes alterations of brain network structure and function. The latter consists of connectivity changes between oscillatory processes at different frequency channels. We proposed a multi-layer network approach to…
The Coulomb explosion is a process that occurs following the formation of multiple charges during Auger cascades, leading to the destruction of solid-state and molecular structures. For unstable multi-charged ions produced at Auger…
We study noisy calcium imaging data, with a focus on the classification of spike traces. As raw traces obscure the true temporal structure of neuron's activity, we performed a tuned filtering of the calcium concentration using two methods:…
In this paper we present a simple microscopic stochastic model describing short term plasticity within a large homogeneous network of interacting neurons. Each neuron is represented by its membrane potential and by the residual calcium…
Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…
Persistent neural activity associated with working memory (WM) lasts for a limited time duration. Current theories suggest that its termination is \textit{actively} obtained via inhibitory currents, and there is currently no theory…
The amyloid $\beta$ peptide (A$\beta$42), whose aggregation is associated with Alzheimer's disease, is an amphiphatic peptide with a high propensity to self-assemble. A$\beta$42 has a net negative charge at physiological pH and modulations…
We show the principal ability of bypassing damaged demyelinated portions of nervous tissue, thereby restoring its normal function for the passage of action potentials. We carry out a theoretical analysis on the basis of the synchronization…
Glioma is the most common form of primary brain tumor. Demographically, the risk of occurrence increases until old age. Here we present a novel computational model to reproduce the probability of glioma incidence across the lifespan.…
The abnormal aggregation of extracellular amyloid-$\beta$ (A\beta) in senile plaques resulting in calcium (Ca^{+2}) dyshomeostasis is one of the primary symptoms of Alzheimer's disease (AD). Significant research efforts have been devoted in…
Functional Connectivity between brain regions is known to be altered in Alzheimer's disease, and promises to be a biomarker for early diagnosis of the disease. While several approaches for functional connectivity obtain an un-directed…
What is aging? Mechanistic answers to this question remain elusive despite decades of research. Here, we propose a mathematical model of cellular aging based on a model gene interaction network. Our network model is made of only non-aging…
Many neurological diseases originate in the dysfunction of cellular ion channels. Their diagnosis presents a challenge especially when alterations in the complement of ion channels are a priori unknown. Current approaches based on voltage…
Cerebral aneurysm rupture, leading to subarachnoid hemorrhage with a high mortality rate, disproportionately affects younger populations, resulting in a significant loss of productive life years. A significant proportion of these deaths is…
Nowadays, due to tremendous improvements in high performance computing, it has become easier to train Neural Networks. We intend to take advantage of this situation and apply this technology in solving real world problems. There was a need…