We first characterize $tau$-complemented modules with relative (pre)-covers. We also introduce an extending module relative to $tau$-pure submodules on a hereditary torsion theory $tau$ and give its relationship with $tau$-complemented modules.

The two hallmarks of Alzheimer's disease (AD) are neurofibrillary tangles and amyloid plaques. Neurofibrillary tangles are formed due to the hyperphosphorylation of tau protein. There is an urgent need to develop a reliable biomarker for the diagnosis of AD. Cerebrospinal fluid (CSF) is surrounding the brain and reflects the major neuropathological features in the AD brain. Diagnosis, disease p...

This study aimed to describe the characteristics of natural disasters and associated losses from 1985 to 2014. The Mann-Kendall method was used to detect any long-term trends and abrupt changes. Hotspot analysis was conducted to detect the spatial clusters of disasters. We found an increasing trend in the occurrence of integrated natural disasters (tau = 0.594, p < 0.001), particularly for floo...

The default mode network (DMN) is particularly relevant to Alzheimer's disease (AD) since its structures are vulnerable to deposition of amyloid. Decreased levels of β-amyloid(1-42) (Aβ42) and increased total tau protein (T-tau) and tau phosphorylated at position threonine 181 (P-tau(181p)) in cerebrospinal fluid (CSF) have been established as valid biomarkers for the diagnosis and prognosis of...

BACKGROUND Insulin resistance (IR) is linked with the occurrence of pathological features observed in Alzheimer's disease (AD), including neurofibrillary tangles and amyloid plaques. However, the extent to which IR is associated with AD pathology in the cognitively asymptomatic stages of preclinical AD remains unclear. OBJECTIVE To determine the extent to which IR is linked with amyloid and t...

It has previously been reported that amyloid-beta (Abeta) peptide is neurotrophic to undifferentiated but neurotoxic to differentiated primary neurons. The underlying reasons for this differential effect is not understood. Recently, the toxicity of Abeta to neurons was shown to be dependent upon the activation of cyclin-dependent kinase 5 (Cdk5), thought to promote tau phosphorylation that lead...

Alzheimer's disease (AD) and vascular dementia (VaD) are the two most common causes of dementia in old people. They remain difficult to differentiate in practice because of lack of sensitivity and specificity of current clinical diagnostic criteria. Recent molecular and cellular advancements indicate that the use of cerebrospinal fluid markers may improve early detection and differential diagno...

Objectives: Traumatic brain injury (TBI) involves axonal injury and accumulation of pathological protein aggregates including amyloid-b (Ab) and hyperphosphorylated tau (p-tau). Biomarker analysis of tau and Ab concentrations in cerebrospinal fluid (CSF) may be an objective marker of cognitive status after TBI. The goal of the current study was to analyze tau and Ab 40–42 in a cohort of militar...

Abstract Introduction We determined whether slow wave sleep is associated with plasma levels of Aβ40, Aβ42, Aβ42/Aβ40, Tau, tau/Aβ42 and NfL this relationship differed between Blacks/African-Americans non-Hispanic Whites. Methods This was a cross-sectional analysis baseline data from 171 community-dwelling cognitively normal older-adults, participating in ongoing NYU studies on memory, aging. N...

we first characterize $tau$-complemented modules with relative (pre)-covers. we also introduce an extending module relative to $tau$-pure submodules on a hereditary torsion theory $tau$ and give its relationship with $tau$-complemented modules.