In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate  and $ (tau,sigma)$-Boolean  in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary  and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...

Tau proteins are abnormally aggregated in a range of neurodegenerative tauopathies including Alzheimer's disease (AD). Recently, tau has emerged as an extensively post-translationally modified protein, among which lysine acetylation is critical for normal tau function and its pathological aggregation. Here, we demonstrate that tau isoforms have different propensities to undergo lysine acetylati...

In Alzheimer's disease (AD), the mechanisms of neuronal loss remain largely unknown. Although tau pathology is closely correlated with neuronal loss, how its accumulation may lead to activation of neurotoxic pathways is unclear. Here we show that tau increased the levels of ubiquitinated proteins in the brain and triggered activation of the unfolded protein response (UPR). This suggested that t...

In this article, we design a novel linearized and momentum-preserving Fourier pseudo-spectral scheme to solve the Rosenau-Korteweg de Vries equation. With aid of new semi-norm equivalence between method finite difference method, prior bound numerical solution in discrete L ∞ $$ {L}^{\infty } -norm is obtained from momentum conservation law. Subsequently, based on energy solution, show that, wit...

The aberrant accumulation of tau protein is a pathological hallmark of a class of neurodegenerative diseases known as tauopathies, including Alzheimer's disease and related dementias. On the basis of previous observations that tau is a direct substrate of histone deacetylase 6 (HDAC6), we sought to map all HDAC6-responsive sites in tau and determine how acetylation in a site-specific manner aff...

The microtubule-associated protein tau is essential for microtubule stabilization in neuronal axons. Hyperphosphorylation and intracellular fibrillar formation of tau protein is a pathology found in Alzheimer's disease (AD) brains, and in a variety of neurodegenerative disorders referred to as 'taupathies'. In the present study, we investigated how brain-derived neurotrophic factor (BDNF), an e...

Activity-dependent neuroprotective protein (ADNP) differentially interacts with chromatin to regulate essential genes. Because complete ADNP deficiency is embryonic lethal, the outcome of partial ADNP deficiency was examined. ADNP(+/-) mice exhibited cognitive deficits, significant increases in phosphorylated tau, tangle-like structures, and neurodegeneration compared with ADNP(+/+) mice. Incre...