ABSTRACT
In this study, we address three key challenges in photonic crystals: modeling of isolated flat bands, electric field prediction, and band separation in dispersion relations. Using twisted square Bravais lattices at specific angles, we create Bravais-Moiré photonic crystals exhibiting unique characteristics. These include band pairing and parallelism in certain Brillouin zones, enabling predictable electric field behavior and identification of isolated, flat band pairs within extensive band gaps. We apply advanced Shape theory-based classification methods for precise band separation, offering significant contributions to photonics research and light manipulation applications.
ABSTRACT
Alzheimer's disease (AD) is the most common cause of dementia among older adults. APOE3 Christchurch (R136S, APOE3Ch ) variant homozygosity was reported in an individual with extreme resistance to autosomal dominant AD due to the PSEN1 E280A mutation. This subject had a delayed clinical age at onset and resistance to tauopathy and neurodegeneration despite extremely high amyloid plaque burden. We established induced pluripotent stem (iPS) cell-derived cerebral organoids from this resistant case and from a non-protected kindred control (with PSEN1 E280A and APOE3/3 ). We used CRISPR/Cas9 gene editing to successfully remove the APOE3Ch to wild type in iPS cells from the protected case and to introduce the APOE3Ch as homozygote in iPS cells from the non-protected case to examine causality. We found significant reduction of tau phosphorylation (pTau 202/205 and pTau396) in cerebral organoids with the APOE3Ch variant, consistent with the strikingly reduced tau pathology found in the resistant case. We identified Cadherin and Wnt pathways as signaling mechanisms regulated by the APOE3Ch variant through single cell RNA sequencing in cerebral organoids. We also identified elevated ß-catenin protein, a regulator of tau phosphorylation, as a candidate mediator of APOE3Ch resistance to tauopathy. Our findings show that APOE3Ch is necessary and sufficient to confer resistance to tauopathy in an experimental ex-vivo model establishing a foundation for the development of novel, protected case-inspired therapeutics for tauopathies, including Alzheimer's.
ABSTRACT
Combined EEG and PET techniques show three activation levels of the cortex: deep sleep, relaxed state and alert. We propose, correspondingly, that a cortical module can be in one of three equivalent states: inactivated, pre-activated, and activated. Neuroimaging techniques can show activated cortical regions in detail. However, the functional connections (FCs) among them are not shown in the image. They can be found by EEG-coherence functions. This can be seen as a 'three-level- cortical graph'. A cortical graph is a mathematical representation where the cortical units (modules or regions) are represented by points (nodes) and the FCs are represented by lines between these points. At the upper level, activated modules can establish FCs implying high electrical coherence (they are the winners of a competitive process between preactivated modules at the middle level). We propose that, during alert state, the activated nodes and the dynamic switching among them always form connected graphs. It means that, for any possible configuration, there always exists a path (direct or indirect) between any couple of nodes. We base our view on (1) analysis of simple tasks by PET; (2) the existence of coordinated behavior in normal subjects; (3) cortical topologies previously proposed; and (4) computer simulations of cortico-cortical connections. We also suggest that disengaged (nonconnected) cortical graphs, produce 'functional disconnection syndromes' which cause some symptoms in schizophrenia, and Alzheimer disease.
