On Tetrahedralisations Containing Knotted and Linked Line Segments

This paper considers a set of twisted line segments in 3d such that they form a knot (a closed curve) or a link of two closed curves. Such line segments appear on the boundary of a family of 3d indecomposable polyhedra (like the Schönhardt polyhedron) whose interior cannot be tetrahedralised without additional vertices added. On the other hand, a 3d (non-convex) polyhedron whose boundary contains such line segments may still be decomposable as long as the twist is not too large. It is therefore interesting to consider the question: when there exists a tetrahedralisation contains a given set of knotted or linked line segments? In this paper, we studied a simplified question with the assumption that all vertices of the line segments are in convex position. It is straightforward to show that no tetrahedralisation of 6 vertices (the three-line-segments case) can contain a trefoil knot. Things become interesting when the number of line segments increases. Since it is necessary to create new interior edges to form a tetrahedralisation. We provided a detailed analysis for the case of a set of 4 line segments. This leads to a crucial condition on the orientation of pairs of new interior edges which determines whether this set is decomposable or not. We then prove a new theorem about the decomposability for a set of n (n ≥ 3) knotted or linked line segments. This theorem implies that the family of polyhedra generalised from the Schonhardt polyhedron by Rambau [1] are all indecomposable

On Tetrahedralisations Containing Knotted and Linked Line Segments

This paper considers a set of twisted line segments in 3d such that they form a knot (a closed curve) or a link of two closed curves. Such line segments appear on the boundary of a family of 3d indecomposable polyhedra (like the Schönhardt polyhedron) whose interior cannot be tetrahedralised without additional vertices added. On the other hand, a 3d (non-convex) polyhedron whose boundary contains such line segments may still be decomposable as long as the twist is not too large. It is therefore interesting to consider the question: when there exists a tetrahedralisation contains a given set of knotted or linked line segments? In this paper, we studied a simplified question with the assumption that all vertices of the line segments are in convex position. It is straightforward to show that no tetrahedralisation of 6 vertices (the three-line-segments case) can contain a trefoil knot. Things become interesting when the number of line segments increases. Since it is necessary to create new interior edges to form a tetrahedralisation. We provided a detailed analysis for the case of a set of 4 line segments. This leads to a crucial condition on the orientation of pairs of new interior edges which determines whether this set is decomposable or not. We then prove a new theorem about the decomposability for a set of n (n ≥ 3) knotted or linked line segments. This theorem implies that the family of polyhedra generalised from the Schonhardt polyhedron by Rambau [1] are all indecomposable

Loss of FKBP5 Affects Neuron Synaptic Plasticity: An Electrophysiology Insight

FKBP5 (FKBP51) is a glucocorticoid receptor (GR) binding protein, which acts as a co-chaperone of heat shock protein 90 (HSP90) and negatively regulates GR. Its association with mental disorders has been identified, but its function in disease development is largely unknown. Long-term potentiation (LTP) is a functional measurement of neuronal connection and communication, and is considered one of the major cellular mechanisms that underlies learning and memory, and is disrupted in many mental diseases. In this study, a reduction in LTP in Fkbp5 knockout (KO) mice was observed when compared to WT mice, which correlated with changes to the glutamatergic and GABAergic signaling pathways. The frequency of mEPSCs was decreased in KO hippocampus, indicating a decrease in excitatory synaptic activity. While no differences were found in levels of glutamate between KO and WT, a reduction was observed in the expression of excitatory glutamate receptors (NMDAR1, NMDAR2B and AMPAR), which initiate and maintain LTP. The expression of the inhibitory neurotransmitter GABA was found to be enhanced in Fkbp5 KO hippocampus. Further investigation suggested that increased expression of GAD65, but not GAD67, accounted for this increase. Additionally, a functional GABAergic alteration was observed in the form of increased mIPSC frequency in the KO hippocampus, indicating an increase in presynaptic GABA release. Our findings uncover a novel role for Fkbp5 in neuronal synaptic plasticity and highlight the value of Fkbp5 KO as a model for studying its role in neurological function and disease development

Catalytic Oxidation of Chlorobenzene over Pd-TiO2 /Pd-Ce/TiO2 Catalysts

A series of Pd-TiO2/Pd-Ce/TiO2 catalysts were prepared by an equal volume impregnation method. The effects of different Pd loadings on the catalytic activity of chlorobenzene (CB) were investigated, and the results showed that the activity of the 0.2%-0.3% Pd/TiO2 catalyst was optimal. The effect of Ce doping enhanced the catalytic activity of the 0.2% Pd-0.5% Ce/TiO2 catalyst. The characterization of the catalysts using BET, TEM, H2-TPR, and O2-TPD showed that the oxidation capacity was enhanced, and the catalytic oxidation efficiency was improved due to the addition of Ce. Ion chromatography and Gas Chromatography-Mass Spectrometer results showed that small amounts of dichlorobenzene (DCB) and trichlorobenzene (TCB) were formed during the decomposition of CB. The results also indicated that the calcination temperature greatly influenced the catalyst activity and a calcination temperature of 550 °C was the best. The concentration of CB affected its decomposition, but gas hourly space velocity had little effect. H2-TPR indicated strong metal–support interactions and increased dispersion of PdO in the presence of Ce. HRTEM data showed PdO with a characteristic spacing of 0.26 nm in both 0.2% Pd /TiO2 and 0.2% Pd-0.5% Ce/TiO2 catalysts. The average sizes of PdO nanoparticles in the 0.2% Pd/TiO2 and 0.2% Pd-0.5% Ce/TiO2 samples were 5.8 and 4.7 nm, respectively. The PdO particles were also deposited on the support and they were separated from each other in both catalysts

Understanding steric hindrance effect of solvent molecule in localized high-concentration electrolyte for lithium metal batteries

Abstract High energy density lithium metal batteries (LMBs) have garnered significant research interests in the past decades. However, the growth of lithium dendrites and the low Coulombic efficiency (CE) of Li metal anode pose significant challenges for the development of LMBs. Herein, we report a triethyl orthoformate (TEOF)-based localized high-concentration electrolyte (LHCE) that facilitates a highly reversible Li metal anode with dendrite-free deposition morphologies and an average Coulombic efficiency of 99.1% for 450 cycles. Mechanistic study reveal that the steric hindrance caused by the terminal ethyl groups in the TEOF solvent molecule results in a weak solvating ability, leading to the formation of anion-dominant solvation structures. The anion-dominant solvation sheaths play an essential role in the formation of a LiF-rich solid-electrolyte interphase (SEI), which effectively suppresses the growth of Li dendrites. Furthermore, the TEOF-based electrolyte demonstrates the stable cycling of high-voltage Li||NMC811 cells. These results provide insights into understanding of steric hindrance effect on electrolyte solvation structure and offer valuable guidance for the design of electrolyte solvents in the development of lithium metal batteries