A Study of Neural Collapse Phenomenon: Grassmannian Frame, Symmetry, Generalization

In this paper, we extends original Neural Collapse Phenomenon by proving Generalized Neural Collapse hypothesis. We obtain Grassmannian Frame structure from the optimization and generalization of classification. This structure maximally separates features of every two classes on a sphere and does not require a larger feature dimension than the number of classes. Out of curiosity about the symmetry of Grassmannian Frame, we conduct experiments to explore if models with different Grassmannian Frames have different performance. As a result, we discover the Symmetric Generalization phenomenon. We provide a theorem to explain Symmetric Generalization of permutation. However, the question of why different directions of features can lead to such different generalization is still open for future investigation.Comment: 25 pages, 2 figure

Pressure induced self-doping and dependence of critical temperature in stoichiometry YBa2Cu3O6.95 predicted by first-principle and BVS calculations

This paper deals with the pressure effect on self-doping and critical temperature in optimum oxygen stoichiometry YBa2Cu3O6.95 of high temperature superconductor (HTS) based on a numerical study combined the first-principle with bond valence sum (BVS) calculations. The microscopic electronic properties and equilibrium ionic position configurations in the superconductor under external pressure are firstly calculated using the first-principle method. The results show that the apex oxygen in the cuprate superconductor shifts towards CuO2 plane due to pressure effect, and the minimum buckling angle of CuO2 plane is correlated with the maximum critical temperature. A BVS formalism is then utilized for evaluating the valences of all ions in the superconductor on the basis of the electronic and ionic properties and the hole concentration in both CuO2 plane and Cu-O chain are deduced. It demonstrates that the pressure-induced charge redistribution leads to a self-doping process of the hole-transfer into CuO2 plane from both Cu-O chain and Y site in the cuprate superconductor, which is the dominant mechanism of pressure effect on the superconductive properties. In order to quantitatively predict critical temperature profile of YBa2Cu3O6.95 under pressure, a modified formula describing pressure-induced charge transfer taking into account pressure dependence of the optimum hole concentration is developed. The predicted results exhibit good agreements with the experimental data in the literature, and the model parameters on the critical characteristics of the superconductor are discussed in details

Mitochondrial Ca²⁺ Homeostasis: Emerging Roles and Clinical Significance in Cardiac Remodeling

Mitochondria are the sites of oxidative metabolism in eukaryotes where the metabolites of sugars, fats, and amino acids are oxidized to harvest energy. Notably, mitochondria store Ca2+ and work in synergy with organelles such as the endoplasmic reticulum and extracellular matrix to control the dynamic balance of Ca2+ concentration in cells. Mitochondria are the vital organelles in heart tissue. Mitochondrial Ca2+ homeostasis is particularly important for maintaining the physiological and pathological mechanisms of the heart. Mitochondrial Ca2+ homeostasis plays a key role in the regulation of cardiac energy metabolism, mechanisms of death, oxygen free radical production, and autophagy. The imbalance of mitochondrial Ca2+ balance is closely associated with cardiac remodeling. The mitochondrial Ca2+ uniporter (mtCU) protein complex is responsible for the uptake and release of mitochondrial Ca2+ and regulation of Ca2+ homeostasis in mitochondria and consequently, in cells. This review summarizes the mechanisms of mitochondrial Ca2+ homeostasis in physiological and pathological cardiac remodeling and the regulatory effects of the mitochondrial calcium regulatory complex on cardiac energy metabolism, cell death, and autophagy, and also provides the theoretical basis for mitochondrial Ca2+ as a novel target for the treatment of cardiovascular diseases

First-principles study on elastic and superconducting properties of Nb3Sn and Nb3Al under hydrostatic pressure

The low temperature superconducting materials, such as Nb3Sn and Nb3Al, have similar crystal structures and elastic properties. However, their critical-temperature degradations always show the distinct way under mechanical stresses. In this study, first-principles calculations for the low temperature superconductors based on plane-wave pseudo-potential density functional theory within the generalized gradient approximation are implemented, and the elastic moduli of Nb3Sn and Nb3Al and those superconductivities in the presence of hydrostatic pressure are evaluated. The Debye temperatures are obtained by the bulk moduli and shear moduli of superconducting materials. The MacMillan equation is further used to acquire the critical temperatures of Nb3Sn and Nb3Al under different hydrostatic pressures. It is found that the elastic constants and bulk moduli of the low temperature superconductors are enhanced by the applied hydrostatic pressure, while the critical temperatures usually are decreased with the pressure. Additionally, the decrease of critical-temperature for Nb3Sn is more sensitive to the hydrostatic pressure than the one for Nb3Al. The prediction results show good agreement with the experimental results in the literatures qualitatively

Investigations on exchange interactions and Curie temperatures of Zr2CoZ compounds by using first-principles and Monte Carlo calculations

We systematically study the electronic and magnetic properties of Zr2CoZ (Z = Al, Ga, In, Tl, Si, Ge, Sn, Pb) compounds by using the first-principle calculations, and further focus on exploring their exchange interactions and Curie temperatures. Results exhibit that Zr2CoGa, Zr2CoIn and Zr2CoTl compounds show a high spin polarization. Moreover, the Heisenberg calculations imply that the Zr(A)-Zr(B), Zr(A)-Zr(A) and Zr(A)-Co(C) exchanges in interactions significantly affect the Curie temperature. In contrast, the Zr(B)-Zr(B), Zr(B)-Co(C) and Co(C)-Co(C) exchanges almost are limited to 15 meV in all cases. Based on these calculated exchange coupling parameters, Curie temperatures are evaluated by adopting the mean field approximation and Monte Carlo simulation, it is found that the Curie temperatures of Zr2CoZ (Z = Al, Ga, In, Tl, Sn, Pb) are noticeably higher than room temperature, indicating that they are promising candidates for spintronics applications

The Role and Molecular Mechanism of Non-Coding RNAs in Pathological Cardiac Remodeling

Non-coding RNAs (ncRNAs) are a class of RNA molecules that do not encode proteins. Studies show that ncRNAs are not only involved in cell proliferation, apoptosis, differentiation, metabolism and other physiological processes, but also involved in the pathogenesis of diseases. Cardiac remodeling is the main pathological basis of a variety of cardiovascular diseases. Many studies have shown that the occurrence and development of cardiac remodeling are closely related with the regulation of ncRNAs. Recent research of ncRNAs in heart disease has achieved rapid development. Thus, we summarize here the latest research progress and mainly the molecular mechanism of ncRNAs, including microRNAs (miRNAs), long non-coding RNAs (lncRNAs) and circular RNAs (circRNAs), in cardiac remodeling, aiming to look for new targets for heart disease treatment

MORF2-mediated plastidial retrograde signaling is involved in stress response and skotomorphogenesis beyond RNA editing

Retrograde signaling modulates the expression of nuclear genome-encoded organelle proteins to adjust organelle function in response to environmental cues. MULTIPLE ORGANELLAR RNA EDITING FACTOR 2 (MORF2) was initially recognized as a plastidial RNA-editing factor but recently shown to interact with GUN1. Given the central role of GUN1 in chloroplast retrograde signaling and the unviable phenotype of morf2 mutants that is inconsistent with many viable mutants involved in RNA editing, we hypothesized that MORF2 has functions either dosage dependent or beyond RNA editing. Using an inducible Clustered Interspaced Short Palindromic Repeat interference (iCRISPRi) approach, we were able to reduce the MORF2 transcripts in a controlled manner. In addition to MORF2-dosage dependent RNA-editing errors, we discovered that reducing MORF2 by iCRISPRi stimulated the expression of stress responsive genes, triggered plastidial retrograde signaling, repressed ethylene signaling and skotomorphogenesis, and increased accumulation of hydrogen peroxide. These findings along with previous discoveries suggest that MORF2 is an effective regulator involved in plastidial metabolic pathways whose reduction can readily activate multiple retrograde signaling molecules possibly involving reactive oxygen species to adjust plant growth. In addition, our newly developed iCRISPRi approach provided a novel genetic tool for quantitative reverse genetics studies on hub genes in plants

Atomic-Scale Imaging of Organic-Inorganic Hybrid Perovskite Using Transmission Electron Microscope

Transmission electron microscope (TEM) is thought as one powerful tool to imaging the atomic-level structure of organic inorganic hybrid perovskite (OIHP) materials, which provides valuable and essential guidance toward high performance OIHP-related devices. However, these OIHPs exhibit poor electron beam stability, severely limiting their practical applications in TEM. Here in this article, the application of TEM to obtain atomic-scale image of OIHPs, main obstacles in identifying the degradation product and future prospects of TEM in the characterization of OIHP materials are reviewed and presented. Three potential strategies (sample protection, low temperature technology, and low-dose technologies) are also proposed to overcome the current drawback of TEM technology

Thermal characteristics analysis of a novel 3-DOF deflection type PM motor

Concerning the problem of the thermal safety and thermal stability of a novel 3-DOF deflection type PM motor, the thermal characteristics of this motor are analyzed. The heat production of this novel motor working in the rated and overload conditions is simulated for temperature field using finite element analysis software, and the motor's temperature contours under different operating conditions are derived. The research results validate the rationality of the structure design of this proposed novel motor, which provides a reference for the structure optimization and performance indicator improvement of this kind of motor