Rough Set Model based on Uncertain Measure

Abstract Probabilistic rough set model based on probability measure is a new rough set model to deal with uncertain information systems. Uncertain measure is a generalization of probability measure. Based on the fundamental knowledge of rough set model and uncertain measure, a rough set model based on uncertain measure is established. Furthermore, by comparative study of the lower approximation and upper approximation, it is true that the rough set model based on uncertain measure is an extension of the probabilistic rough set model

Extremely large magnetoresistance in topologically trivial semimetal α\alpha-WP2_2

Extremely large magnetoresistance (XMR) was recently discovered in many non-magnetic materials, while its underlying mechanism remains poorly understood due to the complex electronic structure of these materials. Here, we report an investigation of the $\alpha$-phase WP$_2$, a topologically trivial semimetal with monoclinic crystal structure (C2/m), which contrasts to the recently discovered robust type-II Weyl semimetal phase in $\beta$-WP$_2$. We found that $\alpha$-WP$_2$ exhibits almost all the characteristics of XMR materials: the near-quadratic field dependence of MR, a field-induced up-turn in resistivity following by a plateau at low temperature, which can be understood by the compensation effect, and high mobility of carriers confirmed by our Hall effect measurements. It was also found that the normalized MRs under different magnetic fields has the same temperature dependence in $\alpha$-WP$_2$, the Kohler scaling law can describe the MR data in a wide temperature range, and there is no obvious change in the anisotropic parameter $\gamma$ value with temperature. The resistance polar diagram has a peanut shape when field is rotated in $\textit{ac}$ plane, which can be understood by the anisotropy of Fermi surface. These results indicate that both field-induced-gap and temperature-induced Lifshitz transition are not the origin of up-turn in resistivity in the $\alpha$-WP$_2$ semimetal. Our findings establish $\alpha$-WP$_2$ as a new reference material for exploring the XMR phenomena.Comment: 18 pages, 12 figure

Projective Quasiparticle Interference of a Single Scatterer to Analyze the Electronic Band Structure of ZrSiS

Quasiparticle interference (QPI) of the electronic states has been widely applied in scanning tunneling microscopy (STM) to analyze the electronic band structure of materials. Single-defect induced QPI reveals defect-dependent interaction between a single atomic defect and electronic states, which deserves special attention. Due to the weak signal of single-defect-induced QPI, the signal-to-noise ratio (SNR) is relatively low in a standard two-dimensional QPI measurement. In this paper, we introduce a projective quasiparticle interference (PQPI) method, in which a one-dimensional measurement is taken along high-symmetry directions centered on a specified defect. We apply the PQPI method to a topological nodal-line semimetal ZrSiS. We focus on two special types of atomic defects that scatter the surface and bulk electronic bands. With enhanced SNR in PQPI, the energy dispersions are clearly resolved along high symmetry directions. We discuss the defect-dependent scattering of bulk bands with the non-symmorphic symmetry-enforced selection rules. Furthermore, an energy shift of the surface floating band is observed and a new branch of energy dispersion (q6) is resolved. This PQPI method can be applied to other complex materials to explore defect-dependent interactions in the future.Comment: 21 pages, 5 figures, supplementary 3 pages, 2 figure

Superconductivity in the nodal-line compound La3_3Pt3_3Bi4_4

Owing to the specific topological states in nodal-line semimetals, novel topological superconductivity is expected to emerge in these systems. In this letter, by combination of the first-principles calculations and resistivity, susceptibility and specific heat measurements, we demonstrate that La$_3$Pt$_3$Bi$_4$ is a topologically nontrivial nodal-ring semimetal protected by the gliding-mirror symmetry even in the presence of spin-orbit coupling. Meanwhile, we discover bulk superconductivity with a transition temperature of $\sim$1.1 K, and an upper critical field of $\sim$0.41 T. These findings demonstrate that La$_3$Pt$_3$Bi$_4$ provides a material platform for studying novel superconductivity in the nodal-ring system

Identification of cuproptosis-related biomarkers and analysis of immune infiltration in allograft lung ischemia-reperfusion injury

Background: Allograft lung ischemia-reperfusion injury (ALIRI) is a major cause of early primary graft dysfunction and poor long-term survival after lung transplantation (LTx); however, its pathogenesis has not been fully elucidated. Cell death is a mechanism underlying ALIRI. Cuproptosis is a recently discovered form of programmed cell death. To date, no studies have been conducted on the mechanisms by which cuproptosis-related genes (CRGs) regulate ALIRI. Therefore, we explored the potential biomarkers related to cuproptosis to provide new insights into the treatment of ALIRI.Materials and methods: Datasets containing pre- and post-LTx lung biopsy samples and CRGs were obtained from the GEO database and previous studies. We identified differentially expressed CRGs (DE-CRGs) and performed functional analyses. Biomarker genes were selected using three machine learning algorithms. The ROC curve and logistic regression model (LRM) of these biomarkers were constructed. CIBERSORT was used to calculate the number of infiltrating immune cells pre- and post-LTx, and the correlation between these biomarkers and immune cells was analyzed. A competing endogenous RNA network was constructed using these biomarkers. Finally, the biomarkers were verified in a validation set and a rat LTx model using qRT-PCR and Western blotting.Results: Fifteen DE-CRGs were identified. GO analysis revealed that DE-CRGs were significantly enriched in the mitochondrial acetyl-CoA biosynthetic process from pyruvate, protein lipoylation, the tricarboxylic acid (TCA) cycle, and copper-transporting ATPase activity. KEGG enrichment analysis showed that the DE-CRGs were mainly enriched in metabolic pathways, carbon metabolism, and the TCA cycle. NFE2L2, NLRP3, LIPT1, and MTF1 were identified as potential biomarker genes. The AUC of the ROC curve for each biomarker was greater than 0.8, and the LRM provided an excellent classifier with an AUC of 0.96. These biomarkers were validated in another dataset and a rat LTx model, which exhibited good performance. In the CIBERSORT analysis, differentially expressed immune cells were identified, and the biomarkers were associated with the immune cells.Conclusion:NFE2L2, NLRP3, LIPT1, and MTF1 may serve as predictors of cuproptosis and play an important role in the pathogenesis of cuproptosis in ALIRI