A Generalization of Noncommuting Graph via Automorphisms of a Group

Let G be a group. By using a family 𝒜 of subsets of automorphisms of G, we introduced a simple graph Γ_𝒜(G), which is a generalization of the non-commuting graph. In this paper, we study the combinatorial properties of Γ_𝒜(G).     

Theoretical Investigation of Optical Bistability and Multistability Via Spontaneously Generated Coherence in Four-Level Rydberg Atoms

In this paper, we have suggested a configuration based on Rydberg atoms for adjusting properties of optical bistability (OB) and optical multistability (OM) via spontaneously generated coherence (SGC) in a unidirectional ring cavity. The Rydberg atoms consist of four energy levels interacts by a weak probe and a strong coupling fields, respectively. We have found that due to presence of SGC, threshold of OB and OM can be controlled when the strong light coupled the intermediate levels to the Rydberg state.

     

1H NMR‐based metabolomics exploring urinary biomarkers correlated with proteinuria in focal segmental glomerulosclerosis: a pilot study

Focal segmental glomerulosclerosis (FSGS) is a common glomerulonephritis, and its rates of occurrence are increasing worldwide. Proteinuria is a clinical defining feature of FSGS which correlates with the severity of podocyte injury in patients with nephrotic‐range protein excretion. Metabolite biomarkers corresponding with the level of proteinuria could be considered as non‐invasive complementary prognostic factors to proteinuria. The urine samples of 15 patients (n = 6 women and n = 9 men) with biopsy‐proven FSGS were collected and subjected to nuclear magnetic resonance (NMR) analysis for metabolite profiling. Multivariate statistical analyses, including principal component analysis and orthogonal projection to latent structure discriminant analysis, were applied to construct a predictive model based on patients with proteinuria >3000 mg/day and <3000 mg/day. In addition, random forest was performed to predict differential metabolites, and pathway analysis was performed to find the defective pathways responsible for proteinuria. Ten metabolites, significant in both statistical methods (orthogonal projection to latent structure discriminant analysis and random forest), were considered as prognostic biomarkers for FSGS: citrulline, dimethylamine, proline, acetoacetate, alpha‐ketoisovaleric acid, valine, isobutyrate, D‐Palmitylcarnitine, histidine, and N‐methylnicotinamide. Pathway analysis revealed impairment of the branched‐chain amino acid degradation pathways in patients with massive proteinuria. This study shows that metabolomics can reveal the molecular changes corresponding with disease progression in patients with FSGS and provide a new insight for pathogenic pathways. Copyright © 2016 John Wiley & Sons, Ltd.     

1 H NMR‐based metabolomics study for identifying urinary biomarkers and perturbed metabolic pathways associated with severity of IgA nephropathy: a pilot study

The severity of IgA nephropathy (IgAN), the most common primary glomerulonephritis, is judged on the basis of histologic and clinical features. A limited number of studies have considered molecular signature of IgAN for this issue, and no reliable biomarkers have been presented non‐invasively for use in patient evaluations. This study aims to identify metabolite markers excreted in the urine and impaired pathways that are associated with a known marker of severity (proteinuria) to predict mild and severe stages of IgAN. Urine samples were analysed using nuclear magnetic resonance from biopsy‐proven IgAN patients at mild and severe stages. Multivariate statistical analysis and pathway analysis were performed. The most changed metabolites were acetoacetate, hypotaurine, homocysteine, L‐kynurenine and phenylalanine. Nine metabolites were positively correlated with proteinuria, including mesaconic acid, trans‐cinnamic acid, fumaric acid, 5‐thymidylic acid, anthranilic acid, indole, deoxyguanosine triphosphate, 13‐cis‐retinoic acid and nicotinamide riboside, while three metabolites were negatively correlated with proteinuria including acetoacetate, hypotaurine and hexanal. ‘Phenylalanine metabolism’ was the most significant pathway which was impaired in severe stage in comparison to mild stage of IgAN. This study indicates that nuclear magnetic resonance is a versatile technique that is capable of detecting metabolite biomarkers in combination with advanced multivariate statistical analysis. Copyright © 2017 John Wiley & Sons, Ltd.