Picture Fuzzy Threshold Graphs with Application in Medicine Replenishment

In this study, a novel concept of picture fuzzy threshold graph (PFTG) is introduced. It has been shown that PFTGs are free from alternating 4-cycle and it can be constructed by repeatedly adding a dominating or an isolated node. Several properties about PFTGs are discussed and obtained the results that every picture fuzzy graph (PFG) is equivalent to a PFTG under certain conditions. Also, the underlying crisp graph (UCG) of PFTG is a split graph (SG), and conversely, a given SG can be applied to constitute a PFTG. A PFTG can be decomposed in a unique way and it generates three distinct fuzzy threshold graphs (FTGs). Furthermore, two important parameters i.e., picture fuzzy (PF) threshold dimension (TD) and PF partition number (PN) of PFGs are defined. Several properties on TD and PN have also been discussed. Lastly, an application of these developed results are presented in controlling medicine resources.     

Differential Expression Analysis of Single-Cell RNA-Seq Data: Current Statistical Approaches and Outstanding Challenges

With the advent of single-cell RNA-sequencing (scRNA-seq), it is possible to measure the expression dynamics of genes at the single-cell level. Through scRNA-seq, a huge amount of expression data for several thousand(s) of genes over million(s) of cells are generated in a single experiment. Differential expression analysis is the primary downstream analysis of such data to identify gene markers for cell type detection and also provide inputs to other secondary analyses. Many statistical approaches for differential expression analysis have been reported in the literature. Therefore, we critically discuss the underlying statistical principles of the approaches and distinctly divide them into six major classes, i.e., generalized linear, generalized additive, Hurdle, mixture models, two-class parametric, and non-parametric approaches. We also succinctly discuss the limitations that are specific to each class of approaches, and how they are addressed by other subsequent classes of approach. A number of challenges are identified in this study that must be addressed to develop the next class of innovative approaches. Furthermore, we also emphasize the methodological challenges involved in differential expression analysis of scRNA-seq data that researchers must address to draw maximum benefit from this recent single-cell technology. This study will serve as a guide to genome researchers and experimental biologists to objectively select options for their analysis.     

Effect of Erosive Agents on Surface Characteristics of Nano-Fluorapatite Ceramic: An In-Vitro Study

Erosive beverages cause dissolution of natural teeth and intra-oral restorations, resulting in surface characteristic changes, particularly roughness and degradation. The purpose of this study was to evaluate the surface roughness and topography of a dental ceramic following immersion in locally available erosive solutions. A total of 160 disc specimens of a nano-fluorapatite type ceramic (12 mm diameter and 2 mm thickness) were fabricated and equally distributed into two groups (n = 80) and then evenly distributed among the following five testing groups (n = 16): lemon juice, citrate buffer solution, 4% acetic acid, soft cola drink, and distilled water which served as a control. The surface roughness (Ra) and topography were evaluated using a profilometer and scanning electron microscope at baseline, 24 h, 96 h, and 168 h respectively. Data were analyzed using ANOVA and Tukey’s multiple comparisons (p ≤ 0.05). Surface changes were observed upon exposure to all acidic beverages except distilled water. Amongst all immersion media, 4% acetic acid produced the most severe surface roughness across all time periods (i.e., baseline, 24 h, 96 h, and 168 h). A statistically significant difference in the surface roughness values between all immersion media and across all four time intervals was observed. Erosive agents had a negative effect on the surface roughness and topography of the tested ceramic. The surface roughness increased with increased storage time intervals.     

The Influence of the Flow-Pattern on Column Leaching Experiments: Formulation and Measurement by Radiotracer

The leaching of microconstituents from granular solid wastes is often studied by column experiments. The underlying assumption is that the flow is of the one-compartment or “backmix” type. The influence of small deviations from this ideal situation on the outcome of the leaching experiment depends slightly on the specific mass-transfer function of the trace involved. The deviation itself may be measured by a simple separate radiotracer experiment.     

A new class of interior solutions for a stress-energy tensor of Segré characteristic [111, 1]

The interior solutions of (the tetrad versions of) Einstein's field equations withT _AB having Segré characteristic [111, 1] (which has all four eigenvalues distinct), are investigated. For this purpose amixed method, which combines Synge'sg method andT method, is introduced. Some of the tetrad equations are solved for the metric functions while the remaining equations are used to define the corresponding components ofT _AB . As necessary conditions of the consistency of the mixed method the conservation equationsT ^AB _B =0 are explicitly verified. Several simplifications and analysis of some differential inequalities show the existence of a new class of solutions which, in addition to having Segré characteristic [111, 1], also satisfy the strong energy conditions of Hawking and Ellis.This Author is a member of the Theoretical Sciences Institute, Simon Fraser University, Burnaby, B.C., V5A 1S6, Canada.     

Algebra of charges in the supersymmetric nonlinear σ model

We examine the algebra of the nonlocal charges in the supersymmetric nonlinear σ model and show that they satisfy a nonlinear algebra at the tree-level. We also discuss other interesting questions like the transformation of these charges under a supersymmetry transformation and speculate that this algebra possibly continues to hold in the full quantum theory.