7 research outputs found
Characterization of lacunary I-convergent sequences in credibility space
No full textThis research paper aims to introduce the concept of lacunary ideal Cauchy sequences of fuzzy variables in a credibility space. We establish the interrelationships between this notion with lacunary ideal convergent sequences in the same structure from several aspects of credibility. Furthermore, we explore the concepts of strongly lacunary Cauchy, strongly I*-lacunary Cauchy, and strongly I-lacunary Cauchy sequences of fuzzy variables within the context of credibility. We also examine the interconnections between these concepts and analyze their relationships
Exploring Strongly Almost ?-Convergence of Fuzzy Variable Sequences via Orlicz Functions in Credibility Space
No full textThe research paper primarily focuses to extend the concepts of strongly almost convergence and statistically almost convergence by incorporating the concept of lambda-convergence for fuzzy variable sequences. Additionally, we aim to introduce new sequence spaces that are associated with the newly introduced conceptions in terms of an Orlicz mapping for these sequences. Furthermore, our goal is to propose and establish inclusion relations within these sequence spaces
Some Results on Statistically Pre-Cauchy Sequences of Fuzzy Variables Defined by Orlicz Functions in Credibility Space
No full textThis study introduces the concept of statistically pre-Cauchy sequences of fuzzy variables in five directions of credibility theory: almost surely, in measure, in mean, in distribution, and uniformly almost surely. However, the main focus is kept on statistically pre-Cauchy sequences in measure, in mean, and in distribution. Furthermore, a correlation between statistically pre-Cauchy sequences and statistically convergent sequences is established using fuzzy variables. Additionally, the exploration of statistically pre-Cauchy sequences of fuzzy variables is initiated through the application of Orlicz functions. The objective is to enhance the understanding of the statistical behavior and convergence properties of fuzzy variables in various credibility scenarios. © 2024 Elsevier B.V., All rights reserved
Influence of scandium on an Al-2% Si alloy processed by high-pressure torsion
No full textHigh-pressure torsion (HPT) was used to process Al–2% Si and Al–2% Si–0.25% Sc alloys for up to five turns and the mechanical properties of the processed materials were evaluated using the ball indentation technique (BIT). The results show that the presence of Al3Sc precipitates is effective in producing higher strength levels and greater grain refinement in the Al–2% Si–0.25% Sc alloy. The introduction of scandium reduces the grain size of the Al–2% Si alloy from not, vert, similar0.38 to not, vert, similar0.15 ?m after 5 turns of HPT and the corresponding maximum tensile strength is increased from not, vert, similar325 to not, vert, similar375 MPa. The grain and substructure formation in the Al–2% Si alloy is similar to aluminum with dislocation cell formation and a reasonably recovered microstructure whereas in the Al–2% Si–0.25% Sc alloy it is non-homogeneous with arrays of non-equilibrium boundaries and dislocation tangles within the grain
Computational analysis of p63 + nuclei distribution pattern by graph theoretic approach in an oral pre-cancer (sub-mucous fibrosis)
No full textBackground: Oral submucous fibrosis (OSF) is a pre-cancerous condition with features of chronic, inflammatory and progressive sub-epithelial fibrotic disorder of the buccal mucosa. In this study, malignant potentiality of OSF has been assessed by quantification of immunohistochemical expression of epithelial prime regulator-p63 molecule in correlation to its malignant (oral squamous cell carcinoma [OSCC] and normal counterpart [normal oral mucosa [NOM]). Attributes of spatial extent and distribution of p63 + expression in the epithelium have been investigated. Further, a correlated assessment of histopathological attributes inferred from H&E staining and their mathematical counterparts (molecular pathology of p63) have been proposed. The suggested analytical framework envisaged standardization of the immunohistochemistry evaluation procedure for the molecular marker, using computer-aided image analysis, toward enhancing its prognostic value. Subjects and Methods: In histopathologically confirmed OSF, OSCC and NOM tissue sections, p63 + nuclei were localized and segmented by identifying regional maxima in plateau-like intensity spatial profiles of nuclei. The clustered nuclei were localized and segmented by identifying concave points in the morphometry and by marker-controlled watersheds. Voronoi tessellations were constructed around nuclei centroids and mean values of spatial-relation metrics such as tessellation area, tessellation perimeter, roundness factor and disorder of the area were extracted. Morphology and extent of expression are characterized by area, diameter, perimeter, compactness, eccentricity and density, fraction of p63 + expression and expression distance of p63 + nuclei. Results: Correlative framework between histopathological features characterizing malignant potentiality and their quantitative p63 counterparts was developed. Statistical analyses of mathematical trends were evaluated between different biologically relevant combinations: (i) NOM to oral submucous fibrosis without dysplasia (OSFWT) (ii) NOM to oral submucous fibrosis with dysplasia (OSFWD) (iii) OSFWT-OSFWD (iv) OSFWD-OSCC. Significant histopathogical correlates and their corroborative mathematical features, inferred from p63 staining, were also investigated into. Conclusion: Quantitative assessment and correlative analysis identified mathematical features related to hyperplasia, cellular stratification, differentiation and maturation, shape and size, nuclear crowding and nucleocytoplasmic ratio. It is envisaged that this approach for analyzing the p63 expression and its distribution pattern may help to establish it as a quantitative bio-marker to predict the malignant potentiality and progression. The proposed work would be a value addition to the gold standard by incorporating an observer-independent framework for the associated molecular pathology
Computational analysis of p63+ nuclei distribution pattern by graph theoretic approach in an oral pre-cancer (sub-mucous fibrosis)
No full textRobust estimation of bacterial cell count from optical density
No full textOptical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data
