Mean Labeling Research Articles

Gamified Crowdsourcing as a Novel Approach to Lung Ultrasound Data Set Labeling: Prospective Analysis.

Machine learning (ML) models can yield faster and more accurate medical diagnoses; however, developing ML models is limited by a lack of high-quality labeled training data. Crowdsourced labeling is a potential solution but can be constrained by concerns about label quality. This study aims to examine whether a gamified crowdsourcing platform with continuous performance assessment, user feedback, and performance-based incentives could produce expert-quality labels on medical imaging data. In this diagnostic comparison study, 2384 lung ultrasound clips were retrospectively collected from 203 emergency department patients. A total of 6 lung ultrasound experts classified 393 of these clips as having no B-lines, one or more discrete B-lines, or confluent B-lines to create 2 sets of reference standard data sets (195 training clips and 198 test clips). Sets were respectively used to (1) train users on a gamified crowdsourcing platform and (2) compare the concordance of the resulting crowd labels to the concordance of individual experts to reference standards. Crowd opinions were sourced from DiagnosUs (Centaur Labs) iOS app users over 8 days, filtered based on past performance, aggregated using majority rule, and analyzed for label concordance compared with a hold-out test set of expert-labeled clips. The primary outcome was comparing the labeling concordance of collated crowd opinions to trained experts in classifying B-lines on lung ultrasound clips. Our clinical data set included patients with a mean age of 60.0 (SD 19.0) years; 105 (51.7%) patients were female and 114 (56.1%) patients were White. Over the 195 training clips, the expert-consensus label distribution was 114 (58%) no B-lines, 56 (29%) discrete B-lines, and 25 (13%) confluent B-lines. Over the 198 test clips, expert-consensus label distribution was 138 (70%) no B-lines, 36 (18%) discrete B-lines, and 24 (12%) confluent B-lines. In total, 99,238 opinions were collected from 426 unique users. On a test set of 198 clips, the mean labeling concordance of individual experts relative to the reference standard was 85.0% (SE 2.0), compared with 87.9% crowdsourced label concordance (P=.15). When individual experts' opinions were compared with reference standard labels created by majority vote excluding their own opinion, crowd concordance was higher than the mean concordance of individual experts to reference standards (87.4% vs 80.8%, SE 1.6 for expert concordance; P<.001). Clips with discrete B-lines had the most disagreement from both the crowd consensus and individual experts with the expert consensus. Using randomly sampled subsets of crowd opinions, 7 quality-filtered opinions were sufficient to achieve near the maximum crowd concordance. Crowdsourced labels for B-line classification on lung ultrasound clips via a gamified approach achieved expert-level accuracy. This suggests a strategic role for gamified crowdsourcing in efficiently generating labeled image data sets for training ML systems.

An Application on Harmonic Mean Labeling of Variations in Triangular Snake Graphs

A graph G with p vertices and q edges is called a harmonic mean(HM) labeling if it is possible to label the vertices x∈v with distinct labels ρ(x) from {1,2,⋯,q+1} in such a way that each edge e=ab is labeled with ρ(ab)=⌈(2ρ(a)ρ(b))/(ρ(a)+ρ(b))⌉ or ⌊(2ρ(a)ρ(b))/(ρ(a)+ρ(b))⌋ then the edge labels are distinct.In this case ρ is called Harmonic mean(HM) labeling of G. In this paper we introduce new graphs obtained from triangular snake graph TS_n such as TS_n∘K_1, and prove that they are Harmonic Mean labeling graphs.

Radio Contra Harmonic Mean Number of Graphs

Objectives: To explore the least upper bound of graphs by radio contra harmonic labeling. Methods: Contra harmonic mean function or , radio mean labeling condition and radio harmonic mean labeling are used. Findings: Here we introduce radio contra harmonic mean labeling and its least upper bound, designated as radio contra harmonic mean number, by formulating the constraints. Novelty: Based on radio mean labeling and contra harmonic mean labeling, the new concept of radio contra harmonic mean labeling was established. The bounds of some special graphs are encountered here. This kind of labeling is employed in secure communication networks and is also applicable in X-rays, crystallography, coding theory, computing etc. Keywords: Radio contra harmonic mean labeling, rchmn (G), Order, Diameter, Smallest span

Further investigation on the super classical mean labeling of graphs obtained from paths

Consider the graph G, with the injection Ω from node set to the first p + q natural numbers. Let us assume that the ceiling function of the classical average of the node labels of the end nodes of each link is the induced link assignment Ω *. If the union of range of Ω of node set and the range of Ω * of link set is all the first p + q natural numbers, then Ω is called a classical mean labeling. A super classical mean graph is a graph with super classical mean labeling. In this research effort, we attempted to address the super classical meanness of graphs generated by paths and those formed by the union of two graphs.

Evaluation of Cytotoxic T Lymphocytes and Natural Killer Cell Distribution in Oral Squamous Cell Carcinoma and Oral Epithelial Dysplasia: An Immunohistochemical Study.

Background The tumor microenvironment comprises stromal cells, a few immune cells, vascular channels, and an extracellular matrix. The immune cells play a pivotal role in arresting the development of various tumors by identifying and killing the abnormal tumor cells. These immune cells with cytotoxic function include the natural killer (NK) cells and CD8+ T lymphocytes. Human NK cells express the cell surface marker CD57 and can be identified by using monoclonal antibodies. CD8+ cytotoxic T cells are a critical subpopulation of T cells and are important mediators of adaptive immunity. The anti-tumor immunity is important to assess the prognosis of tumors and develop new therapies. This study aimed to evaluate the immunohistochemical expression of CD8 and CD57 immune cells in oral squamous cell carcinoma (OSCC), oral epithelial dysplasia (OED), and normal oral mucosa. Methodology Clinically diagnosed and histopathologically confirmed cases of OSCC (n = 22), oral leukoplakia with OED (n = 22), and normal oral mucosa (n = 22) comprised the study groups. The tissue sections were subjected to immunohistochemical analysis for CD8 and CD57 expression by calculation of the mean labeling index. The results were statistically analyzed using a one-way analysis of variance, Bonferroni multiple comparison test, and Student's t-test. SPSS software version 20.0 (IBM Corp., Armonk, NY, USA) was used for the statistical analysis, and the significance level was set at 0.05. Results An overall statistically significant difference was obtained in the number of CD8+ T lymphocyte cells and CD57+ NK cells when compared between OSCC, OED, and normal oral mucosa (p = 0.01). Variations in the number of CD8+ T lymphocyte cells and CD57+ NK cells were observed when a comparison was made between OED and OSCC and between OSCC and normal mucosal samples (p = 0.01). The study results showed that the mean labeling index of CD8 and CD57 increased in OSCC when compared to OED and normal mucosa (p = 0.01). Conclusions Samples of OED with moderate or severe dysplasia and samples of OSCC were accompanied by a higher level of infiltrating immune cells such as T cells, B cells, NK cells, and macrophages when compared to normal mucosa. The results suggested that the expression of CD8 and CD57 cells increased from normal mucosa to OED and the highest expression was found in OSCC. CD8 and CD57 could be used as surrogate markers to assess the malignant potential of the lesion and to determine the prognosis of patients with oral cancer.

Even vertex odd mean labeling of uniform theta graphs

Let $G$ be a graph with $p$ vertices and $q$ edges. A total graph labeling $ f:V(G)\bigcup E(G)\rightarrow \{0,1,2,3,...,2q\}$ is called even vertex odd mean labeling of a graph $G$ if the vertices of the graph $G$ label by distinct even integers from the set $\{0,2,...,2q\}$ and the labels of the edges are defined as the mean of the labels of its end vertices and these labels are $2q-1$ distinct odd integers from the set $\{1,3,5,...,2q-1\}$. In this paper we investigate the even vertex odd mean labeling of uniform theta graphs.

Face Bimagic Mean Labeling of Herschel Graphs and Its Operations

A bijection ϕ: V(G)→{1,2, . . . , |V(G)|} is called a (1,0,0)-F-face bimagic mean labeling (FBMML) of G if the induced face labeling ϕ*(fi) = = = k1 or k2, constant. This work investigates the possibility of face bimagic mean labeling of a Herschel graph. Also, a study of face bimagic mean labeling during the process of fusion of vertices of degree 3 of a Herschel graph and the duplication of vertices by the edge of a Herschel graph is provided in this research paper.

Even vertex odd mean labeling of some graphs

This work introduces the principle of “an even point (vertex) odd ratio (mean) labeling, which is specifically applied to a graph ‘G’ consisting of ‘p’ vertices and ‘q’ edges. Even point (vertex) odd ratio (mean) labeling is exhibited by a graph G in the presence of an injectionbased function f : V of G → {0, 2, 4, ... 2q – 2, 2q} ensuring that the function derived from it (induced map) g* : E of G→{1, 3, 5, ... 2q – 1} specified by g* (uv) = g(u)+g(v)/2 is a bijection. Graphs that meet these criteria are termed an even point (vertex) odd ratio (mean) graphs. This paper explores the properties of an even point (vertex) odd ratio (mean) labeling in various graph structures.

Automatic Fingerprint Data Labeling Using WiFi Signal and Smartphone Camera for Indoor Positioning

WiFi fingerprinting has been one of the most practical approaches for implementing an indoor positioning system. However, the need to measure location labels for fingerprint data has hindered the deployment of WiFi fingerprint‐based positioning systems. To reduce the cost of location labeling, several methods for automatically labeling locations or bypassing location labeling have been proposed. However, these methods still need to measure location labels for partial fingerprint data, or the estimated location labels are inaccurate. In this paper, we propose Heimdall, an automatic fingerprint data labeling method using a smartphone camera and WiFi signal for an indoor positioning system. Since Heimdall utilizes camera geometry for accurate automatic labeling, it aims to find the location labels of unlabeled fingerprint data composed of WiFi received signal strengths (RSSs) and photos collected using smartphones in multiple reference points (RPs). Using structure from motion (SfM) with all photos in the unlabeled fingerprint dataset, the location and orientation of the cameras can be recovered on an arbitrary world coordinate system. However, the world coordinate system derived by SfM is warped. In other words, it is different from the real‐world coordinate system where we express the location labels since SfM has similarity ambiguity, including scale, rotation, and translation ambiguity. Heimdall finds the location labels by estimating and applying an unwarping transformation that removes those ambiguities. We use two types of geometric constraints for estimating the unwarping transformation. First, several geometric entities in the warped‐world coordinates and real‐world coordinates are extracted from the photos and prior information about the indoor layout. The unwarping transformation transforms the geometric entities in warped coordinates to those in real‐world coordinates. Second, we utilize the log‐distance pathloss model with RSSs to derive the constraint about distances from the location label to the access points. We construct the optimization problem subject to those constraints to estimate the unwarping transformation. To evaluate the performance of Heimdall, we performed several experiments. Heimdall yields a mean location labeling error of 0.12 m and a standard deviation of location labeling error of 0.06 m for the best case in the experiment. These results demonstrate that a fingerprint‐based indoor positioning system can use the location labels estimated by Heimdall without performance degradation.

Coding and Descriptions for the Subset of Twin Star Mean Labeling

Coding and Descriptions for the Subset of Twin Star Mean Labeling

Lucky edge geometric mean labeling of graphs and applications in electrical networks

A Lucky Edge Geometric Mean Labeling (LEGML) is a function μ that assigns the integers to the vertices of graph G such that for every edge as ‘{E}’, uv∈E(G) there exists a function μ*:E(G) → N is defined by μ* (uv) = √μ(u)μ(v) (or) √μ(u)μ(v) with the state that μ* (uv) ≠ μ* (vw) whenever {u} and {vw} have a common vertex as {v}. A minor number ‘k→ E = {1, 2, 3 … k} is the LEGML of G and is signified by h¢GM(G). A result that accepts LEGML is the Lucky Edge Geometric Mean Graph (LEGMG). The idea of the Graph Theory (GT) concept is fused into the Electric Circuit (EC), and the related complicated problems are transformed into graph model representation problems; as a result, the valuation method is simplified and optimized. Network analysis means finding the current or voltage in each branch. One application of GT is the representation of EC. An ‘E’ in a diagram can signify anything in an EC. Each part of the diagram can represent a port or a terminal in the EC. In this article, we have to investigate the Middle Graph (MG) of the star, the Total Graph (TG) of the star, and the central graph (CG) of the star, which accepts LEGML and LEGMG. This method also computes the power consumed by all the resistors of the EC by LEGML.

L-HILBERT MEAN LABELING OF SOME PATH RELATED GRAPHS

Let be a graph with vertices and edges. The th hilbert number is denoted by and is defined by where A - hilbert mean labeling is an injective function , where that induces a bijection defined by&#x0D; for all . A graph which admits such labeling is called a - hilbert mean graph. In this paper, a new type of labeling called - hilbert mean labeling is introduced and the path related graphs is studied.&#x0D; AMS Subject Classification – 05C78

Optimization of Automated Radiosynthesis of Gallium-68-Labeled PSMA11 with Two [68Ge]Ge/[68Ga]Ga Generators: Fractional Elution or Prepurification?

Prostate cancer is one of the most common forms of cancer in men. An imaging technique for its diagnosis is [68Ga]-prostate-specific membrane antigen ([68Ga]Ga-PSMA-11) positron emission tomography (PET). To address the increasing demand for [68Ga]-labeled peptides and reduce the cost of radiosynthesis, it is therefore necessary to optimize the elution process of [68Ge]Ge/[68Ga]Ga generators. This study aims to identify the most effective approach for optimizing radiosynthesis using double elution in parallel of two [68Ge]Ge/[68Ga]Ga generators. Two methods have been tested: one using prepurification, and the other using fractionated elution. Five synthesis sequences were conducted using each method. The mean labeling yields for double elution with prepurification were 45.8 ± 29.4 (mean ± standard deviation) and none met the required criteria. The mean labeling yields for the fractionated double elution were 97.5 ± 1.9 (mean ± standard deviation) meeting the criteria, significantly superior to the prepurification method (p = 0.012), and similar to those of simple elution. This study showed that fractionated double elution from [68Ge]Ge/[68Ga]Ga generators produced a significantly higher labeling yield than double elution with prepurification, resulting in a larger activity recovered via radiosynthesis, thereby allowing more diagnostic tests to be performed.

Analytic odd mean labeling of union and identification of some graphs

A graph G is analytic odd mean if there exist an injective function f : V → {0, 1, 3, . . . , 2q − 1} with an induced edge labeling f∗ : E → Z such that for each edge uv with f(u) &lt; f(v), is injective. Clearly the values of f∗ are odd. We say that f is an analytic odd mean labeling of G. In this paper, we show that the union and identification of some graphs admit analytic odd mean labeling by using the operation of joining of two graphs by an edge.

Enhanced Effectiveness in Various Ladder Graphs Based on the F-Centroidal Meanness Criterion

Graph labeling allows for the representation of additional attributes or properties associated with the vertices, edges, or both of graphs. This can provide a more comprehensive and detailed representation of the system being modeled, allowing for a richer analysis and interpretation of the graph. Graph labeling in ladder graphs has a wide range of applications in engineering, computer science, physics, biology, and other fields. It can be applied to various problem domains, such as image processing, wireless sensor networks, VLSI design, bioinformatics, social network analysis, transportation networks, and many others. The versatility of ladder graphs and the ability to apply graph labeling to them make them a powerful tool for modeling and analyzing diverse systems. If a function Υ is an injective vertex assignment in {1,2,…q+1} and the inductive edge assignment function Υ* in {1,2,…q} is expressed as a graph with q edges, defined as Υ*(uv)=2[Υ(u)2+Υ(u)Υ(v)+Υ(v)2]3[Υ(u)+Υ(v)], then the function is referred to as F-centroidal mean labeling. This is known as the F-centroidal mean criterion. Here, we have determined the F-centroidal mean criteria of the graph ladder, slanting ladder, triangular ladder, TLn∘Sm, SLn∘Sm for m≤2, double-sided step ladder, Dn*, and diamond ladder.

Study of Expression of p63 and Ki-67 in Normal, Dysplastic, and Malignant Lesions of Oral Mucosa

Background: The oral cavity is the most common site of cancer in the Indian subcontinent contributing to one-third of all cancers. The prognosis of oral dysplasia and malignant lesions can be predicted by both clinicopathological parameters and molecular markers. Aims and Objectives: The present study was undertaken to examine and compare the expression profile of cell cycle regulatory proteins p63 and Ki-67 in normal dysplastic and malignant lesions of oral mucosa and its correlation with prognosis. Settings and Design: This was a retrospective case–control study in a tertiary referral center. Materials and Methods: We evaluated and compared the expression profile of antigens p63 and Ki-67 on 60 cases of histologically proven oral dysplastic and malignant lesions oral squamous cell carcinoma (OSCC – 35 cases), oral epithelial dysplasia (OED – 15 cases), and 10 cases of benign and inflammatory oral lesions. Statistical Analysis: Mean and standard deviation were calculated and ANOVA statistical test was used to compare the data. Results: The mean labeling index of p63 and KI-67 was higher in OSCC than OED and minimum in inflammatory (controls) groups. Conclusion: p63 expression had a positive correlation with Ki-67 expression. Thus, p63 and Ki-67 may be a marker for tumorigenesis and tumor cell proliferation.

A Study on Power-3 Heronian Odd Mean Labeling for some Path Related Graphs

In this article, we discussed Power-3 Heronian odd Mean Labeling for some path related graphs. A function is said to be Power 3 Heronian odd mean labeling of a graph G with q edges, if f is a bijective function from the vertices of G to the set{1,3,5,.......2p-1}such that when each edges uv is assigned the label, then the resulting edge labels are distinct numbers.

A neural tract tracing study on synaptic connections for cortical glutamatergic terminals and cervical spinal calretinin neurons in rats.

The cerebral cortex innervates motor neurons in the anterior horn of the spinal cord by regulating of interneurons. At present, nerve tracing, immunohistochemistry, and immunoelectron microscopy are used to explore and confirm the characteristics of synaptic connections between the corticospinal tract (CST) and cervical spinal calretinin (Cr) interneurons. Our morphological results revealed that (1) biotinylated dextran amine labeled (BDA+) fibers from the cerebral cortex primarily presented a contralateral spinal distribution, with a denser distribution in the ventral horn (VH) than in the dorsal horn (DH). An electron microscope (EM) showed that BDA+ terminals formed asymmetric synapses with spinal neurons, and their mean labeling rate was not different between the DH and VH. (2) Cr-immunoreactive (Cr+) neurons were unevenly distributed throughout the spinal gray matter, and were denser and larger in the VH than in the DH. At the single labeling electron microscope (EM) level, the labeling rate of Cr+ dendrites was higher in the VH than in the DH, in which Cr+ dendrites mainly received asymmetric synaptic inputs, and between the VH and DH. (3) Immunofluorescence triple labeling showed obvious apposition points among BDA+ terminals, synaptophysin and Cr+ dendrites, with a higher density in the VH than in the DH. (4) Double labeling in EM, BDA+ terminals and Cr+ dendrites presented the same pattern, BDA+ terminals formed asymmetric synapses either with Cr+ dendrites or Cr negative (Cr-) dendrites, and Cr+ dendrites received either BDA+ terminals or BDA- synaptic inputs. The average percentage of BDA+ terminals targeting Cr+ dendrites was higher in the VH than in the DH, but the percentage of BDA+ terminals targeting Cr- dendrites was prominently higher than that targeting Cr+ dendrites. There was no difference in BDA+ terminal size. The percentage rate for Cr+ dendrites receiving BDA+ terminal inputs was lower than that receiving BDA- terminal inputs, and the BDA+ terminal size was larger than the BDA- terminal size received by Cr+ dendrites. The present morphological results suggested that spinal Cr+ interneurons are involved in the regulatory process of the cortico-spinal pathway.

A Study on Root Cube Even Mean Labeling for Some Special Graphs

Abstract: A graph G = (V,E) with p vertices and q edges is said to be a Root Cube Even Mean Graph if it is possible to label the vertices x Vwith distinct elements f(x) from 1,2......,q+1 in such a way that when each edge e = uv is labeled with

A Novel Radio Geometric Mean Algorithm for a Graph

Radio antennas switch signals in the form of radio waves using different frequency bands of the electromagnetic spectrum. To avoid interruption, each radio station is assigned a unique number. The channel assignment problem refers to this application. A radio geometric mean labeling of a connected graph G is an injective function h from the vertex set, V(G) to the set of natural numbers N such that for any two distinct vertices x and y of G, h(x)·h(y)≥diam+1−d(x,y). The radio geometric mean number of h, rgmn(h), is the maximum number assigned to any vertex of G. The radio geometric mean number of G, rgmn(G) is the minimum value of rgmn(h), taken over all radio geometric mean labeling h of G. In this paper, we present two theorems for calculating the exact radio geometric mean number of paths and cycles. We also present a novel algorithm for determining the upper bound for the radio geometric mean number of a given graph. We verify that the upper bounds obtained from this algorithm coincide with the exact value of the radio geometric mean number for paths, cycles, stars, and bi-stars.