Harmonic Mean Research Articles

A combination prediction model based on Theil coefficient and induced continuous aggregation operator for the prediction of Shanghai composite index

This paper proposes an interval combination prediction model for Shanghai composite index, utilizing the Theil coefficient and the induced continuous generalized ordered weighted logarithmic harmonic averaging (ICGOWLHA) operator. The effectiveness of the proposed model under specific weight conditions and the existence of its analytical solution are demonstrated. Shanghai composite index's case analysis demonstrates that, in terms of interval root mean squared error (IRMSE), interval mean absolute error (IMAE), interval mean absolute percentage error (IMAPE), and interval mean squared percentage error (IMSPE), the proposed model's predictive performance improvements over the best-performing single prediction model are 29.33%, 25.72%, 26.10%, and 28.86%, respectively. At the same time, the theoretical properties of the model are verified in the results of the case analysis, and the model's convergence is reflected in sensitivity analysis. Through extensive model comparisons, it is observed that the model proposed in this paper exhibits strong generalization, without specific limitations on data size or feature count. It demonstrates good aggregation prediction performance for interval data. Moreover, it is applicable to various fields, including finance, environment, and others.

Representation formulae for linear hyperbolic curvature flows

In [19], Smoczyk showed that parabolic expansion of convex curves and hypersurfaces by the reciprocal of the harmonic mean curvature gives rise to a linear second order equation for the evolution of the support function, with corresponding representation formulae for solutions. In this article we obtain representation formula for the corresponding linear hyperbolic evolution equation for the support function of locally convex curves of general nonzero rotation number, finding some natural similarities and differences in behaviour of solutions as compared with the parabolic case. As applications, we consider linear hyperbolic flows that preserve length or generalised enclosed area of the evolving curve, flow of curves with Neumann boundary conditions inside cones and hyperbolic approaches to the Yau problem of flowing one curve to another. We also consider radial graphs evolving by similar linear equations and linear higher order hyperbolic equations. Our results may be compared with the corresponding parabolic cases consider by the first author, Schrader and Wheeler, in [17].

High genetic diversity but limited gene flow in Flemish populations of the crested newt, Triturus cristatus

Habitat destruction and fragmentation are among the major causes of amphibian decline. We investigated to what extent geographic distance and barriers affect the genetic composition of the crested newt, Triturus cristatus in Flanders (North Belgium), causing inbreeding or loss of genetic diversity. Data from seven microsatellite loci and 170 individuals from seven metapopulations up to 180km apart revealed heterozygosities of 0.53 to 0.67 within populations and moderate levels of genetic divergence between populations (FST values from 0.074 to 0.141, harmonic means of Dest between 0.070 and 0.189). In all Flemish meta-populations, more than 90% of the individuals from a given geographic region were assigned to the same genetic cluster indicating
 little genetic exchange, even in De Panne where the two populations Oosthoek and Westhoek are only a few kilometres apart. Such sub-structuring on a micro-scale has also been described in other amphibians. Unique alleles in most populations further support the probability that genetic drift has already led to some isolation. With the exception of the Oosthoek population, however, we found no significant evidence for bottlenecks. Connectivity within pool clusters seems essential to the maintenance of genetic diversity in crested newts as is indicated by our findings from Tommelen, the population with the largest number of pools in close proximity, which also shows the highest levels of heterozygosity (He and Ho) and the second highest number and richness of alleles. In conclusion, our study indicates that dispersal and migration rates between the Flemish populations of Triturus cristatus are limited at the geographic scale studied here but that habitat fragmentation has not yet led to a significant loss of genetic diversity of the studied Flemish populations, possibly because crested newts are relatively long-lived, fragmentation of their habitat is relatively recent in Flanders, and most investigated pools are still connected at the local scale.

Multi-path residual attention network for cancer diagnosis robust to a small number of training data of microscopic hyperspectral pathological images

Duct cancer is a malignant disease with higher mortality rates in males than in females, emphasizing the need for early diagnosis to improve treatment outcomes. Although various imaging modalities such as magnetic resonance imaging (MRI) and computed tomography scan (CT-scan) have been used for pathological analysis, hyperspectral imaging stands out as a promising approach, especially when combined with deep learning techniques. Hyperspectral imaging provides detailed information on tissue composition and biochemical properties, enabling better distinction between cancerous and healthy tissues. Although previous research based on hyperspectral imaging shows high accuracy, no previous research has used a small amount of training data, despite this being the usual case in medical image applications. Therefore, we propose a multi-path residual attention network (MRA-Net) with chunked residual channel attention (CRCA), which is a novel deep learning model specifically designed to address the challenges posed by limited training data, with a particular focus on using hyperspectral images. By leveraging the unique spectral information provided by hyperspectral imaging, MRA-Net extracts distinctive features, enhancing its ability to differentiate between cancerous and healthy tissues.We conducted the training and validation of our model using a publicly accessible dataset, resulting in an accuracy of 84.31% and a weighted harmonic mean of precision and recall (F1 score) of 84.29%, demonstrating its state-of-the-art performance compared to existing methods.

A nonlocal Lagrangian traffic flow model and the zero-filter limit

In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangian partial differential equation (PDE) model for traffic flow. We demonstrate the well-posedness of the Lagrangian model in the L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1$$\\end{document} sense. Additionally, we rigorously show that our model coincides with the Lagrangian formulation of the local LWR model in the “zero-filter” (nonlocal-to-local) limit. We present numerical simulations of the new model. One significant advantage of the proposed model is that it allows for simple proofs of (i) estimates that do not depend on the “filter size” and (ii) the dissipation of an arbitrary convex entropy.

Genetic resources of common ash (Fraxinus excelsior L.) in Poland

BackgroundKnowledge of genetic structure and the factors that shape it has an impact on forest management practices. European ash (Fraxinus excelsior L.) has declined dramatically throughout its range as a result of a disease caused by the fungus Hymenoscyphus fraxineus. Despite the need for conservation and restoration of the species, genetic data required to guide these efforts at the country level are scarce. Thereofore, we studied the chloroplast and nuclear genetic diversity of 26 natural common ash populations (1269 trees) in Poland.ResultsChloroplast polymorphisms grouped the populations into two geographically structured phylogenetic lineages ascribed to different glacial refugia (the Balkans and the Eastern Alps). However, the populations demonstrated high genetic diversity (mean AR = 12.35; mean Ho = 0.769; mean He = 0.542) but low differentiation based on nuclear microsatellites (FST = 0.045). Significant spatial genetic structure, consistent with models of isolation by distance, was detected in 14 out of 23 populations. Estimated effective population size was moderate-to-high, with a harmonic mean of 57.5 individuals per population.ConclusionsGenetic diversity was not homogeneously distributed among populations within phylogenetic gene pools, indicating that ash populations are not equal as potential sources of reproductive material. Genetic differences among populations could be related to their histories, including founder effects or gene flow between evolutionary lineages (admixture). Our results suggest that ash stands across Poland could be treated as two main management units (seed zones). Therefore, despite the homogenizing effect of pollen gene flow known for this species, the genetic structure should be taken into account in the management of the genetic resources of the common ash. Although ash dieback poses an additional challenge for the management of genetic resources, efforts should be directed towards protecting populations with high genetic diversity within defined phylogenetic units, as they may be an important source of adaptive variation for future stands.

Evaluation of yield-based selection indices for drought tolerance involving recombinant inbred line population derived from a chickpea cultivar (C. arietinum L.) and its wild relative (C. reticulatum)

AbstractDrought is a major abiotic stress worldwide limiting chickpea yield drastically. Low heritability and high genotype × environment interactions make the trait-based breeding strategy an unreliable approach. This study was planned to identify the drought-tolerant lines by evaluating yield-based selection indices in a recombinant inbred line (RIL) population derived from an inter-specific cross between drought-tolerant genotype GPF 2 (Cicer arietinum L.) and drought-sensitive accession ILWC 292 (C. reticulatum) at two locations in India (Ludhiana and Faridkot). A total of six yield-based selection indices were calculated and significant variation was observed in the RILs and their parents for yield-based selection indices at both locations. A holistic approach across association analysis and principal component analysis identified drought tolerance index, mean productivity, geometric mean productivity and harmonic mean productivity as key selection indices, which could be used for indirect selection of drought-tolerant lines. Overall, on the basis of these approaches, a total of 15 promising RILs were identified for their use in chickpea breeding programme for developing drought-tolerant cultivars.

Multi-Module Fusion Model for Submarine Pipeline Identification Based on YOLOv5

In recent years, the surge in marine activities has increased the frequency of submarine pipeline failures. Detecting and identifying the buried conditions of submarine pipelines has become critical. Sub-bottom profilers (SBPs) are widely employed for pipeline detection, yet manual data interpretation hampers efficiency. The present study proposes an automated detection method for submarine pipelines using deep learning models. The approach enhances the YOLOv5s model by integrating Squeeze and Excitation Networks (SE-Net) and S2-MLPv2 attention modules into the backbone network structure. The Slicing Aided Hyper Inference (SAHI) module is subsequently introduced to recognize original large-image data. Experimental results conducted in the Yellow Sea region demonstrate that the refined model achieves a precision of 82.5%, recall of 99.2%, and harmonic mean (F1 score) of 90.0% on actual submarine pipeline data detected using an SBP. These results demonstrate the efficiency of the proposed method and applicability in real-world scenarios.

A cluster-based SMOTE both-sampling (CSBBoost) ensemble algorithm for classifying imbalanced data

In this paper, a Cluster-based Synthetic minority oversampling technique (SMOTE) Both-sampling (CSBBoost) ensemble algorithm is proposed for classifying imbalanced data. In this algorithm, a combination of over-sampling, under-sampling, and different ensemble algorithms, including Extreme Gradient Boosting (XGBoost), random forest, and bagging, is employed in order to achieve a balanced dataset and address the issues including redundancy of data after over-sampling, information loss in under-sampling, and random sample selection for sampling and sample generation. The performance of the proposed algorithm is evaluated and compared to different state-of-the-art competing algorithms based on 20 benchmark imbalanced datasets in terms of the harmonic mean of precision and recall (F1) and area under the receiver operating characteristics curve (AUC) measures. Based on the results, the proposed CSBBoost algorithm performs significantly better than the competing algorithms. In addition, a real-world dataset is used to demonstrate the applicability of the proposed algorithm.

Interoperability of Botswana’s healthcare systems using semantic prescription ontologies

<p>The developing country of Botswana’s health information system faces interoperability challenges mainly due to the lack of shared patient medical data and histories between private and public healthcare providers, which leads to increased medical errors, increased healthcare costs, and potentially fatal outcomes. This research proposes an intelligent electronic prescription ontology (IEPO) framework to share Botswana’s patient electronic health records (EHRs) between private and public healthcare systems for a standardized and semantically rich data exchange. IEPO was evaluated for interoperability using the recall metric for completeness to capture the degree of all relevant information for exchange and the precision metric for accuracy performance to gauge the degree of error minimization during interoperability. The harmonic means of precision and recall called the F1- score, offered the overall interoperability performance. IEPO outperformed related works by 75% in recall, 54% in precision, and 76% in F1-score, demonstrating improved interoperability performance. Furthermore, IEPO was evaluated for correctness and expressiveness through competency questions via queries, results confirming correct and expressive responses.</p>

Detecting the edges of galaxies with deep learning

Galaxy edges or truncations are low-surface-brightness (LSB) features located in the galaxy outskirts that delimit the distance up to where the gas density enables efficient star formation. As such, they could be interpreted as a non-arbitrary means to determine the galaxy size and this is also reinforced by the smaller scatter in the galaxy mass-size relation when comparing them with other size proxies. However, there are several problems attached to this novel metric, namely, the access to deep imaging and the need to contrast the surface brightness, color, and mass profiles to derive the edge position. While the first hurdle is already overcome by new ultra-deep galaxy observations, we hereby propose the use of machine learning (ML) algorithms to determine the position of these features for very large datasets. We compare the semantic segmentation by our deep learning (DL) models with the results obtained by humans for HST observations of a sample of 1052 massive (Mstellar > 1010 M⊙) galaxies at z < 1. In addition, the concept of astronomic augmentations is introduced to endow the inputs of the networks with a physical meaning. Our findings suggest that similar performances than humans could be routinely achieved, although in the majority of cases, the best results are obtained by combining (with a pixel-by-pixel democratic vote) the output of several neural networks using ensemble learning. Additionally, we find that using edge-aware loss functions allows for the networks to focus their optimization on the galaxy boundaries and, therefore, to provide estimates that are much more sensitive to the presence of neighboring bodies that may affect the shape of the truncation. The experiments reveal a great similarity between the semantic segmentation performed by the AI compared to the human model. For the best model, an average dice of 0.8969 is achieved, while an average dice of 0.9104 is reached by the best ensemble, where the dice coefficient represents the harmonic mean between the precision and the recall. This methodology will be profusely used in future datasets, such as that of Euclid, to derive scaling relations that are expected to closely follow the galaxy mass assembly. We also offer to the community our DL algorithms in the author's github repository.

A New Method to Prove Several Inequalities

As is known to all, to strengthen and refine the famous arithmetic-geometric- harmonic mean inequality H (w, a) ≤ G (w, a) ≤ A (w, a), it has been becoming the focus of the theoretical research of inequality from estimating the mean difference. the difference between the two inequalities mentioned above is estimated by using variance, and these results are strengthened or generalized by using a consistent proof model.

Analysis of MOFTP using Modern Zero Suffix Method

Abstract: In this paper, a new algorithm is introduced for dealing with the Multi-Objective Fuzzy Transportation Problem (MOFTP) where all parameters such as transportation cost, demand and supply are in triangular fuzzy numbers. The approach involves modern zero suffix method using Harmonic Mean. First the Multi-objective fuzzy transportation problem is converted into a crisp value by using a Robust’s Ranking Method. Then the crisp value is solved by Modern Zero Suffix method. The effectiveness of the data is examined by a numerical example.

Pharmacokinetics, Safety, and Tolerability of Cedirogant in Healthy Japanese and Chinese Adults.

Cedirogant is an inverse agonist of retinoic acid-related orphan receptor gamma, thymus (RORγt) developed for treatment of psoriasis. This study aimed to characterize pharmacokinetics, pharmacodynamics, safety, and tolerability of cedirogant following a single oral dose in Japanese participants and multiple oral doses in Japanese and Chinese participants. The single doses evaluated in healthy Japanese participants were 75, 225, and 395mg. The multiple doses evaluated in both healthy Japanese and Chinese participants was 375mg once daily for 14 days. Cedirogant plasma exposure increased dose proportionally with administration of single doses. Maximum cedirogant plasma concentration was reached within a median time of 4-5 hours after dosing. The harmonic mean elimination half-life ranged from 19 to 25 hours. Cedirogant pharmacokinetics were similar between Japanese and Chinese participants. Compared with healthy Western participants in a cross-study analysis, steady-state cedirogant plasma exposure was 38%-73% higher in Japanese or Chinese participants. Ex vivo interleukin-17 inhibition increased in a dose-dependent manner and was maximized by 375mg once-daily doses. The cedirogant regimens tested were generally well tolerated, and no new safety issues were identified. The results supported enrollment of Japanese and Chinese subjects in subsequent clinical trials for cedirogant.

Inequalities for Means Regarding the Trigamma Function

Let G(α, β), A(α, β) and H(α, β), respectively, be the geometric mean, arithmetic mean and harmonic mean of α and β. In this paper, we prove that G(ψ′ (z), ψ′ (1/z)) ≥ π2/6, A(ψ′ (z), ψ′ (1/z)) ≥ π2/6 and H(ψ′ (z), ψ′ (1/z)) ≤ π2/6. This extends the previous results of Alzer and Jameson regarding the digamma function ψ. The mathematical tools used to prove the results include convexity, concavity and monotonicity properties of certain functions as well as the convolution theorem for Laplace transforms.

A multi-objective Grey Wolf–Cuckoo Search algorithm applied to spatial truss design optimization

A novel hybrid algorithm called Multi-Objective Hybrid Grey Wolf Cuckoo Search (MOGWOCS) is developed for spatial truss designs in this study. A new simple yet efficient mechanism to select the best candidates is proposed. Furthermore, harmonic averaging is employed to be a replacement for conventional arithmetic mean for higher effectiveness. Additionally, the Lévy flight in Cuckoo Search (CS) is utilized to increase efficiency in early searching and also reduce local entrapment possibility. For verification purposes, MOGWOCS is first performed on some mathematical functions and 11 CEC2020 mechanical problems. It is then examined on four large-scale truss design problems, in two of which multi-objective optimization is studied for the first time. To demonstrate the superiority of the proposed approach, five up-to-date algorithms, and various indicators are included for validation. It is found that MOGWOCS is able to produce solutions with higher optimality in terms of diversity and accuracy.

The present value discounting convention errors in uniform intra-period cash flow distributions

This study compares the estimation errors of several present value discounting conventions (end-of-year, mid-year, and the more recently proposed harmonic mean convention) for a uniform distribution of intra-period cash flow — continuous and discrete. Our results show that the mid-year convention performs best for continuous uniform cash flow streams, and that the mid-year and harmonic mean conventions produce smaller errors for discrete uniform cash flow streams than the end-of-year convention. We supply conditions for the order of preference in the case of discrete uniform cash flow distributions and provide some additional insights into the errors of the discounting conventions for both continuous and uniform intra-period cash flow distributions.

Extraction frequent patterns in trauma dataset based on automatic generation of minimum support and feature weighting

PurposeData mining has been used to help discover Frequent patterns in health data. it is widely used to diagnose and prevent various diseases and to obtain the causes and factors affecting diseases. Therefore, the aim of the present study is to discover frequent patterns in the data of the Kashan Trauma Registry based on a new method.MethodsWe utilized real data from the Kashan Trauma Registry. After pre-processing, frequent patterns and rules were extracted based on the classical Apriori algorithm and the new method. The new method based on the weight of variables and the harmonic mean was presented for the automatic calculation of minimum support with the Python.ResultsThe results showed that the minimum support generation based on the weighting features is done dynamically and level by level, while in the classic Apriori algorithm considering that only one value is considered for the minimum support manually by the user. Also, the performance of the new method was better compared to the classical Apriori method based on the amount of memory consumption, execution time, the number of frequent patterns found and the generated rules.ConclusionsThis study found that manually determining the minimal support increases execution time and memory usage, which is not cost-effective, especially when the user does not know the dataset's content. In trauma registries and massive healthcare datasets, its ability to uncover common item groups and association rules provides valuable insights. Also, based on the patterns produced in the trauma data, the care of the elderly by their families, education to the general public about encountering patients who have an accident and how to transport them to the hospital, education to motorcyclists to observe safety points in Recommended when using a motorcycle.

Selection of M5 mutant lines of wheat (Triticum aestivum L.) for agronomic traits and biomass allocation under drought stress and non-stressed conditions.

In the face of climate changes and limited water availability for irrigated crop production, enhanced drought tolerance and adaptation is vital to improve wheat productivity. The objective of this study was to determine the responses of newly bred and advanced mutant lines of wheat based on agronomic traits and biomass allocation under drought-stressed and non-stressed environments for production and breeding. Fifty-three mutant lines, including the parental check and six check varieties, were evaluated under non-stressed (NS) and drought stressed (DS) conditions in the field and controlled environments using a 20 x 3 alpha lattice design with two replicates. The following agronomic data were collected: days to 50% heading (DTH), days to maturity (DTM), plant height (PH), number of productive tillers (PTN), shoot biomass (SB), root biomass (RB), total biomass (TB), root: shoot ratio (RSR), spike length (SL), thousand seeds weight (TSW) and grain yield (GY). Data were analyzed and summarized using various statistical procedures and drought tolerance indices were computed based on grain yield under NS and DS conditions. Significant (P < 0.05) differences were recorded among the mutant lines for most assessed traits under NS and DS conditions. Grain yield positively and significantly (p < 0.001) correlated with PTN (r = 0.85), RB (r = 0.75), SB (r = 0.80), SL (r =0.73), TB (r = 0.65), and TSW (r = 0.67) under DS condition. Principal component analysis revealed three components contributing to 78.55% and 77.21% of the total variability for the assessed agronomic traits under DS and NS conditions, respectively. The following traits: GY, RB, SB, and PTN explained most of the variation with high loading scores under DS condition. Geometric mean productivity (GMP), mean productivity (MP), harmonic mean (HM), and stress tolerance index (STI) were identified as the best drought tolerance indices for the identification of tolerant lines with positive correlations with GY under NS and DS conditions. Among the advanced lines tested, LMA16, LMA37, LMA47, LMA2, and LMA42 were selected as the superior lines with high performance and drought tolerance. The selected lines are recommended for multi-environment trails and release for production in water-limited environments in South Africa.

Exploring Two Modified Ali-Mikhail-Haq Copulas and New Bivariate Logistic Distributions

The Ali-Mikhail-Haq copula is a bivariate ratio-type Archimedean copula known for its simplicity and flexibility in modeling moderate negative and positive dependence structures, making it widely used in various fields. However, it is limited to capturing asymmetric dependence features, significant negative correlations, or versatile tail dependence properties. This research paper proposes two modifications of the Ali-Mikhail-Haq copula that overcome these limitations, but at the price of the loss of the positive dependence nature. Contrary to the common approach that focuses on modifying the corresponding generator function, we apply direct functional changes to the Ali-Mikhail-Haq copula. We thus perturb its Archimedean identity. The first copula has the particularity of being non-exchangeable, capable of reaching an interesting level of negative dependence correlations, and possessing flexible tail dependence properties. The second copula offers another modeling option; it is exchangeable like the Ali-Mikhail-Haq copula, but it benefits from a broader range of negative dependence correlations and more adaptable tail dependence properties. For the two proposed copulas, we investigate their main characteristics, including quadrant dependence, copula density function, conditional copulas, couples of value generation, extended variants via standard copula schemes, comprehensive copula orders, and weighted harmonic mean copula transformations. An application on two new bivariate logistic distributions in a two-component system context is given. When possible, numerical and graphical studies are given to strengthen the theory.