Sum Of Squares Research Articles

Exploring morphological diversity in carrot (Daucus carota l.) germplasm: A multivariate analysis approach

This study looks at how quantitative parameter variation changes over two years in different carrot accessions and the genetic diversity that exists in a group of accessions that come from different parts of the world. An analysis of variance (ANOVA) was conducted to assess the significance of different factors, including the block effect, treatment effect, and check effect. The result indicated a significant mean sum of squares across various sources of variation. Both adjusted and unadjusted block and treatment effects were significant for all traits, while the check effect was significant for more. During both years, there was moderate to high variation in quantitative parameters for numerous quantitative traits among carrot accessions. Mature leaf length showed the highest variation, followed by mature leaf width, leaf area, root weight, leaf weight, and plant biomass. Principal component analysis revealed distinct patterns in the contributions of parameters during both years. Plotting carrot accessions on the scatter plot using the first three principal components also revealed an informative spread of accessions. A notable increase in variation during the second year was observed. Moreover, accessions from different continents displayed varying degrees of genetic diversity, with Asian accessions exhibiting the highest levels. These findings underscore the importance of global germplasm collection in breeding programs aimed at enhancing crop resilience and productivity. Leveraging this genetic diversity through advanced breeding strategies holds promise for developing cultivars capable of adapting to changing environmental conditions and meeting the demands of sustainable agriculture.

Nonlinear Robust Stabilization of Ship Roll by Convex Optimization

For ship roll stabilization, this paper presents a nonlinear robust controller design method using the sum of squares (SOS) technique combined with the dual of Lyapunov's stability theorem. Varying ship speed and initial metacentric height are seen as uncertainties, sea waves are regarded as external disturbance, and then the robust nonlinear controller is also designed based on the suggested method. Simulations are performed by taking container ship model as an example. It is shown that the designed system guarantees robust performance with respect to the uncertainties and disturbance.

Discriminating woody species assemblages from National Forest Inventory data based on phylogeny in Georgia.

Classifications of forest vegetation types and characterization of related species assemblages are important analytical tools for mapping and diversity monitoring of forest communities. The discrimination of forest communities is often based on β-diversity, which can be quantified via numerous indices to derive compositional dissimilarity between samples. This study aims to evaluate the applicability of unsupervised classification for National Forest Inventory data from Georgia by comparing two cluster hierarchies. We calculated the mean basal area per hectare for each woody species across 1059 plot observations and quantified interspecies distances for all 87 species. Following an unspuervised cluster analysis, we compared the results derived from the species-neutral dissimilarity (Bray-Curtis) with those based on the Discriminating Avalanche dissimilarity, which incorporates interspecies phylogenetic variation. Incorporating genetic variation in the dissimilarity quantification resulted in a more nuanced discrimination of woody species assemblages and increased cluster coherence. Favorable statistics include the total number of clusters (23 vs. 20), mean distance within clusters (0.773 vs. 0.343), and within sum of squares (344.13 vs. 112.92). Clusters derived from dissimilarities that account for genetic variation showed a more robust alignment with biogeographical units, such as elevation and known habitats. We demonstrate that the applicability of unsupervised classification of species assemblages to large-scale forest inventory data strongly depends on the underlying quantification of dissimilarity. Our results indicate that by incorporating phylogenetic variation, a more precise classification aligned with biogeographic units is attained. This supports the concept that the genetic signal of species assemblages reflects biogeographical patterns and facilitates more precise analyses for mapping, monitoring, and management of forest diversity.

Genetic Variability and Character Association Analysis in Wheat (Triticum aestivum L.) in Saline Water Condition

The study was conducted to evaluate eight germplasms/varieties of wheat during the rabi season (November-April, 2022–23) using a randomized block design with three replications at the research farm of Agricultural Research Sub-Station (ARSS), Nagaur (Rajasthan), India to estimate the variability parameters and characters association for nine characters. The results were revealed that mean sum of squares due to genotypes showed significant differences for all the nine characters under study, suggested that the genotypes were genetically divergent. The phenotypic coefficient of variation values was higher than genotypic coefficient of variation values for all the nine traits which reflect the influence of environment on the expression of traits. Spike length and number of spikelets were showed higher PCV and medium GCV. High heritability estimates were recorded for all the nine characters. High genetic advance as percentage of mean along with high heritability was observed for number of spikelets, spike length, number of effective tillers plant-1, seed yield and number of grains spike-1. This indicated the existence of lesser environmental influence and prevalence of additive gene action in their expression and these traits possessed high selective value. These characters could be further improved through individual plant selection. Grain yield had highly significant and positive genotypic and phenotypic correlations with plant height, number of effective tillers plant-1, spike length, number of spikelets and number of grains spike-1. These characters can be considered as criteria for selection for higher grain yield as these were mutually and directly associated with grain yield.

Sums of squares in function fields over henselian discretely valued fields

Let n∈N and let K be a field with a henselian discrete valuation of rank n with hereditarily euclidean residue field. Let F/K be a function field in one variable. It is known that every sum of squares is a sum of 3 squares. We determine the order of the group of nonzero sums of 3 squares modulo sums of 2 squares in F in terms of equivalence classes of certain discrete valuations of F of rank at most n. In the case of function fields of hyperelliptic curves of genus g, K.J. Becher and J. Van Geel showed that the order of this quotient group is bounded by 2n(g+1). We show that this bound is optimal. Moreover, in the case where n=1, we show that if F/K is a hyperelliptic function field such that the order of this quotient group is 2g+1, then F is nonreal.

Machine learning prediction model for gray-level co-occurrence matrix features of synchronous liver metastasis in colorectal cancer.

Synchronous liver metastasis (SLM) is a significant contributor to morbidity in colorectal cancer (CRC). There are no effective predictive device integration algorithms to predict adverse SLM events during the diagnosis of CRC. To explore the risk factors for SLM in CRC and construct a visual prediction model based on gray-level co-occurrence matrix (GLCM) features collected from magnetic resonance imaging (MRI). Our study retrospectively enrolled 392 patients with CRC from Yichang Central People's Hospital from January 2015 to May 2023. Patients were randomly divided into a training and validation group (3:7). The clinical parameters and GLCM features extracted from MRI were included as candidate variables. The prediction model was constructed using a generalized linear regression model, random forest model (RFM), and artificial neural network model. Receiver operating characteristic curves and decision curves were used to evaluate the prediction model. Among the 392 patients, 48 had SLM (12.24%). We obtained fourteen GLCM imaging data for variable screening of SLM prediction models. Inverse difference, mean sum, sum entropy, sum variance, sum of squares, energy, and difference variance were listed as candidate variables, and the prediction efficiency (area under the curve) of the subsequent RFM in the training set and internal validation set was 0.917 [95% confidence interval (95%CI): 0.866-0.968] and 0.09 (95%CI: 0.858-0.960), respectively. A predictive model combining GLCM image features with machine learning can predict SLM in CRC. This model can assist clinicians in making timely and personalized clinical decisions.

Experimental and drying kinetics study on millet particles by a pulsating fluidized bed dryer

This research studies experimentally the drying of foxtail millet in a pulsation-assisted fluidized bed. The effects of temperature and pulsating flow frequency on millet drying are examined. The experiments are conducted at temperatures of 40 °C, 50 °C, and 60 °C for three pulsating frequencies of 0.5, 1, and 2.5 Hz and continuous flow. The best result is obtained for drying with a frequency of 1 Hz. It shows that the pulsating flow is more effective at 50 °C as compared to other temperatures. Four reliable semi-empirical models are used for predicting the moisture reduction during drying process. Among the fitted dynamic models, the model that has the maximum correlation coefficient (R2) and minimum sum of squares of error (SSE) and root mean squared error (RMSE) and well able to predict the behavior of millet drying in the whole process was chosen.

Study on the Evaluation Genetic Variability of Gladiolus (Gladiolus grandiflorus) Cultivars Under Agro –Climatic Conditions of Prayagraj

Aims: A field experiment was carried out to “Study on Evaluating Genetic Variability of Gladiolus (Gladiolus grandiflorus L.) Cultivars under Agro –Climatic conditions of Prayagraj”. Place and Duration of Study: An experiment was carried out in the Department of Horticulture during the Rabi season of 2023-2024. Study Design: Randomized Block Design. Methodology: The analysis of the data showed that phenotypic coefficient of variation (PCV) was higher than genotypic coefficient of variation (GCV) for all characters studied, indicating that environmental factors had a significant influence on these characters. In addition, positive and highly significant correlations were observed in between tuber yield per plant (gm) and various other traits including the No. of leaves at 30DAS, 60DAS and 90DAS and No. of shoots per plant, days for the first flowering, peduncle length, No. of florets per spike, No. of ears per plant, length of floret, diameter of floret, No. of corms per plant and diameter of corms, weight of corms and No. of corms per hectare and No. of corms per hectare. Results: The mean sum of squares due to genotypes showed significant differences for all characters under study for except days taken for emergence of flower spike and days taken to show color of basal floret. High magnitude of GCV were recorded for No. of leaves (52.70), Corm yield/plant (46.40), No. of cormels/hectare(39.12), Cormel diameter(38.36), No. of corms/hectare(28.97), No. of corms per plant(28.97), No. of leaves at 60DAS(26.64), No. of shoot(26.64). The genotypic and phenotypic correlation coefficient of different characters with Corms yield/plant (g) and their relationship among themselves Conclusion: Genotypic and Phenotypic correlation revealed that corms weight/plant (g) showed positive significant association with plant height, number of leavesper plant, number of shoots per plant, rachis length, no. of cormels per hectare and corm yield/ plant at both levels genotypic and phenotypic.

Stability Analysis in Six-row Barley Genotypes for Grain Yield in Multi-environmental Trails Using Eberhart and Russel (1966)

The current study aimed to determine the phenotypic stability for grain yield per plant under three distinct environmental conditions using fifteen parental lines and three testers with 45 crosses (30 single crosses and 15 three-way crosses) of six-row barley in three replications using Randomized Block Design. Eberhart and Russell (1966) developed the modal to examine stability. The mean sum of squares due to genotype and environment wassquares due to genotype and environment were found to be significant for grain yield per plant, which showed the differential effect of environment on genotypes. For grain yield per plant, it was also observed that the mean sum square resulting from the climate + (G x E) interaction, E (linear), and G x E (linear) was significant. With a non-significant deviation from regression (S2di=0) and regression coefficient near unity (bi=1), the genotypes BG 959, BG 105 x RD 2508, PL 751 x RD 2508, DWRB 137 x RD 3005, and RD 2035 x F1 exhibited higher grain yield than the population mean. These genotypes were the most stable and desirable under variable environmental conditions. These genotypes could be used as donors in regular breeding programs to improve barley grain yield.

Power Mean Inequalities and Sums of Squares

Power Mean Inequalities and Sums of Squares

Driving sustainable development: Role of institutional quality and future of China's mineral resource management projects

The rapid industrial progress in China along with significant dependence on minerals, raises concerns about the influence of its overall reliance on nations’ development trajectory. Moreover, institutional quality also plays an active role in shaping the economic structure of any nation. The study investigates the intricate association among mineral extraction, institutional quality, and economic development in China from 1990 to 2022. For an empirical investigation, the ARDL (Autoregressive distributed lag) co-integration method is employed based on the order of integration of the series defined by the ADF(Augmented Dickey-Fuller) stationarity test. Moreover, CUSUM and CUSUM square (Cumulative sum of square) also confirm the stability of the model. According to the findings mineral rent and mineral exports are found to be positively significant in the short and the long run and increase economic growth. While institutional quality is shown to be positively insignificant in the short term, in the long run, it is shown to have a positive significant effect. Moreover, inflation and population growth are shown to have a positive significant impact in the short term, but trade is found to be insignificant. Lastly, the study intends to suggest policy suggestions based on the results. A country should have a strong institutional setup to ensure sustainable long-term growth.

Stability assessment of selected chrysanthemum (Dendranthema grandiflora Tzvelev) hybrids over the years through AMMI and GGE biplot in the mid hills of North-Western Himalayas

Dendranthema grandiflora is an important cut flower with high economic importance in the floriculture industry. Identification of stable and high yielding genotypes of Dendranthema grandiflora, hence becomes paramount for ensuring its year-round production. In this context, the genotype by environment interaction effects on 22 chrysanthemum hybrids across six test environments were investigated. The experiment was conducted using Randomized Complete Block Design with three replications for 6 years and data on various agro-morphological and yield-contributing traits were evaluated. Our analysis revealed significant mean sum of squares due to environmental, genotypic and genotype by environment interaction variations for all examined traits. A 2D GGE biplot constructed using first two principal components computed as 59.2% and 23.3% of the differences in genotype by environment interaction for flower yield per plant. The GGE biplot identified two top-performing genotypes, G2 and G5, while the AMMI model highlighted genotypes G17, G15, G6, G5, and G2 as the best performers. Genotype G17 ranked highest for multiple traits, while G2 displayed high mean flower yield as well as stability across all environments. According to AEC line, genotypes G2 and G5 exhibited exceptional stability, whereas genotypes G4, G18 and G19 demonstrated lower stability but maintained high average flower yields. Hence, our findings provide valuable insights into chrysanthemum hybrids that were not only best performing but also hold promise to meet the growers demand of the cut flower industry and can be recommended for large scale commercial cultivation.

Balanced Lattice Designs under Uncertain Environment

AbstractBalanced lattice designs are vital in numerous fields, especially in experimental design, where controlling variability among experimental units is crucial. In practical experiments, various sources of uncertainty can lead to ambiguous, vague, and imprecise data, complicating the analysis process. To address these indeterminacies, a novel approach using neutrosophic analysis within a balanced lattice design framework is proposed, termed the neutrosophic balanced lattice design (NBLD). This innovative method employs neutrosophic statistics to derive mathematical neutrosophic sums of squares and construct a neutrosophic analysis of variance (NANOVA) table. The effectiveness of the proposed NBLD is demonstrated through a numerical example, showing that it outperforms traditional methods in handling uncertainty.

Sums of squares III: Hypoellipticity in the infinitely degenerate regime

This is the third paper in a series of three dealing with sums of squares and hypoellipticity in the infinitely degenerate regime. We establish a C^{2,\delta} generalization of M. Christ’s smooth sum of squares theorem, and then use a bootstrap argument with the sum of squares decomposition for matrix functions, obtained in our second paper of this series, to prove a hypoellipticity theorem that generalizes some cases of the results of Christ, Hoshiro, Koike, Kusuoka and Stroock and Morimoto for sums of squares, and of Fedĭi and Kohn for degeneracies not necessarily a sum of squares.

Curing analysis of rubber film on a Hand-Shaped former in the manufacturing of rubber gloves through novel OpenFOAM solver

Vulcanization, or curing, is a crucial aspect of rubber- or polymer-product manufacturing. Determining the optimal curing time for rubbery components is a significant challenge in the rubber industry. This study focuses on enhancing a computational fluid dynamics code used for simulating the conjugate heat transfer of nitrile-butadiene rubber (NBR) glove curing. Non-isothermal differential scanning calorimetry was employed to analyze the NBR glove-curing process, utilizing constant heating rates ranging from 2.5 to 20 °C/min. Activation-energy calculations employing four isoconversional methods and multivariate nonlinear regression played a pivotal role in determining the most appropriate curing-kinetics model. The multivariate nonlinear regression yielded well-fitted outcomes with a residual sum of squares ranking from 0.44 × 10−3 to 1.60 × 10−3, indicating the suitability of the novel curing-kinetics model for the NBR curing process. After obtaining the appropriate model, adjustments were made to the novel conjugate heat-transfer solver in OpenFOAM to forecast the degree of curing during the heating process. Experimental results from a hot-air counter-flow NBR film in the tray affirmed the accuracy of the solver, demonstrating an impressive R2 value of 0.98. Consequently, the novel solver was applied to simulate the curing process of the NBR film coating on a hand-shaped former surface, offering a visual representation of the degree of curing distribution on the NBR glove. The non-uniform curing and weak curing surface of the NBR glove were revealed, which can be used for estimating the optimal conditions for the curing process or designing an appropriate curing oven for rubber glove manufacturing in the future.

Comparison Analysis of Roundness Measurement of Small Cylindrical Workpieces with Different Styluses.

To investigate the high-accuracy roundness metrology of a needle roller 1.5 mm in diameter and 5.8 mm in length using the stitching linear scan method, a ruby ball stylus with a tip radius of 150 μm and a diamond stylus with a tip radius of 2 μm were employed to perform experiments under the same conditions. The precision coordinate data, derived from the needle roller's cross-sectional circumference, were segmented into uniform eighths, each scanned with the stylus of a roughness measuring machine. The roundness profile of the needle roller was obtained by stitching the arc profiles, which were characterized according to the precision coordinate data of the arcs. The cross-correlation function, Euclidean distance, residual sum of squares, position error, and curvature of the measured arcs were used to evaluate the results, which can reflect the performance of the stylus. A comparison of the results obtained using the ruby ball stylus versus the diamond stylus demonstrates the ruby ball stylus' greater suitability for use in the roundness metrology of the needle roller bearing examined in this paper.

Total Carbon Storage in Uneven-Aged Pure Beech Stands in the Western Part of the Balkans

Forest ecosystems represent one of the largest and most important ecosystems on Earth, containing close to 80% of the biomass of our planet. As such, they play a significant role in the global carbon cycle because through photosynthesis, forests absorb more carbon than they emit and thus accumulate it. The most important species in deciduous forests in Europe, European beech (Fagus sylvatica L.), is of exceptional importance from the aspect of carbon storage. Considering that the state of carbon in pure beech forests is poorly investigated in the western part of the Balkans, the need for total carbon research was imposed to complete the picture of its stocks and factors that impact it. Research on total carbon (TC) storage in uneven-aged pure beech stands in the western part of the Balkans was carried out in three regions located approximately at the same latitude, but different longitude, imposing different macro-habitat characteristics. This research aimed to determine the TC stock and to examine the effects of orographic factors, stand canopy, and macroclimate on its values. TC stock in forest biomass was determined using appropriate regression equations and formulas, while soil organic carbon stock was determined using ICP forests methodology. Effects of different factors on carbon stock were examined using ANOVA (Type II Sums of Squares), General Linear Hypothesis Test (GLHT), and regression analyses. It was found that the largest TC stock is located in the region of Eastern Serbia (SRB) where its macroclimate is classified as suitable for hornbeam and sessile oak or mixed beech-oak stands. It was found that anthropogenic activity plays a significant role in the size of the carbon stock stored in above-ground biomass via alteration of forest canopy. The results also indicate that Aboveground Carbon (AGC) stocks are approximately proportional to Belowground Carbon (BGC; C in belowground biomass + soil C) stocks. What makes the difference is the structure of BGC, as the share of Soil Organic Carbon (SOC) is higher in the regions of Eastern Republic of Srpska (ERS) and Western Republic of Srpska (WRS), which are climatically classified as highly suitable for beech. Further analysis has shown that the amount of SOC decreases with increasing aridity levels. Given the results, management goals should be aimed at increasing the stock of biomass for the sake of carbon sequestration and for reducing the adverse effects of climate change, as a large amount of carbon can be stored in the above-ground and belowground biomass.

Limit Law for Zagreb and Wiener Indices of Random Exponential Recursive Trees

The Wiener index is the sum of distances of all pairs of nodes in a graph; and the Zagreb index is defined as the sum of squares of the degrees of nodes in a rooted tree. In this note, we calculate the first two moments of the Wiener and Zagreb indices of random exponential recursive trees (random ERTs) from two systems of recurrence relations. Then, by an application of the contraction method, we characterize the limit law for a scaled Zagreb index of ERTs. Via the martingale convergence theorem, we also show the almost sure convergence and quadratic mean convergence of an appropriately scaled Wiener index that is indicative of the distance of two randomly chosen nodes.

Compact Model Training by Low-Rank Projection With Energy Transfer.

Low-rankness plays an important role in traditional machine learning but is not so popular in deep learning. Most previous low-rank network compression methods compress networks by approximating pretrained models and retraining. However, the optimal solution in the Euclidean space may be quite different from the one with low-rank constraint. A well-pretrained model is not a good initialization for the model with low-rank constraints. Thus, the performance of a low-rank compressed network degrades significantly. Compared with other network compression methods such as pruning, low-rank methods attract less attention in recent years. In this article, we devise a new training method, low-rank projection with energy transfer (LRPET), that trains low-rank compressed networks from scratch and achieves competitive performance. We propose to alternately perform stochastic gradient descent training and projection of each weight matrix onto the corresponding low-rank manifold. Compared to retraining on the compact model, this enables full utilization of model capacity since solution space is relaxed back to Euclidean space after projection. The matrix energy (the sum of squares of singular values) reduction caused by projection is compensated by energy transfer. We uniformly transfer the energy of the pruned singular values to the remaining ones. We theoretically show that energy transfer eases the trend of gradient vanishing caused by projection. In modern networks, a batch normalization (BN) layer can be merged into the previous convolution layer for inference, thereby influencing the optimal low-rank approximation (LRA) of the previous layer. We propose BN rectification to cut off its effect on the optimal LRA, which further improves the performance. Comprehensive experiments on CIFAR-10 and ImageNet have justified that our method is superior to other low-rank compression methods and also outperforms recent state-of-the-art pruning methods. For object detection and semantic segmentation, our method still achieves good compression results. In addition, we combine LRPET with quantization and hashing methods and achieve even better compression than the original single method. We further apply it in Transformer-based models to demonstrate its transferability. Our code is available at https://github.com/BZQLin/LRPET.

Genetic Variability Analysis for Yield and Yield-Associated Traits of Finger Millet [<i>Eleusine coracana</i> (L.) Gaertn.] Accessions at Mechara, Eastern Ethiopia

The genetic enhancement of any crop, including finger millet, requires a certain degree of genetic variation for effective utilization in crop improvement programs. However, in Ethiopia, there is limited information on the extent and pattern of genetic variability of finger millet collections under diversified agro-climatic conditions. This makes it difficult for a population to adapt to changing environmental conditions. As a result, the population may be more vulnerable to extinction, exposure to new diseases, low productivity, and selection acting on any genes that may provide disease resistance. Therefore, knowledge of genetic variability is crucial for breeders in order to develop new cultivars with desired traits that are beneficial for both farmers and breeders. The present investigation was carried out to estimating the genetic variability, heritability, and genetic advance in sixty four finger millet accessions for yield and yield-related traits at Mechara agricultural research center. The experimental design was laid out in 8 x 8 simple lattice design. The analysis of variance for mean sum of squares due to genotypes revealed highly significant differences for all the 17 quantitative characters. The genotypes showed the highest mean performance for grain yield ranged from 1.38 ton per hectare for ACC#208448 to 4.35 ton per hectare for ACC#230255. Whereas, genotypic and phenotypic coefficients of variation were found high for biomass yield, harvest index, and grain yield. Broad-sense heritability ranged from 50.12% for the number of fingers per ear to 93.18% for days to heading. High heritability coupled with high genetic advance as percent of mean were observed for leaf number, finger length, ear weight, thousand grain weight, biomass yield, and harvest index. In general, the results demonstrated that the finger millet accessions exhibited a high degree of genetic variability for the traits studied, which can be helpful for genetic enhancement.