Unraveling blood pressure estimation with a deep learning approach using multiple embeddings.

On the local and global minimizers of the smooth stress function in Euclidean distance matrix problems

Numerous Machine Learning (ML) algorithms require pairwise Euclidean distance computations between all data points in horizontally partitioned datasets. To ensure data privacy, most existing solutions incorporate encryption or cryptographic techniques, allowing secure sharing and computation of data points. In this study, we propose two methodologies for generating Euclidean distance matrices: the Federated Euclidean Distance Matrix (FEDM) and the Predicted Euclidean Distance Matrix (PEDM), derived from the pairwise Euclidean distances of horizontally partitioned data to ensure privacy by design. The proposed approach has significant potential to transform the execution of ML algorithms that rely on Euclidean distance calculations and to eliminate the need for separate encryption methods, thereby potentially reducing communication and computation costs in a Federated Learning (FL) environment. The proposed methods achieve high accuracy and exhibit strong similarity to the actual Euclidean distance matrix. FL has gained prominence as a privacy-preserving ML solution that encapsulates data while appropriately sharing model parameters. To this end, we utilize artificial spike points for the creation of FEDM. We also elucidate the foundational workflows of the method and matrix construction and demonstrate their efficacy through comprehensive experimentation.

Accurate node localization is essential for many Internet of Things (IoT) applications. However, incomplete and noisy distance measurements often degrade the reliability of the Euclidean Distance Matrix (EDM), which is critical for range-based localization. To address this issue, a Low-Rank Matrix Completion approach based on nonconvex rank approximation (LRMCN) is proposed to recover the true EDM. First, the observed EDM is decomposed into a low-rank matrix representing the true distances and a sparse matrix capturing noise. Second, a nonconvex surrogate function is used to approximate the matrix rank, while the l1-norm is utilized to model the sparsity of the noise component. Third, the resulting optimization problem is solved using the Alternating Direction Method of Multipliers (ADMMs). This enables accurate recovery of a complete and denoised EDM from incomplete and corrupted measurements. Finally, relative node locations are estimated using classical multi-dimensional scaling, and absolute coordinates are determined based on a small set of anchor nodes with known locations. The experimental results show that the proposed method achieves superior performance in both matrix completion and localization accuracy, even in the presence of missing and corrupted data.

ABSTRACT Semi‐arid forests in North Africa face growing pressures from climate change, agricultural intensification and urban sprawl, all of which reshape habitats and wildlife communities. Among the species inhabiting these dynamic landscapes, the Maghreb magpie ( Pica mauritanica Malherbe, 1845), an endemic corvid of the Maghreb, offers an insightful model to examine how environmental factors influence breeding strategies and spatial organisation. This study aimed to investigate the nesting ecology and spatial patterns of P. mauritanica in semi‐arid oak‐dominated forests of northeastern Algeria. Specifically, the study assessed nest‐site selection in relation to tree characteristics, compared nesting preferences between holm oak ( Quercus ilex L.) and mixed tree stands and analysed the spatial distribution of inter‐nest distances to evaluate potential clustering. Fieldwork was conducted during the breeding season, where detailed measurements of nest height, supporting tree dimensions and surrounding vegetation were recorded. Independent‐sample t‐tests and linear regression models were applied to examine nest–tree relationships, while spatial analyses employed Euclidean distance matrices and hierarchical clustering to assess inter‐nest distribution. Maghreb magpie nests were built in holm oak trees, particularly those with larger diameters and higher canopies that presumably offer more structurally robust supports. Nest height was positively correlated with tree height and canopy cover, highlighting the importance of vertical structure for breeding. Comparisons between Q. ilex and mixed tree species revealed significant differences in nest placement strategies. Spatial analyses indicated nonrandom nest distribution, with inter‐nest distances forming clustered patterns rather than uniform spacing, suggesting social or ecological drivers behind colony‐like aggregation. These findings emphasise that P. mauritanica exhibited selective nesting strategies strongly shaped by tree attributes and forest structure, while also displaying a clustered spatial distribution of breeding sites. In the context of rapid environmental change and ongoing anthropogenic pressures in North African forests, understanding these ecological requirements provides crucial insights for conserving this endemic species and managing vulnerable semi‐arid ecosystems.

Dampness pattern, a prevalent traditional Chinese medicine (TCM) pattern in chronic gastritis (CG), includes cold dampness (CD) and damp heat (DH) patterns. Tongue coating differences are key diagnostic markers, yet molecular-level analyses are lacking. We applied metabolomics to identify differential metabolites distinguishing these patterns. In this study, the first principal component was analyzed by the OPLS-DA model. The model quality was evaluated by 7-fold cross-validation, and the model validity was evaluated based on R²Y (interpretability of categorical variable Y) and Q² (predictability of the model), and the permutation test was used for further verification. Strict criteria were used for differential metabolite screening. The Euclidean distance matrix of the quantitative values of differential metabolites was calculated, and cluster analysis was performed using the complete linkage method. All pathways mapped by human differential metabolites were retrieved through the KEGG (Kyoto Encyclopedia of Genes and Genomes) Pathway database, and key pathways were screened out by combining enrichment and topological analysis. The spearman algorithm was used to calculate the correlation coefficient and P value matrix. Finally, the effect of the binary classifier was evaluated by drawing the receiver operating characteristic curve (ROC curve) and calculating the area under the curve (AUC), and the combination with the highest AUC was selected as the optimal diagnostic model. Twenty significant differential metabolites emerged (P<0.05). Pathway analysis highlighted three key pathways, notably glycerophospholipid metabolism involving phosphatidylethanolamine. Phenol-based models showed optimal diagnostic performance (highest AUC). Metabolite profiles significantly differed between CD and DH. Glycerophospholipid metabolism was central, with phosphatidylethanolamine as a key metabolite. Phenol requires further validation as a diagnostic biomarker. These findings advance quantitative diagnosis and mechanistic insights into TCM dampness syndrome in CG.

Background: Various factors influence variations in the human dental arch size and shape, and they differ across populations and genders. Euclidean Distance Matrix Analysis (EDMA) is a common method for analyzing differences by measuring distances between anatomical landmarks. Objective: Thus, we aimed to assess if EDMA distinguishes dental arch forms and dimensions between males and females aged 18–30 from Dakshina Kannada, South India, with the morphological assessment to calculate distances between landmarks. Methods: Dental casts of 55 individuals were analyzed. Thirteen landmarks were digitized, and Euclidean distances were computed using ImageJ, TpsUtil, and TpsDig2. Statistical analysis included t-tests for sex differences and discriminant function analysis for classification. Results: In the mandibular arch, inter-landmark distances LM 1–13, LM 2–11, LM 2–12, and LM 2–13 were significantly larger in males than in females (P &lt; 0.05). Likewise, in the maxillary arch, males had significantly higher values for LM 6–7, LM 2–11, and LM 2–12 (P &lt; 0.05). These observations imply that males tend to have a wider arch shape, while females have a comparatively more elongated arch shape in both maxillary and mandibular parts, with chosen landmarks. Conclusion: EDMA identified sex-based differences in dental arch form and size, which stamps value as a tool for anthropological and dental research to explore human diversity.

Sustainable development remains one of the major challenges for contemporary Poland, where dynamic economic growth often collides with social inequalities and environmental degradation. In relation to these challenges, this paper aims to assess the level of sustainable development in voivodships (highest-level administrative division of Poland, equivalent to a province) based on an extended analytical framework that adds an institutionalpolitical dimension to the three core aspects of sustainable development – social, economic and environmental. The study relies on data from 2022 on individual voivodships, from which 20 variables describing the aforementioned aspects of sustainable development are selected. In the extended approach, these aspects are often referred to as ‘orders’. For each voivodship, Hellwig’s measure is calculated using multidimensional comparative analysis and linear ordering. Based on these calculations, rankings of Polish voivodships are created and visualised by means of cartograms created in R. Additionally, an analysis of the similarity of objects relative to each other is conducted using Euclidean distance matrices. The research shows, among other aspects, which orders of sustainable development constitute the strengths and which represent weaknesses of a given voivodship. The study refers to literature discussing the concept of sustainable development and methods of quantifying it, as well as literature describing the applied research methodology.

Fractional Brownian motion (fBm) exhibits both randomness and strong scale-free correlations, posing a challenge for generative artificial intelligence to replicate the underlying stochastic process. In this study, we evaluate the performance of diffusion-based inpainting methods on a specific dataset of corrupted images, which represent incomplete Euclidean distance matrices (EDMs) of fBm across various memory exponents (H). Our dataset reveals that, in the regime of low missing ratios, data imputation is unique, as the remaining partial graph is rigid, thus providing a reliable ground truth for inpainting. We find that conditional diffusion generation effectively reproduces the inherent correlations of fBm paths across different memory regimes, including sub-diffusion, Brownian motion, and super-diffusion trajectories, making it a robust tool for statistical imputation in cases with high missing ratios. Moreover, while recent studies have suggested that diffusion models memorize samples from the training dataset, our findings indicate that diffusion behaves qualitatively differently from simple database searches, allowing for generalization rather than mere memorization of the training data. As a biological application, we utilize our fBm-trained diffusion model to impute microscopy-derived distance matrices of chromosomal segments (FISH data), which are incomplete due to experimental imperfections. We demonstrate that our inpainting method outperforms standard bioinformatic methods, suggesting a novel physics-informed generative approach for the enrichment of high-throughput biological datasets.

Thermo-sensitive genic male sterile (TGMS) lines in rice are crucial for hybrid breeding, enhancing genetic diversity by eliminating the need for manual emasculation and restorer genes. These lines induce sterility at high temperatures and restore fertility at low temperatures, in contrast to cytoplasmic male sterility (CMS) systems that require specific restorative genes. This temperature-sensitive mechanism allows for greater flexibility in pairing parent lines, increasing genetic diversity and enabling recombination of beneficial traits in hybrids. A randomized block design (RBD) with three replications was employed for the evaluation of these TGMS rice lines. This study investigates the molecular diversity and genetic variability among TGMS rice lines. Traits such as single plant yield, grains per panicle, glume angle, and pollen fertility showed significant phenotypic and genotypic variation, indicated by high coefficients of variation (PCV and GCV), heritability estimates, and genetic advance as a percentage of mean (GAM). These results highlight substantial genetic variation and selection potential. Euclidean distance matrix analysis of morphological data revealed notable genetic differences. TNAU 137S 1 and TNAU 137S 2 were the most genetically similar, while TNAU 112S and TNAU 114S showed the greatest divergence. Principal component analysis (PCA) revealed distinct genetic profiles among lines such as TNAU 136S, TNAU 113S, TNAU 142S, and TNAU 126S, important for hybrid development. Molecular diversity analysis using simple sequence repeat (SSR) markers identified 90 alleles and eight genetic clusters. Bayesian analysis further confirmed two major subpopulations with significant genetic divergence. These findings support the selective use of parent lines for hybrid rice breeding.

Measuring Potential of a Candidate for a Job in the Light of Psychotechnical Tests and the Use of Selected Methods of Multivariate Analysis

Sloth bears in Gujarat inhabit fragmented forest patches running across the eastern belt of the state from north to south. With most studies focused on its northern areas; insufficient information is available for sloth bears in central Gujarat. Previous studies show food availability as the key factor influencing their presence, along with the availability of water, human activities, and forest cover. We aimed to understand the factors influencing seasonal presence of the bears in Jambughoda Wildlife Sanctuary. We conducted grid-based habitat surveys from 2020 to 2022 with sloth bear sign surveys in two seasons; winter and summer. We found 45 locations showing presence signs in winter whereas only two in summer. This indicates a seasonal disparity in sloth bears’ presence. Considering the presence of sloth bears as the sampling unit habitat was studied. Two types of variables categorized as sample and site variables were used in the study. The number of termite/ ant hills, water bodies, and sloth bear-preferred trees with their fruiting seasons were considered sample variables while the vegetation types (woody, mixed and undisturbed rugged) and the land use/ land cover patterns (dense, moderately dense, open forest; agriculture and barren land) were considered as the site variables. We studied the variables using the Euclidean distance matrix in RStudio. Our findings show that the key sample variables included the number of termite/ant hills (0.03) during winter and water bodies (0.05) during summer. On analysing the site variables in winter sloth bears were closely associated with dense vegetation (0.02), while in summer they preferred undisturbed/ rugged areas (0.02). Considering sloth bears as seasonal visitors to the sanctuary, these findings shall provide information on the habitat preferred by the bears and are expected to support long-term conservation strategies and management planning in the region.

In contrast to conventional localization methods, connectivity-based localization is a promising approach that leverages wireless links among network nodes. Here, the Euclidean distance matrix (EDM) plays a pivotal role in implementing the multidimensional scaling technique for the localization of wireless nodes based on pairwise distance measurements. This is based on the representation of complex datasets in lower-dimensional spaces, resulting from the mathematical property of an EDM being a low-rank matrix. However, EDM data are inevitably susceptible to contamination due to errors such as measurement imperfections, channel dynamics, and clock asynchronization. Motivated by the low-rank property of the EDM, we introduce a new pre-processor for connectivity-based localization, namely denoising-autoencoder-aided EDM reconstruction (DAE-EDMR). The proposed method is based on optimizing the neural network by inputting and outputting vectors of the eigenvalues of the noisy EDM and the original EDM, respectively. The optimized NN denoises the contaminated EDM, leading to an exceptional performance in connectivity-based localization. Additionally, we introduce a relaxed version of DAE-EDMR, i.e., truncated DAE-EDMR (T-DAE-EDMR), which remains operational regardless of variations in the number of nodes between the training and test phases in NN operations. The proposed algorithms show a superior performance in both EDM denoising and localization accuracy. Moreover, the method of T-DAE-EDMR notably requires a minimal number of training datasets compared to that in conventional approaches such as deep learning algorithms. Overall, our proposed algorithms reduce the required training dataset’s size by approximately one-tenth while achieving more than twice the effectiveness in EDM denoising, as demonstrated through our experiments.

&lt;sec&gt;Dopant-induced quantum dot arrays in silicon-based nanostructures have received much attention due to their great potential applications in fields such as quantum computing and quantum simulation. When quantum dots are arranged in different geometric configurations such as linear, annular, or grid shapes, the differences in their inherent topological properties will lead to significantly different spatial distributions of the Coulomb interaction potential. The potential field distribution directly affects the phase coherence of electron wavefunctions, thereby regulating the dynamic behaviors of electrons such as electron tunneling and hopping between quantum dots, and greatly influencing the electron transport properties in the system.&lt;/sec&gt;&lt;sec&gt;Our study aims to establish a basic theoretical framework to clarify the regulation mechanism of quantum dot geometric configurations on electron hopping transport. Therefore, we construct a generalized Fermi-Hubbard model for silicon-based dopant-induced quantum dot arrays. The model defines the distance between quantum dots through an effective Euclidean distance matrix (&lt;i&gt; &lt;b&gt;D&lt;/b&gt; &lt;/i&gt;), which uniquely determines the geometric shape of the array, and defines the allowed electron hopping modes through an adjacency matrix (&lt;i&gt; &lt;b&gt;A&lt;/b&gt; &lt;/i&gt;). Using the framework and exact diagonalization method, we perform detailed numerical simulations on the electron transport properties in the traditional unit cell of two-dimensional ordered distribution dopant-induced quantum dot arrays. Generally, the primitive unit of a two-dimensional orderly distributed dopant-induced quantum dot array is a regular polygon that satisfies specific translational and rotational symmetries. We thereby refer to the quantum dot arrays distributed according to regular polygons as annular arrays.&lt;/sec&gt;&lt;sec&gt;The geometric features of annular quantum dot arrays and the electron hopping modes including nearest-neighbor hopping (NNH), next-nearest-neighbor hopping (NNNH) and long-range hopping (LRH), exhibit significant regulation of the electron addition energy and quantum conductance. The regulation arises from interactions of key energy parameters, including coupling strength (&lt;i&gt;t&lt;/i&gt;), on-site Coulomb repulsion (&lt;i&gt;U&lt;/i&gt;) and inter-site Coulomb repulsion (&lt;i&gt;W&lt;/i&gt;). In the electron addition energy spectrum, such a regulation is manifested in two aspects: energy band broadening and Coulomb gap size. Band broadening is co-regulated by &lt;i&gt;t&lt;/i&gt; and &lt;i&gt;W&lt;/i&gt;. Under weak coupling conditions, the broadening &lt;i&gt;Δ&lt;/i&gt;&lt;sub&gt;&lt;i&gt;t&lt;/i&gt;&lt;/sub&gt; induced by coupling strength is proportional to &lt;i&gt;t&lt;/i&gt;, with its proportional coefficient increasing with the number of hopping paths (LRH &gt; NNNH &gt; NNH). The broadening &lt;i&gt;Δ&lt;/i&gt;&lt;sub&gt;&lt;i&gt;W&lt;/i&gt;&lt;/sub&gt; caused by inter-site Coulomb repulsion is proportional to &lt;i&gt;W&lt;/i&gt;, with the proportional coefficient being &lt;i&gt;β&lt;/i&gt;, which is a geometry-dependent correlation broadening coefficient. In multi-site annular arrays, &lt;i&gt;β&lt;/i&gt; exhibits a logarithmic relationship with the site number N. The size of Coulomb gap is co-influenced by &lt;i&gt;U&lt;/i&gt;, &lt;i&gt;t&lt;/i&gt; and &lt;i&gt;W&lt;/i&gt;. The competition between &lt;i&gt;U&lt;/i&gt; and &lt;i&gt;W&lt;/i&gt; determines the electron configuration mode (dominated by single-electron occupation of sites or double-electrons occupation of spaced sites), with a critical value &lt;i&gt;α&lt;/i&gt; for electron configuration reconstruction that causes a change in electron configuration across the threshold. When &lt;i&gt;U&lt;/i&gt;/&lt;i&gt;W&lt;/i&gt; &gt; &lt;i&gt;α&lt;/i&gt;, single-electron occupation dominates, and the gap is determined by the competition between &lt;i&gt;U&lt;/i&gt; and &lt;i&gt;t&lt;/i&gt;; when &lt;i&gt;U&lt;/i&gt;/&lt;i&gt;W&lt;/i&gt; &lt; &lt;i&gt;α&lt;/i&gt;, double-electrons occupation dominates, the gap expands under the influence of &lt;i&gt;W&lt;/i&gt;, accompanied by the formation of sub-bands.&lt;/sec&gt;&lt;sec&gt;In the quantum conductance spectrum, regulation is reflected by the distribution of conductance peak intensity. Geometric configurations significantly affect peak intensity distribution. Linear arrays exhibit concentrated peak intensities due to edge states formed by open boundaries, while annular arrays with periodic boundaries and no edge states show more uniform peak distributions. Additionally, in annular arrays, the electron transport direction is non-collinear with the inter-site repulsion direction, endowing them with stronger robustness against transport inhibition induced by &lt;i&gt;W&lt;/i&gt;. The influence of hopping modes is twofold. More hopping paths (LRH &gt; NNNH &gt; NNH) result in more non-zero hopping matrix elements, which causes higher average conductance. Meanwhile, hopping paths affect the phase coherence of wavefunctions, modulating the intensity of individual conductance peaks and forming distinct distribution.&lt;/sec&gt;&lt;sec&gt;In conclusion, we establish a theoretical framework to clarify the physical mechanism, in which the geometric configurations and electron hopping modes of silicon-based dopant-induced quantum dot arrays regulate electron transport properties through synergistic interactions with key energy parameters (&lt;i&gt;t,&lt;/i&gt; &lt;i&gt;U&lt;/i&gt;, &lt;i&gt;W&lt;/i&gt;). Electron addition energy spectra and quantum conductance spectra reveal the regulatory rules of these factors on electron transport behaviors, providing a theoretical guidance for optimally designing silicon-based quantum devices.&lt;/sec&gt;

ABSTRACT This work aims to characterize and estimate soybean genotypes’ productive potential and industrial quality, understand the associations between traits and identify genotypes for a breeding program. Four collections totaling 301 genotypes were used, and ten quantitative characteristics were analyzed, including the mass of one hundred seeds (100 SW, where SW stands for seed weight), protein content (PC), oil content (OIL), fiber (FIB), ash content (ASH), palmitic acid (PA), stearic acid (SA), oleic acid (OA), linoleic acid (LA), linolenic acid (LNA). Descriptive analysis, Tukey's test, Lilliefors statistics, and Pearson correlation were applied. The Euclidean distance matrix generated a network of correlations, and Venn Diagrams analyzed the most promising genotypes. The analyses showed that 100 SW, an average of 15.66 %, was low. Among the seed constituents, only PC was less, with an average of 33.40 % associated with a variability of 2.02. PC and OIL presented possible polygenic control of an additive nature. The strongest correlation was between PC and OIL, with a value of −0.7. The 100 SW correlated positively with PC but negatively with FIB, indicating negligible and weak correlations, with values of 0.18 and 0.31, respectively. Collections 3 and 4 individually presented the lowest and the highest number of high-intensity interactions, respectively. The diagrams underscored the difficulty of simultaneously highlighting genotypes with superior performance considering multiple characteristics. It is concluded that except for collection 3, the genotypes presented low PC and low variability requiring the inclusion of favorable allelic forms, and genotypes with superior performance were identified on account of the characteristics 100 SW and PC or 100 SW and OIL.

Niger is a minor oilseed crop primarily grown in Ethiopia and India. The oil content in niger seeds ranges from 32% to 47%. Niger oil has several nutritional and therapeutic benefits. Despite these benefits, the crop has been widely neglected by breeders due to its low productivity. Therefore, understanding the extent of genetic variability within the niger germplasm is a prerequisite for selecting superior genotypes and enhancing productivity. The present experiment was conducted at the ICAR‐Indian Institute of Oilseeds Research, Hyderabad, Telangana, during the kharif seasons of 2022 and 2023. The study used an augmented randomized complete block design (ARCBD) with 111 accessions and four checks to assess variability in oil content and fatty acid composition. The analysis of variance showed significant differences among the accessions. Oil content ranged from 26.1% to 44.8%, with the highest oil content recorded in IC260240 (44.8%). Unsaturated fatty acids, such as linoleic and oleic acids, constituted the major portion of fatty acids among the accessions. The presence of a higher amount of unsaturated fatty acids indicates low susceptibility to autoxidation and confers a therapeutic advantage to niger oil. The accessions IC260250 and IC211053 exhibited high levels of linoleic and oleic acid content, respectively. Based on the Euclidean distance matrix method, the accessions were grouped into six hierarchical clusters. Cluster II had the highest number of accessions (34), followed by Cluster IV with nine accessions. The maximum genetic distance was observed between Clusters III and VI. Palmitic and stearic acids showed a significant positive correlation, whereas linolenic acid and oleic acid exhibited a significant negative correlation. No discernible variations were observed in the fatty acid composition among the accessions during the two seasons. The elite accessions identified from this study can be utilized as donors in the niger oil quality improvement program.

Machine learning models have gained popularity for environmental variable predictions due to their capacity to capture complex relationships and automate learning. However, incorporating spatial information as covariates into these models remains a challenge, as they may struggle to recognize spatial structures or autocorrelation without explicit training. In this study, we address this challenge by integrating spatial information into a random forest model, enhancing nitrate concentration predictions in groundwater. Using a dataset from 1,550 well locations in Baden-Wuerttemberg, Germany, spanning 2016 through 2019, we consider various environmental covariates including climate data, topography, land cover, soil properties, and hydrology. To incorporate spatial information, we employ eight techniques leveraging spatial coordinates (geographic coordinates, polynomial geographic coordinates, oblique geographic coordinates) or distances (Wendland transformed coordinates, Euclidean distance fields, Euclidean distance matrix, principal component analysis, eigenvector spatial filtering). Results are compared with a baseline model and a univariate ordinary kriging benchmark, evaluated through leave-one-out cross validation, various error metrics, and Moran’s I of residuals. Our findings highlight that integrating spatial information significantly enhances random forest model accuracy in predicting groundwater nitrate concentrations. Distance-based methods, like the Euclidean distance matrix, outperform coordinate-based approaches, albeit with higher computational requirements. Employing a dimension-reduced matrix strikes a balance between performance and accuracy. This study advances groundwater management and demonstrates the effectiveness of machine learning models in environmental studies.

The present study was conducted during June–November, 2019 at Bekoji and Kofele substation of Kulumsa Agricultural Research Center (KARC) with the aim to assess the genetic diversity among field pea genotypes for desired morpho-agronomic traits. A total of 49 Field pea genotypes, representing two different plant types were evaluated for 13 characters. Through cluster analysis, the genotypes were grouped into five categories based on the Euclidean distance matrix using the complete linkage method. Cluster one had the most genotypes (20), while cluster five had the fewest (2). Genetic distances among genotypes estimated by Euclidean distances from 13 traits ranged from 14.76 to 5514.77. Principal component and biplot analyses showed that seed yield, plant height, days to 90% maturity, number of pods per plant and seeds per plant were the main factors contributing to genotype divergence. Additionally, genotypes in the prostrate (leafed) type of field pea had a greater genetic distance (diversity) compared to those in the erect (semi-leafless) type. In general this study showed the presence of considerable diversity for the studied traits in field pea genotypes, with differences between plants types even though the dendrogram and PCA didn’t show clear cut (distinct) grouping pattern in field pea genotypes with respect to their plant types and sources. This implies an opportunity for improving desired traits in a field pea breeding program through selection or hybridization of these divergent genotypes. Thus, crossbreeding promising parents, especially selected from advanced prostrate and erect types, can result in a good level of genetic recombination.

In this article, we study the properties of 4-by-4 metric matrices and characterize their dependence and independence by M4×4=(M4×4−DM4×4)∪DM4×4, where DM4×4 is the set of all dependent metric matrices. DM4×4 is further characterized by DM4×4=DM14×4∪DM24×4, where DM24×4 is characterized by DM24×4=DM214×4∪DM224×4. These characterizations provide some insightful findings that go beyond the Euclidean distance or Euclidean distance matrix and link the distance functions to vector spaces, which offers some theoretical and application-related advantages. In the application parts, we show that the metric matrices associated with all Minkowski distance functions over four different points are linearly independent, and that the metric matrices associated with any four concyclic points are also linearly independent.

Fairphonic Pte Ltd is a technology company operating in the music sector. Fairphonic provides services to detect content on social media that is suspected of copyright infringement. Fairphonic utilizes audio features for the detection process. The current algorithm used by Fairphonic requires pairwise comparison, and the content to be compared is collected through a scraping process immediately after the process is run. Fairphonic has hundreds of thousands of music data in their database. Fairphonic desires a more scalable algorithm to compare an input music piece with the entire Fairphonic music catalog. This research uses features such as Harmonic Pitch Class Profile (HPCP), Chroma, and Rhythm Pattern. The study compares previously researched algorithms, namely binary similarity matrix, Euclidean distance, and similarity matrix profile. The results show that the combination of HPCP with the binary similarity matrix yields the highest Mean Average Precision of 0.989. Speed testing by performing comparisons 10 times shows that the combination of Chroma and the similarity matrix profile is 72% faster compared to the combination of HPCP with the binary similarity matrix. The author recommends the Chroma and similarity matrix profile algorithm for music similarity ranking due to its faster process.