Mathematical Index Research Articles

Elephant in the Room: How to Assess the Vote-weighting System in the Council of the EU

The article emphasises the complementarity of research based on voting power theory with the analysis of the structure of blocking. Combining both methods enables a more comprehensive assessment of the vote weighting system in the Council of the EU, in particular the impact of changes in the voting system on the position of individual Member States and the power balance in this institution. I make two contributions to the existing literature. Firstly, the study develops a non-random voting model, dedicated to QMV in the Council, which abandons the assumption that each coalition of players is equally likely and takes into account the role of the European Commission as an agenda-setter. This not only allows us to exclude many coalitions that are only theoretically possible, but also to analyse the blocking structure from the perspective of different states or coalitions in the Council. Secondly, it shows that the application of blocking structure analysis provides novel insights into the Council’s voting system. Unlike the a priori voting power approach, such analysis does not focus on distribution of winning power in the Council, but on the Member States’ ability to build minimal blocking coalitions. Hence, it complements the application of mathematical indices of voting power in the assessment of the voting system in this institution.

Temporal Variation Analysis in Clean Ice Glacier of Annapurna Basin

Glaciers of the Himalayas are the storehouse of fresh water. The impacts of climate change, mainly the melting of snow cover have been noticed in Nepal’s Himalayas. These changes have local as well as regional implications on water resources, and at global level on the sea level rise. This study is carried out to analyze the temporal variation of glacier retreat in the Annapurna valley from 2000 to 2020 using remote sensing technology. It is a multi-step process and involves the computation of several mathematical indices for glaciers based on the spectral properties of Landsat imagery. The final outcome is the delineation of Clean Ice Glacier (CIG) area of Annapurna basin for the years 2000, 2010 and 2020. The findings from this study reveal that the glaciers of Annapurna basin are shrinking more rapidly in the recent years than before. The decrease in CIG area coupled with the increase in the CIG number clearly indicate that the glaciers are being fragmented into smaller parts creating several disconnected ice bodies. Monitoring the dynamics of glaciers along with their trend analysis is crucial for strengthening the climate change mitigation and adaptation strategies. Key Words: Clean Ice Glacier, Temporal Variation, Annapurna Basin, Remote Sensing, Climate Change

Feed efficiency and enteric methane emissions indices are inconsistent with the outcomes of the rumen microbiome composition

The correlation between enteric methane emissions (eME) and feed efficiency (FE) in cattle is linked to the anaerobic fermentation of feedstuffs that occurs in the rumen. Several mathematical indices have been developed to predict feed efficiency and identify low methane emitters in herds. To investigate this, the current study aimed to evaluate the rumen microbial composition in the same group of animals ranked according to six different indices (three indices for FE and three for eME). Thirty-three heifers were ranked into three groups, each consisting of 11 animals, based on FE (feed conversion efficiency - FCE, residual weight gain - RG, and residual feed intake - RFI) and eME indices (production, yield, and intensity). Rumen fluids were collected using a stomach tube and analyzed using 16S rRNA and 18S rRNA, targeting rumen bacteria, archaea, and protozoa. The sequencing analysis revealed that the presence of unique microbial species in the rumen varies across animals ranked by the FE and eME indices. The High RG group harbored 17 unique prokaryotic taxa, while the High FCE group contained only seven. Significant differences existed in the microbial profiles of the animals based on the FE and eME indices. For instance, Raoultibacter was more abundant in the Intermediate RFI group but less so in the Intermediate RG and Intermediate FCE groups. The abundance of Entodinium was higher while Diplodinium was lower in the High FCE group, in contrast to the High RG and High RFI groups. Methanobrevibacter exhibited similar abundances across eME indices. However, the heifers did not demonstrate the same production, yield, and intensity of eME. The present findings underscore the importance of standardizing the FE and eME indices. This standardization is crucial for ensuring consistent and reliable assessments of the composition and function of the rumen microbiome across different herds.

Mapping terrestrial mammals in China based on species richness of functional groups

Biodiversity loss is one of the most critical environmental issues globally. Functional diversity and functional groups, extending and expanding the concept of species richness, provide a more comprehensive understanding of biodiversity. By integrating mathematical indices calculation with classical geospatial statistical analysis and mapping techniques, we explored and visually illustrated the spatial patterns and regularities of functional diversity. This approach shed light on the functional diversity of China’s terrestrial mammals from a macroecological perspective. We found that in terms of overall quantity composition, underground-living mammals (UG groups) had the highest proportion (55.1%) in the vertical niche dimension, while nocturnal mammals (NO groups) dominated (58.6%) the in temporal niche dimension. Employing grid cells as fundamental units, in most grid cells, the proportion of UG and NO groups exceeded 50%, consistent with the overall quantity results. Examining the spatial distribution of functional group species richness from different perspectives reveals varying patterns. For instance, standard deviations of vertical and temporal niches showed different spatial clustering traits on either side of the Hu Huanyong Line. In a specific dimension of functional diversity, the numerical differences among functional groups are larger in grasslands with homogenous vegetation, while in forests with diverse vegetation types, these differences are minimized. Additionally, if there is a large disparity in species richness among functional groups in one dimension, there may be a smaller disparity in another. These findings offer a macroecological perspective for biodiversity research, providing insights for interdisciplinary studies in basic ecology, conservation biology, and geography, and offering scientific guidance for mammal conservation.

Assessment of Metal Contamination in Soil Adjacent to Mining Activities Using Some Indices

ABSTRACT A thorough assessment of soil contamination with metals allows us to know the ecological and public health risks it poses. In this study, we address the use of mathematical indices derived from the total metal concentration in soil and rock. Soil and rock samples were collected from a total of 19 sites near tailing heaps. Mine tailings were sampled, and total metal concentrations were determined using atomic absorption spectrophotometry, and contamination indices were calculated. The results revealed high metal concentrations in mine tailing (4841, 1488, and 82 mg/kg Zn, Pb, and Cd, respectively) and soils (4539 mg/kg Pb, 6190 mg/kg Zn, and 48 mg/kg Cd, respectively), while rock had a low metal content, consistent with literature reports. The indices indicated various proportions of samples with different degrees of contamination. Individual indices (EF, Igeo, and CF) showed the highest levels of Pb, Zn, and Cu contamination, while overall indices (Cdeg, PLI, and MCI) indicated a higher proportion of samples with moderate contamination, albeit with some highly contaminated ones.

Topology Prediction of Gas-Separating Metal-Organic Frameworks with Low Symmetry Vertices.

Topology serves as a blueprint for the construction of reticular structures such as metal-organic frameworks, especially for those based on building blocks with highly symmetrical shapes. However, it remains a challenge to predict the topology of the frameworks from less symmetrical units, because their corresponding vertex figures are largely deformed from the perfect geometries with no "default" net embedding. Furthermore, vertices involving flexible units may have multiple shape choices, and the competition among their designated topologies makes the structure prediction in large uncertainty. Herein, the deformation index is proposed to characterize the symmetry loss of the vertex figure by comparing it with its ideal geometry. The mathematical index is employed to predict the shapes of two in situ formed Co-based metalloligands (pseudo-tetrahedron and pseudo-square), which further dictate the framework topology (flu and scu) when they are joined with the [Zr6O8]-based cuboid units. The two frameworks with very similar constituents provide an ideal platform to investigate how the pore shapes and interconnectivity influence the gas separation. The net with cylindrical channels outperforms the other with discreate cages in C3H8/C2H6/CH4 separation, benefiting from the facile accessibility of its interaction sites to the guests imposed by the specific framework topology.

Seasonal Dynamics Of Ant Communities In Forest Ecosystems: Statistical Analysis And Ecological Insights

A seasonal diversity was conducted in the forest of Bagepalli range of Chikkaballapur forest of Karnataka, India from August 2022 to August 2023. 21 species of ants were observed in this range belonging to 15 genera by following three methods such as pitfall traps, handpicking and bush beating. The abundant subfamily was Formicinae with 5 genera and under Myrmicinae, two genera were observed under the subfamily Ponerinae and one genus each from Subfamilies Pseudomyrmicinae and Dolichoderinae. The most abundant species were found to be Camponotus compressus followed by Oecophylla smaragdina. From the collection of ants few invasive species were also observed such as Anoplolepis gracilipes and Plagiolepis sp.. Two mathematical indices were followed and those were Shannon-Weaver Index and Simpson Index to study the diversity and compare the species richness from the three seasons – summer, monsoon and winter, and a statistical data was formed, the abundance in species were also observed to study which species were dominant and during which season. The maximum diversity was observed during the monsoon season followed by the summer and the least diversity was during the winter. The ants usually prefer a moist environment. The study assumes that the ant diversity can predict the environment.

The p-value of the test is not a 'mathematical index', it is simply a relative frequency

Leading scientific journals in fields such as medicine, biology and sociology repeatedly publish articles and editorials claiming that a large percentage of doctors do not understand the basics of statistical analysis, which increases the risk of errors in interpreting data, makes them more vulnerable to misinformation and reduces the effectiveness of research. This problem extends throughout their careers and is largely due to the poor training they receive in statistics - a problem that is common in developed countries. As stated by H. Halle and S. Krauss, '90% of German university lecturers who regularly use the p-value in tests do not understand what that value actually measures'. It is important to note that the basic reasoning of statistical analysis is similar to what we do in our daily lives and that understanding the basic concepts of statistical analysis does not require any knowledge of mathematics. Contrary to what many researchers believe, the p-value of the test is not a 'mathematical index' that allows us to clearly conclude whether, for example, a drug is more effective than a placebo. The p-value of the test is simply a percentage.

Segplot: A new method for visualizing patterns of multi-group segregation

Social science research on between-group segregation relies heavily on mathematical indices of exposure and unevenness, which tell us very little about the underlying patterns of segregation. We present a new visual method for analyzing two-group and multi-group segregation patterns, which we call a segplot. Segplots provide an intuitive illustration of segregation between schools, neighborhoods, occupations, or other units, adding to the depth and communicability of scholarly research. The visualization shows the entire segregation pattern, as well as the relevant reference distribution used in many measures of segregation. Segplots are particularly useful when comparing patterns of segregation over time, between locations, or between different types of units. For more complex, high-dimensional segregation patterns, we also present an algorithm that can be used to “compress” the pattern to obtain a visually clearer result. We provide illustrative applications to typical problems in segregation research, demonstrating how segplots can be used to complement and enrich a traditional mathematical analysis of between-group segregation.

Morphometric Analyses of Greek Caves: How Morphology Predicts Cave Origin

Two of the most well-known caves of northern Greece, Petralona and Maaras, were morphometrically analyzed. They were strategically chosen for this morphometric study because they represent caves formed by different speleogenetic factors, resulting in patterns that clearly discriminate them from each other. Caves can display substantial variation in their patterns, depending on the local geology, hydrogeology, tectonics, and other factors. These qualitative parameters of speleogenesis, such as geological and hydrogeological controls, can be reflected in a cave’s pattern. The different speleogenetic factors that create the patterns of the caves can be expressed in the mathematical indices, designating them as morphometrical tools for properly discriminating the two cave patterns. Petralona Cave falls into the category of a ramiform cave pattern. The cave’s hypogenic origin is also supported by meso-scale cave morphology, and the hydrothermal activity of the surrounding area. On the other hand, Maaras Cave has a typical underground river pattern. The horizontal patterns of the two caves were morphometrically scrutinized using Euclidean and fractal geometry.

A Wearable Vibratory Device (The Emma Watch) to Address Action Tremor in Parkinson Disease: Pilot Feasibility Study.

Parkinson disease (PD) is a neurodegenerative disease that has a wide range of motor symptoms, such as tremor. Tremors are involuntary movements that occur in rhythmic oscillations and are typically categorized into rest tremor or action tremor. Action tremor occurs during voluntary movements and is a debilitating symptom of PD. As noninvasive interventions are limited, there is an ever-increasing need for an effective intervention for individuals experiencing action tremors. The Microsoft Emma Watch, a wristband with 5 vibrating motors, is a noninvasive, nonpharmaceutical intervention for tremor attenuation. This pilot study investigated the use of the Emma Watch device to attenuate action tremor in people with PD. The sample included 9 people with PD who were assessed on handwriting and hand function tasks performed on a digitized tablet. Tasks included drawing horizontal or vertical lines, tracing a star, spiral, writing "elelelel" in cursive, and printing a standardized sentence. Each task was completed 3 times with the Emma Watch programmed at different vibration intensities, which were counterbalanced: high intensity, low intensity (sham), and no vibration. Digital analysis from the tablet captured kinematic, dynamic, and spatial attributes of drawing and writing samples to calculate mathematical indices that quantify upper limb motor function. APDM Opal sensors (APDM Wearable Technologies) placed on both wrists were used to calculate metrics of acceleration and jerk. A questionnaire was provided to each participant after using the Emma Watch to gain a better understanding of their perspectives of using the device. In addition, drawings were compared to determine whether there were any visual differences between intensities. In total, 9 people with PD were tested: 4 males and 5 females with a mean age of 67 (SD 9.4) years. There were no differences between conditions in the outcomes of interest measured with the tablet (duration, mean velocity, number of peaks, pause time, and number of pauses). Visual differences were observed within a small subset of participants, some of whom reported perceived improvement. The majority of participants (8/9) reported the Emma Watch was comfortable, and no problems with the device were reported. There were visually depicted and subjectively reported improvements in handwriting for a small subset of individuals. This pilot study was limited by a small sample size, and this should be taken into consideration with the interpretation of the quantitative results. Combining vibratory devices, such as the Emma Watch, with task specific training, or personalizing the frequency to one's individual tremor may be important steps to consider when evaluating the effect of vibratory devices on hand function or writing ability in future studies. While the Emma Watch may help attenuate action tremor, its efficacy in improving fine motor or handwriting skills as a stand-alone tool remains to be demonstrated.

Fractals and artificial intelligence to decrypt ideography and understand the evolution of language.

Self-sufficient ideographies are rare because they are stifled by the issue of standardization. Similar issues arise with abstract art or drawings created by young children or great apes. We propose that mathematical indices and artificial intelligence can help us decode ideography, and if not to understand its meaning, at least to know that meaning exists.

Indices of glycemic variability as the basis for building a prognostic model for the development of diabetic complications

The use of mathematical indices of glycemic variability (IGV) opens up new possibilities in predicting diabetic complications, which allows more accurate correction of therapy and prevention of the development of acute and chronic conditions. Aim. To analyze the predictive capabilities of glycemic variability indices to assess the development and progression of diabetic complications Material and methods. The study included 307 patients with type 1 diabetes mellitus (DM1). In all patients, glycated hemoglobin (HbA1c) was assessed, as well as the main indicators of glycemic control and IGV, which were selected to predict the formation and progression of diabetic complications. Statistical analysis was carried out using the SPSS 23.0 program. To build a model for predicting diabetic complications, the logistic regression method was used. Results. During the work, there was a decrease in HbA1c from 9.0 to 8.0% (p 0.005), as well as a change in the main parameters of carbohydrate metabolism and IGV. A predictive model for diabetic complications was built on the basis of HbA1c, mean glycemia and IGV – SD, CONGA, LI, LBGI, HBGI, MODD, MAGE, ADDR, MAG at the first study visit. The predictive model for the development of diabetic complications was considered significant at p 0.05. The resulting model showed a high sensitivity – 92% and a sufficient specificity of 85%. Not all parameters turned out to be statistically significant, however, with the exclusion of some, the sensitivity and specificity of the model decrease, which indicates the importance of each of the IGVs in predicting diabetic complications. Concludion. By analyzing the IGV, and not just the standard methods for assessing carbohydrate metabolism, the doctor can more accurately judge the compensation for diabetes and give the patient individual recommendations for treatment. Evaluation of GV, in particular its mathematical indices, play a significant role in predicting the development and progression of diabetic complications in patients with DM1 in childhood and adolescence.

Using MLP to locate transformer winding fault based on digital twin

There is no doubt that transformer plays a fundamental role in power system. At the same time, transformer winding fault diagnosis is an important topic. Many works put the most emphasis on the identification of fault type and degree, while ignoring the fault location. However, fault location is an urgent problem to be solved, which is worth studying and discussing. The contribution of this paper lies in the location of Disk space variation (DSV) fault. The introduction of digital twin can solve the problem of insufficient fault cases, and pave the way for the intellectualization of fault diagnosis. In this paper, the digital twin of transformer winding is established based on double ladder network, in which the distributed parameters are calculated by finite element method. Frequency response analysis (FRA) is one of the most widely accepted methods for transformer winding mechanical deformation fault diagnosis. Aiming at the interpretation code of FRA, this paper disproves the view that phase information is useful. Then, by extracting the mathematical index of FRA, multi-layer perceptron (MLP) is trained and DSV fault location is realized. In addition, the popular support vector machine is also compared with the MLP model in this paper, which further highlights the advantages of MLP. The proposed method is verified by an actual transformer, and the results are satisfactory.

Skin Whole-Mount Immunofluorescent Staining Protocol, 3D Visualization, and Spatial Image Analysis.

The use of polychromatic immunofluorescent staining on whole-mount skin enables cell type characterization and aids in the delineation of the physiological and immunological strategies used by the skin to combat pathogens. Using whole-mount skin for polychromatic immunofluorescent staining removes the need for histological sectioning and enables the visualization of anatomical structures and immune cell types in three dimensions. Here we present a detailed protocol for immunostaining with fluorescence-conjugated primary antibodies in whole-mount skin to reveal structural landmarks and specific immune cell types using confocal laser scanning microscopy (CLSM) (Basic Protocol 1). The optimized staining panel reveals structural features such as blood vessels (CD31 antibody) and the lymphatic network (LYVE-1 antibody), in combination with MHCII antibodies for antigen-presenting cells (APCs), CD64 for macrophages and monocytes, CD103 for dendritic epidermal T cells (DETC), and CD326 for Langerhans cells (LC). Basic Protocol 2 describes image visualization pipelines using open-source software (ImageJ/FIJI), enabling four visualization options (z-projections, orthogonal views, 3D visualization, and animation). Basic Protocol 3 describes a quantitative analysis pipeline using CellProfiler to characterize the spatial relationship between cell types using mathematical indices such as Spatial Distribution Index (SDI), Neighborhood Frequency (NF), and Normalized Median Evenness (NME). These protocols will enable researchers to stain, record, analyze, and interpret data from whole-mount skin using commercially available reagents in a CLSM-equipped laboratory and freely available analysis software. © 2023 Wiley Periodicals LLC. Basic Protocol 1: Immunofluorescent staining and imaging for whole-mount mouse skin Basic Protocol 2: File rendering and visualization using FIJI Basic Protocol 3: Spatial image analysis using CellProfiler.

Diversity and persistence of MRSA and VRE in skilled nursing facilities: environmental screening, whole-genome sequencing and development of a dispersion index

Environmental contamination with methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant Enterococcus (VRE) in skilled nursing facilities (SNFs) may contribute to patient acquisition. We assessed diversity and association of MRSA and VRE isolates in a SNF wing and developed a mathematical index to define each strain's tendency to persist in rooms and spread horizontally. Longitudinal study of MRSA and VRE colonization and contamination among successive patient occupancies in a cluster of nine SNF private rooms during eight months characterized by microbiological testing and whole genome isolate typing. 'Dispersion index" of a strain is defined as the number of rooms it was found in (including the patient), divided by the average of times it was found consecutively in the same room. MRSA (ten strain types) and VRE (seven types) were recovered from room or patient in 16.4% and 35.6% of the occupancies, respectively. MRSA showed moderate horizontal spread and several episodes of same-room persistence (three distinct strain types) (overall dispersion index: 1.08). VRE showed high tendency towards horizontal spread /new introductions (overall dispersion index: 3.25), and only one confirmed persistence episode. The emerging picture of high diversity among contaminating strains and high likelihood of room persistence despite terminal cleaning (MRSA) and horizontal spread between rooms (VRE) in this setting calls for improved cleaning practices, heightened contact precautions, and most of all to establish individually tailored facility screening programs to enable informed choices based on local, measurable and actionable epidemiologic parameters. University of Michigan OAIC REC Scholarship to M.C. National Institutes of Health K24 AG050685 to L.M.

63 Fatty Acid Profile of Beef from Feedlot Young Bulls of Two Genetic Groups

Abstract The fatty acid profile of the longissimus thoracis (LT) muscle and the activity of Δ9 desaturase6, Δ9 desaturase8, and elongase enzymes of beef from feedlot cattle of 2 genetic groups were evaluated. Fifty long-yearling young bulls were divided into two groups following their breed composition: Nellore (n = 25) and Angus × Nellore crossbred (n = 25), were randomly assigned into 4 pens (12 or 13 animals/pen) following a completely randomized design. Animals were sourced from the same breeding season and endured a grazing growing phase in Megathyrsus maximus cv. Mombaça pasture, with protein and energy supplement offered at 0.2% of body weight (BW). The feedlot phase comprehended 105 days of feed, and the diet (80% concentrate) was formulated to meet or safely exceed the beef cattle requirements to target an average daily gain (ADG) of 1.6 kg/day, in which major ingredients were represented by (% DM basis): sorghum silage (20%), ground corn (57.6%), ground soybean seed as the lipid source (20.4%), and a mineral/vitamin premix (2%). Samples of the LT muscle (between the 12th and 13th ribs) were taken right after slaughter to determine the profile of intramuscular fat. Lipids were extracted (2:1 chloroform/methanol), and 5 mL of the lipid extract was used for saponification followed by methylation and submitted for analysis using gas chromatography. The activities of Δ9 desaturase6, Δ9 desaturase8, and elongase enzymes were determined through mathematical indexes, in which their respective saturated and monounsaturated fatty acids were used. Data were analyzed using R (R CORE TEAM, 2021), and the effect of breed on the fatty acid profile was evaluated using the completely randomized design one-way, in which animal was used as the experimental unit. The sum of saturated fatty acids and unsaturated fatty acids was not affected (P ≥ 0.12) by genetic groups. Within FA profiles, crossbred bulls had greater (P = 0.05) concentration of monounsaturated fatty acids (49.7 vs. 52.4%), while beef of Nellore cattle showed greater (P ≤ 0.02) concentration of polyunsaturated fatty acids (6.71 vs. 7.67%) and n-3 (0.53 vs. 0.68%). A tendency (P = 0.07) was observed for the sum of n-6 and n-6/n-3 ratio, in which Nellore cattle had numerically greater values (6.63 vs. 4.89%, and 9.75 vs. 9.22, respectively). The activity of Δ9 desaturase6 and Δ9 desaturase8 was not affected (P ≥ 0.14) by genetic groups, while crossbred animals had greater (P = 0.03) activity of elongase (67.8 vs. 65.6%). Although the overall sum of mono and polyunsaturated fatty acids seems not to be affected, the FA profile and unsaturation/elongation enzymatic activity of beef was influenced by the genetic groups evaluated, in which both Nellore and their F-1 crossbreed counterparts had attractive responses.

A Data-Driven Under Frequency Load Shedding Scheme in Power Systems

This paper presents a measurement-based under-frequency load shedding scheme that considers time delays, measurement uncertainties, and communication network faults. Using a moving first-degree polynomial function, an iterative approach to estimate the frequency nadir and the associated frequency nadir time is proposed. Then, a novel method to simultaneously estimate the power imbalance and the system inertia constant is developed. According to an analytical basis, a base system is selected from a set of pre-defined base systems to guarantee accurate power imbalance estimation. Finally, a mathematical index is investigated to calculate a threshold for the generation-load power imbalance beyond which loads should be shed. Further, a systematic approach for specifying the amount of load to be shed in each transmission bus of the system is proposed. The effectiveness of the proposed methodologies is examined on both simulated and actual measured data from 9 historical power system disturbances in a national power grid.

Визначення посухостійкості популяцій люцерни насіннєвого використання за математичними індексами

The purpose of research. To evaluate the response of varieties and populations of seed alfalfa under different environments and to determine the best not only in terms of drought resistance, but also in terms of productivity under stress conditions with their further use in the breeding process. Methods. Research was conducted at the Institute of Irrigated Agriculture of the NAAS (now the Institute of climate smart agriculture of the NAAS) during 2017–2020. The object of study was 24 alfalfa populations for seed use. Resistance of alfalfa genotypes to stress was carried out using various mathematical indices and biplot analysis. Results. The hydrothermal coefficient (HTC) in 2017, 2018 and 2020 varied between 0.51 and 0.55, indicating very dry climatic conditions, while in 2019 it was 0.88, corresponding to dry conditions. 11 populations were characterized by high yield (>400 kg/ha) under stressful conditions. However, the best of these populations, which formed the highest seed productivity in the range of 445.5–472.1 kg/ha, A.–N. d. No. 15, Sin(c). / Prymorka and M.g. / CPU–11. According to the largest number of indices (9), the populations of A.–N. d. No. 15 and Sin(s). / Prymorka. Populations of M.g. / CP–11, which was characterized by the highest yield under stress, stood out according to four indices. The population T. / Emeraude population, which was characterized by one of the smallest reductions in yield and high yield under worse conditions, was distinguished by seven indices. Correlations between seed yield under different growing conditions and drought resistance indices were also analyzed. According to the results of GGE biplot analysis, the most drought–resistant population of M.g. / CP–11, Sin(s) population. / Prymorka and A.–N.d. No. 15 form a high yield of seeds under both conditions, and the selection according to k.s. has low productivity under worse conditions, but dramatically improves it when growing conditions are improved. Conclusions. The most promising alfalfa populations are identified and divided into groups by seed productivity.

A comparative study on salt stress response of Camelina sativa and Carthamus tinctorius during germination

Soil salinization is one of the most significant global problems, leading to reduced agricultural productivity potential and biodiversity. The main salt commonly found on the surface of soils and in water is NaCl, which directly impacts plant growth and land degradation. Therefore, this study was conducted to examine the morpho-physiological characteristics of two genotypes of Camelina sativa (?NS Slatka?; ?NS Zlatka?) and two genotypes of Carthamus tinctorius (?NS Lana?; ?NS Una?), which potentially characterize them as salt-tolerant crops. The levels of salinity tolerance were compared under five NaCl treatments, ranging from 0 mM to 200 mM. Based on the obtained results, seeds of all four genotypes germinated at the highest salt concentration (200mM NaCl), but the germination percentage declined at all salt concentrations. Moreover, lower salt concentrations induced root elongation and reduced shoot length of seedlings of all four genotypes. Salt stress tolerance indexes showed the importance of converting the plant parameters into mathematical indexes, and the significance of comparing all the tolerance indexes according to salt stress.