<abstract xmlns="http://www.w3.org/1999/xhtml">

Oat is a grain in high demand, due to its physiological and nutritional attributes as a functional food. Oat is rich in <italic>β−</italic>glucans, and high in tocopherol and other dietary fibre components. It is also used for forage, fodder, chaff and as a major component of infant foods. In the present study, oat yields from six experimental stations in south-western Poland, obtained in 2019–2022, were analysed using three different linear mixed models that can be associated with three different stabilities. It is shown that the genotype Perun had the highest mean yield among the tested genotypes, while the genotype Armani was the most stable. Armani and Pablo had the lowest values of the GSI index, making them the most favourable genotypes for cultivation in that region.
</abstract>

Department of Mathematical and Statistical Methods

Stability analysis of spring oat genotypes in south-west Poland

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, some qualitative behaviors of solutions for certain second-order nonlinear differential equation with damping and resonance effects are considered. By employing Lyapunov’s direct method, a complete Lyapunov function was used to investigate the stability of the system. Krasnoselskii’s fixed point theorem was used to establish sufficient conditions that guaranteed the existence and boundedness of a unique solution. The results show that the equilibrium point was asymptotically stable. Furthermore, a test for periodicity was conducted using the Bendixson criterion, and the results showed that the solution of the second-order nonlinear differential equation is aperiodic, which extends some results from the literature.
</abstract>

Enugu State University Science and Technology

Existence, uniqueness, boundedness and stability of periodic solutions of a certain second-order nonlinear differential equation with damping and resonance effects

<abstract xmlns="http://www.w3.org/1999/xhtml">

Brain tumor is a very serious disease from which many people die every day. Appropriate early diagnosis is extremely important in treatment. In recent years, machine learning methods have come to the aid of doctors, allowing them to automate the process of brain tumor detection. It is a useful tool that can support doctors in their daily work. We consider here the use of machine learning methods to detect brain tumors based on magnetic resonance images. We use artificial neural networks to classify the images into those containing and those without a brain tumor. More specifically, we apply convolutional neural networks on appropriately transformed input data. The three proposed convolutional neural network models were created based on the pre-trained VGG19, DenseNet-121, and InceptionV3 networks, which achieved an accuracy of 92.59%, with areas under the ROC curve ranging from 0.95 to 0.96. The precision, sensitivity, and F1-score are also satisfactory and promising. These results are better than those for the models presented on the Kaggle platform.
</abstract>

Machine learning methods in the detection of brain tumors

<abstract xmlns="http://www.w3.org/1999/xhtml">

This research fitted a discrete distribution for modeling count data. Specifically, Zero-Inflated Poisson (ZIP) regression was used to model plant protein consumption by 400 randomly sampled individuals in Wukari. The data was collected by questionnaire. The ZIP regression model was used based on its ability to model data with excess zeros present in the collected data. Variables considered and used for the analysis are Age, Body Mass Index, Blood Pressure, Occupation, Gender, Weight, Height, Body Reaction, and Consumption Class. The parameters of the ZIP model were estimated using the maximum likelihood estimation technique. The model was tested for Goodness of Fit (GoF) using deviance, scaled deviance, Pearson–<italic>χ</italic>2 and scaled Pearson–<italic>χ</italic>2 statistics. The results obtained showed that Age, Gender, and Reaction were significant at 5%, and the GoF tests revealed that the Zero-Inflated Poisson regression produces a good fit and is a good model for overcoming the overdispersion effect.
</abstract>

Zero-Inflated Poisson Regression Modeling of Plant Protein Consumption

<abstract xmlns="http://www.w3.org/1999/xhtml">

The theory of inequalities is an essential tool in all fields of the theoretical and practical sciences, especially in statistics and biometrics. Fujiwara’s inequality provides relationships between expected values of products of random variables. Special cases of this inequality include important classical inequalities such as the Cauchy–Schwarz and Chebyshev inequalities.
The purpose of this article is to prove Fujiwara’s inequality in abstract probability spaces with more general assumptions for random variables than those associated with monotonicity as found in the literature. This newly introduced property of random variables will be called synchronicity. As a consequence, we obtain inequalities originated by Chebyshev, Hardy–Littlewood–Pólya and Jensen–Mercer under new conditions.
The results are illustrated by some examples constructed for specific probability measures and specific random variables. In biometrics, the obtained inequalities can be used wherever there is a need to compare the characteristics of experimental data based on means or moments, and the data can be modeled using functions that are synchronous or convex.
</abstract>

Fujiwara’s inequality for synchronous functions and its consequences

<abstract xmlns="http://www.w3.org/1999/xhtml">

Some questions related to the problem of determining a chemical balance weighing design satisfying the criterion of D-optimality are considered. The theory is based on the assumption that the measurements are equally positively correlated and have the same variances. In this paper, we present a method of adding three measurements to a regular D-optimal chemical balance weighing designs to obtain a highly D-efficient chemical balance weighing design. The problem formulated in this way is an extension of results contained in a paper previously published in <italic>Biometrical Letters</italic>.
</abstract>

D-optimal chemical balance weighing designs with positively correlated errors: part II

<abstract xmlns="http://www.w3.org/1999/xhtml">

A field experiment was carried out in the years 2017–2019 on the fields of the Experimental Station in Chrząstowo, belonging to the Research Centre for Cultivar Testing in Słupia Wielka. It was carried out for 3 years in the same split-plot design with 2 experimental factors in 3 field replicates. The following factors were studied: A – 1st order factor – maize variety: A1 – ES Bombastic (FAO 230-240) – single cross hybrid (SC), A2 – ES Abakus (FAO 230-240) – three-way cross hybrid (TC, stay-green), A3 – ES Metronom (FAO 240) – single cross hybrid (SC, stay-green + roots power). B – 2nd order factor – type of nitrogen fertilizer: B1 – control (without N application), B2 – ammonium nitrate, B3 – urea, B4 – ammonium nitrate + N-Lock, B5 – urea + N-Lock, B6 – Super N-46, B7 – UltraGran stabilo. In this study, we investigated whether there was a functional relationship between maize grain yield and ear number, TSW (thousand-seed weight), and seed number per ear. Additionally, we investigated whether there was a functional relationship between maize grain yield and ear number, TSW, and seed number per ear for each type of fertilization in a given study year, as well as for each type of fertilization regardless of year.
</abstract>

Functional relationships between yield of maize (<italic>Zea mays</italic> L.) and its components

<abstract xmlns="http://www.w3.org/1999/xhtml">

Covariance matrices with a linear structure are widely used in multivariate analysis. The choice of covariance structure can be made from a set of possible linear structures. As a result, the most appropriate structure is determined by minimizing the discrepancy function. This paper is a continuation of previous work on identifying linear structures with an entropy loss function as a discrepancy function. We present extensive simulation studies on the correctness of identification with the assumed pentagonal banded Toeplitz structure.
</abstract>

Structure identification for a linearly structured covariance matrix: part II

<abstract xmlns="http://www.w3.org/1999/xhtml">

Starting from a simple Gauss–Markov model, this paper presents notes about criteria for the estimability of parametric functions of the vector of interest in linear models. The results obtained for the transformed models are compared with known results from the literature.
</abstract>

Notes on parametric functions in the linear model

<abstract xmlns="http://www.w3.org/1999/xhtml">

Covariance matrices with a linear structure are widely used in multivariate analysis. The choice of the most appropriate covariance structure can be made from a class of possible linear structures. Once we have made the choice, an important question is how we can estimate the covariance matrix for a given covariance structure. This article describes methods used to estimate the structured covariance matrix, and indicates the advantages and disadvantages of the selected methods.
</abstract>

Estimation methods for a linearly structured covariance matrix

AHEAD OF PRINT

Volume 60 (2023): Issue 2 (December 2023)

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Biometrical Letters

 Biometrical Letters is the official journal of the Polish Biometric Society, founded in 1964, now published with the financial support of the Ministry of Science and Higher Education. The anonymous double-blind peer review by the two independent reviewers is applied to all the papers.  The purposes of Biometrical Letters are:   publishing papers dealing with various aspects of the analysis and interpretation of results from biometrical experiments, using mathematical and statistical methods;  promoting and extending the use of statistical and mathematical methods in the principal disciplines of life sciences by reporting on the development and application of these methods;  presenting statistical and mathematical tools useful in biometry. Methodological developments should be motivated by interesting problems from life sciences, applied or applicable;  publishing review papers and papers presenting practical use of various methods of data analysis and statistical inference.   The core of most Biometrical Letters articles is statistical inference that sets scientific or policy objectives, motivates methodological development and demonstrates the operation of new methods.  The paper should include a description of the biometrical problem and a section detailing the application of the new methodology.  The Journal welcomes the submission of manuscripts from bioscience, mathematical and statistical theory, biology, genetics, medical statistics, agriculture, forestry, ecology, environmental sciences, biometrics and clinical trials. Case studies and articles on the use and development of statistical software are also welcome.  Rejection Rate   20%   Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. 