arXiv subjects

Agnieszka Niemczynowicz

Publications and source records attributed to Agnieszka Niemczynowicz.

11 recordsLinked to original sources

arXiv2026

Diffusion of tacit knowledge in a company: a mathematical model based on diffusion on graphs

This article is devoted to the process of diffusing tacit knowledge. This intangible asset has proven crucial for achieving a competitive advantage among market-oriented companies. A novel model of tacit knowledge diffusion is presented, employing the concept of heat diffusion from physics. Furthermore, graph theory and the dynamics it defines are utilized. We defined a Tacit Knowledge Transfer Graph that encodes data from questionnaires. It enables us to identify employees' learning needs, allowing for the planning of classes within the same period, such as a day, to schedule them optimally. Moreover, the model can be used to identify employees with high knowledge demands. The application is not limited to companies; a simple example of planning classes in a school/university is provided. The presented model can help with optimal scheduling, enhance operational efficiency, and improve talent management within the company. It can also identify risks associated with critical sources of knowledge and help improve organizational culture and knowledge management policy.

econ.TH↗

arXiv2026

Fully tensorial approach to hypercomplex-valued neural networks

A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central observation is that algebra multiplication can be represented by a rank-three tensor, which allows all algebraic operations in neural network layers to be formulated in terms of standard tensor contractions, permutations, and reshaping operations. This tensor-based formulation provides a unified and dimension-independent description of hypercomplex-valued dense and convolutional layers and is directly compatible with modern deep learning libraries supporting optimized tensor operations. The proposed framework recovers existing constructions for four-dimensional algebras as a special case. Within this setting, a tensor-based version of the universal approximation theorem for single-layer hypercomplex-valued perceptrons is established under mild non-degeneracy assumptions on the underlying algebra, thereby providing a rigorous theoretical foundation for the considered class of neural networks.

cs.LG↗

arXiv2026

Elastodynamical properties of Sturmian structured media

In this paper, wave propagation in structured media with quasiperiodic patterns is investigated. We propose a methodology based on Sturmian sequences for the generation of structured mechanical systems from a given parameter. The approach is presented in a general form so that it can be applied to waveguides of different nature, as long as they can be modeled with the transfer matrix method. The bulk spectrum is obtained and its fractal nature analyzed. For validation of the theoretical results, three numerical examples are presented. The obtained bulk spectra show different shapes for the studied examples, but they share features which can be explained from the proposed theoretical setting.

math-ph↗

arXiv2024

KHNNs: hypercomplex neural networks computations via Keras using TensorFlow and PyTorch

Neural networks used in computations with more advanced algebras than real numbers perform better in some applications. However, there is no general framework for constructing hypercomplex neural networks. We propose a library integrated with Keras that can do computations within TensorFlow and PyTorch. It provides Dense and Convolutional 1D, 2D, and 3D layers architectures.

cs.LG↗

arXiv2024

A Critical Analysis of the Theoretical Framework of the Extreme Learning Machine

Despite the number of successful applications of the Extreme Learning Machine (ELM), we show that its underlying foundational principles do not have a rigorous mathematical justification. Specifically, we refute the proofs of two main statements, and we also create a dataset that provides a counterexample to the ELM learning algorithm and explain its design, which leads to many such counterexamples. Finally, we provide alternative statements of the foundations, which justify the efficiency of ELM in some theoretical cases.

cs.LG↗

arXiv2024

Hypercomplex neural network in time series forecasting of stock data

The goal of this paper is to test three classes of neural network (NN) architectures based on four-dimensional (4D) hypercomplex algebras for time series prediction. We evaluate different architectures, varying the input layers to include convolutional, Long Short-Term Memory (LSTM), or dense hypercomplex layers for 4D algebras. Four related Stock Market time series are used as input data, with the prediction focused on one of them. Hyperparameter optimization for each architecture class was conducted to compare the best-performing neural networks within each class. The results indicate that, in most cases, architectures with hypercomplex dense layers achieve similar Mean Absolute Error (MAE) accuracy compared to other architectures, but with significantly fewer trainable parameters. Consequently, hypercomplex neural networks demonstrate the ability to learn and process time series data faster than the other tested architectures. Additionally, it was found that the ordering of the input time series have a notable impact on effectiveness.

cs.NE↗

arXiv2023

Selected aspects of complex, hypercomplex and fuzzy neural networks

This short report reviews the current state of the research and methodology on theoretical and practical aspects of Artificial Neural Networks (ANN). It was prepared to gather state-of-the-art knowledge needed to construct complex, hypercomplex and fuzzy neural networks. The report reflects the individual interests of the authors and, by now means, cannot be treated as a comprehensive review of the ANN discipline. Considering the fast development of this field, it is currently impossible to do a detailed review of a considerable number of pages. The report is an outcome of the Project 'The Strategic Research Partnership for the mathematical aspects of complex, hypercomplex and fuzzy neural networks' meeting at the University of Warmia and Mazury in Olsztyn, Poland, organized in September 2022.

cs.LG↗

arXiv2022

Stimulation of soy seeds using environmentally friendly magnetic and electric fields

The study analyzes the impact of constant and alternating magnetic fields and alternating electric fields on various growth parameters of soy plants: the germination energy and capacity, plants emergence and number, the Yield(II) of the fresh mass of seedlings, protein content, and photosynthetic parameters. Four cultivars were used: MAVKA, MERLIN, VIOLETTA, and ANUSZKA. Moreover, the advanced Machine Learning processing pipeline was proposed to distinguish the impact of physical factors on photosynthetic parameters. It is possible to distinguish exposition on different physical factors for the first three cultivars; therefore, it indicates that the EM factors have some observable effect on soy plants. Moreover, some influence of physical factors on growth parameters was observed. The use of ELM (Electromagnetic) fields had a positive impact on the germination rate in Merlin plants. The highest values were recorded for the constant magnetic field (CMF) - Merlin, and the lowest for the alternating electric field (AEF) - Violetta. An increase in terms of emergence and number of plants after seed stimulation was observed for the Mavka cultivar, except for the AEF treatment (number of plants after 30 days) (...)

q-bio.QM↗

arXiv2022

Model of work motivation based on happiness: pandemic related study

This study aims to enrich the current literature by providing a new approach to motivating Generation Z employees in Poland. Employees need to be motivated in order to be efficient at doing a particular task at the workplace. As young people born between 1995 and 2004 called Generation Z, enter the labour market it, is essential to consider how employees' motivation might be affected. Traditionally identified motivators are known, but many reports indicate that the motivation continues decreasing. This situation causes some perturbations in business and fluctuations of staff. In order to prevent this situation, the employers are looking for new solutions to motivate the employees. A quantitative approach was used to collect new evidence from 200 Polish respondents completing an online survey. The research were conducted before and during pandemic time. We report and analyse the survey results conducted in Poland among representatives of Generation Z, who were employed for at least 6 months. We developed and validated a new approach to motivation using methodologies called Factor Analysis. Based on empirical verification, we found a new tool that connects employee motivation and selected areas of the Hygge concept called Hygge star model, which has the same semantics before and during Covid-19 pandemic.

econ.GN↗

arXiv2021

Towards the global vision of engagement of Generation Z at the workplace: Mathematical modeling

Correlation and cluster analyses (k-Means, Gaussian Mixture Models) were performed on Generation Z engagement surveys at the workplace. The clustering indicates relations between various factors that describe the engagement of employees. The most noticeable factors are a clear statement about the responsibilities at work, and challenging work. These factors are essential in practice. The results of this paper can be used in preparing better motivational systems aimed at Generation Z employees.

econ.GN↗

arXiv2020

TreeGen -- a Monte Carlo generator for data frames

The typical problem in Data Science is creating a structure that encodes the occurrence frequency of unique elements in rows and relations between different rows of a data frame. We present the probability tree abstract data structure, an extension of the decision tree, that facilitates more than two choices with assigned probabilities. Such a tree represents statistical relations between different rows of the data frame. The Probability Tree algorithmic structure is supplied with the Generator module that is a Monte Carlo generator that traverses through the tree. These two components are implemented in TreeGen Python package. The package can be used in increasing data multiplicity, compressing data preserving its statistical information, constructing hierarchical models, exploring data, and in feature extraction.

cs.LG↗