University of Silesia in Katowice
Recent publications
Individual-based models play a special role in applications of mathematics to biological problems. They describe a population as a heterogeneous family of individuals and the relationships between them. This description is relatively simple and convenient to simulate by computer and to determine various model parameters. Moreover, a macroscopic description of the population can be obtained from an individual-based model by appropriate limits. In this chapter we give a general characterization of individual-based models and we present examples of models to illustrate their possible applications. Examples of applications include age, size and phenotype models, coagulation-fragmentation process, and models of genome evolution.
In this chapter we introduce the mathematical apparatus needed to maintain macroscopic models from individual models through appropriate limit passages. We restrict our investigation to pure-jump IBMs. We show that starting from such models we can obtain in limits: phenotype models with intra-species competition, McKenrick’s age-structure model, and a superprocess which is a simplified version of Dawson’s superprocess.
In this chapter we present the Dawson–Watanabe superprocess. It is the limit process for an IBM, describing cells which move according to a Brownian motion and die or divide. We introduce a stochastic partial differential equation related to this superprocess. We also present a historical superprocess and the Fleming-Viot superprocess, which combines Moran’s model of genetic drift with mutations.
We present phenotypic IBMs and the limit passage from these models to a non-linear transport equation. We study two types of models: with random or assortative mating. In the case of random mating we give a theorem on asymptotic stability of the model. We show that assortative mating can lead to a polymorphic population and sympatric speciation.
In some models, individuals interact via some chemical factors. Such models are described by IBMs coupled to partial differential equations. We present two models of this kind: the first—motivating, strictly biological—a model of retinal angiogenesis. And the second, conceptually simpler but preserving most mathematical features, is a model of proliferating cells that undergo chemotaxis.
Chapter 2 was devoted to limit passages of sequences of individual-based models to some, usually deterministic, limit. Here we investigate the behaviour of the fluctuation processes, i.e. the difference between the converging process and the limit. We show that after appropriate rescaling the fluctuation process can converge to some Gaussian process. We use this approach to the models from the previous chapter to prove examples of CLT-type theorems.
IBMs allow us to describe processes of formation of aggregates of phytoplankton and their movement. We present two types of phytoplankton IBMs: the first type is based on fragmentation-coagulation processes. In the second type of models, we consider single cells that move by diffusion and chemical signals. The limit passages in these models lead to nonlinear transport equations and advanced superprocesses.
This study addresses the critical need for effective groundwater (GW) management in Muzaffarabad, Pakistan, amidst challenges posed by rapid urbanization and population growth. By integrating Support Vector Machine (SVM) and Weight of Evidence (WOE) techniques, this study aimed to delineate GW potential zones and assess water quality. This study fills the gap in applying advanced machine learning and geostatistical methods for accurate GW potential mapping. Eight thematic layers based on topography, hydrology, geology, and ecology were utilized to compute the GW potential model. Additionally, water quality analysis was performed on collected samples. The findings indicate that flat and gently sloping terrains, areas with an elevation range of 611 –687 m, and concave slope geometries are associated with higher GW potential. Additionally, proximity to drainage and high-density lineament zones contribute to increased GW potential. The results showed that 31.1% of the area had excellent GW potential according to the WOE model, whereas the SVM model indicated that only 20.3% fell in the excellent potential zone. Results showed that both models performed well in the delineating GW potential zones. Nevertheless, the application of the SVM method is highly recommended which will be benefited in GW resources management related to urban planning. The study also evaluates the spatial distribution of GW quality, with a focus on physical and chemical parameters, including electrical conductivity, pH, turbidity, total dissolved solids, calcium, magnesium, chloride, nitrate, and sulphate. Bacterial contamination assessment reveals that 76% of spring water samples (30 out of 39 samples) are contaminated with E.coli, raising public health concerns. Based on the chemical analysis of GW samples the study identified exceedances of WHO guidelines for calcium in two samples, magnesium in seven samples, sulphate in ten samples, and nitrate levels were below the WHO guideline across all samples. These results highlight localized chemical contamination issues that require targeted remediation efforts to safeguard water quality for public health.
Precipitation is a crucial hydro-meteorological variable for the protection and sustainability of water resources, and it has been significantly affected by climate change. Hence, it is essential to evaluate the effects of climate change on precipitation for effective water resource planning and development. This study aimed to evaluate trends of monthly precipitation in the Lower Mekong Delta River Basin (LMDRB) in southern Vietnam using innovative trend analysis methods. Monthly total precipitation data of eight stations in the basin observed from 1989 to 2018 were used. Mann-Kendall (MK) test, Innovative Polygon Trend Analysis (IPTA), and Improved Visualization of Innovative Trend Analyses (IV-ITA) methods were applied after homogeneity tests to the time series of the stations determined to be homogeneous. The IPTA method examined possible monthly precipitation transitions and seasonal changes, while the IV-ITA method examined the trend of the low and high precipitation categories. The IPTA method was more sensitive than the MK Test method in trend detection as it detected a trend in 85% (approximately 50% increase and 35% decrease) of the 84 (12*7) months. In almost all stations, an increasing trend was observed in September and December at low values, while a significant decrease was observed in April at high values. Continued increases and decreases in precipitation due to climate change impacts will significantly affect rice production in the LMDRB. This study provides valuable insights into the impact of climate change on precipitation in the basin, which could help in effective water resource planning and development.
The article concerns Slovak and Polish augmentative derivatives - nouns and adjectives with their word-forming exponents (suffixes and prefixes) and lexical exponents such as adnominals, which specify the meaning of magnitude (augmentative). The author pays attention to the state of research in this area and to the necessity of comparative Slovak-Polish research. The research material has been extracted mainly from Slovak lexicographical sources and the National Corpora of Slovak and Polish languages. The semantic properties of the described units are also the subject of analysis. Moreover, the suffixal and prefixal formants of selected augmentative derivatives are also characterised based on models proposed in the Slovak dictionary of word formation.
Understanding how water interacts with nanopores of carbonaceous electrodes is crucial for energy storage and conversion applications. A high surface area of carbonaceous materials does not necessarily need to translate to a high electrolyte‐solid interface area. Herein, we study the interaction of water with nanoporous C1N1 materials to explain their very low specific capacitance in aqueous electrolytes despite their high surface area. Water was used to probe chemical environments, provided by pores of different sizes, in ¹H MAS NMR experiments. We observe that regardless of their high hydrophilicity, only a negligible portion of water can enter the nanopores of C1N1, in contrast to a reference pure carbon material with a similar pore structure. The common paradigm that water easily enters hydrophilic pores does not apply to C1N1 nanopores below a few nanometers. Calorimetric and sorption experiments demonstrated strong water adsorption on the C1N1 surface, which restricts water mobility across the interface and impedes its penetration into the nanopores.
Mandelbrot set is one of the most fascinating objects in mathematics, so in the literature, one can find many studies related to this set. Moreover, there are many different extensions and generalizations of the classical Mandelbrot set. The two most popular extensions are the use of various kinds of functions and iterations. In this paper, firstly, we replace the constant c in the classical zp+czp+cz^p + c function used in the definition of Mandelbrot set with logctlogct\log c^t, where t∈RtRt \in \mathbb {R} and t≥1t1t \ge 1. Secondly, we replace the Picard iteration with the CR iteration scheme. For this combination of function and iteration, we prove the escape criterion for the escape-time algorithm used to generate some images of the proposed sets. Moreover, we study the dependency between the iteration’s parameters and two numerical measures (average number of iterations and generation time). We show that this dependency is complex and non-linear.
The glacier environment exhibits a high sensitivity to global climate change, leading to progressive deglaciation and the exposure of previously ice-covered land. The newly exposed terrain provides a valuable opportunity to observe rapid ecosystem changes, such as the accumulation of glacial sediments, the development of soil-forming and progressive alterations in water and biogeochemical cycles. While developing hydrological and hydrogeological models for the Werenskioldbreen proglacial expanding zone, we encountered a significant problem due to insufficient data for parameterizing glacial sediments, which constitute the environment for water flow and storage. This study provides detailed insight into the physicochemical parameters of glacial sediments and classifies them in terms of grain size distribution, hydraulic conductivity, pH and the content of carbon (Corg), nitrogen (Nt) and phosphorus (Pt). We found that the marginal outwash plains of Werenskioldbreen are characterised by gravelly sand, sandy gravel and silty sand (28.6%, 23.8% and 19% of the total sample contents, respectively). The lateral moraine contains sandy clayey silt, silty sandy gravel or sandy gravelly silt (7.1%, 4.8% and 2.4 % of the total sample contents, respectively). The chemical parameters of young glaciofluvial sediments have lower values than those of moraines. Corg ranged from 0.07% to 2.70%. Nt was < 1.00 g kg−1 for 95% of the samples and < 0.5 g kg−1 for 81% of them. Pt was between 0.48 and 1.18 g kg−1. In line with the studies on this subject already published, we confirm that there is clear a relationship between the type of geomorphological form, its age, and the physicochemical parameters of glacial sediments.
Liver cirrhosis and its complications constitute one of the most important causes of hospitalization in internal medicine departments. Liver cirrhosis is not a homogeneous disease entity, but is the final stage of many different liver diseases, and the most important causes leading to the development of liver cirrhosis are alcoholic liver disease and viral hepatitis. One of the typical complications of liver cirrhosis are symptoms of bleeding diathesis. The most common bleeding complication in patients with liver cirrhosis is bleeding from the upper gastrointestinal tract. The aim of this publication is to present a case report of a 32-year-old man in the terminal stage, hospitalized due to decompensated alcoholic cirrhosis of the liver, who during hospitalization developed a spontaneous large hematoma in the rectus abdominis muscle on the left side. The presented case report shows that in the care of patients with decompensated liver cirrhosis, vigilance must be maintained to recognize bleeding complications, including those with an atypical clinical course.
Arctic terrestrial invertebrate biodiversity is generally poorly known, but the archipelago of Svalbard has one of the most up-to-date inventories of its terrestrial and freshwater faunas of any Arctic region, offering a baseline for long term monitoring of invertebrate communities in space and time. Since the most recent review of the Svalbard invertebrate fauna was produced in 2014, knowledge of this fauna has developed and this inventory is here critically revised and updated. Our aims are (1) to critically review the inventory based on current taxonomic knowledge, (2) publish the complete species inventory, including cross-referencing to the relevant publications, in an open access data archive (GBIF), and (3) highlight the particular advantages that working in Svalbard may bring for scientists working on terrestrial, freshwater, and cryospheric environments. The inventory contains a total 1091 valid species names or interim names. A gap analysis in the Barcode of Life Data Systems reveals that 50% of the species currently documented from Svalbard lack COI (Cytochrome c oxidase subunit 1) barcode reference sequences in this database. Gaps in our knowledge of the Svalbard fauna and how these may be resolved are discussed.
The first electrochemical sensors of N-heterocyclic carbene (NHC) coordinated ruthenium organometallic 1-dimensional polymers and their multi-walled carbon nanotube (MWCNT)-based composite for detecting ketamine and scopolamine, are reported.
In this study, we examine the distribution of cryptobiotic abilities, specifically anhydrobiosis and cryobiosis, in tardigrade communities across a habitat gradient from the edge to the centre of a forest bordering a desert. Our study demonstrates no correlation between desiccation and freezing tolerance at the community level. However, communities inhabiting the forest centre show higher cryptobiotic performance, likely due to better energy reserves indicated by slower mortality rates during fasting. The observed distribution pattern of cryptobiotic abilities cannot be explained by differences in community compositions or body sizes, as these variables were uniform across the gradient. Our research highlights the significance of environmental factors in shaping cryptobiotic responses and sheds light on the functional characteristics underlying the distribution of tardigrades in fine-scale habitat gradients. Our findings also challenge the hypothesis of a correlation between desiccation and freezing tolerance in cryptobiotic organisms.
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5,215 members
Jacek Francikowski
  • Faculty of Natural Sciences
Damian Gruszka
  • Faculty of Natural Sciences
Katarzyna Wesierska
  • Department of Humanities; Institute of Linguistics
Michal Apollo
  • Faculty of Natural Sciences
Piotr Świątek
  • Department of Animal Histology and Embryology
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Address
Katowice, Poland
Head of institution
Prof. Ryszard Koziołek