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Povzetek: We study subspaces of tensor-product polynomials of bi-degree $(n, n)$ on the unit square whose restrictions to the domain diagonals have degree reduced by an integer $k \le n$. For maximal reduction $k = n$, these diagonally-reduced spaces coincide with the Bézier-Smart surface spaces and have dimension $n^2 + 2$. We derive exact dimension formulas and solve the boundary-diagonal matching problem: when can such a polynomial be replaced by a total-degree polynomial that agrees on the boundary and both diagonals? The answer is a sharp threshold on the degree parameters, with a complete characterisation of existence, uniqueness, and non-uniqueness. For the first non-trivial reduction parameters we provide explicit matching formulas and closed-form error estimates; when the solution is non-unique, the remaining freedom is resolved by $L^2$ optimality. At the endpoint $k = n$, where matching always fails, we show for $n = 3$ that the $L^2$-best approximation from the total-degree subspace is also the $L^\infty$-best approximation.
Ključne besede: bivariate polynomials, tensor-product polynomials, diagonal curves, boundary-diagonal matching, Bézier-smart surfaces, serendipity elements
Objavljeno v DiRROS: 01.07.2026; Ogledov: 94; Prenosov: 94
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Povzetek: Background Biliary tract cancers (BTCs) are usually diagnosed at an advanced stage, when the disease is incurable. Currently used tumor biomarkers have limited diagnostic value for BTCs, so there is an urgent need for sensitive and specific biomarkers for their earlier diagnosis. Deregulation of the homeostasis of trace elements is involved in the carcinogenesis of different cancers, including BTCs. The objective of the study is to determine/compare the total concentrations of copper (Cu), zinc (Zn) and iron (Fe) and the proportions of free Cu and Cu bound to ceruloplasmin (Cp) and the isotopic ratio of 65Cu/63Cu in serum samples from healthy volunteers and cancer patients using inductively coupled plasma-mass spectrometry-based methods (ICP-MS).
Ključne besede: trace elements, copper, predictive biomarkers of response
Objavljeno v DiRROS: 26.06.2026; Ogledov: 143; Prenosov: 59
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Povzetek: This study introduces hypothetical circuit elements, specifically the Constant Phase Element (CPE) and Zeroth-Order Approximation of a RC Circuit (ZARC), into the SPICE circuit simulation environment to enhance Electrochemical Impedance Spectroscopy (EIS) analysis. EIS, a critical method for understanding electrochemical processes in fields such as fuel cell analysis, corrosion studies, and biomaterials, relies on fitting measured impedance curves to Equivalent Electrical Circuit (EEC) models. However, existing approaches require expert knowledge and significant mathematical effort, limiting automation. By integrating CPE and ZARC into SPICE, this work bridges the gap between EIS analysis and advanced automatic circuit design methodologies, enabling efficient model selection and parameter determination. Experimental results demonstrate the accuracy of the implemented elements through a series of case studies, evaluated using Sheppard’s criteria function. This integration marks a significant step toward automated EIS model fitting and optimization, with potential implications for advancing electrochemical and materials research.
Ključne besede: electrochemical impedance spectroscopy, circuit simulators, hypothetical circuit elements, equivalent electronic circuits
Objavljeno v DiRROS: 18.06.2026; Ogledov: 174; Prenosov: 208
Celotno besedilo (639,78 KB)
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Povzetek: Background. There is almost no data on the combined associations between apolipoprotein E gene (APOE) genotypes, trace elements (TEs), and lipid peroxidation in vivo. The aim of our study was to evaluate the association between APOE genotypes and TE levels in blood (B-TEs) and erythrocytes (E-TEs), and 8-isoprostane in urine (U-8-isoprostane) in women with low exposure to potentially toxic TEs and with adequate supply of essential TEs. Methods. B-TEs, E-TEs and U-8-isoprostane were determined in 172 healthy women of childbearing age (30.1–51.4 years) using ICP-MS and ELISA competitive assay, respectively. All women were divided into three APOE genotype groups according to the presence of the ɛ4 allele, ɛ2 allele or ɛ3 homozygotic allele. The associations between B-TEs, E-TE, U-8-isoprostane, and the APOE genotype groups were estimated by multiple variable linear regression models with relevant explanatory variables (e.g., age, BMI, and seafood). Results. All TE and U-8-isoprostane levels were inside the reference ranges for the healthy population. In the multiple variable linear regression models, our results showed that urine 8-isoprostane levels increased by up to 43.3% in the APOE4 group compared to the APOE3 group and a negligible negative modifying effect for essential TEs. However, the APOE genotype groups were associated also with some TEs. A clear positive association was found between the APOE2 and APOE4 groups (vs. APOE3) with B-molybdenum. Conclusions. Our study suggests that the APOE4 genotype played an important role in 8-isoprostane variability in a population with an adequate supply of essential and with low exposure to potentially toxic TEs. Adequate copper, zinc and selenium status seemed to be protective against, while the levels of nonessential TEs were probably too low to play a decisive role in 8-isoprostane formation. The observed impact of the APOE2 and APOE4 groups on increased B-molybdenum opens a new research topic.
Ključne besede: apolipoprotein E, polymorphisms, trace elements, multiple variable linear regression models
Objavljeno v DiRROS: 05.06.2026; Ogledov: 230; Prenosov: 317
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Povzetek: Background: Autism spectrum disorder (ASD) arises from complex gene–environment interactions. While trace element abnormalities have been studied, associations with autism severity remain inconsistent. Ratios indicating detoxification balance, rather than single toxic elements, may better reflect severity. Objective: To examine the relationships between urinary trace element levels, detoxification-related element ratios, and autism severity measured by the Childhood Autism Rating Scale (CARS). Methods: In a crosssectional study of 168 participants (103 ASD, 65 controls), thirty urinary trace elements were quantified by ICP-MS. ASD patients were stratified by CARS into subthreshold ASD (n = 29), mild–moderate ASD (n = 36), and severe ASD (n = 38). Analyses included Mann–Whitney U, Kruskal–Wallis, and Spearman correlation tests, focusing on Li/Pb, Cu/Pb, and Cr/Pb ratios. Results: Individual elements showed weak associations with CARS; lead correlated positively (ρ = 0.209, p = 0.035) and lithium inversely (ρ = −0.194, p = 0.051). In contrast, element ratios showed stronger links: Li/Pb (ρ = −0.349, p = 0.0003), Cu/Pb (ρ = −0.320, p = 0.0011), and Cr/Pb (ρ = −0.209, p = 0.035). Severe ASD exhibited modest 90th-percentile elevations for toxic elements but high heterogeneity. Conclusions: Single-element levels showed limited associations with ASD severity. Element ratios, particularly Li/Pb, showed stronger statistical associations than individual elements in this cross-sectional dataset; however, these findings should be interpreted as candidate correlates rather than causal or clinically validated biomarkers.
Ključne besede: autism spectrum disorder, trace elements, lead, llithium, detoxification, biomarkers, CARS, element ratios, environmental toxins, metallothionein
Objavljeno v DiRROS: 01.06.2026; Ogledov: 185; Prenosov: 131
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