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Abstract: A $\Gamma$-distance magic labeling of a graph $G = (V, E)$ with $|V| = n$ is a bijection $\ell$ from $V$ to an Abelian group $\Gamma$ of order $n$, for which there exists $\mu \in \Gamma$, such that the weight $w(x) =\sum_{y\in N(x)}\ell(y)$ of every vertex $x \in V$ is equal to $\mu$. In this case, the element $\mu$ is called the magic constant of $G$. A graph $G$ is called a group distance magic if there exists a $\Gamma$-distance magic labeling of $G$ for every Abelian group $\Gamma$ of order $n$. In this paper, we focused on cubic $\Gamma$-distance magic graphs as well as some properties of such graphs.
Keywords: group distance magic labeling, Kotzig array, generalized Petersen graph
Published in RUP: 06.05.2026; Views: 152; Downloads: 5
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Abstract: Motivation Advances in hardware have made molecular dynamics (MD) simulations of protein structures faster and more accessible to the scientific community. However, accurately estimating protein flexibility using MD remains computationally demanding, especially for large systems and long time scales. Several MD-based resources—including MdMD, the DynamD database, and more recently ATLAS and mdCATH—now provide MD trajectories for thousands of proteins, enabling the development of predictive models. Results Here, the Graphlet Degree Vector (GDV) is introduced as a lightweight, fast, and easy-to-implement linear model for predicting protein flexibility directly from atom coordinates. GDV is a 15-dimensional feature vector that captures local packing and the spatial connectivity of each atom with its nearby neighbors. Trained on a subset of globular-like proteins from the ATLAS database, the GDV model achieves a Spearman correlation of 0.828 compared to MD data. The model trained on ATLAS dataset was further evaluated on independent Nuclear Magnetic Resonance and cryo-electron microscopy datasets, demonstrating the robustness and generalizability of the GDV-based approach. A key advantage of the GDV model is that it requires no additional external or experimental data and can be applied in near real time (on the order of 10 seconds) even for large proteins with 20,000 atoms on a standard desktop or laptop. Overall, the results show that a lightweight, fast, and purely coordinate-based model can provide accurate and generalizable predictions of protein flexibility across diverse folds and sizes.
Keywords: protein flexibility, graphlets, predictive model
Published in RUP: 16.04.2026; Views: 270; Downloads: 11
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Abstract: Background: Physical activity, sedentary behaviour, and sleep were shown to be independently associated with low back pain (LBP). The aim of this cross-sectional study was to explore the associations between 24-hour movement behaviour compositions and the occurrence, severity, and estimated level of LBP impact on an individual’s life. Methods: A convenience sample of 197 adults (40% females, 37 ± 11 years of age) were asked to wear an activPAL accelerometer for at least 7 consecutive days to assess their time-use composition consisting of moderate- to vigorous-intensity physical activity (MVPA), light- intensity physical activity (LPA), sedentary behaviour (SB), and sleep and to complete a questionnaire on LBP and sociodemographic characteristics. Compositional isotemporal substitution analyses were conducted separately for the non-domain-specific and domain- specific (including occupational and non-occupational domains) movement behaviour compositions. Results: Reallocating time from MVPA to any other movement behaviour or from sleep to LPA was associated with a higher LBP impact score. For example, reallocating 60 min/day from MVPA to LPA was associated with on average 17 points (95% CI: 6 to 28) higher LBP impact score (on a 0-70 scale). We did not find significant associations between the domain- specific time-use composition and LBP impact score (p = 0.060). We also did not find significant associations of the time-use compositions with occurrence and severity of LBP (p- value range: 0.067 to 0.649). Conclusion: Our study suggests that LBP sufferers with higher MVPA and sleep better cope with LBP. The differences in the LBP impact scores associated with theoretical reallocations between movement behaviours may be deemed clinically important. Future longitudinal and experimental studies in population-representative samples are needed to confirm our findings.
Keywords: musculoskeletal health, physical behaviours, time-use epidemiology
Published in RUP: 30.03.2026; Views: 334; Downloads: 8
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Abstract: Results from the mathematical literature on random walks reveal a closed-form analytical expression for the ▫$\pi$▫-energy and bond number of graphene in the simplest tight-binding model and its Hartree-Fock Hubbard extension. Closed-form expressions follow for all ▫$\pi$▫ spectral moments of graphene. Bond numbers of carbon and boron nitride (BN) zigzag nanotubes are found as finite sums, with graphene and hexagonal boron nitride sheets as asymptotes.
Keywords: graph theory, random walks, graphene, bond number, tight-binding model, spectral moments, Hubbard model, zigzag nanotubes, hexagonal boron nitride, gamma function
Published in RUP: 10.03.2026; Views: 377; Downloads: 6
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Abstract: We present a novel method for solving high-order partial differential equations (PDEs) over planar multi-patch geometries with possibly extraordinary vertices demonstrated on the basis of the polyharmonic equation of order m, m ≥ 1, which is a particular linear elliptic PDE of order 2m. Our approach is based on the concept of Isogeometric Tearing and Interconnecting (IETI) and allows to couple the numerical solution of the PDE with Cs-smoothness, , across the edges of the multi-patch geometry. The proposed technique relies on the use of a particular class of multi-patch geometries, called bilinear-like Gs multi-patch parameterizations, to represent the multi-patch domain. The coupling between the neighboring patches is done via the use of Lagrange multipliers and leads to a saddle point problem, which can be solved first by a small dual problem for a subset of the Lagrange multipliers followed by local, parallelizable problems on the single patches for the coefficients of the numerical solution. Several numerical examples for the polyharmonic equation of order m = 1, m = 2 and m = 3, i.e. for the Poisson’s, the biharmonic and the triharmonic equation, respectively, are shown to demonstrate the potential of our IETI method for solving high-order problems over planar multi-patch geometries with possibly extraordinary vertices.
Keywords: isogeometric analysis, Galerkin method, C^s-smoothness, Tearing and Interconnecting, multi-patch domain, polyharmonic equation
Published in RUP: 02.02.2026; Views: 485; Downloads: 5
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