Ventricular function is vital in patients with single ventricles but repeated surgeries and changes in ventricular volume load may change the relation between longitudinal and radial function. To expand the knowledge of cardiac mechanics in this population, the aim of this study was to assess longitudinal and radial contribution to stroke volume using cardiac magnetic resonance (CMR) imaging in patients before and after Fontan operation. We also aimed to assess whether the atrioventricular coupling was intact in these patients despite multiple pericardiotomies. Twelve children underwent CMR before and after completion of Fontan circulation. Endocardial borders of the atria and the ventricle as well as the epicardial border of the heart were delineated. The percentage of the stroke volume attributed to longitudinal and radial function was calculated and pulmonary venous blood flow during the cardiac cycle was assessed. Longitudinal function correlated strongly with atrial filling (r2 = 0.90, ICC = 0.92) and its contribution to stroke volume was 40 [38-49] % before and 39 [33-45] % after completion of Fontan circulation (P = 0.092). All patients lacked the late systolic flow peak in the pulmonary veins corresponding to the lack of a normal right ventricle. In conclusion, patients with single ventricles exhibit preserved atrioventricular coupling but the ventricle has lower longitudinal and higher radial contribution to stroke volume as a consequence of the passive pulmonary blood flow relative to healthy hearts. Completion of Fontan circulation does not change this relationship.NEW & NOTEWORTHY This study shows that patients with single ventricles exhibit lower longitudinal systolic function than healthy subjects. The longitudinal contribution to stroke volume was about 40% compared with ∼80% in a normal right ventricle and 60% in a normal left ventricle. This difference is likely related to the passive blood flow through the lungs and did not change after Fontan completion. Furthermore, atrioventricular coupling seems to be preserved despite previous pericardiotomies.

The elastic and inelastic longitudinal electron scattering form factors in of chromium isotopes (50,52Cr) isotopes were studied using the radial wave functions of a transformed harmonic oscillator potential in the local scale transformation technique. Occupation numbers from configuration mixing using the Hsieh-Wildenthal (HW) method for 50,52Cr were considered in parallel with those obtained using the adjusted occupation numbers. For shell interactions, the model space for HW interaction is restricted to the 1d3/2 and 1f7/2 subshells. The charge density distributions in the ground state and differential electron scattering cross-sections were computed. The inelastic form factors were studied by including core polarization using the Bohr-Mottelson model. For 50Cr, the three C2 transitions and the two C4 transitions were investigated. For 52Cr, the inelastic form factor for the two C2 transitions and for the two C4 transitions is investigated. In general, the use of the transformed harmonic-oscillator (THO) basis proved itself to be a good candidate to study stable nuclei, where good results (elastic and inelastic Coulomb form factors and differential cross sections) were obtained for 50,52Cr isotopes.

Abstract To every log-concave function f one may associate a pair of measures $$(\mu _{f},\nu _{f})$$ ( μ f , ν f ) which are the surface area measures of f . These are a functional extension of the classical surface area measure of a convex body, and measure how the integral $$\int f$$ ∫ f changes under perturbations. The functional Minkowski problem then asks which pairs of measures can be obtained as the surface area measures of a log-concave function. In this work, we fully solve this problem. Furthermore, we prove that the surface area measures are continuous with respect to a suitable topology: If $$f_{k}\rightarrow f$$ f k → f , then $$\left( \mu _{f_{k}},\nu _{f_{k}}\right) \rightarrow \left( \mu _{f},\nu _{f}\right) $$ μ f k , ν f k → μ f , ν f in a corresponding sense. Finding the appropriate mode of convergence of the pairs $$\left( \mu _{f_{k}},\nu _{f_{k}}\right) $$ μ f k , ν f k sheds a new light on the construction of functional surface area measures. To prove this continuity theorem we associate to every convex function a new type of radial function, which seems to be an interesting construction on its own right. Finally, we prove that the solution to the functional Minkowski problem is continuous in the data, in the sense that if $$\left( \mu _{f_{k}},\nu _{f_{k}}\right) \rightarrow \left( \mu _{f},\nu _{f}\right) $$ μ f k , ν f k → μ f , ν f then $$f_{k}\rightarrow f$$ f k → f up to translations.

The Eastern Cordillera of the Colombian Andes is a high-elevation asymmetric plateau subjected to NW–SE shortening. An interesting aspect of this plateau is the presence of high geothermal gradients (up to 52 °C/km), constrained by wells drilled in sedimentary basins. Radial and transverse receiver functions were computed at key sites in the plateau and the adjacent low-elevation foreland region to better understand the controlling factors of these anomalous gradients. Results indicate the presence of tilted anisotropic layers in the uppermost crust of the Cordillera, and nonexistent to weak anisotropy in the foreland region. The estimated SE fast-axis trend of the anisotropy is related to NNE-striking faults and top-to-the-east tectonic transport during deformation. We interpret the SE fast axis as being associated with shearing of NW-dipping faults in the plateau. Compiled thermochronological data point to high deformation and exhumation rates since the middle Miocene, which we use to propose that the rapid rise of deep and hot blocks along major regional faults is perturbing the background geothermal gradient. Regions near major thrust faults in the Eastern Cordillera are potential areas for geothermal energy exploration due to the perturbed geothermal gradient and enhanced fluid infiltration related to deep fault systems.

The aim of this study was to evaluate the dosimetric characteristics of an IRAsource brachytherapy source using Monte Carlo simulations incorporating source electron effects. The dose rate constant, radial dose function, and two-dimensional (2D) anisotropy function were calculated and compared with those of published data and results of the mHDR-v2r source model. The dose rate constant obtained for the IRAsource was [Formula: see text], which was consistent with previously reported values, within the range of experimental uncertainty. The radial dose function exhibited a pattern similar to that of the mHDR-v2r source, with dose distributions converging at distances of approximately 10 cm, where the effect of capsule thickness became negligible. The 2D anisotropy function did not fully align with other experimental datasets for the IRAsource. Even when comparing the IRAsource with mHDR-v2r sources, the 2D anithotropy function showed a difference of 3% to 6% around 0 degrees at distances of 0.25 cm to 5.0 cm from the source. The results reflected reasonable trends that were consistent with differences in source capsule geometry of the IRAsource and the mHDR-v2r. These findings show that the dosimetric data presented here is reliable. This study provides essential baseline data for accurate dose assessment of the IRAsource in brachytherapy and underscores the importance of further experimental validation to refine dose characterization.

In this paper, the authors give the definition of Barron spectrum space of logarithmic smoothness, and clarify the embedding relationship between Barron spectrum space of logarithmic smoothness and Besov space of logarithmic smoothness. In addition, the decaying behavior of radial functions in the Barron spectrum space of logarithmic smoothness have been studied. Finally, authors provide an application of Barron spectrum space of logarithmic smoothness in neural network approximation. All of these are generalizations of the corresponding results in the classical case.

We present a polynomial basis that exactly tridiagonalizes Teukolsky’s radial equation for quasinormal modes. These polynomials naturally emerge from the radial problem, and they are “canonical” in that they possess key features of classical polynomials. Our canonical polynomials may be constructed using various methods, the simplest of which is the Gram-Schmidt process. In contrast with other polynomial bases, our polynomials allow for Teukolsky’s radial equation to be represented as a simple matrix eigenvalue equation. We expect that our polynomials will be useful for better understanding the Kerr quasinormal modes’ properties, particularly their prospective spatial completeness and orthogonality. We show that our polynomials are closely related to the confluent Heun and Pollaczek-Jacobi type polynomials. Consequently, our construction of polynomials may be used to tridiagonalize other instances of the confluent Heun equation. We apply our polynomials to a series of simple examples, including: (1) the high accuracy numerical computation of radial eigenvalues, (2) the evaluation and validation of quasinormal mode solutions to Teukolsky’s radial equation, and (3) the use of Schwarzschild radial functions to represent those of Kerr. Along the way, a potentially new concept, “polynomial/nonpolynomial duality,” is encountered and applied to show that some quasinormal mode separation constants are well approximated by confluent Heun polynomial eigenvalues. We briefly discuss the implications of our results on various topics, including the prospective spatial completeness of Kerr quasinormal modes.

Abstract A static, spherically symmetric black hole solution in symmetric teleparallel (non‐metricity) gravity sourced by an axion field is constructed. Starting from the modified field equations, exact configurations are obtained characterized by the mass and an axion–geometry coupling , with temporal metric function and a nontrivial radial function . The horizon structure and thermodynamics (temperature, entropy, heat capacity) are analyzed, showing regular outer‐horizon behavior across the explored parameter ranges. The dynamics of test particles and light are studied via the effective potential, from which the conditions for circular orbits and the photon sphere are derived; the latter satisfies and determines the critical impact parameter, bending angle, and shadow size. Using the photon‐sphere/eikonal correspondence, quasinormal‐mode (QNM) frequencies are computed as where and is obtained from the curvature of the effective potential at . The resulting spectrum is damped (), indicating linear stability, and displays a clear ‐dependence: increasing raises both the oscillation frequency and the damping rate. Altogether, the axion–non‐metricity deformation leaves correlated signatures in the thermodynamics, orbital structure, lensing/shadow observables, and ringdown behavior, offering potential observational tests relative to the Schwarzschild limit ().

Quantifying cell morphology is central to understanding cellular regulation, fate, and heterogeneity, yet conventional image-based analyses often struggle with diverse or irregular shapes. We present a computational framework that uses topological data analysis to characterise and compare single-cell morphologies from fluorescence microscopy. Each cell is represented by its contour together with the position of its nucleus, from which we construct a filtration based on a radial distance function and derive a persistence diagram encoding the shape’s topological evolution. The similarity between two cells is quantified using the 2-Wasserstein distance between their diagrams, yielding a shape distance we call the PH distance. We apply this method to two representative experimental systems—primary human mesenchymal stem cells (hMSCs) and HeLa cells—and show that PH distances enable the detection of outliers in those systems, the identification of sub-populations, and the quantification of shape heterogeneity. We benchmark PH against three established contour-based distances (aspect ratio, Fourier descriptors, and elastic shape analysis) and show that PH offers better separation between cell types and greater robustness when clustering heterogeneous populations. Together, these results demonstrate that persistent-homology-based signatures provide a principled and sensitive approach for analysing cell morphology in settings where traditional geometric or image-based descriptors are insufficient.

Transition dipole moments as well as spin-orbit coupling and L-uncoupling matrix elements were evaluated for the LiCs molecule in a wide range of internuclear distances, R, for all electronic states converging to the first four dissociation limits. The asymptotic long-range behavior of the LiCs radial functions was investigated and compared with their counterparts obtained for the lighter LiNa, LiK and LiRb molecules. Electron correlation effects were accounted for in the framework of the configuration interaction (CI) method, where all sub-valence electrons were kept on doubly occupied orbitals and only two valence electrons remained free for explicit treatment. Semi-empirical core polarization potentials (CPPs) were used to account for the residual core-polarization effect. The Li atom was described using an all-electron aug-cc-pCVQZ basis set, while the Cs atom was described using a modified version of the averaged relativistic effective core potential (ECP). Along with the available potential energy curves, the current results can be useful in searching for the optimal optical cycle for laser assembling ultracold Li and Cs atoms by means of the STIRAP method as well as in performing a deperturbation analysis of both singlet and triplet state manifolds in the entire R-range.

While 125I brachytherapy is recognized for treating primary oral tumors, its application for distant oral and maxillofacial metastases remains unexplored. This study evaluates the efficacy and safety of 125I brachytherapy for this specific context using GATE/Geant4 Monte Carlo simulations, adhering to AAPM guidelines. Key dosimetric parameters — dose rate constant, geometry function, radial dose function, and anisotropy function — were calculated for a clinical 125I source. Simulations successfully replicated the source geometry and dosimetry, with results demonstrating excellent agreement against consensus data, published benchmarks, and prior validations. This confirms GATE as a reliable, user-friendly platform for 125I source verification and clinical treatment planning. The validated dosimetric data can be directly integrated into planning systems, establishing a foundation for future development of intensity-modulated brachytherapy (IMBT) for complex oral and maxillofacial metastases.

This study evaluated the dosimetric parameters of the Buchler G089 192Ir high-dose-rate brachytherapy source using the TG-43 formalism and Monte Carlo simulations with the Geant4 toolkit. The radial dose function and the anisotropy function were obtained for this source. For the radial dose function, a small discrepancy could be observed for larger radii. The dose rate constant (Λ) was also calculated in this study (1.114 cGy·h⁻¹·U⁻¹) showing a maximum relative difference of 0.45% when compared with reference values (1.119 and 1.115 cGy·h⁻¹·U⁻¹). The absorbed doses were obtained by positioning the source in the lowest voxel of the ICRP male phantom prostate and benchmarked against previous studies. For comparison criteria, the Amersham 6711-Oncoseed 125I source was also modeled and inserted in the same position of the prostate. Additionally, the dose enhancement effect due to the presence of gold nanoparticles (GNPs) was analyzed for the ¹⁹²Ir source, considering a homogeneous concentration of 30 mg·g⁻¹ in a tumor region simulated in the peripheral zone of the prostate. An approximately 18.5% increase in the absorbed dose was observed in this region, in agreement with results from previous studies.

Dementia is among the most distressing and burdensome health challenges in aging populations. Treatment efficacy is limited; however, early diagnosis can delay or prevent disease progression. Previous machine learning-based prediction models have limitations (e.g., they are based on clinical parameters or are not generalizable). Thus, in this study, prediction models were developed for current and future dementia solely based on demographic, socioeconomic, and health-related features. Demographic, socioeconomic, and health-related variables collected from the Korean Longitudinal Study of Ageing (KLoSA) were used to develop machine learning-based prediction models for current and future dementia with various algorithms. Two sampling strategies were used for feature selection, one based on domain knowledge and the other based on statistical testing. Hyperparameter tuning was performed using grid search with cross-validation on the training set, and model evaluation was conducted on a separate test set. In the initial no-follow-up dataset, 92 of 6,898 participants exhibited dementia. Among 6,207 participants without dementia initially, 69 developed dementia within 2 years. Linear support vector machine (SVM) and radial bias function SVM exhibited the best sensitivity for current and future dementia (79.4% and 77.7%, respectively). The SHAP (SHapley Additive exPlanations) approach improved the transparency of the model by highlighting the top ten features most strongly associated with increased dementia risk. We achieved reasonably accurate prediction results for dementia using only non-clinical features.

Abstract In the present study, we investigate the quasibound states and scalar cloud of relativistic charged scalar fields bound to a Kerr–Newman black hole. We present the exact eigensolutions of the governing Klein–Gordon equation with non-minimal coupling in the black hole background. By imposing boundary conditions on the quasibound states, we are able to find the exact complex quasibound state frequencies of the corresponding radial wave functions in terms of the confluent Heun polynomial. The quantization formula obtained here allows us to determine the exact resonance frequency of a charged scalar cloud, thereby revisiting and extending the earlier result derived through the asymptotic matching approach. Our analysis shows that a stationary configuration can exist only when the charge coupling satisfies $$qr_Q<0$$ q r Q < 0 . In this case, the scalar cloud remains stationary due to a flux balance: an outgoing flux from the Cauchy horizon compensates for the ingoing particle flux at the event horizon. This mechanism distinguishes scalar clouds from ordinary quasibound states, where such a compensating flux is absent.

A Method for Validating a Boson Sampler Based on a Radial Function in the Space of Observable States

Dosimetric characterization of the Xoft Axxent electronic brachytherapy source: A Monte Carlo study.

We demonstrate the time evolution of a free particle in a three-dimensional space given that the initial condition is any arbitrary radial function f(r). The solution is expressed as a series expansion in terms of generalized Bessel functions derived using a 3D recursion formula for Bessel functions in the radial coordinate r. Additionally, we establish that these generalized Bessel functions can be represented through intricate double series, which ultimately enable the construction of the full solution. This work presents a novel solution to the problem, as previous approaches were limited to expressions involving only spherical Bessel functions.

This work addresses the existence of at least one radial solution to the nonlinear magnetic Schr\"odinger equation $$ \Big(\frac{\epsilon}{i} \nabla - A(x) \Big)^2 u + V(x) u = f(|u|^2) u \quad \text{in } \mathbb{R}^N, $$ where both the magnetic potential \(A\) and the electric potential \(V\) are continuous, radial functions. Our main tool is the penalization method developed by del Pino and Felmer [17], which we adapt to the complex-valued setting under magnetic effects. By using the small parameter \(\epsilon\) and radial symmetry, we handle nonlinearities with arbitrary growth. For more information in an the latex files, see https://ejde.math.txstate.edu/Volumes/2025/110/abstr.html

Abstract We study the symmetries and conserved quantities in $$f(R)$$ f ( R ) gravity for the static, spherically symmetric Reissner–Nordström spacetime using two complementary frameworks: Noether symmetries and Mei symmetries. Starting from a canonical Lagrangian for radial metric functions and the curvature scalar $$R$$ R , we derive the associated Hamiltonian and show that the Legendre map is regular whenever both the first derivative of f ( R ) with respect to R and the second derivative with respect to R is non-zero. Within Noether’s approach (variational and Lie-derivative forms), we obtain general, canonical, and internal symmetry classes and identify explicit generators; for the quadratic model $$f(R)=R^{2}$$ f ( R ) = R 2 these include radial translations and scaling symmetries. We then formulate Mei symmetry conditions as invariance of the Euler–Lagrange equations under the first prolongation, which yields an overdetermined partial differential equation (PDE) system for the generator components. Solving this system for $$f(R)=R^{2}$$ f ( R ) = R 2 , we find eight independent Mei generators and construct the corresponding conserved currents, some with no direct Noether analogue. The analysis demonstrates that Mei symmetries extend the standard Noether framework for higher-order Lagrangians and provide additional conserved quantities relevant to black-hole dynamics in modified gravity. We conclude with a comparison of the two symmetry schemes and outline applications to broader $$f(R)$$ f ( R ) models and to rotating spacetimes.

Abstract The existence of black holes in the Universe is nowadays established on the grounds of a blench of astrophysical observations, most notably those of gravitational waves from binary mergers and the imaging of supermassive objects at the heart of M87 and Milky Way galaxies. However, this success of Einstein’s general relativity (GR) to connect theory of black holes with observations is also the source of its doom, since Penrose’s theorem proves that, under physically sensible conditions, the development of a space-time singularity (as defined by the existence of a focal point for some geodesic paths in finite affine time) within black holes as described by GR is unavoidable. In this work, we thoroughly study how to resolve space-time singularities in spherically symmetric black holes. To do it so we find the conditions on the metric functions required for the restoration of geodesic completeness without any regards to the specific theory of the gravitational and matter fields supporting the amended metric. Our discussion considers both the usual trivial radial coordinate case and the bouncing radial function case and arrives to two mechanisms for this restoration: either the focal point is displaced to infinite affine distance or a bounce prevents the focusing of geodesics. Several explicit examples of well known (in)complete space-times are given. Furthermore, we consider the connection of geodesic (in)completeness with another criterion frequently used in the literature to monitor singular space-times: the blow up of (some sets of) curvature scalars and the infinite tidal forces they could bring with them, and discuss the conditions required for the harmlessness upon physical observers according to each criterion.