The formation of the first stars in the universe could be significantly impacted by the effects of Dark Matter (DM). Namely, if DM is in the form of Weakly Interacting Massive Particles (WIMPs), it could lead to the formation (at z∼ 25-10) of stars that are powered by DM annihilations alone, i.e. Dark Stars (DSs). Those objects can grow to become supermassive (M∼ 10^6) and shine as bright as a galaxy (L∼ 10^8 ). Using a simple χ^2 minimization, the first three DSs photometric candidates (i.e. , , and ) were identified by . Our goal is to develop tools to streamline the identification of such candidates within the rather large publicly available high redshift JWST data sets. We present here the key first step in achieving this goal: the development and implementation of a feed-forward neural network (FFNN) search for Dark Star candidates, using data from the JWST Advanced Deep Extragalactic Survey (JADES) photometric catalog. Our method reconfirms JADES-GS-z13 and JADES-GS-z11 as dark star candidates, based on the chi-squared goodness of fit test, yet they are ∼10^4 times faster than the Neadler-Mead χ^2 minimization method used in . We further identify six new photometric Dark Star candidates across redshifts z ∼ 9 to z ∼ 14. These findings underscore the power of neural networks in modeling non-linear relationships and efficiently analyzing large-scale photometric surveys, advancing the search for Dark Stars.
In this paper, we investigate a class of nonlinear singular differential equations of importance in mathematical physics and astrophysics, specifically Lane–Emden–type equations, which have been investigated with classical semi-analytical and numerical methods. Instead of classical methods based on discretization, we introduce a hybrid DNA-based artificial neural network (DNA-ANN) framework with Physics-Informed Neural Networks (PINNs), trained with the quasi-Newton L-BFGS optimization approach, to yield a computationally efficient and stable approach to obtain numerical solutions. First, we establish the existence and regularity of solutions under suitable assumptions on the nonlinear source terms and initial data in order to render the singular initial value problem well-posed. The differential equation is reformulated within a DNA-inspired neural computation framework, where reaction-network concepts provide an interpretable representation of the system dynamics. Rather than replacing the PINN solver, the DNA-inspired formulation provides a biologically motivated dynamical representation that guides the first-order reformulation of the governing equation and offers an interpretable conceptual framework for the subsequent PINN implementation. The differential equation is subsequently solved within a Physics-Informed Neural Network (PINN) framework, where the governing equation and singular initial conditions are incorporated into the loss function. A residual-based theoretical analysis establishes local well-posedness together with consistency, convergence, and stability properties under suitable assumptions. The network parameters are optimized using a hybrid Adam/L-BFGS training strategy.The numerical results demonstrate that the proposed framework provides accurate mesh-free approximations for representative singular Lane–Emden type equations and highlight the potential of DNA-inspired computational abstractions within physics-informed scientific machine learning.
We present a comprehensive framework for galaxy morphology classification that combines enhanced “out-of-distribution (OOD)” detection with improved uncertainty quantification. Using “Galaxy Zoo DECaLS”, we trained a ResNet-34 architecture under three configurations: standard cross-entropy loss as a baseline, IsoMaxPlus (Isotropy Maximization Plus) loss function for OOD detection, and hybrid IsoMaxPlus+Monte Carlo (MC) Dropout for enhanced uncertainty quantification. IsoMaxPlus replaces the conventional SoftMax logits with distance-based class representations, preserving inter-class separability and enabling reliable OOD detection, without requiring additional architectural modifications or hyperparameter tuning. Coalescing IsoMaxPlus with MC Dropout provides a fast Bayesian approximation by performing multiple stochastic forward passes during inference. Our results show that IsoMaxPlus substantially improves OOD detection, increasing TNR@TPR95 by nearly 90% relative to the cross-entropy baseline, while maintaining a competitive accuracy of 97% across nine morphological classes. Additionally, with MC Dropout, the model yields more stable predictions and a reduction in calibration error, providing more reliable uncertainty estimates. The Expected Calibration Error (ECE) is reduced from 0.0095 to 0.0026 (≈73%) for IsoMaxPlus and 0.0033 (≈65%) when combined with MC Dropout, compared to the baseline. Misclassified or underconfident predictions exhibit higher predictive entropy and lower minimum distance scores, providing an interpretable metric for identifying unreliable predictions. IsoMaxPlus does not require additional training or outlier examples during the training process to produce effective separation between “in-distribution (ID)” and OOD samples. These methods are well-suited for current and upcoming large-scale surveys, where reliable automated morphological classification and awareness of uncertainty are essential for identifying rare or previously unseen galaxy morphologies.
Detection of weak hydrogen-line signals under severe noise and interference conditions remains a major challenge in radio astronomy. This paper presents an adaptive multi-delay resonant enhancement framework for weak narrowband spectral detection under stationary and nonstationary conditions.The proposed approach combines phase-compensated multi-delay accumulation with adaptive resonant enhancement. The multi-delay stage improves signal coherence prior to resonance processing, while the adaptive resonator maintains frequency-selective enhancement under spectral drift conditions.The framework was tested using weak hydrogen-line (HI) signals corrupted by additive Gaussian noise and radio-frequency interference. Real observational data of weak hydrogen line signals were used to investigate the spectral behavior of the HI under low signal power conditions.The results show that the classical resonators remain effective under stationary conditions and fail under nonstationary conditions. However, the proposed multi-delayed adaptive approach provides stable enhancement and significant robustness under both conditions. The computational complexity is low since the framework relies on analytical signal processing operations rather than iterative data-driven training methods that require high computational time.
Transient gaps in ground-based gravitational-wave strain data, typically 120–280 ms in duration, arise from glitch gating, telemetry dropouts, and data-quality vetoes. These gaps create sharp discontinuities in the detector output and can introduce spectral leakage and matched-filter ringing in compact-binary searches. Deep learning has been used successfully in several gravitational-wave tasks, but the architectural requirements for reconstructing missing strain samples remain less clear.In this paper, we investigate five neural architectures for sub-second gap inpainting in Advanced LIGO-like strain: a standard convolutional U-Net, an Attention U-Net, a TCN-UNet, a stemmed bidirectional GRU, and a PSD-Conditioned U-Net (PSD-UNet) using Feature-wise Linear Modulation. All models are trained with the same joint time-spectral-boundary loss on 20,000 simulated four-second segments containing precessing-spin compact-binary injections at SNR 8–40. The analysis shows that, on 3000 held-out simulated segments, the standard U-Net is statistically indistinguishable from zero-filling under gap MSE (1.262 ± 0.481 versus 1.261 ± 0.481). Architectures with global temporal context reduce reconstruction error by 30%–36%, and the stemmed bidirectional GRU gives the strongest simulated result (0.812 ± 0.308 gap MSE, with 74.2% of segments exceeding the 97% match threshold). However, validation on ten PyCBC catalog events changes the ranking under time-domain MSE: zero-filling and the standard U-Net obtain the lowest gap MSE, whereas active global-context models are penalized for predicting non-stationary noise samples that cannot be recovered sample by sample. A naive PSD-UNet also shows out-of-distribution extrapolation, with MSE exceeding 107 and match falling to 47.42%. Log-PSD compression, Layer Normalization, and bounded FiLM parameters remove this numerical instability and yield stable real-strain behavior (Gap MSE 1.160 ± 0.450, match 97.31 ± 0.01%). These results suggest that global temporal context is important for simulated waveform inpainting, while physically motivated conditioning must be bounded before real-detector evaluation.
Modern numerical astrophysics applications present a common demand for efficient spatial querying techniques, such as neighbor searches or density estimations over billions of resolution elements. To address the growing need for fast and versatile tools tailored to these tasks, we present cosmokdtree, a fast and flexible multi-purpose k-d tree implementation in Fortran, parallelized with OpenMP directives. Our library supports arbitrary dimensionality and spatial distributions, and is designed for efficient tree construction and fast query performance for moderate-scale applications (performance tested up to ∼109 points). Python bindings coupled to the module are also provided. All these ingredients yield a k-d tree package suitable for analysis purposes.We benchmark cosmokdtree across a variety of scenarios, including different point distributions, dimensionality, and parallel scaling. We also compare its performance against the widely used scipy implementation and other efficient alternatives such as coretran’s and a GPU-based version, showing that cosmokdtree consistently achieves lower construction and query times than CPU alternatives while keeping a reasonable memory usage. Our tree-building phase implementation, executed on a mid-range workstation-class CPU, approaches the performance of GPU-based implementations when run on high-end consumer graphic cards, although data-center GPUs, out of the scope for our comparison, could still deliver substantially higher performance and a broader conclusion cannot be extracted. We further present some applications tackling common problems in astrophysics, namely, the friends-of-friends clustering algorithm and the particle-to-mesh assignment process. The code is publicly released and intended to serve as a flexible multi-purpose tool for computational applications in a wide range of scenarios, particularly in astrophysics.
Forbush decreases (FDs) — transient reductions in galactic cosmic ray intensity driven by interplanetary coronal mass ejections — are key observables in space weather monitoring, yet their automated detection from multivariate solar wind and neutron monitor time series remains a challenging classification problem. Here we report a systematic benchmark of quantum kernel support vector machines (QKSVM) for FD detection, in which the FD magnitude threshold emerges as the governing factor separating two distinct classification regimes. Using 2971 confirmed events from the Forbush Effects and Interplanetary Disturbances (FEID) catalogue, combined with hourly OMNI solar wind parameters — including interplanetary magnetic field (IMF) components, solar wind speed, proton density, proton temperature, and the Kp and Dst geomagnetic indices — and galactic cosmic ray count rates from the Jungfraujoch neutron monitor station (JUNG, NMDB), we construct a balanced FD versus quiet-time classification dataset and extract 121 statistical features across eleven physical channels. A ZZFeatureMap quantum kernel with 4–8 qubits is benchmarked against a classical radial basis function (RBF) SVM across 180 experimental configurations spanning FD magnitude thresholds of 0%–7%, circuit depths of 1–3 repetitions, and quantum training sizes of 50–250 samples. We find that below a magnitude threshold of 4%, the classical kernel consistently outperforms the quantum alternative (mean ΔAUC=−0.100 at min_magn =0%). Above this threshold, the relationship inverts: at min_magn ≥4% the quantum kernel achieves positive mean ΔAUC in 72% of configurations, rising to 100% of configurations at min_magn ≥5% (mean ΔAUC=+0.074, peak AUC=1.000 with 4–8 qubits), indicating that the entanglement structure of the ZZFeatureMap captures non-linear correlations between IMF dynamics and cosmic ray modulation that the RBF kernel cannot represent. The magnitude threshold of 4% thus constitutes a physically interpretable boundary between a noise-dominated regime where classical methods suffice and a signal-rich regime where quantum kernels provide measurable and statistically significant advantage (p<0.001, Wilcoxon signed-rank test). These results establish FD magnitude as a key predictor of quantum classification performance, and suggest that near-term quantum machine learning applications in heliophysics should preferentially target high-amplitude space weather events.
Automated detection of solar coronal loops in extreme ultraviolet imagery has remained an open problem for two decades, despite its practical importance for coronal magnetic field modelling. Loops are observed as bright, arch-like structures in EUV imagery from instruments such as AIA/SDO, EUVI/STEREO, and FSI/Solar Orbiter, but their optically thin nature means that recorded intensity integrates emission along the line of sight rather than isolating individual structures. The result is a superposition of overlapping photon intensities against a diffuse background that defeats simple intensity-based approaches and challenges carefully designed geometric filters. Despite two decades of methodological development, no structured review of computational methods for coronal loop detection currently exists, leaving the field without a consolidated view of what has been attempted, where the structural obstacles lie, and which directions from adjacent disciplines are most likely to close the gap.This paper presents a structured semi-systematic review organised around three themes: the evolution of coronal loop detection from geometric ridge-tracing algorithms to deep learning segmentation models; the suitability of available observational data sources for machine learning tasks; and the transfer of curvilinear structure detection methods from medical imaging and remote sensing to the solar domain. While recent work has demonstrated that machine learning models can reconstruct three-dimensional loop coordinates from two-dimensional projections with high accuracy, those methods assume the 2D loop geometries are already extracted. Robust automated detection and centreline tracing from single-viewpoint EUV images remains understudied and lacks the large-scale annotated datasets that would make modern supervised approaches tractable. The absence of standardised evaluation protocols further limits meaningful comparison across methods. This review identifies the structural obstacles that have prevented a complete end-to-end pipeline and maps the directions most likely to close the remaining gaps.
Estimation of fundamental stellar features, such as their distance, is of paramount importance for understanding stellar evolution and galactic dynamics. Modern astronomical surveys enable gathering a massive amount of data that can be used to train machine learning systems with the aim of automatically gauging the value of specific target variables. Standard deep learning methods usually assign to training samples the same importance, therefore disregarding potentially useful information available from astronomical surveys, such as the uncertainty measurement of various geometric, photometric, and spectroscopic parameters. Moreover, experimental data samples are often affected by missing or invalid values, hindering the training of complex machine learning models. In this study, we introduce a novel approach based on a twofold strategy to address these issues. First, we differentiate the contribution of samples according to their measurement error by designing a set of loss functions conveying this information, which can be used to effectively train deep learning models by handling noisy data, with improved accuracy and generalization capabilities. Second, we complement the proposed methodology with a novel approach to deal with input missing data by properly introducing a mask-based preprocessing layer in the neural network model, further widening the amount of data to be used for training and inference. These methods are implemented in a consistent pipeline that takes the most out of available data. The experimental results obtained on the Gaia mission benchmark data sets show improved precision and robustness of the proposed approach compared to the baseline methods.
Large spectroscopic surveys rely on data reduction pipelines designed to remove instrumental signatures and to produce residuals that are commonly treated as statistically independent noise. In this work, we explicitly test this assumption using SDSS/BOSS optical spectra. Working entirely in the observed frame and without applying redshift corrections, we construct residual spectra through robust normalization, ensemble template subtraction, and spectral whitening based on the global power spectral density. While these steps effectively remove dominant autocorrelations, we find that the resulting residuals exhibit persistent and statistically significant correlations across spectra. This correlated structure is consistently detected through multiple complementary diagnostics, including correlation matrices, eigenvalue spectra, and low-dimensional embeddings, and remains robust under aggressive null tests (phase randomization, block shuffling, and bootstrap resampling). Additional invariance tests, including wavelength reversal and multiscale decompositions, further demonstrate that the observed correlations are not tied to localized spectral features or specific wavelength ordering. Given that astrophysical features are not aligned in the observed frame, the detected structure is most conservatively interpreted as being consistent with residual instrumental or pipeline-induced contributions, while not excluding all possible astrophysical contributions. These results do not challenge the scientific validity of SDSS/BOSS data products, but indicate that residuals are not strictly independent, which has implications for uncertainty estimation and stacking-based analyses. The primary contribution of this work is a reproducible, survey-agnostic framework for diagnosing correlated residual structure in spectroscopic pipelines, enabling more robust statistical interpretation of large spectroscopic datasets.
Automated classification of stars, galaxies, and quasi-stellar objects (QSOs) is essential for large-scale astronomical surveys, where reliable classifiers must remain stable across survey releases, class imbalance, and incomplete observational inputs. In this work, we present a Brain-Inspired Quantum Machine Learning (BIQML) framework for SDSS star–galaxy–QSO classification as a step toward robust source classification for next-generation photometric pipelines. The model combines a spiking Leaky Integrate-and-Fire (LIF) controller with a classically simulated variational quantum circuit (VQC), in which the controller sequentially selects quantum gates using measurement feedback; all circuits are classically simulated, and no hardware-level quantum advantage is claimed. The framework is trained and internally tested on SDSS DR17, with SDSS DR14 used as an external cross-release test set, and is benchmarked against a broad suite of baselines including Random Forest, Extra Trees, HistGradientBoosting, Logistic Regression, Linear Support Vector Machine, and Multilayer Perceptron classifiers under a repeated ten-split protocol with paired statistical significance testing. In the full-feature setting, BIQML is statistically on par with the strongest classical baselines, reaching 97.36±0.05% accuracy (96.90% balanced) on SDSS DR17 and 98.76±0.09% accuracy (98.41% balanced) on the external SDSS DR14 test set, where the leading tree ensembles span 97.3–97.8% and 98.8–99.4%, respectively. To probe robustness when key observational channels are unavailable, we introduce a low-sensor (g,r,i) no-redshift setting in which spectroscopic redshift, the u- and z-bands, and metadata are removed. Under this reduced-feature condition, BIQML remains among the top-performing models on a single controlled split (0.805 balanced accuracy, versus 0.64–0.80 for the classical baselines), achieving 85.58% accuracy on SDSS DR17 and 93.44% accuracy on SDSS DR14, suggesting that it remains competitive, degrading no more than the strongest ensembles, when discriminative information is scarce. A component-level ablation isolates the contributions of the VQC, the spiking controller, and the measurement-feedback loop, while both an analytic noise screening and a finite-shot, IBM-calibrated device-noise benchmark show that BIQML predictions remain stable under representative depolarizing, amplitude-damping, readout, and realistic NISQ-style noise channels. Together, these results position BIQML as a competitive and robust quantum-inspired architecture for astronomical source classification under cross-release shift and limited observational information.
The Extremely Large Telescope (ELT) is a 39-meter optical telescope under advanced construction in the Chilean Atacama desert. The optical design is based on a five-mirror scheme and incorporates adaptive optics. The primary mirror consists of 798 segments. First scientific light is planned for the end of 2030. The status of the project is described in (Tamai et al., 2026).The major challenges for the control of the telescope and the instruments are in the number of sensors (∼25000) and actuators (∼20000) to be controlled in a coordinated fashion, the computing performance and low latency requirements for the phasing of the primary mirror, performing adaptive optics, and coordinating all subsystems in the optical path.Industrial contractors are responsible for the low-level control of individual subsystems and ESO for the development of coordination functions and control strategies requiring astronomical domain knowledge.In this paper we focus on the architecture and the design of the control software in the context of the control system as a whole.
Predicting soft X-ray flux enhancements is crucial for early warning of solar storm impacts on Earth’s space environment and technological systems. In this work, we retrieve one-minute averaged science-quality data from NOAA Space Weather Prediction Center (SWPC) covering the period from 31 March 2010 to 4 March 2020, and construct two datasets: Dataset-A for analyzing the impact of look-back window length, and Dataset-B for five-fold cross-validation to compare model predictive performance and robustness. We apply four deep-learning models, iTransformer, BiLSTM, BiLSTM-CNN, and Seq2Seq, along with MLP baseline, to forecast short-term X-ray flux. Furthermore, we develop a real-time operational system for forecasting X-ray flux using the iTransformer model. The main results are as follows: (1) Based on Dataset-A, we conduct extensive experiments to investigate the impact of different look-back window sizes on soft X-ray flux prediction performance. The results demonstrate that the size of the look-back window does not significantly affect the performance of any model. (2) In the five-fold cross-validation, the mean and variance of the MAE for iTransformer are better than those of the other models. (3) For predictions at future horizons of 1, 5, 10, 15, 20, 25, 30, 35, and 40 min, the mean MAE of iTransformer is 1.36, 1.74, 2.03, 2.24, 2.49, 2.70, 2.93, 3.10, and 3.28 × 10−7, respectively. To the best of our knowledge, this is the first study to perform short-term soft X-ray flux forecasting and to apply the iTransformer model for this purpose.
Transit surveys tend to underestimate how often habitable zone (HZ) planets appear. The core reason is geometric: the chance that an Earth-like planet transits a sun-like star is very low — less than 0.5%. Their long orbital periods (200–400 days) add a further layer of observational bias, making them hard to detect with Kepler's sensitivity. In simple terms, surveys are far more likely to catch hot Jupiters close to their stars than small, Earth-like planets at habitable distances.We analysed 4,510 transit planets from the NASA Exoplanet Archive (March 2026). The raw HZ occurrence rates — the unadjusted numbers straight from the archive — are 0.33% for F/G stars, 0.72% for K stars, and 4.03% for M stars. These numbers are heavily influenced by how surveys select targets, not by nature alone. To correct for this, we developed a three-part analysis.The first part uses a Bayesian Beta-Binomial occurrence-rate model with externally fixed completeness assumptions. It finds corrected rates of about 0.27 for K stars and 0.41 for M stars, with 68% credible intervals that remain stable when we vary the prior or rescale the assumed completeness by ±50%. This indicates that the qualitative K and M dwarf ranking is robust to these specific assumptions; it does not, however, capture the full systematic uncertainty in the completeness model itself (see Sections 3.3 and 8). For F/G stars, the estimate (around 0.10) is far less certain, because only 3 HZ planets from this group appear in the dataset, and we treat it as schematic rather than a measurement.The second part applies a Random Forest regression. Rather than labelling planets as simply HZ or non-HZ, we assign each planet a continuous habitability proximity score. This avoids class-imbalance problems and allows stable cross-validation. The model achieves a cross-validated R² = 0.835 ± 0.039, but this performance is largely driven by orbital-distance features that are also used to define the target, so it should be read as a candidate-ranking tool rather than a measure of predictive skill. When the two orbital-distance features are removed, R² collapses to negative values, although the ablated model still recovers 90.5% of HZ planets by stellar properties alone. We therefore present the Random Forest primarily as a ranking aid, not as evidence that stellar features alone determine habitability.The third part uses logistic regression to estimate detection probabilities for individual planets. These per-planet weights shift the median occurrence rates by less than 8%, suggesting the type-averaged occurrence-rate model is an adequate approximation at the current sample size. All three methods agree on the stellar-type ranking. We also note a marginal signal (p ≈ 0.04) that M-dwarfs may host more HZ planets than expected; given the very small M-dwarf sample (k = 10, of which TRAPPIST-1 contributes three correlated detections), we regard this only as a falsifiable hypothesis for future surveys rather than a detection. The entire analysis can be reproduced using the public API.
Accurate estimation of the inclinations of disk galaxies is essential to infer many of their physical properties. This work proposes a novel method to estimate galaxy inclination solely based on imaging data without any additional information or explicit structural assumptions. We use a probabilistic approach to obtain a properly calibrated predictive distributions over inclinations, i.e. a realistic estimate of the confidence in the predictions. Our method simultaneously accounts for the uncertainty in the true inclinations (obtained from realistic galaxies in cosmological simulations), as well as the degeneracy between intrinsic 3D shape and inclination in galaxy images (learned from synthetic images of the simulated galaxies). Given only an image of a disk galaxy, our method predicts a density distribution of likely inclination angles using a Mixture Density Network. The model is based on a convolutional neural network trained on synthetic images of realistic simulated galaxies. We benchmark the model performance on an independent test set obtained from the same simulation, and compare the predictions of our method to the results of standard ellipse-fitting methods. Our predictions achieve a Continuous Ranked Probability Score (CRPS) of ≈ 3° compared to ≈ 9° for the standard method, indicating that our method is more precise, sharper, and better calibrated. Furthermore, while ellipse-fitting tends to underestimate the true inclinations and fails for values below ∼ 10°, our method is fully able to constrain the inclination of nearly face-on galaxies. Our model provides much better scaling on very large datasets than standard methods, estimating the inclination significantly faster on average.
Coronal mass ejections (CMEs) are among the most energetic manifestations of solar activity, and their relationship with sunspotnumber (SSN)—a standard proxy of magnetic variability—is central to space weather forecasting. Earlier studies identified correla-tions between CME occurrence and SSN but often relied on heterogeneous event samples and coarse temporal averaging. Here wepresent a systematic statistical analysis of CME occurrence rates and SSN spanning Solar Cycles 23–25 (January 1996–September2025). Our approach combines velocity-based population stratification accounting for measurement uncertainties, non-parametriccorrelation analysis with bootstrap confidence intervals, and multi-scale temporal evaluation at annual and monthly resolutions.Results show that CME–sunspot coupling depends strongly on both velocity regime and temporal scale. At the annual scale,moderate-to-fast CMEs (600–1500 km s−1 ) display the strongest correlations with SSN (ρ ≈ 0.93–0.97), despite comprising onlyabout 12% of events, indicating that long-term solar-cycle evolution mainly controls the occurrence of energetic eruptions frommagnetically complex active regions. In contrast, monthly correlations are stronger for slow and moderate CMEs, especially dur-ing the weaker Solar Cycle 24 (ρ ≈ 0.90 for slow events), suggesting that short-term solar variability influences different CMEpopulations in distinct ways. These results demonstrate that CME–sunspot coupling varies with both temporal resolution and eventpopulation, and provide a statistically grounded framework for converting sunspot-based solar-cycle forecasts into velocity-resolvedCME occurrence predictions, thereby improving tools for space weather prediction.
Large-scale sky surveys reveal noticeable spatial variation in stellar surface density, reflecting the structure of the Milky Way and the clustering of stellar populations. Star counts in sky regions often show substantial overdispersion due to the Galactic structure, unresolved substructure, and observational heterogeneity. Using publicly available Gaia DR3 data, we model star counts in 5 degrees & times; 5 degrees sky bins using the two-parameter Negative Binomial (NB2) distribution. This model handles the extra variation while keeping a clear relationship between the mean and variance. We develop profile-likelihood confidence intervals for the mean stellar density, both globally and as a function of Galactic latitude, which provide a statistically rigorous inference for the stellar surface density near and away from the Galactic plane. We compare our results with Wald confidence intervals, parametric bootstrap confidence intervals, and Poisson-based methods to show why it is important to account for extra variation in modern sky surveys. Our approach offers a reliable and practical way to model overdispersed star counts and can be used in many large-scale astronomy surveys.
In this work, we compute the numerical solutions of second order Lane-Emden type equations that arise in a variety of applications, particularly in astrophysics, where they describe the stellar structures and thermionic processes, as well as in certain biological models. In this approach, first we express the Lane-Emden equation in its integral form. This transformation helps in handling the singularity occurring in the Lane-Emden problems. Then the Bell wavelet-based approach reduces the integral representation into a system of algebraic equations. This system is then solved using the Newton-Raphson iterative method. To examine the practical performance of the method, different cases are considered that include models arising in astrophysical and diffusion processes in spherical domain. The results are computed in the form of L-2, L-infinity error norms and residual errors that indicate that the proposed approach produces reliable and accurate approximations that are applicable to a wide range of problems.
