Additional Correction Research Articles

Online calibration of deep learning sub-models for hybrid numerical modeling systems

Defining end-to-end (or online) training schemes for the calibration of neural sub-models in hybrid systems requires working with an optimization problem that involves the solver of the physical equations. Online learning methodologies thus require the numerical model to be differentiable, which is not the case for most modeling systems. To overcome this, we present an efficient and practical online learning approach for hybrid systems. The method, called EGA for Euler Gradient Approximation, assumes an additive neural correction to the physical model, and an explicit Euler approximation of the gradients. We demonstrate that the EGA converges to the exact gradients in the limit of infinitely small time steps. Numerical experiments show significant improvements over offline learning, highlighting the potential of end-to-end learning for hybrid modeling.

Neutrino charge radius and additional one-loop radiative corrections at ultranear reactor experiments

We scrutinize the potential of upcoming ultranear reactor neutrino experiments to detect radiative corrections in the elastic neutrino-electron scattering channel, focusing on the JUNO-TAO and CLOUD detectors, which employ advanced scintillator detection technologies. Previous reactor experiments have already constrained the electron neutrino charge radius, which is a neutrino property associated with a certain subset of the total radiative corrections, and have achieved limits that are only about an order of magnitude away from the Standard Model prediction. Our study demonstrates that JUNO-TAO and CLOUD could discover the neutrino charge radius in the near future, considering the established treatment of the charge radius. However, we show that it is necessary to go beyond this standard treatment. By including the complete set of one-loop level radiative corrections, we find a partial cancellation with the charge radius effect, reducing the experimental sensitivity to this quantity. Nevertheless, JUNO-TAO and CLOUD still have the potential to achieve a 5σ discovery but over longer timescales within a reasonable operational time frame. Published by the American Physical Society 2024

Constraints on dark matter mass in an F(R) gravity model with an additional R2 correction term

Abstract The dominance of dark matter and dark energy presents one of the most significant challenges in cosmology. The chameleon mechanism in F(R) gravity offers a potential solution to this issue. However, many F(R) models encounter a problem known as the singularity problem, where the scalaron mass becomes too heavy to function as dark matter. This study aims to address the singularity problem within the Gogoi-Goswami F(R) model by incorporating an additional R 2 correction term. Assuming the scalaron functions as chameleonic dark matter, its mass must satisfy constraints across various scales, including the electroweak transition phase and galactic structures. By adopting a hierarchical scale with R 0 ≪ R c < m ¯ 2 , where R 0 is the Ricci scalar at late-time de Sitter space and m ¯ represents the inflaton mass scale in Starobinsky's model, and assuming R c ≃ 1 GeV2, the mass constraints during the electroweak transition can be satisfied with α ≃ 1.05. Nevertheless, meeting the required mass constraints on a galactic scale remains a challenge. Alternatively, if R c is considered relevant only in the current universe, such that R 0 ≪ R c ≪ m ¯ 2 , these dark matter mass constraints can be more easily met. For example, setting R c ≃ m φ 2 ( gal ) ≃ ( 1 0 − 32 ) 2 GeV 2 effectively satisfies these constraints.

3D point cloud regularization method for uniform mesh generation of mining excavations

Mine excavation systems are usually dozens of kilometers long with varying geometry on a small scale (roughness and shape of the walls) and on a large scale (varying widths of the tunnels, turns, and crossings). In this article, the authors address the problem of analyzing laser scanning data from large mining structures that can be used for various purposes, with focus on ventilation simulations. Together with the quality of the measurement data (diverse point-cloud density, missing samples, holes induced by obstructions in the field of view, measurement noise), this creates problems that require multi-stage processing of the obtained data. The authors propose a robust methodology to process a single segmented section of the mining system. The presented approach focuses on obtaining a point cloud ready for application in the computational fluid dynamics (CFD) analysis of airflow with minimal need for additional manual corrections on the generated mesh model. This requires the point cloud to have evenly distributed points and reduced noise (together with removal of objects inside) while keeping the unique geometrical properties and shape of the scanned tunnels. Proposed methodology uses trajectory of the excavation either obtained during the measurements or by skeletonization process explained in the article. Cross-sections obtained on planes perpendicular to the trajectory are processed towards the equalization of point distribution, removing measurement noise, holes in the point cloud and objects inside the excavation. The effects of the proposed algorithm are validated by comparing the processed cloud with the original cloud and testing within the CFD environment. The algorithm proved high effectiveness in improving skewness rate of the obtained mesh and geometry mapping accuracy (standard deviation below 5 centimeters in cloud-to-mesh comparison).

Accurate Thermochemistry with Multireference Methods: A Stress Test for Internally Contracted Multireference Coupled-Cluster Theory.

The internally contracted multireference coupled-cluster method with single, double and perturbative triple excitations, icMRCCSD(T), was tested for its performance in the context of computational high-accuracy thermochemistry. The results were gauged against the standard single-reference coupled-cluster hierarchy with up to 5-fold excitations. The test set comprised of a selection of first-row dinuclear compounds and the three 3d-transition metal compounds MnH, FeH, and CoH. The results revealed two problems with the current formulation of icMRCCSD(T). First, the choice of the Dyall Hamiltonian as the zeroth-order Hamiltonian, which leads to a biased description of the different orbital subspaces and particularly poor results for the atomic correlation energies, and second, the tendency to overestimate the perturbative correction for triply excited clusters, in particular in the presence of open shells and correspondingly low orbital-energy gaps. The two problems could be solved by resorting to the effective Fock operator as zeroth-order Hamiltonian and by adopting a modified amplitude equation that includes terms quadratic in the pair clusters. A similar modification was recently proposed by Masios et al. (Phys. Rev. Lett. 2023, 131, 186401) in the context of applying single-reference coupled-cluster theory to systems with small or vanishing band gaps and we chose the acronym '(cT*) correction' in analogy to that work. In contrast to the work of Masios et al., additional terms including single excitation clusters were omitted, as these again lead to an overestimation of correlation effects in more difficult cases. We also tested another alternative for the zeroth-order Hamiltonian and additional higher-order corrections for the correlation energy. These extensions did not significantly improve the results and were also computationally more demanding. The improved icMRCCSD(cT*)F method yields very accurate results with errors, relative to accurate benchmarks, better than 2 kJ/mol for total energies and atomization energies for the entire set of examples considered in this work.

Effect of nutrition on the nutritional status in preterm infants with very low birth weight

Introduction. Postnatal growth retardation in premature infants with very low birth weight (VLBW) remains an unresolved problem. There are different approaches regarding the duration of use of breast milk fortifiers during breastfeeding and specialized formulas during formula feeding, as well as the timing of the appointment of complementary feeding. Objective: to evaluate the physical development and component body composition in VLBW infants, depending on nutritional support over the first year of life. Materials and methods. The study included ninety three VLBW premature infants of 2 to 11 months postnatal age (PNA). The main (1st) group included infants (n = 74) who received dietary correction depending on the nutritional status, while no such intervention was performed in the (2nd) comparison group (n = 19). Up to 64 weeks of postconceptional age (PCA), weight, body length, and head circumference were assessed using INTERGROWTH-21st international growth standards, then in the software “WHO Anthro (2009)”. Fat and fat-free (lean) mass were determined using the air plethysmography method (PEA POD, LMi, USA). Results. The analysis of the nutritional status revealed a moderate deviation, not exceeding 1 sigma, decrease in indices (Z-scores) of anthropometric indices in infants of the 1st and 2nd groups by PNA of 2–3 months. Further in infants of the 1st group on the background of prolonged use of fortified nutrition (breast milk fortifier or specialized formulas for preterm infants) and timely introduction of complementary foods, nutritional deficiencies throughout the first year of life in general were not revealed. In the 2nd group of infants without additional correction of nutrition by 4–5 months of age, the development of mild nutritional deficiency was noted by 6–7 months of age. By 6–7 months of age, it turned into moderate nutritional deficiency, which persisted until 8–9 months of age and then turned into mild nutritional deficiency. Analysis of the component body composition showed that during the observation period, the fat-free body mass (FFM) gain in infants in the 1st group was 3.40 kg, in Group 2 infants — 2.2 kg. At the same time, % body fat mass (FM) in infants in groups 1 and 2 had no significant differences (%FM 1 = 19.3 [15.3–22.5], %FM 2 = 19.9 [16.7–24.6], p = 0.769) and did not exceed the values characteristic of preterm infants. Conclusion. A comprehensive assessment of the nutritional status of VLBW infants during the first year of life allowed us to eva­luate the positive impact of long-term use of fortified diets and timely introduction of certain complementary foods. Optimization of nutrition made it possible to prevent the development of nutritional deficiency, which can have a significant positive impact on their further growth, development, and health status.

A re-assessment of Palaeotanyrhina (Hemiptera: Heteroptera) elucidates the phylogeny of Leptopodoidea

Abstract A morphologically unusual fossil true bug genus, Palaeotanyrhina Poinar, Brown & Kóbor, 2022, placed into Cimicomorpha: Reduvioidea by its authors, is revisited based on an inclusion in mid-Cretaceous Burmese amber. The original description is supplemented with additional details and corrections. It is demonstrated that the placement of Palaeotanyrhina into Cimicomorpha was based on misinterpretations of the morphology of the holotype, and the genus is a member of the infraorder Leptopodomorpha. A phylogenetic analysis is provided for fossil and extant taxa of Leptopodomorpha. Parvilepta Yu, Zhuo & Chen, 2023, Cretaleptus Sun & Chen, 2019, Macrolepta Yu, Zhuo & Chen, 2023 (currently members of Leptopodidae: Leptosaldinae) and Palaeoleptus Poinar, 2009 (the type genus of Palaeoleptidae) are demonstrated to be phylogenetically closely related to Palaeotanyrhina. All the above mentioned genera are recognized to represent stem-group members of Leptopodomorpha: Leptopodidae: Leptopodinae: Leptopodini, and accordingly, they are transferred to the latter tribe. The following new subjective synonyms are proposed: Leptopodidae: Leptopodinae: Leptopodini Brullé, 1836 = Palaeoleptidae Poinar, 2009, syn. nov. = Palaeotanyrhinidae Poinar, Brown & Kóbor, 2022, syn. nov. Based on the analytic results, the subfamilies Leptosaldinae and Leptopodinae of Leptopodidae and the tribes Leotichiini and Leptopodini of Leptopodinae are considered valid, redefined, and a list of their included genera and species are provided. Arguments are provided in support of the placement of Leptosaldinea Popov & Heiss, 2016, formerly placed into Leptosaldinae, into the infraorder Dipsocoromorpha.

Refining current methods: Including comorbidity adjustment in burden of disease estimates

Abstract When quantifying years lost due to disability (YLD), a correction for multimorbidity (or comorbidity, COMO for short, in the Global Burden of Disease study) is necessary to avoid overestimating the morbidity-related burden of disease. Such an overestimation occurs if the calculation of disease frequencies does not consider that persons are counted more than once in a cross-sectional year. In such cases, the time spent with illness at an individual level can add up to a value of more than 1 year. To avoid this, a microsimulation is used that corrects the YLD to a maximum value of 1. A standard approach is to generate a synthetic data set by age, gender and region. Using prevalence estimates and based on (independent) Bernoulli experiments, a vector of diseases is randomly assigned to these (pseudo) individuals. The assignment is usually independent, which means that the presence of one disease has no influence on the presence of another disease. At this level, the individual YLD are then proportionally corrected (the maximum value is 1) and extrapolated to the population. However, there is evidence that disease clusters exist at the individual level. As part of the further development of such multimorbidity correction methods, a new approach will be tested and applied to generate a more realistic population of interest. This considers correlation patterns (1st step) between diseases when generating the synthetic data (2nd step) on the basis of Bernoulli experiments. For this purpose, the existing approaches need to be enriched by (pairwise) correlations between diseases, which requires the inclusion of additional epidemiological data sources. It is assumed that this will lead to an additional correction of the YLD, as they are still overestimated under an independent assignment.

SPECIAL MEASURES FOR SEX OFFENDERS AND POTENTIAL HUMAN RIGHTS VIOLATIONS

Child sexual abuse has attracted enormous attention and occupied significant media space in recent decades. This increased attention has resulted in the creation of strategies aimed at responding to sexual abuse in general, and has been motivated by both the need to prevent reoffending and the desire to adequately respond to the expectations of the wider public. Measures aimed at responding to sexual offenses have become fertile ground for the introduction of various innovations. This may result in the violation of sex offenders’ human rights, and any state based on the rule of law should not allow this. This paper is devoted predominantly to the analysis of the Croatian and Serbian current legal frameworks related to the application of specific measures aimed at sex offenders to establish whether these frameworks are aligned with the relevant human rights protection standards. It has been established that the level of compliance of the two national legislations with the international legal framework is high although there is room for additional corrections. The objective of the paper is to give recommendations for harmonizing the above area with the modern legal acquis, and primarily with the standards established through the case law of the European Court of Human Rights.

Critical short-time behavior of majority-vote model on scale-free networks.

We discuss the short-time behavior of the majority vote dynamics on scale-free networks at the critical threshold. A heterogeneous mean-field theory on the critical short-time behavior of the majority-vote model on scale-free networks is introduced. In addition, the heterogeneous mean-field predictions are compared with extensive Monte Carlo simulations of the short-time dependencies of the order parameter and the susceptibility. Closed expressions of the dynamical exponent z and the time correlation exponent ν_{∥} are obtained. The short-time scaling is compatible with a nonuniversal critical behavior for 5/2<γ<7/2. However, for γ≥7/2, we have the mean-field Ising criticality with additional logarithmic corrections for γ=7/2, the same as the stationary scaling.

Dosimetry in MRgPT: Impact of magnetic fields on TLD dose response during proton irradiation.

Proton beam therapy, when integrated with MRI guidance, presents complex dosimetric challenges due to interactions with magnetic fields. Prior research has emphasized the nuanced impact of magnetic fields on dosimetry. For thermoluminescent dosimeters (TLDs) the electron-return effect, alongside small air cavities surrounding the pellets, can lead to nonuniform dose distributions. Future MR-guided proton therapy will require reliable methods for end-to-end tests and dosimetric audits, which so far are often performed using TLDs equipped with phantoms. This implicates the necessity of accounting for theseinteractions. This study investigates the influence of magnetic fields on TLDs at two proton energies, using magnetic field strengths of 0, 0.25, and , aiming to clarify their impact on dose measurementaccuracy. The study was conducted at a synchrotron-based ion beam therapy beam line, enhanced by a resistive dipole magnet for creating magnetic fields up to to simulate MR-guided proton therapy. Individual correction factors were applied for TLD measurements. The impact of air gaps on the TLD signal was evaluated using three dedicated TLD holders with air gaps of 0.1, 0.25, and 0.5 mm surrounding the TLD pellets using the highest available proton energy of . Additionally, the influence of the magnetic field strength on the TLD response was evaluated for two proton energies of and . The study found no statistically significant variation in TLD dose response attributable to changes in the air gap or the presence of magnetic fields. A power analysis indicated an upper limit on a potential change in dose-response as small as 1.5%. The findings suggested that the impact of air gap variations and magnetic field strengths on the TLD response was below the detection threshold of TLD sensitivity. This emphasizes the suitability of TLDs for dose measurement in MR-guided proton therapy, indicating that additional correction factors may not be necessary despite the influence of magneticfields.

PETAL – LIKE OTOPLASTY IN THE TREATMENT OF PROTRUDING EARS

Introduction. Approximately 5% of humanity suffers from inborn protruding ears, and usually this condition causes marked psychosomatic disorders. Despite years of experience gained in aesthetic surgery, optimal technique of otoplasty is yet to be elaborated. The Aim of the Research. To develop a method of surgical correction of congenital bulging ears in order to optimize the immediate and long-term results of otoplasty. Material and methods. We have analysed the outcomes of 120 patients operated for congenital protruding ears at Lviv City Cosmetologic Hospital between 2020 and 2023. Distance between mastoid process and the concha exceeding 20 mm, and auriculo-cephalic angle over 30° were used as objective criteria of protruding ears. Surgical improvement of tall concha and increased auriculo-cephalic angle were identified as key vectors in elaboration of the original otoplasty technique. Results of the Research. With local anaesthesia, an S-shaped incision is made to the depth of perichondrium of posterior surface of the cartilage of the ear. Once subcutaneous dissection is completed, preoperative markup is transferred with injection needles from anterior surface to posterior surface of the conchal cartilage. A full depth arch-shaped incision of conchal cartilage is made. Perichondrium and skin of anterior surface of the concha are mobilized with a raspatory, from the chondral «petal» to the margin of external meatus. Basis of the chondral «petal» is dissected by 2/3 of its depth along the vertical axis between the pedicle of the helix, and the antitragus. In order to reliably fix the auricula, the cartilage is stitched to the mastoid process with three mattress sutures on the ventral surface of the «petal». Finally, excessive skin is carefully resected, and the wound is closed with continuous suture, with dead space elimination for hematoma prevention. Our technique has the following significant advantages: Unique conchal cartilage is kept entirely, therefore it can be used as auto-transplant in the future. The technique does not significantly affect the rheology of auricula. With this technique correction and modification of antihelical curve and radius is possible; if necessary, width of auricula can be corrected, and auricular height to width ratio can be modified. The proposed «petal» technique significantly reduces the rate of postoperative complications, such as recurrent protruding ears. Postoperatively, the size of external meatus is not reduced, hence no hearing deterioration. The outcomes of the technique we have developed were assessed 6 months after otoplasty as good, satisfactory and unsatisfactory. Good outcome: preservation of symmetry and anatomical «standard» of both auriculas, no recurrence throughout follow-up, and no impairment of sensation in the external ear. Satisfactory outcome: anatomical «standard» of the organ is preserved, with permissible error of up to 3 mm in the symmetrical points on the right and left auriculas, not requiring additional correction. Conclusions. 98 (81,3%) patients operated by the proposed «petal» technique assessed their otoplasty outcome as good, 17 (14,3%) of patients assessed the outcome of surgery as satisfactory. 5 (4,3%) patients were not satisfied with the outcome of surgery. These patients were operated during the early period of development of the technique.

TECHNOLOGY OF MINIMALLY INVASIVE SURGICAL CORRECTION FUNNEL-SHAPED DEFORMATION OF THE CHEST IN CHILDREN

The most common method surgical treatment of pectus excavatum (PE) is thoracoplasty according by D.Nuss at the moment. But serious complications associated with trauma to the pericardium, blood vessels, and bleeding are known. Objective. Development of a modified technology surgical correction of pectus excavatum, which involves exclusively extrapleural passage of the plate, according to the individual size and shape of the deformation of the patient’s chest, in order to prevent intraoperative complications. Methods. 81 patients aged 10 to 17 years were involved in the study. A modified technology of extrapleural surgical correction of PE was performed. The plate was carried level of the VI–VII sternocostal joints through the formed through submuscular-extrapleural retrosternal tunnel from right to left under control of right-sided thoracoscopy. The plate was modeled according by individual deformation parameters chest. The analysis was carried out according to the following criteria: age, gender, type of deformity, Haller index, duration of surgery, intraoperative and early postoperative complications according by Clavien–Dindo classification. Results. The median age of patients was (13.8 ± 1.9) years, of which there were 65 (85.25 %) boys, 16 (19.75 %) girls. 48 (59.3 %) children were diagnosed with type I (symmetric) deformity, and 33 (40.7 %) with type II (asymmetric) according to the classification. The median Haller was (4.07 ± 0.62), which corresponds to 2–3 degrees. Differences in the degree of deformation in children of different sexes were not determined (р = 0.828). Impaired lung function was d iagnosed i n 55.55 % (n = 45), i mpaired h eart f unction — 40.74 % (n = 33). T he d uration of the o peration was on a verage (70.6 ± 15.4) minutes, from 50 to 110 minutes. Early postoperative complications were found in 5 (6.17 %) patients classified as grade I (mild) according to the Clavien–Dindo classification, which did not require additional medical or surgical correction. After the operation, the correction of chest deformation was on average (2.35 ± 0.22) according by Haller index, which was statistically significantly (р = 0.001) different from the initial level. Conclusions. The use of modified technology surgical correction of PE meets safety requirements and minimizes postoperative complications.

Visible diffuse reflectance smartphone spectrometer with high spectral accuracy

A smartphone-based spectrometer employing principle of diffuse reflection is reported for the surface analysis of solid samples. The instrument utilizes a thin-film grating to diffract incoming light, while a diffuse reflecting surface projects the image of this diffracted light onto the detector plane. The CMOS camera of smartphone camera directly captures the diffusely reflected photons within its limited field-of-view thus eliminating the need for collection, conditioning and converging optics. The optical setup of the instrument provides facility to calibrate the spectral response considering the nonlinear distribution of the wavelength across the diffraction direction. Additional correction in the detector response at different light intensity results a reduced spectral error with a maximum wavelength resolution of δλ=0.08 nm/pixel in the camera within the spectral range Δλ = (400 – 700) nm. As a proof of the concept, the instrument demonstrates successful detection of color pigments in food samples by absorption measurement of the samples at an average spectral error < 6 %. The distinct absorption peak associated with standard food colors are compared against the absorption profile of unknown food colors used in pastry cake. This field-functional smart analysis with internet connectivity opens opportunity of identifying food adulteration by using toxic chemical colors at the point-of-test and immediate reporting to others. The overall instrument is fabricated by utilizing low-cost and light weight plastic wood to make compact (110 mm × 105 mm × 125 mm), robust, inexpensive (∼$ 50) and suitable for field-portable (∼145 gm) hand-held operation.

Data-Driven Relationship for Reduction Factor of Ballasted Railway Bridge Deflections Due to Load Distribution Within Track

Increasing the operating speed of the trains on modern networks necessitates performing dynamic analyses to assess the performance of bridges under passage of trains. The detailed investigation of their responses requires constructing complex computational models capable to take the train–track–bridge interaction effects into account. Such models have successfully been developed; however, employing those elaborated models for practical engineering applications, or to perform studies that require a large number of analyses may become infeasible. Among such situations are conducting probabilistic investigations, screening of entire networks, or sensitivity analyses. These concerns have been addressed by employing simplified models mostly relying on moving load modeling strategy which disregards the train–track–bridge interaction effects. Those neglected contributions can be compensated by implementing additional correction factors. The distribution of loads within track is one of those disregarded effects where a reduction factor is recommended by design guidelines to take its contribution into account. It has been shown that the existing relationship for these reduction factors delivers an acceptable performance for vertical accelerations, while showing a less favorable performance for displacements. Then, a data-driven strategy is adopted in this study to propose easy-to-apply relationships for reduction factors of deflections, due to load distribution within the track. In this context, three different distributive lengths of triangular load footprints have been considered, namely 2.0, 2.5 and 3.0[Formula: see text]m. The procedure employed has trained and tested for more than 1[Formula: see text]200 train configurations, comprising conventional, articulated and regular vehicles, and including several tens of thousand data points for each distributive length. The performance observed in the new models revealed a considerable improvement with respect to the existing relationship.

Non-pharmacological interventions for reducing dental anxiety in pediatric dentistry: a network meta-analysis

BackgroundChild dental anxiety is a prevalent issue in the field of pediatric dentistry. At present, several non-pharmacological interventions are employed to mitigate anxiety during dental treatments for children. The objective of this study is to assess the effectiveness of diverse non-pharmacological interventions in reducing dental anxiety, as well as enhancing heart rate during pediatric dental treatments. To achieve this, we conducted a systematic review and a network meta-analysis (NMA) to compare the efficacy of various outcome indicators.MethodsA thorough search was conducted in the databases of PubMed, Embase, Web of Science, Cochrane Library, Scopus, APA PsycInfo, CINAHL, and AMED to identify all eligible randomized controlled trials (RCTs) from the beginning of the databases up to August 1, 2024. The quality assessment was carried out using the Cochrane Collaboration’s bias risk tool. The two outcome measures under consideration were dental anxiety and heart rate. Network graphs, league tables and SUCRA were constructed using R 4.2.3 software and Stata 16 software. This study is registered in PROSPERO under the registration number CRD42023467610.ResultsThe study examined 12 different non-pharmacological approaches, drawing from a pool of 61 research studies involving 6,113 participants aged 4 to 16 years. The results of the network meta-analysis revealed that music (SUCRAs: 93.60%) proved to be the most effective measure in mitigating dental anxiety, followed by aromatherapy (SUCRAs: 78.58%) and game (SUCRAs: 70.99%). Moreover, hypnosis (SUCRAs: 98.80%), music (SUCRAs: 79.58%), and relaxation (SUCRAs: 72.41%) were identified as the top three interventions for decreasing heart rate.ConclusionIn this NMA, when contemplating dental anxiety outcomes, music is recommended as a priority. For heart rate outcomes, hypnosis may be a preferred measure. However, owing to the limited number of articles, the conclusion of this study still requires additional confirmation or correction through more high-quality primary studies in the future.

Corrected generalized cross-validation for finite ensembles of penalized estimators

Abstract Generalized cross-validation (GCV) is a widely used method for estimating the squared out-of-sample prediction risk that employs scalar degrees of freedom adjustment (in a multiplicative sense) to the squared training error. In this paper, we examine the consistency of GCV for estimating the prediction risk of arbitrary ensembles of penalized least-squares estimators. We show that GCV is inconsistent for any finite ensemble of size greater than one. Towards repairing this shortcoming, we identify a correction that involves an additional scalar correction (in an additive sense) based on degrees of freedom adjusted training errors from each ensemble component. The proposed estimator (termed CGCV) maintains the computational advantages of GCV and requires neither sample splitting, model refitting, or out-of-bag risk estimation. The estimator stems from a finer inspection of the ensemble risk decomposition and two intermediate risk estimators for the components in this decomposition. We provide a non-asymptotic analysis of the CGCV and the two intermediate risk estimators for ensembles of convex penalized estimators under Gaussian features and a linear response model. Furthermore, in the special case of ridge regression, we extend the analysis to general feature and response distributions using random matrix theory, which establishes model-free uniform consistency of CGCV.

Exploring canyons beneath Devon Ice Cap for sub-glacial drainage using radar and thermodynamic modeling

Abstract Sub-glacial canyon features up to 580 m deep between flat terraces were identified beneath Devon Ice Cap during a 2023 radar echo sounding (RES) survey. The largest canyon connects a hypothesized brine network near the Devon Ice Cap summit with the marine-terminating Sverdrup outlet glacier. This canyon represents a probable drainage route for the hypothesized water system. Radar bed reflectivity is consistently 30 dB lower along the canyon floor than on the terraces, contradicting the signature expected for sub-glacial water. We compare these data with backscattering simulations to demonstrate that the reflectivity pattern may be topographically induced. Our simulated results indicated a 10 m wide canal-like water feature is unlikely along the canyon floor, but smaller features may be difficult to detect via RES. We calculated basal temperature profiles using a 2D finite difference method and found the floor may be up to 18°C warmer than the terraces. However, temperatures remain below the pressure melting point, and there is limited evidence that the canyon floor supports a connected drainage system between the DIC summit and Sverdrup Glacier. The terrain beneath Devon Ice Cap demonstrates limitations for RES. Future studies should evaluate additional correction methods near complex terrain, such as RES simulation as we demonstrate here.

Prediction–correction projection immersed interface method for interfacial stress-induced flows and applications to electrohydrodynamics

We propose a robust, high-resolution prediction–correction projection immersed interface method (IIM) for solving the unsteady incompressible Navier–Stokes equations with traction boundary conditions, which arise from free surface flows driven by capillary, electric, and elastic forces. This method combines the advantages of traditional body-fitted moving mesh methods and immersed boundary methods (IBM), allowing for the accurate imposition of boundary conditions on free surfaces using Cartesian grids and providing detailed interface information that is typically smoothed out in traditional IBM. The irregular liquid-phase domain is embedded within a square region and discretized using a dynamically adaptive Cartesian mesh. The free surface is captured using a narrow-band level set with hybrid reinitialization. A prediction–correction projection scheme is constructed, incorporating additional pressure predictions and corrections to enhance robustness. The resulting Helmholtz/Poisson equations are solved using the augmented IIM for boundary value problems. Grid refinement analysis demonstrates second-order convergence of the L∞ error, even in challenging cases such as the oscillating drop test with low viscosity. We further apply this method to electrohydrodynamic (EHD) problems, constructing an implicit augmented IIM to solve the equations governing the electric field and charge conservation. Numerical experiments demonstrate that this method accurately addresses highly intense EHD phenomena, such as the formation of Taylor cones, highlighting its robustness.

Axisymmetric phase-field-based lattice Boltzmann model for incompressible two-phase flow with phase change

In this work, a phase-field-based lattice Boltzmann equation (LBE) model for axisymmetric two-phase flow with phase change is proposed. Two sets of discrete particle distribution functions are employed to match the conserved Allen–Cahn equation and the hydrodynamic equations with phase change effect, respectively. Since phase change occurs at the interface, the divergence-free condition of the velocity field is no longer satisfied due to mass transfer, and the conserved Allen–Cahn equation needs to be equipped with a source term dependent on the phase change model. To deal with these, a novel source term in the hydrodynamic LBE is delicately designed to recover the correct target governing equations. Meanwhile, the LBE for the Allen–Cahn equation is modified with a discrete force term to model mass transfer. In particular, an additional correction term is added into the hydrodynamic LBE to reduce the spurious velocity and improve numerical stability. Several axisymmetric benchmark multiphase problems with phase change, including bubble growing in superheated liquid, D2 law, film boiling, bubble rising in superheated liquid under gravity, and droplet impact on a hot surface, have been conducted to test the performance of the proposed model. Numerical results agree well with analytical solutions and available published data in the literature.