Classical Limit Research Articles

Placental Abruption: Pathophysiology, Diagnosis, and Management

Placental abruption is a complete or partial separation of the placenta from the uterine decidua. Clinical manifestations include vaginal bleeding, abdominal pain, uterine contractions, and abnormalities in the fetal heart rate tracing. Placental abruption occurs in 0.4% to 1.0% of all pregnancies. However, the pathophysiology remains incompletely understood. We present a review of the pathophysiology, diagnosis, and management of placental abruption, exploring overlapping processes which contribute to premature placental separation. Classic findings and limitations of ultrasound in evaluating placental abruption are explained. Finally, we discuss the management of placental abruption based on gestational age, fetal status, and maternal hemodynamic stability.

Quantizations of Transposed Poisson algebras by Novikov deformations

Abstract The notions of the Novikov deformation of a commutative associative algebra and the corresponding classical limit are introduced. We show such a classical limit belongs to a subclass of transposed Poisson
 algebras, and hence the Novikov deformation is defined to be the quantization of the corresponding
 transposed Poisson algebra. As a direct
 consequence, we revisit the relationship between transposed
 Poisson algebras and Novikov-Poisson algebras due to the fact that there is a natural Novikov
deformation of the commutative associative algebra in a
Novikov-Poisson algebra. Hence all transposed Poisson algebras of
Novikov-Poisson type, including unital transposed Poisson
algebras, can be quantized. Finally, we classify the
quantizations of $2$-dimensional complex transposed Poisson
algebras in which the Lie brackets are non-abelian up to
equivalence.

Spin-photon entanglement with direct photon emission in the telecom C-band.

Quantum networks, relying on the distribution of quantum entanglement between remote locations, have the potential to transform quantum computation and secure long-distance quantum communication. However, a fundamental ingredient for fibre-based implementations of such networks, namely entanglement between a single spin and a photon directly emitted at telecom wavelengths, has been unattainable so far. Here, we use a negatively charged exciton in an InAs/InP quantum dot to implement an optically active spin qubit taking advantage of the lowest-loss transmission window, the telecom C-band. We investigate the coherent interactions of the spin-qubit system under resonant excitation, demonstrating high fidelity spin initialisation and coherent control using picosecond pulses. We further use these tools to measure the coherence of a single, undisturbed electron spin in our system. Finally, we demonstrate spin-photon entanglement in a solid-state system with entanglement fidelity F = 80.07 ± 2.9%, more than 10 standard deviations above the classical limit.

Equilibrium oxygen isotope fractionation in Mg(OH)2-Ca(OH)2-H2O: Implication from in situ high-temperature and high-pressure vibrational spectra

Abstract Equilibrium oxygen isotope fractionations have been extensively studied between H2O and minerals (like brucite-type hydroxides) in isotope geochemistry. In this study, pure 18O-enriched hydroxides were synthesized through reactions between M3N2 (M = Mg and Ca) powders and H218O water. In situ high-temperature (T) and high-pressure (P) Raman and Fourier transform infrared (FTIR) spectra were systematically collected for these phases. The observed 18O-16O effect on the frequency shifts aligns with the theoretical model, and has little impact on the anharmonic O-H potential well. The calculated intrinsic anharmonic parameters (ai) for both lattice and OH-stretching modes are essentially identical between M(16OH)2 and M(18OH)2, satisfying the classical limit for the Helmholtz free energy at extremely high temperature. Based on the measured vibrational data, the equilibrium oxygen isotope fractionation β(T,P) factors were modeled for both hydroxides. Both the intrinsic and external anharmonic contributions are smaller than the experimental uncertainties, and this model is also validated by ab initio calculation. Next, the 103·lnα(T) profiles were computed between brucite/portlandite and H2O, which are consistent with the reported oxygen isotope exchange measurements above 200 °C. Additionally, the discrepancy between this equilibrium model and the precipitation experiment below 120 °C also provides useful information for investigating the mechanism of kinetic isotope fractionation. The predicted 103·lnαbrucite-portlandite(T) curve also agrees well with points inferred from the 18O-16O exchange measurements, while the pressure effect can be ignored for 18O-16O fractionations. Therefore, vibrational spectroscopic measurements, including both Raman and infrared spectroscopies, have valuable applications in studying equilibrium non-metallic isotope fractionations in minerals.

Mapping membrane biophysical nano-environments

The mammalian plasma membrane is known to contain domains with varying lipid composition and biophysical properties. However, studying these membrane lipid domains presents challenges due to their predicted morphological similarity to the bulk membrane and their scale being below the classical resolution limit of optical microscopy. To address this, we combine the solvatochromic probe di-4-ANEPPDHQ, which reports on its biophysical environment through changes in its fluorescence emission, with spectrally resolved single-molecule localisation microscopy. The resulting data comprises nanometre-precision localisation coordinates and a generalised polarisation value related to the probe’s environment – a marked point pattern. We introduce quantification algorithms based on topological data analysis (PLASMA) to detect and map nano-domains in this marked data, demonstrating their effectiveness in both artificial membranes and live cells. By leveraging environmentally sensitive fluorophores, multi-modal single molecule localisation microscopy, and advanced analysis methods, we achieve nanometre scale mapping of membrane properties and assess changes in response to external perturbation with methyl-β-cyclodextrin. This integrated methodology represents an integrated toolset for investigating marked point pattern data at nanometre spatial scales.

Calibration of the JAGB method for the Magellanic Clouds and Milky Way from Gaia DR3, considering the role of oxygen-rich AGB stars

The JAGB method is a new way of measuring distances in the Universe with the use of asymptotic giant branch (AGB) that are situated in a selected region in a $J$ versus $J- colour--magnitude diagram (CMD), and relying on the fact that the absolute $J$ magnitude is (almost) constant. It is implicitly assumed in the method that the selected stars are carbon-rich AGB stars (carbon stars). However, as the sample selected to determine J $ is purely colour based, there can also be contamination by oxygen-rich AGB stars in principle. As the ratio of carbon-rich to oxygen-rich stars is known to depend on metallicity and initial mass, the star formation history and age--metallicity relation in a galaxy should influence the value of $M_ J $. The aim of this paper is to look at mixed samples of oxygen-rich and carbon-rich stars for the Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), and Milky way (MW) using the Gaia catalogue of long-period variables (LPVs) as a basis. The advantage of this catalogue is that it contains a classification of O- and C-stars based on the analysis of Gaia Rp spectra. The LPV catalogue is correlated with data from the Two Micron All Sky Survey (2MASS) and samples in the LMC, SMC, and the MW are retrieved. Following methods proposed in the literature, we report the mean and median magnitudes of the selected sample using different colour and magnitude cuts and the results of fitting Gaussian and Lorentzian profiles to the luminosity function (LF). For the SMC and LMC, we confirm previous results in the literature. The LFs of the SMC and LMC JAGB stars are clearly different, yet it can be argued that the mean magnitude inside a selection box agrees at the 0.021 mag level. The results of our analysis of the MW sample are less straightforward. The contamination by O-rich stars is substantial for a classical lower limit of $(J- 1.3$, and becomes less than 10<!PCT!> only for $(J- 1.5$. The sample of AGB stars is smaller than for the MCs for two reasons. Nearby AGB stars (with potentially the best determined parallax) tend to be absent as they saturate in the 2MASS catalogue, and the parallax errors of AGB stars tend to be larger compared to non-AGB stars. Several approaches have been taken to improve the situation but finally the JAGB LF for the MW contains about 130 stars and the fit of Gaussian and Lorentzian profiles is essentially meaningless. The mean and median magnitudes are fainter than for the MC samples by about 0.4 mag which is not predicted by theory. We do not confirm the claim in the literature that the absolute calibration of the JAGB method is independent of metallicity up to solar metallicity. A reliable calibration of the JAGB method at (near) solar metallicity should await further data releases, or should be carried out in another environment.

VIRTUAL FLIPPED CLASSROOM FOR DEVELOPING EFL STUDENTS’ SPEAKING SKILLS: DESIGN AND IMPLEMENTATION

developing speaking skills due to limited classroom time and cultural tendencies towards passive learning. This study investigated the effectiveness of a virtual flipped classroom in addressing these challenges and enhancing EFL students' speaking abilities. The research involved 40 Indonesian university students, divided equally into experimental and control groups. The experimental group participated in a virtual flipped classroom, completing pre-class online activities and engaging in in-class speaking exercises, while the control group received traditional instruction. Pre- and post-tests assessed speaking skills, supplemented by student surveys. Results revealed significantly higher post-test scores in the experimental group compared to the control group. Furthermore, survey data indicated that students perceived the virtual flipped classroom as effective in promoting active learning and enhancing their speaking skills. This approach shows promise in overcoming cultural barriers to active participation and maximizing limited class time for speaking practice in Indonesian EFL contexts. However, further research is needed to explore long-term effects and optimal implementation strategies across diverse EFL settings.

AdS4 holography and the Hilbert scheme

We elucidate a holographic relationship between the enumerative geometry of the Hilbert scheme of N points in the plane ℂ2, with N large, and the entropy of certain magnetically charged black holes with AdS4 asymptotics. Specifically, we demonstrate how the entropy functional arises from the asymptotics of ’t Hooft and Wilson line operators in a 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 gauge theory. The gauge-Bethe correspondence allows us to interpret this calculation in terms of the enumerative geometry of the Hilbert scheme and thereby conjecture that the entropy is saturated by expectation values of certain natural operators in the quantum K-theory ring acting on the localised K-theory of the Hilbert scheme. We give numerical evidence that the large N limit is saturated by contributions from a certain vacuum/fixed point on the Hilbert scheme, associated to a particular triangular-shaped Young diagram, by evolving solutions to the Bethe equations numerically at finite (but large) N towards the classical limit. We thus conjecture a concrete geometric holographic dual of the so-called gravitational/Cardy block.

Modeling the distribution of jet fuel price returns based on fat-tail stable Paretian distribution.

Jet fuel plays a crucial role as an essential energy source in aerospace and aviation operations. The recent increase in fuel prices has presented airlines with the new challenge of managing jet fuel costs to ensure consistent cash flow and minimize operational uncertainties. The conventional risk prediction models used by airlines often assume that risks are normally distributed according to the classical Central Limit Theorem, which can lead to under-hedging. This paper proposes an innovative approach using the stable Paretian model to analyze the price return of jet fuel in large samples. It comprehensively compares the fitting effect of the stable Paretian distribution with that of the normal distribution based on specific criteria and non-parametric significance tests. Furthermore, it investigates the accuracy of risk measures such as Value at Risk (VaR) and Conditional Value at Risk (CVaR) predicted by both models. In addition to comparing differences in VaR between predicted values and actual values, this paper provides a more comprehensive comparison of risk measures under rolling window forecast situation. Results suggest that despite indistinguishable results in VaR backtest, the stable Paretian distribution has a overall better fitting effect as well as a less biased predicted CVaR based on the AIC of -14099.46, BIC of -14110.98, p = 0.58 in Kolmogorov-Smirnov test and p = 0.46(0.92) in the 0.01(0.05) significance level of Expected Shortfall Regression Test. This might be explained by its ability to capture asset return dynamics while maintaining shape stability with few parameters. This research can provide valuable insights for guiding airlines' risk management decisions. its ability to capture asset return dynamics while maintaining shape stability with few parameters. This research can provide valuable insights for guiding airlines' risk management decisions.

Bound States and Scattering of Magnons on a Superconducting Vortex in Ferromagnet-superconductor Heterostructures

We study the magnon spectrum in a thin ferromagnetic-superconductor heterostructure in the presence of a single superconducting vortex. We employ the Bogolubov–de Gennes Hamiltonian which describes the magnons in the presence of the stray magnetic field and the non-uniform magnetic texture induced by the vortex. We find that the vortex localizes magnon states approximately in the same way as a charge center produces electron bound states due to screened Coulomb interaction in the two-dimensional electron gas. The number of these localized states is substantially determined by the material parameters of the ferromagnetic film only. We solve the scattering problem for an incident plane spin wave and compute the total and transport cross sections. We demonstrate that the vortex-induced non-uniform magnetic texture in chiral ferromagnetic film produces a skew scattering of magnons. We explore the peculiarities of the quantum scattering problem that correspond to orbiting in the classical limit.

DEVELOPMENT OF CONTEXTUAL-BASED MODULES ON LINES AND ANGLES FOR SEVENTH GRADE STUDENTS AT SMP NEGERI 1 ULUSUSUA

This research aims to develop a module focused on lines and angles to enhance students' contextual skills. The study employs a Research and Development (R&D) approach using the 4D model (define, design, development, disseminate), with data collected through validation, questionnaires, and tests, analyzed both qualitatively and quantitatively. Based on the findings, the lines and angles module is proven to be valid, practical, and effective. Subject matter experts rated it as valid (75%), media experts also rated it valid (74.07%), and language experts rated it as very valid (75%). In limited class trials, practicality was rated very high (average 4.57), and similarly high in field trials (average 4.43). Effectiveness in improving learning outcomes was moderately good in limited class trials (average 0.65) and field trials (average 0.68). The developed module is intended to support independent learning among students and assist teachers in effectively teaching mathematics.

Enhancing Brain Tumor Detection Through Custom Convolutional Neural Networks and Interpretability-Driven Analysis

Brain tumor detection is crucial for effective treatment planning and improved patient outcomes. However, existing methods often face challenges, such as limited interpretability and class imbalance in medical-imaging data. This study presents a novel, custom Convolutional Neural Network (CNN) architecture, specifically designed to address these issues by incorporating interpretability techniques and strategies to mitigate class imbalance. We trained and evaluated four CNN models (proposed CNN, ResNetV2, DenseNet201, and VGG16) using a brain tumor MRI dataset, with oversampling techniques and class weighting employed during training. Our proposed CNN achieved an accuracy of 94.51%, outperforming other models in regard to precision, recall, and F1-Score. Furthermore, interpretability was enhanced through gradient-based attribution methods and saliency maps, providing valuable insights into the model’s decision-making process and fostering collaboration between AI systems and clinicians. This approach contributes a highly accurate and interpretable framework for brain tumor detection, with the potential to significantly enhance diagnostic accuracy and personalized treatment planning in neuro-oncology.

Addressing the Generalizability of AI in Radiology Using a Novel Data Augmentation Framework with Synthetic Patient Image Data: Proof-of-Concept and External Validation for Classification Tasks in Multiple Sclerosis.

Artificial intelligence (AI) models often face performance drops after deployment to external datasets. This study evaluated the potential of a novel data augmentation framework based on generative adversarial networks (GANs) that creates synthetic patient image data for model training to improve model generalizability. Model development and external testing were performed for a given classification task, namely the detection of new fluid-attenuated inversion recovery lesions at MRI during longitudinal follow-up of patients with multiple sclerosis (MS). An internal dataset of 669 patients with MS (n = 3083 examinations) was used to develop an attention-based network, trained both with and without the inclusion of the GAN-based synthetic data augmentation framework. External testing was performed on 134 patients with MS from a different institution, with MR images acquired using different scanners and protocols than images used during training. Models trained using synthetic data augmentation showed a significant performance improvement when applied on external data (area under the receiver operating characteristic curve [AUC], 83.6% without synthetic data vs 93.3% with synthetic data augmentation; P = .03), achieving comparable results to the internal test set (AUC, 95.0%; P = .53), whereas models without synthetic data augmentation demonstrated a performance drop upon external testing (AUC, 93.8% on internal dataset vs 83.6% on external data; P = .03). Data augmentation with synthetic patient data substantially improved performance of AI models on unseen MRI data and may be extended to other clinical conditions or tasks to mitigate domain shift, limit class imbalance, and enhance the robustness of AI applications in medical imaging. Keywords: Brain, Brain Stem, Multiple Sclerosis, Synthetic Data Augmentation, Generative Adversarial Network Supplemental material is available for this article. © RSNA, 2024.

Driven-dissipative phases and dynamics in non-Markovian nonlinear photonics

Interactions between photons (nonlinearities) enable a powerful form of control over the state of light. This control has enabled technologies such as light sources at new wavelengths, ultra-short optical pulses, frequency-comb metrology systems, even quantum light sources. Common to a wide variety of nonlinear optical technologies is an equilibrium between an energy source, such as an external laser, and dissipation, such as radiation loss or absorption. In the vast majority of these systems, the coupling between the system and the outside world (which leads to loss) is well described as “Markovian,” meaning that the outside world has no memory of its past state. In this work, we introduce a class of driven-dissipative systems in which a nonlinear cavity experiences non-Markovian coupling to the outside world. In the classical regime, we show that these non-Markovian cavities can have extremely low thresholds for nonlinear effects, as well as self-pulsing instabilities at THz rates, and rich phase diagrams with alternating regions of stability and instability. In the quantum regime, we show how these systems, when implemented on state-of-the-art platforms, can enable generation of strongly squeezed cavity states with intensity fluctuations that can be more than 15 dB below the classical limit, in contrast to the Markovian driven-dissipative cavity, in which the limit is 3 dB. In the regime of few-photon nonlinearity, such non-Markovian cavities can enable a deterministic protocol to generate Fock states of high order, which are long-desired, but still elusive at optical frequencies. We expect that exploiting non-Markovian couplings in nonlinear optics should in the future lead to even richer possibilities than those discussed here for both classical and quantum light manipulations.

Rectifiability, finite Hausdorff measure, and compactness for non‐minimizing Bernoulli free boundaries

AbstractWhile there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less is known about critical points of the corresponding energy. Saddle points of the energy (or of closely related energies) and solutions of the corresponding time‐dependent problem occur naturally in applied problems such as water waves and combustion theory. For such critical points —which can be obtained as limits of classical solutions or limits of a singular perturbation problem—it has been open since (Weiss, 2003) whether the singular set can be large and what equation the measure satisfies, except for the case of two dimensions. In the present result we use recent techniques such as a frequency formula for the Bernoulli problem as well as the celebrated Naber–Valtorta procedure to answer this more than 20 year old question in an affirmative way: For a closed class we call variational solutions of the Bernoulli problem, we show that the topological free boundary (including degenerate singular points , at which as ) is countably ‐rectifiable and has locally finite ‐measure, and we identify the measure completely. This gives a more precise characterization of the free boundary of in arbitrary dimension than was previously available even in dimension two. We also show that limits of (not necessarily minimizing) classical solutions as well as limits of critical points of a singularly perturbed energy are variational solutions, so that the result above applies directly to all of them.

Algebras and Hilbert spaces from gravitational path integrals. Understanding Ryu-Takayanagi/HRT as entropy without AdS/CFT

Recent works by Chandrasekaran, Penington, and Witten have shown in various special contexts that the quantum-corrected Ryu-Takayanagi (RT) entropy (or its covariant Hubeny-Rangamani-Takayanagi (HRT) generalization) can be understood as computing an entropy on an algebra of bulk observables. These arguments do not rely on the existence of a local holographic dual field theory. We show that analogous-but-stronger results hold in any UV-completion of asymptotically anti-de Sitter quantum gravity with a Euclidean path integral satisfying a simple and (largely) familiar set of axioms. We consider a quantum context in which a standard Lorentz-signature classical bulk limit would have Cauchy slices with asymptotic boundaries BL ⊔ BR where both BL and BR are compact manifolds without boundary. Our main result is then that (the UV-completion of) the quantum gravity path integral defines type I von Neumann algebras ALBL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_L^{B_L} $$\\end{document}, ARBR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_R^{B_R} $$\\end{document} of observables acting respectively at BL, BR such that ALBL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_L^{B_L} $$\\end{document}, ARBR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_R^{B_R} $$\\end{document} are commutants. The path integral also defines entropies on ALBL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_L^{B_L} $$\\end{document}, ARBR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_R^{B_R} $$\\end{document}. Positivity of the Hilbert space inner product then turns out to require the entropy of any projection operator to be quantized in the form ln N for some N ∈ ℤ+ (unless it is infinite). As a result, our entropies can be written in terms of standard density matrices and standard Hilbert space traces. Furthermore, in appropriate semiclassical limits our entropies are computed by the RT-formula with quantum corrections. Our work thus provides a Hilbert space interpretation of the Ryu-Takayanagi entropy. Since our axioms do not severely constrain UV bulk structures, it is plausible that they hold equally well for successful formulations of string field theory, spin-foam models, or any other approach to constructing a UV-complete theory of gravity.

Classical echoes of quantum boundary conditions

Abstract We consider a non-relativistic particle in a one-dimensional box with all possible quantum boundary conditions that make the kinetic-energy operator self-adjoint. We determine the Wigner functions of the corresponding eigenfunctions and analyze in detail their classical limit, governed by their behavior in the high-energy regime. We show that the quantum boundary conditions split into two classes: all local and regular boundary conditions collapse to the same classical boundary condition, while a dependence on singular non-local boundary conditions persists in the classical limit.

Representation theory of the reflection equation algebra II: Theory of shapes

We continue our study of the representations of the Reflection Equation Algebra (=REA) on Hilbert spaces, focusing again on the REA constructed from the R-matrix associated to the standard q-deformation of GL(N,C) for 0<q<1. We consider the Poisson structure appearing as the classical limit of the R-matrix, and parametrize the symplectic leaves explicitly in terms of a type of matrix we call a shape matrix. We then introduce a quantized version of the shape matrix for the REA, and show that each irreducible representation of the REA has a unique shape.

Model-implied simulation-based power estimation for correctly specified and distributionally misspecified models: Applications to nonlinear and linear structural equation models.

Closed-form (asymptotic) analytical power estimation is only available for limited classes of models, requiring correct model specification for most applications. Simulation-based power estimation can be applied in almost all scenarios where data following the model can be estimated. However, a general framework for calculating the required sample sizes for given power rates is still lacking. We propose a new model-implied simulation-based power estimation (MSPE) method for the z-test that makes use of the asymptotic normality property of estimates of a wide class of estimators, the M-estimators, and give theoretical justification for the approach. M-estimators include maximum-likelihood, least squares estimates and limited information estimators, but also estimators used for misspecified models, hence, the new simulation-based power modeling method is widely applicable. The MSPE employs a parametric model to describe the relationship between power and sample size, which can then be used to determine the required sample size for a specified power rate. We highlight its performance in linear and nonlinear structural equation models (SEM) for correctly specified models and models under distributional misspecification. Simulation results suggest that the new power modeling method is unbiased and shows good performance with regard to root mean squared error and type I error rates for the predicted required sample sizes and predicted power rates, outperforming alternative approaches, such as the naïve approach of selecting a discrete selection of sample sizes with linear interpolation of power or simple logistic regression approaches. The MSPE appears to be a valuable tool to estimate power for models without an (asymptotic) analytical power estimation.

Extended system-bath entanglement theorem with multiple baths in the presence of external fields.

The system-bath entanglement theorem (SBET) was established in terms of linear response functions [Du et al., J. Chem. Phys. 152, 034102 (2020)] and generalized to correlation functions [Su et al., J. Chem. Phys. 160, 084104 (2024)] in our previous studies. This theorem connects the entangled system-bath properties to the local system and bare-bath ones. In this work, we extend the SBET to field-dressed conditions with multiple baths at different temperatures. As in reality, the external fields may interact with not only the system but also environments. The extended SBET facilitates, for example, photo-acoustic, photo-thermal, pump-probe related studies. The theorem under the field-free condition (multiple baths) and its counterpart in the classical limit is also presented.