Observing the dayside thermal emissions of rocky exoplanets provides essential insights into their compositions and the presence of atmospheres. Even though no conclusive evidence has been found for atmospheres on small rocky exoplanets orbiting M dwarfs, recent JWST observations identified puzzling thermal emission excesses. Some rocky exoplanets orbiting M dwarfs have dayside emission temperatures higher than the theoretical maximum temperatures, which are calculated assuming stellar irradiation as the sole energy source. Therefore, the observed thermal emission excesses imply that these planets may have internal heat sources. In this work, we simulate three possible internal planetary processes that may generate excess heat in addition to stellar irradiation: residual heating from formation, tidal heating, and induction heating due to interactions with the stellar magnetic field. We found that these mechanisms, even when combined, cannot explain the observed thermal emission excesses, nor can they account for a tentative positive trend in the brightness temperature scaling factor with irradiation temperature. Our results imply that planetary internal processes are unlikely to generate remotely detectable heat, so the observed thermal excesses, if astrophysical, are likely caused by stellar contamination, surface processes, geometric effect, or other internal processes not considered in this study. The ongoing JWST-HST Rocky Worlds Director's Discretionary Time Program and the upcoming Nancy Grace Roman Space Telescope will provide more insights into the thermal emission of rocky exoplanets.

AI-driven speech-to-text (STT) documentation systems are increasingly adopted in clinical settings to reduce documentation burden and improve workflow efficiency. However, adoption has outpaced systematic evaluation of socio-technical risks related to transparency, reliability, patient autonomy, and organizational accountability. This study develops a socio-technical framework for identifying and governing risks associated with clinical STT systems. We synthesize interdisciplinary evidence from automatic speech recognition research, clinical workflow and human factors studies, ethical guidance on consent and autonomy, and regulatory and organizational sources. Using a structured narrative synthesis, literature was iteratively reviewed and thematically analyzed to identify recurring socio-technical risk mechanisms and inform a layered conceptual framework. Findings show that clinical STT systems operate within tightly coupled socio-technical environments where model performance, audio conditions, clinician oversight, patient understanding, workflow design, and institutional governance are interdependent. Key risks include inconsistent consent practices, performance disparities for accented speech and speech disorders, accuracy degradation in real clinical settings, automation complacency, and unclear accountability across vendors and healthcare organizations. These risks inform a six-layer governance model spanning technical, human/workflow, ethical, organizational, regulatory, and sociocultural dimensions. We propose a governance framework and implementation roadmap to support responsible deployment of clinical STT systems, emphasizing transparency, patient autonomy, documentation integrity, and accountable oversight.

We study first-return statistics for photons undergoing three-dimensional Henyey-Greenstein scattering in a semi-infinite medium. In previous work, we showed that one-dimensional first-passage probabilities can be expanded using Catalan and Motzkin generating functions. Extending this framework to three dimensions requires introducing a Boundary Truncation Factor (BTF), which accounts for the restricted angular phase space imposed by the boundary. Extensive Monte Carlo simulations are used to determine the BTF empirically as a function of scattering order and anisotropy. For moderate anisotropy, the BTF is accurately described by a Cauchy kernel, with parameters depending only on the Henyey-Greenstein asymmetry factor. This closed-form expression reproduces Monte Carlo results with 1-2% accuracy over a broad range of scattering orders. At higher anisotropy, systematic deviations from the Cauchy form are observed. These deviations can be reduced using a one-parameter generalized kernel. We further extend the framework to oblique incidence by replacing the normal-incidence return probability with a Legendre-series formulation. The BTF parameters and Motzkin counting machinery remain independent of the incidence angle, so only the anchor point of the algorithm changes. The resulting framework provides a computationally efficient mapping from three-dimensional anisotropic transport at arbitrary incidence to one-dimensional combinatorial first-passage theory.

We explore the feasibility of realizing Dicke states in qubit arrays with always-on isotropic Heisenberg coupling between adjacent qubits, assuming a single Zeeman-type control acting in the $z$ direction on an actuator qubit. The Lie-algebraic criteria of controllability imply that such an array is not completely controllable, but satisfies the conditions for subspace controllability on any subspace with a fixed number of excitations. Therefore, a qubit array described by the model under consideration is state-to-state controllable for an arbitrary choice of initial and final states that have the same Hamming weight. This limited controllability is exploited here for the time-efficient dynamical generation of an $a$-excitation Dicke state $|D^{N}_{a}\rangle$ ($a=1,2,\ldots, N-1$) in a linear array with $N$ qubits starting from a generic Hamming-weight-$a$ product state. To dynamically generate the desired Dicke states -- including $W$ states $|W_{N}\rangle$ as their special ($a=1$) case -- in the shortest possible time with a single local $Z$ control, we employ an optimal-control scheme based on the {\em dressed Chopped RAndom Basis} (dCRAB) algorithm. We optimize the target-state fidelity over the expansion coefficients of smoothly-varying control fields in a truncated random Fourier basis; this is done by combining Nelder-Mead-type local optimizations with the multistart-based clustering algorithm that facilitates searches for global extrema. In this manner, we obtain the optimal control fields for Dicke-state preparation in arrays with up to $9$ qubits. Based on our numerical results, we find that the shortest possible state-preparation times scale as $\mathcal{O}(N^{2.08})$ for $W$ states and $\mathcal{O}(N^{1.78})$ for $a=2$ Dicke states.

Electrochemical systems are important for a sustainable and defossilized energy system of the future. While accurate and precise, the corresponding electrochemical measurements, in which many reactions may occur simultaneously, often do not contain enough information to understand the underlying mechanism and processes. This information, however, is crucial towards rational materials and devices as well as process development and for inventing innovative concepts. In this perspective, we introduce explicitly the concept of "X-ray Coulomb Counting" in which X-ray methods are used to quantify on an absolute scale how much charge is transferred into which reactions during the electrochemical measurements. This allows to interpret the electrochemical measurements in detail and obtain the desired phenomenological and mechanistic understanding. We show a few recent examples from the Li-ion battery literature in which the concept of X-ray Coulomb Counting was employed to obtain foundational understanding.

Ising formulation is important for many NP problems (Lucas, 2014). This formulation enables implementing novel quantum computing methods including Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver (VQE). Here, we investigate closely the traveling salesman problem (TSP). First, we present some non-trivial issues related to Ising model view versus a realistic salesman. Then, focusing on VQE we discuss and clarify the use of: a.-- Conventional VQE and how it is relevant as a novel SAT-solver; b.-- Qubit efficiency and its importance in the Noisy Intermediate Scale Quantum-era; and c.-- the relevance and importance of a novel approach named Discrete Quantum Exhaustive Search (Alfassi, Meirom, and Mor, 2024), for enhancing VQE and other methods using mutually unbiased bases. The approach we present here in details can potentially be extended for analyzing approximating and solving various other NP complete problems. Our approach can also be extended beyond the Ising model and beyond the class NP, for example to the class Quantum Merlin Arthur (QMA) of problems, relevant for quantum chemistry and for general spin problems.

In this paper, we introduce a Grothendieck topology on the category of totally bounded metric spaces and develop a theory of stacks with respect to this topology. We further define the fine moduli stack of compact metric spaces and prove that its coarse moduli space is isometric to the Gromov--Hausdorff space.

Contemporary quantum computers are inherently noisy, posing significant challenges for the development and testing of quantum software. Simplified or outdated noise assumptions can lead to incorrect assessments of program correctness, obscure debugging, and hinder cross-platform portability, creating a critical quantum software development gap. Providing accurate, practical noise characterisation is challenging as traditional reconstruction methods scale exponentially and rapidly become outdated. In this vision paper, we address this gap via a novel classical shadow tomography-based pipeline, SIMSHADOW, enabling efficient, continuously updatable noise fingerprinting from empirical observations, suitable for integration into quantum software development workflows, including testing and validation. We prototyped the pipeline to investigate fingerprints' ability to capture structured, interpretable noise and cross-platform discrepancies affecting quantum programs' behaviour to support realistic testing and debugging in future tools. Our evaluation with Qiskit and Cirq under widely used hardware-informed profiles, IBM Boston and Quantinuum H2, shows fingerprints exhibit channel-specific structure and yield interpretable heatmaps. We observed systematic cross-platform discrepancies under matched noise configurations, quantified by large Frobenius distances at a fraction of full tomography cost. On 69 MQTBENCH programs, larger fingerprint differences correlate with output distributions divergences, highlighting threats for testing and cross-platform debugging tasks.

We evaluate TCP BBRv3 on Wi-Fi 6 home networks under modern AQM schemes using a fully wireless testbed and a simple cross-layer model linking Wi-Fi scheduling, router queueing, and BBRv3's pacing dynamics. Comparing BBR Internet traffic with CUBIC across different AQMs (FIFO, FQ-CoDel, and CAKE) for uplink, downlink, and bidirectional traffic, we find that FIFO destabilizes pacing and raises delay, often letting CUBIC dominate; FQ-CoDel restores fairness and controls latency; and CAKE delivers the best overall performance by keeping delay low and aligning BBRv3's sending and delivered rates. We also identify a Wi-Fi-specific effect where CAKE's rapid queue draining, while improving pacing alignment, can trigger brief retransmission bursts during BBRv3's bandwidth probes. These results follow from the interaction of variable Wi-Fi service rates, AQM delay control, and BBRv3's inflight limits, leading to practical guidance to use FQ-CoDel or CAKE and avoid unmanaged FIFO in home Wi-Fi, with potential for Wi-Fi-aware tuning of BBRv3's probing.

We analyse warping corrections to the scalar potential in flux compactifications of Type IIB string theory, focusing on their effect on $F$-term de Sitter uplifting in Calabi-Yau orientifold models. A systematic inverse-volume expansion allows us to derive the four-dimensional off-shell potential in the presence of warping and non-ISD 3-form fluxes. This corresponds to integrating out all massive Kaluza-Klein modes using the ten-dimensional equations of motion. We further propose a warped Kähler potential in four-dimensional $\mathcal{N}=1$ supergravity, and show that it is consistent with our ten-dimensional results. In the KKLT framework, we find that classical warping corrections, as well as mixed corrections involving non-ISD fluxes and quantum effects, are dominant, rendering the scenario effectively uncontrollable with current methods. By contrast, in LVS-like constructions these corrections are suppressed by inverse powers of the volume, specifically $\mathcal{V}^{1/2}$ or $\mathcal{V}^{1/6}$, depending on the concrete model.

We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that the partition functions of certain self-adjoint models and their complex counterparts are different integral representations of the exact same function. A special case of these equivalences takes a form of newly found dually weighted intermediate field representations, which generalize the standard intermediate field representation. We also find indications of an equivalence between real tensor models and self-transpose tensor models.

A search for long-lived heavy neutral leptons produced in B-meson decays and decaying to a $ μ^\pm π^\mp$ final state is performed with data collected by the LHCb experiment in proton-proton collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of $5\,\mathrm{fb}^{-1}$. The results are interpreted in both lepton-number-conserving and lepton-number-violating scenarios. No significant excess is observed. Constraints are placed on the squared mixing element $|U_{μN}|^2$ to the active muon neutrino, under the assumption that couplings to other lepton flavours are negligible, in the mass range of $1.6$-$5.5$ GeV.

Much of Software Engineering (SE) research assumes that progress depends on massive datasets and CPU-intensive optimizers. Yet has this assumption been rigorously tested? The counter-evidence presented in this paper suggests otherwise. For over 100 optimization tasks from recent SE papers (including software configuration, performance tuning, product line engineering, project health forecasting, defect prediction, software testing, software process and cost estimation, and cross-domain generalization datasets), even with just a few dozen labels, very simple methods (e.g., diversity sampling, a minimal Bayesian learner, its distance-based non-parametric variant, or random probes) achieve over 90% of the best reported results. Furthermore, these simple methods perform just as well as more complex state-of-the-the-art optimizers like SMAC, TPE, DEHB etc. While some tasks would require better outcomes and more sampling, these results seen after a few dozen samples would suffice for many engineering needs (particularly when the goal is rapid and cost-efficient guidance rather than slow and exhaustive optimization). To say that another ways, at least some SE tasks are better served by lightweight approaches that demand fewer labels and far less computation. We hence propose the data-light challenge: when will a handful of labels suffice for SE tasks? To enable a large-scale investigation of this issue, we contribute (1) a mathematical formalization of labeling, (2) lightweight baseline algorithms, and (3) results on public-domain data showing the conditions under which lightweight methods excel or fail. For the purposes of open science, our scripts and data are online at https://github.com/KKGanguly/NEO .

Since the formal introduction of its "dual-carbon" strategy in 2020, China has witnessed the concepts of green development and sustainability evolve from policy directives into a broad societal consensus. Within this transformative context, the Environmental, Social, and Governance (ESG) framework has emerged as a critical enabler, mutually reinforcing and synergizing with the national strategic objectives of achieving carbon peak and carbon neutrality. This integration signifies a fundamental shift in corporate philosophy, urging enterprises to transcend a narrow focus on short-term financial metrics. To align with the national vision of ecological civilization and sustainable growth, companies are now expected to proactively fulfill their social responsibilities and pursue long-term, non-financial value creation. This entails a deep integration of ESG principles into the very core of corporate culture and strategy, ensuring their active implementation in daily operations and decision-making processes.

In two papers, A. Lapi et al. introduce and discuss what they call the $η$CDM model, a stochastic framework in which they claim that fluctuations in the density field at the scale of tens of Mpc due to structure formation would effectively drive the accelerated expansion of the Universe. They claim that this qualitative behaviour would emerge from the dynamics of standard cold dark matter alone, without introducing any new physics. In this short comment, I argue that such a proposition is implausible. Some of my remarks are relevant more generally to frameworks that try to describe cosmological back-reaction.

This study explores the role of nucleon exchange for the generation of the fission fragment angular momenta. For a number of typical fission cases, samples of 10,000 shape evolutions are generated by Langevin simulation and, subsequently, for each such evolution, the nucleon exchange transport theory previously developed for damped nuclear reactions is used to obtain the development of the fragment spin-spin distribution within the Fokker-Planck transport framework. The characteristic evolution of both parallel and perpendicular spin components is discussed. A common feature is that the rotational modes fall out of equilibrium before scission when the temperature rises rapidly while the concurrent shrinking of the neck suppresses further exchange. A number of fission observables are extracted from the event ensembles: the distribution of the magnitude of the fragment spin and its orientation relative to the fission axis, as well as the correlation between the two spins and the distribution of their opening angle. The dependence of these observables on the mass asymmetry is also examined.

This paper investigates the impact of approximation error in data-driven optimal control problem of nonlinear systems while using the Koopman operator. While the Koopman operator enables a simplified representation of nonlinear dynamics through a lifted state space, the presence of approximation error inevitably leads to deviations in the computed optimal controller and the resulting value function. We derive explicit upper bounds for these optimality deviations, which characterize the worst-case effect of approximation error. Supported by numerical examples, these theoretical findings provide a quantitative foundation for improving the robustness of data-driven optimal controller design.

Perturbative calculations of gravitational radiation near the horizons of rotating black holes in the frequency domain have been plagued by divergence issues. We resolve this longstanding obstacle by constructing a nonsingular source term for near-horizon gravitational perturbations, or equivalently perturbed Weyl scalars $ψ_0$ with a spin weight of $s = +2$, within the generalized Sasaki-Nakamura formalism for the first time. As illustrative applications, we compute the dynamical deformation of the event horizon induced by an ultrarelativistic particle plunge, demonstrating the excitation of quasinormal modes at the horizon, and we evaluate the energy flux towards the horizon from an extreme mass-ratio inspiral. This work provides a powerful tool for studying physics near black hole horizons.

We investigate a modified affine Toda model coupled to matter (ATM) which includes a scalar self-interacting potential and demonstrate that its first-order integro-differential structure, preserving a deformed Noether-topological current correspondence, provides a consistent framework for fermion-soliton interactions. In this formulation, the fermion-soliton energy is proportional to the soliton's topological charge. We evaluate the renormalized energy functional, incorporating one-loop quantum corrections, and perform a variational minimization to determine the configuration that extremizes the functional. The fermionic back-reaction and the self-interacting scalar critically shape the fermion-kink energy, the in-gap bound-state spectrum, and the fermionic vacuum-polarization energy, yielding well-defined stability minima of the total energy as functions of the fermion and scalar masses and coupling parameters, in the semiclassical approximation. A key result is that the Heun-equation formalism is necessary to construct nonzero-energy bound and scattering states: unlike the tau-function method, which captures only the zero mode, the Heun approach encodes the full scattering data through local solution matching conditions. These results refine the spectral analysis of deformed integrable models. The stability of soliton-fermion configurations has direct implications for topologically protected states in quantum information and condensed-matter systems.

Research on strongly correlated electron systems faces a fundamental challenge due to the complex nature of intrinsic many-body correlations. A key strategy to address this challenge lies in advancing experimental methods that can directly probe and elucidate the underlying many-body correlations. In this perspective article, we discuss the theoretically proposed coincidence detection techniques, which are designed to directly measure two-body correlations in various particle-particle and particle-hole channels, with momentum, energy, and/or spatial resolution. We also explore the prospects of these coincidence detection techniques for future theoretical and experimental developments. The successful implementation and refinement of these coincidence detection techniques promise to deliver powerful new approaches for unraveling long-standing puzzles in strongly correlated electron systems, such as the enigmatic mechanism of unconventional superconductivity and the long-sought quantum spin liquids. Furthermore, these coincidence detection techniques will offer powerful new methods to investigate novel phenomena like itinerant magnetism and electronic nematicity in quantum materials.

This paper concerns the diffusive limit of the time evolutionary Boltzmann equation in the half space $\mathbb{T}^2\times\mathbb{R}^+$ for a small Knudsen number $\varepsilon>0$. For boundary conditions in the normal direction, it involves diffuse reflection moving with a tangent velocity proportional to $\varepsilon$ on the wall, whereas the far field is described by a global Maxwellian with zero bulk velocity. The incompressible Navier-Stokes equations, as the corresponding formal fluid dynamic limit, admit a specific time-dependent shearing solution known as the Rayleigh profile, which accounts for the effect of the tangentially moving boundary on the flow at rest in the far field. Using the Hilbert expansion method, for well-prepared initial data we construct the Boltzmann solution around the Rayleigh profile without initial singularity over any finite time interval.

Data collected over a two-day period in June 2024 at the CERN SPS H9 test beam using a small-scale GRAiNITA prototype have been analyzed to characterize the detector's energy resolution performance. The measurements allow for a first estimate of the constant term associated with detector non-uniformity. Although the evaluation is limited by the small prototype size and the use of pion beams, the results indicate that the non-uniformity-related constant term is significantly below 1%. Furthermore, the test-beam data confirm that the contribution to the energy resolution arising from photo-electron statistics is approximately 1%/sqrt(E). These findings validate the expected calorimetric performance of the GRAiNITA concept and provide important input for the design and optimization of future full-scale detectors.

Consider the classical Bin Packing problem with $d$ different item sizes $s_i$ and amounts of items $a_i.$ The support of a Bin Packing solution is the number of differently filled bins. In this work, we show that the lower bound on the support of this problem is $2^{Ω(d)}$. Our lower bound matches the upper bound of $2^d$ given by Eisenbrand and Shmonin [Oper.Research Letters '06] up to a constant factor. This result has direct implications for the time complexity of several Bin Packing algorithms, such as Goemans and Rothvoss [SODA '14], Jansen and Klein [SODA '17] and Jansen and Solis-Oba [IPCO '10]. To achieve our main result, we develop a technique to aggregate equality constrained ILPs with many constraints into an equivalent ILP with one constraint. Our technique contrasts existing aggregation techniques as we manage to integrate upper bounds on variables into the resulting constraint. We believe this technique can be useful for solving general ILPs or the $d$-dimensional knapsack problem.

Biological systems achieve adaptive mechanical responses through reaction-diffusion processes that couple chemical wave propagation to structural transitions. Although synthetic hydrogels with enzymatic reactions offer a platform for replicating such autonomous behavior, the mechanistic principles governing chemomechanical transduction remain poorly understood. Here, we present a glucose oxidase-embedded polyacrylamide-alginate hydrogel with slower transduction kinetics that enable independent resolution of chemical waves and mechanical adaptation. Enzymatic pH waves propagate at 15-44 um/min, triggering calcium-mediated alginate crosslinking through pH-responsive calcium-EDTA dissociation. Independent tracking of chemical and mechanical waves reveals that mechanical wavefronts (12 um/min) lag behind chemical propagation, establishing transduction as the rate-limiting step in this chemomechanical coupling. Remarkably, the enzymatic system must continuously supply chemical energy to both propagate the chemical wave and drive ongoing mechanical transitions, imposing energetic costs on reaction-diffusion beyond kinetic constraints alone. Our adaptive system achieves up to 2.1-fold increase in stiffness and enables autonomous conversion of localized stimuli into system-wide mechanical responses. These mechanistic insights establish design principles for engineering adaptive materials with predictable spatiotemporal control in soft robotics and biomedical applications.

The purpose of this paper is to develop the theory of holomorphic functions with modulus bounded by $1$ on the symmetrized skew bidisc \[ \mathbb{G}_{r} \stackrel{\rm def}{=} \Big\{( λ_{1}+rλ_{2} ,rλ_{1}λ_{2}): λ_{1}\in \mathbb{D}, λ_{2}\in\mathbb{D}\Big\}, \] for a fixed $r \in (0,1)$. We show the existence of a realization formula and a model formula for such holomorphic functions.

Predicting the evolving microstructure of hydrating cement is essential for understanding and modeling its mechanical property development. Physics-based continuum approaches offer a rigorous framework for capturing the thermodynamics of dissolution and precipitation processes at the microstructural scale. In this work, we present an adapted Phase-Field (PF) model for cement hydration that resolves key physical inconsistencies in existing PF formulations by introducing a revised free-energy potential and distinct equilibrium constants for clinker dissolution and hydrate precipitation. The resulting PF framework reproduces microstructural evolution, yielding realistic porosity levels and continuous phase boundaries in close agreement with experimental observations. The predicted hydrated microstructures are subsequently used in a computational homogenization scheme to evaluate the elastic response of the material. The PF-derived mechanical properties show good agreement with experimental trends, supporting the ability of the proposed framework to consistently link hydration chemistry, microstructure formation, and the resulting mechanical response.

Local Primordial non-Gaussianities (PNGs), characterized by $f_{\rm NL}^{\rm loc}$, provide a powerful window into the physics of inflation. Cross-correlating high-redshift tracer samples with the CMB lensing potential offers a particularly robust probe of PNGs, mitigating imaging systematics that typically affect large-scale measurements from tracer auto-spectra. In this context, UNIONS enables the selection of $u$-dropout high-redshift Lyman-Break Galaxies (LBGs). We perform a MCMC-based forecast to estimate the uncertainties on $f_{\rm NL}^{\rm loc}$ and on a galaxy bias parameter, which captures our uncertainty in the tracer bias. From the angular cross-power spectrum between LBGs and Planck CMB lensing, we forecast $σ(f_{\rm NL}^{\rm loc})=34$ for an idealized photometric sample of $r<24.3$ LBGs selected with a Random Forest classification algorithm from UNIONS-like $ugriz$ imaging, with a resulting surface density of $1,100$ deg$^{-2}$. This precision can be improved to $σ(f_{\rm NL}^{\rm loc})=20$ after spectroscopic follow-up with DESI, during its next phase starting in 2029, DESI-II. We test a more realistic $u$-dropout LBG selection using early UNIONS data, which yields a denser sample of $r<24.2$ objects at $1,400$ deg$^{-2}$. From this sample, covering a larger footprint and expected to have a higher large-scale galaxy bias, we forecast $σ(f_{\rm NL}^{\rm loc})=20$, with similar precision achievable after DESI spectroscopic follow-up. In addition, we perform preliminary validation of the redshift distribution using the clustering-redshift method with DESI DR1 data, confirming the calibration from deep, small-area photometric fields. However, accounting for uncertainties in the clustering-redshift distribution significantly degrades the $f_{\rm NL}^{\rm loc}$ constraining power.

Quantum Krylov algorithms have emerged as a promising approach for ground-state energy estimation in the near-term quantum computing era. A major challenge, however, lies in their inherently substantial sampling cost, primarily due to the individual measurement of each term in the Hamiltonian. While various techniques have been proposed to mitigate this issue, the sampling overhead remains a significant bottleneck, especially for practical large-scale electronic structure problems. In this work, we introduce an alternative method, dubbed mirror subspace diagonalization (MSD), which approaches the theoretical lower bound of the sampling cost for quantum Krylov algorithms. MSD leverages a finite-difference formula to express the Hamiltonian operator as a linear combination of time-evolution unitaries with symmetrically shifted timesteps, enabling efficient estimation of the Hamiltonian matrix within the Krylov subspace. In this scheme, the finite difference and statistical errors are simultaneously minimized by optimizing the timestep parameter and shifting the energy spectrum. Consequently, MSD attains the lower bound of the sampling cost of the quantum Krylov algorithms up to a logarithmic factor. Furthermore, we employ classical post-processing to infer Hamiltonian moments, which are used to mitigate the ground state energy error based on the Lanczos scheme. Through theoretical analysis of the sampling cost, we demonstrate that MSD is particularly effective when the spectral norm of the Hamiltonian is significantly smaller than its 1-norm. Such a situation arises, for example, in high-accuracy simulations of molecules using large basis sets that incorporate strong electronic correlations. Numerical results for various molecular models reveal that MSD can achieve sampling cost reductions ranging from approximately 10 to 10,000 times compared to the conventional quantum Krylov algorithm.

Solar flares, as one of the most prominent manifestations of solar activity, have a profound impact on both the Earth's space environment and human activities. As a result, accurate solar flare prediction has emerged as a central topic in space weather research. In recent years, substantial progress has been made in the field of solar flare forecasting, driven by the rapid advancements in space observation technology and the continuous improvement of data processing capabilities. This paper presents a comprehensive review of the current state of research in this area, with a particular focus on tracing the evolution of data-driven approaches -- which have progressed from early statistical learning techniques to more sophisticated machine learning and deep learning paradigms, and most recently, to the emergence of Multimodal Large Models (MLMs). Furthermore, this study examines the realistic performance of existing flare forecasting platforms, elucidating their limitations in operational space weather applications and thereby offering a practical reference for future advancements in technological optimization and system design.

Let $G$ be a finite group and \( M \) be a maximal subgroup of \( G \). We call every irreducible constituent \( χ\) of \( (1_M)^G \) a \( \mathcal{P} \)-character of \( G \) with respect to \( M \). In this paper, we prove that all $\mathcal{P}$-characters of $G$ are monomial if and only if $G$ is solvable, which solves a question posed by Qian and Yang.