We present a new mixed-integer programming (MIP) approach for offline multiple change-point detection by casting the problem as a globally optimal piecewise linear (PWL) fitting problem. Our main contribution is a family of strengthened MIP formulations whose linear programming (LP) relaxations admit integral projections onto the segment assignment variables, which encode the segment membership of each data point. This property yields provably tighter relaxations than existing formulations for offline multiple change-point detection. We further extend the framework to two settings of active research interest: (i) multidimensional PWL models with shared change-points, and (ii) sparse change-point detection, where only a subset of dimensions undergo structural change. Extensive computational experiments on benchmark real-world datasets demonstrate that the proposed formulations achieve reductions in solution times under both $\ell_1$ and $\ell_2$ loss functions in comparison to the state-of-the-art.

The timeliness of collected information is essential for monitoring and control in data-driven intelligent infrastructures. It is typically quantified using the Age of Information (AoI) metric, which has been widely adopted to capture the freshness of information received in the form of status updates. While AoI-based metrics quantify how timely the collected information is, they largely overlook the environmental impact associated with frequent transmissions, specifically, the resulting Carbon Footprint (CF). To address this gap, we introduce a carbon-aware AoI framework. We first derive closed-form expressions for the average AoI under constrained CF budgets for the baseline $M/M/1$ and $M/M/1^*$ queuing models, assuming fixed Carbon Intensity (CI). We then extend the analysis by treating CI as a dynamic, time-varying parameter and solve the AoI minimization problem. Our results show that minimizing AoI does not inherently minimize CF, highlighting a clear trade-off between information freshness and environmental impact. CI variability further affects achievable AoI, indicating that sustainable operation requires joint optimization of CF budgets, Signal-to-noise Ratio (SNR), and transmission scheduling. This work lays the foundation for carbon-aware information freshness optimization in next-generation networks.

The integration of topological insulators (TIs) with graphene offers a pathway to engineer hybrid quantum states, yet the impact of strain at the 2D limit remains a critical open question. Here, we investigate the structural properties of ultrathin (1 quintuple layer) Sb$_2$Te$_3$ grown on single-layer graphene and, motivated by the structural modulations observed at the TI surface, explore theoretically how such nanoscale corrugations may influence the electronic behavior of the system. Using low-temperature scanning tunneling microscopy (LT-STM), we observe a periodic rippling of the heterostructure with a wavelength of ~$\sim8.7$ nm. Energetic analysis reveals that these ripples are not intrinsic but are driven by strain from the substrate during cooling. Density functional theory (DFT) calculations show that while the ideal flat heterostructure exhibits a hybridization gap of $\sim40$ meV, the ripple-induced structural modulation closes this gap, restoring a metallic state. This gapless phase is not a trivial metal. By combining an effective moiré ladder model with spin-resolved DFT, we find that the proximity-induced spin-orbit coupling is redistributed across a dense manifold of minibands. The resulting ``Helical Metal'' has a complex spin-texture beyond a simple Rashba splitting. Remarkably, while the flat system is effectively spinless in this ultrathin limit due to hybridization, the ripples actively restore the spin polarization. Our findings suggest that rippled TI/graphene heterostructures provide an interesting platform to develop spintronics, where geometric modulation unlocks dense helical states that are inaccessible in the pristine flat limit.

We obtain height, gradient, and curvature a priori estimates for a modified mean curvature flow in Riemannian manifolds endowed with a Killing vector field. As a consequence, we prove the existence of smooth, entire, longtime solutions for this extrinsic flow with smooth initial data.

The relation between spin and statistics in quantum field theory relies on Poincaré invariance, a symmetry that is lost in the presence of a gravitational field, and replaced in general relativity by the principle of general covariance. In a nonperturbative approach to quantum gravity, beyond the picture of gravitational perturbations propagating on a flat background, it is an open question whether the gravitational field must still satisfy a bosonic statistics. By implementing the principle of general covariance through the requirement of invariance under active diffeomorphisms in loop quantum gravity, we find that the space of kinematical states of the gravitational field includes not only bosonic states, but also subspaces of fermionic and mixed statistics.

We present an analysis of optimal quantization of probability measures with nonuniform densities on spherical curves. We begin by deriving the centroid condition, followed by a high-resolution asymptotic analysis to establish the point-density formula. We further quantify the asymptotic error formula for the nonuniform densities. We apply these theorems to the von Mises distributions and characterize the optimal condition. We also provide applications using the high-resolution asymptotic and its corresponding error formula. Our results can be used in geometric probability theory and quantization theory of spherical curves.

Several Deep Learning (DL)-based techniques have been proposed to automate code review. Still, it is unclear the extent to which these approaches can recommend quality improvements as a human reviewer. We study the similarities and differences between code reviews performed by humans and those automatically generated by DL models, using ChatGPT-4 as representative of the latter. In particular, we run a mining-based study in which we collect and manually inspect 739 comments posted by human reviewers to suggest code changes in 240 PRs. The manual inspection aims at classifying the type of quality improvement recommended by human reviewers (e.g., rename variable/constant). Then, we ask ChatGPT to perform a code review on the same PRs and we compare the quality improvements it recommends against those suggested by the human reviewers. We show that while, on average, ChatGPT tends to recommend a higher number of code changes as compared to human reviewers (~2.4x more), it can only spot 10% of the quality issues reported by humans. However, ~40% of the additional comments generated by the LLM point to meaningful quality issues. In short, our findings show the complementarity of manual and AI-based code review. This finding suggests that, in its current state, DL-based code review can be used as a further quality check on top of the one performed by humans, but should not be considered as a valid alternative to them nor as a mean to save code review time, since human reviewers would still need to perform their manual inspection while also validating the quality issues reported by the DL-based technique.

The demographics of Kepler planets provide a key testbed for models of planet formation and evolution, particularly for explaining the radius valley separating super-Earths and sub-Neptunes. A primordial interpretation based on differences in bulk densities -- where rocky and water-rich planets form via migration pathways -- offers an alternative to atmospheric loss scenarios. Updated interior structure models of water worlds with adiabatic steam atmospheres reproduce the observed valley near $\sim2~R_\oplus$ more accurately. Furthermore, migration models from our Genesis library suggest that these formation pathways can also account for the distinct period distributions of super-Earths and sub-Neptunes, as well as the emergence of the hot Neptune desert. Motivated by this, we develop a Bayesian hierarchical mixture model for close-in Kepler planets ($P<100$ days), combining rocky planets and water worlds without H/He envelopes. The inferred mass distributions of rocky and water-rich planets peak at $\sim2.6~M_\oplus$ and $\sim7~M_\oplus$, respectively, with the water mass fraction of water worlds peaking at $\sim41\%$. Water worlds provide a good representation of the Kepler sub-Neptune population, with the radius cliff emerging as a ``waterfall" -- a sharp decline in their occurrence. However, our mass-radius analysis shows that water worlds alone cannot explain planets with $R \gtrsim 3~R_\oplus$, implying that at least $\sim20\%$ of sub-Neptunes in the sample are enriched in H/He gas.

Let $\mathcal{A}$ be a unital $C^\ast$-algebra equipped with a faithful tracial positive linear functional $τ$. Denote by $\mathcal{A}_+$ its positive cone. For $p>0$ and $A,B\in\mathcal{A}_+$, we consider the operations $$ Aκ_p B := \bigl(A^{p/4} B^{p/2} A^{p/4}\bigr)^{1/p}, \qquad A\nabla B := \frac{A+B}{2}. $$ We prove that, for all $p>0$ and all $A,B\in\mathcal{A}_+$, $$ τ(Aκ_p B)\le \sqrt{τ(A)τ(B)}\le τ(A\nabla B), $$ thereby answering \cite[Problem~1]{KM24}, posed by Á.~Komálovics and L.~Molnár, in the affirmative. We also record a unitarily invariant norm analogue of the key estimate in the matrix case, and we provide explicit $2\times2$ counterexamples showing that the triangle inequality for $d_p$ may fail when $0<p<1$ (already for $p=\tfrac12$), giving a partial answer to \cite[Problem~2]{KM24}.

While active matter physics has traditionally focused on particles with overdamped dynamics, recent years have seen an increase of experimental and theoretical work on active systems with inertia. This also leads to an increased need for theoretical models that describe inertial active dynamics. Here, we present a microscopic derivation for a general continuum model describing the nonequilibrium thermodynamics of inertial active matter that generalizes several previously existing works. It applies to particles with translational and rotational inertia and contains particle density, velocity, angular velocity, temperature, polarization, velocity polarization, and angular velocity polarization as dynamical variables. We moreover discuss to which extend commonly used approximations (factorization and local equilibrium) used in the derivation of hydrodynamic models are applicable to inertial active matter.

We study an approximation scheme for a variational theory of quasi-static crack growth based on an eigendeformation approach. We consider a family of energy functionals depending on a small parameter $\varepsilon$ and on two fields, the displacement field and an eigendeformation field that approximates the crack in the material. By imposing a suitable irreversibility condition and adopting an incremental minimization scheme, we define a notion of quasi-static evolution for this model. We then show that, as $\varepsilon \to 0$, these evolutions converge to a quasi-static crack evolution for the Griffith energy of brittle fracture, characterized by irreversibility, global stability, and an energy balance.

Shortlisting is a common and effective method for pre-selecting participants in competitive settings. To ensure fairness, a cut-off score is typically announced, allowing only contestants who exceed it to enter the contest, while others are eliminated. In this paper, we study rank-order contests with shortlisting and cut-off score disclosure. We fully characterize the equilibrium behavior of shortlisted contestants for any given prize structure and shortlist size. We examine two objective functions: the highest individual performance and total performance. For both objectives, the optimal contest is in a winner-take-all format. For the highest individual performance, the optimal shortlist size is exactly two contestants, but, in contrast, for total performance, the shortlist size does not affect the outcome, i.e., any size yields the same total performance. Furthermore, we compare the highest individual performance achieved with and without shortlisting, and show that the former is 4/3 times greater than the latter.

Superconducting qubit parameters drift on sub-second timescales, motivating calibration and benchmarking techniques that can be executed on millisecond timescales. We demonstrate an on-FPGA workflow that co-locates pulse generation, data acquisition, analysis, and feed-forward, eliminating CPU round trips. Within this workflow, we introduce sparse-sampling and on-FPGA inference tools, including computationally efficient methods for estimation of exponential and sine-like response functions, as well as on-FPGA implementations of Nelder-Mead optimization and golden-section search. These methods enable low-latency primitives for readout calibration, spectroscopy, pulse-amplitude calibration, coherence estimation, and benchmarking. We deploy this toolset to estimate $T_1$ in 10 ms, optimize readout parameters in 100 ms, optimize pulse amplitudes in 1 ms, and perform Clifford randomized gate benchmarking in 107 ms on a flux-tunable superconducting transmon qubit. Running a closed-loop on-FPGA recalibration protocol continuously for 6 hours enables more than 74,000 consecutive recalibrations and yields gate errors that consistently retain better performance than the baseline initial calibration. Correlation analysis shows that recalibration suppresses coupling of gate error to control-parameter drift while preserving a coherence-linked performance. Finally, we quantify uncertainty versus time-to-decision under our sparse sampling approaches and identify optimal parameter regimes for efficient estimation of qubit and pulse parameters.

Large language models (LLMs) have shown remarkable capabilities in automated code generation. While effective for mainstream languages, they may underperform on less common or domain-specific languages, prompting companies to develop in-house code generators. While open-source models can be trained for this, only LLMs with tens of billions of parameters match the performance of commercial tools, demanding costly training and deployment. Recent work proposed supporting code generation with smaller models (SLMs) by generating multiple candidate solutions and using another SLM to select the most likely correct one. The most recent work in this area is the one by Sun et al. [29] presenting RankEF, a T5 model trained to rank code solutions using both execution-based and non-execution-based information. However, Sun et al. do not assess the T5 ranker's classification accuracy, that is, how often it misjudges correct implementations as incorrect or vice versa, leaving open questions about the reliability of LMs as code correctness judges for other tasks (e.g., automated code review). Moreover, their experiments involve relatively old models, making it unclear the extent to which such a methodology would still help companies in cheaply training their own code generators with performance comparable to those of massive LLMs. We present a study addressing these limitations. We train several state-of-the-art SLMs as code correctness judges and assess their ability to discriminate between correct and wrong implementations. We show that modern SLMs outperform RankEF, even without exploiting execution-based information. When used as code rankers, they achieve higher performance gains than RankEF and perform competitively with LLMs 5-25x larger, at a fraction of the cost.

We extend the polynomial method of Chen--Garza-Vargas--Tropp--van Handel and Magee--Puder--van Handel for operator-norm bounds in random permutation models to the setting where torsion is present. The main new feature is that asymptotic expansion of traces naturally involves fractional powers of $N$ rather than an ordinary Laurent series. We formulate fractional-power analogues of the method's key hypotheses and prove they lead to strong convergence. We verify these analogues for free products of finite groups $Γ=G_1*\cdots*G_m$. Concretely, for a uniformly random $ϕ_N\in{\rm hom}(Γ,{\rm Sym}(N))$, set $π_N = {\rm std} \circ ϕ_N$, where ${\rm std}$ denotes the standard $(N-1)$-dimensional representation of ${\rm Sym}(N)$ (the permutation representation with the trivial subrepresentation removed). We deduce strong convergence of $π_N$ to the left regular representation of $Γ$. As applications, we obtain asymptotically sharp spectral gaps for the associated random Schreier graphs, including almost Ramanujan behavior for $C_2*C_2*C_2$ and an explicit non-Ramanujan limiting spectral radius for $C_2*C_3 \cong {\rm PSL}_2({\bf Z})$.

We consider a Jordan domain diffeomorphic to a closed two-dimensional disk with a smooth boundary. Assuming the Gauss curvature of the domain has a negative lower bound, the Gauss-Bonnet formula provides an upper bound for the total geodesic curvature of the boundary curve. This bound, however, inherently depends on the interior geometry of the region. In this paper, we derive an upper bound for the total geodesic curvature expressed solely in terms of the boundary data. Notably, the proof is connected to the positivity of the hyperbolic Hamiltonian mass in the (2+1)-dimensional gravity theory.

This paper investigates gradient-based adaptive prediction and control for nonlinear stochastic dynamical systems under a weak convexity condition on the prediction-based loss. This condition accommodates a broad range of nonlinear models in control and machine learning such as saturation functions, sigmoid, ReLU and tanh activation functions, and standard classification models. Without requiring any persistent excitation of the data, we establish global convergence of the proposed adaptive predictor and derive explicit rates for its asymptotic performance. Furthermore, under a classical nonlinear minimum-phase condition and with a linear growth bound on the nonlinearities, we establish the convergence rate of the resulting closed-loop control error. Finally, we demonstrate the effectiveness of the proposed adaptive prediction algorithm on a real-world judicial sentencing dataset. The adaptive control performance will also be evaluated via a numerical simulation.

The logistics industry is widely regarded as a promising application domain for emerging optimization paradigms, including quantum computing. The Rider-Order Assignment problem is a practically motivated optimization problem arising in online food delivery and related logistics applications. While the problem is closely related to the classical matching problem, the inclusion of realistic operational constraints renders it computationally challenging. In this work, we formulate the Rider-Order Assignment problem as a constrained binary optimization problem and perform a comparative analysis of classical, quantum-inspired, and gate-based quantum solvers for this problem across multiple instance sizes. Solver performance is assessed using solution quality, computational runtime, and constraint satisfaction, with a consistent post-processing procedure applied to ensure feasibility.

We investigate the charge and spin transport in a non-Hermitian ring of electrons subject to an external Zeeman field. By introducing non-Hermiticity through anti-Hermitian hopping in the nearest neighbour bonds, we demonstrate that anti-Hermiticity, along with the applied Zeeman field significantly modify the energy spectrum and strongly influence transport properties. As a result, we obtain that when antiferromagnetic Zeeman field is considered, a finite charge current emerges in both the real and imaginary parts of the current, which are in contrast to the ferromagnetic case where only the imaginary current exist. On the other hand, in both cases, the spin current vanishes. Interestingly, we reveal an emergence and strong enhancement of spin currents under balanced spin population upon introducing quasiperiodicity in the presence of antiferromagnetic ordering. At the same time, the charge current also exhibits substantial enhancement due to quasiperiodic modulation. These results highlight non-Hermitian quantum rings as versatile platforms for unconventional spin-charge transport.

We prove several results about matroids and matroidal families associated with rigidity in dimension $2$. In particular, we establish new properties of the generic rigidity matroid family $\mathcal{R}$ and Kalai's hyperconnectivity matroid family $\mathcal{H}$. We show that $\mathcal{R}$ is the unique matroidal $2$-rigidity family in which $K_{3,3}$ is not a circuit. As a geometric corollary of this result and the Bolker-Roth theorem, it follows that $\mathcal{H}$ and $\mathcal{R}$ are the only $2$-rigidity families associated with algebraic curves in $\mathbb{R}^2$. Bernstein used tropical geometry to characterize $\mathcal{H}$-independent graphs as those admitting an edge-ordering without directed cycles and alternating closed trails. We provide a combinatorial proof of the sufficiency direction and extend Bernstein's theorem to positive characteristic. It follows that the wedge power matroid of $n$ generic points in dimension $n-2$ does not depend on the field characteristic. Our proof method allows to identify many graphs that are independent in every $2$-rigidity family. In particular, we show this for all connected cubic graphs, with exceptions of $K_4$ and $K_{3,3}$. This gives a complete classification of cubic graphs in this respect and answers a question of Kalai in a strong form. As a corollary, we obtain a new property of cubic graphs: every connected cubic graph except $K_4$ and $K_{3,3}$ has an orientation without directed and alternating cycles. Equivalently, it can be edge-partitioned into two forests in a special `interlocked' way.

We study a singular elliptic problem driven by a mixed local-nonlocal operator of the form \begin{equation*} \begin{aligned} -Δ_p u + (-Δ_q)^s u &= \fracλ{u^δ} + u^r \text{ in } Ω\newline u > 0 \text{ in } Ω,\ u &= 0 \text{ in } \mathbb{R}^N \setminus Ω \end{aligned} \end{equation*} where $p > sq$, $0<δ<1$ and $λ> 0$ is a parameter. The nonlinearity exhibits a singular power-type behavior near zero and displays at most a critical growth at infinity. We establish a global multiplicity result with respect to the parameter $λ$ by identifying a sharp threshold that separates existence, non-existence, and multiplicity regimes, a result that is new for singular problems involving mixed local-nonlocal operators. We also derive a Hopf-type strong comparison principle adapted to this nonlinear setting, which provides the main analytical tool for the global multiplicity result. Additionally, we investigate qualitative properties of solutions that are essential for the variational analysis, such as a uniform $L^{\infty}$-estimate and a Sobolev versus Hölder local minimizer result. The analytical tools developed herein are of independent mathematical interest, with their applicability extending over a broader class of mixed local-nonlocal problems.

Verifying that a compiled binary originates from its claimed source code is a fundamental security requirement, called source code provenance. Achieving verifiable source code provenance in practice remains challenging. The most popular technique, called reproducible builds, requires difficult matching and reexecution of build toolchains and environments. We propose a novel approach to verifiable provenance based on compiling software with zero-knowledge virtual machines (zkVMs). By executing a compiler within a zkVM, our system produces both the compiled output and a cryptographic proof attesting that the compilation was performed on the claimed source code with the claimed compiler. We implement a proof-of-concept implementation using the RISC Zero zkVM and the ChibiCC C compiler, and evaluate it on 200 synthetic programs as well as 31 OpenSSL and 21 libsodium source files. Our results show that zk-compilation is applicable to real-world software and provides strong security guarantees: all adversarial tests targeting compiler substitution, source tampering, output manipulation, and replay attacks are successfully blocked.

Large-amplitude decaying kink oscillations of coronal loops are strongly influenced by nonlinear processes, such as Kelvin-Helmholtz instability (KHI) and turbulence, though comprehensive theory and observational confirmation remain limited. Building on the recently developed theory on nonlinear damping by KHI-induced turbulence in impulsively driven transverse loop oscillations, we investigate its observational signatures using 3D magnetohydrodynamic simulations and forward-modelled EUV images. The simulated oscillations exhibit time-varying frequency shifts and damping rates, which are broadly consistent with nonlinear turbulence-damping theory. Additionally, they exhibit excitation of higher-order modes, slightly increased periods relative to the linear kink period, and reduced displacement amplitudes. These features are generally preserved in synthetic observations, though resolving higher-order modes requires higher spatial resolution than currently available. For loops embedded in a hotter background, hotter channels (e.g., 193 Angstroms) are more sensitive to boundary dynamics, thus their oscillations decay faster with smaller displacements and larger phase shifts than those in cooler channels (e.g., 171 Angstroms). Comparisons of simulated and synthetic oscillations show close agreement at the early stage. At later times, synthetic oscillations exhibit smaller displacements and larger phase shifts, due to turbulence-induced asymmetry in the loop cross-section. Bayesian fitting shows that the initial oscillation amplitude and kink period are robustly constrained, whereas parameters controlling the damping profile are degenerate, indicating that additional observables would aid reliable seismological inference. These results provide a quantitative basis for identifying nonlinear damping and detecting KHI-driven turbulence in transverse loop oscillations.

We revisit the notion of massive particle hypersurfaces and place it within a unified framework alongside photon hypersurfaces in stationary spacetimes. More precisely, for Killing-invariant timelike hypersurfaces $T=\mathbb{R}\times S_0$, where $S_0$ is a smooth embedded surface in a spacelike slice $S$ of the stationary spacetime, we show that $T$ is a photon hypersurface or a massive particle hypersurface if and only if $S_0$ is totally geodesic with respect to certain associated Finsler structures on the slice: a Randers metric governing null geodesics and a Jacobi--Randers metric governing timelike solutions of the Lorentz force equation at fixed energy and charge-to-mass ratio. We also prove existence and multiplicity results for proper-time parametrized solutions of the Lorentz force equation with fixed energy and charge-to-mass ratio, either connecting a point to a flow line of the Killing vector field or having periodic, non-constant projection on $S$.

We present the first complete $\mathcal{O}(α_s^2)$ and $\mathcal{O}(α_s^3)$ perturbative QCD corrections to all five heavy-to-light structure functions underlying the triple-differential semi-leptonic decay rates of heavy quarks. This is achieved via a hybrid computational strategy that combines an efficient linear interpolation (with a suitable function basis) based on stratified Gauss-Kronrod points in the leptonic-mass $q^2$ with the differential equations in the other variable, further armed with reduced numerical $\varepsilon$-dependence. Among the selected applications, we highlight the state-of-the-art prediction $Γ(B \rightarrow X_u \ell \barν_{\ell}) = \frac{|V_{ub}|^2}{|3.82\times 10^{-3}|^2}\,\big( 6.53 \,\pm 0.12 \, \pm 0.13\, \pm 0.03\, \big) \times 10^{-16}\,\text{GeV}\,$ derived in the kinetic-mass scheme. We report several notable observations regarding the convergence of the first three orders of QCD corrections to the $q^2$-spectrum and to inclusive moments of the lepton-energy spectrum in semi-leptonic weak decays of $b$- and $c$-quark in different quark-mass schemes; they are important both for improving the inclusive determinations of the relevant CKM elements, non-perturbative dynamical parameters, and for gaining new insights into the potential impact of high-order QCD corrections. Lastly we discuss a novel interesting point encountered in the consistent perturbative reformulation of the differential $q^2$-spectrum from the pole-mass to other mass schemes: certain boundary-effect terms are identified that are non-vanishing for $b \rightarrow u \ell \barν_{\ell}$ firstly at $\mathcal{O}(α_s^3)$; their incorporation is essential to preserve the integrity of the integrated moments of the perturbatively re-expanded $q^2$-spectrum but necessitates histogramming from $\mathcal{O}(α_s^3)$ onward even within pure perturbation theory.

Following the previously developed approach to the calculation of quantum corrections to the effective potential in arbitrary scalar field theories in the leading logarithmic approximation, we extended it to the next-to-leading order. Based on Bogoliubov-Parasiuk-Hepp-Zimmerman renormalization procedure and the Bogoliubov-Parasiuk theorem, we construct recurrence relations and renormalization group equations that allow one to sum up the leading and subleading logarithms in all orders of perturbation theory. The formalism is applicable to an arbitrary scalar potential, renormalizable or not. To verify the results, we compare them with a renormalizable model treated within the standard renormalization group approach.

The origin of the large-amplitude, quasi-periodic X-ray flux variations in several classes of the Galactic microquasar GRS~1915+105 remains unresolved. We address this issue through flux-resolved, broadband (0.8-20 keV) spectral modelling and simultaneous covariance spectral analysis during two $κ$ and two $ω$ class observations using \textit{AstroSat}/SXT and LAXPC. The lightcurves show strong, quasi-periodic oscillations involving rapid transitions between bright bursts and deep dips on timescales of a few tens of seconds. Flux-resolved spectroscopy indicates that high-flux intervals in both classes are dominated by a hot, optically thick accretion disc with steep Comptonized emission, whereas low-flux intervals correspond to a cooler or partially recessed disc and a harder coronal continuum. These transitions involve a systematic 1-2 keV drop in disc temperature and a pronounced hardening of the Comptonized component, with flux reductions of up to a factor of five. Using covariance spectra across 0.015-5 Hz, we show that the rapid coherent variability arises almost entirely from the disc, which exhibits strong energy-dependent variations, while the Comptonized component contributes minimally. The combined results suggest that radiation-pressure-driven structural changes in the disc, with a slower coronal response, produce the observed oscillations, consistent with cyclic disc evacuation and refilling in the $κ$ and $ω$ classes.

Journalistic fact-checking, as well as social or economic research, require analyzing high-quality statistics datasets (SDs, in short). However, retrieving SD corpora at scale may be hard, inefficient, or impossible, depending on how they are published online. To improve open statistics data accessibility, we present a focused Web crawling algorithm that retrieves as many targets, i.e., resources of certain types, as possible, from a given website, in an efficient and scalable way, by crawling (much) less than the full website. We show that optimally solving this problem is intractable, and propose an approach based on reinforcement learning, namely using sleeping bandits. We propose SB-CLASSIFIER, a crawler that efficiently learns which hyperlinks lead to pages that link to many targets, based on the paths leading to the links in their enclosing webpages. Our experiments on websites with millions of webpages show that our crawler is highly efficient, delivering high fractions of a site's targets while crawling only a small part.

Multi-objective integer optimization problems are hard to solve, mainly because the number of nondominated images is often extremely large. We present the first exact algorithm, called PEA, that fully utilizes the multicore architecture of modern hardware. By exploiting the structure of the parameter set of the underlying scalarization, PEA can use a high number of threads while avoiding the usual pitfalls of parallel computing. It is highly scalable and easy to implement. As a result, PEA can solve much larger instances than previous state-of-the-art algorithms. Besides, PEA has a sound theoretical foundation. Unlike other existing parallel algorithms, it always solves the same number of scalarization problems as comparable sequential algorithms. We demonstrate the potential of PEA in a computational study.

We present the novel Reduced Basis Virtual Element Method (rbVEM) for solving the Laplace eigenvalue problem. This approach is based on the virtual element method and exploits the reduced basis technique to obtain an explicit representation of the virtual (non-polynomial) contribution to the discrete space. rbVEM yields a fully conforming discretization of the considered problem, so that stabilization terms are avoided. We prove that rbVEM provides the correct spectral approximation with optimal error estimates. Theoretical results are supplemented by an exhaustive numerical investigation.