We introduce a new class of conditional autoregressive models for spatially dependent functional data, formulated through conditional means given neighboring functional observations and characterized by a covariance operator and a spatial dependence parameter. Our estimation strategy consists of three components: (i) estimating the covariance operator using conditionally centered data, (ii) estimating the spatial dependence parameter by maximizing the likelihood of projected observations, and (iii) applying a novel profile-based approach to obtain the final estimators. Under an expanding lattice framework, we establish two key theoretical results. First, we establish the consistency of the proposed covariance estimator, which is not attainable using naive methods based on marginally centered data. Second, we prove that the spatial dependence parameter estimator is superconsistent and asymptotically normal, where the latter property enables statistical inference for spatial dependence in functional data -- a contribution that is novel in the existing literature. Numerical studies support the theoretical results and demonstrate the computational efficiency of our method. Finally, we illustrate its practical utility by analyzing weekly PM$_{2.5}$ concentration trajectories in 2019 across counties in the Midwestern United States.

We prove that every 0/1-polytope has a unique Minkowski decomposition into indecomposable polytopes, up to translation of summands. The summands lie in pairwise orthogonal subspaces. Thus, every 0/1-polytope is the Cartesian product of indecomposable 0/1-polytopes. As applications, we obtain uniform combinatorial indecomposability criteria for order and chain polytopes, matroid polytopes, stable set and clique polytopes, edge polytopes, flow polytopes, and 2-level/compressed polytopes. We also show that every nontrivial factorization of a multi-affine polynomial is a product of multi-affine polynomials in disjoint sets of variables.

Information Technology (IT) security professionals have ready access to open-source platforms such as Kali Linux. But no such platform exists for Operational Technology (OT) that underpins Industrial Control Systems. We discuss experiences of architecting, building and releasing LINICS, an open-source platform for OT pentesting and security analysis.

Federated Unlearning (FU) is emerging as a powerful tool that enables the selective removal of client data to effectively address data contamination and meet strict privacy regulations in mobile edge computing (MEC) systems. Although FU has recently drawn attention in the AI community, existing approaches suffer from low unlearning precision and lack temporal information reflection, which results in suboptimal forgetting performance. To address these issues, we propose SCALE, a dual-level unlearning framework combining historical contribution analysis with information freshness-aware adaptive sparsification. Our framework first employs a historical contribution-based layer sensitivity analysis to identify layers most influenced by target clients, then performs fine-grained unlearning through adaptive sparsification at the weight sub-group level to balance information freshness with forgetting effectiveness. Through theoretical analysis, the proposed framework demonstrates the convergence properties and acceleration advantages. Our experiments and testbed results demonstrate superior unlearning effectiveness compared to state-of-the-art baselines, with significantly improved forgetting performance.

Non-pharmaceutical interventions (NPIs), including mask-wearing, physical distancing, and hygiene measures, provide the primary means of reducing transmission in the early stages of an epidemic. Individuals adopt one of two strategies-adherence (A) or non-adherence (N) to NPIs. These strategies influence the transmission rate and thus the number of infections, but they also come with inherent costs and benefits. We propose a model coupling behavior and disease dynamics in adherers and non-adherers based on the SIR framework. This gives rise to six behavioral-epidemiological compartments. Using numerical simulations and analytical considerations, we first examine the case where strategies are fixed. Stronger NPIs and more initial adherers lead to fewer infections, and adherers consistently experience lower infection risk than non-adherers. We then introduce behavioral switching based on the benefits and costs of the two strategies. When NPIs are effective, higher transmission rates promote adherence, resulting in fewer infections. Strikingly, in high-severity outbreaks, even modestly effective NPIs can significantly reduce infections. These findings highlight the critical role of the coupling between behavior and disease dynamics, and underscore how individual choices can compromise or compensate public health interventions.

In its early days, online dating was heralded as a great equalizer, removing biases built into the structures of heterosexuality courtship. However, as repeatedly observed, that prophecy was never fulfilled, and some biases have even become exacerbated. In this paper, we identify a general endogenous mechanism that drives the widening of the gender gap in first-contact rates of heterosexual dating. This mechanism relies on assumptions about the participants' expectations of new contacts and their time constraints. We formulate this symmetry-breaking mechanism as a system of differential equations and analyze its fixed points and their stability.

Arguably the most widely used approaches for obtaining highly accurate molecular ground-state energies are coupled cluster methods. Despite introducing two layers of approximation, a linear and a nonlinear one, coupled cluster methods remain computationally intensive, with the complexity scaling as $O(poly(N))$, where $N$ is the number of electrons. Moreover, this method must be applied over a large set of different nuclear coordinates in order to study certain chemical phenomena. Therefore, in this work, we investigate the regularity of single-reference coupled cluster amplitudes with respect to nuclear coordinate displacements, with the aim of enabling interpolation or extrapolation approaches that rely on only a limited number of reference geometries. We show that, in theory, under certain non-degeneracy assumptions on the Hartree-Fock level of theory, and the coupled cluster level of theory the amplitudes behave real analytic. Furthermore, we analyze the artifacts that arise in practical calculations that use canonical orbitals, which hinder this high degree of regularity, and suggest strategies to mitigate these issues. Finally, we validate our findings through numerical experiments by interpolating the amplitudes and comparing the performance of the interpolants with that of the exact amplitudes.

Measurement-based quantum heat engines have attracted significant interest as alternatives to conventional thermal engines, as they replace the hot thermal reservoir with quantum measurements, thereby offering greater controllability and simpler implementation. Motivated by these advantages, we investigate a measurement-driven quantum Otto engine with a qubit working substance and study the optimal work extractable from such engines, including whether their performance can surpass that of conventional quantum Otto cycles. We analyze the engine in both the infinite-time (adiabatic) and finite-time (non-adiabatic) regimes, considering two distinct implementations obtained through optimization over all projection-valued measurements (PVMs) and over all two-outcome positive operator-valued measurements (POVMs). We show that measurement-based engines can outperform conventional quantum Otto engines within specific parameter regimes and that POVM-based engines can yield higher optimal work extraction than PVM-based ones. Furthermore, by incorporating the thermodynamic cost associated with resetting the auxiliary system required for POVM implementation, we demonstrate that the resulting net work output can still exceed that of PVM-based engines under suitable conditions on the spectral gaps and cold bath temperature. We also identify regimes in which non-adiabatic implementations can yield higher work output and efficiency than their adiabatic counterparts. Our study provides operational guidelines for designing improved measurement-driven quantum Otto engines.

We investigate the solid-state implementation of a Dicke-like quantum battery consisting of a two-dimensional material-based Josephson junction inductively coupled to a resonator, using graphene as a representative example. In this configuration, Andreev bound states naturally act as non-interacting, energetically non-degenerate two-level systems, and the setup allows for both single-photon and two-photon resonant processes. The coupling between the LC-circuit flux and the supercurrent through the junction gives rise to peculiar longitudinal interaction terms that have no counterpart in the conventional Dicke model. These additional couplings can enhance energy storage for a proper range of parameters. The proposed architecture also enables an alternative, but equivalent, charging protocol that relies on tuning the superconducting phase difference across the junction.

We demonstrate a practical countermeasure against a well-known class of attacks on quantum key distribution (QKD) systems that exploit detection efficiency mismatch, where the receiver's detectors do not exhibit identical responses to incoming photons across all degrees of freedom. This class of quantum hacking strategies is broad and significantly includes the time-shift attack, which targets an arrival-time-dependent side channel at the receiver. The four-state countermeasure, previously only proven to be secure in theory, is implemented here on a GHz-clocked prototype QKD system and evaluated for its security and performance. We show that its presence enables almost complete recovery of the system's ideal secret key rate. Our results provide strong justification for adopting this countermeasure as a standard component in future scalable and practical QKD systems.

In this work, we introduce a non-volatile heterogeneous quantum dot (QD) III-V/Al2O3/Si distributed feedback (DFB) laser exhibiting optical memristive behavior. The device operates in the O-band (~1300 nm) with a threshold current density of 234 A/cm2 and a side-mode suppression ratio exceeding 48 dB. Co-integrated Al2O3-based memristors produce bipolar resistive switching, yielding non-volatile wavelength shifts of ~ 46 pm and ~ 17 dB peak power contrast with zero static holding power. The III-V/Al2O3/Si heterojunction memristor I-V hysteresis is also modeled. This new device enables simultaneous coherent light generation and persistent optical state storage, establishing a new class of active photonic memory for neuromorphic and reconfigurable WDM applications.

Modern economies depend critically on satellite infrastructure, yet the aggregate economic consequences of extreme solar energetic particle (SEP) events have not been rigorously assessed. This study develops an integrated framework linking SEP hazard characterization, dynamic geomagnetic cutoff rigidity modeling, radiation dose transport, and fleet-wide failure probability estimation to macroeconomic impact analysis. Using extreme-value analysis of 160 SEP events over 27.4 years (1996-2025), failure probability is estimated for ~10,650 US operational satellites under orbital regime-dependent shielding assumptions. The assessment reveals that ~100 satellites (1.0%) are at Critical risk, concentrated in high-altitude low Earth orbit and highly elliptical orbit, while medium Earth orbit and geosynchronous orbit satellites fall in the Negligible class (P_fail < 10^-9) under the assumed radiation-hardened components and shielding. The expected capital loss across the ~$254B fleet totals ~$5.2B. Three failure scenarios, expanding from Critical satellites only (P_fail > 10^-2), to Critical and Elevated (P_fail > 10^-3), and to all satellites with non-negligible risk (P_fail > 10^-6), yield daily economic impacts of ~$70M, ~$270M, and ~$1.3B, respectively. Earth observation suffers up to 95.6% capacity loss in the worst case, while military services experience 16.1-20.4% disruption across scenarios. Results are first-order estimates: hardware failure counts are conservative because only total ionizing dose is modeled, and daily economic impacts represent upper bounds because operator response and recovery are not included.

We show that the morphology of the core-collapse supernova (CCSN) remnant RCW 103 is very similar to the morphology of the brightest regions in the recently released JWST IR images of the jet-shaped planetary nebula (PN) PMR 1, and conclude that two energetic pairs of jets shaped RCW 103, compatible with the jittering-jets explosion mechanism (JJEM). The PN PMR 1 IR image exhibits two opposite, large, and prominent ears with a narrow, faint region connecting them through the center, a pipe. Observations and simulations have shown that a pair of jets inflates such a pair of ears in PNe. The brightest regions of PN PMR 1 form two clumpy sectors, each shaped like a wide pizza slice, with a faint region between them; the CCSN remnant RCW 103 has a very similar morphology. We identify two shells in the X-ray image of RCW 103 and suggest that two close pairs of energetic jets shaped this CCSN remnant. We find only traces of two of the four expected ears in RCW 103. The ears in RCW 103 were already dispersed and are very faint. Deeper X-ray observations might detect them. Such energetically misaligned pairs of jets are compatible with the JJEM, which predicts that a few to about 20 pairs of jets are responsible for most CCSN explosions.

While the Seiberg-Witten equations have been well-studied on 3-manifolds, their multiple spinor generalisation exhibits some unexpected behaviour. Most notably, the count of these "multi-monopoles" does not define a topological invariant. Instead, the count can jump as parameters of the equations cross between certain regions in the parameter space, known as chambers. This wall-crossing phenomenon is related to deep questions about multi-valued harmonic spinors and higher-dimensional gauge theory. However, concrete examples of this behaviour have not been studied, primarily because the existing constructions of multi-monopoles are not rich enough for wall-crossing to be observed. We address this by proving an adiabatic limit theorem, which constructs multi-monopoles for a wide range of parameters on mapping tori. These solutions are obtained by perturbing the fixed points of the monodromy map associated to a family of multi-vortex moduli spaces. We use our theorem to produce the first explicit constructions of multi-monopoles on non-product 3-manifolds in various chambers.

Iron fluorescence is produced by the irradiation of the solar photosphere by coronal X-rays during flares. This study presents the first comprehensive analysis of iron K$α$ fluorescence characteristics in 47 X-class flares observed during the inaugural year of the Solar Low Energy X-ray Spectrometer (SoLEXS) on board India's Aditya-L1 mission. Leveraging the capability of modern silicon drift detectors (SDDs) for simultaneous broadband continuum and line measurements, the Fe K$α$ flux and the exciting flux ($F_{>7.11 \text{ keV}}$) are quantified for each event, establishing a well-determined relationship between them across the sample. The derived fluorescence efficiencies exhibit a center-to-limb dependence consistent with theoretical models, offering a potential diagnostic to probe coronal source heights and viewing geometries. While statistical uncertainties currently limit the ability to track rapid height variations on short timescales, the mean fluorescence efficiency during the flare peak provides a potential constraint on the effective coronal source height. However, this derivation remains subject to a fundamental degeneracy, as the estimated source height cannot be uniquely determined without assuming a specific value for the photospheric iron abundance. These findings demonstrate that SDDs, despite having lower spectral resolution than traditional crystal spectrometers, provide a new diagnostic for the solar iron fluorescence observations.

We use Nakajima's geometric approach to representations of quantum affine algebras and recent results on explicit descriptions of specific canonical basis elements, to derive closed positive formulas for certain decomposition numbers of representations of quantum affine $\mathfrak{sl}_2$. Moreover, we obtain a piecewise-linear closed formula for the $q$-characters of irreducible representations of quantum affine $\mathfrak{sl}_2$.

An adversary copies your encrypted traffic today and waits for a quantum computer to decrypt it later. How exposed are you? We show that the functional form of the answer is not merely a calibration choice -- it is structurally justified by three assumptions about adversarial production and value-decay dynamics. Under those assumptions, the HNDL compromise probability factorises into a temporal hazard, a multiplicative cryptographic-vulnerability and operational-exposure term, and a saturation denominator governed by the defense-attack intensity ratio; the marginal sensitivity to each dimension is endogenous to the organisation's position in the vulnerability-exposure plane, not a fixed global constant. Additive scoring frameworks cannot reproduce this structure because the interaction between cryptographic vulnerability and operational exposure is absent by construction, regardless of calibration. The resulting framework provides a structurally grounded basis for operational HNDL exposure prioritisation under partial observability.

From a multi-input-multi-output (MIMO) discrete-time linear system, we collect input-output data affected by noise in the form of an unknown exosignal and, from these data points (without knowledge of the system model), we design a feedback controller that asymptotically annihilates the effect of that exosignal on the output. This amounts to solving an output regulation problem purely from input-output data, for MIMO linear systems. The design of the controller corresponds to a semidefinite program and is pursued on a suitable auxiliary system. Such design carries over from the auxiliary system to the original one by a rigorous examination of the relation between the solutions of the two systems.

Classical A-polynomials $A(\ell,m)$ define constraints on coordinates $\ell$ and $m$ in $SL(2,\mathbb{C})$ (a complexification of $SU(2)$) character varieties associated to knot complements $S^3\setminus K$. Quantum A-polynomials $\hat A(\hat \ell,\hat m)$ are difference operators annihilating Jones polynomials believed to represent wave functions of 3d Chern-Simons theory with gauge group $SU(2)$ on a toroidal pipe surrounding the knot $K$ strand -- a boundary of the knot complements $S^3\setminus K$. We suggest a construction of classical shaded A-polynomials $A_a(\ell_b,m_c)$ associated to Lie groups $SU(N)$. We exploit a formalism of Clebsh-Gordan (CG) chords, where indices $a$, $b$, $c$ run over $1,\ldots,N-1$. CG chords have a natural interpretation in terms of 2d CFTs of WZW type, or, alternatively, in terms of quantum group $U_q(\mathfrak{su}_N)$. In the case of $\mathfrak{su}_2$ CG chords could be associated to Reeb chords in a knot contact homology (KCH) framework. KCH suggests its own analogue of A-polynomials known as augmentation polynomials allowed to have extra spurious roots in principle. Yet the CG chord formalism could be easily extended to arbitrary $\mathfrak{su}_N$ allowing us to generalize the construction of A(ugmentation)-polynomials to arbitrary $\mathfrak{su}_N$ and arbitrary representation as well. Primarily we aim at classical A-polynomials by considering a double scaling limit when $q=e^{\hbar}$, $\hbar\to 0$ and the representations are huge, in particular, highest weight vector components $w_i\to \infty$ so that $\hbar w_i\sim m_i$ remain finite. Still we expect the presented techniques would be helpful in deriving quantum A-polynomials for arbitrary Lie (super)algebras $\mathfrak{g}$. Also we discuss explicit examples of A-polynomials for knots $3_1$, $4_1$ and $5_1$ for $\mathfrak{g}=\mathfrak{su}_3$.

The ABCStar is a mixed-signal front-end readout ASIC for the strips sensor portion of the ATLAS ITk detector being developed as part of the High-Luminosity LHC upgrade. In pre-production testing, a subtle design flaw was uncovered in the ABCStar that was reducing wafer yields in some manufactured lots from the expected 90% to as low as 2%. The root cause was determined to be a timing issue in the logic synthesized to control previously silicon proven memory blocks re-used for this ASIC. The solutions proposed included manufacturing process changes by the wafer foundry, changes to the operating parameters for the ABCStar in the detector, and the possibility that a redesign might be required. The two mitigation efforts were undertaken in parallel, with the process modification route a less desirable solution since already manufactured wafers would need to be scrapped in favour of the new ones. Based on a knowledge of the existing process, and testing done on the worst performing wafers, it was proposed that raising the core operating voltage of the ABCStar from 1.20V to 1.25V could address the timing issue by sufficiently speeding up its transistors. An extensive testing program that included the effects of temperature and radiation expected over the lifetime of the ITk detector was conducted to validate that approach. Those tests and studies proved that even the worst performing wafers would have yields over 80% with the 1.25V core voltage, and neither the modified process nor redesign would be required for ensuring reliable operation of the ITk. Based on testing, a further timing mitigation was implemented to provide an additional margin of reliability by increasing the duty cycle of the clock to the ABCStar. Testing of all ABCStar wafers has been completed and the production of the detector modules using these ASICs is now well underway as a result of the efforts detailed herein.

We compute the entanglement dynamics across a monitored quantum point contact, where particle losses are recorded on a given site, and demonstrate how this single-site local monitoring substantially reshapes the entanglement production. Contrary to the unitary case, where entanglement entropy grows logarithmically in time, here we find first a linear growth, up to a maximum value displaying volume-law scaling, and then a slow decay to zero, as the system empties out. We capture this crossover using a quasiparticle picture, where the first linear growth arises due to an emergent bias voltage established by the losses, which eventually decays away as the system depletes. We connect our results to studies of the Page curve and to experimentally relevant probes, via full counting statistics of charge transfer across a subregion, with only a single channel to unravel leading to a favorable scaling of the postselection overhead. Natural platforms for this setting include mesoscopic systems and ultracold atoms.

We study symplectic and projective structures on small covers over products of polygons. We introduce the factor-compatible class for small covers over products of polygons and prove that every factor-compatible small cover admits a smooth projective model as a finite quotient of a product of curves. Furthermore, we show that the graded mod~$2$ cohomology ring determines the Hodge diamond of the associated projective model. We also prove that every factor-compatible small cover admits an iterated equivariant bundle structure.

We investigated the possibility that a single measurement run with a definite outcome is a joint unitary evolution of all the participating systems, and measurement runs with different definite outcomes correspond to different unitary maps. With reasonable assumptions, we derived a lower bound of the dependence of the environment after measurement on the state of the system before measurement, conditioned on the same measurement outcome. An experimental test of this dependence relation can either serve as evidence that the unitary dynamics and the definite outcome in the orthodox sense cannot be true together or suggest a deviation from the von Neumann measurement model plus a "conditioning" interpretational step.

This study explores the excitation and ionization of an atomic beam as a pathway to optimize focused ion beams (FIBs) for high-precision applications. Leveraging the unique advantages of Rydberg excitation followed by field ionization -- specifically its ability to minimize velocity and position dispersions -- we present a method to generate ion beams with good performance at low energies. A custom Lua program, integrated into the SIMION simulation platform, models the intricate processes of particle distributions, laser excitation, and Rydberg ionization. This integrated approach incorporates essential parameters such as excitation and ionization rates, Stark shifts, Doppler effects, and electric fields, enabling a detailed analysis of ion beam properties. Our simulations demonstrate the influence of critical factors such as the chosen Rydberg state, ionization region characteristics, and velocity dispersions on the final ion beam quality. By optimizing these parameters, we achieve significant reduction of the axial energy spread and the longitudinal extent of the ionization region. This framework bridges theoretical modeling and experimental validation, offering a comprehensive toolkit for the development of next-generation ion sources and advancing FIB technologies across various scientific domains.

During the phase of landing, an important aircraft-noise source emanates from the interaction of the landing-gear wake with the deployed flap. In the present work we cast this problem in an academic framework, by studying a simplified configuration that consists of a cylinder placed upstream and perpendicularly to a symmetrical NACA-0012 airfoil. An experimental campaign is conducted, followed by modelling approaches to explore the flow phenomena associated with the acoustic field. Simultaneous acoustic and stereoscopic Time-Resolved Particle Image Velocimetry measurements are taken, to study the sound and flow-fields generated by the interaction of the cylinder-wake with the downstream airfoil, when the spans of the two objects are orthogonally aligned. The experimental data highlight the three-dimensional nature of the problem. The maximum sound pressure levels are obtained at frequencies close to $St \equiv f d/U = 0.38$ (cylinder's drag fluctuation frequency), where also the maximum linear coherence between the acoustic and cylinder-span-oriented fluctuation velocity is observed, demonstrating that the measured acoustic-field is an outcome of the three-dimensional cylinder-wake. Powell-Howe vortex-sound theory combined with an acoustically compact Green function for the NACA-0012 are employed for the aeroacoustic modelling. A linearised source-term based on the analysed experimental data is used as input to estimate the acoustic field and identify the acoustically important coherent structures of the flow-field. A reasonable agreement is obtained between the sound field estimations and the measurements. To further explore the mechanisms of sound generation, a semi-empirical source-model, informed by the experimental data, is proposed, based on Fourier modes in the cylinder's span direction.

$ξ$ Tau is one of the most compact multiple stellar systems, which is sufficiently close (67 pc) to be constrained by all kinds of observations. To better constrain its current configuration, we utilized new observational data: (i) photometry from TESS and astrometry from WDS, and (ii) our own photometry from the MOST spacecraft and spectroscopy from the CTIO observatory. [...] Given the hierarchical architecture of $ξ$ Tau, ((Aa+Ab)+B)+C, we detected the orbital evolution on all time scales. Oscillations of periods $P$ occur on the shortest, orbital time scales ($P_1$, $P_2$); the variation of eccentricity $e_1$ is from 0 to 0.008, and of $e_2$ from 0.202 to 0.207, respectively. Oscillations of projected $i$, $Ω$ are coupled, and occur on the secular time scale of about 7000 d. The inclination $i_1$ of the inner, eclipsing pair (Aa+Ab) changes from $86.1^\circ$ to $87.1^\circ$, which is clearly manifested in eclipse depths. There is also a long-term trend due to the outer orbit ($P_3 \doteq 18900\,{\rm d}$), with a perihelion passage (a `bump') of component C, which is manifested in radial velocities. The mutual inclinations between the three orbital planes, ${\simeq}\,0.5^\circ$ and $71^\circ$, are very different. Long-term stability is ensured by suppressing Kozai oscillations due to the fast precession rate $\dotω_2$. The best model requires tidal dissipation in the inner binary (with the time lag of ${\sim}100\,{\rm s}$) and five components, where component C is a binary (Ca+Cb). Although the masses of the three components ($2.27$, $2.15$, $3.78\,M_\odot$) are now constrained to within 1%, the suspected binary (Ca+Cb), offset by $600\,{\rm mas}$, should be better characterized. A key question remains whether this bright stellar system contains additional dwarf or exoplanetary components with low masses. Continuing monitoring of $ξ$ Tau is highly desirable.

Explicitly correlated methods such as MP2-F12 and CCSD(F12*) exhibit much faster basis set convergence (asymptotically $\propto L^{-7}$, with L the highest angular momentum) than orbital-only approaches. Yet it has been pointed out that cc-pVnZ-F12 basis sets themselves are substantially larger than the corresponding cc-pVnZ, and specifically that cc-pVDZ-F12 is the size of cc-pVTZ. One way to generate compact basis sets in an orbital-only context are Atomic Natural Orbital (ANO) basis sets [J. Almlöf and P. R. Taylor, JCP 86, 4070 (1987)]. However, obtaining the required first-order reduced density matrix while properly accounting for the F12 geminal is problematic. In this work, we show that an energy minimization-based contraction process under linear independence constraints yields `pseudo-ANO' (pANO) basis sets that are functionally equivalent in quality. Subsequently, we apply this recipe to obtain pANO-F12 basis sets from the same elements, then validate them for several thermochemical benchmarks and for the hypersensitive out-of-plane vibrations of benzene. We show that, unlike cc-pVnZ-F12, pANO-F12 exhibits the familiar shell structure seen in cc-pVnZ and ANO basis sets, and that pANO-F12 offers a route to more compact F12 basis sets more amenable to medium-sized systems, especially in conjunction with localized pair natural orbital approaches. Overall, the pANO approach is most beneficial for the smaller double-and triple-zeta basis sets, offering either superior performance to cc-pVnZ-F12 at same cost, or similar performance at lower cost.

The dynamical role of the magnetic field in the star formation process is tightly linked to the coupling between matter and the field. This coupling is due to the interaction between ions and neutrals in the partially ionized interstellar medium. When the ionization degree drops in the dense environment of prestellar cores, the magnetic field and the matter may decouple, leading to differences in the infalling velocities of ions and neutrals known as ambipolar diffusion. The onset of gravitational collapse resulting from ion-neutral decoupling has never been observed. The aim of this work is to search for signatures of ambipolar diffusion within a prestellar core. We observed the deuterated N$_2$D$^+$ ion and the neutral para-NH$_2$D species towards the prototypical prestellar core L1544. These two species are ideal tracers of prestellar cores sampling the same high densities in the core interior. We compared the velocity centroid and linewidth maps of the ion-neutral pair. We find a mean ion-neutral velocity difference of $\sim$0.05 km/s towards the core. By comparing with predictions from self-consistent calculations of the ambipolar resistivity including dust grain growth, we interpret the observed ion-neutral velocity difference in L1544 as a signature of ambipolar diffusion. We do not detect a significant ion-neutral linewidth difference that may be attributed to the subsonic infall motions of the gas in L1544 and geometrical effects in the presence of inclination. These results emphasize the role of dust grain growth at the prestellar core stage in setting the ambipolar resistivity and regulating the dynamical evolution of dense cores towards their collapse into protostars. We propose that measurements of ion-neutral drift velocities provide new constraints on the total magnetic field strength and the dust size distribution within prestellar cores.

We consider the problem of minimizing the sum of a Lipschitz differentiable convex function $f$ and a proper closed convex function $h$ that admits efficient linear minimization oracles, subject to multiple smooth convex inequality constraints. We adapt the classical augmented Lagrangian (AL) method for these problems: in each iteration, our algorithm consists of one step of the conditional gradient (CG) method applied to the AL function, followed by an update of the dual variable as in classical AL methods with a diminishing dual stepsize. We study the convergence rate of our algorithm under two standard stepsize rules for the CG method, namely, an open-loop stepsize and the short stepsize, and obtain a convergence rate that matches the best-known complexity for this class of problems. We also establish accelerated rates when $h$ is the indicator function of a uniformly convex set.

AI coding agents increasingly submit pull requests (Agentic-PRs) to open-source repositories, yet their performance is commonly assessed using merge and rejection outcomes alone. We hypothesized that these outcome labels do not reliably reflect agent capability without considering review interactions. To test this, we conducted a decision-oriented analysis of 11,048 closed Agentic Pull Requests, refined to 9,799 human-reviewed PRs, and manually inspected 717 representative cases to recover decision rationale from interaction artifacts. We found that rejection outcomes substantially overstate agent error: only 35.7% of rejected PRs reflected clear agentic failures, while 31.2% were driven by workflow constraints and 33.1% lacked observable decision rationale. Among merged PRs, 15.4% required explicit reviewer involvement through feedback or direct commits, and 5.5% showed no visible interaction trace. We further observed systematic differences across agents, with Copilot and Devin more often embedded in reviewer-mediated workflows, while Codex and Cursor PRs were typically merged with minimal interaction. These results reject the assumption that PR outcomes alone capture agent performance and demonstrate the need for interaction-aware evaluation grounded in review behavior.