Papers

The present notes are based on a series of lectures prepared for an introductory eight-class course on the modern framework of the off-shell double copy. The course was held from April 16 to May 4, 2026, at Universidad de Buenos Aires (UBA). These lectures, aimed at PhD and master's students, are self-contained and require only a basic knowledge of classical field theory. The main goal is to review the fundamental concepts of gauge and gravitational theories in order to explore the off-shell frameworks of the single and double copy. In the final part of the course, we explore modern approaches to reinterpreting the single and double copy within T-duality-invariant frameworks.

Since the initial disclosure of the extraordinary piezoelectric coefficients of Potassium sodium niobate (KNN) in near-equimolar bulk ceramics, its development trajectory has resembled a rollercoaster, with its integration into microelectronics severely lagging due to thermodynamic stability issues and poor planar process compatibility. In this work, we revisit the bulk-derived phase diagram for the specific case of thin films integrated on silicon. By systematically investigating Mn-doped K1-xNaxNbO3 films grown on 8-inch wafers, we demonstrate that the optimal stoichiometry for thin films fundamentally diverges from the bulk equimolar standard. A Na-rich composition (> 70 at.%) is required to overcome substrate-induced constraints, effectively suppressing pyrochlore formation and chemical phase segregation while promoting dense columnar growth with a complete (001) out-of-plane polar orientation. Consequently, Na-rich films deliver outstanding functional properties, reaching remanent polarizations up to 14 uC cm-2, with piezoelectric coefficients of d33f= 79 pm/V and e31f = 10 C/m2. Supported by Density Functional Theory simulations, we correlate this enhancement with improved stability and a strain-driven structural reorientation toward a lower-symmetry monoclinic phase with tilted polarization. By redefining the phase engineering rules for wafer-scale thin films, our results establish a clear route toward KNN integration in microsystems.

A metric graph with a mechanical Hamiltonian on each edge does not, by itself, define a deterministic classical motion through a branching vertex: conservation of energy fixes only the outgoing speed, not the outgoing edge-end. We study the deterministic problem obtained after this missing vertex datum is supplied. On each edge $e$, with coordinate $q\in[0,\ell_e]$, the Hamiltonian is $H_e(q,p)=p^2/2+V_e(q)$, where $V$is continuous on the graph and $C^2$ on every edge. At each vertex we prescribe an energy-preserving Borel isomorphism from incoming to outgoing nonzero boundary covectors. The resulting phase space is the measurable quotient that identifies each incoming boundary covector with its prescribed outgoing one. After excluding the finitely many energy levels $V(v)$, the edgewise Hamilton equations and the vertex laws concatenate to a global one-parameter group of bimeasurable transformations. The group preserves energy and the quotient measure induced by the edgewise Liouville measures $dq\,dp$. The proof uses no smooth symplectic structure on the quotient; the invariance follows from ordinary edgewise Liouville invariance, a uniform no-Zeno estimate on compact regular energy windows, and preservation of the transverse Liouville flux $r\,dr$ by the speedwise vertex permutations. If the vertex laws are compatible with momentum reversal, then the quotient dynamics is reversible. On regular energy surfaces satisfying the usual regular-value condition, the induced time-parametrization measure is invariant as well.

Understanding when and how galaxies quench their star formation is crucial for understanding the dominant physical processes at play. The spectral energy distribution (SED) of galaxies encodes significant information on their past histories: the relative importance of different physical processes influences the observed distribution of SED shapes in the galaxy population. We use a simulation based inference (SBI) approach to directly constrain the distribution of formation times, quenching times and quenching timescales within the massive galaxy population at z >~ 2 from their broad band photometric colour distribution at 1.7<z<2. We demonstrate that a simple distribution of double power-law star formation histories accurately fits the distribution of SED shapes of galaxies with log10(M*/Msol)>10.3. We measure a quenched galaxy fraction of 0.24+/-0.02, with the number density of quenched galaxies rising rapidly 2.5Gyr after the Big Bang (z<~2.6). Galaxies must quench rapidly to achieve the precise bimodal colour distribution: defining the quenching timescale as the time from peak star formation rate (SFR_peak) -> 0.5xSFR_peak, the quenching timescale distribution has a mode at 97_{-25}^{+31}Myr, a median of 182+/-16Myr and a tail to ~700Myr. To achieve full quiescence takes a median time of ~400Myr. Comparing to direct number density measurements of quenched galaxies at z>2 the combination of recent and rapid quenching inferred from the fossil record suggests a substantial rejuvenation and/or merger rate for quenched galaxies observed directly at z>3.5.

This article develops a rigorous Lagrangian formulation of variational calculus for minimal surfaces, using extensively the concept of pullback covariant derivative. It is shown, in particular, using a geometric argument that all tangential variations vanish. First and second normal variations are then derived.

Fixed-ansatz Variational Quantum Eigensolvers (VQE), such as the Unitary Coupled Cluster with Singles and Doubles (UCCSD) framework, frequently suffer from severe initialization paralyzation and zero-gradient traps when evaluated using the non-local Bravyi-Kitaev (BK) fermion-to-qubit mapping. In this work, we systematically demonstrate how the Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT-VQE) framework shatters these structural limitations across three distinct electronic and geometric molecular pillars: Lithium Hydride ($\text{LiH}$), Hydrogen Fluoride ($\text{HF}$), and Water ($\text{H}_2\text{O}$), under heavily stretched or asymmetric multi-reference configurations. While conventional UCCSD-VQE flatlines completely at a zero energy shift ($0.000000$~Ha) due to global phase cancellations inherent to the BK tree structures, our dynamic ADAPT-VQE loop successfully isolates the dominant symmetry-breaking operators using analytical commutator gradients. To bypass the severe $\mathcal{O}(N^3)$ computational bottlenecks of dense matrix exponentiation and Singular Value Decomposition on larger registers, we implement a highly optimized, vector-based Taylor series expansion state-evolution engine. Our numerical results show that the accelerated ADAPT-VQE framework achieves instant, exact Full Configuration Interaction (FCI) convergence within the very first macro-cycle across all three molecular systems, maintaining absolute numerical stability up to a 12-qubit register space. This study establishes a robust, hardware-efficient path for simulating strongly correlated, highly polarized triatomic chemical environments on near-term local architectures.

We investigate the sensitivity to TeV-scale heavy Majorana neutrinos at a future muon-proton collider with $\sqrt{s}=5.3$~TeV, based on 1~TeV muon and 7~TeV proton beams. We focus on the lepton-number-violating (LNV) process $\mu^- p \to jN$, followed by $N\to\mu^+W^-\to\mu^+J$, leading to the characteristic final state $j\mu^+J$. Here, $j$ denotes the associated light jet from heavy-neutrino production, while $J$ denotes the fat jet originating from the hadronic decay of the highly boosted $W$ boson. This topology provides a clean experimental signature with strongly suppressed Standard Model backgrounds. A comprehensive signal and background analysis is performed using parton showering, fast detector simulation, and dedicated fat-jet reconstruction. We derive the projected $2\sigma$ exclusion limits on the muon-flavor mixing parameter $|V_{\mu N}|^2$ for integrated luminosities of $100$~fb$^{-1}$ and $1$~ab$^{-1}$. For heavy-neutrino masses in the range $1~\mathrm{TeV}\leq m_N\leq3~\mathrm{TeV}$, the projected upper limits on $|V_{\mu N}|^2$ range from $2.6\times10^{-6}$ to $5.9\times10^{-5}$ at $1$~ab$^{-1}$. These results show that a future $\mu p$ collider can provide competitive and complementary sensitivity to TeV-scale heavy Majorana neutrinos compared with other proposed high-energy facilities.

Large Language Models (LLMs) are increasingly employed as proxies for human behavior in computational social science. However, their tendency to internalize biases from training data raises concerns about their reliability in politically sensitive domains, specifically regarding their endorsement of persuasive language. In this work, we examine whether LLMs endorse persuasion-infused messages and whether partisan persona prompting modulates such endorsement. We evaluate six LLMs from different geographic regions on content annotated with persuasion techniques drawn from real-world media sources, measuring the likelihood of endorsement using a five-point Likert scale. The models are prompted as either a neutral social media user or as a user with left- or right-leaning political views. Results show that, without political conditioning, LLMs generally do not endorse messages containing persuasion techniques, although model-level differences emerge, and that partisan persona prompting increases polarization of endorsement, particularly for persuasion-infused content. Endorsement further varies across persuasion techniques and topics. These findings reveal how political conditioning influences LLMs' endorsement behavior toward persuasion-infused content, raising concerns about their deployment as agents in politically sensitive environments and complicating their use as reliable simulators of human political cognition.

In this paper, we re-examine the well-known question of why electric charges exist only in quantized portions. In this context, we revisit the motion of a charged particle in a field-free region around a current-carrying solenoid. Solving the corresponding Schrödinger equation leads to a simultaneous quantization condition for the magnetic flux and the electric charge. We also demonstrate the Lorentz invariance of this condition by showing that the magnetic flux behaves like a pseudoscalar under Lorentz transformations.

Understanding the processes behind the evolution of complex networks is a key objective in network science. An effective framework for tackling this challenge is network model selection, which involves finding the model from a set of candidates that best explains a given network. This book is a systematic review of methods for this purpose. Each method is outlined in three parts: its core principle (used to organize methods into four categories), other relevant details including my own observations, and software availability. The book provides a comprehensive overview of the state-of-the-art in network model selection and concludes by exploring future directions. A unified, optimal method could identify the mechanisms that shape real-world networks more precisely than any current approach. This work represents the first step toward developing such an optimal method. It will be a valuable resource for students and researchers in network science.

Practical requirements such as improving wall-plug efficiency and reducing system footprint have become increasingly important with the introduction of extreme ultraviolet (EUV) lithography into high-volume semiconductor manufacturing. These demands motivate the development of solid-state mid-infrared lasers as alternatives to current CO2 lasers. Systematic exploration of laser-to-EUV conversion efficiency (EUV-CE) over a broad parameter space is essential when altering the drive laser's wavelength, because the EUV-CE depends on the laser parameters in a complex manner. In this work, we performed a large-scale grid search of more than 140,000 parameter combinations for laser-produced tin plasma EUV sources using the radiation-hydrodynamics code STAR-1D, which is validated against EUV source experiments. The systematic wavelength dependence of the optimum pulse width and target size is governed by the requirement to simultaneously achieve the electron temperature and density optimal for EUV emission, maintain efficient laser absorption, and suppress EUV self-absorption. The resulting CE map predicts a global maximum of 5.63% at 5.5 {\mu}m. For the practically relevant 2 {\mu}m solid-state driver, a maximum CE of 4.64% is obtained, in good agreement with recent experimental results. Multiple operating points are identified over a broad range of pulse parameters, providing guidance for 2 {\mu}m-driven EUV source development.

We propose quantum algorithms for preparing thermal states via the simulation of the thermofield double states. The key idea is to leverage double-bracket quantum algorithms to implement imaginary-time evolution on thermofield double states, whose reduced state realizes the Gibbs state. Our method, termed double-bracket thermofield double (DB-TFD), introduces two variants. The first, the vanilla DB-TFD algorithm, directly implements imaginary-time evolution using double-bracket quantum imaginary-time evolution. The second, poly DB-TFD, employs double-bracket quantum signal processing to approximate the imaginary-time evolution operator via a polynomial transformation. We demonstrate that the complexity of the poly DB-TFD algorithm scales exponentially with the inverse temperature in a broad practical regime. This scaling is consistent with existing methods, and numerical simulations support the corresponding theoretical bound. We further demonstrate the utility of DB-TFD in quantum Boltzmann machines for generative modeling, achieving improved performance compared with variational imaginary-time evolution approaches. These results establish DB-TFD as a promising route for thermal state preparation in the near-term and early-fault-tolerant regimes.

The complex radio light curves of tidal disruption events (TDEs) challenge our understanding of the properties of both the outflows and the circumnuclear medium (CNM) surrounding supermassive black holes. In this work, we explore outflow-CNM interactions across a broad parameter space using three-dimensional hydrodynamic simulations, adopting a broken power-law CNM density profile with a transition near the Bondi radius. The outflow-CNM interaction inside Bondi radius produces an early radio flare (\(\lesssim 2\) yr) once the emitting region becomes optically thin. A second radio rebrightening can appear a few years later if the outflow decelerates beyond Bondi radius. We also find that either a very dense inner CNM, which causes rapid deceleration, or a rarefied outer CNM suppresses the late rebrightening that will produces a single early-peaked flare. In contrast, a rarefied CNM inside the Bondi radius suppresses the early flare and yields a single late-peaked event. For the case of very dense CNM at large radii, the interaction will trigger a sharp late-time rise as observed in some TDEs. We further explore the interaction of a relativistic jet with a broken power-law CNM, which can reproduce the characteristic light curves as observed in jetted TDEs without invoking complex jet structure.

The BRUIT-FM Challenge asks participants to reduce ”noise” — defined as any signal that masks the signal of interest — on an open dataset of real and synthetic broadband seafloor seismology data. The dataset includes signals from earthquakes, ocean infragravity waves and seafloor currents. It also includes training datasets of synthetic data with reference solutions. Participants are asked to remove or separate these signals to obtain the best earthquake and seafloor compliance signals. The authors will make a first assessment of the submissions, based on noise reduction, signal deformation and ease of use. Participants are invited to a community workshop, in which they will validate the preliminary assessment and collaborate on a community paper describing the results, identifying promising pathways and proposing new directions. The best results will be added to a new version of the dataset, which will persist as a benchmark for future developments.

We investigate physics-informed neural networks (PINNs) for computing the $s$-wave bound states of the hypernucleus $_{\Lambda}^{208}$Pb, modeled as a two-body system composed of a $\Lambda$ hyperon and a $^{207}$Pb core. The interaction is described by a Woods–Saxon potential without spin–orbit coupling. In the PINN formulation, the radial bound-state wave function is represented by an artificial neural network, and the eigenenergies are obtained from the Rayleigh–Ritz variational quotient. Because PINN eigenvalue calculations can depend on the residual-loss formulation and random-seed initialization, two residual losses are compared across four independent random seeds. Their performance is assessed using eigenvalue accuracy, coefficient of variation, signal-to-noise ratio, bias–variance decomposition, and Hermitian spectral-ordering consistency. The normalized residual loss gives the most stable and physically consistent bound-state spectrum for the four seeds considered. With this loss, the computed bound-state energies and root-mean-square radii are in very good agreement with the corresponding theoretical values. The resulting wave functions are used to construct the Jost functions through the Wronskian with incoming and outgoing Riccati–Hankel functions. From these Jost functions, the residue of the partial-wave $S$-matrix at the bound-state pole, the Asymptotic Normalization and the Nuclear Vertex Constants are extracted. These quantities show reasonable agreement with theoretical values, although with larger standard deviations than those obtained for the eigenenergies and radii. The results indicate that the Rayleigh–Ritz formulation combined with a seed-robust normalized residual loss provides a stable PINN framework for bound-state and Jost-function-based calculations in hypernuclear two-body systems.

High-order thermodynamic nonequilibrium (TNE) in three-dimensional compressible flows reflects the breakdown of low-order kinetic moment closure in strong-gradient regions. Using Chapman-Enskog analysis, we identify the kinetic moment constraints required to describe third-order TNE. The analysis yields the third-order constitutive relations and evolution equations for the viscous stress and heat flux, together with second-order expressions for their associated higher-order fluxes. These constraints enable the construction of a three-dimensional super-Burnett-level discrete Boltzmann model with 91 discrete velocities. The resulting D3V91 model reproduces shock-tube wave structures and resolves high-order TNE contributions that lower-order DBMs do not capture reliably. These results demonstrate that high-order TNE has a multigradient, rather than single-gradient, origin. For the four TNE quantities considered here, odd-order central moments, including the heat flux and the viscous-stress flux , are primarily governed by temperature gradients, whereas even-order central moments, including the viscous stress and the heat-flux-related flux , are dominated by velocity gradients. These leading-gradient dependences are not exclusive; they are substantially modified by density gradients, secondary gradients and transition-layer widths through higher-order derivative terms, gradient products and cross-couplings. When the secondary contributions become comparable to the leading-gradient terms, the nonequilibrium response transitions from a near-linear regime to an approximately exponential regime. This work establishes a super-Burnett-level DBM framework that treats kinetic moment closure and multigradient coupling consistently, providing a basis for resolving and interpreting high-order TNE in three-dimensional compressible flows.

Binary systems composed of stars with similar parameters should have identical chemical composition. However, many chemically anomalous pairs have been found in the literature, such as the binary HD 129171/HD 129209. It is still unclear whether these anomalies originate from inhomogeneities of protostellar clouds, with important implications for chemical tagging and theories of star formation, or if they are caused by a planet engulfment event suffered by one binary component. In this work, we measure precise differential abundances for the system HD 129171/HD 129209 to explore the planet engulfment hypothesis proposed in the literature. We focus particularly on the Be abundance, showing that this element can serve as a diagnostic of engulfment events for solar-type stars. Atmospheric parameters were determined imposing spectroscopic equilibrium of iron lines. Masses and ages were estimated with the isochronal method. Li, Be, N and O abundances were determined via spectral synthesis. Other elemental abundances (up to Zn) were determined by equivalent width measurements. The spectra adopted in the analysis were gathered using UVES/ESO. We confirm the large difference in [Fe/H] (0.120 $\pm$ 0.004 dex) and A(Li) (-1.00 $\pm$ 0.02 dex) among the members of the pair, and the trend between differential abundances and condensation temperature of the elements. The binary system also shows detectable differences in Be abundances (-0.20 $\pm$ 0.04 dex). The abundance pattern of the pair is reasonably reproduced by an engulfment model of 11.2 M$_\oplus$ of rocky material. The difference in chemical abundances of the HD 129171/HD 129209 pair provides strong evidence in favor of the planet engulfment scenario. In this context, the detection of a Be difference among chemically inhomogeneous binary systems can be used as a diagnostic of rocky material ingestion suffered by a member of the pair.

When a horizontal plate vibrates strongly enough, it causes small particles such as sand grains to continually bounce on it and, over time, to diffuse across its surface. This phenomenon is the cause of the well-known Chladni figure, which is drawn by a higher density of grains gathering along the nodal lines of a resonating elastic plate. Using a heterogeneous, non-resonating plate, we investigate experimentally this type of diffusion. We find that, for the most part, is it comparable to classical molecular diffusion. We can define a temperature for the bouncing grains, and the system then obeys the fluctuation-dissipation theorem. We also recover Maxwell-Boltzmann statistics at equilibrium, when temperature is uniform. However, when temperature varies across the vibrating plate, the microscopic details of the grains' dynamics affect their macroscopic behavior: Fick's law, for instance, no longer applies. Instead, our experiments support a new transport relation that was recently proposed to represent diffusion in Chladni's experiment. Finally, we propose an expression for the heat flux associated to the non-equilibrium steady state predicted by this new relation, and test it against observations.

The nitrogen-vacancy (NV) center in diamond has attracted considerable attention as a highly sensitive quantum sensor that can operate at room temperature. In particular, continuous-wave optically detected magnetic resonance (CW-ODMR) is promising for a wide range of applications because of its simplicity. However, conventional AC magnetic-field sensing schemes based on CW-ODMR suffer from a limited detection bandwidth: the detectable frequency is either fixed by intrinsic physical parameters of the NV center or, even when tunable, restricted to a narrow range of only a few MHz. Here, we propose a broadband AC magnetometry scheme based on CW-ODMR with NV centers using microwave-driven dressed states.Through theoretical analysis and numerical simulations, we show that the proposed scheme enables the detection of AC magnetic fields with frequencies up to the order of 100 MHz, which has been difficult to achieve using conventional CW-ODMR-based methods.

The continuous regulation of transport properties through softness remains a longstanding challenge in active matter. Here, we show that encasing a programmable active particle within a deformable membrane naturally gives rise to intermittent stop-and-go dynamics, with ballistic motion at short times crossing over to diffusion at long times. Crucially, membrane softness acts as a single control parameter that continuously tunes persistence, intermittency, and long-time transport, linking the internal driving to the emergent locomotion of the synthetic cell. Combining experiments, simulations, and a run-and-tumble theoretical framework, we identify the minimal physical ingredients underlying this behavior and establish design principles for programmable soft active transport, opening new avenues at the interface of active matter physics and synthetic robotics.

The study of synchronization in complex systems has recently been revolutionized by incorporating higher-order interactions through simplicial complexes. Building in particular upon the higher-order Kuramoto model, which considers oscillators on nodes, links, and higher-dimensional simplices. This work extends the monolayer framework of the higher-order Kuramoto model to multilayer networks where the layers are adaptively coupled through order parameters of the oscillators placed on the simplices. We propose two multilayer architectures: one that allows interactions between signals of the same dimension across layers and the other that permits cross-dimensional interactions. We observe that a higher coupling strength is required for synchronization transitions of the node signals and the projected uplink and downlink signals during adaptation. For example, incorporating node dynamics into link evolution delays the onset of synchronization. This study opens an avenue for understanding complex dynamical processes within interconnected higher-order structures. Finally, we present a comprehensive theoretical framework, first for a bilayer network where layers are random networks treated under the annealed approximation, and then extend the analysis to the case of fully connected layers. The theoretical predictions align remarkably well with numerical simulations, accurately capturing the dynamics of the original model in a globally coupled scenario.

Random walkers usually diffuse according to Fick's law. On average, they move down the gradient of their concentration and, in the absence of external force, tend to distribute themselves uniformly. In some experiments, however, this familiar notion is at odds with observation. Sand grains, for instance, gather along the nodal lines of a vibrated elastic plate to form a Chladni figure, thus accumulating where fluctuations are weak – a fact that escapes the reach of Fick's law. On theoretical grounds, Büttiker [Zeitschrift für Physik B, 68, 1987] and Landauer [J Stat Phys, 53, 1988] proposed that particles submitted to a non-uniform temperature field would indeed gather where the temperature is low. They also predicted that, in the presence of a potential force, a non-uniform temperature could drive a steady current of particles, powered only by noise. Here, we present an experimental realization of these phenomena in a macroscopic system, which confirms the quantitative predictions of Büttiker.

The radiation mechanism of gamma-ray burst (GRB) prompt emission remains uncertain. Although the fast-cooling synchrotron model in a decaying magnetic field can account for the characteristic nonthermal spectral shape, its computational cost has limited its use in systematic observational fitting and statistical model comparison. We develop a convolutional neural network (CNN)-based spectral emulator for this physical model and train it on a large synthetic data set generated over a physically motivated parameter space. The trained network reproduces the numerical spectra with high fidelity while reducing the cost of spectral evaluation to the millisecond level. We then incorporate the emulator into a Bayesian spectral-analysis framework and apply it to the time-resolved spectra of GRB 231020A observed by Fermi/GBM. In most time intervals, the decaying-field fast-cooling synchrotron model provides better fits and smaller Bayesian information criterion values than the standard fast-cooling synchrotron model. These results suggest that a radially decaying magnetic field provides a plausible and more physically motivated interpretation of the prompt-emission spectrum of this burst, while also indicating that the emulator offers a practical route for large-sample Bayesian inference and systematic comparisons of GRB prompt-emission models.

We investigate star formation activity in galaxies belonging to two Hickson Compact Groups (HCGs), HCG 56 and HCG 92 (Stephan's Quintet), both of which show clear evidence of interactions, using spectral energy distribution (SED) analysis across the near- to far-infrared range. By combining data from the Infrared Satellite AKARI, the Spitzer Space Telescope, and the Herschel Space Observatory, we examine how galactic interactions influence the physical conditions and the evolution of group members. The observed SEDs of member galaxies are compared with model SEDs representing both star-forming galaxies and active galactic nuclei (AGN). Star formation rates (SFRs) are estimated using two independent methods: (i) the strength of mid-infrared polycyclic aromatic hydrocarbon (PAH) bands and (ii) far-infrared luminosities attributed to star formation, as derived from the models. Although both methods yield generally consistent results, SFRs based on PAH features are systematically lower, possibly due to the PAH destruction in some interacting galaxies. When plotted against the stellar mass, all member galaxies are found below the main sequence of star-forming galaxies in the SDSS field, suggesting that interaction-induced starbursts are not seen in HCG 56 and HCG 92.

We show the emergence of memory effects in the dynamics of a driven two-level system interacting with a composite environment, and analyze their influence on work, heat and entropy production. We further investigate how the interplay between driving, dissipation and memory effects, stemming from the finiteness of the environment, shapes the thermodynamic response of the system, thus providing insight into quantum thermodynamics beyond the Markovian approximation.

We develop a high-dimensional statistical theory of low-rank adaptation (LoRA) in attention models, capturing the interplay between pre-training and fine-tuning. We introduce a solvable framework in which a single-head attention layer is first pre-trained on a data-abundant task and subsequently adapted via a rank-one LoRA update on limited data. In the high-dimensional limit, both stages admit a sharp asymptotic characterization in terms of a finite set of order parameters, yielding explicit predictions for test errors and representation alignment. Our analysis shows that the impact of pre-training on LoRA is summarized by an effective noise term, from which we derive prescriptions for the optimal pre-training procedure. We also demonstrate a regime with a mismatch between the value of the test error and representation quality, and propose an application of our theory to active fine-tuning.

To improve the accuracy of Monte Carlo estimation of expectations, a set of zero-mean feature functions, known as control variates, can be used. They can be used as feature functions for linear regression of the target function, and we can obtain an unbiased and variance-reduced estimate using its residual. One known way to construct such functions is a method using an equality called Stein's identity, but these functions are not sufficient for the case where the target distribution is multimodal. We propose a different approach to constructing these zero-mean functions based on distribution approximation and the density ratio. We demonstrate that combining the functions constructed by these two strategies can effectively reduce the estimation variance for a bimodal distribution.

Recent measurements of Higgs boson properties using proton-proton collision data recorded at $\sqrt{s}=13$ TeV and $\sqrt{s}=13.6$ TeV with the ATLAS and CMS detectors at the LHC are presented. CMS results on the Higgs boson mass and width in the $H\to\gamma\gamma$ channel are reported, together with a measurement of the Higgs boson width in the $H\to WW^*$ final state. A combined measurement of the charge-parity (CP) nature of the Higgs-vector boson couplings by the ATLAS collaboration, as well as improved results in individual channels by both experiments are summarised. Finally, the latest CMS analysis of the CP structure of the Higgs-tau lepton Yukawa coupling is reported.

We describe fully coupled simulations that bridge atomistic cathode dynamics and plasma formation during the earliest stages of vacuum arcing. The model combines molecular dynamics, finite element electrothermal calculations, electron emission and particle-in-cell plasma simulations via dynamic transfer of particles between the surface and plasma domains. Simulations of Cu nanoprotrusions reveal two routes to thermal runaway: direct Joule heating-driven instability and a novel nanoparticle-assisted mechanism, where detached nanoparticles generate neutral vapor that becomes ionized.

\abstract{Errors in observatory coordinates directly impact the precision of pulsar time-scale construction. Using the pulsar timing software TEMPO2, this study simulates various station position errors within the three-dimensional terrestrial reference frame for three different types of millisecond pulsars, over periods of 13 days and 5 years, and analyzes their effects on pulsar timing results.The findings demonstrate that,for both 13-day and 5-year observation spans, station coordinate errors substantially reduce the accuracy of pulsar timescale construction when the zenith angle exhibits long-term variations. This effect is independent of pulsar type and the daily observable time of the station antenna for the pulsar. A linear relationship is found between station coordinate errors and the Root-Mean-Square (RMS) of pulsar timing residuals, with fitted linear coefficients ranging from $1.36 \times 10^{-11}$ to $1.61 \times 10^{-9}$ for the three pulsars. The Roemer delay error caused by coordinate inaccuracies is notably larger than other delay and correction terms. Errors along the x- and y-axes have comparable influences on timing precision, whereas errors along the z-axis have a relatively smaller effect. Kendall correlation analysis between station error-induced Roemer delay and RMS yields a correlation coefficient $r = 1.67\%$ and $p = 100\%$ in all cases, indicating that, at current timing precision levels, coordinate errors primarily affect the Roemer delay term and thus the pulse arrival times, which is highly consistent with theoretical models.While these findings offer valuable insights into the key factors influencing pulsar timescale accuracy and related applications, they may not hold under conditions of a constant zenith angle or limited elevation angles, such as those at FAST.}