We present a formalism for semiclassical time evolution in quantum mechanics, building on a century of work. We identify complex saddle points in real time, real saddle points in complex time, and complex saddle points in complex time that reproduce the known answers in classic problems. For the decay of a metastable state, we find finite time and finite energy analogs of the "bounce" which do not have strict zero or negative modes. The one-loop phase of the wave function and the multiplicity of bounce solutions at late times are discussed. The motivation of this work is to learn how to compute decay rates in quantum field theory in situations with non-trivial time dependence, by first taking a humble step backwards to the fascinating world of quantum mechanics.

We introduce and analyze a broad class of continuous directed polymers in $\mathbb{R}^d$ driven by Gaussian environments that are white in time and spatially correlated, under Dalang's condition. Using an Itô-renormalized stochastic-heat-equation representation, we establish structural properties of the partition function, including positivity, stationarity, scaling, homogeneity, and a Chapman--Kolmogorov relation. On finite time intervals, we prove Brownian-type pathwise behavior, namely Hölder continuity and identification of the quadratic variation. We then obtain a sharp measure-theoretic dichotomy: the quenched polymer measure is singular with respect to Wiener measure if and only if $\widehat f(\mathbb{R}^d)=\infty$ (equivalently, the noise is non-trace-class), and it is equivalent otherwise. Finally, in dimension $d\ge 3$, we prove diffusive behavior at large times in the high-temperature regime. This extends the Alberts--Khanin--Quastel framework from the $1+1$ white-noise setting to higher-dimensional Gaussian environments with general spatial covariance.

We present the calculation of the so far missing ${\cal O}(α^2α_\mathrm{s})$ corrections to the quantity $Δr$, which relates the Fermi constant to the W-boson mass, and enables precision predictions of the latter. While the ${\cal O}(α^2α_\mathrm{s})$ corrections from diagrams with two closed fermion loops are already known, we here focus on the subset with one closed fermion loop, which is a substantially more complex problem. The calculation has been carried out through a combination of analytical and numerical techniques for the three-loop integrals and the on-shell renormalization. The impact of the new corrections is numerically significant, raising the Standard Model prediction for the W-boson mass by more than 3 MeV.

We build upon our previously developed multi-ion radiative transfer (RT) framework, PEACOCK, to investigate the kinematic and energetic structure of cool-to-warm galactic winds in a sample of 50 nearby star-forming galaxies. Using self-consistent constraints derived from joint modeling of Ly-alpha and multiple ultraviolet metal lines, we analyze how bulk outflows and turbulent motions contribute to the dynamics and energy budget of galactic winds in the circumgalactic medium (CGM). We find that macroscopic turbulent velocities are often comparable to, and sometimes exceed, the coherent bulk outflow velocity. The associated turbulent pressure frequently dominates over both microscopic pressure and ram pressure, indicating that turbulence is a major contributor to the kinetic energy budget of the CGM wind. Wind kinematics, ionic column densities, and metal mass outflow rates all scale systematically with stellar mass and star formation rate, demonstrating a strong coupling between stellar feedback and CGM structure. Including turbulent motions strengthens these CGM-galaxy scaling relations and favors an energy-driven feedback regime. The total kinetic energy flux of the cool-to-warm CGM correlates tightly with the mechanical energy injection rate from star formation, implying that stellar feedback provides sufficient power to sustain both coherent outflows and turbulence. Comparisons with phenomenological line-profile fitting methods further show that simplified treatments can introduce systematic biases in inferred wind properties. Together these results support a turbulence-regulated picture of galactic winds in which a substantial fraction of feedback energy is stored in turbulent motions within a multiphase CGM.

Machine-learning interatomic potentials (MLIPs) have advanced rapidly, with many top models relying on strong physics-based inductive biases. However, as models scale to larger systems like biomolecules and electrolytes, they struggle to accurately capture long-range (LR) interactions, leading current approaches to rely on explicit physics-based terms or components. In this work, we propose AllScAIP, a straightforward, attention-based, and energy-conserving MLIP model that scales to O(100 million) training samples. It addresses the long-range challenge using an all-to-all node attention component that is data-driven. Extensive ablations reveal that in low-data/small-model regimes, inductive biases improve sample efficiency. However, as data and model size scale, these benefits diminish or even reverse, while all-to-all attention remains critical for capturing LR interactions. Our model achieves state-of-the-art energy/force accuracy on molecular systems, as well as a number of physics-based evaluations (OMol25), while being competitive on materials (OMat24) and catalysts (OC20). Furthermore, it enables stable, long-timescale MD simulations that accurately recover experimental observables, including density and heat of vaporization predictions.

The rapidly expanding Gravitational-Wave Transient Catalog (GWTC) necessitates the development of model-independent techniques to uncover trends and subpopulations within the binary black hole (BBH) population. We present the first usage of the Uniform Manifold Approximation and Projection (UMAP) algorithm, a novel dimensionality-reduction technique, for the purpose of analyzing BBH mergers in GWTC-3. We show that UMAP, paired with a clustering algorithm, effectively partitions the population into four well-segregated subgroups principally via their primary and secondary mass components along with an outlier event, GW$190521\_030229$. UMAP clearly identifies objects in the ${\sim}10~M_\odot$ buildup in the BBH mass spectrum as their own group with aligned spins and mass ratios of ${\sim}0.2{-}0.7$ while objects in or above the ${\sim}35~M_\odot$ overdensity are all in the same, largest group and display typically lower effective spins as well as larger mass ratios (${\sim}0.5{-}0.9$) on average. With the aid of hierarchical population inference, we interpret these as subpopulations from different formation pathways, consistent with previous findings. We also find a transitional group of a handful of objects with masses in between the aforementioned buildups and broad support for anti-aligned spins. We examine the low-mass UMAP subgroup, which exhibits anti-correlation between the mass ratio and effective spin, and show that it drives such anti-correlation for the entire GWTC-3 sample. Overall, we demonstrate that UMAP is an interpretable, non-parametric framework that can not only be used for visualization but also for probing the astrophysics of the BBH population.

Analogously to classical computers, quantum processors exhibit side channels that may give attackers access to potentially proprietary algorithms. We identify and exploit a previously unexplored side channel in trapped-ion quantum processors that arises from the radio-frequency (RF) signals used to modulate lasers for ion cooling, gate execution, and readout. In these quantum processors, acousto-optical modulators (AOMs) imprint phase and frequency modulations onto laser fields interacting with the ions to implement individual and collective unitaries. The AOMs are driven by strong RF signals, a fraction of which leaks out of the device. We discuss general strategies to exploit this side channel and demonstrate how to detect RF leakage from a state-of-the-art qudit-based quantum processor using off-the-shelf components. From this data, we extract pulse characteristics of single-ion and entangling gates, thereby implementing a proof-of-principle exploitation of the novel attack vector. Finally, we outline ways to mitigate the information leakage through the presented side channel.

Chaotic BKL dynamics provides a canonical description of the approach to spacelike singularities as a sequence of Kasner epochs grouped into eras. While this paradigm is well established for cosmological singularities, explicit realizations inside black holes have been scarce, despite renewed interest from holography. Here, we construct a broad class of asymptotically AdS black holes in $D\ge 4$ whose interiors exhibit bona fide BKL dynamics as the singularity is approached. In the near-singularity regime, the evolution reduces to billiard-like motion in a compact domain that forms a regular $(D-2)$-simplex. We derive closed-form bouncing rules for the Kasner exponents in arbitrary dimension and prove the ensuing chaotic dynamics. A key novelty for $D\ge 5$ is a richer internal organization of eras: inequivalent transitions between epochs lead to distinct Kasner seasons, yielding new patterns of epoch/era structure for both electric and gravitational walls. Finally, we investigate a holographic diagnostic, the thermal $a$-function, whose monotonic flow captures individual epochs and eras and can display near-walking behavior in suitable Kasner regimes.

Temporal modes of photons are a promising encoding scheme for high-dimensional quantum networks due to their high channel capacity and fiber compatibility. However, realizing their full potential requires devices capable of synchronizing, processing and interfacing these modes across photonic and atomic bandwidths. In this work, we demonstrate a programmable high-dimensional temporal mode processor using a Raman quantum memory in warm cesium vapor. We exploit the single-mode nature of the Raman interaction kernel, dynamically shaping the control field to synthesize a tunable coherent filter that selectively addresses specific temporal waveforms. This mechanism enables on-demand storage, filtering, and conversion, providing a coherent interface between MHz- and GHz-bandwidth modes. We validate the platform's selectivity across a basis of 30 orthogonal Hermite-Gaussian modes and certify high-fidelity quantum operation via 5-dimensional process tomography. By combining deterministic mode conversion with bidirectional bandwidth interfacing, we establish the Raman memory as a critical active node for scalable quantum information processing.

We reveal a striking correspondence between electron- and phonon-driven pairing in twisted bilayer graphene (TBG) by mapping an atomistic electronically driven pairing model onto an effective inter-valley, intra-Chern description, originally proposed for phonon-mediated superconductivity. Within the unified framework of intra-Chern pairing, we analyze the competition between nematic and chiral superconducting states. The latter corresponds to the extreme Chern-polarized limit and thus hosts unpaired flat bands within the superconducting gap, which generally disfavors it relative to the nematic states. Crucially, nematic order is locally preferred at each momenta, but the optimal nematic directions are incompatible across the Brillouin zone due to the broken rotation symmetry. This momentum-space frustration enables a chiral ground state at large fillings or weak interactions. Our results thereby both provide a unified understanding of superconductivity in TBG, with a natural cooperation of electron- and phonon-mediated pairing, and clarify the microscopic origin of the competition between the chiral and nematic superconducting states.

In order to meet the precision requirements for the LHC and future colliders, next-to-next-to-leading order corrections to a wide range of processes are essential, making general automated tools highly desirable. Extending the strategy of the widespread one-loop program OpenLoops to two loops, there are three major ingredients: process-dependent tensor coefficients, tensor integrals, and process-independent counterterms. In these proceedings, we focus on the second part and present a new recursive algorithm to reduce arbitrary two-loop tensor integrals to scalar integrals numerically.

We develop an analytic, fully field-theoretic description of how a hadronic medium can induce photon condensation in a cavity. Starting from leading-order Chiral Perturbation Theory minimally coupled to Maxwell theory, we construct a consistent truncation to the lowest hadronic and gauge modes that still supports a non-vanishing baryon (topological) density. The resulting reduced dynamics is an effective \(1+1\) theory whose couplings retain memory of the three-dimensional cavity through discrete winding and transverse holonomy data. Integrating out the heavy hadronic mode at one loop yields a gauge-invariant effective potential for the lowest photonic cavity mode, from which we derive analytic criteria for a condensed window. In the opposite hierarchy, integrating out the gauge mode produces a one-loop deformation of a sine--Gordon-type EFT for the chiral mode and makes explicit where scale separation fails and the full coupled system must be kept. Upon quantization, the reduced theory maps onto standard nonlinear quantum-optics Hamiltonians, including a two-photon Rabi limit and quartic single-mode photonic models whose trivial and condensed branches obey distinct selection rules. This provides a concrete bridge between finite-density hadronic physics and experimentally familiar nonlinear-cavity diagnostics.

We present PEACOCK, a three-dimensional Monte Carlo radiative transfer (RT) framework designed to self-consistently model rest-frame ultraviolet emission and absorption lines arising from multiphase, clumpy galactic winds. Applied to deep HST/COS spectra of 50 nearby star-forming galaxies, PEACOCK reproduces 220 observed profiles of Ly-alpha, Si II, C II, Si III, Si IV, and C IV spanning absorption, emission, and P-Cygni-like morphologies within a single CGM model. By combining Monte Carlo RT with deep-learning acceleration and nested sampling, the framework enables fully converged multi-line inference at a small fraction of the cost of traditional RT grids. Systematic experiments show that ion column densities, bulk outflow velocities, and turbulent motions leave distinct imprints on line profiles, allowing the underlying gas properties to be constrained with minimal degeneracy. Purely radial accelerating flows often fail to reproduce the observed absorption morphologies, whereas macroscopic velocity dispersion naturally produces the broad asymmetric troughs seen in the data, indicating that turbulent motions are a key component of outflow kinematics. The inferred kinematics reveal strong coherence among low- and high-ionization metal lines in both bulk and turbulent velocities, consistent with a dynamically coupled multiphase wind. In contrast, neutral hydrogen shows weaker correspondence with metals, suggesting incomplete mixing and a distinct kinematic structure. By unifying emission and absorption diagnostics across multiple ions, PEACOCK provides a physically grounded bridge between UV observations and theoretical models of galactic winds.

Understanding how local structural order governs electronic correlations is essential for revealing the microscopic mechanism underlying emergent behavior in two-dimensional magnets. In the layered van der Waals ferromagnet Fe\textsubscript{5-x}GeTe\textsubscript{2}, intrinsic Fe-site disorder provides a natural platform to probe this interplay. Here, we establish a direct atomic scale correlation between Fe-site ordering and local electronic structure by combining high-resolution scanning tunneling microscopy with density functional theory calculations. Scanning tunneling microscopy resolves two coexisting surface phases, a $\sqrt{3} \times \sqrt{3}$ superstructure associated with ordered Fe(1) configurations and an undistorted $1 \times 1$ hexagonal Te lattice in Fe(1)-deficient regions. Spatially resolved spectroscopy shows that the $\sqrt{3}$-ordered domains exhibit metallic behavior, whereas Fe(1) vacant areas display a suppressed density of states(DOS) near the Fermi level, indicative of pseudogapped electronic states. The nanoscale coexistence of these distinct electronic responses provides direct evidence of electronic phase separation driven by Fe-site ordering. First-principles calculations reveal that symmetry allowed hybridization between Fe 3d and Te 5p orbitals reconstructs the low-energy electronic structure, giving rise to the contrasting tunneling signatures of ordered and disordered phases. Bias-dependent local DOS simulations reproduce the experimentally observed contrast evolution and reveal that hybridization induced out of plane orbital character governs the spatial modulation of tunneling conductance. These results provide a microscopic framework linking atomic-scale structural order to nanoscale electronic inhomogeneity in van der Waals magnets.

This note aims to continue our study about the applications of Poisson quasi-Nijenhuis geometry to the theory of classical completely integrable systems. More precisely, we will present new versions of the deformation and involutivity theorems, under the hypothesis that the closed 2-form triggering the deformation and the closed 3-form defining the Poisson quasi-Nijenhuis structure are factorized. These results will be supplemented by several examples of involutive Poisson quasi- Nijenhuis manifolds.

We present a method for calculating the ground state energy of the Fermi-Hubbard model leveraging Rydberg atom processors and sample-based quantum diagonalization (SQD). By exploiting the perturbative relationship between the Fermi-Hubbard and Heisenberg models, the procedure samples from the Heisenberg model as prepared on the Rydberg atom processor, and uses the samples to diagonalize the Fermi-Hubbard model for large U. We include anisotropy and next-nearest-neighbor interactions and discuss the relevant regime for quasi-superconductivity in the 1-dimensional Fermi- Hubbard model. Numerical and experimental results on the Aquila quantum processor are presented for ground state energy calculations as well as the chemical potential. We find that the Heisenberg model sampling in the studied regime is sufficient to converge near to the ground state for up to 56 qubits, and we see a clear advantage of Rydberg atom sampling as opposed to random sampling even with 10x more samples for diagonalization. We also present a gate-based implementation of the gate-based SQD algorithm on IBM Quantum hardware for 56-qubit Hubbard model as a benchmark. Finally, we provide a gap analysis for studying emergent superconductivity using this method.

Numerous cell types relate to their immediate environment by exerting a three-dimensional pressure field on their environment, with components both longitudinal and transverse to the cell membrane. This pressure field can in principle be measured by traction force microscopy experiments. Compared to other approaches, the technique of Protrusion Force Microscopy gives access with high spatial resolution to the pressure field by measuring the deformation of a thin elastic membrane using atomic force microscopy (AFM). However, while the pressure field under interest is three-dimensional, the height profile measured by AFM is only one-dimensional. We propose a solution to this inverse problem and we explore its regime of applicability in the experimental context.

We present a reanalysis of archived data from the ALEPH experiment at LEP in the $\mathrm{Z \to q\bar{q}}$ final state. We apply modern jet flavour tagging techniques to improve the separation between the different hadronic decay channels of the Z boson, achieving up to one order of magnitude improvement in misidentification rate for b- and c-quark jets compared to the legacy algorithms used for the most recent ALEPH results, for the same identification efficiency. We also present the first implementation of strange quark jet tagging with LEP data, which allows for the selection of a $\mathrm{Z \to s\bar{s}}$ enriched event sample. These improvements in the flavour tagging performance are achieved by leveraging the lifetime, particle identification, and secondary vertex information, as well as modern classifiers based on a deep learning approach. We also demonstrate the calibration of the tagger in data using a tag-and-probe method, obtaining good data to simulation agreement for all quark flavours. These results pave the way for improved measurements of electroweak precision observables with LEP archived data, and can serve as a guidance for the development of detectors and algorithms for future electron-positron colliders.

The calculation of the error threshold of quantum error correcting codes typically proceeds as follows. First, syndromes are measured. Then, a decoder infers the error chain and the corresponding correction is applied. The threshold is then defined as the largest correctable error rate, with the maximum-likelihood decoder corresponding to the ``optimal'' threshold. However, a broader set of operations could be used to recover quantum information. The true optimal threshold should be optimised over all possible recovery schemes, which can be described by quantum channels. Here, we study such optimal recovery channels and their thresholds $p_\mathrm{th}^\mathrm{opt}$. We introduce an information-theoretic quantity, mutual trace distance, which provides a necessary and sufficient diagnostic for sharply determining $p_\mathrm{th}^\mathrm{opt}$ without explicit optimisation. In contrast, previous works give a lower bound on $p_\mathrm{th}^\mathrm{opt}$ by specifying particular recovery schemes, e.g. Schumacher-Westmoreland (SW) which provides coherent information as a diagnostic to lower bound $p^\mathrm{opt}_\mathrm{th}$. We prove that the Petz and SW recovery schemes are optimal, i.e. their threshold is $p_\mathrm{th}^\mathrm{opt}$. With their optimality established, we explore the structure of optimal and non-optimal recovery schemes and their phase diagrams.

We investigate the nonlinear heat-diffusion equation \( C(u)\,\frac{\partial u}{\partial t} = \frac{\partial}{\partial x}\!\left( K(u)\,\frac{\partial u}{\partial x} \right) \), where \( C(u) \) and \( K(u) \) are coefficients that depend on \( u \). By applying the classical Lie symmetry method, we determine the admitted Lie point symmetries and compute the corresponding infinitesimal generators according to the functional relationship between \( C(u) \) and \( K(u) \). The admitted symmetries are used to reduce the partial differential equation to ordinary differential equations and to construct invariant solutions. Particular cases of physical interest are analyzed in detail, including Storm-type materials and power-law dependence of \( C(u) \) and \( K(u) \) on \( u \). For these cases, similarity solutions are obtained.

Spatially-resolved X-ray observations are the key to understanding electron acceleration in solar flares. Currently, the underlying processes that efficiently energize solar flare particles are poorly constrained. Abundant flare observations suggest that turbulence plays a crucial role in transferring energy between the magnetic field and energetic electrons. For the first time, we connect inhomogeneous acceleration from turbulence and hard X-ray spectroscopy and imaging observations with kinetic modeling to constrain the properties of flare acceleration. Observing three large flares with RHESSI, or Solar Orbiter/STIX, we extract X-ray imaging and spectroscopy observables. We compare with modeling results, mapping observables to electron acceleration and turbulent properties. We determine that extended regions of turbulence are required to match multiple X-ray observables, suggesting electrons are accelerated over a large fraction (~25%) of the flare loop; a property that is usually unconstrained from X-ray observations alone. Additionally, we determine acceleration timescales that vary between 7 and 22s by using fixed values for the turbulent scattering timescale and the velocity dependence of the acceleration diffusion coefficient. These fixed values are effectively unconstrained, but yield acceleration timescales that will help to restrict possible viable stochastic models.

AI weather foundation models now achieve forecast skill comparable to numerical weather prediction at far lower computational cost, yet their predictability for high-impact extremes across dynamical regimes remains uncertain. We evaluate Aurora using an event-based framework spanning tropical cyclones, freezes, heatwaves, atmospheric rivers, and extreme precipitation at lead times from 1 to 21 days. Aurora demonstrates strong short-range (1-7 day) skill across event types, including competitive tropical cyclone track accuracy and high spatial agreement for temperature and moisture extremes. However, a consistent subseasonal failure mode emerges: while large-scale circulation patterns remain moderately skillful at 14-21 day leads, threshold-based extreme intensity collapses as fields regress toward climatology. This divergence indicates that Aurora retains synoptic-scale dynamical structure but loses surface-impact amplitude beyond 7-10 days. The practical predictability horizon for deterministic AI extreme-event forecasting therefore remains constrained by intrinsic atmospheric dynamics.

The Galaxy UV Legacy Project (GULP) is a Cycle 28 Treasury program with the Hubble Space Telescope (HST) designed to characterize resolved massive stars, OB associations, and young star clusters (YSCs) in 26 nearby star-forming galaxies. Utilizing the ACS/SBC F150LP and WFC3/UVIS F218W filters, combined with extensive archival observations, GULP provides an unprecedented panchromatic 8-band view from the Far-UV to the I-band. The target galaxies were carefully selected to span a broad range of metallicities, masses, morphological types, and star formation rates, thereby enabling detailed studies of star formation processes across different galactic environments. This paper introduces the GULP survey, detailing its observational strategy, data processing, and initial scientific results for the irregular barred starburst dwarf galaxy NGC 4449, used as a test case. We derived the physical parameters and ages for thousands of stars using the Binary Populations And Spectral Synthesis (BPASS) models, and found that the younger stars and clusters are predominantly concentrated along the galaxy's central bar, and that over the past <50 Myr star formation progressively migrated from northeast to southwest. We used the F150LP, F218W, and F275W filters to investigate how the UV-bump at lambda 2175 A correlates with the intensity of the UV radiation. The UV-bump is detected in many areas of the galaxy, but is absent in the regions of most intense and recent star formation. This strongly supports the scenario where UV radiation from young, massive stars effectively destroys the small dust grains responsible for the UV-bump.

Particle in Cell (PIC) simulations have become a vital tool for the investigation of kinetic processes in plasma physics. Many of the systems investigated with PIC simulations contain particles with relativistic velocities. The correct integration and the knowledge of possible sources of errors in relativistic particle trajectories is of importance to accurately judge the validity of the simulation results. Over the past few decades, various new integration schemes for relativistic particle trajectories in PIC simulations have been proposed. These are aimed at improving numerical accuracy in specific scenarios. This article presents a comprehensive comparison of particle pushers with a focus on explicit schemes. An important class of these schemes is found to be generalisable to arbitrary high order. A comparison of the fourth order variants of these schemes with their second order counterpart is also presented.

The Sanford Underground Research Facility (SURF) began operation in 2007 as a facility dedicated to advancing compelling multidisciplinary scientific research. SURF is one of the deepest laboratory sites and offers the largest footprint in the world for scientific pursuits, including physics campuses on the 4850-foot level where the LUX-ZEPLIN, MAJORANA DEMONSTRATOR, and CASPAR experiments are located. SURF is also home to the Long-Baseline Neutrino Facility (LBNF) that will host the international Deep Underground Neutrino Experiment (DUNE). SURF provides ultra-low background environments, low-background assay capabilities, and electroformed copper is produced at the facility. In this review, we discuss the history, features and status of the facility, as well as the current scientific program and future evolution and plans.

We report the epitaxial stabilization of GdAuSb films and GdAuSb/LaAuSb superlattices via molecular beam epitaxy on (0001)-oriented Al$_{2}$O$_{3}$ substrates. GdAuSb crystallize in the Au-Au dimerized YPtAs structure type (space group $P6_{3}/mmc$), the same structure as the Dirac semimetal LaAuSb. Angle-resolved photoemission spectroscopy (ARPES) measurements show similar near $E_F$ bandstructures for GdAuSb and LaAuSb, plus a rigid band shift for GdAuSb towards more hole-like behavior and core-like Gd $4f$ states $\sim 9$~eV below the Fermi energy. LaAuSb/GdAuSb superlattices exhibit sharp superlattice fringes by X-ray diffraction and atomically-precise interfaces by scanning transmission electron microscopy. Superlattices display two transitions in temperature-dependent resistvity, compared to a single Néel temperature for thick GdAuSb films. Superlattices of $Ln$AuSb materials ($Ln=$ rare earth) with atomically abrupt interfaces offer a new epitaxial platform for control of magnetic and topological order via tunable intralayer exchange and reduced dimensionality.

In this paper, we consider the near-critical dimer model in the setup of isoradial superpositions with Temperleyan boundary conditions. We show that the centered height function converges as the mesh size tends to zero to a limiting field which agrees with the (electromagnetically tilted) sine-Gordon model, whose derivative correlations are described by Grassmann variables (or equivalently determinants involving a massive Dirac operator). This answers a longstanding question in the field. A crucial part of the work is to develop a notion of discrete massive holomorphic functions and the tools to study such functions, in particular finding an exact discrete form of the massive Cauchy--Riemann equations, which is satisfied by the inverse Kasteleyn matrix. In comparison with previous studies, a key novelty of this part of our work is that the mass is not only allowed to be non-constant but can be complex-valued.

Estimating brain microstructure has important applications in medicine and neuroscience. Diffusion-weighted magnetic resonance imaging enables measuring microstructure \textit{in vivo}. Conventional biophysical model fitting can be accurate but is slow and impractical for time-critical clinical use, where machine learning can offer a potential route to rapid estimation. We address the problem of microstructure estimation under arbitrary acquisition protocols where most existing learning-based methods fail due to protocol assumptions, requiring retraining when the protocol changes. We present a graph neural network that represents input data as a point cloud in the 3D space where diffusion-weighted measurements are made and performs rotation-invariant message passing with permutation-invariant pooling, producing fixed-size embeddings that encode microstructure. The inductive biases of our relatively small model were guided by the underlying physics and symmetries of the problem rather than by generic model architectures. Trained on randomised simulated data, our model demonstrates domain generalisation, accurately estimating microstructure from data with unseen real-world protocols without retraining. This approach represents a step towards a "train once, deploy anywhere" architecture, bringing rapid learning-based microstructure mapping closer to clinical deployment.

In this paper we consider the operad of holomorphic disk embeddings of the unit disk $\mathbb D \subset \mathbb C$. We introduce a suboperad $\mathbb{CE}_2^{HS}$ defined by square-integrability conditions and show that the symmetric algebra $\mathrm{Sym} A^{2}(\mathbb D)$ of the Bergman space carries a natural $\mathbb{CE}_2^{HS}$-algebra structure. Conformally flat factorization homology with coefficients in $\mathrm{Sym} A^{2}(\mathbb D)$ then yields metric-dependent invariants of two-dimensional Riemannian manifolds. Moreover, $\mathrm{Sym} A^{2}(\mathbb D)$ is identified with the ind-Hilbert space completion of the affine Heisenberg vertex operator algebra.

Here, we present a simple, low-cost format for structured speaking and listening on historical, cultural, and equity-related topics within a physics institute. In this article, we describe how we run hour-long Learning Together sessions, including what you need, how to set expectations (this is not a debate, nor is it open discussion), and practical facilitation moves that help participants reflect safely on unfamiliar and sometimes difficult material. We aim to offer a replicable recipe that instructors and departments can adapt to their own contexts.