We study invariants of bosonic and fermionic (Grassmann-valued) matrices under the adjoint action of $U(N)$, weighted by the fermion number. Such models naturally appear as the supersymmetric indices of supersymmetric gauge theories and are captured by $U(N)$ matrix models. We discuss two features of the fermionic models that are qualitatively different from bosonic models. Firstly, the $2N^\text{th}$ power of a Grassmann matrix vanishes, which gives rise to many new trace relations. Secondly, trace relations in models involving fermions could cause an increase in the supersymmetric index as $N$ decreases, in contrast with purely bosonic models. We focus on a simple model involving one fermion and one derivative that corresponds to a $\frac14$-BPS supersymmetric index in $\mathcal{N}=4$ SYM theory, in which we find that the index is independent of $N$. We prove this rank-independence analytically, and experimentally study the cancellations between bosonic and fermionic trace relations that lead to it. Based on these observations, we make some conjectures on resulting algebraic structures, including the analogue of the polarized Cayley-Hamilton identities and the Second Fundamental Theorem of invariants in the presence of Grassmann matrices. Finally, we present various (smooth and singular) limits of the most general supersymmetric index in $\mathcal{N}=4$ SYM theory, and study some patterns in their behavior as a function of $N$.

This paper reviews recent advances in quantum learning theory for continuous-variable (CV) systems. Quantum learning theory investigates how to extract classical information from quantum systems as efficiently as possible. CV systems are ubiquitous in nature and in quantum technologies, as they describe bosonic and quantum-optical systems. While quantum learning theory for finite-dimensional systems has been extensively studied, the corresponding theory for CV systems has only recently begun to develop; here we provide a concise review. We focus on the following questions: what is the minimum number of copies (the sample complexity) required to learn a non-Gaussian state, possibly under energy constraints? What is the sample complexity for learning Gaussian states? How does the performance of CV state learning depend on non-Gaussianity? How can one test whether a state is Gaussian or far from the set of Gaussian states? And how can Gaussian processes be learned efficiently? Central to these topics, we also review several bounds on the trace distance between CV states in terms of their covariance matrices, which may be of independent interest. Overall, this work summarises selected developments in tomography of CV systems and highlights a selection of open problems.

Leptophilic sub-MeV spin-1 dark matter (DM) can be converted into a photon via inelastic scattering with a free electron or absorption by a neutral hydrogen atom in the primordial plasma. We study for the first time the impact of the energy injection resulting from such processes on cosmic microwave background (CMB) anisotropies. We obtain upper limits on the vector and axial-vector DM-electron couplings using Planck 2018 temperature, polarization, and lensing data for DM masses between 100 eV and 100 keV. We find that, due to the suppression of the hydrogen atomic form factor at high energies, inelastic scattering provides the dominant constraint for DM masses above the keV scale. At lower masses, hydrogen ionization through DM absorption is the leading channel, driven by the higher efficiency of post-recombination energy injection in modifying the free-electron fraction. Although the bounds we derive are considerably weaker than existing laboratory and astrophysical limits, they provide a robust and independent cosmological probe of leptophilic DM interactions.

The eigenstate thermalization hypothesis provides a framework for understanding thermalization in isolated quantum many-body systems by characterizing statistical properties of local observables in energy eigenstates. Here we demonstrate that distributions of matrix elements in macroscopic systems may depend not only on the macrostate parameters, such as the densities of local conserved charges, but generally also on the properties of ensembles used in sampling eigenstates. To this end, we depart from the conventional analysis of microcanonical windows and consider statistical ensembles with an adjustable scale parameter prescribing the magnitude of charge fluctuations. We specifically consider an integrable field theory that permits efficient numerical sampling of matrix elements and reliable extrapolation to the thermodynamic limit. Moreover, in this system, we identify a class of states that enables explicit closed-form computation of the suppression rate of matrix elements. Our findings reveal an underlying multiscale structure of matrix elements captured by a non-analytic fluctuation-scale dependence of algebraic exponents governing their statistical properties.

The structure of entanglement in the ground state of the harmonic chain is studied. A class of two-mode squeezed states, useful for this purpose, is identified. The entanglement of the local modes at the ends of the chain, after tracing out the centre, rapidly falls to zero as the length of the chain increases. However, if the central modes are measured, and the result communicated to systems interacting with the outer modes, the latter exhibit greatly enhanced entanglement, including in conditions where none was otherwise available. These ideas can be demonstrated in experiments in trapped ions, among other systems. The extension to the continuous case yields enhanced entanglement extracted from the vacuum state of a bosonic quantum field.

The chiral magnetic effect (CME), arising from the chiral anomaly and enabling a mutual conversion between magnetic topology and fermionic chirality, is a key mechanism in magnetar field evolution. Previous work by Dehman & Pons (2025) demonstrated that the CME can efficiently generate dipolar fields ($B_{\rm dip} \gtrsim 10^{14}~\mathrm{G}$), consistent with magnetar timing measurements, provided that the initial magnetic field carries net helicity. However, whether neutron stars are born with magnetic helicity remains uncertain. In this work, we investigate the CME across a range of initial helicity configurations, including non-helical initial conditions. We find that the CME efficiently generates magnetar-strength dipoles on timescales of decades, independently of the initial helicity content. The instability is driven by localized helical structures that induce a residual chiral asymmetry and is primarily governed by the maximum chiral chemical potential, requiring $μ_5^{\rm max} \gtrsim \mathrm{few}\times10^{-11}~\mathrm{MeV}$ for onset in the magnetar regime. Our results further show that these dipoles may either remain stable and subsequently evolve through standard Ohmic decay, or become unstable if they acquire sufficient helicity, in which case they decay through the chiral anomaly, transferring energy to less helical modes. This outcome depends sensitively on the initial helicity distribution. These findings extend the applicability of the CME to more realistic magnetic-field configurations and underscore the importance of the helicity distribution at birth, a quantity that remains poorly constrained in neutron star formation, yet is crucial for determining neutron star magnetic evolution and magnetar formation.

Fractional magnetization plateaus provide a sensitive probe of many-body spin states in frustrated quantum magnets, yet their microscopic origin in kagome antiferromagnets remains unresolved. This is particularly true of the mysterious $1/9$ plateau, which is predicted by theory but infrequently observed in experiment. Here, we investigate this problem in the $S = 1/2$ anisotropic kagome antiferromagnet Y-kapellasite, Y$_3$Cu$_9$(OH)$_{19}$Cl$_8$, using pulsed-field magnetization measurements on single crystals and high-field $^{35}$Cl NMR. We identify a hierarchy of field-induced fractional features, including $1/3$ and $1/9$ plateaus, as well as a weaker low-field feature. Analysis of the NMR spectra and the magnetic susceptibility across the $1/9$ plateau demonstrate that it is accompanied by an ordered local spin configuration, a strong suppression of low-energy spin fluctuations and activated behavior, consistent with a gapped fractional state. These features differ from those in the only other material YCu$_3$(OH)$_6$Br$_2$[Br$_{1-y}$(OH)$_y$] in which this plateau is observed, implying a surprising robustness of the $1/9$ state to the details of the underlying magnetism.

Preventing signal detection in communication and active sensing requires careful control of transmission power. In fact, the square-root laws (SRL) for covert classical and quantum communication and sensing prescribe that the average output power per channel use scales as $1/\sqrt{n}$ for $n$ channel uses. Two strategies for achieving this are diffuse and sparse signaling. The former transmits signals with power decaying as $1/\sqrt{n}$ on all $n$ channel uses, which is convenient for mathematical analysis. The latter transmits constant-power signals rarely, on approximately $\sqrt{n}$ out of $n$ channel uses, while remaining silent on the others. This offers significant practical advantages in compatibility with modern digital transmitters. Here, we study sparse signaling over lossy thermal-noise bosonic channels, which describe quantumly many practical channels (including optical, microwave, and radio-frequency). We characterize the input signal state that minimizes detectability. We find an unintuitive optimal quantum state structure: a mixture of just two consecutive photon-number states. In particular, in the low-brightness regime, the optimal signal state is a mixture of vacuum and a single photon. Since these states are generally suboptimal for both communication and active sensing, we explore the resulting trade-off and identify input-power thresholds for transitions between optimizing for covertness vs. performance in communication and sensing tasks.

We studied the constrained Hamiltonian formulation of a supersymmetric Korteweg-de Vries (KdV) equation, which is observed to be a constrained system similar to its classical version. We found a nontrivial Lagrangian description, where we select $a=2$ for the free parameter $a$ in the supersymmetric extension. The corresponding degenerate Lagrangian requires an exclusive consideration and the utilization of the Dirac-Bergmann algorithm. We explicitly determined the full set of primary and secondary constraints and constructed the total Hamiltonian governing the dynamics of the system. In this analysis, in addition to a nontrivial constraint involving the fermionic fields, the consistency conditions give rise to a nonlocal contribution to the Hamiltonian density. This highlights a distinctive feature of this supersymmetric extension. We showed that the resulting Hamilton equations of motion reproduce the supersymmetric KdV system in the component form. Finally, we derived a compact superspace representation of the Hamiltonian and demonstrated its consistency with the component-level formulation.

We consider three-dimensional Einstein gravity in Euclidean signature with a finite boundary of torus topology endowed with an induced metric of fixed conformal class and a constant trace of extrinsic curvature $K$. For vanishing, positive, and negative cosmological constant $Λ$, we analytically determine boundaries enclosing different patches of locally flat, de Sitter (dS$_3$), and Anti-de Sitter (AdS$_3$) spaces. We find solutions that depend non-trivially on either cycle of the torus, noting that some of them exhibit self-intersections. Adapting the Gibbons-Hawking prescription of interpreting the Euclidean gravitational path integral as a thermal partition function, we explore the rich semi-classical thermodynamic phase space of the problem. While most saddles are found to be either thermally unstable or metastable compared to those with uniform boundaries, we find inhomogeneous solutions that are thermodynamically favourable in the case of $Λ< 0$ and $2<K|Λ|^{-1/2}<3/\sqrt{2}$. Moreover, for all values of $Λ$, there exist patches of space with a non-contractible thermal circle and a macroscopic entropy. We further analyse the problem in both the AdS$_3$ boundary limit and the stretched dS$_3$ horizon limit, and comment on a recasting of the problem in terms of classical strings.

We consider the phase ordering problem for the low-temperature Ising dynamics initialized from a biased and disordered initialization. Work of Fontes, Schonmann, Sidoravicius (2002) showed that at zero-temperature, Ising Glauber dynamics on $\mathbb Z^d$ for $d\ge 2$ initialized from i.i.d. spins on each vertex that are $+1$ with sufficiently large probability, absorbs into the all-plus configuration quickly. We prove that analogous behavior holds throughout the low-temperature regime of the Ising model in two dimensions. Namely, there exists $p_0 <1$ such that Ising Glauber dynamics initialized from i.i.d. spins that are $+1$ with probability $p>p_0$, run at any low temperature $β>β_c$ converges rapidly to the plus phase measure $π^+$. The result is proved using a spacetime multiscale coupling valid in any $d\ge 2$, that boosts a uniform-in-$β$ quasi-polynomial bound on the mixing time of Ising dynamics with plus boundary conditions, into rapid phase ordering from biased initializations with no boundary conditions.

Asteroseismology is the study of resonant oscillations of stars to infer their internal structure and dynamics. It is also a powerful tool for precisely determining stellar parameters such as mass, radius, surface gravity, and age. The ongoing TESS mission, with its nearly complete sky coverage, presents a unique opportunity to uniformly probe stellar populations across the Milky Way. TESS is estimated to have observed more than 300,000 oscillating red giants, most of which have one to two months of observations. Given the scale of this dataset, we need a fast, efficient, and robust way to analyse the data. In this work, our objective is to develop a machine learning (ML) based method to infer asteroseismic parameters from short-duration observations. Specifically, we focus on two global seismic parameters, the large frequency separation ($Δν$) and the frequency at maximum power ($ν_{\mathrm{max}}$), from one-month-long TESS observations of red giants. Meanwhile, for K2 data, our focus extends to inferring the period spacings of dipolar gravity modes ($ΔΠ_{1}$), in addition to $Δν$ and $ν_{\mathrm{max}}$. Our findings demonstrate that our machine learning algorithm can accurately infer $Δν$ and $ν_{\mathrm{max}}$ for approximately 50% of samples created by taking one-month Kepler and K2 observations. For TESS one sector data however, we recover reliable $Δν$ for only about 23% of the stars. Additionally, we get reliable $ΔΠ_{1}$ inferences for about 200 young red-giants from K2. For these $ΔΠ_{1}$ inferences, we see a good match with the well known $Δν-ΔΠ_{1}$ degenerate sequence observed in Kepler red-giants.

Hidden multipolar orders in spin-orbit-coupled Mott insulators provide a promising setting for correlated quantum matter, yet their control and detection remain major challenges. Here, we demonstrate that circularly polarized light enables both in $4d^2/5d^2$ systems with edge-sharing octahedra. Using a Floquet Schrieffer-Wolff expansion of a driven Hubbard-Kanamori model, we derive a low-energy multipolar Hamiltonian with two qualitatively new light-driven terms. One is an effective static field that couples linearly to the magnetic octupole, realizing an octupolar inverse Faraday effect. The other is a bond-dependent anisotropic exchange interaction absent in equilibrium. These two couplings are the key result of this work: the first provides a direct optical handle on hidden octupolar order, while the second reorganizes the multipolar exchange landscape and opens an enlarged Kitaev-like multipolar liquid regime. Their interplay produces a nonequilibrium multipolar phase space inaccessible in equilibrium, enabling optical tuning among antiferro-octupolar, ferro-octupolar, partially polarized ferro-quadrupolar, Ising octupolar, and multipolar liquid phases. We further show that the induced multipolar order couples to the lattice, generating reversible trigonal and tetragonal distortions that provide structural fingerprints in pump-probe experiments. Our work establishes a general mechanism for the optical generation, control, and detection of hidden multipolar quantum states.

This paper presents a time domain (TD) formulation for modeling the transient electromagnetic response of two-dimensional (2D) metasurfaces using the Method of Auxiliary Sources (MAS) combined with the Generalized Sheet Transition Condition (GSTC). In the proposed approach, the frequency-domain impedance type GSTC is transformed into a causal, convolution-based TD representation and integrated within the MAS formulation. rfaces.

In his 1976 paper "More about the massive Schwinger model", Coleman introduced $1+1$-dimensional Quantum Electrodynamics coupled to two charged massive fermions. By applying Abelian bosonization, he elucidated much of the physics of this two-flavor Schwinger model, but he listed three puzzles at the end of his paper. We present new analytical and numerical calculations to solve Coleman's three puzzles and thereby deepen our understanding of this model. These puzzles pertain to the theory with equal fermion masses at $θ= 0$ and at $θ= π$, as well as the size of isospin-breaking effects when the fermion masses are unequal. For the puzzle at $θ= π$, the solution is related to the structure of the zero-temperature phase diagram arXiv:2305.04437: for equal fermion masses $m$, the model exhibits spontaneous breaking of charge conjugation symmetry and absence of confinement for any value of the gauge coupling $g$, so that there is a smooth interpolation from weak to strong coupling. Using two-loop Renormalization Group and integrability methods, we show that the mass gap behaves as $\sim m e^{-0.111 g^2/m^2}$ in the strong coupling regime $m\ll g$. Our numerical results using the lattice Hamiltonian are in good agreement with this behavior. For the puzzle at $θ= 0$, the solution is related to a level crossing between two isosinglet particles with different discrete quantum numbers; we demonstrate the necessity of such a crossing by comparing integrability and weak coupling calculations, and we also exhibit the crossing numerically. Finally, we provide a new estimate for the size of isospin-breaking effects caused by different fermion masses at strong coupling.

A powerful means to understanding condensed matter that possesses a multi-constituent, non-isolated, and complex nature, with a preeminent example being two-dimensional (2D) materials, is studying many-body interactions. However, experimentally observing high-order many-body interactions is a daunting task due to its heavy reliance on the abundance of low-order complexes. Here, we report the observation of four-body hot biexcitons in an energetically unfavorable bilayer of tungsten disulfide (WS2) through creating extreme optical confinement. Specifically, we integrate a non-radiative bound state in the continuum (BIC) into a photonic crystal (PhC) defect cavity, forming a quasi-three-dimensional (q-3D) but open confinement for photons at the driving frequency. The extremely confined photons in both reciprocal and physical spaces then excite inherently unproductive two-body hot excitons situated slightly above the indirect bandgap so efficiently that they form overwhelmed higher-order four-body hot biexcitons. Distinctively, these hot biexcitons exhibit substantial valley polarization and coherence at room temperature, which we attribute to the topological nature of BICs and the associated q-3D confinement with an orbital angular momentum. Besides achieving room-temperature biexcitons, the q-3D confinement could be valuable for higher-order interactions, such as triexcitons, and many other many-body phenomena, including Bose-Einstein condensation.

The celebrated Kronig-Penney model traditionally has been formulated with square well potentials representing atomic centres. Here, we use a slightly more realistic potential, the truncated harmonic oscillator, in lieu of square well potentials, and solve the model analytically. We derive the energy dispersion and wave functions for this model. This configuration has some important similarities and differences compared to the usual model. In particular, we write the governing equation in a form suggestive of the tight-binding approximation, as can be done for the usual model. In this way, it is straightforward to derive an expression for the tunneling amplitude used in tight-binding in terms of the harmonic oscillator potential parameters.

Driven nonlinear quantum oscillators are a central platform for quantum technologies, yet their dissipative dynamics are typically described using Lindblad or Caldeira-Leggett master equations derived under assumptions that exclude nonlinearities and driving. Here, we derive a generalized Caldeira-Leggett master equation for driven nonlinear oscillators by retaining the full nonlinear and time-dependent system dynamics in the construction of the dissipator. For position- and momentum-dependent system-bath coupling, the dissipator itself becomes dynamically dressed, generating nonlinear and drive-dependent dissipative channels beyond conventional fixed-dissipator approaches. This produces nonlinear damping together with dissipation-induced corrections to the effective drive. The resulting dissipative dynamics suppress large-amplitude excitations and reduce phase-space fluctuations. For a driven Kerr oscillator, this leads to the suppression of bistability, asymmetric resonance responses, and strongly modified fluctuation distributions. More broadly, our results establish a microscopic framework in which nonlinear dynamics and driving directly reshape the dissipative sector of driven open quantum systems.

To be useful, quantum computers will be required to successfully correct errors occurring at the hardware level. Bosonic codes provide a hardware-efficient option for error correction, but fault-tolerance further requires that the available gate interactions be compatible with the code. A promising bosonic code is the Gottesman-Kitaev-Preskill (GKP) code, for which a linear beamsplitter-like coupling between two bosonic modes is fault-tolerant, making this a key primitive for building larger systems. Here, using two motional modes of a trapped ion, we demonstrate the generation of entangled states of GKP qubits by interfering two qunaught states, which have a grid structure but carry no logical information, on a beamsplitter. We generate all four Bell states with an average fidelity of 69%, and subsequently demonstrate an extension of the entangled state lifetime through the use of quantum error correction. These results complete the set of Gaussian operations required for quantum computing with GKP codes and enable explorations of multi-mode bosonic encodings as well as fundamental tests of information channels.

We prove that the KSGNS construction can be viewed as an endofunctor on a category whose objects are positive $C^*$-correspondences from a fixed $C^*$-algebra and morphisms are given by intertwiners which account for automorphisms of the fixed $C^*$-algebra. Using this perspective, we provide a functorial perspective for strict positive equivariant $C^*$-correspondences of $C^*$-dynamical systems and show every strict positive equivariant $C^*$-correspondence of $C^*$-dynamical systems unitarily uniquely dilates under the KSGNS construction to an equivariant $C^*$-correspondence of the dynamical systems.

I present the Spitzer Spectroscopic Data Fusion, a collection of merged spectroscopic redshift catalogs covering fourteen of the most widely studied extragalactic survey fields. Building on the Spitzer Data Fusion multi-wavelength photometric database, the collection merges several publicly available spectroscopic redshift catalogs within each field using a 1 arcsec matching radius, delivers a single best redshift per source together with provenance and overlap flags, and is available on Zenodo at https://zenodo.org/doi/10.5281/zenodo.6368347 The dataset is regularly updated as new spectroscopic surveys are published. It is intended as a community calibration resource for photometric redshift training, SED fitting, and multi-wavelength cross-identification studies.

In the heavy-quark and large-energy limits, symmetry relations reduce the number of independent form factors governing heavy-to-light $B$-meson decays. Exploiting these relations, the form factors can be parametrized while systematically incorporating symmetry-breaking corrections from perturbative QCD. Using vertex renormalization together with light-cone distribution amplitudes, we compute the vertex and hard-spectator contributions for the $B \to K_0^*(1430)$ transition. We then analyze the impact of these form factors on physical observables, including the branching ratio and lepton polarization asymmetries $(P_L, P_N)$, in $B \to K_0^*(1430)μ^+μ^-$. Our results indicate that perturbative corrections induce modest shifts of $\sim 3\%$ in both the branching ratio and the normal lepton polarization asymmetry. Consequently, any significant deviation observed experimentally from these predictions would provide a clear signal of potential New Physics effects.

The [$^{12}$C II] emission at 158 $μ$m is a key cooling line of the interstellar medium and traces gas kinematics in spectrally resolved observations. Its spectral profile is often modified by optical depth effects. The intrinsic line shape can be reconstructed by comparison with emission from the less abundant $^{13}$C isotope. Due to the additional neutron spin, [$^{13}$C II] emission splits into three hyperfine structure (hfs) transitions. Laboratory measurements have provided the centroid frequency and the strongest component ($F=2-1$); the two weaker components ($F=1-0$ and $F=1-1$) have been inferred only from quantum-mechanical calculations. The magnetic-dipole hfs constants, from which the transition frequencies follow, have not been measured experimentally. The high spectral resolution of observations with the upgraded German Receiver for Astronomy at Terahertz Frequencies (upGREAT) on board SOFIA enabled simultaneous detection of all three hfs transitions. From these astronomical data we determine, for the first time, the magnetic-dipole hfs constants $A_{1/2}^{\rm hf} = 810.71(11)$ MHz and $A_{3/2}^{\rm hf} = 162.18(5)$ MHz of the [$^{13}$C II] $2s^2\,2p\,{}^2P^\circ$ ground term. Combined with the laboratory centroid frequency, this yields the rest frequencies of all three hfs lines. Using [$^{12}$C II] as a reference, we also improve the precision of the [$^{13}$C II] centroid frequency. This work shows that spectrally resolved astronomical observations can constrain fundamental atomic properties, with hfs precision rivaling laboratory measurements. The approach extends to other atomic and molecular transitions where laboratory data are difficult to obtain.

We consider quantum gravity corrections to the maximum entropic force that arise from several gravitational uncertainty principles. These include the Generalized Uncertainty Principle (GUP), the Extended Uncertainty Principle (EUP), the Generalized Extended Uncertainty Principle (GEUP), and the Linear-Quadratic GUP (LQGUP). We find that the modified entropic force depends on the dimensionless parameters of the uncertainty principles and, thus, on the underlying quantum gravity theory. Furthermore, the entropic force, which is quantum gravity corrected in the framework of the extended uncertainty principles, also depends on the number of Planck areas that made the ``EUP area".

A promising approach to achieving scalable fault-tolerant quantum computation is the use of quantum error correction (QEC) codes augmented with magic states i.e. resource states produced via distillation, cultivation, or $R_z$ synthesis and teleported into the circuit as needed. Because magic-state production dominates the space-time volume of fault-tolerant programs, system architects must decide how many production units to allocate. Current approaches rely on deterministic analysis that either provisions for worst-case peak demand (wasting valuable qubit resources on factories that are never simultaneously utilized) or assumes average demand, which increases execution time. In this work, we build a simulation framework that couples circuit scheduling with different stochastic magic state production models, and use it to quantify the impact of non-determinism on circuit execution. We show that non-determinism has a dual effect that deterministic models cannot capture: it inflates total execution time (the price), while deflating peak per-cycle resource demand (the payoff). For distillation-based architectures, this demand smoothing shifts the space-time-optimal provisioning point: fewer factories are needed to minimize space-time volume than deterministic analysis predicts. Across benchmarks, stochastic-aware provisioning reduces space-time volume by up to 27% compared to the deterministic optimum for distillation, while requiring up to 30% fewer factories. We characterize these effects across each preparation mechanism, map the resulting design-space tradeoffs, and demonstrate that static resource estimation systematically mis-characterizes the cost of fault-tolerant execution. Our results establish that stochastic-aware analysis is necessary for right-sizing the factory allocations and should replace deterministic heuristics as the standard methodology for FTQC resource planning.

Turbulence is a phenomena that is {\it locally} and statistically characterized by measurements, but it is caused by {\it nonlocal} energy cascades associated with the environment. The presence of turbulence coincides with fluctuations in the refractive index, which impact optical sensing, imaging, and signaling applications. Here, we study the machine learning models that predict near-surface optical turbulence strength $C_n^2$, derived from anemometer-based surface flux measurements through Monin-Obukhov similarity theory, using ERA5 reanalysis data as model inputs. We evaluate the model's ability to perform temporal extrapolation by training on one year of co-located $C_n^2$ observations and ERA5 data, and applying the model to ERA5 data from other years at the same site to reconstruct a multi-year time series. We compare the predictions across Southern California and New York. In spite of varying weather and terrain, the ML models show consistent performance and seasonal behavior across training years. All models show greater correlation, faster convergence, and lower prediction errors in the summer. However, some ERA5 features drive predictions in New York but not California and vice versa, and such feature dependence depends on the season. Seasonal error and feature trends suggest that turbulence is affected by atmospheric composition or other seasonal environmental considerations that are not currently monitored by ERA5. We find, regardless of terrain, the primary feature of importance to turbulence prediction is solar radiation, which underlines the central role of radiative energy transfer in driving atmospheric turbulence. We point toward physics-informed ML translation and feature selection as tools for improving the generalizability of data-driven models.

These notes introduce the theory of susceptibilities as developed in [arXiv:2504.18274, arXiv:2601.12703] for interpreting neural networks. The susceptibility of an observable $ϕ$ to a data perturbation is defined as a derivative of a posterior expectation, which by the fluctuation--dissipation theorem equals a posterior covariance. Different choices of $ϕ$ yield different objects: per-sample losses give the influence matrix (the Bayesian influence function of [arXiv:2509.26544]), while component-localized observables give the structural susceptibility matrix that pairs model components with data patterns. The susceptibility matrix is (up to a factor of $nβ$) the Jacobian of the map from data distributions to structural coordinates; its pseudo-inverse provides a linearized solution to the patterning problem of [arXiv:2601.13548]: finding data perturbations that produce a desired structural change. We motivate the theory from its statistical-mechanical foundations, then give a detailed exposition of susceptibilities, their empirical estimators, and their connection to the geometry of the loss landscape.

In the black hole star (BH*) model, the characteristic "V"-shaped SED of LRDs is produced by an accreting BH embedded in a dense neutral-gas envelope with a near-unity covering factor. This envelope reprocesses radiation and emits as a ~5,000K blackbody, producing the optical continuum. Meanwhile, the UV is powered by a low-mass, dust-free, metal-poor host. The BH* scenario is promising, but it has yet to undergo detailed testing; conducting a self-consistent UV-to-optical spectral-fitting analysis of LRDs would provide a robust assessment of the model. In this work, we test the BH* scenario by fitting the full JWST/NIRSpec PRISM spectrum of The Cliff ($z_{spec}=3.55$), an LRD that played a pivotal role in the development of this model. A Bagpipes fit that allows stellar, nebular, AGN, and blackbody components naturally yields a BH*-like solution for The Cliff, even with broad priors. Our method allows us to characterize its host, despite remaining unresolved in JWST imaging. From the continuum, we infer the host to be low-mass (log $M_\star/M_\odot$~7.7), star-forming, metal-poor, affected by non-negligible dust attenuation ($A_V$~0.5 mag) acting on both stellar and nebular components. Larger $M_\star$ (up to log $M_\star/M_\odot$~8.1) and attenuations (up to $A_V$~1 mag) are obtained depending on the assumed dust attenuation law. Modest AGN UV leakage is consistently allowed by the code, but remains weak and not robustly constrained, with both AGN+host and host-dominated UV scenarios yielding equivalent fits. The star formation history of the host is relatively smooth, with the galaxy already assembling log $M_\star/M_\odot$~7 about 200 Myr before $z_{spec}=3.55$. The BH-to-$M_\star$ ratio exceeds the values expected from BH-host scaling relations, especially at recent times. This tension may indicate either inaccurate estimates of the BH properties or non-coeval BH-host evolution.

Acoustic droplet vaporization denotes the phase-change of micron- and sub-micron-sized droplets upon the application of high-amplitude ultrasound. The asymmetric collapse of the incepted vapor bubbles within the droplets can give rise to high-speed liquid microjets. Here, we describe acoustically-driven and bubble-pair jetting arising within the vaporizing droplet, observed experimentally with ultra-high-speed imaging at the microscale. The existence of complex pressure fields due to the continued acoustic wave-droplet interaction and the nucleation of multiple bubbles within the droplet leads to rich dynamics, with the jets presenting behavioral self-similarity to millimetric bubbles under comparable conditions. Evaporative instabilities that develop during bubble growth impede jet formation during bubble collapse. Furthermore, the ability of the jets to pierce the droplet interface and penetrate into the surrounding fluid is discussed. These powerful microjets could be harnessed to induce cell permeabilization for targeted drug delivery and treatment of cancerous tissue.

Extreme sudden changes in the flow of accreting gas onto SMBHs manifest themselves via large-amplitude continuum variability and changes to broad Balmer emission profiles, driving changing-look AGN. X-ray flux monitoring with SRG/eROSITA revealed that in the Seyfert AGN HE 1237-2252 the soft X-ray flux dipped abruptly, by a factor of 17 within 18 months. We initiated a follow-up campaign that caught the luminosity recovery after the dip, and enabled us to study how the various accretion components responded during this flux recovery. Our campaign included multiband photometry, X-ray spectroscopy, and optical spectroscopy. We tracked as the accretion rate relative to Eddington increased by a factor of 7 in 3 years. Based on broad Hbeta variability, HE 1237-2252 was subtype 1.0-1.2 in 2002, transitioned to subtype 1.8 by the time of the luminosity dip, and then transitioned back to subtype 1.0 within 3 months as luminosity recovered. Both transitions saw broad Hbeta integrated line flux change by factors of 4-6. The broad Balmer profile is decomposed into a broad Gaussian consistent with virialized gas at 27+/-3 lt-dy, plus a double-peaked profile, consistent with a diskline structure at more than roughly 5 lt-dy. The diskline component's relative contribution to the total profile increases as continuum flux rises. The lack of obscuration in the X-ray spectra, as well as the IR continuum dip, point to an intrinsic pause in the accretion rate as opposed to variable line-of-sight obscuration. Candidates for the underlying mechanisms include propagating cold and warm fronts in the accretion disk. The increased prominence of the diskline BLR component's emission could be due to evolution in the physical extent of the X-ray corona, and in the fraction of >13.6 eV photons intercepted by the diskline, as the accretion rate increases.