Recent experiments in moiré quantum materials exhibit quantized Hall states without an external magnetic field, motivating continuum mechanisms based on smooth moiré-periodic pseudospin textures. We present a controlled theory of skyrmion Chern bands generated by such textures. An exact local $SU(2)$ transformation reveals an emergent non-Abelian gauge field; for large branch splitting we perform an operator-level Schrieffer-Wolff expansion, yielding a single-branch Hamiltonian together with systematically dressed physical operators that define the projected interacting theory beyond strict adiabaticity. The leading dynamics is governed by a $U(1)$ Berry connection whose flux is set by the skyrmion density, while controlled non-adiabatic corrections are fixed by the texture's real-space quantum geometric tensor. In a Landau-level representation built from the averaged emergent field, moiré-periodic modulations induce Umklapp-resolved deformations of Girvin-MacDonald-Platzman kinematics and microscopic sources of excess optical quantum weight above the topological lower bound. Assuming a gapped Hall phase, we further derive a skyrmion-crystal effective field theory with a universal Berry-phase term and a noncommutative magnetophonon. Our results provide experimentally accessible signatures for twisted transition-metal dichalcogenide homobilayers and rhombohedral graphene aligned with hexagonal boron nitride.

TouchFusion is a wristband that enables touch interactions on nearby surfaces without any additional instrumentation or computer vision. TouchFusion combines surface electromyography (sEMG), bioimpedance, inertial, and optical sensing to capture multiple facets of hand activity during touch interactions. Through a combination of early and late fusion, TouchFusion enables stateful touch detection on both environmental and body surfaces, simple surface gestures, and tracking functionality for contextually adaptive interfaces as well as basic trackpad-like interactions. We validate our approach on a dataset of 100 participants, significantly exceeding the population size of typical wearable sensing studies to capture a wider variance of wrist anatomies, skin conductivities, and behavioral patterns. We show that TouchFusion can enable several common touch interaction tasks. Using TouchFusion, a wearer can summon a trackpad on any surface, control contextually adaptive interfaces based on where they tap, or use their palm as an always-available touch surface. When paired with smart glasses or augmented reality devices, TouchFusion enables a ubiquitous, contextually adaptive interaction model.

Given a finitely generated group $Γ$ and $g\inΓ$, we prove sufficient conditions in terms of various growth/decay functions for freeness of the action of $g$ on the Furstenberg boundary of $Γ$. In this context, we also give a description of the support of stationary states on the reduced C*-algebra of $Γ$.

Individual-level epidemic models are increasingly being used to help understand the transmission dynamics of various infectious diseases. However, fitting such models to individual-level epidemic data is challenging, as we often only know when an individual's disease status was detected (e.g., when they showed symptoms) and not when they were infected or removed. We propose an autoregressive coupled hidden Markov model to infer unknown infection and removal times, as well as other model parameters, from a single observed detection time for each detected individual. Unlike more traditional data augmentation methods used in epidemic modelling, we do not assume that this detection time corresponds to infection or removal or that infected individuals must at some point be detected. Bayesian coupled hidden Markov models have been used previously for individual-level epidemic data. However, these approaches assumed each individual was continuously tested and that the tests were independent. In practice, individuals are often only tested until their first positive test, and even if they are continuously tested, only the initial detection times may be reported. In addition, multiple tests on the same individual may not be independent. We accommodate these scenarios by assuming that the probability of detecting the disease can depend on past observations, which allows us to fit a much wider range of practical applications. We illustrate the flexibility of our approach by fitting two examples: an experiment on the spread of tomato spot wilt virus in pepper plants and an outbreak of norovirus among nurses in a hospital.

The frequency-dependent complex optical conductivity reflects key properties of superconductors, such as the energy gap in the density of states (DOS) and the superfluid density. For disordered superconductors, the optical conductivity often can be described within Bardeen-Cooper-Schrieffer (BCS) theory, while in corresponding tunneling experiments, deviations in the observed DOS typically require modelling by the phenomenological Dynes formula. The implications of such Dynes DOS for optics were rarely discussed so far. Here we probe the terahertz conductivity of superconducting NbN thin films with thicknesses ranging from 4.5 to 20nm, which were grown by atomic layer deposition (ALD). Our frequency range from 0.3 to 2.1 THz covers energies below and above the spectral gap. For 20nm thick NbN, we find in the optical conductivity distinct deviations from the BCS model, including a step-like characteristic in the absorption at half the zero-temperature spectral gap. These observations can be fully captured by Dynes electrodynamics with a small and temperature-independent pair-breaking rate. For the other films, we also observe signs of Dynes electrodynamics, and we discuss the evolution of the energy gap, the superfluid density, and the pair-breaking rate as function of film thickness.

Cross-plane heat transport is a critical bottleneck for van der Waals (vdW) electronics, yet its microscopic governing principles remain elusive. We demonstrate that stacking order is an effective control knob for cross-plane phonon transport in multilayer Rhenium Disulfide (ReS2). Thickness-dependent thermal conductivity measurements reveal remarkably long cross-plane phonon mean free paths (MFPs) (>= 200-300 nm) and provide a direct experimental observation of the transition from quasi-ballistic transport to a thickness-independent ballistic limit. AA stacking exhibits nearly double the cross-plane thermal conductivity of AB stacking, driven by longer acoustic phonon lifetimes from a more "coherent" interlayer registry. Integrated deep neural-network molecular dynamics reveals that phonon filtering in ReS2 is fundamentally frequency-selective: weak vdW coupling acts as a low-pass filter, whereas stronger coupling broadens the transmission passband. These results establish ReS2 as a model system where stacking order and interlayer coupling can be engineered to tune heat conduction across diffusive, quasi-ballistic, and ballistic regimes, offering a new framework for thermal management in 2D electronics.

We propose ALiA, a novel adaptive variant of the alternating direction method of multipliers (ADMM). Specifically, ALiA is a variant of function-linearized proximal ADMM (FLiP ADMM), which generalizes the classical ADMM by leveraging the differentiable structure of the objective function, making it highly versatile. Notably, ALiA features an adaptive stepsize selection scheme that eliminates the need for backtracking linesearch. Motivated by recent advances in adaptive gradient and proximal methods, we establish point convergence of ALiA for convex and differentiable objectives. Furthermore, by introducing negligible computational overhead, we develop an alternative stepsize selection scheme for ALiA that improves the convergence speed both theoretically and empirically. Extensive numerical experiments on practical datasets confirm the accelerated performance of ALiA compared to standard FLiP ADMM. Additionally, we demonstrate that ALiA either outperforms or matches the practical performance of existing adaptive methods across problem classes where it is applicable.

The unitary coupled cluster (UCC) algorithm is one of the most promising implementations of the variational quantum eigensolver for quantum computers. However, for large systems, the number of UCC factors leads to deep quantum circuits, which are prohibitive for execution on quantum hardware. To address this, circuit depth can be reduced at the cost of more measurements with a Taylor series expansion of UCC factors with small angles, while treating the large-angle factors exactly. We implement this approach to quadratic order (qUCC) for systems with strong correlations and systems where conventional methods like coupled cluster (CC) with low excitation levels fail, but UCC and qUCC perform well. We study hydrogen chains and the BeH2 molecule that allow us to change the degree of strong correlation due to geometrical distortions. We show, via a dramatic increase in number of factors able to handle exactly, a systematic convergence of these results as more exact UCC factors are included in the calculations -- the hardest to converge regime is in the crossover from weak to strong coupling. In all cases the total number of UCC factors needed to be treated exactly is much less than the total number of UCC factors available (typically about one-third to one-half of the total number of factors).

A random geometric graph (RGG) with kernel $K$ is constructed by first sampling latent points $x_1,\ldots,x_n$ independently and uniformly from the $d$-dimensional unit sphere, then connecting each pair $(i,j)$ with probability $K(\langle x_i,x_j\rangle)$. We study the sharp detection threshold, namely the highest dimension at which an RGG can be distinguished from its Erdős--Rényi counterpart with the same edge density. For dense graphs, we show that for smooth kernels the critical scaling is $d = n^{3/4}$, substantially lower than the threshold $d = n^3$ known for the hard RGG with step-function kernels \cite{bubeck2016testing}. We further extend our results to kernels whose signal-to-noise ratio scales with $n$, and formulate a unifying conjecture that the critical dimension is determined by $n^3 \mathop{\rm tr}^2(κ^3) = 1$, where $κ$ is the standardized kernel operator on the sphere. Departing from the prevailing approach of bounding the Kullback-Leibler divergence by successively exposing latent points, which breaks down in the sublinear regime of $d=o(n)$, our key technical contribution is a careful analysis of the posterior distribution of the latent points given the observed graph, in particular, the overlap between two independent posterior samples. As a by-product, we establish that $d=\sqrt{n}$ is the critical dimension for non-trivial estimation of the latent vectors up to a global rotation.

We study the hyperbolic defocusing sinh-Gordon model with parameter $β^2>0$ and its associated Gibbs dynamics on the two-dimensional torus. We establish global well-posedness of the model for a certain range of parameters $β^2>0$ with the corresponding Gibbs measure initial data and prove invariance of the Gibbs measure under the flow, thereby resolving a question posed by Oh, Robert, and Wang (2019). Our physical space approach hinges on developing a novel $L^\infty$-based well-posedness theory for wave equations with exponential-type nonlinearities, going beyond the classical $L^2$-based framework. This refinement allows us to fully leverage structural properties of Gaussian multiplicative chaos. As a by-product of our method, we also obtain an improved well-posedness theory for the hyperbolic Liouville model.

ISRO's terrain characterization and hazard mapping from Chandrayaan-2 Orbiter High Resolution Camera (OHRC) stereo imagery were central to the safe landing of Chandrayaan-3 - the first successful landing in the lunar south polar region. However, these elevation products were generated with a proprietary pipeline and have not been publicly released. We present a 0.30 m/pixel digital elevation model (DEM) of the Chandrayaan-3 Vikram landing site using a fully open workflow based on ISIS, the Ames Stereo Pipeline, and ALE, achieving sub-meter resolution comparable to mission-reported products. The reconstruction covers 2.18 x 2.24 km with 91.2% valid pixel coverage, 8.1 cm median triangulation error, and 40-50 cm relative vertical precision. The Vikram lander and Pragyan rover are individually resolved. Geodetic alignment to an LROC NAC stereo DEM achieves approximately 30 m horizontal accuracy; pixel-wise validation at 3 m resolution confirms negligible vertical bias (median dz = +0.28 m) and robust dispersion (NMAD = 2.88 m). Stable OHRC stereo convergence requires Community Sensor Model (CSM) camera models; the legacy ISIS camera model failed across two independent sites. At 0.30 m, these DEMs complement LROC NAC DTMs (approximately 1 m), resolving sub-meter hazards below the NAC detection threshold. Applied to the extensive OHRC south polar archive, this methodology provides independent capability for hazard mapping and landing site analysis for upcoming missions including Chandrayaan-4, LUPEX, and Artemis.

A fascinating effect belonging to the field of vacuum forces and fluctuations is that of quantum friction. It refers to the prediction of a dissipative force acting on a moving object due to the quantum vacuum field. In this work, we investigate rotational quantum friction where a diatomic polar molecule rotates around its own center of mass in free space. We quantize the rotational motion and investigate the resulting dissipation due to spontaneous decay. We find in the Markovian regime that a friction torque $\propto Ω^3$ persists even for zero temperature, and in agreement with the classical result in the limit of large rotational quantum number $l$. Within the non-Markovian short-time regime we find a friction $\proptoΩ$.

Huntington's disease (HD) is an autosomal dominant neurodegenerative disorder characterized by motor dysfunction, psychiatric disturbances, and cognitive decline. The onset of HD is marked by severe motor impairment, which may be predicted by prior cognitive decline and, in turn, exacerbate cognitive deficits. Clinical data, however, are often collected at discrete time points, so the timing of disease onset is subject to interval censoring. To address the challenges posed by such data, we develop a joint model for multivariate longitudinal biomarkers with a change point anchored at an interval-censored event time. The model simultaneously assesses the effects of longitudinal biomarkers on the event time and the changes in biomarker trajectories following the event. We conduct a comprehensive simulation study to demonstrate the finite-sample performance of the proposed method for causal inference. Finally, we apply the method to PREDICT-HD, a multisite observational cohort study of prodromal HD individuals, to ascertain how cognitive impairment and motor dysfunction interact during disease progression.

This paper undertakes the study of the topology of T-manifolds of arbitrary codimension obtained by combinatorial patchworking with real phase structure as described by Brugallé, López de Medrano and Rau (2024). We prove new bounds on the number of connected components of T-curves and T-surfaces. For sufficiently high codimension, this improves the results of Brugallé, López de Medrano and Rau (2024). In addition, we present a new description of patchworking à la Viro for T-manifold of codimension 2. We use this method to construct a family of maximal real algebraic curves in $\mathbb RP^3$.

We present a model-based approach to learning robust runtime monitors for autonomous systems. Runtime monitors play a crucial role in raising the level of assurance by observing system behavior and predicting potential safety violations. In our approach, we propose to capture a system's (stochastic) behavior using interval Hidden Markov Models (iHMMs). The monitor then uses this learned iHMM to derive risk estimates for potential safety violations. The paper makes three key contributions: (1) it provides a formalization of the problem of learning robust runtime monitors, (2) introduces a novel framework that uses conformance-testing-based refinement for learning robust iHMMs with convergence guarantees, and (3) presents an efficient monitoring algorithm for computing risk estimates over iHMMs. Our empirical results demonstrate the efficacy of monitors learned using our approach, particularly when compared to model-free monitoring approaches that rely solely on collected data without access to a system model.

The Quantum Approximate Optimization Algorithm (QAOA) is a leading approach for combinatorial optimization on near-term quantum devices, yet its scalability is limited by the difficulty of optimizing \(2p\) variational parameters for a large number \(p\) of layers. Recent empirical studies indicate that optimal QAOA angles exhibit concentration and transferability across problem sizes. Leveraging this observation, we propose a schedule-learning framework that transfers spectral-gap-informed adiabatic control strategies from small-scale instances to larger systems. Our method extracts the spectral gap profile of small problems and constructs a continuous schedule governed by \(\partial_t s = κg^q(s)\), where \(g(s)\) is the instantaneous gap and \((κ, q)\) are global hyperparameters. Discretizing this schedule yields closed-form expressions for all QAOA angles, reducing the classical optimization task from \(2p\) parameters to only \(2\), independent of circuit depth. This drastic parameter compression mitigates classical optimization overhead and reduces sensitivity to barren plateau phenomena. Numerical simulations on random QUBO and 3-regular MaxCut instances demonstrate that the learnt schedules transfer effectively to larger systems while achieving competitive approximation ratios. Our results suggest that gap-informed schedule transfers provide a scalable and parameter-efficient strategy for QAOA.

Multi-static backscatter networks (BNs) are strong candidates for joint communication and localization in the ambient IoT paradigm for 6G. Enabling real-time localization in large-scale multi-static deployments with thousands of devices require highly efficient algorithms for estimating key parameters such as range and angle of arrival (AoA), and for fusing these parameters into location estimates. We propose two low-complexity algorithms, Joint Range-Angle Clustering (JRAC) and Stage-wise Range-Angle Estimation (SRAE). Both deliver range and angle estimation accuracy comparable to FFT- and subspace-based baselines while significantly reducing the computation. We then introduce two real-time localization algorithms that fuse the estimated ranges and AoAs: a maximum-likelihood (ML) method solved via gradient search and an iterative re-weighted least squares (IRLS) method. Both achieve localization accuracy comparable to ML-based brute force search albeit with far lower complexity. Experiments on a real-world large-scale multi-static testbed with 4 illuminators, 1 multi-antenna receiver, and 100 tags show that JRAC and SRAE reduce runtime by up to 40X and IRLS achieves up to 500X reduction over ML-based brute force search without degrading localization accuracy. The proposed methods achieve 3 m median localization error across all 100 tags in a sub-6GHz band with 40 MHz bandwidth. These results demonstrate that multi-static range-angle estimation and localization algorithms can make real-time, scalable backscatter localization practical for next-generation ambient IoT networks.

We extend a recently developed three-dimensional semiclassical model [\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.033106}{Phys. Rev. \textbf{A} 109, 033106 (2024)}] to study multielectron ionization and the formation of highly excited Rydberg states in O$_{2}^+$ driven by intense infrared laser pulses. Our model fully accounts for the Coulomb interaction between all particles, except for the Coulomb repulsion between bound electrons which is replaced by effective potentials. This replacement overcomes the hurdle of artificial autoinization. In addition, the multielectron motion is treated on an equal footing with nuclear motion, that is, electrons and nuclei are both allowed to move at the same time. We focus on triple and double ionization as well as frustrated triple and double ionization. For these processes, we identify and explain the main features of the sum of the kinetic energies of the final ion fragments resulting from the break-up of O$_{2}^+$. We also describe a physical mechanism that underlies frustrated triple ionization.

Quantum electrodynamics (QED), the first relativistic quantum field theory, describes light-matter interactions at a fundamental level and is one of the pillars of the Standard Model (SM). Through the extraordinary precision of QED, the SM predicts the energy levels of simple systems such as the hydrogen atom with up to 13 significant digits, making hydrogen spectroscopy an ideal test bed. The consistency of physical constants extracted from different transitions in hydrogen using QED, such as the proton charge radius $r_\mathrm{p}$, constitutes a test of the theory. However, values of $r_\mathrm{p}$ from recent measurements of atomic hydrogen are partly discrepant with each other and with a more precise value from spectroscopy of muonic hydrogen. This prevents a test of QED at the level of experimental uncertainties. Here we present a measurement of the 2S-6P transition in atomic hydrogen with sufficient precision to distinguish between the discrepant values of $r_\mathrm{p}$ and enable rigorous testing of QED and the SM overall. Our result $ν^{}_{\text{2S-6P}}$ = 730,690,248,610.79(48) kHz gives a value of $r_\mathrm{p}$ = 0.8406(15) fm at least 2.5-fold more precise than from other atomic hydrogen determinations and in excellent agreement with the muonic value. The SM prediction of the transition frequency (730,690,248,610.79(23) kHz) is in excellent agreement with our result, testing the SM to 0.7 parts per trillion (ppt) and, specifically, bound-state QED corrections to 0.5 parts per million (ppm), their most precise test so far.

More than 150 measurements of the HeII 4686A emission line in spectra of SS433 were obtained during 388 nights in 2020-2025 with the Transient Double-beam Spectrograph on the 2.5 m telescope of Caucasian Mountain Observatory of Sternberg Astronomical Institute. We found that the HeII emission line formation region is not eclipsed and is significantly larger than both the donor star and the photosphere of the supercritical accretion disk. The HeII radial velocity curve was found to be independent of the precessional phase and inconsistent with the photometric curve. These findings suggest that the HeII line does not reflect the orbital motion of the compact object. Therefore, spectroscopic estimates of the masses of the components in SS433 based on the HeII emission line can be unrealistic.

The article deals with Gödel-like solutions in the context of Galilean gravity, a geometric formulation of non-relativistic gravitation defined on a five-dimensional Galilean manifold. Within this framework, non-relativistic matter fields admit a covariant description, while the physical Newtonian dynamics is recovered through an immersion into the usual $3+1$ spacetime. By adopting a Gödel-like metric ansatz and coupling the gravitational field to a Galilean fluid derived from a variational principle, we obtain a system of highly nonlinear and coupled field equations. Exact solutions are constructed by fixing the matter sector consistently with the field equations. The resulting configurations describe rotating non-relativistic universes and satisfy $D(x)>H(x)$ throughout the entire spatial domain. As a consequence, the associated Killing vector remains spacelike everywhere and no closed timelike curves arise.

The full lattices in a finite dimensional commutative ${\mathbb Q}$-algebra form a commutative semigroup. In the case of an algebraic number field the top part of a certain quotient semigroup is the class group. For a separable algebra some basic results, especially the Jordan-Zassenhaus theorem, are known for this quotient semigroup. This paper considers also algebras which are not separable. It studies the commutative semigroup of full lattices in such an algebra and also the quotient semigroup. This leads in this commutative, but not separable situation to a certain extension of the Jordan-Zassenhaus theorem. One application concerns $GL_n({\mathbb Z})$-conjugacy classes of regular integer $n\times n$ matrices.

We argue that for finite energy windows, the final states in gravitational scattering in dimension $d > 4$ are normalizable coherent states in Fock space. However, as the center of the energy window goes to infinity, black hole physics predicts that these states become orthogonal to every state with a finite number of particles. Given that the spectral measure in energy is determined by Poincare invariance, the S-matrix cannot be a unitary operator in Fock space, despite having finite matrix elements in Fock space, and satisfying perturbative unitarity, to all orders in string perturbation theory. We identify regimes in the BFSS matrix model\cite{bfss} and the definition of the S-matrix as the limit of CFT correlators\cite{polchsuss}, which point to the same conclusion. We review a scattering theory based on the quantum mechanics of a finite number of fermionic oscillators, whose algebra formally converges to the Super-Poincare covariant Awada-Gibbons-Shaw\cite{ags} algebra, and argue that a certain class of limiting states on that algebra satisfy all the properties required by physical unitarity in the algebraic formulation of quantum mechanics. The only missing ingredient for a consistent theory is a proof that the S matrix amplitudes themselves are Poincare invariant. We provide suggestive arguments, but no real proof, that this is so.

Given data $\{({\boldsymbol x}_i,y_i): i\le n\}$, with ${\boldsymbol x}_i$ standard $d$-dimensional Gaussian feature vectors, and $y_i\in{\mathbb R}$ response variables, we study the general problem of learning a model parametrized by ${\boldsymbol θ}\in{\mathbb R}^d$, by minimizing a loss function that depends on ${\boldsymbol θ}$ via the one-dimensional projections ${\boldsymbol θ}^{\sf T}{\boldsymbol x}_i$. While previous work mostly dealt with convex losses, our approach assumes general (non-convex) losses hence covering classical, yet poorly understood examples such as the perceptron and non-convex robust regression. We use the Kac-Rice formula to control the asymptotics of the expected number of local minima of the empirical risk, under the proportional asymptotics $n,d\to\infty$, $n/d\toα>1$. Specifically, we prove a finite dimensional variational formula for the exponential growth rate of the expected number of local minima. Further we provide sufficient conditions under which the exponential growth rate vanishes and all empirical risk minimizers have the same asymptotic properties (in fact, we expect the minimizer to be unique in these circumstances). We refer to this phenomenon as `rate trivialization.' If the population risk has a unique minimizer, our sufficient condition for rate trivialization is typically verified when the samples/parameters ratio $α$ is larger than a suitable constant $α_{\star}$. Previous general results of this type required $n\ge Cd \log d$. We illustrate our results in the case of non-convex robust regression. Based on heuristic arguments and numerical simulations, we present a conjecture for the exact location of the trivialization phase transition $α_{\text{tr}}$.

We introduce the proximal Galerkin (PG) method for non-symmetric variational inequalities. The proposed approach is asymptotically mesh-independent and yields constraint-preserving approximations. We present both a conforming PG formulation and a hybrid mixed first-order system variant (FOSPG). We establish optimal a priori error estimates for each variant, which are verified numerically. We conclude by applying the method to American option pricing, free boundary problems in porous media, advection-diffusion with a semipermeable boundary, and the enforcement of discrete maximum principles.

Challenge the Champ is a simple tournament format, where an ordering of the players -- called a seeding -- is decided. The first player in this order is the initial champ, and faces the next player. The outcome of each match decides the current champion, who faces the next player in the order. Each player also has a popularity, and the value of each match is the popularity of the winner. Value maximization in tournaments has been previously studied when each match has a deterministic outcome. However, match outcomes are often probabilistic, rather than deterministic. We study robust value maximization in Challenge the Champ tournaments, when the winner of a match may be probabilistic. That is, we seek to maximize the total value that is obtained, irrespective of the outcome of probabilistic matches. We show that even in simple binary settings, for non-adaptive algorithms, the optimal robust value -- which we term the \textsc{VnaR}, or the value not at risk -- is hard to approximate. However, if we allow adaptive algorithms that determine the order of challengers based on the outcomes of previous matches, or restrict the matches with probabilistic outcomes, we can obtain good approximations to the optimal \textsc{VnaR}.

We investigate the nematic phase transition in the Heisenberg $J_1$-$J_2$-model on square and triangular lattices, accounting for finite lattice compressibility and bond-length-dependent magnetic exchange. Using Nematic Bond Theory, a diagrammatic self-consistent method, we study the nematostriction that happens when the onset of nematic order in the spin-system drives a concomitant structural phase transition. We analyze the mechanisms by which the magnetoelastic couplings renormalize the critical temperature and modify the phonon spectrum. The magnetoelastic feeback can also alter fundamentally the nature of the phase transition. Specifically, on the square lattice, the transition shifts from continuous to weakly first-order (discontinuous) beyond a critical magnetoelastic coupling threshold. Conversely, on the triangular lattice, the transition remains discontinuous regardless of coupling strength.

Spectral distortion anisotropies of the cosmic microwave background (CMB) provide a new probe of the early Universe that can be accessed using traditional CMB imaging techniques. It is possible to compute the creation and evolution of anisotropic signals for various scenarios using the frequency hierarchy method recently developed for CosmoTherm. However, the current treatment is not perfect and some approximations had to be made. Here, we carefully construct a modified form for the evolution equations that has the full equilibrium solutions built into the formulation. We improve the formalism to account for i) additional stimulated scattering effects, ii) kinematic corrections to the thermalization terms, iii) corrections to the standard perturbation variables and iv) direct photon sources. These effect could not be captured with the original formulation of the frequency hierarchy method but are indeed important for cleanly separating real distortions from temperature signals. However, we show that previous results are not altered significantly when compared to the improved formulation presented here. As a new worked example, which could indeed not be treated before, we also illustrate how possible changes in the temperature-redshift relation would create spectral distortion anisotropies in the pre-recombination era. The theoretical methods presented here are also an important step towards being able to consistently predict the CMB spectral distortion anisotropies in photon-dark photon and photon-axion conversion scenarios.

We initiate the study of distortion in stable matching. Concretely, we aim to design algorithms that have limited access to the agents' cardinal preferences and compute stable matchings of high quality with respect to some aggregate objective, e.g., the social welfare. Our first result is a strong impossibility: the classic Deferred Acceptance (DA) algorithm of Gale and Shapley [1962], as well as any deterministic algorithm that relies solely on ordinal information about the agents' preferences, has unbounded distortion. To circumvent this impossibility, we consider algorithms that either (a) use randomization or (b) perform a small number of value queries to the agents' cardinal preferences. In the former case, we prove that a simple randomized version of the DA algorithm achieves a distortion of $2$, and that this is optimal among all randomized stable matching algorithms. For the latter case, we prove that the same bound of $2$ can be achieved with only $1$ query per agent, and improving upon this bound requires $Ω(\log n)$ queries per agent. We further show that this query bound is asymptotically optimal for any constant approximation: for any $\varepsilon >0$, there exists an algorithm which uses $O(\log n /\varepsilon^2)$ queries, and achieves a distortion of $1+\varepsilon$. Moreover, under natural structural restrictions on the instances of the problem, we provide improved upper bounds on the number of queries required for a $(1+\varepsilon)$-approximation. We complement our main findings above with theoretical and empirical results on the average-case performance of stable matching algorithms, when the preferences of the agents are drawn i.i.d. from a given distribution.

Neural models are increasingly used in Web-scale Information Retrieval (IR). However, relying on these models introduces substantial computational and energy requirements, leading to increasing attention toward their environmental cost and the sustainability of large-scale deployments. While neural IR models deliver high retrieval effectiveness, their scalability is constrained in multi-domain scenarios, where training and maintaining domain-specific models is inefficient and achieving robust cross-domain generalisation within a unified model remains difficult. This paper introduces DRAMA (Domain Retrieval using Adaptive Module Allocation), an energy- and parameter-efficient framework designed to reduce the environmental footprint of neural retrieval. DRAMA integrates domain-specific adapter modules with a dynamic gating mechanism that selects the most relevant domain knowledge for each query. New domains can be added efficiently through lightweight adapter training, avoiding full model retraining. We evaluate DRAMA on multiple Web retrieval benchmarks covering different domains. Our extensive evaluation shows that DRAMA achieves comparable effectiveness to domain-specific models while using only a fraction of their parameters and computational resources. These findings show that energy-aware model design can significantly improve scalability and sustainability in neural IR.