As large language model (LLM) agents become more prevalent in real world social settings, social intelligence will play an increasingly critical role. But social intelligence is still a poorly defined construct, for humans and artificial agents. We introduce a multiplayer arena of mixed cooperative and competitive social games to study LLM social intelligence. The controllability of LLM based agents enables systematic evaluation, which also supports broader inferences about social intelligence per se. We evaluated eight diverse LLMs (24B to 1T parameters) using a Communicate Predict Act (COMPACT) interaction protocol and fine grained probing of social dynamics. Elo style ratings reveal consistent performance differences across models, but this scalar measure provides only a partial characterization of social intelligence. To address this limitation, we analyze gameplay traces to extract sociocognitive metrics capturing action prediction, communicative influence, strategic reasoning, and tradeoffs under conflicting interests. These sociocognitive metrics exhibit strong intramodel consistency and they reliably predict pairwise agent advantage in game outcomes (AUC ROC = 0.82). Feature importance analysis indicates that surprisingly, influence, transparency, and adaptability are more predictive of success than Theory of Mind inference or deep planning. Together, our results advance a testable, multidimensional conception of social intelligence and provide empirical insights into the capacities that underpin it.

Discrete symmetries of Calabi-Yau moduli spaces, generated by isomorphic flops, constrain the instanton expansion of the 4D $\mathcal{N}=2$ Type~IIA prepotential. We show that the Coxeter-invariant functions into which the prepotential organizes are eigenfunctions of a Laplace-Beltrami operator built from the Coxeter-invariant symmetric bilinear form on the moduli space. This means that the Gromov-Witten expansion can be interpreted as a superposition of waves propagating on the Coxeter quotient of the moduli space, and its resummation is the corresponding spectral decomposition. For the dihedral Coxeter groups, separation of variables in the eigenvalue equation explains from first principles why special modified Bessel functions, ordinary Bessel functions and Jacobi theta functions appear as the natural building blocks of the prepotential, depending on whether the Coxeter rotation acts hyperbolically, elliptically, or parabolically. The resulting spectral representations converge efficiently in the interior of the moduli space, complementing the standard large-volume instanton expansion.

The theory of subfactors of groups, together with the associated notions of subindices and index stability for groupsandtheirsubsets, hasrecentlybeenintroducedandsystematicallydeveloped. Theseconceptsexhibitdeepconnections with additive combinatorics and number theory, relating to important topics such as packing and covering numbers, syndetic sets, group diameters, special integer sequences (e.g., primes and Fibonacci numbers), and classical rational sequences (e.g., Bernoulli numbers). Following the initial paper presented in 2020, two subsequent works further investigated these ideas within the framework of finite groups. In the present paper, in addition to advancing several aspects of the topic, we focus on infinite groups, with particular emphasis on groups of numbers. In this context, we introduce the RSFA (Right Subfactor Algorithm) for infinite groups and resolve several previously open problems. One of the important results is that every infinite group is index-unstable. We also correct several earlier inaccuracies and establish a weak version of a conjecture concerning differences of prime numbers. Furthermore, we determine the exact subindices for several notable sequences of integers and provide a general criterion for index stability and non-index stability of subsets in countable groups. Finally, we investigate the index stability of infinite groups and present a collection of related projects, problems, questions, and conjectures.

This paper studies stabilization and its corresponding closed-loop region-of-attraction (ROA) for homogeneous polynomial dynamical systems whose nonlinear term admits an orthogonally decomposable (ODECO) tensor representation. While recent tensor-based results provide explicit solutions and sharp global characterizations for open-loop ODECO systems, closed-loop synthesis and computable ROA estimates are still often dominated by local linearization or Lyapunov/SOS (sum of squares) methods, which can be conservative and computationally demanding. We propose a structure-preserving linear feedback design that shares the ODECO eigenbasis of the system's tensor, thereby enabling closed-form trajectory expressions, explicit convergence/escape thresholds, and sharp ROA characterizations. Under mild conditions, we further derive robustness/ISS-type bounds for bounded disturbances. Numerical examples validate the theoretical results.

Temporally multimode squeezed states have been a topic of recent interest due to their applications in quantum communication, information processing, and sensing. Characterizing the mode shapes is crucial for effectively manipulating these states, but current mode shape and state characterization techniques necessitate constraining assumptions and complicated experimental setups. Here, we propose a characterization technique that simultaneously recovers the complex temporal mode shapes and quadrature variances of ultrafast multimode squeezed states based on frequency resolved optical gating (FROG) using an optical parametric amplifier (OPA). FROG is a promising tool for quantum state characterization due to its flexibility of implementation and high temporal resolution. Using an OPA as the nonlinear process in FROG has the benefit of amplifying weak quantum states to a detectable level while preserving quantum information. Numerical simulations demonstrate the recovery of the mode shapes and levels of squeezing and anti-squeezing of ultrafast multimode squeezed states. This scheme offers a practical experimental approach to measuring arbitrary temporal mode shapes and characterizing large-scale multimode ultrafast Gaussian quantum states.

In this paper, we present a general framework for constructively proving the existence and of stationary localized solutions, spatially periodic solutions, and branches of spatially periodic solutions in the 1D Thomas model. Specifically, we develop the necessary analysis to compute explicit upper bounds required in a Newton--Kantorovich approach. Given an approximate solution $\bar{\mathbf{u}}$, this approach relies on establishing that a well-chosen fixed point map is contracting on a neighborhood $\bar{\mathbf{u}}$. For this matter, we construct an approximate inverse of the linearization around $\bar{\mathbf{u}}$, and establish sufficient conditions under which the contraction is achieved. This provides a framework for which computer-assisted analysis can be applied to verify the existence and local uniqueness of solutions in a vicinity of $\bar{\mathbf{u}}$, and control the linearization around $\bar{\mathbf{u}}$. Furthermore, as the Thomas model has a non-polynomial nonlinearity, we will need to use different techniques to handle it during our analysis. The code to perform the rigorous proofs is available on Github.

Immiscible to miscible quenching transitions (IMQT) in homogeneous Bose-Einstein condensate are investigated, considering rubidium isotopes $^{85}$Rb and $^{87}$Rb confined in a two-dimensional (2D) circular box, under two different initial configurations. These IMQT instabilities, triggered by sudden reductions in the two-body interspecies scattering length $a_{12}$, are explored under two distinct initialconditions, highlighting the critical role of nonlinear dynamics in their evolution. The numerical simulations indicate that the instability dynamics are primarily driven by the production of large vortices and the propagation of sound waves (phonons), with sound wave excitations prevailing in the long-term evolution. The compressible and incompressible parts of the kinetic energy spectra, in terms of the wave number $k$, are confronted with the classical Kolmogorov scaling, $k^{-5/3}$ for turbulence, which is observed in the onset of instabilities. Before reaching the ultraviolet dissipation region at small scales, the IMQT spectra exhibit a bottleneck effect, indicating a clear departure from classical scaling behavior. In the time asymptotic miscible regime, it is observed that the vorticity and sound-wave production remain practically stable. In this regime, for both cases investigated, a linear relation is also recognized between the miscibility parameter and the initial IMQT configuration.

Code reuse is a widespread practice across software development projects, suggesting an inherent trust in the reused code. Yet, there is a lack of a fundamental understanding of developers' trust and how various factors mold their trust-based cognitive processes. Drawing from the psychology of compliance and trust, we present the results of the first controlled experiment (n=37) which uses eye tracking to explore how urgency (represented by code priority level) and reputation (represented by the experience level of the code's author) influence developers' perceptions of code trustworthiness. Our research revealed that the priority assigned to a code patch significantly influenced developers' code review behavior, impacting their evaluation time, cognitive load, and perceived quality. However, the decision to incorporate and implement the code was not affected . Eye tracking data revealed that there were variations in overall visual code scanning and the distribution of attention across identical code patches labeled as written by senior vs. junior developers. Yet, there were no significant performance differences. Moreover, our participants nominate code functionality, quality, and comprehensibility as primary factors in code evaluation. Despite noticeable changes in code review behavior, our participants surprisingly overlooked the substantial influence of urgency and reputation on their decisions to review and reuse code changes. This study takes the next step toward a better understanding of trust in software engineering and may inform future research about code review platforms and guidelines, code reuse, and automated code generation.

Understanding solar wind variability throughout the heliosphere is essential for fundamental space physics and future exploration of the Moon and Mars. The Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft has provided upstream solar wind measurements at Mars spanning Solar Cycles 24 and 25, enabling a statistical investigation of solar wind regimes at this heliocentric distance. In this work, we apply an unsupervised machine-learning framework combining Principal Component Analysis and K-Means clustering to a normalized, multi-dimensional solar wind dataset to identify recurrent solar wind regimes in a physically interpretable, data-driven manner. The resulting classification reveals distinct slow, fast, intermediate, and compressed solar wind regimes whose relative occurrence and temporal organization are strongly modulated by solar activity. This manuscript is part of the Heliophysics Summer School Machine Learning Special Collection.

Conversational AI has made significant progress, yet generating expressive and controllable text-to-speech (TTS) remains challenging. Specifically, controlling fine-grained voice styles and emotions is notoriously difficult and typically requires massive amounts of heavily annotated training data. To overcome this data bottleneck, we present a scalable, data-efficient cascaded framework that pairs textual style tokens with human-curated, high-quality audio prompts. This approach enables single-shot adaptation to fine-grained speaking styles and character voices. In the context of TTS, this audio prompting acts as In-Context Learning (ICL), guiding the model's prosody and timbre without requiring massive parameter updates or large-scale retraining. To further enhance generation quality and mitigate hallucinations, we introduce a novel ICL-based online reinforcement learning (RL) strategy. This strategy directly optimizes the autoregressive prosody model using subjective aesthetic rewards while being constrained by Connectionist Temporal Classification (CTC) alignment to preserve intelligibility. Comprehensive human perception evaluations demonstrate significant improvements in both the naturalness and expressivity of the synthesized speech, establishing the efficacy of our ICL-based online RL approach.

Adiabatic Quantum-Flux-Parametron (AQFP) logic is an ultra-low-power superconducting logic family with energy consumption approaching the Shannon limit, making it attractive for quantum computing control and cryogenic computing systems. Traditional AQFP designs face significant physical design challenges due to strict gate-level clocking requirements and limited interconnect lengths, leading to substantial buffer overhead and difficult timing closure. Recently, delay-line clocking of AQFP has been proposed to improve timing margins and reduce latency by enabling more flexible clock scheduling. However, prior work has primarily focused on placement and latency minimization, while relying on fixed timing parameters that do not capture the frequency dependence of AQFP setup and hold constraints. To address this limitation, we propose a frequency-aware post-routing optimization framework that jointly optimizes clock period, latency, and timing slack under user-specified weighting. Experimental results across common benchmarks achieve 100% post-routing timing closure across a range of performance--latency--slack trade-offs. Our approach also automates phase-skipping, reducing path-balancing buffer insertion by 34% on average while only reducing operating frequency by 4%.

Many-body topological quantum states host exotic quantum phenomena and lie at the forefront of developing next-generation quantum technologies. Recently emerged neural network wavefunction methods have established themselves as a powerful computational framework for accessing these states, enabling the variational machine learning calculation of the system's ground state wavefunction. However, reliable computation of topological invariants remains an open challenge when the whole deterministic energy spectrum is not available. In this work, we introduce a robust approach to determining topological invariant based on simulating the charge pumping process, by monitoring the response of polarization upon flux insertion. By applying this method, we accurately extract the Chern numbers for Abelian fractional Chern insulators. Our approach also enables the first neural-network-wavefunction-based identification of anomalous composite Fermi liquid states. Our work resolves a key bottleneck in applying neural network wavefunctions to correlated topological matter, and the method proposed is also generally applicable to other many-body approaches, thereby opening up new avenues for future research in this field.

A $\left(γ_{1}, γ_{2}\right)$ space of order $n$ is a space of univariate functions spanned by $\left\{γ_{1}^{n-k}(x), γ_{2}^{k}(x)\right\}_{k=0}^{n}$. A $\left(γ_{1}, γ_{2}\right)$ space is said to be translation invariant if $γ_{1}(x-h)$ and $γ_{2}(x-h)$ can be expressed as nonsingular linear combinations of $γ_{1}(x)$ and $γ_{2}(x)$. Translation invariant $\left(γ_{1}, γ_{2}\right)$ spaces include polynomials $\left(γ_{1}(x)=1, γ_{2}(x)=x\right)$, trigonometric functions $\left(γ_{1}(x)=\cos x, γ_{2}(x)=\sin x\right)$, hyperbolic functions $\left(γ_{1}(x)=\cosh x, γ_{2}(x)=\sinh x\right)$, and their discrete analogues. We merge $γ$-blossoming for $\left(γ_{1}, γ_{2}\right)$ spaces with $h$-blossoming for $h$-Bernstein bases and $h$-Bézier curves to construct a novel $h$-$γ$ blossom for translation invariant $\left(γ_{1}, γ_{2}\right)$ spaces generated by two continuous, linearly independent functions $γ_{1}$ and $γ_{2}$. Based on this $h$-$γ$ blossom, we define $h$-$γ$ Bernstein bases and $h$-$γ$ Bézier curves and study their properties. We derive recursive evaluation algorithms, subdivision procedures, Marsden identities, and formulas for degree elevation and interpolation for these $h$-$γ$ Bernstein and $h$-$γ$ Bézier schemes.

Cavitation-assisted Ag paste is a promising route for fine-line, low-silver metallization in silicon solar cells because it improves paste dispersion, extends shelf life, and reduces Ag consumption, but matching the contact performance of commercial pastes remains a challenge. Here, cavitated paste was evaluated on PERC solar cells at peak firing temperatures of 720, 740, 750, and 762 C, with and without laser-enhanced contact optimization (LECO). The results show a clear firing window: 720 and 740 °C produced high series resistance and reduced fill factor, 750 C gave the best pre-LECO performance, and 762 C showed additional electrical limitations with only limited LECO benefit. LECO selectively recovered the under-activated states, increasing fill factor from 76.8 to 80.2% at 720 C and from 76.7 to 79.8% at 740 C. Electroluminescence and conductive AFM further indicated improved current collection and stronger localized conduction after LECO. These results show that cavitated paste performance is governed primarily by a shifted contact-formation window, and that firing optimization combined with LECO provides a practical route to retain the fine-line advantage while improving electrical performance.

We report on the high-pressure synthesis of a CrS$_2$ phase in the form of single-crystalline nanorods. A structural refinement of Precession Electron Diffraction Tomography data confirms the nominal CrS$_2$ composition and unveils a ladder-type structure formed by portions of 1T-type CrS$_2$ layers characteristic of two-dimensional (2D) dichalcogenides connected by chains of edge-sharing CrS$_6$ octahedra characteristic of 3D dichalcogenides with marcasite structure. Ab initio density functional theory calculations of the relaxed structure confirm the stability of this structure and indicate a strong overlap of the 3d states of Cr with the 3p states of S, thus suggesting strong covalent Cr-S bonds and metallic behavior. Electrical resistivity, $\varrho$, measurements on single nanorods confirm this behavior and yield $\varrho \sim 2-20$ m$Ω$ cm at 4 K. The proposed ladder-like structure of CrS$_2$ forms open channels along the chain direction, which may be suitable for ionic conduction.

Pretrained encoders for mathematical texts have achieved significant improvements on various tasks such as formula classification and information retrieval. Yet they remain limited in representing and capturing student strategies for entire solution pathways. Previously, this has been accomplished either through labor-intensive manual labeling, which does not scale, or by learning representations tied to platform-specific actions, which limits generalizability. In this work, we present a novel approach for learning problem-invariant representations of entire algebraic solution pathways. We first construct transition embeddings by computing vector differences between consecutive algebraic states encoded by high-capacity pretrained models, emphasizing transformations rather than problem-specific features. Sequence-level embeddings are then learned via SimCSE, using contrastive objectives to position semantically similar solution pathways close in embedding space while separating dissimilar strategies. We evaluate these embeddings through multiple tasks, including multi-label action classification, solution efficiency prediction, and sequence reconstruction, and demonstrate their capacity to encode meaningful strategy information. Furthermore, we derive embedding-based measures of strategy uniqueness, diversity, and conformity that correlate with both short-term and distal learning outcomes, providing scalable proxies for mathematical creativity and divergent thinking. This approach facilitates platform-agnostic and cross-problem analyses of student problem-solving behaviors, demonstrating the effectiveness of transition-based sequence embeddings for educational data mining and automated assessment.

A quantum network's purpose is to enable users to execute applications on end nodes. This requires the network to provide the service of creating entangled links between those nodes. Users of mature networks, such as the internet or the telephone network expect accepted service demands to be met reliably. We first define reliability requirements that extend classical computer network concepts to quantum network service delivery. We then introduce Arqon, a suite of control applications designed to deliver reliable service in centrally controlled quantum networks. We demonstrate through both analytic and numerical evaluation that Arqon satisfies all reliability requirements for accepted demands. These evaluations consider static network topologies. We provide a complete Python implementation and perform complexity analysis showing that admission control scales as $O(k^3)$ in the number of incoming demands $k$ and schedule computation scales as ${O(N^3)}$ in the number of accepted demands to schedule $N$.

We investigate the sensitivity of a future 10 TeV muon collider to dimension-6 operators in the Standard Model Effective Field Theory (SMEFT), focusing on Higgs and top quark production processes. The analysis includes two-fermion and four-fermion operators that induce electroweak vector and axial-vector interactions, as well as dipole, scalar, and tensor interactions involving muons. Many of these operators are only weakly constrained or difficult to probe at the LHC due to limited sensitivity and large SM backgrounds. We study the processes $μ^+μ^- \to Zh$, $μ^+μ^- \to μ^+μ^-h$, $μ^+μ^- \to t\bar t$, and $μ^+μ^- \to t\bar t h$, exploiting the energy-enhanced SMEFT effects at multi-TeV scales accessible to a muon collider. Using detailed simulations that incorporate differential information and angular distributions, we derive projected bounds on the relevant Wilson coefficients. We find that a 10 TeV muon collider can strengthen existing limits on muon-Higgs-gauge and muon-top interactions by up to an order of magnitude, surpassing even FCC-ee projections. Finally, we interpret these bounds in the context of representative UV scenarios, including models with vector-like lepton and scalar leptoquarks, highlighting the potential of a muon collider to probe new physics at scales well beyond the LHC reach.

We report the discovery of GLIMPSED-329380, a z=6.64 galaxy behind Abell S1063, which shows signs of an extreme ionised outflow driven by an active galactic nucleus (AGN). The deep JWST/NIRSpec medium grating observations show spatially resolved structures of a host galaxy containing the very fast outflow and an AGN, which we analyse separately. The outflow, mainly traced by broad [O III]λ5008 and Hα emissions in the host, reaches a full-width half-maximum velocity of ~5500km/s, velocities only observed in AGN-dominated systems. From the Balmer decrement, we observe that while the narrow emission lines show no dust attenuation, the outflowing gas is dusty. We use emission lines diagnostics to infer gas abundances within the host galaxy. The oxygen abundance is 12+log(O/H) ~ 7.95 (~18% solar) and the host is slightly nitrogen-enriched with log(N/O) ~ -0.75. Despite its extreme velocity, the mass loading factor (<0.1) and the kinematic energy of the outflow (~10^43 erg/s) suggest limited impact on star formation. The AGN component shows many similarities with little red dots (LRDs): a characteristic "V-shape", exponential profile in hydrogen lines, numerous detection of forbidden [Fe II] lines, a Balmer break, and a broad absorption feature at ~4550 Å. This detection of a fast outflow in an LRD, rare in surveys dominated by low-resolution (e.g. PRISM) spectra, provides direct evidence of AGN activity in these systems.

The Galactic core-collapse supernova (SN) rate is estimated at $\approx 1-3$ per century; however, no optically visible SN has been discovered in the past 400 years. Although records of the last optically detected SN (Cassiopeia A) are debated, it is revealed today via its bright, variable mid-infrared (MIR) dust echoes -- offering the possibility of identifying dust-obscured, missed events via their dust echoes. We present the first all-sky, untargeted search for thermal dust echoes of luminous Galactic transients using difference imaging on 12 years of time-resolved NEOWISE co-adds (spanning $2009-2022$) followed by statistical detection of variable extended sources. We use echo features around Cas A, together with archival catalogs to train a convolutional neural network to classify transient candidates as dust echoes, point sources, artifacts, and high proper motion stars. Our model achieves $\approx 94$% accuracy in distinguishing echoes from other variable sources. Applying the classifier to $\approx 11$ million transient candidates, we search for spatial over-densities of echoes across the Galactic plane. We find that Cas A is the only region exhibiting echoes at the WISE sensitivity threshold of $W2$ surface brightness of $\approx 20$ Vega mag arcsec$^{-2}$ -- reflecting its unique combination of young age and luminous shock breakout. We present the largest catalog of time-resolved echo positions of Cas A (20477 within 10$^\circ$) that are being used for studies of the surrounding interstellar medium with the James Webb Space Telescope. Our results lay the groundwork for the imminent Roman space telescope surveys -- which will achieve $\approx 100\times$ higher sensitivity and $\approx 30\times$ better spatial resolution at wavelengths of $\lesssim 2.5\,μ$m.

In this paper, we study the long-time behavior of a stochastic heat equation with multiplicative noise and localized control. We begin by analyzing the uncontrolled dynamics and derive explicit decay rates for both mean-square and almost sure exponential stability. These estimates show that the two notions of stability may hold under different conditions on the parameters, reflecting the interplay between the drift and the multiplicative noise. We then introduce a finite-dimensional feedback control acting on a measurable subset of positive measure, built from finitely many Fourier modes of the solution. In particular, we show that the number of controlled modes determines the decay rate and allows for arbitrarily fast stabilization in the mean-square sense. As a consequence, almost sure exponential stability is recovered via a probabilistic argument, so that both notions of stability are achieved within the same framework and with the same decay rate. As an application, we provide a new proof of controllability for the stochastic heat equation based on an iterative construction of adapted controls in feedback form, avoiding the use of the adjoint equation.

Whether the "Hubble sequence" of galaxy morphologies exists up to z~4 is still disputed, and one of the challenges is characterizing galaxy structure consistently across a wide range of redshifts. To enable a fair comparison across cosmic time, we constructed "absolute" images of galaxies spanning 0.15<z<4.5 and 8<log $M_{\star}$<11 from HST CANDELS and JWST CEERS surveys, by matching the effective resolution and surface brightness limit of galaxies, accounting for cosmological dimming and evolution in size and mass-to-light ratio. We measured the structural parameters of 2825 galaxies and used the UMAP technique to study the evolution of the morphological phase space. We find a continuous sequence spanning late-type to early-type galaxies, with no redshift gradient - indicating that a Hubble-like sequence is established by z~4. We show that our approach recovers a cleaner separation between early- and late-type galaxies than visual classifications. By tracing progenitors using empirical mass assembly histories, we find that progenitors of low-mass galaxies are predominantly star-forming disks at all epochs. Progenitors of massive galaxies follow two distinct paths: a stable star-forming disk population with little structural evolution, and an early-type population that builds up rapidly from irregular progenitors and quenches within a few Gyr, consistent with a compaction-driven quenching scenario.

Gravitational waves generated by moving sources in Schwarzschild spacetime can be decomposed into three principal components: quasinormal modes, tail, and prompt response. While the first two have been extensively studied, a systematic and exact treatment of the prompt response has received comparatively little attention. In this work, building on recent progress in elucidating the structure of the Green's function of the Regge-Wheeler equation, we place the prompt response on a firm theoretical footing and investigate its morphology for sources inspiraling and plunging into a Schwarzschild black hole. We find that during the inspiral phase, the prompt response is stronger than the dynamical excitation of quasinormal modes by a factor of ~1.2, with both contributions modulated by the instantaneous orbital motion. Near the waveform peak, the prompt response rapidly decays, while the quasinormal modes transition into the ringdown regime. By combining the prompt response, quasinormal modes, and tail contributions, we achieve an accurate reconstruction of the full time-domain inspiral-merger-ringdown waveform at the 99$\%$ level, thereby providing strong support for the accuracy of this decomposition. These results offer new insight into the transition from inspiral to merger and ringdown.

The tidal response of compact objects provides a powerful probe of their internal structure and of the surrounding gravitational field. We provide a comprehensive and unified overview of tidal effects in black holes, neutron stars, and exotic compact objects, with emphasis on both static and dynamical responses to external fields, encoded in Love numbers and dissipation numbers. We discuss the vanishing of static bosonic Love numbers for black holes in vacuum General Relativity, their modifications in alternative theories, in non-standard models of compact objects, and in the presence of matter, as well as their role in testing deviations from Einstein's theory and environmental effects. A fundamental distinction between bosonic and fermionic perturbations is highlighted, as the latter yield nonzero static Love numbers even for black holes in General Relativity. For neutron stars, we overview the dependence of tidal Love numbers on the equation of state, the emergence of quasi-universal relations, and the impact of rotation, nonlinearities, and dynamical effects. Exotic compact objects typically feature nonvanishing static tidal Love numbers -- a striking observational signature that differentiates them from black holes. We further review how tidal effects influence the gravitational-wave signals from binary inspirals, and explore their implications for gravitational-wave astronomy. In particular, we stress their significance for current and future detectors as tools to test General Relativity, constrain the nuclear equation of state, and probe the fundamental nature of compact objects and their environments.

The main aim of this paper is to study the steady-state properties of a general Bond-type endogenous growth model, considering that both sectors are modeled by two distinct $CES$ production functions. We prove here that in this case, we cannot claim the saddle-path stability.

Time-series stationarity is a property that statistical characteristics such as trend, variance, seasonality remain constant over time. It is considered fundamental to many forecasting and analysis methods. Different tests detect different types of non-stationarity: structural breaks or deterministic trends, clustered or time-dependent variance, stochastic or deterministic seasonality. A series might pass one test while failing another; single-test approaches seldom distinguish between conceptually different types of non-stationarity that require different types of tests and transformations. `StationarityToolkit` addresses this by providing a comprehensive Python library that runs 10 statistical tests across three categories: trend (4 tests), variance (4 tests), and seasonality (2 tests). Rather than a binary stationary/non-stationary verdict, users receive detailed diagnostics with actionable notes for each detection. The toolkit automatically infers the frequency of the data provided (requires datetime index), provides clear interpretations with test statistics and p-values, and supports an iterative test-transform-retest workflow essential for real-world data sets.

We consider mixed four-point correlators of 1/2-BPS operators $ϕ_{k}$ in SCFTs with eight real Poincaré supercharges, namely the 3d $\mathcal{N}=4$, 4d $\mathcal{N}=2$, 5d $\mathcal{N}=1$, and 6d $\mathcal{N}=(1,0)$ theories. Using the basis of solutions to the superconformal Ward identity introduced in arXiv:hep-th/0405180, we demonstrate that the dynamical data in mixed correlators of extremality $\mathcal{E}=2$ is encoded in certain simpler ``reduced correlator" functions that admit a block expansion, in close analogy to the recent result for maximally supersymmetric CFTs in arXiv:2601.15407. These reduced blocks similarly involve ordinary blocks with shifted kinematics and reproduce what is known in 4d, generalize a known example in 6d, and offer novel results in 3d and 5d.

Quantum error correction using erasure qubits offers higher fault-tolerant thresholds and improved scaling by converting dominant physical errors into detectable erasures. In superconducting circuits, erasure qubits can be constructed using the dual-rail approach, which, however, requires additional qubit-count overhead and tailored coupling elements. Here, we demonstrate a hardware-efficient scheme that operates transmon qutrits as erasure qubits, which is compatible with standard superconducting circuit-QED hardware. The logical states $\ket{0_\text{L}}$ and $\ket{1_\text{L}}$ are represented by the ground and second excited states, while the dominant relaxation errors can be detected via an ancilla qubit using a microwave-activated two-qutrit SWAP gate. We demonstrate a logical qubit $T_1$ lifetime exceeding $500\,μ\mathrm{s}$, post-selected with repeated mid-circuit erasure detection, which is ten times longer than the $T_1$ time of the transmon physical qubit. Coherence times beyond $300\,μ\mathrm{s}$ are achieved using dynamical decoupling. Single-qubit gate operations reach average Clifford gate infidelity on the order of $10^{-4}$. We further demonstrate dual-purposing an ancilla qubit for both erasure detection and parity checking, showing heralded generation of Bell states between erasure qubits. These results suggest that mainstream architectures of transmon qubit arrays may already be capable of implementing erasure-based QEC strategies for hardware-efficient fault-tolerant quantum computing.

Recent advances in the observation of black-hole candidates have renewed interest in probing their near-horizon structure and in searching for departures from the standard singular solutions of general relativity. In this context, significant effort has been devoted to regular black holes and to horizonless black-hole mimickers, motivated primarily by quantum-gravitational effects. Depending on the value of the regularization parameter relative to the object mass, typical spherically symmetric solutions can describe either of these two scenarios. Regular black-hole configurations generically feature an outer and an inner horizon surrounding a maximally symmetric core; the inner horizon in turn triggers mass inflation and semiclassical instabilities. The horizonless branch of the same solutions, by contrast, supports stable inner light rings when sufficiently compact, yet is itself subject to instabilities associated with long-lived quasinormal modes. Here we investigate how to emulate these spacetimes in an analogue-gravity platform based on surface-gravity waves in a shallow-water basin, with the aim of reproducing these instabilities experimentally. We begin by identifying the flow profiles and boundary conditions required to replicate the relevant effective geometries. In particular, we show that the inner-core metrics can be simulated with a non-rotating central-drainage configuration, and we propose a graded-drainage profile to connect them to an asymptotically flat exterior region. We then assess the experimental feasibility of studying the instabilities mentioned above with current technology. Our conclusion is that, while the required setup is realizable in principle, alternative media, such as Bose-Einstein condensates, may offer a more practical route to faithfully capturing the targeted physical features.

We study how a fluctuating domain wall in three dimensions modifies bulk observables in a gapped phase. We introduce an effective interaction between the wall and the lightest bulk massive mode, and identify the regime in which this description is controlled: nearly on-shell bulk exchange with small momentum along the wall. In this regime, several observables are controlled by a renormalized dimensionless coupling $λ$, including the large-$L_z$ correction to the wall free energy and the large-$|x_\perp|$ tail of two-point functions in the presence of the wall. Other observables, such as one-point functions and two-point functions in the nearby-regime, retain non-universal dependence on operator data and on the bulk spectral density. We test the universal kinematic consequences of wall fluctuations, and find good agreement with the predicted rough-wall broadening and nearby Gaussian behavior in Monte Carlo simulations of the 3D Ising model with anti-periodic boundary conditions.