Plasmonic nanocavities enable the synchronization of spatially distant emissive dipoles through strong near-field coupling in sub-nm gaps. We report formation of a room-temperature synchronized dipole state in locally-ordered plasmonic nanogap 2D arrays under non-resonant continuous-wave pumping. Unlike lasers, photonic Bose-Einstein condensates, or exciton-polariton condensates, this system exhibits spatial coherence across the dipoles, while rapid radiative and non-radiative emission suppresses temporal photon coherence. A change of behaviour is observed with increasing pumping, marked by the spatial spread of g(1) coherence, but without spectral narrowing or directional emission. This driven-dissipative system exhibits fast temporal coherence decay and complex spatial correlations, offering a new platform for studying synchronization at room temperature. Combining ultralow mode volumes, high Purcell enhancement, and scalable ambient operation, it opens pathways for novel photonic and quantum technologies.

Central Limit Theorems for integrals of third degree Hermite polynomials of Berry's random wave model on increasingly large domains are proved in dimensions 2 and 3. These were the missing cases for a complete description of limit theorems for integral functionals of monochromatic random waves based on the Wiener chaos decomposition.

We prove modified scattering for small data solutions to the Vlasov-Poisson system in a functional framework where the initial data, scattering states, and asymptotic convergence are measured in the same topology. In addition, we show that the corresponding wave operators define homeomorphisms between the spaces of initial and scattering data, while enjoying a local Lipschitz continuity property in weaker norms. As a consequence, in the repulsive case, large spherically symmetric solutions are asymptotically stable. The proof relies in particular on the introduction of a suitable system of dynamic coordinates adapted to the asymptotic nonlinear flow.

We derive equations of motion for scalar particles self-consistently interacting with a scalar field,including the radiation produced by the particles' acceleration. Our approach differs in three key aspects from current methods: (1) we assume a small but finite discretization length scale $h$, which allows us to treat the particle as a small but finite object, (2) we choose the state vector for the system before deriving equations of motion, and (3) we formulate the equations explicitly in the lab frame and not in a manifestly covariant manner. This approach, which is self-consistent, happens to greatly simplify the resulting equations and their derivation, and is directly suitable for numerical calculations. The result is an effective source method which generalizes to electrodynamics or general relativity in a straightforward manner (although we do not consider this here). We then provide two possible discretizations of these equations, based on finite volumes and spectral methods, and show results of one-dimensional calculations. These calculations show excellent agreement with analytic solutions.

We study the phenomenology of early QCD confinement during inflation, driven by a direct coupling between the inflaton and Standard Model gluons. This coupling dynamically raises the QCD confinement scale, making the axion sufficiently heavy to suppress isocurvature perturbations during the CMB epoch. As inflation proceeds, the confinement scale decreases and the axion becomes light, allowing de Sitter fluctuations during the late stages of inflation or post-inflationary thermal fluctuations to generate the observed dark matter abundance. In addition, QCD-induced corrections to the inflationary potential can shift the scalar spectral index towards smaller values, providing a further observational handle. We embed this mechanism in an $α$-attractor model of inflation and explore the resulting parameter space. We show that, in the minimal scenario with reheating into gluons, successful dark matter production requires deconfinement to occur shortly after the CMB window. Extensions involving reheating through heavy right-handed neutrinos generally require large Yukawa couplings, which induce sizable loop corrections that spoil inflationary dynamics. We show that this tension can be resolved in the presence of supersymmetry and derive constraints on the SUSY breaking scale that allow the mechanism to remain viable within plateau models of inflation. Treating the reheat temperature as a free parameter further enlarges the viable parameter space.

Given multiple data matrices, many problems in statistics and data science rely on estimating a common subspace that captures certain structure shared by all the data matrices. In this paper we investigate the statistical and computational limits for the common subspace model in which one observes a collection of symmetric low-rank matrices perturbed by noise, where each low-rank matrix shares the same common subspace. Our main results identify several regimes of the signal-to-noise ratio (SNR) such that estimation and inference are statistically or computationally optimal, and we refer to these regimes as weak SNR, moderate SNR, strong estimation SNR, and strong inference SNR. First, we propose an estimator based on projected gradient descent initialized via spectral sum of squares and show that it achieves the optimal $\sinΘ$ error rate under strong estimation SNR. These results are complemented by both statistical and computational lower bounds identifying the weak and moderate estimation SNR regimes. Next, we turn to statistical inference for the $\sinΘ$ distance itself, and we show that our estimator has an asymptotically Gaussian distribution in the strong inference SNR regime. Based on this limiting result we propose confidence intervals and show that they are adaptively minimax optimal in the strong inference SNR regime, where adaptivity is measured in terms of the SNR. Finally, we show that adaptive confidence intervals are information-theoretically impossible below the strong inference SNR regime. Consequently, our results unveil a novel phenomenon: despite the SNR being ``above'' the computational limit for estimation, adaptive statistical inference may still be information-theoretically impossible.

We study charge-dependent modifications of identical-pion and identical-kaon femtoscopic correlation functions from two sources: the residual Coulomb field of the charged source and isospin-related hadronic dynamics. The residual Coulomb effect is modeled with a modified Retiere--Lisa blast-wave source, where the same emitted particles are propagated with positive and negative charge signs through an effective residual field. The residual Coulomb field produces a small but systematic positive-to-negative splitting of the correlation functions, strongest at low $k_T$ and sensitive to the effective charge, spatial width, and expansion velocity of the residual source. It also modifies the height and shape of the correlation function, complicating interpretation of the fitted radii. UrQMD 3.4 cascade calculations for Au+Au collisions at $\sqrt{s_{NN}}=7.7~\mathrm{GeV}$ show that charge-dependent splittings can also appear even without a residual Coulomb field. For pions, this difference is mainly driven by the initial isospin composition, while for kaons it is strongly affected by different $K^+$ and $K^-$ production mechanisms and subsequent hadronic evolution. These results show that residual Coulomb and isospin-related effects can compete, and neither can be interpreted reliably without constraining the other within the same model framework.

During the core-collapse of a rotating massive star, the standing accretion shock instability (SASI) favours the development of non-axisymmetric motions which can imprint specific frequency signatures on the neutrino and gravitational wave signals.This study establishes analytical approximations for the eigenfrequencies of the dominant SASI modes. It also explains the physical mechanism responsible for the further destabilization of prograde SASI modes by differential rotation. A perturbative analysis is used to calculate the eigenfrequencies of a stalled accretion shock in spherical geometry, taking into account the rotation of the collapsing stellar core. The formulation of the perturbative equations as a self-forced oscillator is extended to include differential rotation and interpret the results physically. The oscillation frequency of the dominant mode weakly depends on the detailed formulation of neutrino emission if the shock radius exceeds ~1.5 times the radius r_nabla of maximum deceleration. Analytical expressions are obtained for the one and two-armed spiral modes with a 10% accuracy in this regime. The effect of differential rotation is explained by the role of phase mixing between the advective forcing and the acoustic structure. The radial wavelength of vorticity perturbations associated with the prograde mode is increased by differential rotation, leading to a better phase match with the large radial scale of the acoustic structure. Even when rotation is too modest to involve a corotation radius, its adverse effect on phase mixing can be significant at small radius due to the steep inward increase of the rotation frequency ~1/r^2 in the region of stationary accretion. In the regime of stronger rotation involving a corotation radius, the stationary phase approximation sheds light on the dominant advective-acoustic coupling, located between the corotation zone and the shock.

We investigate the interacting non-Hermitian Su-Schrieffer-Heeger (SSH) model, focusing on the interplay between topology and charge ordering. Using a real-space topological marker, charge correlations, and the complex many-body spectrum, we map out the phase diagram under periodic and open boundary conditions. We show that the topological marker remains a robust diagnostic of non-Hermitian topological phases in the presence of interactions and consistently signals their breakdown at the onset of a charge density wave (CDW). We further demonstrate that non-Hermiticity enhances interaction effects: While moderate changes occur under periodic boundary conditions, open boundary conditions lead to a pronounced amplification of staggered charge correlations near exceptional points. This enhancement arises from the accumulation of low-energy states near exceptional points, which promotes electronic instabilities and strengthens CDW tendencies.

Non-reciprocal supercurrents enable non-dissipative rectification, holding great promise for superconducting electronics. Conventionally, this non-reciprocity, termed the superconducting diode effect, requires the simultaneous breaking of time-reversal and parity symmetries. Here, we propose a superconducting triode effect in an asymmetric quantum-dot Josephson junction coupled to an additional metallic top gate, which breaks the parity symmetry while explicitly preserving time-reversal symmetry. We demonstrate that the supercurrent across this junction exhibits a strong non-reciprocal effect that can be continuously manipulated via the top gate to achieve an ideal unidirectional supercurrent, thus manifesting a superconducting triode effect. Furthermore, under radio-frequency radiation, this junction exhibits highly asymmetric Shapiro steps, realizing fully quantized supercurrent rectification. Our work not only provides an alternative physical mechanism for the superconducting diode effect observed in Josephson junctions with explicit time-reversal symmetry, but also introduces a new tuning knob to manipulate supercurrent non-reciprocity.

We study the defocusing $k$-dispersion generalized Benjamin-Ono equation. For every even integer $k\geq 4$, we prove that solutions with initial data in the energy space $H^{\fracα{2}}$ are global in time and scatter. The proof combines the concentration-compactness-rigidity method of Kenig and Merle with techniques based on the Caffarelli-Silvestre extension and Tao's monotonicity formula adapted to the fractional dispersion setting.

We present a comprehensive analysis of the Orion star-forming complex (OSFC), combining structural, kinematic, and dynamical information to constrain the present-day state and future evolution of its stellar substructures. Using \textit{Gaia} DR3 astrometry and complementary radial velocities from high-resolution spectroscopic surveys, we derived three-dimensional velocity distributions and structural parameters for 13 young clusters. For the stellar component, we estimated a correction of the present-day mass function for observational incompleteness and calculated the virial state, $α_{\rm vir}$, finding that all clusters are supervirial. Direct $N$-body simulations initialized from the present-day global parameters and evolved for 300~Myr in a Galactic potential suggest a separation of the OSFC clusters into two regimes: seven clusters with $α_{\rm vir}\lesssim 7$ evolve in a Galactic-potential-regulated regime that retains a bound core for $\gtrsim 170$ Myr as long-lived open clusters, whereas six clusters with $α_{\rm vir}\gtrsim 7$ enter an internal-dynamics--dominated regime, dissolving before 120 Myr and rapidly populating the Galactic stellar field. For both regimes, a control test indicates negligible cluster--cluster interactions under current OSFC conditions. Finally, long-lived clusters show low-amplitude modulations in the bound fraction correlated with the Galactic vertical motion, consistent with disk-crossing tidal heating and the temporary recapture of marginal members. These results highlight the OSFC as a natural laboratory where heterogeneous initial conditions give rise to persistent open clusters and dispersing groups.

Quantum algorithms for basic numerical linear algebraic tasks have proven essential for translating diverse problems to a unified quantum computational context. Many of these tasks -- e.g., applying a polynomial function to the spectrum of a matrix embedded in a unitary process (a so-called block encoding), or taking linear combinations of block encodings -- are well-addressed by techniques like quantum singular value transformation (QSVT) or linear combination of unitaries (LCU). However, there exist useful matrix transforms whose realization by existing quantum algorithms is unclear or inefficient. In this work we construct improved quantum algorithms for some of these transforms, the simplest of which is a polynomial function applied element-wise. We show the space required to compute quantum element-wise transforms can be reduced exponentially in the degree of the applied function compared to prior work, and raise and rectify errors in previous constructions. We present our algorithms alongside applications to machine learning, simulation, and signal processing.

High-rate quantum low-density parity-check (qLDPC) codes are a leading candidate for fault-tolerant quantum computing. They feature higher encoding rates than planar alternatives such as the surface code, but their implementation often entails significant hardware hurdles like the need for long-range couplers. We leverage the flexibility of a trapped-ion quantum computer to demonstrate nine quantum error-correcting codes with starkly different qubit connectivity requirements on a single device without any hardware reconfiguration. These experiments span three families of quantum error-correcting codes: qLDPC codes, topological codes, and concatenated codes. With a qLDPC code encoding 4 logical qubits into 18 physical qubits, we achieve a logical error rate up to $9\times$ better than a previous demonstration of a similar code on superconducting solid-state qubits. Moreover, our implementation exhibits breakeven performance, with some instances achieving qubit lifetimes comparable to or slightly exceeding that of our trapped-ion qubits. We use a novel implementation of the optical-metastable-ground (OMG) architecture for addressable mid-circuit measurement and reset, which enables us to perform these experiments without any ion transport or dedicated coolant ions, requirements that typically consume a large fraction of the runtime or ion count of trapped-ion quantum computers.

There are two common classes of fairness notions that are considered when allocating $m$ indivisible items to $n$ agents of equal entitlements. One is that of share-based fairness notions, with the maximin share (MMS) and its relaxations to $ρ$-MMS being prominent representatives of this class. The other is that of comparison-based fairness notions, with envy-freeness (EF) and its relaxations such as EF1 being prominent representatives of this class. In general, no class offers good guarantees for the other class. In this work, we design allocations that simultaneously satisfy notions from both classes, and specifically, are $ρ$-MMS for constant $ρ$ and EF1 (in fact, also EFL). Such results were previously known when agents have additive valuations, and we prove such results for the more general class of submodular valuations.

In celebration of the 2025 UN International Year of Quantum Science and Technology, this Resource Letter surveys the rapidly-growing field of scholarship in quantum information science and engineering (QISE) education. It is primarily written as a guide for educators wishing to get started teaching QISE using research-based teaching methods, as well as for discipline-based education research (DBER) practitioners looking to get started in this field. Topics covered include scoping the field of QISE education, research into student reasoning in QISE, research-based and research-inspired curricular materials from the high school to graduate level, research-based assessments, simulation and gamification tools, and tools for incorporating discussion of the societal and ethical implications of quantum technologies into the classroom.

In many oncology clinical trials where overall survival is a key endpoint, patients are permitted to switch from the control arm to the experimental treatment arm or other suitable therapies. Switching can occur for various reasons, including disease progression. This violates the causal guarantees of randomized treatment assignment, resulting in biased treatment effect estimates. Existing methods often require strong assumptions, complicated model specifications, or both. In this paper, we propose a general framework that incorporates external controls to account for treatment switching in randomized controlled trials. Leveraging the synthetic control method and balancing weights from observational causal inference, we propose several estimators that use multiple imputation and time-varying weights to adjust for treatment switching. We also discuss approaches to selecting the risk set of external controls to impute from. Through extensive simulation studies, we show that our proposed methods lead to meaningful statistical improvements relative to standard adjustment methods that utilize external controls in naive ways or those that do not utilize external controls at all. We then demonstrate the utility of our external control-based approaches with two phase III oncology trials.

We study maximum matching problems in temporal graphs whose underlying graph is a tree. We consider two temporal models. In a $Δ$-matching, selected time edges sharing an endpoint must have time ticks differing by at least $Δ$. In a $γ$-matching, the selected objects are blocks of $γ$ consecutive appearances of the same underlying edge. We also consider the related ordered static problem of $d$-distance matchings. We show that maximum $Δ$-matching remains NP-hard on temporal trees for every $Δ\geq 2$, even in the sparse case where each edge appears at most twice. Using a reduction between the temporal models, we obtain the analogous result for maximum $γ$-matching on temporal trees, even when each edge admits at most two $γ$-edges. We also show, via a reduction from $d$-distance matching, that maximum $γ$-matching is APX-hard even when the underlying graph is bipartite. Complementing these hardness results, we identify several tractable cases. We prove that maximum $Δ$-matching is polynomial-time solvable on temporal trees in which every edge appears exactly once, and that maximum $γ$-matching is polynomial-time solvable when each edge admits at most one $γ$-edge. We also give dynamic-programming algorithms under bounded local-use and local-sparsity assumptions, and derive polynomial-time solvability of maximum $d$-distance matching when the input bipartite graph is a tree. Finally, we prove that both maximum $Δ$-matching and maximum $γ$-matching admit polynomial-time approximation schemes on temporal trees.

As the demand for information and communication technologies (ICT) continues to rise, the environmental impact of computing systems is becoming an increasingly critical concern. Although newer hardware often improves performance and energy efficiency, these gains do not always offset the carbon cost of premature replacement, particularly under low-utilization workloads or low-carbon electricity grids. We present CarbonSim, a lifecycle-aware simulation framework for evaluating carbon tradeoffs in hardware upgrade decisions. CarbonSim combines workload execution profiles, machine-level power characteristics, embodied carbon inventories, scheduling policies, and time-varying grid carbon intensity to estimate total emissions under alternative deployment scenarios. The framework supports multiple embodied-carbon accounting strategies, including uniform amortization and front-loaded lifecycle attribution, enabling analysis under different hardware lifespan assumptions. Using heterogeneous CPU generations as calibration platforms, we demonstrate that newer machines do not always minimize total emissions: under lightly loaded workloads or cleaner electricity mixes, extending the useful life of existing hardware can reduce lifecycle carbon despite lower operational efficiency. These results highlight that hardware refresh decisions should be workload-aware, location-aware, and lifecycle-aware.

Mirror-assisted optical interference can improve the fidelity of Young's double-slit interference. Here we discuss an electron analogue: particle-hole interference in superconductors produced by a single impurity near a line defect, terrace edge, or phase boundary. Quasiparticle waves scattered directly from the impurity interfere with waves reflected by the boundary, generating a ``ghost'' interference pattern that combines conventional $2k_F$ Friedel oscillations with additional hyperbolic fringes. Compared to the recently studied two-impurity Young's interference, this effect appears already at first order in the impurity potential and is therefore parametrically stronger. The resulting spatial modulation extends beyond $λ_F/2$ and is directly sensitive to the quasiparticle structure of the paired state, including possible Fermi-surface anisotropy of the superconducting order parameter. These findings point to boundary-assisted impurity interference as a robust local probe of superconducting electronic order, with clear signatures accessible to STM/STS measurements.

The study of quartic couplings of electroweak gauge bosons not only provides a test of the Standard Model (SM) predictions, but also can look for signals of new physics beyond the SM. We present a comprehensive study of anomalous quartic gauge couplings in same-sign $W^\pm W^\pm$ production via vector boson scattering at the LHC. The analysis is carried out within the framework of the SM Effective Field Theory, exploiting polarization and spin-correlation effects encoded in angular asymmetries in addition to conventional kinematic observables. We demonstrate that spin-correlation asymmetries provide sensitivity to anomalous $WWWW$ interactions that is comparable to that obtained from the transverse mass distribution of the $WW$ system. By identifying a minimal set of the most sensitive asymmetries, we show that the dominant constraints on the Wilson coefficients can be captured with a reduced number of observables. A combined analysis of angular asymmetries and kinematic information leads to improved limits compared to either approach alone. The impact of unitarity considerations is also examined by imposing invariant-mass cut-offs on the $WW$ system, allowing us to determine unitarity-safe regions for the anomalous couplings.

We present a new static solution describing a charged black string immersed in a Kiselev-type quintessence fluid and a cloud of strings. The metric and field equations are solved for a general quintessence state parameter, with explicit results provided for the physically relevant case $w_q = -2/3$. We analyze the event-horizon structure and the Kretschmann scalar, verify energy-condition constraints, and derive thermodynamic properties including the Hawking temperature and heat capacity to identify stability regimes. Finally, we investigate the photon cylinder for null geodesics. The solution generalizes known charged black-string spacetimes by simultaneously including quintessence and a string-cloud parameter.

Restriction site-associated DNA sequencing (RAD-seq) is widely used to discover sex-linked markers in non-model organisms, but large studies produce marker tables with millions of RAD tags. RADSex provides the reference workflow for building marker-by-individual depth tables and testing sex-biased marker distributions, but its depth, merge, and related table-building commands grow memory-hungry, and its standard output reports frequentist calls with no posterior evidence and no direct Python or C integration. We present rsx, a Rust implementation of the complete RADSex command set that preserves marker-table semantics and command-line compatibility. rsx combines 2-bit DNA keys, parallel ingestion, memory-mapped marker tables, external sorting, bitset group counts, and streamed Gram-matrix PCA so that memory stays bounded by the number of individuals or by explicit buffers. It adds conjugate Beta-Binomial Bayes factors and posterior probabilities under XY and ZW hypotheses, returning strict, posterior-supported, and Bayes-factor-only evidence grades. A portable, libm-independent minimax approximation of the error function keeps the chi-squared tail reproducible across platforms without changing the underlying Yates test. On four real RAD-seq datasets comprising 41.9 billion bases and 29 million markers, rsx reproduced published RADSex v1.2.0 calls, achieved an 8.38-fold geometric-mean speedup across 56 paired timings (2.77-fold for FASTQ processing), and recovered every Bonferroni-significant positive-control marker. In Danio albolineatus, treated as null in the source publication, the posterior layer surfaced 30 W-linked marker hypotheses; in Notothenia rossii it withheld 400 Bayes-factor-only rows compatible with a low-prevalence null. Python bindings, a C API, and a reproducibility archive provide the workflows used for all reported numbers. rsx is released under GPL-3.0-or-later.

Context. Neutral helium (He I) produces several spectral lines that are widely used for solar diagnostics. The role of collisions between He I atoms and neutral hydrogen (H I) in the modeling of solar He I lines remains insufficiently quantified. Accurate determination of collisional rates affecting atomic polarization is needed for solar spectropolarimetry. Aims. Our aim is to provide a set of multi-level and multi-term collisional depolarization, polarization-transfer, and population-transfer rates, due to isotropic collisions with neutral hydrogen, for He I levels and terms involved in the main solar He I diagnostic lines. Methods. The calculations are performed within the frozen-core approximation, in which the inner 1s electron is treated as a core with Lc = 0, Sc = 1/2, and Jc = 1/2, while the outer electron is treated as the active valence electron. Results. We compute both multi-level rates, describing depolarization and polarization transfer between fine-structure J-levels, and multi-term rates, which additionally account for coherences between different J-levels belonging to the same term. Conclusions. Our results provide the collisional input needed for the statistical equilibrium equations (SEE) of the polarization of the main He I solar lines, including the 10830 Å, D3 5876 Å, and related triplet transitions, and allow a quantitative reassessment of the role of neutral-hydrogen collisions in He I spectropolarimetry.

We propose a new concept for quantum thermal logic gates -- analogous to classical electronic logic gates -- that exploit the heat current in a coupled quantum-dot system tunnel-coupled to metallic thermal reservoirs for logic operations in quantum circuits. We obtained a remarkable one-to-one correspondence with the structure of classical electronic logic gate circuits. An experimental setup is presented that demonstrates a realizable nano-electronic quantum circuit architecture for implementing such quantum thermal logic operations.

We study an inverse source problem for fully nonlinear elliptic equations of the form \[ F(D^2u)=f \quad \text{in } Ω. \] The question is whether the source term can be recovered from the Dirichlet-to-Neumann map. In two dimensions, the first linearization does not immediately give uniqueness: it leaves a natural conformal ambiguity in the linearized coefficients. For homogeneous nonlinearities $F$ with injective differential $DF$, we show that this ambiguity has a precise meaning at the level of the equation itself, namely that the source is determined up to an explicit scalar factor. The main point of the paper is to show how this remaining factor can be removed. We use the second linearization to extract information which is invisible at first order, and combine it with an algebraic nondegeneracy condition on the nonlinearity. Under this condition, the residual ambiguity is forced to be trivial, and the Dirichlet-to-Neumann map uniquely determines the source. The result applies, in particular, to homogeneous admissible Hessian equations of Monge--Ampère type and related examples.

Strontium ruthenate (Sr$_2$RuO$_4$, SRO) has been the subject of intense research as a model quasi-two-dimensional metal with strong electronic correlations and potential exotic multi-component superconductor. Yet the nature of the superconducting state and its emergence remain debated, despite highly detailed knowledge of the normal-state electronic properties. Here we use diffuse neutron and x-ray scattering to uncover self-organized structural inhomogeneity on the picosecond timescale in SRO. We show that these structural correlations do not originate from extrinsic disorder but rather involve correlated displacements of oxygen atoms in the quintessential RuO$_2$ planes. Moreover, the observed displacement pattern is consistent with distortions due to orbital order that we obtain in first-principles calculations, which suggests that orbital effects could play a pivotal role in the physics of SRO. The appearance of such dynamic inhomogeneity may be relevant for a wide range of prominent oxides with similar lamellar structures, such as the cuprates and nickelates.

Decision-making in urban infrastructure management during extreme events relies heavily on human operators, yet current computational support systems often fail to account for non-monotonic human adaptation and latent psychological biases like overconfidence and defensive overcorrection. This study addresses this gap by integrating Instance-Based Learning Theory (IBLT) into the domain of civil engineering computing. We establish a computational cognitive architecture that simulates operator decision processes through the mathematical mechanisms of memory retrieval and utility blending. This model functions as a computational baseline, representing boundedly rational adaptation driven by experiential priors, thus allowing for the algorithmic isolation of latent psychological biases from the baseline dynamics of memory-based learning. We demonstrated this framework using a human-in-the-loop microworld experiment simulating subway flood-induced track suspensions, where dispatchers must balance passenger safety against service efficiency. Analysis revealed a complex, non-linear human adaptation cycle consisting of four phases: acquisition, overconfidence, overcorrection, and recalibration. Specifically, the computational model exposed a significant divergence during the post-accident "overcorrection" phase: while human operators exhibited immediate, defensive risk overestimation, the model maintained a stable trajectory based on accumulated experience. This strategic divergence confirms that operational instability following failure is often attributable to acute psychological bias overriding stable memory-based adaptation, a pattern theoretically expected to recur across analogous high-stakes environments and validatable through multi-modal behavioral and sensor data from professional operators.

We study an inverse problem for translation-invariant symmetric stable operators of the form \begin{equation*} L_a u(x)=\mathrm{P.V.}\int_{\mathbb R^n}(u(x)-u(y))\frac{a((x-y)/|x-y|)}{|x-y|^{n+2s}}\,dy, \quad 0<s<1, \end{equation*} where the unknown is the even angular density $a$ on $\mathbb Sn$. For a bounded open set $Ω\subset\mathbb R^n$, with $Ω_e=\mathbb R^n\setminus\overlineΩ$, we consider restricted exterior Dirichlet-to-Neumann maps $Λ_a^{W_1,W_2}$, where exterior data are supported in $W_1\SubsetΩ_e$ and the nonlocal Neumann data are observed on $W_2\SubsetΩ_e$. We prove three recovery results for the leading angular density. In the overlapping regime $W_1\cap W_2\ne\emptyset$, the exterior diagonal singularity determines every smooth elliptic angular density. In the separated regime $\overline W_1\cap\overline W_2=\emptyset$, where this singularity is absent, we prove uniqueness in the finite harmonic angular class by an exact factorization of the stable symbol. We also prove separated-data uniqueness for real-analytic angular densities when the source and observation sets lie in the unbounded exterior component, using analytic continuation of the off-diagonal Dirichlet-to-Neumann kernel and a far-field asymptotic argument.

This paper addresses model order selection under large-dimensional, correlated, non-Gaussian noise. Sources are assumed to be embedded in additive Complex Elliptically Symmetric (CES) noise with an unknown Toeplitz-structured scatter matrix. We propose a two-stage robust framework: (i) a noise-whitening step based on a Toeplitz-rectified $M$-estimator of the scatter matrix, and (ii) signal subspace rank inference via large-dimensional Random Matrix Theory (RMT). Almost sure consistency of the proposed estimators is established, together with explicit RMT eigenvalue upper bounds separating signal from noise components, in the regime where the observation dimension $m$ and the sample size $N$ grow proportionally. Three estimation branches are derived, based respectively on the sample covariance matrix (SCM), Maronna's $M$-estimator, and the distribution-free Tyler $M$-estimator for whitening. The methodology is validated on synthetic data, real hyperspectral images, EEG recordings, and financial data, with significant gains over AIC and unwhitened methods.