Magnetars are usually interpreted as highly magnetized neutron stars, yet a small subset of low spin-down sources has motivated alternative scenarios involving highly magnetized white dwarfs. We test whether the observed magnetar sample is consistent with a single neutron-star population or whether the data favor an additional compact-object channel. We combine exploratory machine-learning diagnostics with hierarchical Bayesian population modeling. First, we apply principal component analysis and K-means clustering in $(P,\dot{P},L_X)$ space, and then train a Random Forest classifier with leave-one-out cross-validation to identify the observables driving the empirical split. We subsequently construct a hierarchical Bayesian mixture model that links spin parameters to magnetic-field distributions through covariate-dependent mixing fractions. Posterior inference is performed with Hamiltonian Monte Carlo, and predictive performance is assessed with Pareto-smoothed importance sampling leave-one-out cross-validation. The exploratory analysis reveals a reproducible sub-structure: the Random Forest reaches $>95\%$ LOOCV accuracy, with $L_X$, $\dot{P}$, and $kT$ emerging as the dominant predictors. However, the Bayesian comparison shows no statistically significant preference for a two-population model. Instead, a few low spin-down sources receive intermediate posterior membership probabilities, indicating that they are better interpreted as transitional or outlying objects than as members of a clearly distinct class. Overall, current data do not require a separate white-dwarf magnetar population. The main result is therefore conservative but strong: the observed sample is adequately described by a predominantly neutron-star population, while still allowing physically interesting deviations in specific sources.

We unite two of the most widely used approaches for strongly damped, non-Markovian open quantum dynamics, the Hierarchical Equations of Motion (HEOM) and the pseudomode method by proving two statements: First, every physical bath correlation function (BCF) that can be written as a sum of $N$ exponential terms can be obtained from a physical model with $N$ interacting pseudomodes which are damped in Lindblad form. Second, for every such BCF there exists a non-unitary, linear transformation which mirrors the evolution of the system-pseudomode state onto the HEOM hierarchy, and vice versa. Our proofs are constructive and we give explicit expressions for the mirror transformation as well as for the pseudomode Lindbladian corresponding to a given exponential BCF. This approach also gives insight and provides elegant derivations of the corresponding Hierarchy of stochastic Pure States (HOPS) method and its nearly-unitary version, nuHOPS. Our result opens several avenues for further optimization of non-Markovian open quantum system dynamics methods.

Ensuring safety under unknown and stochastic dynamics remains a significant challenge in reinforcement learning (RL). In this paper, we propose a model predictive control (MPC)-based safe RL framework, called Probabilistic Ensembles with CBF-constrained Trajectory Sampling (PECTS), to address this challenge. PECTS jointly learns stochastic system dynamics with probabilistic neural networks (PNNs) and control barrier functions (CBFs) with Lipschitz-bounded neural networks. Safety is enforced by incorporating learned CBF constraints into the MPC formulation while accounting for the model stochasticity. This enables probabilistic safety under model uncertainty. To solve the resulting MPC problem, we utilize a sampling-based optimizer together with a safe trajectory sampling method that discards unsafe trajectories based on the learned system model and CBF. We validate PECTS in various simulation studies, where it outperforms baseline methods.

Non-reciprocal interactions in active matter gives rise to a multitude of fascinating phenomena among which are collective oscillatory states without intrinsic particle chirality and active turbulence. Here we show that in a paradigmatic model for non-reciprocal flocking, the two species Vicsek model, these two states coexist: chiral order for small flocks, and extensive spatiotemporal chaos for large flocks, both separated by a finite wavelength instability whose scale is set by the rotation radius of the chiral orbits. For system sizes larger than this length scale extensive spatiotemporal chaos unfolds, as manifested by an extensive number of Floquet exponents for the unstable chiral state, a positive Lyapunov exponent, a finite correlation and chaotic length and a broad energy spectrum. Our results suggest that complex, turbulent behavior is a generic possibility in any system where particles or fields interact asymmetrically and may have significant implications for understanding how non-reciprocal interactions could drive chaotic, fluid-like behavior in active matter.

Ultracompact binary systems, consisting of two compact objects in an orbit $\lesssim 0.5 R_\odot$, should exhibit measurable rates of orbital period change ($\dot{P} \neq 0$) due to the emission of gravitational waves (GWs). Measurements of \pdot\ have so far been limited to the shortest-period ultracompact binaries ($\lesssim 20$\,min). Among the AM\,CVn-type subclass, several works have proposed the presence of extra angular momentum loss beyond GW emission, with magnetic braking being a widely discussed mechanism. If present, this magnetic braking would dominate the angular momentum loss of AM\,CVn-type binaries with orbital periods $\gtrsim 30$\,min. In this work, we present a long-term eclipse timing study of two AM\,CVn-type binaries, YZ\,LMi and Gaia14aae, with respective orbital periods of 28.3\,min and 49.7\,min and continuous observations since 2006 and 2015. Both systems show $\dot{P}$ consistent with zero within $2σ$. Their $3σ$ upper limits are $1.1 \times 10^{-13}\,{\rm s \, s}^{-1}$ and $9.7 \times 10^{-14}\,{\rm s \, s}^{-1}$ respectively. These non-detections are most simply explained by a scenario in which secular angular momentum loss is not substantially stronger than GW emission at all orbital periods, but is combined with deviations from the secular $\dot{P}$ whose timescales span decades but whose amplitude is $\lesssim 10^{-13}\,{\rm s \, s}^{-1}$. %, orders of magnitude smaller than the eclipse timing variations seen in hydrogen-dominated cataclysmic variables. Our non-detections of $\dot{P}$ represent a limit on the strength of any enhanced angular momentum loss beyond pure GW emission.

The Neutron Optics Parity and Time-Reversal Violation Experiment (NOPTREX) Collaboration has developed a modular array of 24 NaI(Tl) detectors to measure parity and time-reversal symmetry violation in neutron-nucleus interactions. These detectors feature custom electronics that allow for operation in pulse or current mode. This paper describes the design, construction, characterization, and testing of the detectors in this array. We demonstrate the ability of the array to detect parity-odd asymmetries in neutron resonances by observing the known 0.7 eV parity-violating resonance in 139La in measurements at LANSCE.

Heavy-ion collisions produce final states with thousands to tens of thousands of particles, making their simulation among the most computationally intensive tasks in high-energy nuclear physics. We present a fast, high-fidelity generative model for heavy-ion events based on a score-driven diffusion process and the Point-Edge Transformer architecture within the OmniLearn framework. A two-stage training strategy is performed: Stage-1 training on lower-multiplicity O-O collisions allowing the model to learn a stable event and particles representation, followed by fine-tuning on challenging high-multiplicity Pb-Pb collisions. We benchmark the generator with a broad set of closure checks, including agreement of event- and particle-level observables in one and two dimensions, flow consistency reconstructed from the generated particles, end-to-end jet finding with FastJet including key jet and substructure observables, and a classifier-based application to quantify the sample fidelity. The results are promising, showing that a compact generative model can produce realistic, high-multiplicity heavy-ion events, at a level that makes local-scale generation for heavy-ion collisions at high energies a practical goal.

Although quantum random number generators rely on the inherent indeterminism of quantum mechanics, ensuring that the numbers produced are secure remains a significant challenge. We introduce two semi-device-independent randomness expansion protocols in a prepare-and-measure setting, where the source and measurement devices are treated as uncharacterised and we assume trust only in testing device, which could be implemented using a photodiode. One protocol achieves expansion by recycling the input randomness, while the other uses a biased input distribution to achieve expansion in settings where recycling is not possible. The protocols are proven secure against quantum side information. Our results show that high randomness rates are achievable under experimentally realistic conditions, with expansion obtained in as few as $10^5$ to $10^6$ rounds with the recycling protocol.

We develop a dissipative extension of classical mechanics based on a complex, and more generally quaternionic, action principle that endows every classical system with an intrinsic environment. Decomposing the action into conservative and divergence-induced components yields two coupled Hamilton Jacobi equations describing a dynamically intertwined system environment pair. This motivates a Dual Sector or Dual Environmental Interpretation (DSI/DEI), in which the additional degrees of freedom behave as an image sector exchanging energy, information, and phase with the system. Applying a generalized Madelung transform produces a nonlinear dissipative wave equation whose symmetric equilibrium limit reduces to the Schroedinger equation, with the quantum potential and linearity emerging from balanced intersector coupling. In this framework, the wavefunction is not fundamental but encodes the interaction geometry between system and environment, providing a classical origin for interference, amplitude phase coupling, and probabilistic structure. Extending the imaginary structure to multiple independent directions yields a multienvironment generalization capable of representing measurement-like processes, nonMarkovian memory, and entanglement type correlations. The formulation unifies aspects of dual-system models, hydrodynamic approaches, and non-Hermitian dynamics within a single action-based framework, and suggests that quantum mechanics corresponds to a stable symmetric phase of a broader dissipative classical theory.

Correlated electron systems that host multiple electronic orders offer routes to multifunctional quantum materials, but strong competition between these orders often prevents their coexistence. Here we show that nanoscale, metastable intercalated heterostructures can stabilize a rare combination of long-range magnetism and a commensurate charge density wave (C-CDW) order in a single material. We synthesize a two-dimensional (2D) metastable crystal, T/H-Fe$_x$TaS2, which comprises an endotaxial polytype heterostructure of 1T-TaS$_2$ and H-TaS$_2$ with Fe intercalated in the van der Waals interfaces. In T/H-Fe$_x$TaS2, Fe intercalants provide localized spins that support ferromagnetism, while 1T layers host a robust commensurate charge density wave (C-CDW) that persists to room temperature. In these intercalated heterostructures, Fe content simultaneously tunes ordering of spin and charge degrees of freedom, positioning topochemically-prepared intercalated endotaxial heterostructures as a route to stabilize and control competing quantum phases in 2D materials.

A basic model is provided that places active, intentional choices by biological organisms on a solid physical footing. The model is provisionally called "Agent Choice via Quantum Flux." It brings to bear specific physics on living systems in a way that allows for intentional choices not pre-determined by physical laws, but remaining consistent with those laws. It does so by exploring a possible many-to-one relation of quantum states to agent choices, with a parallel to the relation of thermodynamic microstates to macrostates.

We investigate the effective dynamics of a spatially flat FLRW universe coupled to a massless scalar field by applying the improved generalized uncertainty principle (GUP)-inspired deformations to the algebra of Ashtekar-Barbero variables. We consider deformations, once only in the geometry sector, and once in both the geometry and matter sectors. We show that in both cases, the classical singularity is replaced with a non-singular, emergent universe coasting from a constant-volume state in the infinite relational past time without a bounce. As expected, a constant geometric GUP parameter leads to fiducial anomalies, but we resolve it by employing an improved scheme in which this parameter is inversely proportional to the gravitational momentum. This leads to a universal, invariant maximum energy density while preserving the emergent nature of the universe. A Lyapunov stability analysis reveals that the improved scheme drives the universe toward classicality faster than the constant scheme.

A principal with cheap capital optimally forces her counterparty to borrow at above-market rates. The reason: the form of finance is a screening device. Advances provide liquidity but pool types; contingent transfers separate types, but, because they are not pledgeable, impose financing costs. The optimal contract preserves outside-finance exposure to maintain screening power. Two sufficient statistics pin down the optimal advance share. With complementary counterparties, a uniform subsidy that cheapens finance across every relationship can reduce the value of each. This explains the coexistence of early payment and contingent compensation in trade credit, venture capital, and internal capital markets.

Let $O$ be a discrete valuation ring and $A := O[X_{m \times n}]/I_{m}(X)$ the determinantal ring of maximal minors. We consider algebra maps $λ\colon A \to O$, which is tantamount to choosing rank-deficient matrices $a \in O^{m \times n}$. Following Iyengar--Khare--Manning, we compute the congruence module and the Wiles defect of $A$ at $λ$, expressing them in terms of the $(m - 1)$-sized minors of $a$.

Statistical inference for stochastic block models typically relies on the spectrum of the normalized adjacency matrix $\A^*$. In practice, the true probability matrix $\mathbf{B}$ is unknown and must be replaced by a plug-in estimator $\hat{\mathbf{B}}$. This substitution introduces two distinct types of estimation error: a simple perturbation $\boldsymbolΔ$, arising when $\hat{\mathbf{B}}$ replaces $\mathbf{B}$ only in the numerator, and a composite perturbation $\tilde{\boldsymbolΔ}$, arising when the replacement occurs in both the numerator and the denominator. Under both perturbation regimes, we decompose the total sum of squares into three components and conduct a detailed analysis of their asymptotic properties. This reveals a key, and perhaps surprising, distinction between simple and composite perturbations: the cross term $\tr({\A^*}\bDelta)$ is asymptotically negligible, whereas its composite counterpart $\tr({\A^*}\tilde{\bDelta})$ is not. Motivated by this, we develop a unified decomposition framework, expressing the composite perturbation matrix as $\tilde{\bDelta}=\check{\A}+\bDelta+\check{\bDelta}$, where $\check{\A}$ is a bias matrix of the normalized adjacency matrix, $\bDelta$ is the simple perturbation, and $\check{\bDelta}$ is a bias matrix of $\bDelta$. This structured decomposition allows us to precisely isolate and control each source of error, leading to a refined limiting theory for two key classes of test statistics. Concretely, for the largest eigenvalue statistic, we improve the existing condition from $K=O(n^{1/6-τ})$ to the optimal rate $K=o(n^{1/6})$ under both simple and composite perturbations. For the linear spectral statistic, our unified decomposition framework provides the necessary structure to systematically control these errors term by term, leading to a complete and rigorous proof of asymptotic normality.

This paper presents a field-based evaluation of Long Range Wide Area Network (LoRaWAN) signal propagation conducted at two locations within the Aerial Experimentation and Research Platform for Advanced Wireless (AERPAW) testbed: Lake Wheeler Field and NC State University's Centennial Campus. Three distinct transmission platforms were deployed, a ground vehicle, a multirotor drone at 50 meters, and a helikite at a steady altitude of 150 meters and 300 meters approximately. These platforms enabled a comparative study on how altitude, mobility, and terrain influence wireless signal reception across a LoRaWAN gateway network. We analyze received signal strength (RSSI) and signal-to-noise ratio (SNR) as functions of distance and spreading factor (SF). Three complementary metrics are visualized: SNR versus distance with demodulation thresholds, probability of successful reception, and SNR boxplots grouped by distance bins. These plots reveal link degradation patterns and demonstrate the role of adaptive SF selection in maintaining communication reliability. To characterize propagation behavior, we apply a log-distance path loss model to empirical data from the ground vehicle experiment, which encompass both rural and urban non-line-of-sight (NLOS) conditions. Model parameters are optimized through error minimization techniques. Our results show that the helikite platform, due to its stable high-altitude position, provided the most reliable and consistent link performance. Conversely, the drone and vehicle exhibited higher variability due to movement, obstructions, and terrain-induced multipath. These findings demonstrate the influence of platform dynamics and altitude on LoRaWAN reception performance, providing support for future aerial network planning efforts.

We assess the descriptive complexity of *bisimilarity* or "equality of behavior" on a family of Markov decision processes over uncountable standard Borel spaces, namely *nondeterministic labelled Markov processes* (NLMP). We show that bisimilarity is analytic for processes with a uniform assignment of finitely-supported measures to each state and label. More finely, we obtain that bisimilarity on the space of countable Kripke frames (or labelled transition systems) is classifiable by countable structures. We show that bisimilarity of well-founded ("terminating") processes is Borel. We also provide a lower complexity bound by reducing the relation of eventual equality of binary sequences $E_0$ to the former. As a consequence, there is no countable fragment of basic modal logic with denumerable conjunctions that characterizes bisimilarity for processes of small rank. We finally apply the previous Borel definability to study the well-founded part of discrete uniform processes over uncountable spaces.

As opposed to the ordinary Hall effect, the anomalous Hall effect (AHE) remained unexplained for decades, and, amazingly, some misconceptions have survived even now, in particular, the claim that AHE is linearly related to the net magnetization. Karplus and Luttinger provided a quantum-mechanical explanation of AHE by explicitly including the SOC and the Berry curvature of electronic bands. They did address the question of linearity, but only in the relatively uncommon limit of the exchange coupling smaller than SOC. Now the linear relation in traditional ferromagnets is understood as a domain population effect: both AHE and magnetization are independently proportional to the domain disbalance. In this connection, it is interesting to check to what extent this relation will hold in {\em single-domain} itinerant ferromagnet, the closest case to that analyzed by Karplus and Luttinger? We answer this question by direct calculations, using the Karplus-Luttinger formula, of AHE in a prototypical itinerant ferromagnet, ZrZn$_2$. We show that in the zero-magnetization limit, $M\rightarrow 0$, the linear relation hold, but at rather small moments of $\sim 0.4\ μ_B$/Zr breaks down completely and even flips the sign.

We show that on any weakly pseudoconvex $B$-regular domain, the classical Dirichlet problem for the complex Monge--Ampère equation with $\mathcal{C}^\infty$-smooth data does not in general admit $\mathcal{C}^{1,1}$-smooth solutions. This working draft is a prelude to potential-theoretic solutions to some extension problems for mappings that were thought to rely on such $\mathcal{C}^{1,1}$-smooth solutions.

Event-by-event transverse momentum correlations are sensitive to the equation of state of strongly interacting matter and are expected to exhibit anomalous fluctuations in the vicinity of the QCD critical point. We report the first measurements of two-particle transverse momentum ($p_T$) correlations for mid-rapidity charged particles in fixed-target Au+Au collisions at nucleon-nucleon center-of-mass energies $\sqrt{s_{NN}} = 3.0--7.7$ GeV, measured by the STAR experiment during the Beam Energy Scan (BES) Phase II program. The dependence of the scaled correlator on the number of participating nucleons ($N_{part}$) is studied to test expectations from an independent-source scenario, where the correlations are expected to scale as $1/\sqrt{N_{part}}$. We observe a clear breakdown of the expected scaling behavior in central collisions and identify a statistically significant non-monotonic dependence of the $p_T$ correlations on collision energy, with a significance of approximately $5σ$. In contrast, transport-model calculations and data from mid-central collisions yield significances of only $2σ$ and $1.4σ$, respectively, insufficient to support a claim of non-monotonicity. These observations provide new constraints on the equation of state at high baryon density and may be sensitive to the presence of a QCD critical point.

We present a geometric framework for adaptive whitening in gravitational-wave detectors, reformulating the problem from a sequence of spectral factorizations to parallel transport on a principal bundle. We identify the whitening filter as a section over the manifold of power spectra and derive the minimum-phase connection as the unique geometric structure that enforces signal causality while preserving signal-to-noise ratio. This construction yields a rigorous definition of geometric drift, a coordinate-independent scalar measuring the intrinsic instability of the detector noise floor. The central result is the flatness theorem, which proves that the curvature of the connection vanishes for scalar fields. This establishes a holonomic update law, guaranteeing that the optimal filter correction is path-independent and determined solely by the instantaneous noise state, free from geometric phase or hysteresis. This framework unifies the static theory of Wiener-Hopf factorization with the dynamic requirements of real-time control, providing a rigorous certification for the stability of zero-latency calibration routines and establishing a foundation for gauge-theoretic signal processing (GTSP) in next-generation detector networks.

Quasisymmetric functions in superspace were introduced as a natural extension of classical quasisymmetric functions involving both commuting and anticommuting variables. In this paper, we first provide a characterization of the algebra of quasisymmetric functions in superspace as an algebra of invariants under a quasisymmetrizing action of the symmetric group. Furthermore, we complete the superspace analogue of the classical hierarchy of combinatorial Hopf algebras by introducing the algebra of quasisymmetric functions in noncommuting variables in superspace. We endow this algebra with a Hopf superalgebra structure and thoroughly investigate its $Q$-basis and monomial basis, which are indexed by set supercompositions. By restricting to the minimal elements of the underlying poset, we construct the Hopf superalgebra of superpermutations, serving as the superspace analogue of the Malvenuto--Reutenauer algebra. We provide explicit product and coproduct formulas for these bases in terms of super-shuffles and global descents. Finally, via an abelianization morphism, we apply these noncommutative structures to derive a product formula for fundamental quasisymmetric functions in superspace.

We study asynchronous distributed decision-making for scalable multi-agent bandit submodular maximization. We are motivated by distributed information-gathering tasks in unknown environments and under heterogeneous inter-agent communication delays. To enable scalability despite limited communication delays, existing approaches restrict each agent to coordinate only with its one-hop neighbors. But these approaches assume homogeneous communication delays among the agents and a synchronous global clock. In practice, however, delays are heterogeneous, and agents operate with mismatched local clocks. That is, each agent does not receive information from all neighbors at the same time, compromising decision-making. In this paper, we provide an asynchronous coordination algorithm to overcome the challenges. We establish a provable approximation guarantee against the optimal synchronized centralized solution, where the suboptimality gap explicitly depends on communication delays and clock mismatches. The bounds also depend on the topology of each neighborhood, capturing the effect of distributed decision-making via one-hop-neighborhood messages only. We validate the approach through numerical simulations on multi-camera area monitoring.

We discuss a coupled-cluster formalism for carrying out imaginary-time evolution from an arbitrary reference, and study the properties of the resulting evolution trajectories. The evolution converges to a solution of the standard coupled-cluster amplitude equations in the long-time limit if a finite valued limit exists, but when such a limit does not exist, the trajectories still contain additional information beyond the standard solutions. We introduce the coupled-cluster energy variance which through its minima identifies physically regularized coupled-cluster amplitudes when the solutions of the amplitude equations are unreasonable. We demonstrate the value of this formalism in several exploratory examples within single- and multi-reference coupled-cluster formulations.

The Chambolle-Pock method, also known as the primal-dual hybrid gradient method, is a standard first-order algorithm for convex-concave saddle-point problems and composite convex optimization involving two proper, lower semicontinuous, convex functions and a bounded linear operator $L$. We study its convergence in real Hilbert spaces for step sizes $τ,σ>0$ and relaxation parameter $0<θ\le 1$. We prove that, if $τσ|L|^{2} \leq 4θ(2-θ)/(1 - 2θ+ 9θ^{2} - 4θ^{3})$, then the ergodic duality gap converges at rate $O(1/k)$, and that, when the inequality is strict, the primal-dual iterates converge weakly to a KKT point. In particular, this extends the weak-convergence theory to the previously unexplored regime $0<θ\le 1/2$. The proof is based on a Lyapunov function that remains uniformly valid over the entire interval $0<θ\le 1$.

Conversational AI companions have grown prominent in public discourse, yet scholarly understanding of user experiences remains limited, with existing research organized around evaluative poles of harm and benefit rather than examining what users seek, how affordances mediate need fulfillment, or how use evolves over time. Drawing on interviews with 20 users of AI companionship platforms and qualitative content analysis informed by Uses and Gratifications (U&G) theory, this study offers three contributions. First, participants reported gratifications mapping onto established U&G categories but qualitatively inflected by conversational AI's distinctive affordances, such as persistent availability, personalization, and absence of social judgment. Second, several gratifications, creative collaboration as relational co-production, relational simulation as interpersonal training, and sexual/romantic satisfaction as reclamation, do not map onto existing typologies, instead emerging through interactive processes in which users actively simulate experiences with AI. Third, gratifications shifted over time, moving from instrumental entry points toward emotional engagement and, in some cases, self-regulated moderation after therapeutic functions were fulfilled. These findings extend U&G by identifying gratification processes unique to interactive AI and suggest governance efforts would benefit from an empirically grounded understanding of how and why users engage with AI companions.

Background and Context: Artificial intelligence (AI) tools have been reshaping computing and computer science education. Trust in AI is a determining factor in the adoption of these tools. Recent studies have shown different trust factors across gender and first-generation status among students. However, these studies have focused mainly on Western, Educated, Industrialized, Rich, and Democratic (WEIRD) populations, and their generalizability to other populations with different languages and cultures is unclear. Objective: This study aims to evaluate trust in AI among Middle Eastern computer science students and the factors that can impact it. Method. We replicate a recent study of trust in four universities in three Middle Eastern, Arabic-speaking countries: Saudi Arabia, Kuwait, and Jordan. We analyze trust among students across different factors such as gender and first-generation status. Findings: Our results suggest that language fluency can predict trust in AI. Moreover, unlike the results from the US population where female students tended to trust AI more than their male peers, female students in Saudi Arabia indicated lower trust compared to their male counterparts, and we did not observe any noticeable differences across gender in the other countries. We also found a generally negative correlation between English language proficiency and students' confidence. Implications: This study highlights differences in students' adoption and trust in AI even within the same region. It emphasizes the need for more investigation into students' adoption and interaction in non-WEIRD regions for equitable adoption of this technology. It also suggests a need for efforts in designing effective AI systems tailored to the cultural and linguistic needs of the region.

This paper proposes niching importance sampling, a framework that combines concepts from reliability analysis, e.g. Markov chains, importance sampling, and relative cross entropy minimisation, with niching techniques from evolutionary multi-modal optimisation. The result is a highly robust estimator of the probability of failure, that can tackle sampling challenges posed by the underlying geometry of a reliability problem. Niching importance sampling is tested on a range of numerical examples and is shown to consistently avoid the degenerate behaviour observed for existing reliability methods on several multi-modal performance functions.

The declining synchronous inertia in power systems undergoing the energy transition increases the sensitivity of system frequency to generation and interconnector disturbances, making accurate frequency risk quantification increasingly important. Existing methods for frequency risk assessment, while valuable, lack formal uncertainty quantification, continuous hazard curves, and source-level disaggregation. This paper introduces Probabilistic Frequency Hazard Analysis (PFHA), a framework that adapts the mathematical architecture of Probabilistic Seismic Hazard Analysis (PSHA), the standard methodology in earthquake engineering, to power system frequency exceedance risk. The PFHA hazard integral computes annual exceedance rates by integrating over all combinations of loss sources, disturbance sizes, and system operating states through a frequency response prediction equation with calibrated aleatory variability. The framework is implemented with a 51-source catalogue constructed from operational data, empirical loss distributions from settlement-period generation records, Bayesian occurrence rate estimation, a dual analytical and physics-based frequency response prediction architecture, and a 324-path logic tree for epistemic uncertainty quantification. Application to the Great Britain power system using four years of operational data demonstrates agreement with the independently developed Frequency Risk and Control Report to within a factor of 1.5 at 49.2 Hz, while also quantifying the risk reduction from Dynamic Containment and Low-Frequency Demand Disconnection controls. To the author's knowledge, this is the first published explicit PSHA-style hazard-integral formulation for bulk power-system frequency exceedance risk.

Complex numbers are central to the formulation of quantum mechanics, yet their role as a genuine resource is only beginning to be understood. In this work, we demonstrate that quantum states with intrinsically complex amplitudes provide a fundamental advantage in state discrimination. We construct a set of five orthogonal three qubit pure states and show that the set is strongly nonlocal if and only if it includes imaginary components. Such a set becomes locally indistinguishable not only under local measurements but also against bipartite joint measurements. This enhanced robustness makes imaginarity a valuable resource for quantum cryptography since information encoded in these states remains secure against collaborative group attacks. Our results highlight a new operational role of complex numbers in quantum theory and establish imaginarity as a key enabler of cryptographic security. However, we reconstruct the set by replacing the only product state with a biseparable state whose shared entanglement between two parties nullifies the effect of imaginarity in exhibiting strong nonlocality. In fact, we show how entangling correlations between two distant parties can dilute the effect of imaginarity, and conversely, how imaginarity itself can mimic the role of entanglement. Nevertheless, the set spans a locally indistinguishable subspace, while its complement, in turn, produces distillable genuine entanglement. Notably, this is the smallest possible Unextendible Biseparable Basis (UBB) that resolves the open problem regarding the existence of a UBB of cardinality $d^2+d-1$ in $d^{\otimes 3}$. Our construction yields a highly powerful set, rich in resources from multiple perspectives of quantum information theory, including many-copy discrimination, unambiguous identification, entanglement creation from product state, and non-entangling perturbations.