Muon-catalyzed nuclear fusion (\mucf) replaces atomic electrons with negative muons, compressing atomic orbitals by about two orders of magnitude and enabling deuterium--tritium (D--T) fusion under near-room-temperature conditions. This paper reviews the physical principles of \mucf{} and formulates its essential dynamics as a four-step cycle: muonic-atom formation, muon transfer, resonant \dtmu{} molecular formation, and D--T fusion with muon release and recycling. A kinetic model is used to quantify the number of catalysis cycles per muon and the corresponding energy gain. We focus on the central limitation of catalytic efficiency, namely the alpha-sticking effect, and discuss possible breakthrough routes including nuclear-spin and muon dual polarization, in-flight muon-catalyzed fusion, and heavy-ion-driven magneto-inertial fusion. Within the idealized assumptions of the present model, a four-dimensional synergistic scheme combining dual polarization, high-density confinement, electric-field-assisted muon recovery, and resonant enhancement may increase the number of catalysis cycles per muon from the present experimental record of about 150 to more than 500, potentially enabling an energy gain \(Q>2\). On this basis, we propose a conceptual fusion--fission fuel-breeding hybrid reactor, denoted as \mucf-FBR, which exploits the 14.1-MeV neutron yield of \mucf{} to breed \({}^{239}\mathrm{Pu}\) from a \({}^{238}\mathrm{U}\) blanket in a decoupled fusion--fission operating mode. This concept may offer advantages in engineering robustness, radiation-damage tolerance, and natural-uranium utilization.

Narrow-linewidth lasers with absolute frequency anchoring are essential for precision metrology, coherent sensing, and emerging quantum technologies beyond laboratory environments. Optical cavities and interferometers provide exceptional short-term spectral purity but lack intrinsic absolute frequency references. Atomic transitions, in contrast, provide stable frequency anchors but offer limited discrimination sensitivity. Recent hybrid approaches have demonstrated the combination of compact optical resonators with atomic references, yet achieving the Hz-level regime remains challenging. Here, we present a hybrid architecture that enables simultaneous realization of Hz-level linewidth and atomic-referenced frequency stability. An external-cavity diode laser is first stabilized to a fiber interferometer to achieve Hz-level spectral purity, while the interferometer is subsequently anchored to an 87Rb D2 transition via modulation transfer spectroscopy to suppress long-term drift and define the laser frequency relative to the atomic transition. This dual-stabilization scheme realizes a compact atomic-referenced laser with a 3.4-Hz linewidth (1-rad integrated-phase method), a minimum fractional frequency stability of 3.4x10-14 at 0.56 s, and 9x10-13 at 100 s. This architecture establishes a practical and scalable route toward compact and field-deployable atomic-referenced narrow-linewidth lasers for precision metrology and quantum technologies.

Estimating equations arise in a wide range of statistical applications, including longitudinal and clustered data analysis, survival analysis, econometrics, and semiparametric inference. In high-dimensional settings, adding sparsity-inducing regularization often leads to computational challenges that are not fully addressed by standard penalized optimization routines. These challenges are closely tied to the structural form of the underlying estimating problem: mainly, the estimating function needs not be the gradient of a scalar objective and may involve asymmetric Jacobians, overidentification, nonsmoothness, nonconvexity, or nested optimization. This article first reviews the application areas of estimating equations, and then the computational methods for regularized estimating equations by organizing them into four broad formulations: minimization-type, Dantzig-type, regularization-type, and fixed-point-type approaches. We discuss the main numerical strategies associated with each formulation, including penalized optimization, constrained linear programming, iterative root-solving, and proximal fixed-point iteration. We also highlight the connection between regularized estimating equations and fixed-point problems, which provides a unified computational perspective for analyzing and solving regularized estimating equations.

Structural and dynamic correlations in the ground state of the one-dimensional Fermi one-component plasma are studied by Quantum Monte Carlo simulations. Results are presented for the pair correlation function, static structure factor, the one-particle density matrix and the momentum distribution, for the cases of full, partial and no polarization. Evidence is reported of density correlations slowly decaying with distance, with the concurrent emergence of quasi-crystalline order even in the weakly correlated regime. Effects of quantum statistics in the momentum distribution are discussed.

Quantifying structural stress in transaction networks requires metrics that capture structural organization beyond transaction volume alone. In this work, we introduce the Inefficiency Metric, a deterministic indicator designed to characterize the routing structure of capital flows in decentralized systems. Using Principal Component Analysis and Pearson correlation matrices computed from a six-year Hedera transaction dataset, we identify two dominant and largely independent structural dimensions: the effective diameter, related to the spatial extension of transaction propagation, and the closeness centrality, associated with the efficiency of network-level flow processing. The proposed metric reveals significant topological fluctuations associated with major macroeconomic and ecosystem-level events. Increased inefficiency is observed during periods marked by intermediary fragmentation or rapid smart-contract expansion, whereas lower inefficiency corresponds to phases of network compaction during market stress or institutional concentration. Comparison with a seven-dimensional Isolation Forest approach shows that the metric effectively captures severe multidimensional anomalies while preserving a clear structural interpretation. Overall, these results provide a physics-inspired framework for relating the large-scale organization of decentralized transaction networks to observable economic dynamics.

Classical Proper Orthogonal Decomposition (POD)-based Galerkin projection models of chaotic flows typically require a large number of modes as well as stabilization or closure terms to achieve adequate accuracy and long-term stability. We present a novel differentiable programming framework that stabilizes low-rank POD-Galerkin models without increasing the number of modes or introducing additional closure terms, thereby delivering both high efficiency and high accuracy. Model stabilization is achieved by tuning the linear and quadratic tensors in the POD-Galerkin using differentiable programming, trained on short-term trajectory data. A key finding of this study is that a purely point-wise trajectory-based loss function yields poor long-term accuracy for chaotic systems. In contrast, a hybrid loss function that combines trajectory error with a physics-based conservation-of-energy term provides superior long-term performance. We demonstrate the approach on a chaotic lid-driven cavity flow at Re = 30,000. The stabilized ROM achieves an order-of-magnitude reduction in computational cost compared with the classical POD-Galerkin method: it remains accurate and stable with only 20 modes, whereas the classical ROM requires 80 POD modes.

Many problems in nonlinear and statistical physics are formulated through represented flows, including physical-space vector fields, phase-space drift fields, and truncated renormalization-group beta functions. We introduce a complementary representation-dependent diagnostic for testing whether finite-separation flow geometry is stable across observational resolution. For two separated points, states, or theories, the method compares the direction of the corresponding vector-field increment after the field has been smoothed at two resolutions. Averaging this normalized comparison over sampled separations gives a coherence matrix tied to the chosen variables, coarse graining, metric, and sampling protocol; it is a consistency test, not a coordinate-invariant quantity. We demonstrate the diagnostic in three settings. Synthetic divergence-free fields with identical Fourier amplitudes, spectra, and scalar two-point correlations nevertheless produce distinct coherence matrices, showing that second-order statistics do not determine cross-resolution increment geometry. Lorenz phase-space tests show that a smooth coordinate wrinkling changes represented drift geometry without changing the underlying dynamics, and that a weak model perturbation lowers finite-separation coherence even when local stretching proxies remain closely matched. Finally, for functional renormalization-group flows of the three-dimensional \(O(1)\) scalar theory, projected \(M=4,5,6\) LPA beta fields remain internally coherent, while cross-truncation coherence decreases as higher-order coupling directions are activated. The diagnostic provides a practical field-level check of how representations, models, and truncations preserve finite-separation flow geometry, complementing rather than replacing standard local, spectral, or fixed-point diagnostics.

We formulate and prove a constant-curvature, holonomy-valued Lorentzian analogue of Minkowski theorem for generalized tetrahedra in the constant-curvature Lorentzian spaces ${\rm dS}^3$ and ${\rm AdS}^3$. Four non-trivial based ${\rm SO}^+(1,2)$ holonomies, or equivalently ${\rm SL}(2,\mathbb{R})$ spin lifts, determine intrinsic face normals, a dihedral Gram matrix $G$, and oriented triple products of intrinsic face normals. Under closure, nondegeneracy, and the outward convex branch condition, these data reconstruct a unique strictly convex tetrahedron up to ambient isometry. The sign of $\det G$ selects the de Sitter or anti-de Sitter model, and the prescribed holonomies are exactly the based Levi-Civita face holonomies of the reconstructed tetrahedron. The extrinsic face normals also define a polar-dual projective tetrahedron. In particular, the all-null AdS sector gives ideal dual tetrahedra, and the all-timelike AdS sector gives hyperideal dual tetrahedra. In the all-spacelike sector, changing to ${\rm SU}(2)$ real form recovers the reconstruction theorem for Euclidean spherical and hyperbolic tetrahedra.

We produce refined index obstructions, generalizing recently constructed index obstructions due to de Jong and Perry, for topologically trivial Brauer classes on smooth and projective complex varieties. We show that our refined obstructions are more stringent than previous obstructions and, as a consequence, we produce more counterexamples to the integral Hodge conjecture. Throughout this work, we focus on algorithmic aspects of these obstructions and we illustrate many of these aspects through the concrete examples of complex abelian varieties.

3D reconstruction techniques such as LiDAR scanning and photogrammetry have made it practical to build detailed geometric models of real-world environments. Such reconstructed models can potentially serve as the foundation for wireless digital twins and support network planning and optimization. The core challenge is that reconstructed models inevitably contain geometric artifacts such as holes and noisy surfaces, and wireless simulation is highly sensitive to such noise. To solve this problem, we propose a differentiable directional scattering model to approximate the noise-sensitive specular reflection. This approximation smoothly distributes reflected power among nearby ray directions, making the simulator inherently robust to local geometric artifacts in the reconstructed model. We prove mathematically that this approximation preserves asymptotic path-gain accuracy. Building on this idea, we propose mmDiff, an end-to-end differentiable framework for calibrating material properties from sparse mmWave measurements and predicting mmWave channels. We evaluate mmDiff on both real-world and synthetic datasets, and demonstrate its superior performance over prior methods using pure specular reflection in noisy reconstructed geometry.

Modern online services rely on third-party APIs for authentication, payments, communication, identity verification, fraud detection, observability, and fulfillment. These dependencies are outside the direct operational control of the application owner and may experience regional outages, throttling, latency spikes, quota exhaustion, or behavior changes that surface as user-visible failures. This paper presents configuration-driven dynamic API routing, an architecture for resilient third-party service integration based on pluggable factor lists, real-time telemetry, circuit breakers, bulkhead isolation, and a closed-loop decision engine. A factor list defines operation-specific hard gates and weighted scoring functions that evaluate candidate providers using live metrics, regional policy constraints, quota state, latency, cost, and incident signals. The router separates routing policy from application code, allowing operators to adapt vendor selection at runtime without redeploying applications. We formalize the factor-list model, describe a request-time routing algorithm, present the event pipeline that computes sliding-window provider health metrics, and analyze failover behavior under degraded-provider scenarios. We also describe an anonymized SMS verification case study in which manual vendor switching was replaced by automated routing driven by completion-rate telemetry.

We study the fluctuations of the number of real roots of random polynomials with independent, nonzero-mean coefficients. Such non-centered ensembles arise naturally in signal-plus-noise models and in random perturbations of deterministic polynomials. While Ibragimov and Maslova (1971) established the leading asymptotics of the expected number of real roots for non-centered polynomials with i.i.d. coefficients, the corresponding variance asymptotics and central limit theorem have remained open for more than fifty years. This stands in sharp contrast to the centered case, where the fluctuation theory is now well understood across a wide range of ensembles. We resolve this gap by developing novel comparison principles that reduce the fluctuation theory of a non-centered ensemble to that of its centered counterpart. These principles yield sharp variance asymptotics and central limit theorems for broad classes of ensembles, including Kac and hyperbolic polynomials, their derivatives, and related extensions. In particular, for both Kac and hyperbolic polynomials, the leading variance constant equals exactly one-half of that in the centered case, reflecting asymmetric suppression of fluctuations across the two regions where roots concentrate. Our results provide the first comprehensive fluctuation theory for the number of real roots of non-centered random polynomials.

Small-area precipitation forecasts support real-time decisions for reservoir operation, irrigation planning, drought monitoring, and flash-flood response. Operational value depends not only on point accuracy, but also on calibrated exceedance probabilities and warning rules that remain stable when local weather regimes depart from the training climatology. We evaluate a reverse-martingale regularized recurrent neural network (\RMRNN) for probabilistic precipitation forecasting and sequential early warning. A backward-coherence penalty is added to the recurrent hidden state; the resulting residual process drives a Shiryaev--Roberts (SR) detector, so the same latent trajectory that produces the forecast also supplies a continuously updated drought or flood-regime indicator. The framework is tested on the Taiwan CWA dense rain-gauge network, CHIRPS v2 daily gridded precipitation over Taiwan and the Horn of Africa, and NOAA GHCN-Daily stations over the Texas Hill Country. Across 1{,}000 replications, \RMRNN{} matches or slightly improves the GRU baseline in RMSE, MAE, and CRPS at 1~h--72~h lead while substantially improving alarm characteristics. The SR detector reduces false-alarm ratios by a factor of three to five at matched detection power. In the 2020--2021 Taiwan drought, onset is flagged 8--12 days earlier than SPI-3 thresholding; in the 2023 Typhoon Haikui flood, flash-flood risk is signalled 4~h before the CWA operational alert.

In this thesis we use the Beauville-Bogomolov decomposition to compute the LLV algebra of smooth projective complex varieties admitting a holomorphic symplectic form, generalizing known results from hyperkähler and abelian varieties. Using this explicit computation, we prove for many such varieties that Orlovs conjecture holds, which states that for two derived equivalent smooth projective varieties there exists an isomorphism of rational cohomology preserving the grading and Hodge structure. Moreover, we prove that this conjecture holds for all four-dimensional smooth projective varieties admitting a holomorphic symplectic form.

We study circular motion of charged test particles on the equatorial slice of a Taub--NUT black hole with Manko--Ruiz parameter $C$, immersed in a weak external magnetic field introduced via Wald's prescription. Because the Taub--NUT metric is not reflection-symmetric about the equator once $l\neq 0$, generic charged orbits lie on cones $x=\cosθ\neq 0$ rather than on the equatorial plane. We therefore analyse \emph{constrained} circular orbits obtained by imposing $x=\dot x=0$, and we exhibit in closed form the residual angular constraint that a fully self-consistent orbit would have to satisfy. Within this scope we derive the circularity and marginal-stability conditions and study how $B$ and $C$ shift the ISCO radius for prograde and retrograde branches. Increasing $B$ monotonically decreases $r_{\mathrm{ISCO}}$; the sign of the particle charge splits the two branches, with the ordering reversed between prograde and retrograde motion; and $C$ contributes only subleading corrections. The extension to self-consistent conical orbits is the natural direction for follow-up work.

Controlling the stacking and rotational registry of graphene layers provides a powerful handle on atomic-scale structural reconstructions that alter the electronic landscape at the nanoscale. In particular, this governs how massless and massive Dirac fermions coexist and interact at the monolayer-bilayer graphene interface. In the limit of marginal twist, the system reconstructs into domains of distinct vertical stacking order, introducing characteristic electronic properties and new electronic length scales, a regime that, despite its structural richness, remains largely unexplored. Here, using scanning tunnelling microscopy and spectroscopy, we demonstrate that at very low rotation angles the monolayer-bilayer graphene system relaxes into a network of three distinct stacking domains with individual electronic textures revealed through spatially resolved spectroscopic mapping and corroborated by computed local density of states. We report switching of the hierarchy of the tunnelling characteristics between Bernal and rhombohedral domains as a function of bias voltage. Furthermore, the measured spectroscopic maps exhibit theoretically anticipated domain wall 'twirling' around energetically unfavorable AAB stacking nodes, promoted by out-of-plane deformations. Our results shed light on fundamental structure-property relationships underpinning moiré-driven phenomena, opening new avenues for harnessing structural degrees of freedom in van der Waals heterostructures.

Decarbonizing electricity generation, heating, and transportation simultaneously requires integrated planning tools that can coordinate multiple energy production sources and demand points while remaining reliable under uncertainty. This paper develops a carbon-aware and uncertainty-resilient optimization framework for a grid-connected multiple source hub that co-optimizes electricity, heating, cooling, and transport energy services with an explicit hydrogen sub-hub. The proposed model is formulated as an MILP over a 25-year planning horizon (2025-2050). The hub integrates renewable electricity (Photovoltaic and wind), dispatchable resources (including natural-gas-based conversion), storage systems, demand response, and a hydrogen subsystem comprising an electrolyzer and hydrogen storage to supply hydrogen-vehicle demand and provide temporal flexibility. Two policy archetypes are examined: a Carbon Tax (price instrument), and a Net-Zero pathway (quantity instrument). To hedge feasibility-critical operational uncertainty, the deterministic model is extended using budgeted robust optimization and a tunable uncertainty budget. The developed scheme is applied to the province of Ontario, Canada; the results indicate substantial long-term hydrogen expansion, with the electrolyzer capacity increasing from 300~MW (2025) to 3,800~MW (2050) and hydrogen storage from 2,000~MWh to 37,000~MWh (2050), accompanied by sharply higher hydrogen production. Compared with deterministic solutions, robust solutions preserve feasibility under adverse realizations but incur a moderate robustness premium of approximately 6.6-9.0\% in total cost across the policy cases studied, while slightly reducing hydrogen utilization and renewable share and increasing reliance on dispatchable balancing.

We consider polynomial maps of affine space over an algebraically closed field of characteristic zero. We prove that every irreducible component of the zero locus of the Jacobian determinant corresponds to either a contracted divisor or a branching divisor. We further consider polynomial maps of degree two without contracted divisors and show that the Jacobian determinant is irreducible, anti-invariant under the Galois involution, and coincides with the defining equation of the unique branching divisor.

The eigenstate thermalization hypothesis (ETH) provides a fundamental mechanism for emergent statistical mechanics in isolated chaotic quantum systems, asserting that individual energy eigenstates behave as pseudorandom vectors within an energy window. This enables a complete characterization of nontrivial correlations among matrix elements in the energy eigenbasis, as described by the full ETH ansatz. Nevertheless, this description breaks down in systems exhibiting quantum many-body scars, which host non-thermal eigenstates with extensive energy. In this Letter, we address this problem by formulating the \textit{scar full ETH}, which captures correlations among matrix elements involving scar states. The corresponding scaling forms and factorization properties are established using typicality arguments. Multi-time correlation functions for scar states are then organized in terms of both thermal and scar cumulants, providing a nontrivial reorganization of higher-order correlations. We numerically demonstrate the validity of this framework in the paradigmatic model of quantum scars, the PXP model. Our results pave the way for a systematic understanding of intriguing correlations in systems with quantum many-body scars.

Electron and ion-cyclotron waves are well known to exist in solar system plasmas but their existence and importance in galaxy clusters is an open question. Guided by numerical simulations, (Ley et al. (2024)) argued that whistlers (electron-cyclotron) and ion-cyclotron (IC) waves are generated by trapped particles in mirror modes in the nonlinear stages of the mirror instability under ICM conditions. Building on this work, we construct a novel particle propagation simulation of the ICM plasma based on the static electromagnetic field configuration from the fully kinetic particle-in-cell (PIC) simulation of the nonlinear mirror instability by (Ley et al. (2024)). We study how the trapping rate of particles is related to the secondary waves driven by mirror modes. We observe that secondary whistlers and IC waves enhance trapped particle escape from mirror modes. We measure the particle-wave scattering rate by whistlers and IC waves, demonstrate that the scattering rates and wave amplitudes follow the proportionality relation expected from quasilinear theory, and show the existence of a significant correlation between scattering rates and the excitation of secondary instabilities.

We investigate black hole area quantization by imposing Landauer's principle on the discrete entropy change between consecutive area levels. The elementary transition is identified with the entropy cost of erasing one bit of information, \(ΔS=k_B\ln 2\). For the Bekenstein--Hawking entropy, this gives the standard Bekenstein--Mukhanov value of the area spectrum parameter, which is used as the reference limit. The same discrete construction is then applied to generalized entropy functionals. For Barrow entropy, the parameter \(γ\) becomes level dependent, while the relative separation between adjacent area levels still vanishes for large \(n\). For the modified Rényi entropy, the nonsingular branch has vanishing relative spacing at large \(n\), whereas the singular branch develops a finite-level pole. For the modified Kaniadakis entropy, the small \(κ\) expansion shows that a fixed deformation parameter prevents the relative area spacing from vanishing in the large \(n\) limit. Overall, the results suggest that Landauer's principle provides a useful framework for analyzing generalized entropic extensions of the Bekenstein--Mukhanov area spectrum.

At global scale, data-center electricity demand is growing faster than the grids that supply it, while system operators increasingly require large flexible loads that can adjust power within seconds to absorb variable wind and solar generation. For multi-megawatt AI/HPC facilities, the key unresolved question is practical and measurable: how quickly can the software stack translate a grid request into a real change in GPU power at the facility meter, where commitments are settled? We answer this on real hardware with GridPilot, a three-tier predictive controller operating across milliseconds, seconds, and hours, augmented by a deterministic safety-island bypass for fast response. On a three-GPU NVIDIA V100 testbed, GridPilot achieves a measured end-to-end trigger-to-target response of 97.2 ms, which is 6.9x faster than the 700 ms requirement of Nordic Fast Frequency Reserve. We further incorporate an instantaneous Power Usage Effectiveness (PUE) correction so dispatched commitments remain robust at meter level rather than only at IT load level. In replay experiments across six representative European grids (from Sweden to Poland), the PUE-aware controller closes 2.5-5.8 percentage points of cooling-overhead drag. GridPilot is released as open source and serves as a proof of concept that MW-scale AI/HPC demand can be engineered as controllable, grid-responsive flexibility by design.

Quantum-enhanced multiparameter sensing is often associated with distributed architectures or 2-anticoherent states, whereas squeezing in a single collective ensemble is typically limited to single-parameter metrology. Here, we show that a single ensemble can support simultaneous multiparameter squeezing when each sensor is promoted from a qubit to a qudit (i.e., spin with $d$ energy levels). We develop a general framework in which the optimal product probe state, the corresponding global readout observables, and the associated squeezing parameters are all determined from the single-site quantum Fisher information matrix. We then present a minimal qudit construction for two-parameter vector magnetic field sensing with local dimension $d=3$. We further identify a collective twisting-like interacting Hamiltonian that generates such multiparameter-squeezed states and numerically demonstrate scalable metrological gain. In particular, for a trapped-ion qutrit chain with power-law interactions, we obtain up to 12 dB enhancement in two-parameter sensing for $N=256$ sensors. Our results establish qudit-enabled multiparameter squeezing in a single ensemble as a distinct route to multiparameter quantum metrology with global readout, and highlight its potential advantage over distributed multi-ensemble strategies in the fixed-sensor-budget regime.

Quantum complementarity is a fundamental feature of quantum systems and has captivated the physics research community for nearly a century, with significant advancements emerging in recent decades. This review traces the historical evolution of the concept of complementarity, beginning with Bohr's original formulation. It then explores its modern quantification through complementarity relations and its profound connection to the foundational postulates of quantum theory. Furthermore, it delves into key related developments, such as the operational definition of complementarity in the context of incompatible observables, its potential links with quantum uncertainty relations and contextuality, its various applications, and other pertinent topics. This review aims to serve physicists interested in quantum resources, quantum correlations, and the foundational principles of quantum mechanics.

Lezama \cite{LezamaLatorre2017} introduced the notion of semi-graded ring with the aim of generalizing $\mathbb{Z}$-graded rings and several families of noncommutative rings of polynomial type non-$\mathbb{N}$-graded such as the skew Poincaré-Birkhoff-Witt extensions defined by him \cite{GallegoLezama2010}. In a series of papers, \cite{Lezama2020, Lezama2021, LezamaGomez2019, LezamaLatorre2017}, he studied problems of non-commutative projective algebraic geometry generalizing the original ideas of Artin et al. \cite{Artin1992, ArtinSchelter1987, ArtinTateVandenBergh2007, ArtinTateVandenBergh1991, ArtinZhang1994} on $\mathbb{N}$-graded rings, in the categorical context of the category $\mathsf{SGR}-R$ of left semi-graded modules over a semi-graded ring $R$. In this note we prove that $\mathsf{SGR}-R$ possesses a canonical set of free generators via shifted twists, which endows the category with a {\em Grothendieck structure} and guarantees the existence of enough injective and projective objects. This categorical robustness allows us to formulate a semi-graded analogue of Baer's criterion for injectivity and to establish a first approach to the dual theory of projective resolutions using shifted twists.

In this work, we investigate the thermodynamic properties and quasinormal modes of a regular Dymnikova-Letelier black hole. Starting from the Einstein field equations sourced by an effective anisotropic fluid, we analyze the resulting spacetime geometry and derive the associated thermodynamic quantities, including the Hawking temperature, heat capacity, and Gibbs free energy. The thermodynamic analysis reveals the existence of phase transitions characterized by divergences in the heat capacity, whose location depends sensitively on the string fluid parameter. We then study the dynamical response of the system under scalar perturbations by computing the quasinormal mode spectrum using the sixth-order WKB approximation. Our results show that, for all considered values of the parameters, the imaginary part of the quasinormal frequencies remains negative, while the real part stays positive, indicating the stability of the black hole under scalar perturbations. Furthermore, the presence of the string fluid leads to systematic shifts in both the oscillation frequencies and damping rates. These results demonstrate that the string fluid significantly affects both the thermodynamic behavior and the dynamical stability of the Dymnikova-Letelier spacetime.

We study rotating black holes in general relativity coupled to nonlinear electrodynamics (NED), focusing on an axisymmetric solution with deformation parameter g. On the spherical seed, weak-field lensing via the Gauss-Bonnet method and the shadow radius yield a spin-insensitive bound by enforcing a conservative ~10% tolerance on the Sgr A* ring size, namely g/M \lesssim 1.26. In the eikonal regime we derive analytic quasinormal-mode shifts, even in g, and obtain an independent ceiling consistent with the shadow constraint. For the rotating geometry, we provide closed-form ZAMO scalars, chart horizons and ergoregion, and analyze equatorial geodesics (photon orbits and ISCO). We then formulate in the ZAMO frame the Comisso-Asenjo reconnection channel, identify the negative-energy window, and integrate the extracted power over the allowed radii; from the tolerated fractional departure from the Kerr power we define a spin-dependent extraction bound g_δ(a|σ_0,ξ). Taken together, the QNM/shadow ceiling and the extraction bound appreciably narrow the admissible region for g/M in the (a/M, g/M) plane, so even within our deliberately simplified, single-layer equatorial setup, the two complementary probes already provide informative constraints on NED deformations, testable with present data and upcoming horizon-scale and ringdown campaigns.

We study stochastic object assignment problems in which objects may have minimum and maximum requirements, such as with classes with upper and lower enrollment bounds. We construct a new random assignment mechanism, the minimums probabilistic serial (MPS) mechanism, which generalizes the Probabilistic Serial mechanism of Bogomolnaia and Moulin (2001). The random allocation produced by MPS is guaranteed to be Pareto efficient; that is, there is no other implementable allocation that all agents prefer via first order stochastic dominance. We also show that MPS is i) envy-free, in that no agent will strictly prefer another agent's assignment, and ii) weak strategyproof, in that agents cannot achieve a better assignment by misreporting their preferences.

Previous density functional theory (DFT) calculations for random solid solution (RSS) CoCrNi predict negative intrinsic stacking-fault energy (ISFE) at 0 K, contrary to experimental observations of finite stacking-fault widths. Two explanations have been proposed: finite-temperature stabilization of the RSS state, suggested by harmonic approximations showing increasing ISFE with temperature, and local chemical order (LCO), which shifts the ISFE to positive values at 0 K. Here, we compute temperature-dependent generalized stacking-fault free energies for RSS and LCO CoCrNi using a near-quantum-accuracy machine learning interatomic potential and the fully anharmonic projected average force integrator. Unlike harmonic approximations, our anharmonic calculations show that the RSS ISFE decreases with temperature and remains negative, indicating that RSS stacking faults are not thermally stabilized at elevated temperatures. By contrast, LCO maintains positive ISFE over 0-1000 K. Molecular dynamics simulations further confirm unbounded dislocation dissociation in RSS CoCrNi but finite stacking-fault widths in the LCO state.

Policy learning in modern operations environments faces a fundamental tension between limited operational data and the large, often continuous, state and action spaces over which good decisions must be identified and deployed. We study value-based policy learning in stochastic optimal control: a greedy policy induced by an estimate of the optimal action-value function $Q^*$ is deployed, and its performance is measured by regret. The empirical success of this approach calls for statistical insight into the structures that enable fast regret convergence. We show that, in continuous action spaces, fast policy learning is induced by three geometric structures: a growth exponent $p$, which quantifies how quickly $Q^*$ separates suboptimal actions from its maximizers; a margin-mass exponent $m$, which controls how much deployment mass lies on states with weak growth; and an action-wise regularity exponent $q$, which measures the smoothness of the $Q^*$-estimation error across actions. Given a $n^{-1/2}$-accurate estimator of $Q^*$, we show that the minimax-optimal policy regret convergence rate is \[ \widetildeΘ\left( n^{-\min\left\{\frac{p}{2(p-q)},\frac{m+1}{2m}\right\}} \right), \] up to a logarithmic factor at the boundary between the two regimes. The exponent $q$ is crucial: $q>0$ yields faster-than-$n^{-1/2}$ regret. This regime is natural in operations applications. In particular, we verify $q>0$ under mild regularity conditions in dynamic inventory control and service allocation examples, while the mechanism underlying this fast rate regime extends beyond these settings.