Papers

Tidal disruption event (TDE) progenitors are commonly modelled as single stars on parabolic orbits around a supermassive black hole (SMBH), yet observations reveal a richer diversity of dynamical pathways. We show that tidal separation of stellar binaries by a $10^6\,M_\odot$ SMBH provides a natural mechanism for producing eccentric TDEs. Using restricted three-body and SPH simulations, we model a solar-like star (SLS)–white dwarf (WD) binary on a parabolic orbit. The binary orbital phase governs the outcome: one component is captured onto a tightly bound orbit while the other is ejected as a hypervelocity object, naturally producing TDEs with eccentricities $e \neq 1$. We classify these into Elliptical TDEs (eTDEs) and Hyperbolic TDEs (hTDEs), occurring with equal probability. For $\sim 88\%$ of orientations the disruption is clean, with no mass accreted by the WD. The remaining $\sim 12\%$, in two narrow phase windows, leaves the WD with a captured debris envelope (WDDE). About a third of that, $\sim 4\%$ of orientations, involves a direct WD–SLS collision near pericenter, with fallback peaking up to five times earlier and twenty times higher than for a single star; for the innermost $\sim 1.5\%$ the total WDDE mass exceeds $1.4\,M_\odot$, though the degenerate core does not, since the captured material forms a non-degenerate envelope, suggesting outcomes ranging from nova-like events to peculiar red giant-like objects. Depending on the phase, the mechanism may also produce repeating partial TDEs (rTDEs) and quasi-periodic eruptions (QPEs). Binary–SMBH encounters provide a robust channel for generating diverse TDEs with distinct observational signatures.

Everettian quantum mechanics is often said to lack coherent probability because every possible measurement result occurs. If all of them exist globally, what is probability supposed to be a probability of? This paper defends an axiomatic answer: normalized Born measure is postulated as objective probability over the records borne by an observer's future continuations. Collapse interpretations likewise postulate the Born probabilities, but instead assign them to possible global outcomes. Neither theory derives the probabilities from its ontology. The contribution is an explicit record-level probability model that separates probabilities for future local records from certainty about their global existence. I use this model to answer objections to the axiomatic approach and argue that neither global selection nor a further theory of personal persistence is required. At the level of recorded results, the Everettian law supports the same predictions and empirical inferences as the collapse law, despite the theories' different ontologies.

AU-scale structures in the interstellar medium have become relevant across several areas of astrophysics, from ISM microphysics to pulsar timing arrays and cosmic-ray (CR) propagation. Current sheets formed at magnetic-field reversals have drawn particular attention because they can deflect the dominant GeV CR population through large angles. Pulsar scintillation, an outstanding probe of plasma density, resolves these structures—but not their magnetic configuration. Conventional Faraday rotation measures (RM) are only marginally sensitive at AU scales and are further compromised by ionospheric systematics. We propose a method that isolates birefringence-induced polarization—the signature of magnetic reversal—by applying phase retrieval to polarized data. Pulsar scintillation further resolves ray paths separated by $\sim 1\,\rm{AU}$, enabling differential RM measurements that suppress the ionospheric common mode while preserving the AU-scale magnetic signal. We demonstrate the method on an archival observation of PSR B0834+06. Phase retrieval resolves the 1-ms scattering feature into two branches in Doppler-delay space. Under the corrugated current-sheet interpretation, these branches correspond to ray paths sampling opposite sides of an AU-scale current sheet. We measure a branch-to-branch RM difference of $(-9.3\pm3.2)\times 10^{-3}\text{ rad m}^{-2}$ at 2.9$\sigma$ across a 10-MHz band. The signal is consistent with a field reversal of $|\Delta\langle B_\parallel \rangle| \simeq4.4\pm2.1\,\mu\rm G$, sufficient to sustain a long-lived sheet. With only six independent subbands, we present this as a proof of concept rather than a definitive detection. If it proves scalable, its full implementation could constrain cosmic-ray transport and inform models of propagation-induced noise in pulsar timing arrays.

We present an observational study of the kinematic coherence between satellite orbital planes and the cosmic web. Using the SDSS DR12 galaxy sample combined with the Bisous filament catalogue, we investigate whether the orbital motion of satellites preserves the memory of filamentary accretion. For each satellite system, we define a projected orbital-normal vector using galaxy sky positions and line-of-sight velocity offsets. By measuring the angle $\theta$ between this vector and the local projected filament direction, we detect a distinctive preferred orientation: satellite orbital planes tend to contain or lie parallel to the filament axis. This signal deviates from the isotropic expectation at a high significance level of $12.8\sigma$. The strength of this kinematic connection depend strongly on environment and host properties. The preference for orbital planes to track the filament direction is most pronounced for groups in close distance to the filament spine and for more massive hosts. Conversely, at intermediate distances from the filament and at large group-centric radii, the signal reverses, indicating a tendency for orbital planes to be oriented perpendicular to the filament. Our findings provide direct observational evidence for the two-phase model of filamentary accretion, where a transition from initial perpendicular collapse toward the filament spine to subsequent parallel streamwise infall into dark matter haloes governs the orientation of satellite orbital angular momentum and galaxy spin. The observed transition may further trace the characteristic radial scale of filaments, offering a dynamical perspective on the internal structure and assembly of the cosmic filament.

This work presents a real-time disruption prediction and mitigation system developed for high-current operations in the EXL-50U Spherical Torus. By leveraging Reflective Memory (RFM) technology, the system establishes a low-latency real-time data path, creating a fully integrated pipeline that synchronizes multi-channel diagnostic acquisition, online preprocessing, real-time inference, and Massive Gas Injection (MGI) triggering. At its core, a lightweight prediction model based on a Temporal Convolutional Network (TCN) with a channel attention mechanism extracts disruption precursor features while adaptively weighting the importance of different diagnostic channels. {Tested across discharges \#14036–\#14790, the system achieves a true positive rate of 82.4% and a false positive rate of 16.5%, with end-to-end latency below $1~\mathrm{ms}$ in online operation.} Mitigation experiments further show that the MGI system can supply the required gas inventory and trigger a rapid post-injection plasma response, supporting the operational requirements of EXL-50U and providing engineering guidance for future devices such as EHL-2. These results confirm the engineering feasibility of integrated real-time disruption control on EXL-50U, offering a robust basis for future research in higher-parameter fusion devices.

Nonlinear waveguide QED serves as a platform for studying correlated photon dynamics, where its interplay with topological bound states can give rise to unconventional phenomena. We investigate a triangular ladder waveguide in which a pair of emitters forms a doublon bound state through strong nearest-neighbor interactions. By mapping the doublon dynamics onto an effective SSH chain, we show that the system is equivalent to an effective emitter coupled to a topological doublon bath. Using the vacancy-like dressed state approach, we demonstrate the existence of a chiral bound state with a node at the coupling site and an exponentially localized wave function inherited from the SSH edge states. Extending this picture to two emitter pairs, we derive an effective four-body interaction whose strength is determined by the relative chirality and the separation parity of the bound states. When the two bound states face each other, coherent Rabi oscillations emerge; when they are arranged back-to-back or have an even separation, the interaction vanishes. Our results provide a route toward engineering tunable many-body interactions between correlated photon pairs and realizing nonlinear quantum networks based on flying doublons.

We study the one-dimensional quasilinear Majda–McLaughlin–Tabak (MMT) equation on a large torus $[0,L]$: \begin{align*} i \partial_t u +2\pi|\nabla|^\sigma u +\lambda^{2}|\nabla|^\beta\left[ \left||\nabla|^\beta u\right|^{2} |\nabla|^\beta u\right]=0, \end{align*} with $\sigma\in(0,1)\cup (1,2]$ and $0<\beta<\sigma/4$. We consider Gaussian random initial data and work in the joint limit $L\to\infty$ with $\alpha=\lambda^2L^{-1}\to0$. The quasilinear structure leads to unavoidable derivative loss, which prevents the direct construction of solutions via iteration of the Duhamel formula. For $\sigma\in(1,2]$, we prove that, with high probability, solutions exist up to time scales ${T} \sim\alpha^{-{\frac43}+} \wedge \alpha^{-\frac1{\sigma/2-\beta}+}$, and that only trivial four-wave resonances occur, leading to a degenerate wave kinetic equation. For $\sigma\in(0,1)$, we prove the existence up to time scales $T\sim \alpha^{-\frac43+}$, and show that the second-order statistics are well approximated by the wave kinetic equation. In both cases, the solutions remain smooth while exhibiting smallness in suitable $L^\infty$-based norms. The proof combines propagation of randomness for a truncated equation with deterministic energy estimates and a bootstrap argument. The main technical difficulties arise in the regime $\sigma\in(0,1)$. At low frequencies, the counting argument requires simultaneous control of the frequency gap and the associated resonant phase gap. In the energy estimate, nontrivial resonances generate quartic terms that prevent the energy estimates from closing the bootstrap on $[0,T]$. To overcome this obstruction, we develop a new normal-form $L^2$ energy estimates, using distinct frequency truncations for the initial data and the nonlinearity.

Hyperon spin correlations serve as sensitive probes of spin dynamics in high-energy collisions, yet their extraction from weak-decay angular distributions can be contaminated by femtoscopic effects due to quantum statistics and final-state interactions. In this work, we quantitatively assess this contamination for $\Lambda\Lambda$ and $\Lambda\bar{\Lambda}$ pairs using the AMPT model combined with spin-dependent weights from the Lednický–Lyuboshits formalism. Because the singlet and triplet spin configurations contribute differently to the decay-angle distribution, femtoscopic weighting induces an apparent angular modulation, creating a fake correlation signal even when no intrinsic spin correlation is present. We find that the induced bias can become substantial in the low-$q_{\mathrm{inv}}$ region, where the combined femtoscopic effect reaches a magnitude comparable to that of the preliminary CMS measurements. Our results establish a framework for evaluating such systematics, highlighting that femtoscopic corrections must be carefully considered in future differential analyses that emphasize the low-relative-momentum region.

Cooperation is ubiquitous in both natural and human societies, yet its evolutionary basis remains a major challenge. A long-standing puzzle is whether having more information leads to better decision-making and thus a higher level of cooperation. To address this question, we adopt a recently developed reinforcement learning framework in which individuals learn through trial and error to maximize cumulative rewards - a paradigm that has successfully explained diverse emergent patterns in human behaviors. Specifically, we equip a structured population with the Q-learning algorithm and systematically vary the size of the interactive neighborhood, which serves as a proxy for perceived information. Interestingly, we observe a non-monotonic relationship between cooperation prevalence and neighborhood size in both two-dimensional square lattices and Barabasi-Albert scale-free networks. This inverted U-shaped dependence reveals that an optimal amount of information exists, yielding the highest level of cooperation. Mechanistic analyses show that a moderate neighborhood size enables individuals to strike an optimal balance between information sufficiency and decision-making tractability. This balance allows them to detect reciprocal opportunities while avoiding the deterioration of decision quality due to information overload. Our findings challenge everyday intuition, suggesting that a proper amount of information - not more - is optimal for the emergence of cooperation.

A companion paper \cite{ItkinDF2026} introduced the Diagonal Frog (DF) positivity-preserving schemes for anisotropic Fokker–Planck equations, advancing each directional substep by a Krylov-computed matrix exponential, which dominates the cost. Replacing that exponential by a rational map $r(\gamma L)$ reduces the substep to a banded solve, but the positivity argument no longer applies. We prove that for eventually exponentially positive generators the entrywise sign of $r(\gamma L)$ at large steps is decided by a single number, the value $r(\infty)$ taken on infinitely stiff modes. Nonnegativity holds above a computable threshold when $0\le r(\infty)<1$, and at most on a bounded interval, empty or vanishingly narrow in all our tests, when $r(\infty)<0$. The criterion rejects the Crank–Nicolson (trapezoidal) method, where $r(\infty)=-1$, and selects the subdiagonal Padé$(0,2)$ method, which is second order, L-stable and provably positive above an explicit threshold. The resulting DF-ADI scheme costs $O(N)$ per step, keeps the implicit factorized mixed derivative unchanged, is second order in space and time, and conserves discrete mass exactly. In the strong cross-diffusion regime, however, the directional factors demand a step larger than the mixed derivative permits, so the composite second-order scheme is only empirically positive there, and the criterion serves to discriminate the well-behaved multiplicative factors from the stabilizing-correction schemes rather than to guarantee positivity. Against the Krylov exponential it runs ten to thirty-two times faster at matched accuracy in our tests with the gain growing with the mesh. We extend the construction to the backward Kolmogorov equation and to jump-diffusion models.

Low-dimensional van der Waals semiconductors with reduced symmetry provide a unique platform for exploring anisotropic physical properties. The quasi-one-dimensional family MXQ$_3$ (M = Hf, Zr; X = Sn; Q = S, Se) exhibits notable structural anisotropy, where zigzag atomic chains influence optical phenomena such as birefringence. This study investigates anisotropic lattice dynamics in ZrSnS$_3$ using angle- and polarization-dependent Raman spectroscopy. Temperature-dependent measurements reveal anharmonic phonon behavior, indicating strong phonon-phonon coupling. Density functional theory calculations show good agreement with the experimentally observed Raman spectra, validating the microscopic description of the lattice dynamics. We also observe a helicity-dependent intensity and a reversal in phonon intensity between lower- and higher-frequency modes under circularly polarized light, which is characteristic of chiral phonons governed by the polarization of the Zr/Sn chains. Our first-principles analysis further shows that angular-momentum-like phonon textures can emerge away from the $\Gamma$-point near mode-hybridization and avoided-crossing regions, providing microscopic insight into the observed helicity-dependent Raman signatures. Furthermore, we fabricate an optoelectronic device from a thin ZrSnS$_3$ nanowire, demonstrating a photoresponsivity of 50~mA/W under 520~nm laser excitation (1~mW/cm$^2$). The device exhibits a pronounced, power-scalable anisotropic photoresponse with a clear preferred polarization direction. These results highlight the coupling mechanisms between polarization, lattice vibrations, and charge carriers in ZrSnS$_3$, establishing it as a promising material for polarization-sensitive optoelectronics and directional quantum transport.

Azimuthal hadronic flow measured in ultra-relativistic ion–ion collisions provides a new means of imaging multipole correlations in the ground state of atomic nuclei. Early interpretations largely relied on a classical-rotor picture, in which the measured mean-square elliptic flow is directly related to an intrinsic quadrupole deformation. Atomic nuclei, however, contain additional many-body correlations generated by the Pauli exclusion principle, collective shape fluctuations and non-collective dynamical processes, whose impact on this correspondence has not yet been elucidated. Here, we resolve this issue through an ab initio analysis of $^{16}$O and $^{20}$Ne based on chiral nuclear interactions, combining the in-medium similarity renormalization group with the quantum-number-projected generator coordinate method. By successively isolating antisymmetrization, collective rotational and vibrational, and non-collective dynamical correlations, we determine, for the first time, how each component contributes to the mean-square quadrupole eccentricity. We uncover an unexpected compensation among these distinct correlation mechanisms: despite sizable individual contributions, the squared effective quadrupole deformation inferred from the elliptic flow remains close to the square intrinsic deformation of the nucleus. This result provides a microscopic explanation for the surprising success of the classical-rotor approximation and establishes a quantitative foundation for interpreting $^{16}$O+$^{16}$O and $^{20}$Ne+$^{20}$Ne collision data recently collected at the Large Hadron Collider.

This work develops a discrete-time framework for identifying probability localization dynamics through finite stochastic representations adapted in space, time, memory, and state information. A compact dynamically relevant set is localized by a finite measurable partition, producing an observable probability state and a relational graph of admissible transitions. Structured stochastic liftings derived from Stochastically Structured Reservoir Computing (SSRC) give lossless polynomial representations of the observable state, while stochastic delay liftings add finite observable memory. These are distinguished from dynamically informed state-space enrichment: refinement of observational fibers containing states with the same present observation but different observable futures, yielding an exact obstruction-to-closure criterion. A route-network toy problem gives a minimal obstruction example, while four numerical laboratories (rotational phase dynamics, the chaotic logistic map, the Van der Pol oscillator, and a synthetic cyclic inventory system) show how spatial scale, temporal scale, polynomial degree, and delay depth interact. The logistic map isolates representation-induced memory in an otherwise Markovian chaotic system, using its exact invariant law as an ergodic benchmark and its zero-mass pseudospectrum to separate relaxation from transient amplification. An exact rotational cycle calibrates pseudospectra as a robustness diagnostic rather than a closure certificate. The inventory example gives a closure-driven enrichment procedure: residence-age hazards trigger age-refined states that improve predictive scores. These results motivate a minimal adequate representation: the least complex representation meeting predictive, structural, and identifiability requirements.

In this paper, we investigate the characterization of multipartite entanglement based on the unified $(q,s)$-entropy framework. For bipartite quantum states, we propose an entanglement measure $E_{q,s}^{A|B}(\rho)$ based on unified entropy and derive several analytical lower bounds for it using local orthonormal observables. We demonstrate with concrete examples that our lower bounds provide tighter estimates of quantum entanglement than several existing analytical bounds. For multipartite quantum states, based on unified entropy, we propose two measures $A^k_{q,s}(\rho)$ and $G^k_{q,s}(\rho)$ for quantifying $k$-nonseparability, and prove that these measures satisfy several desirable properties, such as faithfulness, local unitary invariance, and convexity. Moreover, we rigorously prove that when the parameters $q$ and $s$ are in certain ranges, $A^k_{q,s}(\rho)$ and $G^k_{q,s}(\rho)$ also satisfy monotonicity and strong monotonicity. Furthermore, we establish the order relations of the measures $A^k_{q,s}(\rho)$ and $G^k_{q,s}(\rho)$ with respect to the parameters $q$ and $s$ for fixed quantum states. In addition, for fixed $q$ and $s$, we also give their order relations for any two pure states.

Retrograde S-type planets have been observed in several binary systems, yet their formation pathway remains poorly understood. With high-resolution hydrodynamic simulations, we demonstrate that a polar circumbinary disk around an eccentric, unequal-mass binary can form and sustain a retrograde mini disk around the primary star. This provides a direct in-situ formation channel for retrograde S-type planets. The mini disk forms via a sub-Keplerian accretion stream that is slightly misaligned from the polar disk. The mini disk initially undergoes von Zeipel-Kozai-Lidov (ZKL) oscillations, driving coupled eccentricity and inclination evolution. Rather than oscillating indefinitely, the inner mini disk evolves past the critical ZKL inclination, decouples from the outer disk, and settles into a stable retrograde orbit. This evolution is sensitive to numerical resolution: the retrograde configuration is absent in previous lower-resolution simulations, where the mini disk accretion timescale is too short to sustain ZKL-driven evolution. For a higher disk viscosity, the mini disk remains near-polar due to a shorter accretion timescale. Since protoplanetary disks typically have low viscosity, our results suggest that retrograde S-type planets can form in-situ from retrograde mini disks around polar circumbinary disks, and their occurrence rate may be higher than currently estimated.

In this work, we propose a model-based feedback controller that regulates the vertical instability growth rate ($\gamma_{gr}$) of a high-elongation, double-null tokamak directly, using only out-vessel poloidal field (PF) coils. High elongation raises the achievable plasma current and fusion performance but makes the plasma vertically unstable, and in a fusion power plant the in-vessel coils that present devices rely on for stabilization may be absent, leaving only distant out-vessel circuits. The controller couples a machine learning surrogate of non-rigid, profile agnostic vertical instability metric to a constrained quadratic program: the surrogate supplies real-time $\gamma_{gr}$ estimates and, via automatic differentiation, the actuator sensitivities, while the program allocates coil voltages to track a target growth rate, maintain double-null divertor balance, and respect electromechanical limits. We tested this method on the ARC~V3A power plant design configuration across 24 closed-loop simulations spanning equilibrium variations, actuator degradations, and transient disturbances. We achieved full or marginal success in 83% of these cases (full in 50%, marginal in a further 33%) and lose control in the remaining 17%; the failures map the boundary of out-vessel controllability (occurring at the highest growth rates) and under actuator limits. The controller does not regulate boundary shape explicitly: separatrix geometry follows indirectly from growth rate and flux balance control and would require a separate shape control layer for sustained scenario evolution.

We harness two established ingredients for collective demixing: differential speed and curvature to create a self-sorting device. In binary mixtures, motility differences drive spontaneous spatial segregation, while confinement geometry determines how rapidly and strongly this demixing develops. Using particle based simulations, we systematically identify the geometrical conditions that promote efficient segregation and use these results to guide the design of a finite sorting architecture. We then translate these physical mechanisms into a sequence of curved microfluidic units that progressively amplify the separation of the two species and direct them toward distinct collection regions. Experiments with binary Quincke-roller mixtures confirm that an initially mixed suspension progressively demixes as it propagates through the device, leading to strong enrichment downstream. Our results demonstrate how collective active demixing can be converted into a functional continuous sorting strategy, providing a route toward autonomous microfluidic separation based on particle motility and confinement geometry.

Periodic density structures (PDS) are trains of plasma enhancements carried into the heliosphere, but their repeated timing does not by itself identify where the cadence is set. We test whether PDS selected independently in the outer corona can be traced back to a low-coronal clock, and whether that organization survives through the EUVI–COR1–COR2 observing chain. We analyze 12 STEREO-A/SECCHI events on 2008 January 11–14 along a nonradial path. EUVI 171 A at 1.10–1.20 R_sun shows an unusual concentration of power in the predeclared 80–130 minute band relative to filter-matched red-noise controls, while the ensemble is most strongly organized in upper COR1 at 2.5–3.0 R_sun. These signatures identify a low-coronal modulation candidate and an intermediate-height organization domain, but they do not form a unique phase-preserving clock extending into COR2. Instead, the more persistent observable is spatial order. Events 9 and 12 retain expansion-stable outward ordering. In polar r–theta maps, intersections of oppositely inclined, expansion-aware matched-filter ridge supports form repeated X-/diamond-like patterns. The morphology is compatible with stationary or quasi-stationary shock-cell processing, although the brightness diagnostics are insufficient to establish a stationary MHD shock branch. The observations therefore favor an intermittent source–gate–transfer picture: a low-coronal cadence may modulate plasma release, while event-dependent propagation progressively destroys exact phase coherence. The outward ordering of the density structures can survive, providing a more persistent signature of the source-to-wind transfer than phase locking itself.

We study the one-loop relation between an effective-field-theory extension of Poincaré gauge theories of gravity with propagating torsion and its unimodular counterpart. In the Einstein representation, we consider two representative quadratic torsion subsectors, namely totally antisymmetric (axial) torsion and the vector component of hook-antisymmetric torsion. On maximally symmetric metric backgrounds with vanishing background torsion, the diffeomorphism-invariant and genuine unimodular theories yield identical one-loop determinants in both sectors, reproducing the same local logarithmic divergences. We further examine flat backgrounds with homogeneous axial or vector torsion, where metric-torsion mixing is present. In each case, the torsion-dependent one-loop effective action in unimodular gauge and in the genuine unimodular formulation is controlled by the same physical determinant. Thus, for the actions and backgrounds considered, the unimodular constraint does not modify local one-loop torsion dynamics. We also delineate the limitations of this equivalence and the extensions needed for generic torsionful curved backgrounds.

The ability to tailor photon-number statistics is central to the generation and control of nonclassical states of light. Here, we investigate how Fock-state filtering of squeezed coherent states can be used to engineer their photon statistics. We consider the selective removal of the $m=0$ and $m=1$ Fock components and show that this process can enhance the sub-Poissonian character of the field, depending on the coherent amplitude. We then analyze the evolution of these engineered states in a thermal environment. Although all states eventually relax toward thermal statistics, the signatures of the filtering process may persist over a significant part of the evolution, while the purity of the filtered states is rapidly degraded by incoherent population redistribution. Our results illustrate both the potential and the limitations of photon-number engineering in realistic, dissipative settings.

We explore a unified axion framework connecting grand unification, string-inspired axion-like particles (ALPs), and cosmology. Starting from the QCD axion associated with Peccei–Quinn symmetry in supersymmetric SO(10) GUT, we consider the broader spectrum of ultralight ALPs motivated by heterotic string theory. Within this multi-axion structure, we focus on two ultralight scales selected by cosmological requirements. A mode of order $10^{-22}$ eV is assumed to constitute the dominant dark-matter component and can form a Bose–Einstein condensate whose attractive self-interaction leads to nonlinear collapse, providing possible seeds for high-redshift supermassive black holes. A lighter eigen-direction with a characteristic dynamical scale of order $10^{-28}$ eV can transiently increase the pre-recombination expansion rate and reduce the sound horizon. An order-of-magnitude estimate shows that addressing the Hubble tension requires a sound-horizon-weighted axion fraction of order 0.1, corresponding, for a large initial displacement, to an effective decay constant of order $10^{18}$ GeV. We show that a multi-axion–multi-instanton system can in principle provide both the required aligned light direction and a higher-order effective potential that makes the $10^{-28}$ eV contribution transient. The framework links theoretically motivated axionic degrees of freedom to the distinct scales required by dark-matter, early-black-hole, and Hubble-tension phenomenology.

We present a systematic high-throughput density-functional theory study of the thermodynamic stability, collinear magnetic ground states, and electronic structures of layered kagome compounds in the AT6X4 and AT6X5 families. Using the experimentally reported structure types as templates, we screened 78 substitutional compositions in each family. Our calculations reproduce the stability and antiferromagnetic character of the known Fe-based Ge compounds and identify six additional stable candidates with robust ferromagnetism. Within collinear spin configurations, we find a clear chemistry-dependent trend: stable Fe-based Ge compounds predominantly adopt AFM2 ground states, whereas stable Mn-based Ge compounds consistently favor ferromagnetic order. Exchange analysis further shows that the magnetic phase space is governed by competing interlayer interactions, consistent with the mechanism established for AT6X6 kagome magnets. Representative ferromagnetic members from the two structural families also retain kagome-derived dispersive band features near K, although the AT6X5 phase exhibits stronger band folding and hybridization. Overall, these results establish AT6X4 and AT6X5 as promising layered kagome families for realizing ferromagnetism and kagome-derived electronic states.

Cooperative emission from three-level ensembles is conventionally diagnosed through the radiated intensity alone, which cannot say which channels carry the photons at each instant. We promote every transition of the cooperative-decay graph into a time-dependent edge flux and show that node-wise conservation of this flux is an exact restatement of the Pauli master equation. Suppose the graph carries a depth function that decreases by one along every edge. Then the total cooperative rate is the descent speed of the mean graph depth, and its energy-weighted form gives the radiated intensity as $I(t)=-\dd\langle E\rangle/\dd t$ for arbitrary level spacings. The same ordering triangularizes the generator. This delivers the relaxation spectrum from the state exit rates, together with a generalized Bateman closed form for every population on an arbitrary finite directed acyclic graph, in which all exit-rate degeneracies are absorbed into a polynomial-times-exponential recursion.

Reconstructing the state of a large networked system from measurements at only a few nodes is a challenge for monitoring, prediction, and intervention. Here we ask whether such reconstruction is possible and whether it can transfer across different nonlinear dynamics. We study this question across various networks and across $16$ nonlinear dynamics on networks from different domains. For each network, we observe only a vanishingly small fraction of sentinel nodes and train either a neural network or linear decoder. We find that accurate reconstruction is often possible, and that transferability is structured rather than universal. Eleven dynamics with adjacency-matrix-type coupling form a robust transferable class. By contrast, five diffusively coupled dynamics form isolated transfer components. Non-random sentinel selection is consistently important, and linear decoders often approach neural-network performance. These results show that sparse node observations can encode enough information to reconstruct full network equilibria across broad families of nonlinear dynamics, while also revealing sharp limits to universal transfer.

A null mode of the bordered Faddeev–Jackiw matrix is not, in general, a gauge generator. We determine exactly what the residual kernel encodes and identify the additional condition required for genuine gauge symmetry. Writing $f^{(m)}=\begin{pmatrix}f^{(0)}&B\\-B^{\mathsf T}&0\end{pmatrix}$ and $\Gamma=N^{\mathsf T}B$, we prove $\dim\ker f^{(m)}=\dim\ker\Gamma^{\mathsf T}+\dim\ker\Gamma-\operatorname{rank}(\Pi M\Pi)$, where $M=B^{\mathsf T}f^{(0)+}B$ and $\Pi$ projects onto $\ker\Gamma$. The two kernel contributions have distinct meanings: the first consists of null directions of $f^{(0)}$ tangent to the constraint surface, while the second counts independent first-class combinations. We then show that $\Gamma$ is not the Dirac constraint matrix: it is the primary–secondary block of the reduced constraint matrix, with $M$ providing the secondary–secondary block. For a residual null mode with nonzero multiplier component, we derive the associated two-step chain and prove that it closes to an exact gauge symmetry precisely when the chain contraction vanishes in the effective ring modulo the constraint ideal. A four-variable counterexample shows that the Faddeev–Jackiw stopping condition can hold while the system has no gauge freedom, and that the chain criterion rejects the false generators. Mechanical examples then exhibit the criterion and show that parameter strata can carry distinct gauge and dynamical content that is erased by premature cancellation.

Thunderstorm electrical discharges, which vary in their type of initiation and development (including compact intracloud discharges and initial breakdown pulses), also manifest differently as recorded electromagnetic signals in both the radio and optical ranges. A unique ionospheric optical imprint of a discharge is an ELVES - a sub-millisecond glow at altitudes around 90 km with a characteristic spatiotemporal pattern in the form of an expanding ring, reaching a diameter of several hundred or even a thousand kilometers. The position of the elve, its expansion velocity, the azimuthal and radial distribution of the glow intensity (and their temporal dynamics) contain information about the location and orientation of the discharge, as well as its current function. This information is most fully represented in the data recorded by orbital detectors of dynamic images with a wide field of view and microsecond temporal resolution, such as the TUS and Mini-EUSO. Recovering the parameters of a discharge from orbital detector data is associated with solving a complex inverse problem, since the phenomenon of interest is mediated by several processes, including the interaction of the discharge's electromagnetic pulse with the ionosphere and the non-trivial instrument response function of the detector. These additional sources of uncertainty are most consistently accounted for within the Bayesian paradigm. The application of simulation-based inference (SBI) allows for the reconstruction of discharge parameters within a dynamic model, thereby taking a step towards creating a new method for studying the thunderstorm atmosphere – elveslocation. This work presents a dynamic model of an elve, which enables both the identification of characteristic spatiotemporal patterns of an event (generator mode) and the reconstruction of discharge parameters (SBI simulator mode).

Zhou and Yu [Appl. Math. Lett. 178 (2026) 109937] studied the space-time shifted nonlocal nonlinear Schrödinger (NLS) equation $iq_t(x,t)=q_{xx}(x,t)-2\sigma q^2(x,t) \bar{q}(x_0-x,t_0+\lambda t),\,\, \lambda=\pm1$, and claimed that for both choices of $\lambda$ the equation is integrable. Here we examine this claim from the perspective of reductions of the standard integrable NLS system. We find that the compatibility of the equation with the NLS system is true only when there is no time reversal in the argument. In other words, for this equation it requires $\lambda=1$ and $t_0=0$. The case with $\lambda=-1$ is a valid nonlocal equation, but cannot be derived from the standard NLS system by the corresponding complex conjugate shifted nonlocal reduction, and its integrability therefore does not follow from that integrable NLS system. We also discuss the equivalence between shifted (with real shifts) and unshifted nonlocal reductions and give the adjusted form of the Hirota bilinear equation.

In recent years, both academia and industry have focused on the development of computational architectures inspired by the distributed, adaptive, and event-driven characteristics of biological neural systems, with the aim of reducing the computational cost associated with conventional training approaches [1]. However, a major challenge is the lack of general models and design guidelines for emerging computational systems and hardware. This work introduces a general model based on an input-dependent stochastic weight network, referred to as a substrate. The substrate weights evolve through input-triggered stochastic updates, with correlations between weight coefficients described by a matrix-valued covariance kernel. The proposed framework is implemented using quadratic polynomial weight functions, where the input amplitude controls the magnitude of the stochastic perturbation and a substrate-dependent distance determines the correlation structure. Numerical simulations show that correlations in the stochastic weight evolution significantly affect the system response, suggesting a potential mechanism for neuromorphic-inspired computation without conventional weight training. The aim of this work is to provide a general formulation of the model and identify its main properties and characteristics. 1 H. Jaeger, Towards a generalized theory comprising digital, neuromorphic and unconventional computing, Neuromorphic Comput. Eng., vol. 1, no. 1, p. 012002, Sep. 2021

A downward fin thrust near a cohesive seabed lofts sediment. Whether this cloud settles or organizes into a self-sustaining down-slope current determines if a diver loses visibility briefly or catastrophically. We reduce the layer-averaged balances of fluid mass, sediment mass, and momentum to a temporal slab of fixed thickness in the weakly entraining limit. This yields an autonomous planar vector field in dimensionless near-bed speed and suspended load, governed by three dimensionless groups: drag against settling, erosion strength, and near-bed concentration. The field possesses a quiescent equilibrium at the origin and, above a critical bed slope obtained in closed form as the ratio of near-bed concentration times drag-settling number to erosion-strength number, an interior saddle equilibrium. The saddle's stable manifold partitions the state space into basins of decay and unbounded growth, establishing the exact threshold between self-limiting and igniting disturbances. On a flat bed, the origin attracts globally for all admissible erosion laws. For representative silt, the ignition threshold is near a 17-degree bed angle. The closed-form structure is confirmed numerically to machine precision. A closure study demonstrates the critical slope is robust in existence but closure-dependent in value, identifying the linear erosion law as the conservative choice. The model thus isolates bed slope as the controlling parameter for ignition.

We derive the rank-two string-Carroll limit of the canonical stress–spin Ward system for probe matter on a fixed torsion-free background. Beyond rank-one Carroll spin hydrodynamics, this retains the coupled Riemann–spin force, a second longitudinal momentum projection, and the longitudinal boost bivector allowed only by a two-dimensional longitudinal kernel. We first extract the term linear in an independent spin amplitude $\varsigma$ and then expand in the near-horizon parameter $\lambda=\epsilon^2$, avoiding contamination by the omitted $\mathcal{O}(\varsigma^2)$ thermodynamic spin feedback. For finite mixed stress and $S^{\lambda\mu\nu}=\mathcal{O}(\varsigma\epsilon^p)$, $p=0$ is the unique sector in which the induced stress and curvature source balance at the first generic Ward order. On the regular branch of a smooth nonextremal static spherical outer horizon, locally normalized longitudinal and transverse spin amplitudes obey the same dilution law, while the curvature force first appears at $\mathcal{O}(\varsigma\lambda^2)$. For a general barotrope, the stationary system reduces to one thermodynamic quadrature and one local inverse. For the affine constant-sound-speed family $p=\alpha\mathcal E+\Pi$, $0\leq\alpha<1$, we obtain an explicit closed-form parametric solution, leading profiles for both spin channels, and fixed-radius, linear-spin corrections to enthalpy, pressure, and rapidity away from the sonic point. The response is governed by $\mathcal R^{(L)}_h=(f_2+3f_1\psi_1)/2$ and the longitudinal spin flux. We prove that the stationary closed-sphere Killing flux is invariant under regular pseudo-gauge improvements. In Reissner–Nordström, the response vanishes at the radial-tidal inversion $|Q|/M=2\sqrt{2}/3$; in the Einstein–Maxwell–dilaton family, its zero is $R_-/R_+=(1+a^2)/2$ for $0\leq a<1$. The Frenkel limit removes this response and the longitudinal boost sector.