Daily Papers

We explore a minimal scenario where the sole Standard-Model Higgs is responsible for reheating the Universe after inflation, produces a significant background of gravitational waves and maintains the full classical stability of the electroweak vacuum. As the Higgs self-coupling runs toward negative values at high energy scales, a non-minimal interaction with curvature during a stiff background expansion era drives the Higgs fluctuations closer to the instability scale. This curvature-induced tachyonic instability leads to an intense production of Higgs particles, accompanied by a stochastic gravitational-wave background. The characteristic features of such signal can be directly correlated to the inflationary scale, the non-minimal coupling parameter and the top quark Yukawa coupling. We distinguish between three possible scenarios: absolute stability with low top quark masses, potential vacuum instability, and absolute stability with new physics above the instability scale. Our findings suggest that the detection of a peaked background of gravitational waves together with its inflationary tail has the potential to unveil the features of the Higgs effective potential at very high energy scales while providing a minimal explanation for the reheating phase and the emergence of the Standard-Model plasma in the early Universe. Unlike other studies in the literature, the generation of gravitational waves in our scenario does not depend on the quantum instability of the Standard Model vacuum.

Scalar field theories of modified gravity are strongly constrained by the absence of detectable long range fifth forces in laboratory and Solar System environments. The chameleon mechanism addresses this problem by making the equilibrium value and effective mass of the scalar field dependent on the ambient matter density. In this work, we investigate an effective phenomenological extension of the chameleon framework in which the scalar potential contains an additional quadratic environmental contribution characterized by a density dependent background frequency. This background frequency is distinct from the frequency of scalar perturbations and parametrizes unresolved environmental effects beyond the conventional matter coupling. For an inverse power law scalar potential, we derive the modified equilibrium configuration and identify a frequency dominated regime in which the environmental contribution controls the density dependence of the field. Linear perturbations about the environmental minimum obey a Klein Gordon dispersion relation with a density-dependent effective mass, and the absence of tachyonic instability requires a positive environmental coupling. We further derive analytical consistency conditions associated with frequency dominance, thin shell screening, fifth-force suppression, and the weak field approximation. Numerical illustrations for representative parameter choices demonstrate how the modified density scaling can enhance fifth-force suppression relative to the conventional chameleon case.

We demonstrate a universal mechanism of a class of instabilities in infrared regions for massless Abelian p-form gauge theories with topological interactions, which we call generalized chiral instabilities. Such instabilities occur in the presence of initial electric fields for the p-form gauge fields. We show that the dynamically generated magnetic fields tend to decrease the initial electric fields and result in configurations with linking numbers, which can be characterized by non-invertible global symmetries. The so-called chiral plasma instability and instabilities of the axion electrodynamics and (4+1)-dimensional Maxwell-Chern-Simons theory in electric fields can be described by the generalized chiral instabilities in a unified manner. We also illustrate this mechanism in the (2+1)-dimensional Goldstone-Maxwell model in electric field.

Under the standard split, Muon gets hidden matrices and AdamW embeddings/output head. Muon groks modular addition faster, but its solutions do not hold. All nine configurations on (a+b) bmod 113 grok and later lose generalization. Across five seeds the selected AdamW reference falls below threshold on four, reaching 27.59%. Instability persists across two moduli, two widths, two training fractions, subtraction, and depth. The failure arises at the representation-readout interface, identified only jointly up to an invertible map unselected by the loss. After solving the training set, the gradient falls to order 10^{-6} and the optimizers respond differently: step-size elasticity is -0.03 for Muon versus +1.5 for AdamW, and the Muon group moves 8.0 times faster per parameter. From bit-identical states, freezing either group prevents failure. Freezing embeddings/readout removes it in five runs over 451,400 post-grokking steps and five paired seeds: unfrozen arms record 137-321 sub-threshold evaluations, frozen arms none. Removing Muon's normalization and orthogonalization is no substitute: it collapses representation from 326 effective conjugate pairs to 4, shows no recurrent collapse, and fails terminally. Fourier filtering separates circuit failure from masking. Across 43 checkpoints over five seeds and three regimes, the task-aligned family reaches exactly 100% alone. In circuit failure it no longer solves the task; in masking it remains perfect while the full model reaches 45.85%, giving a positive margin on every example, including errors, but being outvoted by a near-equal adversarial remainder. Rescaling it restores 99.9%; grokking is the same condition resolving upward. The task selects the family, swapping (k,k) for (k,-k) under subtraction. Across an abrupt collapse, standard Fourier support is unchanged and the power-distribution cosine remains 0.9899.

The basic framework of the superfluid vortex model for pulsar glitches, though, is well accepted; there is a lack of consensus on the possible trigger mechanism responsible for the simultaneous release of a large number (sim 10^{17}) of superfluid vortices from the inner crust. Here, we propose a simple trigger mechanism to explain such catastrophic events of vortex unpinning. We treat a superfluid vortex line as a classical massive straight string with well-defined string tension stretching along the rotation axis of pulsars. The crustquake-induced lattice vibration of the inner crust can act as a driving force for the transverse oscillation of the string. Such forced oscillation near resonance causes the bending of the vortex lines, disturbing their equilibrium configuration and resulting in the unpinning of vortices. We consider unpinning from the inner crust's so-called {\it strong (nuclear)} pinning region, where the vortices are likely pinned to the nuclear sites. We also comment on vortex unpinning from the interstitial pinning region of the inner crust. We sense that unifying crustquake with the superfluid vortex model can naturally explain the cause of large-scale vortex unpinning and generation of large-size pulsar glitches.

We investigate the stability of superconducting strings as bound states of strings and fermion zero modes at both the classical and quantum levels. The dynamics of these superconducting strings can result in a stable configuration, known as a vorton. We mainly focus on global strings, but the majority of the discussion can be applied to local strings. Using lattice simulations, we study the classical dynamics of superconducting strings and confirm that they relax to the vorton configuration through Nambu-Goldstone boson radiation, with no evidence of over-shooting that would destabilize the vorton. We explore the tunneling of fermion zero modes out of the strings. Both our classical analysis and quantum calculations yield consistent results: the maximum energy of the zero mode significantly exceeds the fermion mass, in contrast to previous literature. Additionally, we introduce a world-sheet formalism to evaluate the decay rate of zero modes into other particles, which constitute the dominant decay channel. We also identify additional processes that trigger zero-mode decay due to non-adiabatic changes of the string configuration. In these decay processes, the rates are suppressed by the curvature of string loops, with exponential suppression for large masses of the final states. We further study the scattering with light charged particles surrounding the string core produced by the zero-mode current and find that a wide zero-mode wavefunction can enhance vorton stability.

We present a non-perturbative formulation of quantum gravity in asymptotically flat spacetimes using Witten's cubic open string field theory (OSFT) on unstable D-branes. Given that the massless spin-2 sector of the closed string spectrum inherently encodes the degrees of freedom of quantum gravity, we establish this connection by mapping on-shell closed string excitations directly to gauge-invariant operators in OSFT, realizing a concrete flat-space analogue of the AdS/CFT correspondence. By evaluating the OSFT correlation functions of these operators perturbatively around the tachyon vacuum, we systematically reproduce the all-orders genus expansion of the closed string S-matrix for the associated states. This demonstrates that closed string theory-and thus quantum gravity-emerges dynamically from the open string tachyon vacuum, establishing Witten's OSFT as a fully calculable, non-perturbative framework for flat-space quantum gravity.

We investigate magnetic-field amplification driven by the nonresonant hybrid (NRH or Bell) instability and its impact on cosmic-ray (CR) acceleration at reverse shocks of ultrafast outflows (UFOs) from active galactic nuclei (AGN). Previous kinetic studies by particle-in-cell simulations have demonstrated that when maximum CR energy is near the injection scale, NRH instability efficiently amplifies magnetic field up to the saturation level. However, the efficiency of NRH instability goes down as maximum energy increase since CR current is carried by escaping CRs near the maximum energy. We employ a one-dimensional MHD--CR framework solving telegraph-type diffusion--convection equations to trace the coupled evolution of CRs, magnetic fields, and shock dynamics under realistic parameters. We find a distinct transition with magnetic field strength: for weak background fields (B_{0}!lesssim!10^{-4},G), NRH instability efficiently amplifies upstream turbulence, driving a self-regulated state where E_{max} becomes independent of initial strength of magnetic turbulence. In contrast, for stronger background fields (B_{0}!gtrsim!10^{-3},G), the escaping CR current is too weak to drive NRH instability, and magnetic turbulence further decays through parametric instabilities, potentially reducing the acceleration efficiency. We give the physical interpretation for the transition and discuss conditions for PeV--EeV acceleration at UFO reverse shocks.

At high energies, the dynamics of a plasma with charged fermions can be described in terms of chiral magnetohydrodynamics. Using direct numerical simulations, we demonstrate that chiral magnetic waves (CMWs) can produce a chiral asymmetry μ_5 = μ_L - μ_R from a spatially fluctuating (inhomogeneous) chemical potential μ= μ_L + μ_R, where μ_L and μ_R are the chemical potentials of left- and right-handed electrically charged fermions, respectively. If the frequency of the CMW is less than or comparable to the characteristic growth rate of the chiral dynamo instability, the magnetic field can be amplified on small spatial scales. The growth rate of this small-scale chiral dynamo instability is determined by the spatial maximum value of μ_5 fluctuations. Therefore, the magnetic field amplification occurs during periods when μ_5 reaches temporal maxima during the CMW. If the small-scale chiral dynamo instability leads to a magnetic field strength that exceeds a critical value, which depends on the resistivity and the initial value of μ, magnetically dominated turbulence is produced. Turbulence gives rise to a large-scale dynamo instability, which we find to be caused by the magnetic alpha effect. Our results have consequences for the dynamics of certain high-energy plasmas, such as the early Universe.

We prove that all excited states -sin(nx), ngeq2, of the De Gregorio equation on the torus are nonlinearly unstable in the sense of Hadamard. More precisely, perturbations arbitrarily small in H^2 leave a fixed H^1 neighborhood of the state. For every ngeq2, the linearized operator has a real eigenvalue λ_nin(0.56,0.6). To prove this, we transform the eigenvalue problem into a Fuchsian equation on the complex disk and obtain a matching condition for the eigenvalue. This condition is verified rigorously using interval arithmetic. The nonlinear instability follows from a bootstrap argument in the spirit of Guo, Hallstrom, and Spirn.

Global stability of differentially rotating plasma is investigated using a generalized effective potential. We first, for a current-free system, obtain a general form of an effective potential in terms of the free energies of global curvature and gradients of rotation for non-axisymmetric disturbances. We then examine the stability of differentially rotating disks for several rotation profiles and present the associated effective potential for the onset of these instabilities in the MHD regime. In particular, results for global axisymmetric magnetorotational instability (MRI) as well as local and global non-axisymmetric modes are presented. The latter constitute two distinct non-axisymmetric modes, a high frequency local MRI and a global low-frequency non-axisymmetric mode (the magneto-curvature mode, introduced in Ebrahimi&Pharr, ApJ 2022), confined either between two Alfv\'enic resonances or an Alfv\'enic resonance and a boundary.

We investigate modified gravity with quadratic curvature terms (R^2, R_{AB}R^{AB}, and R_{ABCD}R^{ABCD}). In this framework, the geometry of the extra dimensions is determined by the higher-dimensional field equations together with auxiliary conditions. For inhomogeneous metrics, we derive new stability conditions under radion excitations. The central result is that stable solutions satisfying these conditions are not isolated: a typical stable regular metric belongs to a continuous family of stable metrics in its immediate neighbourhood. Since the effective four-dimensional physical parameters depend on the extra-dimensional geometry, this geometrical landscape of stable metrics induces a continuous landscape of effective four-dimensional parameters. Transitions between distinct static solutions within the landscape cannot be induced by spatially localized perturbations, whose asymptotic decay (|x|toinfty) preserves the boundary data distinguishing the states. We also note a possible topological transition from a two-brane to a one-brane configuration, associated with a change in the number of regular zeros of the metric function r(u).

In this work, we consider the generalized Benjamin-Bona-Mahony equation $partial_t u+partial_x u+partial_x( |u|^pu)-partial_t partial_x^{2}u=0, quad(t,x) in R times R, with p>4. This equation has the traveling wave solutions \phi_{c}(x-ct), for any frequency c>1. It has been proved by Souganidis and Strauss Strauss-1990 that, there exists a number c_{0}(p)>1, such that solitary waves \phi_{c}(x-ct) with 1<c<c_{0}(p) is orbitally unstable, while for c>c_{0}(p), \phi_{c}(x-ct) is orbitally stable. The linear exponential instability in the former case was further proved by Pego and Weinstein Pego-1991-eigenvalue. In this paper, we prove the orbital instability in the critical case c=c_{0}(p)$.

Initial states of dense matter with nonzero electron chiral imbalance could potentially give rise to strong magnetic fields through chiral plasma instability. Previous work indicated that unless chiral chemical potential is as large as the electron vector chemical potential, the growth of magnetic fields due to the instability is washed out by chirality flipping rate enabled by electron mass. We re-examine this claim in a broader range of parameters and find that at higher temperatures the hierarchy is reversed supporting a growing magnetic field for an initial electron chiral chemical potential much smaller than the electron vector chemical potential. Further, we identify a qualitatively new effect relevant for magnetized hot and dense medium where chiral magnetic effect (CME) sourced by density fluctuation acts as a powerful source of Joule heating. Remarkably, even modest chiral chemical potentials (keV) in such environment can deposit energy densities set by the QCD scale in a relatively short time of the order of a few milliseconds or seconds. We speculate how this mechanism makes CME-driven Joule heating a potentially critical ingredient in the dynamics of turbulent density fluctuation of supernovae and neutron star mergers.

Reasoning failures in large language models (LLMs) are typically measured only at the end of a generation, yet many failures manifest as a process-level breakdown: the model "loses the thread" mid-reasoning. We study whether such breakdowns are detectable from inference-time observables available in standard APIs (token log probabilities), without any training or fine-tuning. We define a simple instability signal that combines consecutive-step distributional shift (JSD) and uncertainty (entropy), summarize each trace by its peak instability strength, and show that this signal reliably predicts failure. Across GSM8K and HotpotQA, instability strength predicts wrong answers with above-chance AUC and yields monotonic bucket-level accuracy decline at scale across model sizes. Crucially, we show that instability is not uniformly harmful: early instability can reflect subsequent stabilization and a correct final answer (corrective instability), whereas late instability is more often followed by failure (destructive instability), even at comparable peak magnitudes, indicating that recoverability depends not only on how strongly the distribution changes but also on when such changes occur relative to the remaining decoding horizon. The method is model-agnostic, training-free, and reproducible, and is presented as a diagnostic lens rather than a corrective or control mechanism.

Teams that have trained large Transformer-based models have reported training instabilities at large scale that did not appear when training with the same hyperparameters at smaller scales. Although the causes of such instabilities are of scientific interest, the amount of resources required to reproduce them has made investigation difficult. In this work, we seek ways to reproduce and study training stability and instability at smaller scales. First, we focus on two sources of training instability described in previous work: the growth of logits in attention layers (Dehghani et al., 2023) and divergence of the output logits from the log probabilities (Chowdhery et al., 2022). By measuring the relationship between learning rate and loss across scales, we show that these instabilities also appear in small models when training at high learning rates, and that mitigations previously employed at large scales are equally effective in this regime. This prompts us to investigate the extent to which other known optimizer and model interventions influence the sensitivity of the final loss to changes in the learning rate. To this end, we study methods such as warm-up, weight decay, and the muParam (Yang et al., 2022), and combine techniques to train small models that achieve similar losses across orders of magnitude of learning rate variation. Finally, to conclude our exploration we study two cases where instabilities can be predicted before they emerge by examining the scaling behavior of model activation and gradient norms.

We study the pseudospectrum of the Kerr black hole for gravitational perturbations with spin weight s=2, the case of greatest interest in gravitational-wave astronomy. In the hyperboloidal framework with two-dimensional Chebyshev collocation, we formulate the quasinormal mode problem as a non-self-adjoint eigenvalue problem. For sneq0 the fields Ψ^{(s)} and Ψ^{(-s)} are independent, so the conserved current method yields no single-field energy norm. We overcome this with the Teukolsky--Starobinsky identities, which relate Ψ^{(-2)} to a fourth-order operator on Ψ^{(2)} and yield an H^2 energy norm after symmetrization. With the H^1 norm known for s=0, this suggests the pattern H^{|s|}, verified for s=0 and s=2. All results use an ω-independent two-field hierarchy. We find that the pseudospectrum tightens by 1.1 to 3.5 decades at each step of L^2to H^1to H^2, yet stays large in every norm. The s=+2 and s=-2 operators are isospectral but not isopseudospectral: at twelve of fourteen probes the ψ_0 resolvent exceeds the ψ_4 one by 0.19 to 0.82 decades in the H^2 norm, while at the two probes furthest along the QNM line the ordering reverses by 0.18 to 0.19 decades. The gravitational pseudospectrum exceeds the scalar one by 0.5 to 5.2 decades in the window minimum and by 5.9 decades in L^2 at ωM=0.47-0.17,i, while along the damping direction the s=2 resolvent is non-monotonic and the s=0 resolvent smooth. QNM spectral instability is therefore a universal feature of Kerr, and is stronger for gravitational perturbations.

We present a spacetime that serves as a horizonless mimicker of extremal black holes. Unlike previously studied mimickers of black holes with non-degenerate horizons, whose geometries are of the wormhole type and consist of two asymptotically flat regions connected by a very long throat, the mimicker of an extremal black hole possesses a single asymptotically flat region at one end and an infinitely long throat at the other. In the throat region, the spacetime approaches the direct-product geometry M_{1,1} times S^2, where M_{1,1} is two-dimensional Minkowski spacetime and S^2 is the two-sphere. We investigate scalar-field dynamics and the fate of the Aretakis instability. Although Aretakis-like modes arise in a local analysis of the throat, they do not lead to a physical instability of the mimicker. A scalar perturbation initially localized in the throat gives rise, at late times, to a sequence of signals with a characteristic separation t_{rm delay}sim 1/λ, where λll 1 is a deformation parameter. This timescale is parametrically larger than the echo time t_{rm echo}sim ln(1/λ) characteristic of non-extremal black-hole mimickers. We refer to this sequence as a {\it long-delay signal train}. Geometrically, the periodicity of the long-delay signals is associated with periodic geodesics on S^2. We then extend the construction to extremal Kerr. In this case, the throat region approaches a generalized product geometry involving M_{1,1} and a two-dimensional surface Σ_2. The corresponding signals are expected to form a quasi-periodic signal train, reflecting the quasi-periodic geodesic motion on Σ_2. We also comment on the generalization to wormhole mimickers of non-extremal black holes and on the implications of these results for unitarity in the context of the AdS/CFT correspondence.

We revisit axion monodromy inflation in the context of UV-complete theories and point out that its cosmological observables are sensitive to heavy fields with masses far above the Hubble scale, such as the moduli of flux compactifications. By studying a string-inspired two-field extension of axion monodromy, we reveal that the oscillatory modulation of the axion potential leads to continuous excitation of heavy fields during inflation when the modulation frequency exceeds the field masses. This finding challenges the conventional single-field description, as heavy moduli cannot be simply integrated out. Using a full bootstrap analysis, we demonstrate that this mechanism produces cosmological collider signals that bypass the usual Boltzmann suppression for heavy masses. Specifically, we identify detectably large signatures of heavy moduli in the primordial bispectrum, offering a promising avenue for probing high-energy physics through cosmological observations.

This paper investigates the stability of steady transonic shocks with constant states in rectangular nozzles under small three dimensional perturbations of the external force and the exit pressure. Mathematically, the problem can be formulated as a nonlinear free boundary problem for a hyperbolic-elliptic coupled PDE system. One of the key difficulties lies in the arbitrary location of the background shock, which may lead to multiple shock solutions for the same external force and exit pressure under perturbations, revealing the instability of the background shock. We reformulate the steady Euler equations in terms of deformation and vorticity to effectively decompose the hyperbolic and elliptic modes. Linearizing the reformulated system and the Rankine-Hugoniot conditions at background transonic shocks, we find that the class of nonzero horizontal external forces helps to uniquely determine the shock location, where the conservation of mass plays a critical role. A delicate iteration is developed to establish the existence and structural stability of transonic shock solutions. Our analysis shows that the stability mechanisms of steady transonic shocks in flat and divergent nozzles are quite different in many aspects.

It has been shown that a gravitational dual to a superconductor can be obtained by coupling anti-de Sitter gravity to a Maxwell field and charged scalar. We review our earlier analysis of this theory and extend it in two directions. First, we consider all values for the charge of the scalar field. Away from the large charge limit, backreaction on the spacetime metric is important. While the qualitative behaviour of the dual superconductor is found to be similar for all charges, in the limit of arbitrarily small charge a new type of black hole instability is found. We go on to add a perpendicular magnetic field B and obtain the London equation and magnetic penetration depth. We show that these holographic superconductors are Type II, i.e., starting in a normal phase at large B and low temperatures, they develop superconducting droplets as B is reduced.

The transition of an impulsively excited kink oscillation of a solar coronal loop to an oscillation with a stationary amplitude, i.e., the damping pattern, is determined using the low-dimensional self-oscillation model. In the model, the decayless kink oscillations are sustained by the interaction of the oscillating loop with an external quasi-steady flow. The analytical solution is based on the assumption that the combined effect of the effective dissipation, for example, by resonant absorption, and interaction with an external flow, is weak. The effect is characterised by a dimensionless coupling parameter. The damping pattern is found to depend upon the initial amplitude and the coupling parameter. The approximate expression shows a good agreement with a numerical solution of the self-oscillation equation. The plausibility of the established damping pattern is demonstrated by an observational example. Notably, the damping pattern is not exponential, and the characteristic decay time is different from the time determined by the traditionally used exponential damping fit. Implications of this finding for seismology of the solar coronal plasmas are discussed. In particular, it is suggested that a very rapid, in less than the oscillation period, decay of the oscillation to the stationary level, achieved for larger values of the coupling parameter, can explain the relative rareness of the kink oscillation events.

Traveling waves of activity in neural tissue can be halted by spatial inhomogeneity in synaptic coupling. We study an integrate-and-fire network in which each neuron fires once and the coupling decays exponentially. For this model the leading-edge firing map reduces exactly to a scalar equation for the wave speed in space, with a slow unstable and a fast stable homogeneous speed, c_1 and c_2, and a periodic modulation of the coupling enters this equation pointwise. Positive periodic waves terminate in folds. For slowly varying modulation the fold amplitude approaches a plateau set by the trough of the modulation, where the local bottleneck speed is c_1 c_2; the approach to the plateau is set by the local geometry of the trough. For rapidly varying modulation the fold amplitude grows linearly with frequency, with a slope given by a full-amplitude average over the integrated modulation profile; a weak-ripple truncation of that average overestimates the slope about 2.5-fold at the default coupling. A perturbative recursion in the amplitude gives the speed profile explicitly. We distinguish loss of the periodic wave from failure of a particular launch, and the excitatory regime εle 1 from its sign-changing extension. The results are checked against direct integration of the reduced equation and first-spike firing-map simulations of the network.

This study introduces amangkurat, an open-source Python library designed for the robust numerical simulation of relativistic scalar field dynamics governed by the nonlinear Klein-Gordon equation in (1+1)D spacetime. The software implements a hybrid computational strategy that couples Fourier pseudo-spectral spatial discretization with a symplectic Størmer-Verlet temporal integrator, ensuring both exponential spatial convergence for smooth solutions and long-term preservation of Hamiltonian structure. To optimize performance, the solver incorporates adaptive timestepping based on Courant-Friedrichs-Lewy (CFL) stability criteria and utilizes Just-In-Time (JIT) compilation for parallelized force computation. The library's capabilities are validated across four canonical physical regimes: dispersive linear wave propagation, static topological kink preservation in phi-fourth theory, integrable breather dynamics in the sine-Gordon model, and non-integrable kink-antikink collisions. Beyond standard numerical validation, this work establishes a multi-faceted analysis framework employing information-theoretic entropy metrics (Shannon, Rényi, and Tsallis), kernel density estimation, and phase space reconstruction to quantify the distinct phenomenological signatures of these regimes. Statistical hypothesis testing confirms that these scenarios represent statistically distinguishable dynamical populations. Benchmarks on standard workstation hardware demonstrate that the implementation achieves high computational efficiency, making it a viable platform for exploratory research and education in nonlinear field theory.

Astrocytes are increasingly recognized as active regulators of neural dynamics, yet their role in large-scale synchronization remains incompletely understood. Building on the discovery of breathing cluster synchronization in neuron-astrocyte networks, we investigate whether this phenomenon persists under more biologically realistic conditions by incorporating thermosensitive neuronal dynamics, intrinsic electric-field interactions, stochastic perturbations, and delayed astrocytic feedback. Through systematic numerical simulations of a network containing structurally symmetric neuronal subsets, we show that breathing clusters characterized by intermittent alternations between synchronized and desynchronized states, remain robust across a broad range of biophysical conditions. The results reveal a non-monotonic dependence on astrocytic attenuation and feedback parameters, with intermediate values maximizing rhythmic switching through a slow push-pull regulatory mechanism. Temperature and electric-field effects primarily modulate neuronal excitability and the tolerance of the breathing state to noise, while elevated stochastic perturbations progressively destabilize cluster coherence. In contrast, the phenomenon exhibits remarkable robustness to biologically realistic astrocytic delays. Importantly, our findings indicate that the emergence of breathing synchronization remains fundamentally governed by the interplay between network symmetry and astrocyte-mediated feedback, whereas temperature, electric fields, and noise act as modulators of its stability and temporal organization. These results establish breathing cluster synchronization as a robust organizing principle of astrocyte-regulated networks and provide a quantitative framework for understanding how glial regulation shapes cortical state-switching under realistic physiological conditions.

Differentiable programming techniques are widely used in the community and are responsible for the machine learning renaissance of the past several decades. While these methods are powerful, they have limits. In this short report, we discuss a common chaos based failure mode which appears in a variety of differentiable circumstances, ranging from recurrent neural networks and numerical physics simulation to training learned optimizers. We trace this failure to the spectrum of the Jacobian of the system under study, and provide criteria for when a practitioner might expect this failure to spoil their differentiation based optimization algorithms.

Multi-agent large language model (LLM) systems often rely on verifier and critic agents to suppress hallucinations, but verification is delayed. During this delay, false claims can propagate through the agent network. We model this process as delayed consensus on a graph with grounded corrector nodes. Spectral decomposition by the grounded Laplacian yields a closed-form stability threshold for the verification dose: correction that is too strong or too delayed can turn consensus into oscillation. The most unstable regime occurs when the communication and verification delays coincide; for delay two, the threshold is the inverse golden ratio. The same framework gives a supermodular placement objective and a greedy (1-1/e)-approximation rule for assigning a limited corrector budget to influential nodes. Experiments across five open models confirm the predicted dose-delay oscillations. By contrast, grounded factual answering makes truth an absorbing boundary and eliminates the effect, suggesting that the instability is specific to signed-belief tasks while grounded verification remains stabilizing

Frontier large language model training consumes massive accelerator fleets and long wall-clock computation, making stability failures costly when they occur. After a numerical or a hyperparameter fault has already destabilized the training dynamics, it may continue for thousands of steps while loss and gradient norms still appear normal. We study mechanism-driven detection of training instability by deriving internal monitors from the functional role of each critical module and from the earliest computational sites where failures are expected to produce measurable signatures. For low-precision flash attention, we monitor the spectral entropy of a QK bilinear decomposition, whose first-order term becomes abnormal before the loss fully collapses. For MoE routers, we derive indicators from their role in expert selection. Our fault-injection experiments on low-precision attention, large learning-rate, and combined faults show that these signals provide distinct signatures for different failures, triggering thousands of steps before loss divergence.

External potentials break the translational invariance of nonlinear Schrödinger (NLS) equations and generally convert a continuous family of standing wave solutions into isolated pinned states. We study this mechanism for the prototypical case of a kink in the NLS equation with competing focusing cubic and defocusing quintic nonlinearities. The Lyapunov--Schmidt reduction method is used to prove that the location s_0 of the pinned kinks is selected near roots of an effective potential V_{rm eff}(s). We then determine how the translational zero eigenvalue of the Jacobian operator splits under the perturbation and prove that the sign of V_{rm eff}'(s_0) distinguishes eigendirections of positive and negative energy. We further show that if the Jacobian operator admits a negative eigenvalue, then the stability problem contains a real unstable eigenvalue. The derivation of the asymptotic expansion for the unstable eigenvalue is nonstandard because the zero eigenvalue is embedded in the continuous spectrum of the linearized operator. Finally, we show that the persistence of kinks lacks parity symmetry even if the external potential is odd. Numerical continuation, spectral computations with domains adapted to the slowly decaying eigenfunctions, and direct dynamical simulations of the time evolution corroborate the analytical predictions for different representative examples.

We study a one dimensional nonlinear Klein-Gordon equation with a potential, a localized quadratic nonlinearity, and a non-localized quartic nonlinearity. We assume that the linearized operator has a single discrete eigenvalue below the continuous spectrum, corresponding to an ''internal mode''. This eigenvalue generates localized, time-periodic solutions for the linear equation. Assuming the natural Fermi Golden Rule, we give a global description of the dynamics of the amplitude of the internal mode through the radiation damping mechanism, and prove scattering for the radiation. Our approach is based on the distorted Fourier transform and a collection of refined dispersive decay and smoothing estimates. The corresponding cubic problem is closely related to the question of global-in-space dispersive asymptotics for perturbations of kink solutions in the classical ϕ^4 model, which remains a challenging open question. From the perspective of nonlinear estimates, a quartic (non-localized) interaction is essentially sharp for our analysis, and closing the estimates with such a low degree nonlinear term requires a careful and delicate treatment. As a direct application of our analysis, we prove a result on the asymptotic stability of kinks for classes of scalar field models that can be seen as perturbations of the ϕ^4 model.

Blue large-amplitude pulsators (BLAPs) are a recently discovered group of hot stars pulsating in radial modes. Their origin needs to be explained, and several scenarios for their formation have already been proposed. We investigate whether BLAPs can originate as the product of a merger of two low-mass white dwarfs (WDs) and estimate how many BLAPs can be formed in this evolutionary channel. We used the MESA code to model the merger of three different double extremely low-mass (DELM) WDs and the subsequent evolution of the merger product. We also performed a population synthesis of Galactic DELM WDs using the COSMIC code. We find that BLAPs can be formed from DELM WDs provided that the total mass of the system ranges between 0.32 and 0.7 M_odot. BLAPs born in this scenario either do not have any thermonuclear fusion at all or show off-centre He burning. The final product evolves to hot subdwarfs and eventually finishes its evolution either as a cooling He WD or a hybrid He/CO WD. The merger products become BLAPs only a few thousand years after coalescence, and it takes them 20 to 70 thousand years to pass the BLAP region. We found the instability of the fundamental radial mode to be in fair agreement with observations, but we also observed instability of the radial first overtone. From the population synthesis, we found that up to a few hundred BLAPs born in this scenario can exist at present in the Galaxy. Given the estimated number of BLAPs formed in the studied DELM WD merger scenario, there is a good chance to observe BLAPs that originated through this scenario. Since strong magnetic fields can be generated during mergers, this scenario could lead to the formation of magnetic BLAPs. This fits well with the discovery of two likely magnetic BLAPs whose pulsations can be explained in terms of the oblique rotator model.

In the BCS theory of superconductivity the amplitude (Higgs) mode is degenerate with the pair-breaking threshold: its frequency coincides with 2Δ, so it is an edge singularity rather than a true collective mode. This is why after a sudden weak perturbation at t=0 its oscillations decay algebraically as 1/t. We show that the retardation effects due to the phonon dynamics in the strong-coupling theory lift this degeneracy. The Higgs mode detaches from the pair-breaking edge 2Δ_g, set by the spectral gap, and becomes a sharp subgap excitation. We determine its frequency from the longitudinal pair susceptibility evaluated directly on the real frequency axis, using the Eilenberger equations for Migdal--Eliashberg theory with the Einstein phonon spectrum. The response of the mass renormalization supplies at least two fifths of the displacement, and possibly all of it: with it switched off, the binding falls below the resolution of the calculation. Its consequences, however, are significant because a percent-level shift transfers about a quarter of the spectral weight of the amplitude channel out of the two-quasiparticle continuum into a discrete energy level. What experiment sees is therefore not the displacement itself but its consequence: amplitude oscillations that persist instead of decaying as 1/t.

The dynamical realisation of the equation of state p +rho =0 is studied. A non-pathological dynamics for the perturbations of such a system mimicking a dynamical cosmological constant (DCC) requires to go beyond the perfect fluid paradigm. It is shown that an anisotropic stress must be always present. The Hamiltonian of the system in isolation resembles the one of a Pais-Uhlenbeck oscillator and linear stability requires that it cannot be positive definite. The dynamics of linear cosmological perturbations in a DCC dominated Universe is studied in detail showing that when DCC is minimally coupled to gravity no dramatic instability is present. In contrast to what happens in a cosmological constant dominated Universe, the non-relativistic matter contrast is no longer constant and exhibits an oscillator behaviour at small scales while it grows weakly at large scales. In the gravitational waves sector, at small scales, the amplitude is still suppressed as the inverse power of the scale factor while it grows logarithmically at large scales. Also the vector modes propagate, though no growing mode is found.

We address effects of spin-orbit coupling (SOC), phenomenologically added to a two-component Bose-Einstein condensate composed of particles moving by Levy flights, in one- and two-dimensional (1D and 2D) settings. The corresponding system of coupled Gross-Pitaevskii equations includes fractional kinetic-energy operators, characterized by the Levy index, \alpha < 2 (the normal kinetic energy corresponds to \alpha = 2). The SOC terms, with strength \lambda, produce strong effects in the 2D case: they create families of stable solitons of the semi-vortex (SV) and mixed-mode (MM) types in the interval of 1 < \alpha < 2, where the supercritical collapse does not admit the existence of stable solitons in the absence of the SOC. At \lambda --> 0, amplitudes of these solitons vanish as (\lambda)^{1/(\alpha - 1)}.

We update predictions for observables in the "delicate" D3/anti-D3 inflationary model on the conifold. We use a full CMB likelihood calculation to assess goodness-of-fit, which is necessary because in this model the zeta power spectrum often cannot be modelled as a power-law over observable scales. For the first time we are able to provide accurate forecasts for the amplitude of three-point correlations. In a significant portion of its parameter space the model follows Maldacena's single-field prediction fNL ~ -(5/12)(ns-1) if nt << 1. Therefore |fNL| is usually small when the power spectrum satisfies observational constraints. In a small number of cases the bispectrum is instead dominated by effects from rapid switching between angular minima. The resulting amplitudes are larger, but mostly with unacceptable spectral behaviour. In the most extreme case we obtain |fNLeq| ~ 75 at kt/3 = 0.002/Mpc. It has been suggested that the quasi-single field inflation ("QSFI") mechanism could produce significant 3-point correlations in this model. We do observe rare shifts in amplitude between equilateral and squeezed configurations that could possibly be associated with QSFI effects, but more investigation is needed to establish the full bispectrum shape. There is evidence of "shape" running between equilateral and squeezed configurations that may be inherited from the scale dependence of the spectrum. We explore the dependence of observables on discrete choices such as the truncation point of the potential. Our analysis illustrates the advantages of a standard format for information exchange within the inflationary model-building and testing community.

In this Essay, we will look at the relation between the No Transmission principle and the Strong cosmic censorship (SCC), which we will highlight in the background of quantum gravity. We show that taking quantum gravity into account, one can provide a complete picture of the instability of the inner horizon and the principle that two independent CFTs, under the gauge-gravity duality, imply that the dual bulks must also be independent in that there must not exist a way to transmit a signal between the two spacetimes. We show that this can simply be interpreted as SCC, and that the inner horizon must be unstable (at either linear or nonlinear orders) to be in accordance with holographic quantum gravity.

We study a mechanism to produce the circular polarization of primordial gravitational waves. The circular polarization is generated during the super-inflation driven by the Gauss-Bonnet term in the string-inspired cosmology. The instability in the tensor mode caused by the Gauss-Bonnet term and the parity violation due to the gravitational Chern-Simons term are the essential ingredients of the mechanism. We also discuss detectability of the produced circular polarization of gravitational waves. It turns out that the simple model of single-field inflation contradicts CMB observations. To circumvent this difficulty, we propose a two-field inflation model. In this two-field model, the circular polarization of gravitational waves is created in the frequency range designed by the Big-Bang Observer (BBO) or the deci-hertz gravitational-wave observatory (DECIGO).

Classical resistive tearing theory assumes a prescribed current-sheet equilibrium, but a finite normal magnetic field can evolve the background on the tearing timescale. For a transversely pressure-balanced Harris profile of initial half-thickness a and asymptotic reconnecting-field magnitude B_0, threaded by uniform B_n (ξ=B_n/B_0), we derive an exact evolution in ideal magnetohydrodynamics: counter-propagating Alfvenic fronts broaden the neutral layer and generate a central sheet-parallel flow with shear at its flanks. Inner-layer estimates recover ξ_{crit}sim S^{-3/4} for breakdown of the classical resistive balance, where S is the Lundquist number based on a. Numerical frozen-profile calculations show loss of central resistive dominance and decreasing tearing growth as the neutral layer expands. Eigenfunction comparisons at fixed wavenumber and predominantly Doppler-shifted propagation support a normal-field-modified continuation of classical tearing. The normal field supplies no net perturbation energy. Energy extraction from the reconnecting-field gradient weakens as the sheet broadens. The velocity-gradient contribution becomes comparable when the neutral-layer width approaches the initial sheet thickness, without reversing the decline in growth. For S=10^6, Pr_m=0, and ξ=10^{-4}, the maximum growth rate falls by a factor of about ten from its initial value at neutral-layer half-width wsimeq1.59a, where the growth and broadening times become equal. Only about 0.18 additional upper-envelope e-folds are estimated between this crossing and w/a=2, where the growth rate is about 25 times smaller than its initial value. These results support dynamical suppression of further linear amplification over the sampled evolution, even though the instantaneous spectrum remains unstable.

Repeated impacts of a droplet on a vertically forced bath can produce a growing Faraday-wave response under forcing conditions for which the corresponding initially undisturbed bath remains linearly stable. We investigate this mechanism using axisymmetric two-phase direct numerical simulations over a wide range of Reynolds and Weber numbers. The resulting phenomenological regime map identifies quasi-periodic, decaying, faint, and unstable-bath responses. Along the parameter path considered here, the transition to the unstable-bath regime occurs over a narrow range of Weber numbers and varies only weakly with Reynolds number. In the unstable regime, the bath develops a coherent subharmonic response at half the forcing frequency, while disturbances in the decaying regime remain broadband and weaken between successive rebounds. Bath-only simulations show that a finite-amplitude perturbation representative of droplet impact can seed the confined radial mode susceptible to parametric forcing, initiating a growing subharmonic response below the linear instability threshold of the initially flat bath. A reduced capillary-dominated model provides a scaling estimate for the impact-equivalent perturbation amplitude, and bath-only simulations initialized with these perturbations reproduce the bounded-to-growing transition observed in the coupled simulations. Floquet analysis of the finite cylindrical bath identifies the first axisymmetric Neumann mode as having the lowest subharmonic instability threshold. A time-resolved Bessel decomposition independently shows that the growing bath response is dominated by the same radial mode, while the droplet-induced subharmonic response projects predominantly onto this structure. These results identify a finite-amplitude route by which localized droplet impacts can access Faraday-wave dynamics below the linear onset threshold of an initially undisturbed bath.

Baryons in the holographic Witten-Sakai-Sugimoto model are described by instanton solutions on the flavor branes. A commonly used approximation for dense baryonic matter replaces the many-instanton solution by a simpler, spatially homogeneous, ansatz, which requires a discontinuity in the holographic direction of the non-abelian gauge field in order to account for topological baryon number. We point out that the simplest configuration with a single jump - often used in previous studies - results in matter at saturation density that is much stiffer than real-world nuclear matter. This is improved, although not completely remedied, by adding a second jump. We present a systematic discussion of all possible configurations up to four jumps, dynamically computing locations of and behavior at the discontinuities. We find solutions that continuously connect to those based on pointlike baryons, thus, for the first time, establishing a concrete link between the instantonic and homogeneous pictures. This is supported by translating the multi-jump profiles of the gauge field into gauge invariant multi-layer charge distributions. The most important of our novel configurations has a block-like structure in the bulk, becomes pointlike at low density and/or large coupling, and is energetically preferred over all previously studied configurations. Therefore, our work lays the ground for improved predictions from holography for dense nuclear matter in neutron stars.

Runaway electron current generated during the Current Quench phase of tokamak disruptions could result in severe damage to future high performance devices. To control and mitigate such runaway electron current, it is important to accurately describe the runaway electron current dominated equilibrium, based on which further stability analysis could be carried out. In this paper, we derive a Grad-Shafranov-like equation solving for the axisymmetric drift surfaces of the runaway electrons for the simple case that all runaway electron share the same parallel momentum. This new equilibrium equation is then numerically solved with simple rectangular wall with ITER-like and MAST-like geometry parameters. The deviation between the drift surfaces and the flux surfaces is readily obtained, and runaway electrons is found to be well confined even in regions with open field lines. The change of the runaway electron parallel momentum is found to result in a horizontal current center displacement without any changes in the total current or the external field. The runaway current density profile is found to affect the susceptibility of such displacement, with flatter profiles result in more displacement by the same momentum change. With up-down asymmetry in the external poloidal field, such displacement is accompanied by a vertical displacement of runaway electron current. It is found that this effect is more pronounced in smaller, compact device and weaker poloidal field cases. The above results demonstrate the dynamics of current center displacement caused by the momentum space change in the runaway electrons, and pave way for future, more sophisticated runaway current equilibrium theory with more realistic consideration on the runaway electron momentum distribution. This new equilibrium theory also provides foundation for future stability analysis of the runaway electron current.

We discuss the perturbative stability of warped anti-de Sitter (WAdS_3) spaces in three-dimensional gauged supergravity. To this end, we first derive the analogue of the Breitenlohner-Freedman bound for a single scalar field on such a curved background. We then apply this analysis to the half-maximal D=3 gauged supergravity obtained from the compactification of the D=6, N=(1,1) supergravity on S^3. Families of three-dimensional configurations, uplifting to spaces of the form WAdS_3 times WS^3, are found by turning on appropriate vector and scalar fields, supporting the AdS_3 and S^3 warpings, respectively. Finally, we show that the spectra of scalar fluctuations satisfy the stability criteria for each solution.

Online Surgical Phase Recognition (SPR) models can reach high frame-wise accuracy, yet their predictions often lack temporal stability, fragmenting workflow understanding and reducing the reliability of downstream assistance. We show that this instability is not random noise but arises from two mechanisms: early misclassifications corrupt temporal feature states and propagate forward to form error cascades, and phase transitions follow evidence-accumulation dynamics whereas most online SPR systems rely on memoryless frame-wise decisions, making them sensitive to transient confidence fluctuations. We propose a unified Train-Inference-Evaluation framework that explicitly stabilizes temporal inference dynamics using model-agnostic, plug-and-play components. For training, the Temporal Error-Cascade (TEC) loss suppresses error onset and mitigates forward error propagation by stabilizing temporal feature evolution. For inference, the Evidence-Gated Transition Predictor (EGTP) enforces evidence-driven state transitions, allowing phase changes only when accumulated evidence exceeds a confidence boundary. For evaluation, we introduce the Temporal Fragmentation Index (TFI), a reliability-aware metric that quantifies instability-induced temporal disagreement beyond conventional frame-wise and token-based measures. Experiments on Cholec80 and AutoLaparo across three representative backbones show that the proposed framework substantially improves temporal stability and reduces prediction fragmentation, while maintaining or modestly improving frame-wise performance.

Large Language Models (LLMs) have demonstrated exceptional performance across diverse tasks, yet their training remains highly resource-intensive and susceptible to critical challenges such as training instability. A predominant source of this instability stems from gradient and loss spikes, which disrupt the learning process, often leading to costly interventions like checkpoint recovery and experiment restarts, further amplifying inefficiencies. This paper presents a comprehensive investigation into gradient spikes observed during LLM training, revealing their prevalence across multiple architectures and datasets. Our analysis shows that these spikes can be up to 1000times larger than typical gradients, substantially deteriorating model performance. To address this issue, we propose Spike-Aware Adam with Momentum Reset SPAM, a novel optimizer designed to counteract gradient spikes through momentum reset and spike-aware gradient clipping. Extensive experiments, including both pre-training and fine-tuning, demonstrate that SPAM consistently surpasses Adam and its variants across various tasks, including (1) LLM pre-training from 60M to 1B, (2) 4-bit LLM pre-training,(3) reinforcement learning, and (4) Time Series Forecasting. Additionally, SPAM facilitates memory-efficient training by enabling sparse momentum, where only a subset of momentum terms are maintained and updated. When operating under memory constraints, SPAM outperforms state-of-the-art memory-efficient optimizers such as GaLore and Adam-Mini. Our work underscores the importance of mitigating gradient spikes in LLM training and introduces an effective optimization strategy that enhances both training stability and resource efficiency at scale. Code is available at https://github.com/TianjinYellow/SPAM-Optimizer.git

Although deep learning (DL) has received much attention in accelerated magnetic resonance imaging (MRI), recent studies show that tiny input perturbations may lead to instabilities of DL-based MRI reconstruction models. However, the approaches of robustifying these models are underdeveloped. Compared to image classification, it could be much more challenging to achieve a robust MRI image reconstruction network considering its regression-based learning objective, limited amount of training data, and lack of efficient robustness metrics. To circumvent the above limitations, our work revisits the problem of DL-based image reconstruction through the lens of robust machine learning. We find a new instability source of MRI image reconstruction, i.e., the lack of reconstruction robustness against spatial transformations of an input, e.g., rotation and cutout. Inspired by this new robustness metric, we develop a robustness-aware image reconstruction method that can defend against both pixel-wise adversarial perturbations as well as spatial transformations. Extensive experiments are also conducted to demonstrate the effectiveness of our proposed approaches.

Falling is an inherent risk of humanoid mobility. Maintaining stability is thus a primary safety focus in robot control and learning, yet no existing approach fully averts loss of balance. When instability does occur, prior work addresses only isolated aspects of falling: avoiding falls, choreographing a controlled descent, or standing up afterward. Consequently, humanoid robots lack integrated strategies for impact mitigation and prompt recovery when real falls defy these scripts. We aim to go beyond keeping balance to make the entire fall-and-recovery process safe and autonomous: prevent falls when possible, reduce impact when unavoidable, and stand up when fallen. By fusing sparse human demonstrations with reinforcement learning and an adaptive diffusion-based memory of safe reactions, we learn adaptive whole-body behaviors that unify fall prevention, impact mitigation, and rapid recovery in one policy. Experiments in simulation and on a Unitree G1 demonstrate robust sim-to-real transfer, lower impact forces, and consistently fast recovery across diverse disturbances, pointing towards safer, more resilient humanoids in real environments. Videos are available at https://firm2025.github.io/.

Turbulent magnetic fields are to some extent a universal feature in astrophysical phenomena. Charged particles that encounter these turbulence get on average accelerated according to the so-called second-order Fermi process. However, in most astrophysical environments there are additional competing processes, such as different kinds of first-order energy changes and particle escape, that effect the resulting momentum distribution of the particles. In this work we provide to our knowledge the first semi-analytical solution of the isotropic steady-state momentum diffusion equation including continuous and catastrophic momentum changes that can be applied to any arbitrary astrophysical system of interest. Here, we adopt that the assigned magnetic turbulence is constrained on a finite range and the particle flux vanishes beyond these boundaries. Consequently, we show that the so-called pile-up bump -- that has for some special cases long been established -- is a universal feature of stochastic acceleration that emerges around the momentum chi_{rm eq} where acceleration and continuous loss are in equilibrium if the particle's residence time in the system is sufficient at chi_{rm eq}. In general, the impact of continuous and catastrophic momentum changes plays a crucial role in the shape of the steady-state momentum distribution of the accelerated particles, where simplified unbroken power-law approximations are often not adequate.

We study linear perturbations of the Maldacena-Milekhin-Popov (MMP) wormhole in the parity sector that pairs axial metric perturbations with polar gauge perturbations. It contains the axial gravitational mode and the electric field along the magnetic field lines. The lowest Landau level (LLL) of the charged fermions responds through its charge. The gauge components a_τ, a_ρ form a two-dimensional gauge field on the worldsheet of each field line, and the fermions respond with the exact Schwinger current. Lifted over the sphere, it gives the electric field the MMP screening mass m_S^2=αq^2, which is not small and survives in the mouth. In the throat the perturbation tilts the worldsheets, and the Casimir stress tensor acquires mixed components. Force balance then requires a current across the field lines, and charge conservation fixes an accompanying polarisation current, the counterpart of the Hall current of the polar sector. These currents close the Bianchi identities at first order in the fermionic backreaction α. The system reduces to three coupled master equations, given in closed form and matched to the fermion-free mouth. Consistency alone does not select the fermionic constitutive relation, but locality, covariance and the index theorem do. At α=0 the throat reduces to Poschl-Teller problems with masses l(l-1) and (l+1)(l+2) at m_S^2=0. At finite m_S^2 one mode is screened, one tends to the mass l^2+l+2, and one neutral charge-density wave stays exactly massless. The O(α) shifts of the massive normal frequencies are real and negative. The two parity sectors are isospectral only without fermions. The neutral channel sees an attractive region in each mouth, and a numerical solution coupled to the gravitational channel in the exact mouth potential finds no bound state. The sector has no growing mode for lge2 at this order.

We show that a scale-invariant U(1) gauge theory can naturally realize large curvature perturbations around the end of thermal inflation, seeding the formation of primordial black holes (PBHs). The allowed nonminimal gravitational interaction ξ of the Higgs field induces a Hubble-scale negative mass-squared term for positive ξsim O(1), and triggers a second order phase transition that ends thermal inflation while keeping the extra e-folds small. This sharp contrast to the minimally coupled case allows the gauge coupling to be much smaller than unity. It turns out that field fluctuations are dominated by thermal fluctuations around the onset of the phase transition, and sufficiently amplified to produce an appreciable amount of PBHs with a wide range of possible masses. The associated scalar-induced gravitational waves (GWs) are accompanied by cosmic-string induced GWs coming from the breaking of the U(1) symmetry. As a result, the generated PBH population can have a correlated GW signature relevant to pulsar timing arrays, space-based interferometers, or ground-based detectors.

An expanding bubble in AdS_5 has a dS_4 geometry; the dark bubble scenario explores whether this can be our Universe. Motivated by this, we consider new non-supersymmetric AdS_5 compactifications of M-theory and investigate their non-perturbative instabilities. We focus on a compactification on the flag manifold. In certain regions of the flux landscape, the non-supersymmetric vacua become unstable under the nucleation of M5-brane bubbles wrapping an internal two-cycle, thus realising the dark bubble scenario. The cosmological constant on the bubble can be made parametrically small by tuning the internal fluxes, making the M5-branes close to the extremality bound. The solution relates the induced cosmological constant on the brane and the typical largest length scale of the extra dimensions through R^{-1}sim Λ_4^{1/4} in 4d Planck units, allowing for extra dimensions of the order of tens of microns. We also consider various alternatives, which for various reasons are currently not as successful.

In the axion model, electromagnetic waves interacting with axions induce frequency-dependent time delays, determined by the axion mass and decay constant. These small delays are difficult to detect, making traditional methods ineffective. To address this, we computed time delays for various parameters and found a prominent dispersion signal when the wave frequency equals half the axion mass. Based on this, we developed a machine learning-based pipeline, achieving 95\% classification accuracy and demonstrating strong detection capability in low signal-to-noise data. Applying this to PSR J1933-6211, we found no axion-induced delays within current sensitivity limits. While existing constraints are limited by atomic clock resolution in radio telescopes, future advances in optical clocks and broader bandwidths will enable more extensive searches. In particular, combining high-precision optical clocks with next-generation radio telescopes, such as the Qitai Radio Telescope, could improve decay constant constraints by four orders of magnitude for axion masses in the 10^{-6} sim 10^{-4} eV range.

Motivated by the peculiar features of the trans-Neptunian object (TNO) Máni and the discovery of ring systems around Centaurs and trans-Neptunian bodies, we investigate the stability of particles around a small irregular body hosting a deep equatorial crater. This study is the third contribution in a sequence devoted to the dynamics around non-spherically symmetric bodies. Using Máni as a reference model, whose crater depth exceeds 10% of its radius, we map the system stability through complementary methods: Poincaré surfaces of section (PSS), survival maps, and the finite-time Lyapunov exponent (FTLE). In the nominal case, the 1!:!1, 2!:!1, 3!:!1, and 4!:!1 spin-orbit resonances (SORs) are consistently identified by all techniques. The prominent 3!:!1 SOR exhibits a bifurcated structure at high eccentricities, matching structural transitions observed at lower Jacobi constant values in the PSSs. Increasing the rotation rate (λ) and crater mass ratio (μ) enlarges resonance widths and promotes overlap, making the 2!:!1 and 4!:!1 SORs progressively dominant. Lower rotation rates allow stable trajectories to persist at higher eccentricities, whereas the 1!:!1 SOR is highly sensitive to stronger perturbations and disappears in the most extreme cases. In contrast to mass-anomaly models, which can clear the region interior to the 2!:!1 SOR, the crater configuration considered here preserves stable regions in this vicinity, suggesting alternative scenarios for the formation and maintenance of debris structures around irregular minor bodies.

Whether physics foundation models can be usefully deployed on laboratory experiments remains an open question for scientific machine learning (ML). We test this question on the Rayleigh-Taylor instability (RTI), a ubiquitous and demanding fluid instability seen from tabletop flows to supernova explosions, in which small perturbations at a density interface grow into chaotic, multiscale mixing as a lighter fluid accelerates into a heavier one. Standard ML models struggle with RTI, and despite over a century of theoretical, numerical, and experimental work, it carries an unresolved discrepancy between simulation and experiment: the late-time mixing growth rate, α, measured in most laboratory experiments (sim 0.06-0.07), is roughly three times the value from idealized direct numerical simulations (DNS, sim 0.02). The gap's origin remains debated. These properties make RTI a stringent test for a question that matters well beyond RTI: can foundation models trained only on simulations generalise to sparse, messy, and noisy laboratory settings? We finetune Walrus, a foundation model for continuum dynamics, on three or fewer DNS realizations and recover key RTI physics over long rollouts. Applied zero-shot to sliding-barrier laboratory data, the finetuned model leaves the DNS-like regime and enters the observed growth band, having never seen a single experimental sample. These results provide independent, data-driven evidence that initial conditions play a crucial role in the longstanding sim-experiment gap in α. The model also generalises zero-shot to stable stratification, a buoyancy regime absent from training, correctly slowing mixing-layer growth. Together, our results show that foundation models can generalise well beyond their training data, predicting laboratory behavior and unseen physical regimes, opening new ways to probe longstanding simulation-experiment gaps.

Recent work suggests that (stochastic) gradient descent self-organizes near an instability boundary, shaping both optimization and the solutions found. Momentum and mini-batch gradients are widely used in practical deep learning optimization, but it remains unclear whether they operate in a comparable regime of instability. We demonstrate that SGD with momentum exhibits an Edge of Stochastic Stability (EoSS)-like regime with batch-size-dependent behavior that cannot be explained by a single momentum-adjusted stability threshold. Batch Sharpness (the expected directional mini-batch curvature) stabilizes in two distinct regimes: at small batch sizes it converges to a lower plateau 2(1-β)/η, reflecting amplification of stochastic fluctuations by momentum and favoring flatter regions than vanilla SGD; at large batch sizes it converges to a higher plateau 2(1+β)/η, where momentum recovers its classical stabilizing effect and favors sharper regions consistent with full-batch dynamics. We further show that this aligns with linear stability thresholds and discuss the implications for hyperparameter tuning and coupling.

We present a neural flow wavefunction, Gauge-Fermion FlowNet, and use it to simulate 2+1D lattice compact quantum electrodynamics with finite density dynamical fermions. The gauge field is represented by a neural network which parameterizes a discretized flow-based transformation of the amplitude while the fermionic sign structure is represented by a neural net backflow. This approach directly represents the U(1) degree of freedom without any truncation, obeys Guass's law by construction, samples autoregressively avoiding any equilibration time, and variationally simulates Gauge-Fermion systems with sign problems accurately. In this model, we investigate confinement and string breaking phenomena in different fermion density and hopping regimes. We study the phase transition from the charge crystal phase to the vacuum phase at zero density, and observe the phase seperation and the net charge penetration blocking effect under magnetic interaction at finite density. In addition, we investigate a magnetic phase transition due to the competition effect between the kinetic energy of fermions and the magnetic energy of the gauge field. With our method, we further note potential differences on the order of the phase transitions between a continuous U(1) system and one with finite truncation. Our state-of-the-art neural network approach opens up new possibilities to study different gauge theories coupled to dynamical matter in higher dimensions.

We numerically investigate some properties of unbalanced St\"{u}ckelberg holographic superconductors, by considering backreaction effects of fields on the background geometry. More precisely, we study the impacts of the chemical potential mismatch and St\"{u}ckelberg mechanism on the condensation and conductivity types (electrical, spin, mixed, thermo-electric, thermo-spin and thermal conductivity). Our results show that the St\"{u}ckelberg's model parameters C_{alpha} and alpha not only have significant impacts on the phase transition, but also affect the conductivity pseudo-gap and the strength of conductivity fluctuations. Moreover, the effects of these parameters on a system will be gradually reduced as the imbalance grows. We also find that the influence of alpha on the amplitude of conductivity fluctuations depends on the magnitude of the both C_{alpha} and deltamu/mu in the electric and thermal conductivity cases. This results in that increasing alpha can damp the conductivity fluctuations of an unbalanced system in contrast to balanced ones.

Static spherically symmetric asymptotically flat configurations in General Relativity with a minimally coupled scalar field typically possess naked singularities. We study a linear stability of these configurations against radial (monopole) perturbations in case of power-law scalar field potentials. We employ a new shooting method that extracts the eigenvalues corresponding to the exponentially growing modes of the perturbation. The problem is reduced to one second order ``master'' equation in a divergent form with a regularized effective potential. We confirm our previous results showing that instability modes exist for sufficiently small scalar charges of the initial static configurations.

We develop a linear perturbative formalism to compute the response of an inhomogeneous stellar disk embedded in a non-responsive dark matter halo to perturbations like bars, spiral arms and satellite galaxy encounters. Without self-gravity to reinforce it, the response of a Fourier mode phase mixes away due to an intrinsic spread in the vertical (Omega_z), radial (Omega_r) and azimuthal (Omega_phi) frequencies, giving rise to local phase-space spirals. Collisional diffusion due to scattering of stars by structures like giant molecular clouds causes super-exponential damping of the phase-spiral amplitude. The z-v_z phase-spiral is 1-armed (2-armed) for vertically anti-symmetric (symmetric) bending (breathing) modes. Only transient perturbations with timescales (tau_{P}) comparable to the vertical oscillation period (tau_z sim 1/Omega_z) trigger z-v_z phase-spirals. Each (n,l,m) mode of the response to impulsive (tau_{P}<tau=1/(nOmega_z+lOmega_r+mOmega_phi)) perturbations is power law (sim tau_{P}/tau) suppressed, but that to adiabatic (tau_{P}>tau) perturbations is exponentially weak (sim left[-left(tau_{mathrm{P}/tauright)^alpharight]}) except resonant (tauto infty) modes. Slower (tau_{P}>tau_z) perturbations, e.g., distant encounters with satellite galaxies, induce stronger bending modes. If the Gaia phase-spiral was triggered by a satellite, Sagittarius is the leading contender as it dominates the Solar neighborhood response of the Milky Way disk to satellite encounters. However, survival against collisional damping necessitates that the impact occurred within sim 0.6-0.7 Gyr ago. We discuss how the detailed galactic potential dictates the phase-spiral shape: phase mixing occurs slower and phase-spirals are less wound in the outer disk and in presence of an ambient halo.

Spacetime singularities displayed by classical black hole solutions are expected to be cured by high-energy effects, beyond the regime of validity of General Relativity. On the other hand, there are well-known examples of classical theories allowing for nonsingular black hole solutions. The most prominent is obtained by complementing the gravitational sector of General Relativity with a minimally coupled nonlinear-electrodynamics sector. It has recently been shown that purely electric/purely magnetic nonsingular black holes in an Einstein-nonlinear-electrodynamics setup are always plagued by a gradient instability. In this work, we derive the quadratic action for linear perturbations of static, spherically symmetric dyonic solutions of Einstein-nonlinear-electrodynamics theories with a general dependence on both invariants. We show that regularity of the center, absence of ghosts and angular gradient stability cannot hold simultaneously: arbitrarily close to a regular center, at least one photon polarization has a negative squared angular propagation speed. We further show that regularity drives one electromagnetic kinetic eigenvalue to zero at the center, which may limit perturbative control near the core. Evading the obstruction requires extending the theory, for example by introducing additional degrees of freedom.

We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t to lambda^z t, x to lambda x; we focus on the case with z=2. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.

Anomalies in transverse Ward--Takahashi identities are studied, allowing discussion of the feasibility of anomalies arising in general non-symmetry Ward--Takahashi identities. We adopt the popular Fujikawa's method and rigorous dimensional renormalization to verify the existence of transverse anomalies to one-loop order and any loop order, respectively. The arbitrariness of coefficients of transverse anomalies is revealed, and a way out is also proposed after relating transverse anomalies to Schwinger terms and comparing symmetry and non-symmetry anomalies. Papers that claim the non-existence of transverse anomalies are reviewed to find anomalies hidden in their approaches. The role played by transverse anomalies is discussed.

Latent Diffusion Models (LDMs) achieve high-fidelity synthesis but suffer from latent space brittleness, causing discontinuous semantic jumps during editing. We introduce a Riemannian framework to diagnose this instability by analyzing the generative Jacobian, decomposing geometry into Local Scaling (capacity) and Local Complexity (curvature). Our study uncovers a ``Geometric Decoupling": while curvature in normal generation functionally encodes image detail, OOD generation exhibits a functional decoupling where extreme curvature is wasted on unstable semantic boundaries rather than perceptible details. This geometric misallocation identifies ``Geometric Hotspots" as the structural root of instability, providing a robust intrinsic metric for diagnosing generative reliability.

A scuba diver holding constant depth balances on an unstable equilibrium: the gas carried in the suit and buoyancy compensator compresses with depth, so the buoyant force falls as the diver sinks and rises as the diver ascends. We represent the diver as a proportional-derivative controller that regulates this compressible-buoyancy saddle after a finite reaction delay, and we derive the governing delay differential equation from the vertical force balance and the isothermal gas law, reducing it to a damping ratio, two control gains, and a dimensionless delay. The characteristic spectrum, obtained by pseudospectral collocation of the semigroup generator and checked against a direct Newton solution of the characteristic equation, locates the Hopf boundary that separates stable hovering from sustained porpoising; for the baseline diver the critical reaction delay is 3.36 s and the onset period is 28.8 s. The bifurcation is supercritical, and because the saturating force is the quadratic hydrodynamic drag, the limit-cycle amplitude grows in proportion to the delay excess rather than as its square root. The safe-operating envelope shows that runaway ascent is triggered by saturation of the compensator, not by loss of linear stability, so a stable and an unstable diver can share the same escape threshold. As onset is approached, the lag-one autocorrelation and variance rise while the fitted recovery rate falls and matches the spectral abscissa, giving an eigenvalue-exact early warning of the transition.

Relativistic magnetic turbulence has been proposed as a process for producing nonthermal particles in high-energy astrophysics. Particle energization may be contributed by both magnetic reconnection and turbulent fluctuations, but their interplay is poorly understood. It has been suggested that during magnetic reconnection the parallel electric field dominates particle acceleration up to the lower bound of the power-law particle spectrum, but recent studies show that electric fields perpendicular to magnetic field can play an important, if not dominant role. In this study, we carry out 2D fully kinetic particle-in-cell simulations of magnetically dominated decaying turbulence in a relativistic pair plasma. For a fixed magnetization parameter sigma_0=20, we find that the injection energy {varepsilon}_{rm inj} converges with increasing domain size to {varepsilon}_{rm inj}simeq 10m_ec^2. In contrast, the power-law index, the cut-off energy, and the power-law extent increase steadily with domain size. We trace a large number of particles and evaluate the contributions of the work done by the parallel (W_parallel) and perpendicular (W_perp) electric fields during both the injection phase and the post-injection phase. We find that during the injection phase, the W_perp contribution increases with domain size, suggesting that it may eventually dominate injection for a sufficiently large domain. In contrast, both components contribute equally during the post-injection phase, insensitive to the domain size. For high energy ({varepsilon}varepsilon_{rm inj}) particles, W_perp dominates the subsequent energization. These findings may improve our understanding of nonthermal particles and their emissions in astrophysical plasmas.

We present the first general-relativistic resistive magnetohydrodynamics simulations of self-consistent, rotating neutron stars with mixed poloidal and toroidal magnetic fields. Specifically, we investigate the role of resistivity in the dynamical evolution of neutron stars over a period of up to 100 ms and its effects on their quasi-equilibrium configurations. Our results demonstrate that resistivity can significantly influence the development of magnetohydrodynamic instabilities, resulting in markedly different magnetic field geometries. Additionally, resistivity suppresses the growth of these instabilities, leading to a reduction in the amplitude of emitted gravitational waves. Despite the variations in magnetic field geometries, the ratio of poloidal to toroidal field energies remains consistently 9:1 throughout the simulations, for the models we investigated.

We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects with the first kind trace of non-metricity. The mainstream formulation exhibits several conceptual and technical shortcomings, most notably a hierarchy inconsistency, the non-exictence of a genuine metric formulation, and the potential emergence of Ostrogradsky-type instabilities. These issues have motivated us to develop a new framework, namely a generalized teleparallel geometric theory of defects. In our model, dislocations are identified with the trace of torsion, disclinations with the second kind trace of the non-metricity, and point defects with the first kind trace of the non-metricity. In addition, we retain the scalar part torsion as a free parameter for describing some possible unknown degrees of freedom in the theory of defects. The proposed geometric theory of defects is free from all of the aforementioned drawbacks and is therefore worthy of further investigation. To ensure the coherence and completeness of the discussion, we begin our analysis with elastic deformations, then summarize the existing metric-affine geometric theory of defects, and finally proceed to our original contribution, namely the new theory introduced here. We formulate the entire theory in Eulerian coordinates. Naturally, all results can be reformulated in Lagrangian coordinates as well. All analyses and formulae are expressed in the language of exterior algebra and are carried out in coordinate-independent orthonormal frames.

We propose a self-consistent explanation of Rieger-type periodicities, the Schwabe cycle, and the Suess-de Vries cycle of the solar dynamo in terms of resonances of various wave phenomena with gravitational forces exerted by the orbiting planets. Starting on the high-frequency side, we show that the two-planet spring tides of Venus, Earth and Jupiter are able to excite magneto-Rossby waves which can be linked with typical Rieger-type periods. We argue then that the 11.07-year beat period of those magneto-Rossby waves synchronizes an underlying conventional alpha-Omega-dynamo, by periodically changing either the field storage capacity in the tachocline or some portion of the alpha-effect therein. We also strengthen the argument that the Suess-de Vries cycle appears as an 193-year beat period between the 22.14-year Hale cycle and a spin-orbit coupling effect related with the 19.86-year rosette-like motion of the Sun around the barycenter.

In this paper, we consider the stability of the Lamb dipole solution of the two-dimensional Euler equations in R^{2} and question under which initial disturbance the Lamb dipole is stable, motivated by experimental work on the formation of a large vortex dipole in two-dimensional turbulence. We assume (O) odd symmetry for the x_2-variable and (N) non-negativity in the upper half plane for the initial disturbance of vorticity, and establish the stability theorem of the Lamb dipole without assuming (F) finite mass condition. The proof is based on a new variational characterization of the Lamb dipole using an improved energy inequality.

Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers (SCS) showed that random recurrent networks undergo a transition from quiescence to asynchronous chaos, establishing a paradigmatic link between random connectivity, dynamical instability, and internally generated fluctuations in neural circuits. Here, we extend this framework to two-population firing-rate networks with segregated excitatory and inhibitory neurons and target-specific inhibitory couplings that break excitation--inhibition balance. Using dynamical mean-field theory, we derive self-consistent equations for the macroscopic mean activities and autocorrelations, together with stability criteria distinguishing mean-driven and fluctuation-driven instabilities. We show that target-specific inhibition organizes the phase diagram into three qualitative classes: inhibition-dominated or strictly balanced networks display only quiescent activity and asynchronous chaos; excitation-dominated networks display persistent activity together with either synchronous chaos with non-vanishing mean activity or coherent oscillations, depending on the stability-matrix eigenvalues. Crucially, coherent oscillations do not coexist with chaotic fluctuations around the periodic mean trajectory; rather, their onset suppresses the chaotic component, reminiscent of input-induced suppression of chaos. These results generalize SCS theory to recurrent networks with explicit excitatory--inhibitory structure and identify target-specific inhibition as a key control parameter for large-scale neural dynamics.

We investigate the signatures of Fermi liquid formation in the N=4 super Yang-Mills theory coupled to fundamental hypermultiplet at nonvanishing chemical potential for the global U(1) vector symmetry. At strong 't Hooft coupling the system can be analyzed in terms of the D7 brane dynamics in AdS_5 x S^5 background. The phases with vanishing and finite charge density are separated at zero temperature by a quantum phase transition. In case of vanishing hypermultiplet mass, Karch, Son and Starinets discovered a gapless excitation whose speed equals the speed of sound. We find that this zero sound mode persists to all values of the hypermultiplet mass, and its speed vanishes at the point of phase transition. The value of critical exponent and the ratio of the velocities of zero and first sounds are consistent with the predictions of Landau Fermi liquid theory at strong coupling.

This work studies training instabilities of behavior cloning with deep neural networks. We observe that minibatch SGD updates to the policy network during training result in sharp oscillations in long-horizon rewards, despite negligibly affecting the behavior cloning loss. We empirically disentangle the statistical and computational causes of these oscillations, and find them to stem from the chaotic propagation of minibatch SGD noise through unstable closed-loop dynamics. While SGD noise is benign in the single-step action prediction objective, it results in catastrophic error accumulation over long horizons, an effect we term gradient variance amplification (GVA). We show that many standard mitigation techniques do not alleviate GVA, but find an exponential moving average (EMA) of iterates to be surprisingly effective at doing so. We illustrate the generality of this phenomenon by showing the existence of GVA and its amelioration by EMA in both continuous control and autoregressive language generation. Finally, we provide theoretical vignettes that highlight the benefits of EMA in alleviating GVA and shed light on the extent to which classical convex models can help in understanding the benefits of iterate averaging in deep learning.

We investigate the exceptional points (EPs) and their pseudospectra in black hole perturbation theory. By considering a Gaussian bump modification to the Regge-Wheeler potential with variable amplitude, position, and width parameters, (varepsilon,d,σ_0), a continuous line of EPs (exceptional line, EL) in this three-dimensional parameter space is revealed. We find that the vorticity ν=pm1/2 and the Berry phase γ=π for loops encircling the EL, while ν=0 and γ=0 for those do not encircle the EL. Through matrix perturbation theory, we prove that the ε-pseudospectrum contour size scales as ε^{1/q} at an EP, where q is the order of the largest Jordan block of the Hamiltonian-like operator, contrasting with the linear ε scaling at non-EPs. Numerical implements confirm this observation, demonstrating enhanced spectral instability at EPs for non-Hermitian systems including black holes.

In order to study oscillators coupled by pulses emitted at discrete times, it is generally assumed that the effect of each pulse is an instantaneous phase shift, with a possible conduction delay between emission and receipt. However, we are interested in neural oscillators in which each pulse (action potential) activates a biexponential synapse, and at high frequencies, the duration of the synaptic conductance may be greater than the network period. Therefore, the effect of received pulses can summate over the course of several cycles. To overcome this limitation, we previously defined a mean field approach for a single synchronous population. Here, we extend it to two alternating synchronous populations by assuming a perturbation of a single oscillator from one of the synchronous populations which is represented by a single self-connected neural oscillator. The train of delayed biexponential synapses emitted by each oscillator is divided into a tonic and a phasic component. Because of the continuous rather than pulsatile nature of the input, we had to drop the concept of oscillator phase and derive self-consistent criteria for the existence and stability of an alternating firing pattern between two synchronous populations based solely on the perturbation of time intervals from their steady state values. Simulations showed that for high frequency oscillations as defined above, the mean field approach predicts the existence and stability of phase-locking between two synchronous populations better than the instantaneous phase shift approach. This approach may generalize to other forms of coupling amongst non-neural oscillators.

We develop a dynamical mean-field theory for random recurrent networks with low-rank structure and firing-rate-driven adaptation. When the random connectivity is strong enough to generate chaos, increasing adaptation strength drives the network through four regimes: a static coherent state, noise-sustained oscillations that progress from regular to irregular, stochastic switching between symmetric wells, and a global limit cycle. The theory identifies two instability mechanisms, chaos onset from the random connectivity and a Hopf bifurcation of the coherent mode, and shows how adaptation shapes both through the frequency-dependent single-neuron transfer function. A reduced three-dimensional model captures the bifurcation structure of the full network. Above the chaos threshold, coherent population-level oscillations coexist with heterogeneous firing rates and network-generated stochasticity at the single-neuron level. The interaction of adaptation with random and low-rank connectivity produces a rich oscillatory repertoire, including waxing-and-waning rhythmic episodes, persistent state switching, and slow Up-Down alternations, dynamics that have been observed during wakefulness, sleep, and anesthesia.

A new method of analyzing grid, or aliasing, instabilities is described, in particle-in-cell (PIC) codes for plasma kinetic theory. It starts with a meshfree approach with N_{p} macroparticles, with N_{p}<infty. Linearization of these equations is done about a uniform density non-drifting equilibrium prescribed by macroparticles on a uniform lattice. Macroparticle positions perturbations are induced about this lattice. The resulting linear equations are analyzed for stability and dispersion relations. The linearized equations are then discretized on a grid of N_{g} points with N_{g} le N_{p}, in both momentum conserving (MCP) and energy conserving (ECP) formulations. For a cold stationary plasma, this leads a dynamical matrix. For ECP, the matrix is symmetric and positive definite (SPD) and immediately shows stability. For MCP, the dynamical matrix is neither symmetric nor positive definite, preventing immediate conclusions on stability. For both MCP and ECP and for a cold stationary plasma, the resulting matrix elements vary relative to the meshfree value, a result of aliasing. This deviation is periodic in the displacement of the particle lattice relative to the grid. In the MCP discretization, eigenvalues occur in complex conjugate pairs for general placement of the particle lattice relative to the grid. These conjugate pairs indicate nonnegative growth rates. The nature of the aliasing is studied and shown to be related to the trapezoidal rule error over the grid. The scaling of the linear growth rates with respect to N_{g} and especially with respect to N_{ppc} is studied. These analytical results are compared with PIC simulations and found to be in excellent agreement. The connection with a cold drifting beam is discussed briefly, specifically, grid-induced instabilities for both the MCP and ECP.

A cumulative variational framework for solid deformation is proposed. Its central organizing principle is the recursive combination of three structural components of one material body: a compatible Cosserat component, a distributed-incompatibility component, and a defect-source component. At any prescribed external condition these components constitute a combined material state. They are governed under common physical boundary and initial conditions and are coupled through one cumulative energy and the associated field equations. They are not separate boundary-value problems and need not appear in a prescribed temporal sequence. The cumulative character of the framework concerns the response of the combined state to variation of externally prescribed conditions. For the special case of an initially perfect body, loss of stability may produce successive branches with defect and then source participation. Such a sequence is a bifurcation property of the selected initial state and constitutive energy, rather than a defining hierarchy of the framework. A one-dimensional specialization illustrates structural bifurcation, residual deformation and residual stress produced by retained structure, dependence on the initial combined state, directional memory under reverse loading, parametric cumulative hysteresis, and changes of observable tangent stiffness associated with structural stabilization. A spatial extension introduces defect and source gradient terms and yields a size-dependent structural stability operator. For the stable quartic energy considered, the gradient terms regularize nonuniform perturbations but do not by themselves generate a finite-wavelength localization instability on an already stable three-component branch. The examples thereby distinguish consequences of the cumulative structure and energy from phenomena requiring additional constitutive evolution laws.

We consider the D4-D8-D8 brane system which serves as ultraviolet completion of the Nambu-Jona-Lasinio model, where the only degrees of freedom carrying baryon charge are fermions. By turning on chemical potential for this charge one may expect the formation of the Fermi liquid ground state. At strong coupling we use the dual holographic description to investigate the responses of the system to small perturbations. In the chirally symmetric phase we find that the density dependent part of the heat capacity vanishes linearly with temperature. We also observe a zero sound excitation in the collisionless regime, whose speed is equal to that of normal sound in the hydrodynamic regime. Both the linear dependence of the heat capacity and the existence of zero sound are properties of the Fermi liquid ground state. We also compute the two-point function of the currents at vanishing frequency but do not find any singularities at finite values of the momentum.

We investigate soliton formation and interactions in the non-integrable Gardner-Ostrovsky equation (alias the rotation-modified Gardner equation) with anomalous (positive) dispersion. This equation is relevant to the description of wave dynamics in plasmas and other dispersive media. We show that a special class of solitons, characterized by zero total mass and non-monotonic asymptotics, can emerge from pulse-like initial perturbations. Depending on the initial conditions, these solitons may form regular amplitude-ordered trains, irregular nonstationary ensembles of interacting localized structures, or stationary propagating multi-soliton complexes. We further demonstrate that soliton interactions in the Gardner-Ostrovsky equation are inherently inelastic, leading to the emergence of a dominant "soliton-champion" in closed systems. For example, under periodic boundary conditions, only the largest-amplitude soliton ultimately survives, while all smaller solitons are gradually eliminated through successive interactions. Despite their inelastic interactions, Gardner-Ostrovsky solitons exhibit remarkable robustness.

We report observations of solar wind turbulence derived from measurements by the Parker Solar Probe. Our findings reveal the emergence of finite magnetic helicity within the transition range of the turbulence, aligning with signatures of kinetic Alfv\'en waves (KAWs). Notably, as the wave scale transitions from super-ion to sub-ion scales, the ratio of KAWs with opposing signs of magnetic helicity initially increases from approximately 1 to 6 before returning to 1. This observation provides, for the first time, compelling evidence for the transition from imbalanced kinetic Alfv\'enic turbulence to balanced kinetic Alfv\'enic turbulence.

Bubbles frequently emerge in dense chiral active fluids, yet it remains unclear whether they result from an instability of the homogeneous state or from rare nucleation events within a metastable phase. Here we develop a nucleation theory for chiral bubble formation by reducing the hydrodynamic equations to a single collective coordinate, the bubble radius. This reduction yields an effective nonlinear potential that captures the radial dynamics and predicts distinct stable, metastable, and unstable regimes of the homogeneous state. In the metastable regime, the theory identifies a critical bubble radius and an associated effective mechanical-work barrier, while its large-radius behavior determines whether bubble growth saturates at a finite size or becomes unbounded. We further analyze the stability of circular bubbles against noncircular perturbations, finding growing modes that can lead to elongation and breakup. The theoretical predictions are tested against event-driven molecular-dynamics simulations of chiral hard disks, which reproduce the predicted trends in the critical radius, nucleation barrier, and selected bubble size. Our results establish a unified framework for stability and nucleation in chiral active fluids and suggest routes to control bubble formation in experiments with spinning colloids and chiral spinners.

Spiral density waves are ubiquitous phenomena in differentially rotating flows. They are non-modal, non-axisymmetric perturbations that, due to shear in the background flow, possess time-evolving wavenumbers, frequencies, and amplitudes. In global simulations of optically thin, low-luminosity black-hole accretion flows, the excitation of such waves leads to spiral patterns in the plasma density that influence the morphology of the emission region. As such, the observed variabilities of such accretion flows are expected to be affected by the behavior of spiral density waves. Thus far, investigations of spiral density waves in accretion flows have exclusively used the assumption that the accretion-flow plasmas are in local thermodynamic equilibrium (LTE) at all times. In reality, hot and diffuse accretion-flow plasmas are expected to deviate far from LTE, and should be modeled accordingly. Here, we employ a combination of kinetic and fluid models to describe spiral density wave propagation, damping, and excitation in a collisionless shearing sheet, which more accurately represents the plasma conditions of low-luminosity accretion flows than do models that assume LTE. We find that micro-physical plasma instabilities are especially important in determining how spiral density waves behave, because the weak particle scattering that they induce leads to appreciable viscous damping. Observational implications of these results include reduced emission-region variability, which may improve agreement between Event Horizon Telescope (EHT) observations and simulation/theory, as well as a reduction in emission-region pattern speeds compared to simulations employing LTE, which bears on the interpretation of eventual EHT movies.

We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural field model with a simple functional form that still able to predict or reproduce empirical findings. Each neural unit was modelled using a neural mass and the accompanying field theory was derived in the continuum limit. The field theory comprised coupled (real) Klein-Gordon fields, where predictions of the model fall within the range of experimental findings. These predictions included the frequency spectrum of electric activity measured from the cortex, which was derived using an equipartition of energy over eigenfunctions of the neural fields. Moreover, the neural field model was invariant, within a set of parameters, to the dynamical system used to model each neuronal mass. Specifically, topologically equivalent dynamical systems resulted in the same neural field model when connected in a lattice; indicating that the fields derived could be read as a canonical cortical field theory. We specifically investigated non-dispersive fields that provide a structure for the coding (or representation) of afferent information. Further elaboration of the ensuing neural field theory, including the effect of dispersive forces, could be of importance in the understanding of the cortical processing of information.

The solar wind is a medium characterized by strong turbulence and significant field fluctuations on various scales. Recent observations have revealed that magnetic turbulence exhibits a self-similar behavior. Similarly, high-resolution measurements of the proton density have shown comparable characteristics, prompting several studies into the multifractal properties of these density fluctuations. In this work, we show that low-resolution observations of the solar wind proton density over time, recorded by various spacecraft at Lagrange point L1, also exhibit non-linear and multifractal structures. The novelty of our study lies in the fact that this is the first systematic analysis of solar wind proton density using low-resolution (hourly) data collected by multiple spacecraft at the L1 Lagrange point over a span of 17 years. Furthermore, we interpret our results within the framework of non-extensive statistical mechanics, which appears to be consistent with the observed nonlinear behavior. Based on the data, we successfully validate the q-triplet predicted by non-extensive statistical theory. To the best of our knowledge, this represents the most rigorous and systematic validation to date of the q-triplet in the solar wind.

We study black branes carrying both electric and magnetic charges in Einstein-Maxwell theory coupled to a dilaton-axion in asymptotically anti de Sitter space. After reviewing and extending earlier results for the case of electrically charged branes, we characterise the thermodynamics of magnetically charged branes. We then focus on dyonic branes in theories which enjoy an SL(2,R) electric-magnetic duality. Using SL(2,R), we are able to generate solutions with arbitrary charges starting with the electrically charged solution, and also calculate transport coefficients. These solutions all exhibit a Lifshitz-like near-horizon geometry. The system behaves as expected for a charged fluid in a magnetic field, with non-vanishing Hall conductance and vanishing DC longitudinal conductivity at low temperatures. Its response is characterised by a cyclotron resonance at a frequency proportional to the magnetic field, for small magnetic fields. Interestingly, the DC Hall conductance is related to the attractor value of the axion. We also study the attractor flows of the dilaton-axion, both in cases with and without an additional modular-invariant scalar potential. The flows exhibit intricate behaviour related to the duality symmetry. Finally, we briefly discuss attractor flows in more general dilaton-axion theories which do not enjoy SL(2,R) symmetry.

The Rayleigh-Plateau instability predicts that infinitesimal perturbations of a liquid jet grow only for kR < 1, with kR = 1 marking the classical stability boundary. Here, we show that femtosecond-laser-induced cavitation generates a localized, impulsive recoil perturbation on a flowing liquid jet, enabling a two-dimensional map of jet breakup across the (kR, epsilon/R) plane. The perturbation's spacing (wavelength) and strength (amplitude) are set independently by the laser repetition rate and pulse energy, respectively. At low amplitudes, tuning the repetition rate recovers the classical Rayleigh-Plateau dispersion relation and its kR = 1 cutoff, while increasing the wavelength enables controlled generation of monodisperse droplet trains, bidisperse droplet populations, and ultimately isolated single droplets. Along the amplitude axis, low pulse energies produce a seed that amplifies only the imposed wavenumber, whereas above a critical energy Ec, the seed broadens to excite many wavenumbers simultaneously. At still higher amplitudes, we demonstrate deterministic breakup for kR > 1, extending to kR = 1.9, with laser-synchronized droplet production rates up to 0.2 MHz. These results establish localized femtosecond-laser-induced cavitation as a route to controlled Rayleigh-Plateau breakup both within and beyond the classical linear-stability boundary.

We discuss the effect of a strong magnetic field on the chemical freezeout points in the ultrarelativistic heavy-ion collision. As a result of the inverse magnetic catalysis or the magnetic inhibition, the crossover onset to hot and dense matter out of quarks and gluons should be shifted to a lower temperature. To quantify this shift we employ the hadron resonance gas model and an empirical condition for the chemical freezeout. We point out that the charged particle abundances are significantly affected by the magnetic field so that the electric charge fluctuation is largely enhanced especially at high baryon density. The charge conservation partially cancels the enhancement but our calculation shows that the electric charge fluctuation and the charge chemical potential could serve as a magnetometer. We find that the fluctuation exhibits a crossover behavior rapidly increased for eB >~ (0.4GeV)^2, while the charge chemical potential has better sensitivity to the magnetic field.

Scaling model performance typically requires increasing model size. Looped Transformer offers a compelling alternative by iteratively reusing the same Transformer blocks, trading additional computation for improved performance without increasing parameter count or context length. Because the number of loop iterations can be adjusted at inference, it also provides a natural mechanism for balancing performance and test-time compute. However, Looped Transformer still suffers from training instability when the number of loop iterations increases. Our analysis reveals that this instability stems from two sources: gradient oscillation and residual explosion. To address these two problems, we propose the Fully Looped Transformer, which introduces two parameter-free modifications: (1) Fully Looped Architecture, which distributes inter-loop signals across all layers to mitigate residual explosion; (2) Attention Injection, which reuses the existing attention block to suppress gradient oscillation. These modifications stabilize training dynamics, enabling the Fully Looped Transformer to be trained stably up to 12 loop iterations, whereas other baseline looped models collapse in this regime. In milder settings where Looped Transformer does not collapse, Fully Looped Transformer still improves average downstream-task performance by up to 13.2\%. Overall, our experiments demonstrate that Fully Looped Transformer improves training stability, enhances downstream performance, and provides preliminary adaptability under different test-time compute budgets by varying loop iterations at inference.

WIMP-type dark matter may have additional interactions that break baryon number, leading to induced nucleon decays which are subject to direct experimental constraints from proton decay experiments. In this work, we analyze the possibility of continuous baryon destruction, deriving strong limits from the dark matter accumulating inside old neutron stars, as such a process leads to excess heat generation. We construct the simplest particle dark matter model that breaks baryon and lepton numbers separately but conserves B-L. Virtual exchange by DM particles in this model results in di-nucleon decay via nnto nbarnu and npto ne^+ processes.

We explore the consequences of multi-trace deformations in applications of gauge-gravity duality to condensed matter physics. We find that they introduce a powerful new "knob" that can implement spontaneous symmetry breaking, and can be used to construct a new type of holographic superconductor. This knob can be tuned to drive the critical temperature to zero, leading to a new quantum critical point. We calculate nontrivial critical exponents, and show that fluctuations of the order parameter are `locally' quantum critical in the disordered phase. Most notably the dynamical critical exponent is determined by the dimension of an operator at the critical point. We argue that the results are robust against quantum corrections and discuss various generalizations.

We address hallucination detection in Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) by framing the problem through the lens of dynamical systems stability theory. Rather than treating hallucination as a straightforward classification task, we conceptualize (M)LLMs as dynamical systems, where factual knowledge is represented by stable equilibrium points within the representation space. Our main insight is that hallucinations tend to arise at the boundaries of knowledge-transition regions separating stable and unstable zones. To capture this phenomenon, we propose Lyapunov Probes: lightweight networks trained with derivative-based stability constraints that enforce a monotonic decay in confidence under input perturbations. By performing systematic perturbation analysis and applying a two-stage training process, these probes reliably distinguish between stable factual regions and unstable, hallucination-prone regions. Experiments on diverse datasets and models demonstrate consistent improvements over existing baselines.

Preference learning in large language models relies on reward models as proxies for human judgment. However, these models frequently exhibit preference instability, producing contradictory preference assignments in response to subtle, meaning-preserving input variations. We analyze this instability at the representation level under three semantic-preserving perturbation types: paraphrasing, pattern injection, and backdoor triggers. We attribute this instability to over-reliance on predictive yet brittle features, which we term unstable features, and isolate them via Sparse Autoencoders (SAEs) in a sparse latent space where benign and perturbed inputs activate distinctly separable patterns. Building on this separability, we propose two SAE-based instability mitigation strategies: SAE Feature Steering, which identifies and suppresses anomalously activated features at inference, and SAE Residual Correction, which learns adaptive adjustments over SAE features to restore correct preferences. Our methods substantially reduce incorrect preference assignments on harmlessness and hallucination benchmarks while preserving benign performance and general utility on other tasks, without retraining the reward model. Our code and data are available in https://github.com/shunchang-liu/pisa.

Gradient-based algorithms are a cornerstone of artificial neural network training, yet it remains unclear whether biological neural networks use similar gradient-based strategies during learning. Experiments often discover a diversity of synaptic plasticity rules, but whether these amount to an approximation to gradient descent is unclear. Here we investigate a previously overlooked possibility: that learning dynamics may include fundamentally non-gradient "curl"-like components while still being able to effectively optimize a loss function. Curl terms naturally emerge in networks with inhibitory-excitatory connectivity or Hebbian/anti-Hebbian plasticity, resulting in learning dynamics that cannot be framed as gradient descent on any objective. To investigate the impact of these curl terms, we analyze feedforward networks within an analytically tractable student-teacher framework, systematically introducing non-gradient dynamics through neurons exhibiting rule-flipped plasticity. Small curl terms preserve the stability of the original solution manifold, resulting in learning dynamics similar to gradient descent. Beyond a critical value, strong curl terms destabilize the solution manifold. Depending on the network architecture, this loss of stability can lead to chaotic learning dynamics that destroy performance. In other cases, the curl terms can counterintuitively speed learning compared to gradient descent by allowing the weight dynamics to escape saddles by temporarily ascending the loss. Our results identify specific architectures capable of supporting robust learning via diverse learning rules, providing an important counterpoint to normative theories of gradient-based learning in neural networks.

In this paper, we study the long time dynamics of small perturbations of static domain walls in weighted Sobolev spaces for the one dimensional Schrödinger map with constant Dzyaloshinskii-Moriya interaction. The perturbation equation contains derivative nonlinearities, and its linearized operator has a threshold resonance. The results are twofold. (i) We prove the asymptotic stability of the domain wall modulo the translation and rotation symmetries. More precisely, the corresponding modulation parameters converge as time tends to infinity, while the radiation decays at the sharp rate t^{-1/2}. (ii) We prove that the radiation exhibits modified scattering, with an explicit logarithmic phase correction generated by the long range cubic interaction. The proof develops geometric reduction to overcome the loss of derivatives and exploits structural cancellations in the nonlinear interactions.

Electroencephalography (EEG) is a cornerstone of brain-computer interfaces and clinical neuroscience, yet deep learning models are typically trained and evaluated under a single, unreported preprocessing pipeline. We formalize preprocessing choices as a counterfactual intervention space and show that EEG predictions are surprisingly unstable under this space: across six datasets spanning four paradigms, up to 42% of trial-level predictions flip when only the preprocessing changes, a variability that standard uncertainty methods do not explicitly quantify because they condition on a fixed preprocessing pipeline. We provide three tools to make this instability measurable, decomposable, and reducible. First, a Walsh-Hadamard decomposition of the 2^7 pipeline space reveals that sensitivity is near-additive in practice under the binary intervention design, enabling efficient step-by-step optimization. Second, we introduce Preprocessing Uncertainty (PU), a per-trial diagnostic that captures a dimension of instability complementary to model-based confidence. Third, we study Normalized Adaptive PGI (NA-PGI), a graph-structured regularizer that exploits the compositional structure of preprocessing interventions as one mitigation strategy with clear scope conditions.

We present a continuous geometric framework that models the discrete algebraic operations of the Transformer architecture as an integro-differential equation (IDE) on a semantic fiber bundle calE = calM times R^d. Beginning from a single geometric axiom -- that the token sequence forms a discrete 1-manifold equipped with a canonical measure lattice -- we translate every core component of the modern Transformer (RMSNorm, RoPE, Softmax Attention, FFN, Residual Stream, SGD, Weight Decay) into a cohesive vocabulary of differential geometry, measure theory, and stochastic calculus. The resulting framework yields quantitative predictions spanning entropic optimal transport (Attention as a Schrödinger bridge) and non-equilibrium thermodynamics (SGD as Itô diffusion violating detailed balance). We conduct a six-part experimental campaign across five architectures (Qwen3, LLaMA\nobreakdash-3.1, Gemma\nobreakdash-3, GPT-2, Mistral) spanning 124M to 8B parameters. The empirical observables are quantitatively consistent with the geometric predictions: the ε^{-1/2} Lipschitz scaling calibration at machine precision (R^2 = 1.000), the Lie--Trotter operator-splitting torsion, the symmetric ablation instability confirming the Dual-Law of Topological Stability, the calO(1/k) thermodynamic suppression of Poincaré recurrence on the RoPE torus, the thermodynamic context-limit phase transition, and the Non-Equilibrium Steady State parameter vortex -- verified across two optimizers (AdamW and Pure SGD) to exclude momentum artifacts. The results demonstrate that analyzing Transformers through the lens of continuous stochastic differential geometry provides a predictive descriptive vocabulary for the stability limits, context bounds, and optimization dynamics of Large Language Models.

Regulatory institutions (from content moderation platforms to financial supervisors) observe, deliberate, and intervene only after a characteristic delay. We ask whether this processing lag alone can destabilize a multi-agent system that would otherwise remain stable, without exogenous shocks, coordination among agents, or malicious actors. We study this question in two stages. First, we analyze a delayed replicator equation in which autonomous agents receive a benefit from radical behavior but face punishment based on a lagged institutional alarm signal. We derive a closed-form critical delay threshold beyond which the unique interior equilibrium loses stability through a Hopf bifurcation, and prove via center manifold reduction that the bifurcation is supercritical (producing bounded oscillations, not explosive growth) for the entire sigmoid response-function family. Second, we embed N=240 agents on a network and equip them with reinforcement learning (tabular Q-learning), comparing three decision architectures in a factorial design: non-reactive agents (fixed policy), reactive agents (threshold heuristic without memory), and Q-learning agents (adaptive with cumulative value estimates). The results reveal a hierarchy opposite to the naive expectation that learning amplifies instability: non-reactive agents are immune to delay (0% runaway across all tested values), reactive agents collapse catastrophically (96% runaway by delay geq 8 steps), and Q-learning agents achieve partial resilience (66% runaway at delay = 20). The destabilizing ingredient is reactivity to delayed signals: agents that immediately exploit low-alarm windows trigger oscillatory feedback loops. Learning buffers this through implicit punishment memory encoded in Q-values

We use two-dimensional particle-in-cell simulations to investigate the generation and evolution of the magnetic field associated with the propagation of a jet for various initial conditions. We demonstrate that, in general, the magnetic field is initially grown by the Weibel and Mushroom instabilities. However, the field is saturated by the Alfv'en current limit. For initially non-magnetized plasma, we show that the growth of the magnetic field is delayed when the matter density of the jet environment is lower, which are in agreement with simple analytical predictions. We show that the higher Lorentz factor (gtrsim 2) prevents rapid growth of the magnetic fields. When the initial field is troidal, the position of the magnetic filaments moves away from the jet as the field strength increases. The axial initial field helps the jet maintain its shape more effectively than the troidal initial field.

The gamma-ray burst (GRB) GRB 211211A and GRB 060614, believed to originate from the merger of compact objects, exhibit similarities to the jetted tidal disruption event (TDE) Sw J1644+57, by showing violent variabilities in the light-curve during the decay phase. Previous studies suggest that such fluctuations in TDE may arise from the fallback of tidal disrupted debris. In this paper, we introduce the fluctuations of the mass distribution {rm d}M/{rm d}E for the debris ejected during the tidal disruption (with energy E) and study their impact on jet power. Turbulence induced by tidal force and the self-gravity of the debris may imprint variabilities in {rm d}M/{rm d}E during fallback. We model these fluctuations with a power density spectrum propto f_{rm E}^{beta}, where f_{rm E} = 1/E and beta is the power-law index. We find that the resulting light curve can preserve the fluctuation characteristics from {rm d}M/{rm d}E. In addition, the observed fluctuations in the light-curves can be reproduced for a given suitable beta. Based on the observations, we find that the value of beta should be around -1.

Reduction in effective spacetime dimensionality can occur in field-theory models more general than the widely studied dimensional reductions based on technically consistent truncations. Situations where wavefunction factors depend nontrivially on coordinates transverse to the effective lower dimension can give rise to unusual patterns of gauge symmetry breaking. Leading-order gauge modes can be left massless, but naturally occurring Stueckelberg modes can couple importantly at quartic order and higher, thus generating a "covert" pattern of gauge symmetry breaking. Such a situation is illustrated in a five-dimensional model of scalar electrodynamics in which one spatial dimension is taken to be an interval with Dirichlet/Robin boundary conditions on opposing ends. This simple model illuminates a mechanism which also has been found in gravitational braneworld scenarios.

Modern deep neural networks treat parameters as static floating-point matrices stored in physical memory, incurring Von Neumann memory bottlenecks and representation collapse. We formulate Orbital Error Dynamics (OED), an analytical framework wherein synaptic weights are not stored masses (O(W)), but transient topological resonances (O(1)) derived procedurally from the complex quadratic polynomial map z_{n+1} = z_n^2 + c. We introduce the Bent Sine Wave Hypothesis, demonstrating that non-equilibrium living systems emerge when harmonic waves curl inward through environmental drag toward the cardioid cusp (c = 1/4). We define the Observer Horizon Geometry in parameter space, identifying interior resonance shoulder loci X_upper = (0.25, +0.18) and X_lower = (0.25, -0.18) between the fixed-point basin and the true boundary at c = 0.25 +/- 0.50i. To escape non-convex stagnation without loss zeroing, we introduce a heavy-tailed Biomimetic Perturbed Jump Operator (Omega_tunneling) inspired by mammalian fertilization zinc sparks. We further couple an enteric-cranial Dual-Brain architecture shielded by adaptive CD4+ regulatory immune gating (M_CD4), and project the 4-nucleotide genetic basis (A, T, C, G) across quadrants in C. Multi-seed empirical validation on the Two-Moons manifold (5 seeds, 80/20 train/test split, 32x32 grid, zero test-time updates, zero label leakage) demonstrates that procedural parameterization from a 24-byte coordinate seed achieves 77.67% +/- 5.35% clean test accuracy (within an 8.00-point paired difference of an unconstrained gradient baseline at 85.67% +/- 5.35%, 95% CI: [-1.07%, 17.07%]) and 71.33% +/- 3.80% under distribution shift (N(1.2, 0.4)), alongside conceptual equivalence with an analog optical co-processor.

We prove nonlinear stability of the Guderley imploding shock under radial perturbations for the three-dimensional compressible Euler equations in the adiabatic range 1<γleq5{3}. The perturbed solutions develop an asymptotically self-similar implosion in finite time. Our result allows perturbations with small, nonzero constant pressure in the quiescent region ahead of the shock. The proof combines weighted L^infty estimates along characteristics with a computer-assisted proof of stability inequalities for the Guderley profile.

A cylindrical TM_{0,1,0} mode microwave cavity resonator was excited using a balanced interferometric configuration that allowed manipulation of the electric field and potential within the resonator by adjusting the phase and amplitude of the interferometer arms driving the resonator. With precise tuning of the phase and amplitude, 25 dB suppression of the electric field at the resonance frequency was achieved while simultaneously resonantly enhancing the time-varying electric-scalar potential. Under these conditions, the system demonstrated electromagnetically induced absorption in the cavity response due to the annulment of the electric field at the resonance frequency. This phenomena can be regarded as a form of extreme dispersion, and led to a sharp increase in the cavity phase versus frequency response by an order of magnitude when compared to the cavity Q-factor. This work presents an experimental setup that will allow the electric-scalar Aharonov-Bohm effect to be tested under conditions involving a time-varying electric-scalar potential, without the presence of an electric field or magnetic vector potential, an experiment that has not yet been realised.

In this work we update the L-Galaxies semi-analytic model (SAM) to better follow the physical processes responsible for the growth of bulges via disc instabilities (leading to pseudo-bulges) and mergers (leading to classical bulges). We address the former by considering the contribution of both stellar and gaseous discs in the stability of the galaxy, and we update the latter by including dissipation of energy in gas-rich mergers. Furthermore, we introduce angular momentum losses during cooling and find that an accurate match to the observed correlation between stellar disc scale length and mass at z ~ 0.0 requires that the gas loses 20% of its initial specific angular momentum to the corresponding dark matter halo during the formation of the cold gas disc. We reproduce the observed trends between the stellar mass and specific angular momentum for both disc- and bulge-dominated galaxies, with the former rotating faster than the latter of the same mass. We conclude that a two-component instability recipe provides a morphologically diverse galaxy sample which matches the observed fractional breakdown of galaxies into different morphological types. This recipe also enables us to obtain an excellent fit to the morphology-mass relation and stellar mass function of different galactic types. Finally, we find that energy dissipation during mergers reduces the merger remnant sizes and allows us to match the observed mass-size relation for bulge-dominated systems.

High-fidelity scientific simulations are now producing unprecedented amounts of data, creating a storage and analysis bottleneck. A single simulation can generate tremendous data volumes, often forcing researchers to discard valuable information. A prime example of this is plasma turbulence described by the gyrokinetic equations: nonlinear, multiscale, and 5D in phase space. It constitutes one of the most computationally demanding frontiers of modern science, with runs taking weeks and yielding tens of terabytes of data dumps. The increasing storage demands underscore the importance of compression. However, reconstructed snapshots do not necessarily preserve essential physical quantities. We present a spatiotemporal evaluation pipeline, accounting for structural phenomena and multi-scale transient fluctuations to assess the degree of physical fidelity. Indeed, we find that various compression techniques lack preservation of both spatial mode structure and temporal turbulence characteristics. Therefore, we explore Physics-Informed Neural Compression (PINC), which incorporates physics-informed losses tailored to gyrokinetics and enables extreme compressions ratios of over 70,000x. Entropy coding on top of PINC further pushes it to 120,000x. This direction provides a viable and scalable solution to the prohibitive storage demands of gyrokinetics, enabling post-hoc analyses that were previously infeasible.

Weather Jiu-Jitsu is a control paradigm for extreme climatological events, inspired by chaos theory. As a proposition, small, precise, targeted, and cost-inexpensive perturbations can redirect trajectories of a large dynamical system. This strategy has been demonstrated analytically in the Lorenz-63 system, where a naturally chaotic trajectory switching between two attractors can be confined to a single attractor, indefinitely, via arbitrarily small perturbations. This paper examines the feasibility of Microsoft's Aurora -- a 1.3 billion parameter global atmospheric model -- as a test bed for this strategy. This paper explores three questions: (1) Is Aurora a reliable enough simulation environment to serve as a meaningful testbed? (2) Are the perturbations required to redirect its trajectories small enough to be physically plausible? (3) Does Aurora's learned latent space (the parametric estimators on climatological attributes) yield any apparent, structured, and/or perhaps interpretable features that can convey a geo/atmospheric response to initial conditions? We find evidence consistent with all three: Aurora's modeled trajectories respond to perturbations beyond measurement drift, the perturbation magnitudes required are small relative to the model's own forecast uncertainty, and its latent representations exhibit directional structure that responds to Jiu-Jitsu-type interventions, even though that structure does not separate extreme from normal states outright. These results should be read as feasibility diagnostics rather than a demonstration of control: we do not implement or test an actual steering intervention on Aurora, and several of our findings, particularly around the model's latent-space geometry, are exploratory.

Spiking Neural Networks (SNNs) offer a promising, biologically inspired approach for processing spatiotemporal data, particularly for time series forecasting. However, conventional neuron models like the Leaky Integrate-and-Fire (LIF) struggle to capture long-term dependencies and effectively process multi-scale temporal dynamics. To overcome these limitations, we introduce the Temporal Segment Leaky Integrate-and-Fire (TS-LIF) model, featuring a novel dual-compartment architecture. The dendritic and somatic compartments specialize in capturing distinct frequency components, providing functional heterogeneity that enhances the neuron's ability to process both low- and high-frequency information. Furthermore, the newly introduced direct somatic current injection reduces information loss during intra-neuronal transmission, while dendritic spike generation improves multi-scale information extraction. We provide a theoretical stability analysis of the TS-LIF model and explain how each compartment contributes to distinct frequency response characteristics. Experimental results show that TS-LIF outperforms traditional SNNs in time series forecasting, demonstrating better accuracy and robustness, even with missing data. TS-LIF advances the application of SNNs in time-series forecasting, providing a biologically inspired approach that captures complex temporal dynamics and offers potential for practical implementation in diverse forecasting scenarios. The source code is available at https://github.com/kkking-kk/TS-LIF.

Recurrent models are a popular choice for video enhancement tasks such as video denoising or super-resolution. In this work, we focus on their stability as dynamical systems and show that they tend to fail catastrophically at inference time on long video sequences. To address this issue, we (1) introduce a diagnostic tool which produces input sequences optimized to trigger instabilities and that can be interpreted as visualizations of temporal receptive fields, and (2) propose two approaches to enforce the stability of a model during training: constraining the spectral norm or constraining the stable rank of its convolutional layers. We then introduce Stable Rank Normalization for Convolutional layers (SRN-C), a new algorithm that enforces these constraints. Our experimental results suggest that SRN-C successfully enforces stability in recurrent video processing models without a significant performance loss.

In this article, we consider a newly proposed parameterization of the viscosity coefficient zeta, specifically zeta=zeta_0 {Omega^s_m} H , where zeta_0 = zeta_0{{Omega^s_{m_0}}} within the coincident f(Q) gravity formalism. We consider a non-linear function f(Q)= -Q +alpha Q^n, where alpha and n are arbitrary model parameters, which is a power-law correction to the STEGR scenario. We find an autonomous system by invoking the dimensionless density parameters as the governing phase-space variables. We discuss the physical significance of the model corresponding to the parameter choices n=-1 and n=2 along with the exponent choices s=0, 0.5, and 1.05. We find that model I shows the stable de-Sitter type or stable phantom type (depending on the choice of exponent s) behavior with no transition epoch, whereas model II shows the evolutionary phase from the radiation epoch to the accelerated de-Sitter epoch via passing through the matter-dominated epoch. Hence, we conclude that model I provides a good description of the late-time cosmology but fails to describe the transition epoch, whereas model II modifies the description in the context of the early universe and provides a good description of the matter and radiation era along with the transition phase.

The Korteweg-de Vries (KdV) equation serves as a foundational model in nonlinear wave physics, describing the balance between dispersive spreading and nonlinear steepening that gives rise to solitons. This article introduces sangkuriang, an open-source Python library for solving this equation using Fourier pseudo-spectral spatial discretization coupled with adaptive high-order time integration. The implementation leverages just-in-time (JIT) compilation for computational efficiency while maintaining accessibility for instructional purposes. Validation encompasses progressively complex scenarios including isolated soliton propagation, symmetric two-wave configurations, overtaking collisions between waves of differing amplitudes, and three-body interactions. Conservation of the classical invariants is monitored throughout, with deviations remaining small across all test cases. Measured soliton velocities conform closely to theoretical predictions based on the amplitude-velocity relationship characteristic of integrable systems. Complementary diagnostics drawn from information theory and recurrence analysis confirm that computed solutions preserve the regular phase-space structure expected for completely integrable dynamics. The solver outputs data in standard scientific formats compatible with common analysis tools and generates visualizations of spatiotemporal wave evolution. By combining numerical accuracy with practical accessibility on modest computational resources, sangkuriang offers a platform suitable for both classroom demonstrations of nonlinear wave phenomena and exploratory research into soliton dynamics.

We present new limits on an isotropic stochastic gravitational-wave background (GWB) using a six pulsar dataset spanning 18 yr of observations from the 2015 European Pulsar Timing Array data release. Performing a Bayesian analysis, we fit simultaneously for the intrinsic noise parameters for each pulsar, along with common correlated signals including clock, and Solar System ephemeris errors, obtaining a robust 95% upper limit on the dimensionless strain amplitude A of the background of A<3.0times 10^{-15} at a reference frequency of 1yr^{-1} and a spectral index of 13/3, corresponding to a background from inspiralling super-massive black hole binaries, constraining the GW energy density to Omega_gw(f)h^2 < 1.1times10^{-9} at 2.8 nHz. We also present limits on the correlated power spectrum at a series of discrete frequencies, and show that our sensitivity to a fiducial isotropic GWB is highest at a frequency of sim 5times10^{-9}~Hz. Finally we discuss the implications of our analysis for the astrophysics of supermassive black hole binaries, and present 95% upper limits on the string tension, Gmu/c^2, characterising a background produced by a cosmic string network for a set of possible scenarios, and for a stochastic relic GWB. For a Nambu-Goto field theory cosmic string network, we set a limit Gmu/c^2<1.3times10^{-7}, identical to that set by the {\it Planck} Collaboration, when combining {\it Planck} and high-ell Cosmic Microwave Background data from other experiments. For a stochastic relic background we set a limit of Omega^relic_gw(f)h^2<1.2 times10^{-9}, a factor of 9 improvement over the most stringent limits previously set by a pulsar timing array.

Individual chemically active drops suspended in a surfactant solution were observed to self-propel spontaneously with straight, helical, or chaotic trajectories. To elucidate how these drops can exhibit such strikingly different dynamics and `decide' what to do, we propose a minimal axisymmetric model of a spherical active drop, and show that simple and linear interface properties can lead to both steady self-propulsion of the droplet as well as chaotic behavior. The model includes two different mobility mechanisms, namely, diffusiophoresis and the Marangoni effect, that convert self-generated gradients of surfactant concentration into the flow at the droplet surface. In turn, surface-driven flow initiates surfactant advection that is the only nonlinear mechanism and, thus, the only source of dynamical complexity in our model. Numerical investigation of the fully-coupled hydrodynamic and advection diffusion problems reveals that strong advection (e.g., large droplet size) may destabilize a steadily self-propelling drop; once destabilized, the droplet spontaneously stops and a symmetric extensile flow emerges. If advection is strengthened even further in comparison with molecular diffusion, the droplet may perform chaotic oscillations. Our results indicate that the thresholds of these instabilities depend heavily on the balance between diffusiophoresis and the Marangoni effect. Using linear stability analysis, we demonstrate that diffusiophoresis promotes the onset of high-order modes of monotonic instability of the motionless drop. We argue that diffusiophoresis has a similar effect on the instabilities of a moving drop.

Coexistent phase of kaon condensates and hyperons [(Y+K) phase] in beta equilibrium with electrons and muons is investigated as a possible form of dense hadronic phase with multi-strangeness. The effective chiral Lagrangian for kaon-baryon and kaon-kaon interactions is utilized within chiral symmetry approach in combination with the interaction model between baryons. For the baryon-baryon interactions, we adopt the minimal relativistic mean-field theory with exchange of scalar mesons and vector mesons between baryons without including the nonlinear self-interacting meson field terms. In addition, the universal three-baryon repulsion and the phenomenological three-nucleon attraction are introduced as density-dependent effective two-body potentials. The repulsive effects leading to stiff equation of state at high densities consist of both the two-baryon repulsion via the vector-meson exchange and the universal three-baryon repulsion. Interplay of kaon condensates with hyperons through chiral dynamics in dense matter is clarified, and resulting onset mechanisms of kaon condensation in hyperon-mixed matter and the equation of state with the (Y+K) phase and characteristic features of the system are presented. It is shown that the slope L of the symmetry energy controls the two-baryon repulsion beyond the saturation density and resulting stiffness of the equation of state. The stiffness of the equation of state in turn controls admixture of hyperons and the onset and development of kaon condensates as a result of competing effect between kaon condensates and hyperons. The equation of state with the (Y+K) phase becomes stiff enough to be consistent with recent observations of massive neutron stars. Static properties of neutron stars with the (Y+K) phase are discussed.

Muon orthogonalizes the momentum buffer before each update, replacing its singular values with ones via Newton-Schulz iterations. This simple change lets Muon tolerate far larger learning rates and converge faster than other optimizers, but why? We show that the mechanism is spectral flattening, and develop two results around it. First, we prove that Muon's maximal stable step size scales with the average singular value of the gradient rather than the largest, which bottlenecks standard gradient descent. Second, we recast Muon as a preconditioned gradient method and show, under a Kronecker-factored curvature model, that it improves the effective convergence factor, with the improvement controlled by the spectrum of the gradient covariance. Extensive experiments validate both results: Muon remains stable at learning rates that cause SGD to diverge within the first few iterations, and reaches accuracy milestones several epochs earlier even at identical step sizes. Taken together, our results offer a principled, geometric explanation for Muon's empirical success.

The all-sky 408 MHz map of Haslam et al. is one the most important total-power radio surveys. It has been widely used to study diffuse synchrotron radiation from our Galaxy and as a template to remove foregrounds in cosmic microwave background data. However, there are a number of issues associated with it that must be dealt with, including large-scale striations and contamination from extragalactic radio sources. We have re-evaluated and re-processed the rawest data available to produce a new and improved 408 MHz all-sky map. We first quantify the positional accuracy (approx 7 arcmin) and effective beam (56.0pm1.0 arcmin) of the four individual surveys from which it was assembled. Large-scale striations associated with 1/f noise in the scan direction are reduced to a level ll 1 K using a Fourier-based filtering technique. The most important improvement results from the removal of extragalactic sources. We have used an iterative combination of two techniques -- two-dimensional Gaussian fitting and minimum curvature spline surface inpainting -- to remove the brightest sources (gtrsim 2 Jy), which provides a significant improvement over previous versions of the map. We quantify the impact with power spectra and a template fitting analysis of foregrounds to the WMAP data. The new map is publicly available and is recommended as the template of choice for large-scale diffuse Galactic synchrotron emission. We also provide a higher resolution map with small-scale fluctuations added, assuming a power-law angular power spectrum down to the pixel scale (1.7 arcmin). This should prove useful in simulations used for studying the feasibility of detecting HI fluctuations from the Epoch of Reionization.

How momentum, energy, and magnetic fields are transported in the presence of macroscopic gradients is a fundamental question in plasma physics. Answering this question is especially challenging for weakly collisional, magnetized plasmas, where macroscopic gradients influence the plasma's microphysical structure. In this paper, we introduce thermodynamic forcing, a new method for systematically modeling how macroscopic gradients in magnetized or unmagnetized plasmas shape the distribution functions of constituent particles. In this method, we propose to apply an anomalous force to those particles inducing the anisotropy that would naturally emerge due to macroscopic gradients in weakly collisional plasmas. We implement thermodynamic forcing in particle-in-cell (TF-PIC) simulations using a modified Vay particle pusher and validate it against analytic solutions of the equations of motion. We then carry out a series of simulations of electron-proton plasmas with periodic boundary conditions using TF-PIC. First, we confirm that the properties of two electron-scale kinetic instabilities -- one driven by a temperature gradient and the other by pressure anisotropy -- are consistent with previous results. Then, we demonstrate that in the presence of multiple macroscopic gradients, the saturated state can differ significantly from current expectations. This work enables, for the first time, systematic and self-consistent transport modeling in weakly collisional plasmas, with broad applications in astrophysics, laser-plasma physics, and inertial confinement fusion.

It has been suggested previously that an ultra-soft fermionic excitation develops, albeit with a small spectral weight, in a system of massless fermions and scalar bosons with Yukawa interaction at high temperature (T). In this paper we study how this excitation is modified at finite chemical potential (μ). We relate the existence of the ultra-soft mode to symmetries, in particular charge conjugation, and a supersymmetry of the free system which is spontaneously broken by finite temperature and finite density effects, as argued earlier by Lebedev and Smilga. A non vanishing chemical potential breaks both symmetries explicitly, and maximally at zero temperature where the mode ceases to exist. A detailed calculation indicates that the ultra-soft excitation persists as long as Tgtrsim μ.

We investigate the cosmological moduli problem (CMP) in the context of supersymmetric models where discrete R-symmetries are used to suppress the mu term, and where mu is regenerated via Kim--Nilles superpotential operators. In such theories, a global U(1)_{PQ} emerges as an accidental, approximate symmetry which solves the strong CP problem. R-parity is also generated as accidental but approximate, where RPV operators gain a (f_a/m_P)^n suppression. When n=1, the thermally-produced LSPs may decay before BBN in the early universe, leaving axion-only dark matter of the SUSY DFSZ type. Meanwhile, the dominant cosmological constraint on light stringy moduli previously came from the modulus-induced WIMP overproduction problem. WIMP overproduction is now ameliorated by the RPV WIMP decays, but the moduli-induced BBN bound may be exacerbated by convolving long-lived modulus decay with long-lived RPV WIMP decay: long-lived particle (LLP) cascade decays. In this context, moduli as light as m_ϕ~ 130 TeV may be allowed which can reconcile naturalness with the presence of stringy moduli in the early universe.

We demonstrate that an axion field can develop perturbations peaked at an intermediate wavenumber through its inflationary dynamics. We compute the resultant spectrum of gravitational waves (GWs) and primordial black holes (PBHs) generated through the curvaton mechanism. The GW spectrum exhibits a triangular shape, with UV and IR slopes determined by the axion's inflationary evolution and treatable as free parameters. In computing the PBH abundance, we properly account for the nonlinear relation between curvature and density perturbations and the primordial non-Gaussianity generated by the curvaton. The PBHs can account for all of dark matter, accompanied by blue-tilted isocurvature perturbations at small scales. The IR slope of the GW spectrum is anti-correlated with the magnitude of the dark matter isocurvature perturbations, offering a multi-messenger test of the model.

Differentiable matching layers and residual connection paradigms, often implemented via entropy-regularized Optimal Transport (OT), serve as critical mechanisms in structural prediction and architectural scaling. However, recovering discrete permutations or maintaining identity mappings via annealing εto 0 is notoriously unstable. In this work, we identify a fundamental mechanism for this failure: Premature Mode Collapse. By analyzing the non-normal dynamics of the Sinkhorn fixed-point map, we reveal a theoretical thermodynamic speed limit: standard exponential cooling outpaces the contraction rate of the inference operator, which degrades as O(1/ε). To address this, we propose Efficient Piecewise Hybrid Adaptive Stability Control (EPH-ASC), an adaptive scheduling algorithm that monitors the stability of the inference process. We demonstrate that EPH-ASC is essential for stabilizing Manifold-Constrained Hyper-Connections (mHC) during large-scale training on the FineWeb-Edu dataset, effectively preventing late-stage gradient explosions by enforcing a linear stability law.

We study complex saddle points of the worldline path integral for massive charged particles in two-dimensional maximally symmetric backgrounds threaded by homogeneous electric fields. Within the worldline formalism, we show that the semiclassical saddles generically require complexifying both the target spacetime and the proper-time parameter. The resulting solutions comprise two slices of a single complex family, distinguished by the direction of proper-time evolution. The one evolving in imaginary proper time carries an action that typically controls the exponential suppression of non-perturbative effects, while that evolving in real proper time may encode additional complex phases responsible for quantum interference between saddles. Treating this family as a whole, we give a prescription for constructing and classifying all topologically inequivalent instanton sectors, and we find that the worldline action depends only on their topological data, namely winding numbers around the compact directions and certain isolated punctures. Moreover, in Anti-de Sitter spacetime, the qualitative structure of the solutions is governed by the dimensionless ratio R |eE|/m (R being the curvature radius), which distinguishes sub-extremal, extremal, and super-extremal regimes. By contrast, no analogous distinction occurs in de Sitter---where the instantons are insensitive to this ratio---or in Minkowski spacetime, which lacks a curvature scale altogether. We also recast the action as a sum over residues of the relevant (non-conserved) conjugate momentum, making transparent which analytic data control each contribution. Finally, we discuss the subtleties that arise when solutions built in various local patches are lifted to global (Anti-)de Sitter space. These impose further necessary conditions on which saddles can in principle contribute to the one-loop path integral.