High-energy nuclear physics explores the properties of strongly interacting matter created in relativistic collisions of nuclei. Femtoscopy, a subfield of high-energy physics, utilizes quantum-statistical correlations of particles to characterize the space-time geometry of the particle-emitting source. Recent measurements and phenomenological investigations indicated that the shape of the source for identical pions can be well-described by Lévy-stable distributions. The significant power-law tail of the pion source observed both in experiment and in simulations has been shown to originate from the process of Lévy walk during the hadronic scattering phase of the collisions. To better understand the physical processes behind the formation of such power laws, an important next step is to investigate particle species dependence, especially the source shape of identical kaon and proton pairs. As a direct continuation of our previous studies, in this Letter, we present a detailed three-dimensional investigation of the two-particle source shape in simulations of Au+Au collisions at 200 GeV per nucleon pair collision energy using the EPOS3 model. We show the dependence of the extracted femtoscopic source parameters on particle species, centrality and average transverse mass. We find that the scale parameters do not show a clear transverse mass scaling between particle species, as there are systematic differences in the overlapping regions. The power-law exponents of pion and kaon pairs are compatible, while for protons it is higher, closer to the Gaussian limit. When new experimental measurements of kaon and proton correlations become available, these results will provide the basis of a data-model comparison.

We study caplet stripping, the problem of recovering a caplet volatility term structure consistent with quoted cap volatilities. Many academic papers on the Libor market model assume caplet volatilities are readily available, whereas practitioners know they are not and extracting them is a complex task. This paper presents a practical workflow, structuring the presentation around a constructive algorithm. We start with criteria on the input data based on cap time-value monotonicity. If time values fail this check, we show how to correct the quotes using robust outlier detection based on the modified Z-score. The time-value proposition naturally leads to a direct non-bootstrap stripping approach by interpolating cap time values, which yields arbitrage-free caplet volatilities by construction. We then revisit the classic sequential bootstrap approach. We introduce compact-kernel transition interpolants (flat-linear and $C^1$ flat-smooth) that preserve bootstrap equivalence. Finally, for a richer, smoother curve, we introduce global search methods using midpoint node placement with positivity-preserving calibration. Pathological cases and detailed analyses of oscillations are provided in the appendix.

We propose Acc-Sinkhorn, a simple accelerated variant of Sinkhorn for entropy-regularized optimal transport (EOT). The method is derived from a bilevel optimization view: Sinkhorn row scaling solves the inner variable $u$ exactly and defines the reduced dual objective $f(v)=\min_u F(u,v)$, while the remaining column scaling is a unit-step dual mirror descent step in $v$. This structure yields a Hessian-driven Nesterov acceleration that keeps Sinkhorn's scaling form and per-iteration cost, using only extrapolated combinations of Sinkhorn iterates. We prove an $\mathcal{O}(1/k^2)$ rate under a verifiable stability condition. For an $\varepsilon$-approximation of unregularized OT, the resulting complexity is $\widetilde{\mathcal{O}}(n^2/\varepsilon)$, improved from $\widetilde{\mathcal{O}}(n^2/\varepsilon^2)$ for Sinkhorn. On synthetic problems, color transfer, and word alignment, Acc-Sinkhorn gives a $10\times$--$30\times$ speedup over Sinkhorn at small regularization.

In static lattice systems, the Nielsen-Ninomiya theorem enforces the pairing of Weyl points with opposite chiralities, which precludes the chiral magnetic effect (CME) in equilibrium. Periodic driving provides a viable route to circumvent this no-go constraint. Here, we propose a scheme to realize and control unpaired Weyl points using ultracold atoms in a three-dimensional (3D) optical Raman lattice under continuous periodic driving. By engineering distinct relative symmetries between the lattice and multiple Raman potentials, the configuration generates an effective 3D spin-orbit coupling and yields a tunable topological-insulator phase. Through adiabatic periodic modulation of this system, we show that eight Weyl points emerge in the quasienergy spectrum of the low-energy sector, whose net chirality can be precisely tuned. A nonzero total chirality directly corresponds to the formation of unpaired Weyl points. Furthermore, by implementing a synthetic magnetic field via laser-assisted tunneling in this setup, we demonstrate that the chirality imbalance drives a quantized charge current in the weak-field regime, providing a direct signature of the CME. We verify that the adiabatic condition of the driving protocol, as well as the proposed experimental preparation and detection techniques, are within reach of current ultracold-atom experiments. This work establishes a realistic and controllable platform for exploring chiral-anomaly physics and nonequilibrium topological phenomena linked to Weyl fermions.

We analyse generating functions for trees and for connected subgraphs on the complete graph, and identify a single scaling profile which applies for both generating functions in a critical window. Our motivation comes from the analysis of the finite-size scaling of lattice trees and lattice animals on a high-dimensional discrete torus, for which we conjecture that the identical profile applies in dimensions $d \ge 8$.

Energy correlators exhibit well-understood scaling behavior in the collinear limit, governed by perturbative QCD dynamics. We explore how this scaling regime is broken by new physics, converting precise energy correlator measurements into a broadband search for new physics. Under generic assumptions, unitarity and positivity are sufficient to classify and constrain the relevant signatures, which imprint an angular resonance on top of this smoothly scaling background. This converts the search into bump hunting within jets. As a proof of principle, we derive projected LHC sensitivity for a light hadrophilic $Z'$, finding competitive constraints with existing searches.

Biological intelligence is distinguished by neural reuse, the capacity to preserve established learning memory while repurposing it for new tasks and dynamic environments. Bringing this capability to photonic hardware requires hybrid plasticity, namely the coexistence of long-term synaptic plasticity for persistent weight storage and short-term synaptic plasticity for rapid, reversible adaptation within a single synaptic element; however, current photonic architectures lack such a unified mechanism. Here, we demonstrate a hybrid-plasticity photonic synapse on thin-film lead zirconate titanate (PZT) that couples non-volatile and volatile modes to enable hardware-level neural reuse. Crucially, high-speed refresh operations can be superimposed without perturbing the stored weight. Such a neural-reuse framework yields a convergence speedup of over 20-fold and reduces the weight updates by approximately 30-fold compared with random initialization. These results establish hybrid-plasticity photonic synapses as a pathway toward on-chip learning systems that are both memory-preserving and rapidly adaptable.

Dynamic alignment in magnetohydrodynamic (MHD) turbulence is often interpreted as a scale-dependent tendency of counterpropagating Elsässer increments to become increasingly aligned at smaller perpendicular scales, with direct implications for the inertial-range spectrum of space and astrophysical plasma turbulence. We show that this is not the correct physical interpretation of the standard amplitude-weighted measurements. Using high-resolution incompressible MHD simulations from the Johns Hopkins Turbulence Database and near-Earth in situ solar-wind measurements from the Wind spacecraft, we separate angular statistics from Elsässer-amplitude weighting and measure the finite-time retention of amplitude--angle states. In the simulations, the unweighted folded angle remains only moderately below the random three-dimensional baseline and shows no monotonic scale-dependent decrease over the resolved inertial-range separations. The much smaller angles inferred from weighted diagnostics arise primarily from large-\(A_r=|δ_r z^+||δ_r z^-|\) events, producing a negative covariance between \(A_r\) and \(\sinθ_r\) that is removed by shuffled controls. Time-resolved transition measurements show that high-amplitude large-angle states deplete faster than high-amplitude small-angle states. The measured source--depletion balance reconstructs the second-order Elsässer amplitudes without fitting their scale dependence and gives an effective root-mean-square increment scaling close to \(\ell_\perp^{1/4}\), although the typical folded angle is nearly scale independent. Wind measurements reproduce the same amplitude--angle hierarchy and negative covariance under Taylor sampling. Conventional dynamic-alignment diagnostics therefore measure selective retention of intense Elsässer fluctuations, not volume-filling progressive alignment of typical fluctuations.

Saddle point problems with smooth convex-concave objective functions are often used to model min-max problems arising in machine learning. First-order methods are the standard paradigm for solving such problems. Therefore, it is important to know how those methods behave in the worst-case scenarios. In order to derive the guarantees, one would require the inequalities that appropriately constrain the iterates, gradients and function values. In this paper, we present stronger constraints for smooth convex-concave functions and show that they could allow tighter upper bounds for first-order methods.

X-ray variability is a well-established characteristic of active galactic nuclei (AGN), known to correlate inversely with both the supermassive black hole mass and luminosity, although the degree of each remains a topic of debate. The potential of X-ray variability as a proxy for MBH or for intrinsic LX has led to proposals to use AGN as standard candles to test cosmological models. However, the large intrinsic dispersion in these relations has limited their practical applications. In this work, we investigate the dependence of X-ray variability on AGN physical properties using a sample of 134 Seyfert 1 galaxies from the BAT AGN Spectroscopic Survey (BASS), which is the largest sample to date, more than three times larger than those used in previous studies. Contrary to earlier findings, we observe that X-ray variability correlates with luminosity just as strongly as with MBH. Furthermore, we still do not find evidence for the expected anti-correlation between variability and Eddington ratio, even when using refined bolometric luminosities from SED fitting to compute the Eddington ratio. From a cosmological perspective, the increased sample size reduces the scatter in the log(L)-log(exvar) relation to ~0.63 dex - a significant improvement over previous results, but still too large to serve as competitive standard candles, when compared to SNIa (uncertainties on distances of ~5-10%) or the L(X)-L(UV) relation in quasars (uncertainties of 10-12%). We tested including the width of broad emission lines as additional parameters, but found that this does not significantly lower the observed dispersion, contrary to previous studies on smaller samples. Finally, we discuss how future X-ray missions such as AXIS and NewAthena will improve this scenario by enabling precise variability measurements for thousands of AGN up to redshift z~3, thereby enabling it as a new cosmological probe.

Recently, [25] observed that, among the currently unresolved cases of the axially symmetric Navier-Stokes equations (ASNS), the most relatively tractable one is where the fluid passes the exterior of a cone. In this paper, we investigate this case with the classical Navier total-slip boundary condition. We show that there exists an absolute constant $C_* > 0$ such that if \[ \sup_{x\in D}r|v_{0,θ}|\leq C_* \quad\text{and}\quad \int_{D} r v_{0,θ}(x) \mathrm{d} x = 0, \] then there exists a unique global bounded strong solution with finite energy. We point out that there is no size restriction on other components of the initial velocity. Compared with [25], no parity symmetry assumption on $\boldsymbol{v}_0$ is required. There are four key ingredients in the proof. (1) In spherical coordinates, we introduce three new quantities \[ \mathcal{K}\buildrel\hbox{def}\over =\frac{\sinϕ}{ρ^2}\partial_ϕ\Big(\frac{v_θ}{\sinϕ}\Big) \,,\quad\quad\mathcal{F}\buildrel\hbox{def}\over =-\partial_ρ\Big(\frac{v_θ}ρ\Big) \,,\quad\quad \mathcal{O}\buildrel\hbox{def}\over =\frac{1}{ρ\sinϕ}\Big(ω_θ-\frac{2v_ϕη(ρ)}ρ\Big) \,, \] and derive a self-closed energy estimate for them, where $η$ is a cut-off function which vanishes near the origin and equals $1$ away from the origin. (2) A boundary value problem of the pressure $P$ is proposed and an elliptic estimate for $P$ is established in order to control boundary terms arising from the Navier total-slip boundary condition. (3) A De Giorgi iteration scheme is applied to establish the boundedness of the quantity $rv_θ$ whose integral on $D$ vanishes for all the time. (4) A new anisotropic Hardy's inequality is derived for functions whose integral on $D$ vanish to overcome the lack of parity symmetry of $\boldsymbol{v}$.

Identifying spatial quantum correlations in mixed states is challenging because thermal mixed-state contributions obscure the entanglement encoded in subsystem entropy. Here, we introduce the entanglement projected entropy (EPE), a purification-independent Gaussian spatial filter for mixed fermionic states. By resolving subsystem entropy into Gaussian entropy channels and projecting their purification partners onto the physical complement, we obtain a closed-form expression in terms of the physical covariance matrix. In a one-dimensional free-fermion chain, it removes the volume-law mixed-state background and recovers the zero-temperature conformal scaling with the $c/3$ coefficient. In a two-dimensional half-filled $π$-flux model, it reveals a universal finite-temperature scaling collapse governed by a Dirac infrared length fixed by the low-energy velocity. These results establish EPE as an entropy-channel filter that exposes boundary-sensitive universal scaling hidden beneath mixed-state entropy.

Itenberg-Katzarkov-Mikhalkin-Zharkov gave an isomorphism of tropical cohomology and cohomology of some maximally degenerate algebraic varieties. Their proof was based on tropical analogs of Steenbrink's geometric monodromy-weight spectral sequences. These were generalized to the non-realizable case by Amini-Piquerez. In this paper, we give a new construction of these tropical spectral sequences in the same way as Steenbrink's ones. For this purpose, we introduce reductions of tropical varieties. We also show that eigenwave actions are given by tropical Gauss-Manin connections.

Si/SiGe quantum wells that incorporate Ge concentration oscillations, known as long-period Wiggle Wells, have been shown to enhance the Dresselhaus spin-orbit coupling of conduction-band electrons. Such intrinsic spin-orbit coupling is desirable when performing spin-qubit gate operations based on electric dipole spin resonance (EDSR) because it eliminates the need for external micromagnets. However, random-alloy disorder plays a key role in this materials system by spatially randomizing the valley splitting and the valley phase $ϕ_{s,s}$, and it has not been fully accounted for in recent EDSR analyses. Here, we show that alloy disorder affects EDSR in two main ways. First, the Rabi frequency $Ω$ acquires a dependence on the valley phase, given by $\cosϕ_{s,s}$, which causes spatial randomization of $Ω$. Despite this variability, we show that fast EDSR can be achieved at most locations across a given sample. Second, a new Rabi driving mechanism emerges, enabled by valley dipoles and the hybridization of ground and excited valley states, which arise from alloy disorder and EDSR driving, respectively. This mechanism is dominant in regions of low valley splitting. Alloy disorder can therefore strengthen EDSR, but it can also cause gradients in $Ω$ that lead to dephasing in the rotating frame. We explore this problem by first locating "sweet spots," where EDSR is relatively insensitive to electric-field fluctuations. We then show that high-fidelity Rabi oscillations can be achieved in the presence of realistic charge noise. These results suggest that Wiggle Wells are a promising platform for high-quality, micromagnet-free gate operations.

We investigate Fourier multipliers associated with the Strichartz Fourier transform on the Heisenberg group. In particular, we establish Hörmander-type $L^{p}-L^{q}$ boundedness results for the range $1<p\leq 2\leq q<\infty$. The analysis is based on deriving suitable analogues of the Hausdorff-Young and Paley inequalities for the Strichartz Fourier transform, followed by interpolation arguments to obtain the desired multiplier estimates. As an application, we study the local well-posedness of certain nonlinear partial differential equations. Furthermore, we establish an $L^{p}$-boundedness theorem for Fourier multipliers associated with the Strichartz Fourier transform for the full range $1<p<\infty$.

The mapping class group $M(X)$ of a smooth manifold $X$ is the group of smooth isotopy classes of orientation preserving diffeomorphisms of $X$. We prove a number of results about the mapping class groups of compact, simply-connected, smooth $4$-manifolds. We prove that $M(X)$ is non-finitely generated for $X = 2n \mathbb{CP}^2 # 10n \overline{\mathbb{CP}^2}$, where $n \ge 3$ is odd. Let $Γ(X)$ denote the group of automorphisms of the intersection lattice of $X$ that can be realised by diffeomorphisms. Then $M(X)$ is an extension of $Γ(X)$ by $T(X)$, the Torelli group of isotopy classes of diffeomorphisms that act trivially in cohomology. We prove that this extension is split for connected sums of $\mathbb{CP}^2$, but is not split for $2\mathbb{CP}^2 # n \overline{\mathbb{CP}^2}$, where $n \ge 11$. We prove that the Nielsen realisation problem fails for certain finite subgroups of $M( p \mathbb{CP}^2 # q \overline{\mathbb{CP}^2} )$ whenever $p+q \ge 4$. Lastly we study the extension $M_1(X) \to M(X)$, where $M_1(X)$ is the group of isotopy classes of diffeomorphisms of $X$ which fix a neighbourhood of a point. When $X = K3$ or $K3 # (S^2 \times S^2)$ we prove that $M_1(X) \to M(X)$ is a non-trivial extension of $M(X)$ by $\mathbb{Z}_2$. Moreover, we completely determine the extension class of $M_1(K3) \to M(K3)$.

We find novel confined states in the spin-$S$ nearest-neighbor antiferromagnetic Heisenberg model on the two-dimensional Penrose lattice. Linear spin waves have massively degenerate eigenstates strictly confined to tricoordinated sites. They contrast with the well-known itinerant analogs in the tight-binding model, where electrons are confined but extended to both tricoordinated and pentacoordinated sites. It is the site potentials in the spin-wave Hamiltonian, originating from Coulomb interactions between electrons, that confine spin waves to minimally coordinated sites only. Confined states in the tight-binding Hamiltonian consist of six types of building blocks, whereas those in the spin-wave Hamiltonian consist of only four of them. Confined spin waves are robust against $1/S$ corrections. Emergent $O(S^{0})$ interactions further confine -- superconfine -- spin waves into two separate groups within tricoordinated sites.

Rhombohedral (ABC-stacked) multilayer graphene hosts interaction-driven phases enabled by surface flat bands at large displacement fields. In thick flakes, however, strong screening suppresses internal electric fields, raising the question of whether a flat-band regime is accessible within the same experimental paradigm. Here, we show that self-consistent, nonlinear electrostatics provides a robust alternative mechanism: even in the absence of a displacement field, a nonuniform near-surface potential flattens the surface-band dispersion and enhances the density of states. In the strong-coupling limit, electrostatics drives the system toward uniform half-filling at each momentum, yielding an asymptotically flat surface band without any gating. At realistic interaction strengths, surface-band flatness is tuned by the proximal gate, with maximal flatness achieved at hole doping when the band is empty. Combining analytic arguments with fully self-consistent calculations in a realistic model, we map the resulting low-field regime and connect to finite $N\!\sim\! 6-15$ layered samples, providing a framework for analyzing the symmetry-broken phases observed in these systems. Our results motivate future experiments in large-$N$ devices and establish a low-field regime for exploring electrostatically induced flat-band physics.

We construct a local decoder for the 2D toric code using ideas from the hierarchical classical cellular automata of Tsirelson and Gács. Our decoder is a circuit of strictly local quantum operations preserving a logical state for exponential time in the presence of circuit-level noise without the need for non-local classical computation or communication. Our construction is not translation invariant in spacetime, but can be made time-translation invariant in 3D with stacks of 2D toric codes. This solves the open problem of constructing a local topological quantum memory below four dimensions.

Probing the dynamics of superconducting transitions induced by strong electromagnetic fields is vital to designing high power devices leveraging these materials. The development of high temperature superconductors (HTS) is particularly interesting due to critical temperatures ($T_c$) approaching 90\,K, the ability to support high current densities, and their ability to operate in strong static magnetic fields. This work aims to determine the transition dynamics of these materials at radio-frequencies (rf) in the microwave range where they have enormous potential for new applications ranging from particle accelerators to dark matter searches. We have tested two types of coatings formed from rare earth barium copper oxide (REBCO): a film deposited by electron-beam physical vapor deposition, and HTS conductor tapes soldered to a copper substrate with exposed REBCO surfaces. Testing was performed via a hemispherical transverse-electric mode cavity that maximizes the surface rf magnetic field and minimizes the surface electric field on a 2-inch diameter sample. We report on steady-state measurements at low rf power, as well as fully time-resolved transition dynamics on the microsecond timescale seen for the first time with strong surface rf fields.

The prime number graph is the set of points $(n,p_n)$ where $p_n$ denotes the $n^{\rm th}$ prime. Let $L(n)$ be the minimum number of straight line segments needed to cover the first $n$ points in this set. Let $B(n)$ be the largest number of points $(k,p_k)$ with $k\le n$ covered by a single line. Recently Sloane conjectured that $L(n) = O(n/\log n)$. We show that $L(n)=O(n \log \log n / \log n)$ and $B(n)\ge c\log n$ for a constant $c>0$ and all large $n$. Under RH we show that for large $n$ we have $B(n)=O(n^{3/4}(\log n)^{1/2})$ and $ L(n)\ge c' n^{1/4} (\log n) ^{-1/2}$ for some constant $c'>0.$

We present a spectral variability study of the ultraluminous X-ray source NGC 4490 ULX-8 based on 14 Chandra, 6 XMM-Newton and 19 Swift-XRT observations obtained between 2000 and 2024. The X-ray spectra are modelled using absorbed power-law and absorbed multicolour disc blackbody models. The best-fit photon indices span 0.9-2.7, while the inferred inner disc temperatures lie in the range 1.0-1.6 keV. We detect pronounced long-term variability in the unabsorbed X-ray luminosity on multi-year timescales, while variability within individual observations is comparatively modest. A Hardness-Intensity Diagram of the source shows no clear transition between hard and soft states; however, two recent observations taken on 2022 December 1 and 2024 May 4 show a sharp increase in brightness. The spectra across all observations are dominated by smooth, single-component curvature in the 0.3-10 keV band, consistent with the broadened-disc regime of ultraluminous X-ray sources. A correlation analysis reveals a weak positive X-ray luminosity-photon index trend that remains statistically supported after controlling for related degeneracies, indicating that it is not driven solely by fitting covariance. The luminosity-inner disc temperature relation is only weakly constrained, but remains compatible, within uncertainties, with both thin-disc and slim-disc scalings. Using disc parameters derived from higher-quality XMM-Newton spectra, we obtain model-dependent estimates of the characteristic inner disc radius and compact-object mass as functions of inclination and spin. The reported results are consistent with a stellar-mass black hole accretor operating at or near the Eddington limit.

The Schwarzschild interior solution, when combined with the assumption of a finite central pressure, leads to the well-known Buchdahl bound. This bound establishes an upper limit on the mass-to-radius ratio of an object, which is equivalent to imposing an upper limit on the gravitational potential. Remarkably, this limit exhibits considerable universality, as it applies to a broader class of solutions beyond the original Schwarzschild interior metric. By reversing this argument, one can define the most compact horizonless object that satisfies this gravitational bound. Intriguingly, the same bound arises when applying the Virial theorem to an appropriately chosen combination of gravitational and potential energy. In this work, we explore the generalised Buchdahl compactness bound in the presence of a cosmological constant. We investigate its implications, define a suitable gravitational energy and an associated potential energy that incorporate the cosmological term, and demonstrate that the universality of the Buchdahl bound persists. However, we also observe that different bounds emerge depending on the chosen approach.

Separation logic is successful for software verification of heap-manipulating programs. Numbers are necessary to be added to separation logic for verification of practical software where numbers are important. However, properties of the validity such as decidability and complexity for separation logic with numbers have not been fully studied yet. This paper presents the translation of Pi-0-1 formulas in Peano arithmetic to formulas in a small fragment of separation logic with numbers, which consists only of the intuitionistic points-to predicate, 0 and the successor function. Then this paper proves that a formula in Peano arithmetic is valid in the standard model if and only if its translation in this fragment is valid in the standard interpretation. As a corollary, this paper also gives a perspective proof for the undecidability of the validity in this fragment. Since Pi-0-1 formulas can describe consistency of logical systems and non-termination of computations, this result also shows that these properties discussed in Peano arithmetic can also be discussed in such a small fragment of separation logic with numbers.

Aberration-corrected environmental transmission electron microscopy (ETEM) enables atomic-resolution imaging of dynamic catalytic processes. Correlating atomic-scale structural changes with reaction products detected by mass spectrometry offers a powerful route to uncover catalytic mechanisms. However, current approaches face fundamental limitations: closed-cell ETEM setups suffer from diffuse scattering by SiN windows, degrading spatial resolution and sensitivity, while open-cell configurations enable high-resolution imaging and maintain high sensitivity but suffer from significant dilution of reaction products during transport to the mass spectrometer (MS). To overcome these challenges, we develop a Local Probe Mass Spectrometer (LPMS) integrated with aberration-corrected ETEM. The setup combines a DENSsolution Stream holder with a MS. To preserve spatial resolution, both top and bottom SiN membranes of the MEMS chip are removed, while the gas environment is maintained via the ETEM chamber. Reaction products are sampled locally via a micro-capillary positioned near the catalyst and connected to a holder gas line that delivers the gas to the MS. Initial validation in environmental SEM confirmed controlled gas delivery to the MS. Co3O4 nanoplates serve as a model catalyst due to their inherent electron transparency, enabling atomic-resolution imaging without FIB lamella preparation and associated ion-beam damage. A novel micro-shuttle transfer strategy enables controlled placement of a defined number of nanoplates at the reaction site with precise crystallographic orientation. This establishes the foundation for quantitative structure reactivity correlation by enabling simultaneous, spatially resolved detection of reaction products and atomic-scale structural dynamics.

Internal magnetic fields have recently been detected and measured in the radiative core of red giant stars using asteroseismology. Being one of red giant stars progenitors and exhibiting high radial order gravity modes, $γ$ Doradus stars are also good candidates to hold detectable magnetic fields in their radiative envelope. We aim to detect internal magnetic field in a rapidly rotating $γ$ Doradus star for the first time, through its influence on the propagation of Kelvin gravito-inertial modes. We used the seismic variable $δK_a$, defined as a combination of Kelvin modes frequencies, which is sensible to the presence of a magnetic field. Following the detection, we carried out a modelling of the star oscillation spectrum considering a magnetic component following a Bayesian approach. We found a magnetic signature into the radiative envelope of KIC 2309579. If located just above the core, in the layers that were previously convective, the magnetic field would reach $\sim$ 4 kG.

Some time ago, we published the full count of degrees of freedom in the linearised weak gravity limit of arbitrary New GR models. We did it by considering the linear weak gravity equations and presented a thorough analysis with no ambiguity left. A bit later, we generalised it to linear cosmological perturbations and discussed the strong coupling issues that appear already at this level. Recently, there were claims that some dynamical modes had been missed in our work. However, the authors of the new claims did not look at the equations of motion and analysed the quadratic Lagrangian densities instead. In this paper, I take one of the most elementary cases, namely the vector modes in New GR of Type 3, and show what was their mistake that had led them to claiming that those were dynamical. The main message: Do not substitute constraint equations into a Lagrangian.

Quantum backflow refers to the appearance of negative probability current in a state whose momentum distribution is essentially positive. We propose a scheme to prepare such states in a noninteracting Bose-Einstein condensate using large-momentum-transfer (LMT) atom interferometry. Our approach extends the single-pulse proposal of Palmero et al. by allowing one interferometer arm to undergo a tunable sequence of momentum-transfer pulses before recombination with a freely propagating arm. For realistic parameters for Sr-88, the protocol generates interference states with tunable probability current and negligible negative-momentum contamination. We evaluate both the probability current and the critical-density criterion introduced by Palmero et al., and identify parameter regimes in which the backflow signature is enhanced relative to the single-pulse scheme. These results present LMT interferometry as a flexible route for preparing candidate quantum-backflow states in cold-atom experiments.

We propose an efficient classical algorithm to estimate the Neural Tangent Kernel (NTK) associated with a broad class of quantum neural networks. These networks consist of arbitrary unitary operators belonging to the Clifford group interleaved with parametric gates given by the time evolution generated by an arbitrary Hamiltonian belonging to the Pauli group. The proposed algorithm leverages a key insight: the average over the distribution of initialization parameters in the NTK definition can be exactly replaced by an average over just four discrete values, chosen such that the corresponding parametric gates are Clifford operations. This reduction enables an efficient classical simulation of the circuit. Combined with recent results establishing the equivalence between wide quantum neural networks and Gaussian processes [Girardi \emph{et al.}, Comm. Math. Phys. 406, 92 (2025); Melchor Hernandez \emph{et al.}, Ann. Henri Poincar{é} (2025)], our method enables efficient computation of the expected output of wide, trained quantum neural networks, and therefore shows that such networks cannot achieve quantum advantage.

We prove that there are globally hyperbolic spacetimes which are refocusing but not strongly refocusing. In fact, every globally hyperbolic strongly refocusing spacetime of dimension at least $3$ admits globally hyperbolic metrics which are refocusing but not strongly refocusing. This answers a question by Chernov, Kinlaw, and Sadykov. We then prove that globally hyperbolic spacetimes which are Legendrian refocusing (a notion introduced in this paper) admit globally hyperbolic strongly refocusing metrics.