Papers

Some voters conceal their opinions, causing a mismatch between visible and private opinions in polls. Conventional voter models do not account for such concealment. Here, we introduce a shy voter model that incorporates a hidden state in addition to two visible states, as an extension of the conventional majority-rule voter model. The model exhibits continuous and hybrid transitions, yielding a rich phase diagram organized by the hidden fraction, i.e., the fraction of voters in the hidden state. For a large hidden fraction, the system undergoes a hybrid transition from the ordered state to the symmetric (disordered) state, whereas for a small hidden fraction, it exhibits a continuous transition, with a tricritical point separating the two regimes. Near criticality, both the order-parameter variance and the susceptibility diverge. The hidden fraction also governs the entropy flux, a quantity that is not directly observable in real-world situations. Thus, opinion concealment qualitatively reshapes opinion dynamics, while the present framework provides a basis for further extensions toward more realistic forms of social interactions.

Manipulating spin using contactless and non-invasive optical approaches is one of the forefront topic in the modern spintronic science and technology. Prior studies on optically-induced spin reorientation usually scales with spin-orbit coupling strength, setting a limitation on composing heavy elements. In this work, we extend such a limit into nonrelativistic regime by exploring noncollinear magnetic configuration. Using a general spin group-theoretical investigation, we show how the symmetric operators in both spin and lattice spaces control the spin torque and quantum geometry of Bloch wavefunction–including both quantum metric and Berry curvature. We describe their site-resolved spin symmetries and unravel their selection rules. Furthermore, we adopt a Kagomé lattice model and a realistic material family to showcase the local spin torque under light irradiation. Since the nonrelativistic spin splitting usually spans on the order of electron-volt, significantly larger than typical spin-orbit induced splitting, the nonrelativistic light-induced spin torque is concomitantly much stronger. This work extends the previous opto-spintronics from relativistic to nonrelativistic limit, significantly broadening its realization platform.

Topological insulators lie outside the standard Landau paradigm: Instead of being characterized by local order parameters and spontaneous symmetry breaking, their defining properties are encoded in the global structure of their quantum states and manifested as robust boundary states. Crystalline higher-order topological insulators can extend this principle by hosting localized corner modes in two and higher dimensions. Although these boundary modes can be detected spectroscopically through the local density of states, determining the underlying bulk topology, for example through nested Wilson loops, remains an outstanding experimental challenge. Here we use up to 728 qubits in a superconducting analogue-digital quantum simulator to realize and probe a hierarchy of one-, two-, and three-dimensional topological insulators governed by effective tight-binding Hamiltonians. By reconstructing complex propagators from real-space measurements, we obtain complementary boundary and bulk characterizations: local densities of states reveal localized boundary modes, whereas experimentally reconstructed band projectors yield bulk topological invariants, culminating in a three-dimensional octupole moment extracted through third nested Wilson loops. These results establish a route to realizing, characterizing, and manipulating topologically protected states in programmable three-dimensional quantum matter.

Models of curvature-driven membrane sorting couple composition directly to membrane bending elasticity. Here we show that shape deformations can destabilize a homogeneous state without this composition-dependent mechanical coupling. We analyze the eigenspectrum of the Laplace-Beltrami operator on deformed spheres analytically, and verify it numerically. As the deformation amplitude increases, the spectral degeneracy breaks, and the lowest nonzero eigenvalue decreases substantially. Using Cahn-Hilliard dynamics, we show that this eigenvalue softening provides a purely geometric route to phase separation.

Orbital optimization within the variational quantum eigensolver (VQE) framework is useful for improving active-space quality and accurately capturing electron correlation with shallow quantum circuits. The orbital-optimized unitary coupled cluster (OO-UCC) method [W. Mizukami et al., Phys. Rev. Res. 2, 033421 (2020)], in its original formulation, employs the orbital gradient and Hessian in a Newton–Laphson procedure. In this study, we propose sequential orbital-optimized unitary coupled cluster doubles (SOO-UCCD), extending the gradient-free sequential minimal optimization approach [K. M. Nakanishi et al., Phys. Rev. Res. 2, 043158 (2020)] to orbital rotation parameters. Based on the frequency structure implied by the algebraic properties of the orbital rotation generators, our method determines each orbital rotation angle from a nine-point energy profile. The energy landscape is evaluated by classically transforming the Hamiltonian integrals and contracting them with the reduced density matrices already measured for the VQE energy evaluation. This allows for orbital optimization without evaluating the orbital gradient or Hessian. By building on the core benefits of the OO-UCC framework, our method provides a gradient-free and hyperparameter-free orbital-optimization procedure. State-vector simulations for LiH in the STO-3G basis show that SOO-UCCD reproduces UCCSD-level accuracy along the bond-stretching curve and exhibits macro-iteration convergence comparable to that of L-BFGS-based orbital optimization.

Planet formation requires growth over 12 orders of magnitude in size, from micron-sized dust grains to fully formed planets. The formation of km sized planetesimals is the most challenging stage, where radial drift and fragmentation rapidly remove meter- sized solids from the protoplanetary disc. Overcoming this barrier requires favourable conditions for streaming instability to concentrate solids. These problems are exacerbated in binary star systems, where gravitational perturbations and disc truncation reduce the efficiency of planetesimal formation pathways. Planetesimal capture provides an alternative mechanism where unbound planetesimals are captured by the protoplanetary disc through gas-drag, potentially bypassing the most restrictive growth stages. We investigate this process in circumstellar and circumbinary discs using over 30 million numerical experiments across a range of binary separations. For circumstellar discs, capture of large planetesimals is suppressed below 50 au, with the strongest reduction at around 10 au, broadly consistent with the observed decrease in planet occurrence in binaries. Tight binaries can still capture O(1) km-sized planetesimals, increasing to O(10) km-sized in wider systems during the birth cluster's lifetime. Circumbinary discs are much less efficient, with capture rates dropping to around 1 percent of the single-star case for binaries above 1 au and becoming negligible for large planetesimals at wider separations. Overall, planetesimal capture provides a supplementary channel for delivering solids to binary systems and mitigating inefficiencies in in-situ planetesimal formation.

The increasing event complexity and data rates foreseen for future LHC coinditions motivate a transition from selecting proton-proton ($pp$) collision events by reconstructing predefined signal candidates to constructing a reduced data stream by interpreting the relevant event features in a signal-agnostic way. We explore the capabilities of deep-learning-based architectures on heavy-flavour physics using LHCb as a case study. Graph-based full-event interpretation techniques address the problem by representing visible products of $pp$ collisions as nodes of a graph, and reconstructing heavy-hadron decay chains hierarchically. A new neutral-particle-aware architecture extends the input data from charged tracks to calorimeter clusters, and uses metric learning to clusterize particles from the same decay chain in a common latent space. Tests on inclusive simulated $pp\to b\bar b$ events show that this approach retains its ability to reconstruct decay chains across a broad range of topologies and multiplicities. We discuss the resulting physics opportunities, with a focus on inclusive $b\to s\ell\ell$ measurements and on searches for exotic hadrons.

Entanglement witnesses are a key instrument in determining the entanglement of unknown bipartite qubit systems without requiring a full tomography. Riccardi et al. (2020) proposed a set of two-qubit witnesses, denoted $\{W^3\}$, which require a set of local measurements in three bases. In this work we propose an additional set of witnesses, denoted $\{W^5\}$, that build on $\{W^3\}$ and require measurements in two additional bases. We present an adaptive two-step method that uses the measurement results obtained for $\{W^3\}$ to select which $W^5$ to evaluate. We computationally demonstrate that our adaptive two-step protocol can identify 72% of entangled states generated according to the methods of Roik et al. (2021) while requiring measurements in only five of the nine bases needed for full quantum tomography. Additionally, we experimentally verify the behavior of both sets of witnesses using polarization-entangled photon pairs.

The results from [Fluid Dyn 61, 20 (2026)], concerning the generalized Chapman-Enskog method and a nonlocal (i.e., non-diffusive, spatially integral) viscous stress tensor in the Navier-Stokes equation, are extended to the case of arbitrary gradients of not only hydrodynamic velocity but also temperature. The resulting equations simplify the description of tangential discontinuities and separated flows. For the specific case of an incompressible medium, a nonlocal vorticity transport equation is derived that is structurally identical to the Biberman-Holstein equation for resonant radiation transport in plasmas and gases. A power-law form has been determined for the velocity distribution function of long-free-path vorticity carriers that satisfies empirical Richardson t^3 law for the mean square of relative separation of a pair of particles in a turbulent liquid or gaseous medium.

We present two and three dimensional direct numerical simulations of planar intrusions injected from a continuously supplied, narrow source into a linearly stratified ambient at the level of neutral buoyancy. The evolution passes through three phases. A laminar leading vortex dipole first advances at constant speed with a varicose wave train behind it; the trailing jet then undergoes a sinuous instability whose initial growth rate and wavelength agree with inviscid unstratified planar-jet theory evaluated on the local jet; the flow finally relaxes into a buoyancy-controlled wedge whose area grows linearly in time. Three-dimensional simulations show that the transition remains organized by the planar instability, while three-dimensionality reshapes the near-source region into a slowly evolving, actively mixing zone that entrains an additional twenty to one hundred percent of the source flux depending on source width. Rescaled with this measured effective flux, the downstream intrusion collapses reasonably well onto the similarity solution for a wide-source intrusion.

We present TractorJAX, an open-source GPU reimplementation of the catalog-forced mode of The Tractor. We use it to test whether regularization or external flux priors enable reliable fitting of reference catalogs that extend below the depth directly constrained by undersampled SPHEREx images. For full-depth regularized fits, TractorJAX fits $100\times100$-pixel cutouts at 11.9 ms each on a single NVIDIA H100 GPU. In simulated images of the Abell 2537 galaxy-cluster field, extending the fitted catalog from $m_z<21$ to the full DESI Legacy Imaging Surveys DR10 catalog increases the scatter in fractional flux residuals by 34%, even with regularization. We also test the methods using SPHEREx observations in nine fields, assessing the number of reliably measured sources and photometric-redshift accuracy. Requiring S/N $>5$ in more than half of the 102 channels, we find that the regularized full-depth fit yields 40% fewer sources than the truncated fit. For sources meeting this requirement in both fits, the normalized median absolute deviation of the photometric redshifts, $\sigma_{\rm NMAD}$, is 17% larger in the full-depth fit. External flux priors recover nearly as many sources as the $m_z<21$ fit, but increase $\sigma_{\rm NMAD}$ by 0.0015 for the common calibrated sample. Neither regularization nor the external flux priors tested here simultaneously preserve the sample size and photometric-redshift accuracy achieved by the truncated fit. Our results suggest that the optimal fitted-catalog depth cannot be determined from image-level performance alone, but should be selected through end-to-end tests tailored to the intended science measurement.

We present an empirical model that analytically relates the parameters of the extended Kubo-Toyabe (KT) function $G_z^{\rm EA}(t;\Delta,\nu_{\rm i},Q)$, which describes muon spin relaxation ($\mu$SR) induced by jump diffusion of ions using the Edwards-Anderson parameter $Q$, to those of the conventional KT function $G_z^{\rm KT}(t;\Delta_{\rm KT},\nu_{\rm KT})$ that serves as an approximation of $G_z^{\rm EA}(t)$. The proposed formulae successfully reproduce the anomalous temperature dependences of the linewidth $\Delta_{\rm KT}(T)$ and the fluctuation rate $\nu_{\rm KT}(T)$ which are artifacts observed upon analyzing $\mu$SR data on ion diffusion using $G_z^{\rm KT}(t)$. Applying this model to $\Delta_{\rm KT}$ and $\nu_{\rm KT}$ published in the literature of battery materials yields activation energy $E_{\rm i}$ and pre-exponential factor $\nu_{\rm i0}$ in the Arrhenius equation for ion diffusion, $\nu_{\rm i}(T)=\nu_{\rm i0} e^{-E_{\rm i}/kT}$, that are in excellent agreement with those deduced using other techniques, transforming peculiar artifacts into a powerful diagnostic tool.

Accurate prediction of the magnetic structure of interplanetary coronal mass ejections (ICMEs) remains a key challenge in space weather forecasting. Despite several efforts using global MHD modeling, it remains difficult to deduce a flux-rope solution that can accurately and reliably reproduce the magnetic structure of a CME. We present FROST (Flux Rope embedded in the Solar Magnetic Field), a new flux-rope model implementation within the European Heliospheric Forecast Information Asset (EUHFORIA), featuring an initially force-free toroidal flux rope embedded in the low-coronal magnetic field. FROST employs a novel embedding technique that self-consistently generates a draping magnetic field around the flux-rope, ensuring continuity of the normal magnetic field component at the CME boundary. The dynamics of the flux-rope in the low and middle corona is solved by a non-uniform advection constrained by the observed kinematics of the event. This results in a global, non-toroidal, stretched loop-like magnetic structure. At heliospheric distances, the evolution is modeled as an MHD process using EUHFORIA. We validate the FROST model implementation by simulating the CME event of 2013 April 11 and comparing the results with in situ magnetic field measurements at 1 au. The modeled magnetic field profiles of the flux-rope exhibit strong agreement with the observations, with correlation coefficients ranging from 0.64-0.93 for Bx, 0.92-0.95 for By, and 0.82-0.87 for Bz component of the magnetic field. These results demonstrate the capability of the proposed flux-rope model to significantly improve ICME magnetic field prediction, highlighting its strong potential for advancing space-weather forecasting capabilities.

Cluster lens models are constrained almost entirely by observed lensed image positions, leaving a large space of mass perturbations with arbitrary amplitudes such that they reproduce every image exactly. Such degeneracies are known as shape degeneracies (ShaDes). We show that these ShaDes shift the observed time delays, by the difference of the perturbing potential between the two images, without depending on the number of source/lens planes. Bounding their amplitude by preserving the positivity of the convergence, image multiplicity, and parity, in MACS J0138.0$-$2155, they can contribute at least $\simeq7$ days to the delay between the detected images of SN-Encore (i.e., $17.5\%$ of the measured value of $39.8$ days) and $\simeq112$ days (i.e., $2.8$–$3.7\%$ of predicted value of $3,000-4000$ days) to the reappearance intervals predicted for SN-Encore and SN-Requiem. These error bars transfer one-to-one to $H_0$, and remain invisible in comparisons of independent models.

In the canonical Casimir effect, the quantum vacuum is isotropic, and the minimization of vacuum energy drives only a linear attractive force between the plates. However, the introduction of an axion gradient breaks this rotational symmetry. It can be demonstrated that these asymmetric zero-point fluctuations exert a macroscopic mechanical twist on the plates proportional to $\vec{b}^2 \sin (2\vartheta)$ where $\vec{b}$ is the spatial axion gradient and $\vartheta$ is the angle between the axion gradient and the normal to the plates.

In this paper we provide an introduction to some of the efficient features of the Raspberry Pi Pico (RP2) family of microconroller boards (RP2040 and RP2350). More exactly, we show how to use PIO (Programmable Input/Output) and DMA (Direct Memory Access) to program the RP2 boards for efficient DAC (Digital to Analog) and ADC (Analog to Digital) conversions. Using OP-AMPS (Operational Amplifiers) we also show how to build a minimal electronic frontend interface for signal input/output. Finally, we integrate all these components into a product, the O-SCOPE, which is a practical and easy to use oscilloscope and wave function generator. The RP2 component of the O-SCOPE is built using Micropython, while the user interface is developed using vanilla Javascript and it runs on the web browser of any computer, interacting with the RP2 board via the Web Serial API. The O-SCOPE web interface is hosted on GitHub Pages such that it is directly accessible everywhere using a web browser, such that no local installation is required. Also, the RP2 software component is freely distributed on GitHub using the UF2 (USB Flashing Format) mass storage file, and it can be installed by simply dragging the file on the RP2 boards. These features make the O-SCOPE easily accessible, transforming it into a very low cost and useful tool for laboratories everywhere in the world.

Entanglement entropies of multipartite pure states satisfy linear inequalities; for stabilizer states, the backbone of quantum error correction, the achievable entropy vectors generate a convex cone. We show that, after a linear lift, the closure of this cone is exactly the self-dual slice of a classical object on one more element than there are parties: the closed cone generated by the rank functions of arrangements of subspaces over $\mathrm{GF}(d)$ for a prime local dimension $d$, and of subgroups of abelian groups of exponent dividing $d$ in general. This correspondence brings two features of rank inequalities into play. First, the purifier acts as an extra variable: already for five parties the stabilizer cone is strictly smaller than the quantum linear rank cone, with which earlier evidence suggested it might coincide; an explicit six-variable inequality witnesses the gap. Second, the characteristic of the field enters, so the cone depends on the local dimension. It does not for up to four parties. With enough parties, the cone of $\mathbb{Z}_d$ qudits is contained in that of $\mathbb{Z}_{d'}$ qudits if and only if $d$ divides $d'$, and already for six parties the logical zero state of Steane's code lies outside the stabilizer cone of every odd local dimension. For this last result we show that the seven-variable characteristic-dependent inequalities we checked all follow from Shannon inequalities on the self-dual slice, and instead transfer one of them through a family of subgroups derived from the Fano plane.

Spontaneous symmetry breaking (SSB) is conventionally understood through static vacuum selection in low-energy approximations. However, the nonperturbative dynamical pathways connecting symmetric configurations to asymmetric states remain an open question. In this paper, we propose an operator-theoretic framework that characterizes $Z_{2}$ symmetry breaking in scalar field theory through spectral branching. Specifically, we identify an effective invariant manifold of the nonlinear Klein-Gordon equation termed the "symmetric dual breather mode," whose phase-space geometry is traced using a $t$-dependent finite-dimensional representation. Our analysis demonstrates that static SSB represents merely a small-amplitude limit ($A \ll \phi_{v1}$). As the amplitude increases into the heteroclinic regime ($A > \phi_{v1}$), the field dynamically overflows the central barrier, yielding a vanishing time-averaged order parameter ($\langle \phi \rangle = 0$) and driving a geometric curvature cancellation ($\langle V''(\phi) \rangle_{t} \to 0$). Governed by a universal scaling function $\mathfrak{F}(y)$, the logarithmic period divergence near the heteroclinic boundary naturally generates sub-eV effective mass scales without fine-tuning bare parameters. Furthermore, this dynamic barrier overflow naturally favors Majorana-like self-conjugate states over Dirac-type states. Additionally, nonlinear phase interference along the heteroclinic channel induces asymmetric phase-space contraction, decoupling the right-handed mode and dynamically giving rise to the left-handed Weyl equation. These results bridge nonperturbative wave dynamics, topological mass suppression, chiral selection, and the dynamic origin of active neutrino masses.

Superionic conductors are promising electrolyte candidates for all-solid-state batteries, thanks to their liquid-like ionic mobility. In the prototypical lithium-ion oxide superionic conductor with antifluorite structure, the high-temperature transition to the fast-ion regime has long been attributed to volume-driven harmonic phonon softening. However, this quasi-harmonic picture neglects the strong lattice anharmonicity inherent to the fast-ion regime, leaving the microscopic origin of the transition unresolved. Here, we apply non-perturbative lattice dynamics combined with a first-principles-accurate machine-learning interatomic potential to study the phase transition in Li$_2$O. We demonstrate that anharmonicity, rather than volume expansion alone as commonly assumed, plays the decisive role in determining the transition temperature and the underlying mechanism. Finally, we analyze the spectral properties using the time-dependent self-consistent harmonic approximation, revealing the breakdown of the quasi-particle picture in this material. The spectral function and the infrared response provide signtures of the phase transition that can be investigated experimentally using inelastic neutron or X-ray scattering and infrared spectroscopy. All these results establish the extreme anharmonicity of Li$_2$O near the superionic regime and provide a lattice-dynamic framework for understanding and engineering the fast-ion transition in this type of materials.

The accurate estimation of the ionic activity coefficients is paramount for the characterization of the electrochemical reactions driving energy storage processes as well as the biological mechanisms involving ATP hydrolysis. The numerical evaluation of the ionic activity coefficients by computational methods is rendered difficult by the infinite dilution limit involved in the integral identity between the Helmholtz free energy and the equation of state of the electrolyte. By combining a recently introduced self-consistent Debye-Huckel formalism and its analytically tractable low density limit, we develop a computationally efficient approach enabling the accurate calculation of the free energy and the related thermodynamic functions of aqueous electrolytes over a broad range of ionic concentration and electrostatic coupling strength. Via comparison with numerical simulations and experimental data, it is shown that our approach can predict the salt dependence of the Helmholtz free energy, the entropy, and the ionic activity coefficients from the electrostatically driven submolar ion concentrations to the hard-core dominated molar density regime.

Fault-tolerant quantum design relies on simulating noisy quantum error correction (QEC) circuits with hundreds to thousands of physical qubits and large circuit depths. High-throughput stabilizer simulators, such as Stim, are the de facto tools for this regime. However, these simulators typically support only Clifford gates and stochastic Pauli noise. As a result, more realistic device noise models-such as coherent control errors and thermal relaxation-are often approximated using Pauli Twirling. This replacement offers speed but can introduce inaccuracies. To address this, we propose QuasiStim for scalable exact QEC simulation of realistic noise, with QuasiFold as a compiler frontend and DeltaFrame as a sampling backend. QuasiFold lowers sampling overhead by merging equivalent non-Pauli sites in the quantum circuit. DeltaFrame samples the resulting stabilizer trajectories by reusing precomputed predicted references instead of resimulating the full tableau for each shot. QuasiFold can reduce the number of shots by over $100\times$ on bivariate-bicycle (BB) codes. Compared to a per-shot tableau simulator, DeltaFrame is $166\times$–$1331\times$ faster on rotated surface-code memory under coherent $R_Z$ noise as $d$ grows from 5 to 35. QuasiStim also makes the PTA bias measurable: the gap is non-negligible and varies with noise strength, decoder, and circuit schedule. QuasiStim will be open-sourced upon publication at https://github.com/isaachyw/QuasiStim

Due to the importance of studying quantum-gravity-induced corrections to Einstein's theory of gravity, it is of interest to consider non-extensive entropies whose potential applications include identifying such corrections. In this Letter, we investigate possible corrections to a universal relation associated with the extremality bound of the mass of a black hole by employing entropies defined as functions of the Bekenstein-Hawking entropy.

High-pileup conditions in CMS during the HL-LHC era make charged-particle tracking increasingly challenging as detector occupancy and combinatorics grow. We present a hybrid approach that exploits Line Segment Tracking (LST) objects rather than individual hits to enable the first CMS ML-based track reconstruction algorithm. The LST objects, namely the triplets used in this study, are built according to geometry- and physics-driven criteria and carry richer local structure, geometrical cues, and physics quantities such as transverse momentum, which helps the model incorporate detector-level information from the start. We apply a Transformer encoder with geometrically masked sparse self-attention to embed these objects in a learned latent space, and use object condensation to assemble full tracks in a single inference step. This object-based representation reduces complexity in dense environments and makes the model less sensitive to ambiguities introduced by high pileup. Evaluated on CMS Phase-2 simulation of $t\bar{t}$ events at $\langle \mu \rangle = 200$, the approach achieves reconstruction efficiency comparable to the LST quintuplet baseline while reducing the fake rate by roughly a factor of three and suppressing duplicates almost entirely, demonstrating the promise of advanced ML architectures for next-generation particle tracking.

Fracture in polymer networks is strongly influenced by how network architecture and topology organize damage in space. Although these materials can sustain large deformations under homogeneous loading, they often fail in a brittle and flaw-sensitive manner once defects are present. Here we show that network heterogeneity is one key architectural parameter controlling this transition. Using a discrete mesoscale network model that explicitly resolves strand-level prestretch, force transmission, and irreversible bond scission, we demonstrate that heterogeneity in prestretch and strand lengths broadens crack-induced deformation, delocalizes bond rupture, and enlarges the fracture process zone. In polydisperse networks, increasing contour-length disorder broadens the prestretch distribution and systematically increases both toughness and the intrinsic length scale governing flaw sensitivity. Bimodal networks amplify this mechanism further through combined contrasts in prestretch and strand lengths, producing the largest damage zones and the highest toughness among the architectures studied. Inspired by the results, we derive a scaling estimate relating the emergent fracture-active length to the spatial range of crack-induced deformation and the logarithmic spread of strands' remaining stretch to rupture.

A multiple-access channel transmits messages from several senders to one receiver. For quantum outputs, the receiver must distinguish states depending on all messages, while tests for different decoding errors may not commute. In this paper, we give a self-contained account of simultaneous decoding, in which one joint measurement recovers the messages at the established achievable rates using independent codebooks. The proof combines Sen's tilted-subspace method with Cheng's analysis of the pretty-good measurement, a standard measurement for distinguishing quantum states. Auxiliary labels close to a common reference state separate the geometric directions associated with different errors. A Gram-matrix bound then allows separately chosen binary tests to certify the performance of one measurement. The labels are removed from the completed decoder, leading to a deterministic packing theorem that applies to finite state ensembles, including unequal priors. We develop the two-sender case first, with worked examples and figures, before treating any fixed number of senders. Sharper finite-error guarantees for the same decoder are developed separately, with sharp bounds for two specified steps of the analysis rather than a claim of globally optimal decoding. Applications recover known achievable rates for unassisted and entanglement-assisted classical communication, distributed classical compression with quantum side information, and coherent-state communication through a beamsplitter or passive multiport device. The common proof makes the geometric mechanism and its quantitative consequences available without repeating the construction for each application.

The ancient stellar populations and simple structure of the local dwarf spheroidal galaxies (dSphs) make them excellent laboratories for studying the chemical evolution of the early universe. In this paper, we fit one-zone galactic chemical evolution models to C, Mg, Si, Ca, Fe, Sr, Y, Ba, and Eu abundances in the dSphs Sculptor and Draco. By including the s- and r-processes in our model, we are able to place constraints on the timescale of r-process enrichment in these dSphs. We find that neutron star mergers cannot be the only source of the r-process in Sculptor and Draco, and that a prompt r-process source is required to explain the observed stellar abundances. When neutron star mergers are the only source of the r-process in our models, their minimum delay time must be just 14-16 Myr. The neutron-capture abundances in Sculptor and Draco can also be fit by models with a longer neutron star merger minimum delay time combined with a prompt r-process source that operates on the same timescale as massive star evolution, such as magneto-rotational supernovae. Additionally, the Sr and Y abundances in the dSphs set limits on the Sr and Y yields per r-process event. We find that theoretical r-process yields overestimate Sr and Y production by a factor of up to 100.

Short-wavelength spin waves are central to miniaturizing magnonic devices and to studying exchange-dominated magnetization dynamics. Yet the wave-vector range between roughly 30 and 300 radians per micrometre has remained difficult to access experimentally, posing challenges for both excitation and detection. This Perspective reviews recent advances in emerging measurement techniques and discusses prospects for their future development. Optical and microwave techniques are restricted to the vicinity of the Brillouin-zone centre. Inelastic neutron, electron and resonant hard x-ray scattering cover the full Brillouin zone but lack the energy resolution needed for low-frequency magnons at intermediate wave vectors. This Perspective examines five emerging approaches that are beginning to close this gap: Mie-enhanced Brillouin light scattering, colour-centre magnetometry, magnon momentum microscopy, extreme-ultraviolet transient-grating spectroscopy, and time-resolved scanning transmission x-ray microscopy. For each, we discuss the physical principle, demonstrated capabilities, current limitations and prospects for development. Compared side by side, the techniques give complementary access to magnon frequencies, local stray fields, real-space dynamics and momentum-space distributions, and they differ in their sensitivity to coherent and incoherent excitations. We therefore discuss the main advantages and use cases of each technique and consider the practical requirements for addressing different scientific questions. We highlight opportunities for further development, including higher sensitivity, improved spatial and temporal resolution, and broader frequency and wave-vector coverage. Together, these advances could enable, for example, systematic studies of nonlinear magnon interactions at nanoscale wavelengths and investigations of emerging magnetic materials such as altermagnets.

Projection-based model-order reduction (MOR) offers a promising approach for accelerating expensive full-order model (FOM) by constructing reduced-order models (ROMs) that retain the majority of FOM accuracy while significantly reducing the computational cost. However, conventional static ROMs, often following offline/online training strategy, can exhibit limited predictive capability for convection-dominated problems featuring strongly evolving physics such as shocks. Adaptive ROMs emerge as a promising alternative and address such limitation by dynamically updating the low-dimensional subspace during online simulation to track locally evolving system dynamics, thereby enabling accurate predictions even for shock-dominated flows. However, such online adaptation introduces additional computational overhead, and frequent basis and sampling-point updates can substantially reduce their computational advantage relative to their static counterpart. To reconcile this tradeoff, the current work introduces a self-adaptive MOR framework that dynamically constructs and deploys the most appropriate ROM formulation (either adaptive or static) on the fly according to the evolving characteristics of the solution. to achieve optimal computational efficiency while maintaining high modeling accuracy of the local physics during the online model execution. In this regard, the proposed framework seeks to exploit the advantages of both adaptive- and static-ROM approaches to achieve an optimal computational efficiency and predictive accuracy while reducing reliance on extensive offline training. The framework is developed and evaluated for modeling rotating detonation engines (RDEs), which provide a challenging test environment involving strongly convection-dominated, transient, and multiscale reacting-flow dynamics.

Asteroseismology of $\delta$ Sct stars has strong potential for determining the ages of young stars through individual mode fitting. We present a neural-network emulator trained on approximately 46 million rotating pulsation models. From stellar mass, metallicity, age, and equatorial rotation velocity, it predicts 12 classical observables, two asteroseismic scalars, and the p mode, f mode and low-order g mode frequencies for degrees $\ell=0$-3, including the individual $m$ components of rotationally split multiplets. We couple the emulator to nested sampling through a multivariate likelihood that propagates correlated emulator residuals, making full Bayesian posterior exploration practical. Applied to five $\delta$ Sct stars in the Pleiades observed by TESS, the framework gives mutually consistent individual asteroseismic ages of 107-117 Myr. Combining their age posteriors gives a cluster age of $113.3\pm4.5$ Myr (statistical), consistent with the $112 \pm 5$ Myr lithium-depletion-boundary age and the 110-160 Myr range from rotating-isochrone fitting. Together with spectroscopic $v\sin i$, the inferred equatorial velocities also provide post-fit inclination estimates. Separate perturbed-grid tests using 100 matched synthetic pairs per input-physics variation give median absolute age shifts of $2.1$, $2.3$, and $5.2$ Myr for $|\Delta f_{\rm ov}|=0.005$, $|\Delta\alpha_{\rm MLT}|=0.1$, and $|\Delta Y|=0.02$, respectively; the corresponding 90th percentile shifts are $6.5$, $7.6$, and $16.2$ Myr. These tests describe conditional population sensitivities, not a systematic uncertainty on the Pleiades age. Together, the cluster-age agreement and the scale of these input-physics sensitivities support $\delta$ Sct asteroseismology as a complementary age estimation method for young stars.

In Fermi's 1926 note, the expression assigned to the probability that all partial sums remain below a threshold is the complementary crossing probability. We obtain the correct probability from the same diffusion equation and locate the inconsistency in the final integration. We then state the limit for independent increments under the Lindeberg condition. A counterexample with smooth densities shows that small individual variances do not suffice to justify this limit. The probabilistic results are classical; the purpose of this note is to reconcile the stated event with the printed calculation and to make the sufficient hypotheses for the discrete limit explicit.