We investigate the effect of spatial exchange anisotropy on the spin-$1/2$ kagome antiferromagnet using Schwinger-boson mean-field theory. The anisotropy is introduced by strengthening the Heisenberg exchange along one set of nearest-neighbor bonds relative to the other two, and is controlled by a parameter $δ$ that measures the deviation from the isotropic limit. Incorporating the reduced lattice symmetry, we construct the corresponding projective-symmetry-group ansätze and focus on representative $0$- and $π$-flux states connected to the conventional $q=0$ and $\sqrt{3}\times\sqrt{3}$ kagome states. We find that anisotropy predominantly reconstructs the low-energy spinon sector, leading to a strong softening of the lowest spinon branch and a downward shift of the two-spinon continuum. At sufficiently large $δ$, the spinon gap closes at ansatz-dependent values, signaling an instability toward spinon condensation and the onset of magnetic order. From the soft Bogoliubov eigenmodes, we reconstruct the associated incipient spin textures and show that the resulting magnetic orders are intrinsically anisotropic, with suppressed moments on strongly coupled bonds and enhanced moments on more weakly connected sites. These results provide a microscopic picture of how exchange anisotropy drives the transition from kagome spin-liquid states to magnetic order, and offer a framework for interpreting recent experiments on anisotropic kagome materials, particularly titanium-based spin-$1/2$ compounds.

This paper is a continuation of the work in \cite{kimzhang2024} concerning Hele-Shaw flow with both drift and source terms. We prove that, in a local neighborhood, if the free boundary is Lipschitz continuous with a sufficiently small Lipschitz constant, then the free boundary is $C^{1}$. As a corollary, we also consider the 2D vertical Hele-Shaw (or one-phase Muskat) problem with an advection term. We show that, provided the initial data and the advection term are small and the propagation speed is large, the free boundary becomes uniformly $C^1$ after a finite time.

This paper considers the homogeneous Neumann initial-boundary value problem for Alopecia Areata chemotaxis model with weakly singular sensitivity. For any appropriately regular initial conditions,it is shown that the problem admits a global boundedness of classical solutions in two spatial dimensions. Moreover, through the explicit construction of Lyapunov functions, we establish that the globally bounded solution converges exponentially to a constant steady state. The paper concludes with numerical experiments that serve to visually illustrate and corroborate some of the theoretically derived findings.

If $H$ is a numerical semigroup (that is, a cofinite subset of the non-negative integers closed under addition), then the non-empty subsets of $H$ form a semigroup $\mathcal P(H)$ under the sumset operation induced by addition in $H$. Moreover, if $0 \in H$, then $\mathcal P(H)$ is a monoid with identity element $\{0\}$, and the family $\mathcal P_0(H)$ of all subsets of $H$ containing $0$ is a submonoid of $\mathcal P(H)$. We show that the automorphism group of $\mathcal P(H)$ is trivial, and the same holds for $\mathcal P_0(H)$ when $0 \in H$. The proofs blend ideas from combinatorics and semigroup theory.

We consider the problem of quantum channel certification to unitary, where one is given access to an unknown $d$-dimensional channel $\mathcal{E}$, and wants to test whether $\mathcal{E}$ is equal to a target unitary channel or is $\varepsilon$-far from it in the diamond norm. We present optimal quantum algorithms for this problem, settling the query complexities in three access models with increasing power. Specifically, we show that: (i) $Θ(d/\varepsilon^2)$ queries suffice for incoherent access model, matching the lower bound due to Fawzi, Flammarion, Garivier, and Oufkir (COLT 2023). (ii) $Θ(d/\varepsilon)$ queries suffice for coherent access model, matching the lower bound due to Regev and Schiff (ICALP 2008). (iii) $Θ(\sqrt{d}/\varepsilon)$ queries suffice for source-code access model, matching the lower bound due to Jeon and Oh (npj Quantum Inf. 2026). This demonstrates a strict hierarchy of complexities for quantum channel certification to unitary across various access models.

Continuous data assimilation (CDA) nudges observational data into governing equations to recover the underlying flow and improve predictions. Existing rigorous CDA analyses focus primarily on incompressible flows, yet no physical flow is perfectly incompressible. Approximating a slightly compressible flow with an incompressible model introduces non-negligible model errors. Data assimilation for compressible flows remains challenging due to strong nonlinearities and the presence of shocks. We design an algorithm that addresses the limitations of velocity-only nudging for slightly compressible flow. This work incorporates both velocity and pressure data from the slightly compressible flow and nudges both quantities into the incompressible Navier--Stokes equations. Our analysis shows that the model error decays exponentially in the initial error, with an asymptotic residual of order $\mathcal{O}(H)$, where H denotes the observation resolution. The analysis also identifies a scaling for the pressure nudging parameter $μ_1 = O(1/H^2)$ that ensures effective assimilation. We validate the theoretical results through a suite of numerical experiments: a convergence study confirming optimal rates, a modified Taylor--Green vortex benchmark demonstrating synchronization of energy, enstrophy, and pressure, and an acoustic wave propagation test that isolates the role of pressure nudging and achieves a $97.9\%$ reduction in pressure error relative to velocity-only assimilation. Together, these results provide a foundation for discrete error estimates and realistic compressible applications.

We investigate, both analytically and numerically, the scattering of quasi-one-dimensional quantum droplets from Pöschl-Teller potential wells and barriers. For attractive wells, we find a sharp transition between complete reflection and transmission at a critical incident velocity for both small and large flat-top droplets. The scattering interactions differ: small, soliton-like droplets form a spatially symmetric trapped mode at the critical velocity, showing their compressibility and coherence characteristics, while large droplets develop a spatially asymmetric trapped state, revealing incompressibility and internal structure. The critical velocity depends non-monotonically on atom number: it rises in the small, compressible-droplet regime, falls in the incompressible, flat-top regime, and turns at the crossover point. We also show that the reflectionless well generates a $π$-phase shift, strongly altering droplet-droplet collisions relative to free space. The persistence of a confined mode after collisions between trapped and incident droplets depends sensitively on their relative phase. For the repulsive barrier, we identify regimes of complete reflection, partial return, and full transmission, depending on incident velocity, barrier height, and particle number. Our predictions match direct numerical simulations in all cases.

We prove a generalization of the infinite quantum Ramsey theorem of Kennedy et al. (arXiv:1711.09526), showing that it follows from an archetypical "selective" pattern satisfied by certain families of projections in an infinite-dimensional Hilbert space.

Despite the operational importance of hot fixes, large-scale evidence on how they reshape routine maintenance workflows, particularly in the era of autonomous coding agents, remains limited. We analyse hot fixes present in over 61,000 GitHub repositories from the Hao-Li/AIDev dataset and find consistent patterns of urgency: reduced collaboration (typically a single contributor), smaller and more targeted changes (median 2-3 commits and files, with <10 line modifications), limited review (often fewer than two reviewers), and substantially fewer test file modifications than regular bug fixes, consistent with their urgency-driven character. Leveraging the same urgency contexts, we examine differences between human- and AI-agent-authored hot fixes, revealing over 10 distinct repair behaviours, thus offering insights into future human-automation collaboration for hot fixing. Our study is the first to empirically analyse hot fix code changes at scale using a repository-level operationalisation of urgency. The comparison of human and agentbehaviours delineates their distinct characteristics, providing a foundation for understanding hot fixing in real-world practice

Foreground removal remains an ongoing challenge in radio cosmology, and increasingly sensitive experiments necessitate more robust analysis techniques. In this work, we model simulated data from a single-dish intensity mapping experiment, and use the Gibbs sampling and Gaussian constrained realisation (GCR) techniques to draw samples from the posterior probability distribution of the model parameters. This allows for a separation of the foregrounds and 21 cm signal at the map level, as well as recovery of the 1-dimensional HI power spectrum to within statistical uncertainties. Despite the model consisting of over 2 million free parameters in the example presented here, these methods allow us to sample from the Bayesian posterior at a rate of $<30$ seconds per iteration. This framework is also resilient to frequency channel flagging (e.g. due to RFI excision), with the GCR steps effectively in-painting the missing data with statistically-consistent model realisations. The power spectrum is recovered accurately in the presence of strong foreground contamination and RFI flagging -- the estimate falling within $2σ$ of the true model in our example, similar to the commonly-used transfer function correction method. Statistical realisations of foreground and HI maps are also recovered, with associated uncertainties available from the full joint posterior distribution of all parameters.

For NVIDIA GPUs, CUDA is the primary interface through which applications orchestrate GPU execution, yet much of the logic that realizes CUDA operations resides in NVIDIA's closed-source userspace driver. As a result, the translation from high-level CUDA APIs to low-level hardware commands remains opaque, limiting both software understanding and performance attribution. This paper makes that command path visible. We recover the hardware command streams emitted by NVIDIA's closed-source userspace driver with full integrity by leveraging the recently open-sourced kernel driver, instrumenting the memory-mapping path, and installing a hardware watchpoint on the userspace mapping of the GPU doorbell register. This lets us capture complete command submissions at the moment they are committed. Using this methodology, we present two case studies. For CUDA data movement, we identify the DMA submission modes selected by the driver and characterize their raw hardware performance independently of driver overhead through CUDA-bypassing controlled command issuance. For CUDA Graphs, we show that the reduced launch overhead in newer CUDA releases is associated with a smaller command footprint and a more efficient submission pattern. Together, these results show that command-level visibility provides a practical basis for understanding and optimizing GPU middleware behavior, improving performance interpretation, and informing future hardware--software co-design for CUDA and related accelerator stacks.

The layered delafossite-like antiferromagnet AgCrSe$_2$ is a superionic conductor at high temperatures and has been reported to exhibit anomalous Hall behavior and Kondo physics at low temperatures. These extraordinary transport properties have been established almost exclusively on single crystals grown by chemical vapor transport, raising questions about the role of growth-induced off-stoichiometry. Using elemental analysis, single-crystal X-ray diffraction, and magnetization measurements, we show that such crystals are indeed systematically off-stoichiometric, with a general composition of Ag$_{1-x}$Cr(Se$_{2-y}$Cl$_y$) ($x \approx y \approx 0.08$) arising from the use of CrCl$_3$ as a transport agent. This off-stoichiometry manifests in altered magnetic properties, most notably a suppressed Néel temperature of 46\,K compared to 58\,K in stoichiometric polycrystalline samples prepared by solid-state synthesis. By optimizing an Ag/Se self-flux growth method, we obtained large single crystals of AgCrSe$_2$ that recover the magnetic transition temperature and saturation field of stoichiometric powder samples. These results establish self-flux growth as a route to high-quality stoichiometric AgCrSe$_2$ single crystals and provide a reliable platform for reassessing whether the reported anomalous transport phenomena are intrinsic or arise from off-stoichiometry.

The 21cm emission line from neutral hydrogen (HI) contained within galaxies provides a way to make accurate spectroscopic redshift determinations in the radio part of the spectrum. Large radio arrays such as SKA-MID are coming online that will have the sensitivity and survey time required to catalogue hundreds of thousands to millions of HI galaxies, opening up the possibility of studying the cosmological large scale structure using this technique. The expected number counts and clustering properties of the galaxies are still quite poorly understood however. We use three different simulated galaxy catalogues to predict the properties of the HI galaxy distribution that SKA-MID will be able to observe, along with estimates of the error on these predictions due to modelling uncertainty. The simulations in question are from S$^3$-SAX (semi-analytic models based on the Millennium dark matter-only simulation); GAEA (an updated semi-analytic model partially calibrated on hydrodynamical simulations); and IllustrisTNG (a hydrodynamical simulation). We present predictions for galaxy number counts as a function of sensitivity cut and redshift, and use these to forecast the cosmological performance of a proposed SKA-MID cosmological survey. Finally, we fit a halo occupation distribution model to low-redshift angular correlation functions to constrain clustering properties of multiple sub-volumes of the simulations to gain insight into the expected variation (sample variance) over smaller survey areas.

Observing the Epoch of Reionisation using 21cm radio interferometry has proven to be a challenging task. Extraction of the extremely faint redshifted signal is complicated by the presence of bright foregrounds, radio frequency interference (RFI), and systematic artefacts. We discuss the challenge of accounting for systematic effects, particularly cable reflections, that appear in the visibility data obtained from 21cm interferometers. Cable reflections cause attenuated copies of the foreground signal to appear outside the 'foreground wedge' region in which foreground contamination is supposed to be localised. We build on the hydra-pspec Gibbs sampler to implement a model of the systematics as a multiplicative effect in delay-fringe rate space. We include this model in the inference of the joint posterior distribution, in addition to the 21cm signal, its power spectrum, and foregrounds. This allows the systematics contribution to be marginalised, rather than filtering it out and causing additional signal loss. We demonstrate the method on simulated visibility data for a single baseline, showing that the 21cm delay power spectrum can be recovered well regardless of the location of the systematics in delay-fringe rate space. Our implementation is suitable for modelling other multiplicative factors on the visibilities, e.g. residual gain errors.

Accurate, localised rainfall information is essential for applications such as agricultural planning, climate risk assessment, and water resources management. Gridded climate products provide rainfall information over large areas but can lack the accuracy needed at local scales, often requiring bias correction before use in local impact studies. Bias correction of daily rainfall is particularly challenging due to its complex characteristics. Local intensity scaling (LOCI) and quantile mapping (QM) are two widely used bias correction methods which adjust both rainfall frequency and intensity, but do not account for the temporal structure of daily rainfall. This can lead to biases in the representation of wet and dry spells. This study proposes integrating a two-state first-order Markov chain directly into existing bias correction methods through state-dependent rain day thresholds and rainfall adjustments, aimed at improving the temporal structure of rainfall. Two implementations of this framework are presented: Markov chain local intensity scaling (MC LOCI) and Markov chain quantile mapping (MC QM). The proposed methods were applied to AgERA5 reanalysis data with rainfall data from five stations in Zimbabwe. Results showed that the Markov chain methods outperformed LOCI and QM by improving the representation of rainfall persistence, onset, and wet and dry spell characteristics, while maintaining improvements in rain day frequency and overall rainfall statistics. These results demonstrate that the proposed methods could be beneficial for applications such as crop simulation, hydrological modelling and other applications which rely on accurate representation of rainfall sequencing.

We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow problems, the nonlinearities inherent in potential-based networks introduce significant new challenges. We address these challenges through intricate reductions to classical combinatorial optimization problems, such as (constrained) shortest path problems, enabling the application of well-established algorithmic techniques to compute exact and approximate solutions efficiently. Finally, we complement these algorithmic results with matching complexity results concerning the hardness and non-approximability of the considered problem variants.

The Standard Model (SM) predicts the universality of lepton couplings with the electroweak gauge bosons. Semileptonic decays of $b$-hadrons provide a powerful framework for testing the SM and probing possible New Physics effects. In particular, the processes mediated by charged-current interactions benefit from a relatively large branching fractions and theoretically well-controlled hadronic matrix elements. This contribution presents three recent results from the LHCb experiment: the first measurement of the ratio of branching fractions $\mathcal{R}(D^{**})$ using $B^{-} \to D^{**0} τ^{-} \barν_τ$ decays, the determination of the branching fraction for $Λ\to p μ^{-} \barν_μ$ and the extraction of form-factor parameters from $B^0 \to D^{*-} μ^{+} ν_μ$ decays.

The study of Entanglement Asymmetry has emerged in recent years as a powerful tool to characterise the symmetry properties of quantum states in relation to a given charge operator through the lens of entanglement. While extremely powerful and general, the standard definition of asymmetry introduces significant non-Gaussian features in free-fermionic systems, leading to certain analytical limitations. In this work, we introduce an asymmetry measure that remains strictly within the Gaussian manifold and analyse its properties. In particular, we show that it quantifies the minimal distance between a Gaussian state and the manifold of symmetric Gaussian states. We further demonstrate that this measure captures the established dynamical signatures of entanglement asymmetry, such as the Mpemba effect, symmetry restoration, and the lack thereof. The Gaussian structure allows these novel asymmetry measures to be computed exactly using correlation matrix techniques, and to be described asymptotically through the quasiparticle picture. We also comment on the possibility of using charge fluctuations to characterise the asymmetry of a Gaussian state.

We study the entropy solution for a class of systems of nonlocal conservation laws in which the convective flux is convoluted with a kernel in both spatial and temporal variables. This formulation models the flux dependence on the solution within its spatial neighbourhood (nonlocal in space) as well as on prior states in time (nonlocal in time), thereby incorporating memory effects. In addition, employing a convergent finite volume approximation, the existence of the entropy solution is discussed. The uniqueness of such entropy solutions is also established. In addition, we analyze the asymptotic behaviour of the solutions as the support of the temporal convolution kernel shrinks, demonstrating the "memory-to-memoryless" effect and convergence to the entropy solution of the corresponding nonlocal conservation law without memory (i.e., nonlocal only in space). Convergence rate estimates are derived. In addition, the proposed numerical approximations are shown to be asymptotically compatible with this passage to the memoryless limit by deriving the corresponding asymptotic convergence rate estimates. The analysis is carried out in a very general setting, without imposing any geometric restrictions such as the convexity of the spatial and temporal convolution kernels, unlike the existing literature on the asymptotic analysis of nonlocal-in-space only conservation laws. To the best of our knowledge, this provides the first convergence and asymptotic analysis for finite volume schemes applied to nonlocal conservation laws with memory. Numerical experiments are included to illustrate the theory.

This is a brief overview of the connection between neutron skin thickness in finite nuclei and the equation of state of neutron-rich matter, with applications to neutron stars. Multiple experimental probes are discussed, including dipole polarizability, parity-violating electron scattering, heavy-ion fragmentation, quasi-free scattering, and ultraperipheral collisions. A consistent picture emerges from Bayesian analyses combining experimental data and energy density functionals, providing constraints on the symmetry energy and its slope.

Africa is the primary source of cyclonic vortices over the tropical Atlantic. Over both land and sea, these vortices are entwined with deep convective activity, with the majority being African Easterly Wave troughs. Their convective interactions have downstream impacts, since the same vortices provide the seed population for Atlantic basin tropical cyclone (TC) genesis. Understanding the dynamics of East Atlantic seed populations, particularly the processes that distinguish vortices which undergo cyclogenesis, is crucial for understanding the formation of Atlantic hurricanes and model representations of their populations. Here we investigate these questions in three one-year, atmosphere-only global km-scale Met Office Unified Model simulations. We use objective tracking algorithms to independently identify seed vortices, easterly waves, TCs, and Mesoscale Convective Systems (MCSs), benchmarking against reanalysis and satellite-derived climatologies. Despite the simulations displaying comparable continental vortex populations, we show that the highest-resolution simulation with explicit convection produces fewer, weaker hurricanes than coarser, parameterised counterparts due to a failure to amplify vortices crossing the West African coastline. We identify a failure to maintain strong top-heavy mass flux profiles experienced by seeds as the primary cause, demonstrating profiles' roles in low-level circulation development through vortex stretching. Using MCS tracks, we show that systematic differences in convective organisation between the simulations can explain the differences in mass flux profiles, and thus vortex evolution. Deficiencies in the explicit simulation stem from underestimation of MCS stratiform components, a bias shared with other explicit convection models; and a latitudinal offset between offshore seed vortex and MCS trains.

The pure-loss channel is a fundamental model for describing noise in bosonic quantum platforms. It is characterised by a single parameter, the transmissivity, which quantifies the fraction of the input energy that reaches the output of the channel. In realistic scenarios, however, such as free-space quantum communication, the transmissivity is not fixed but fluctuates from one channel use to another. In this setting, the overall channel is effectively described as a convex combination of pure-loss channels, known as a fading channel. Despite its practical relevance, the quantum Shannon theory of the fading channel has remained largely unexplored. Here, we address this gap, specifically investigating degradability, anti-degradability, entanglement breakingness, and capacities of the fading channel. Of particular relevance to practical quantum-internet applications, we prove that entanglement distribution and quantum key distribution can always be achieved at a strictly positive rate over any fading channel, no matter how noisy it is or how strongly the transmissivity fluctuates, provided the channel is not completely noisy. Moreover, we prove that thermal states, which are optimal for a broad class of static bosonic Gaussian channels, fail to achieve the entanglement-assisted classical capacity of fading channels: non-Gaussian Fock-diagonal states strictly outperform all Gaussian encodings. Most strikingly, we identify regimes where the coherent information of thermal inputs vanishes, while optimized non-Gaussian states achieve strictly positive values, thereby activating the channel for quantum communication. For a paradigmatic binary fading model we establish this result analytically, deriving the exact capacity-achieving state in closed form. For general fading distributions, we design an iterative variational algorithm to optimize the coherent and mutual information.

This study presents a versatile ontology and a useful codification scheme for describing all kinds of engineered living materials (ELMs). The different components of the ontology, namely: families according to the taxonomy for ELMs, industrial applications and synthesis or processing methods, are systematically organized, enumerated, classified, codified and explained. The methodic application of the ontology to a set of 100 relevant examples of ELMs helps to demonstrate its utility and adaptability to many different types of ELMs with a wide range of industrial applications and obtained through numerous synthesis and processing methods. This proves that the developed ontology and codification schemes, with the glossary provided to support its implementation and application, can serve as a comprehensive classification tool for the emergent field of ELMs. Furthermore, the usability of the ELMs ontology and codification by a generative artificial intelligence (AI) is explored and validated by different means, checking that both natural language and the codification are understandable for describing ELMs, verifying that the generative AI adequately codifies examples of ELMs according to the ontology, and validating the synergic applicability of the ontology and codification with generative AI tools for illustrating novel ELMs and supporting their conceptual design. This study is expected to provide a universal language to facilitate communication in the ELMs field and to foster the discovery of new ELMs and related innovations, hoping it may accelerate scientific and technological discoveries.

Moiré superlattices of transition-metal dichalcogenides (TMDs) host strongly interacting Bose-Fermi mixtures in which bosonic excitons coexist with correlated electron lattices. Using ultrafast, time- and energy-resolved photoluminescence (PL) and reflectance microscopy, we show that strong exciton-electron and exciton-exciton repulsion can enable collective ballistic exciton transport in a WSe$_2$/WS$_2$ heterobilayer. The ballistic transport is energy-selective: repulsive interactions drive excitons into a higher moiré exciton band, where enhanced intersite hopping enables rapid spatial expansion. Correspondingly, the exciton mean-squared displacement (MSD) exhibits a quadratic time dependence ($\propto t^2$). This ballistic expansion is enhanced at fractional electron fillings where the electrons form generalized Wigner-crystal (GWC) orders. Afterwards, the system transitions into a mixed electron-exciton Mott state as Auger recombination and density depletion conclude the ballistic expansion. A one-dimensional Bose-Fermi Hubbard model solved using density-matrix renormalization group (DMRG) qualitatively reproduces the measured exciton transport and time-dependent response. It further confirms that strong cross-species interactions allow the electron crystal to perforate the exciton Mott background, accelerating its melting and enhancing exciton motion. Our results establish moiré TMDs as highly tunable platforms for realizing strongly interacting Bose-Fermi mixtures, which we employ here to demonstrate real-time control of intertwined bosonic and electronic order and to establish a route to the exciton insulator-fluid transition.

Differential-difference matrix Lax representations (Lax pairs), gauge transformations, and discrete Miura-type transformations (MTs) belong to the main tools in the theory of (nonlinear) integrable differential-difference equations. For a given equation, two matrix Lax representations (MLRs) are said to be gauge equivalent if one of them can be obtained from the other by applying a matrix gauge transformation. Generalizing and extending several previous works on MLRs and MTs, we present new results on the following problems: - When and how can one simplify a given MLR by means of gauge transformations? - How can one use MLRs and gauge transformations for constructing MTs? - A MLR is called fake if it is gauge equivalent to a trivial MLR. How to determine whether a given MLR is not fake? We consider the general (1+1)-dimensional evolutionary differential-difference case when a MLR can depend on any shifts of dependent variables and can be non-autonomous. As applications and illustrations of the presented general theory, we construct several new two-component integrable equations (with new MLRs) connected by new MTs to known integrable equations from the papers [S. Konstantinou-Rizos, A.V. Mikhailov, P. Xenitidis, J. Math. Phys. 2015], [E. Mansfield, G. Mari Beffa, Jing Ping Wang, Found. Comput. Math. 2013]), including non-autonomous examples.

We consider the free boundary problem for relativistic plasma--vacuum interfaces in two and three spatial dimensions. The plasma flow is governed by the equations of ideal relativistic magnetohydrodynamics, while the vacuum magnetic and electric fields satisfy Maxwell's equations. The plasma and vacuum magnetic fields are tangential to the interface, which moves with the plasma flow. This yields a nonlinear, multidimensional hyperbolic problem with a free boundary that is characteristic of variable multiplicity. We identify a quantitative stability condition and establish the linear stability of three-dimensional relativistic plasma--vacuum interfaces in the sense that the variable-coefficient linearized problem satisfies energy estimates in anisotropic Sobolev spaces. In estimating tangential derivatives, we exploit an intrinsic cancellation effect to convert the boundary term into an instant integral. We then separate the estimate involving spatial derivatives from that involving time derivatives, so that the instant integral can be mainly absorbed by the instant energy under the stability condition. Moreover, we prove the local-in-time existence and uniqueness of solutions to the nonlinear problem in two-dimensional space, provided that the plasma and vacuum magnetic fields do not vanish simultaneously at any point of the initial interface. The proof combines the solvability and tame estimate of the linearized problem with a suitable modified Nash--Moser iteration. In particular, to establish its solvability, the two-dimensional linearized problem is reduced to a transport equation for the interface function and a hyperbolic boundary problem with maximally nonnegative boundary conditions.

We consider a system of two coupled first-order linear hyperbolic partial differential equations modeling heat transport in a counter-flow heat exchanger: one equation describes the transport of a hot fluid, and the other the transport of a cold fluid in the opposite direction. For this system, we design a boundary observer that uses only the temperature of the cold fluid measured at one boundary. Our approach is spectral: by assigning the spectrum of the operator governing the observation error dynamics to a prescribed region within the open left-half complex plane, we can freely tune the convergence rate of the observation error to zero in the $L^2$ norm. The main technical contribution is the proof that spectral stability, that is, the location of the spectrum in the open left-half plane, is equivalent to $L^2$ exponential stability of the origin for the observation error dynamics. This equivalence is established by showing that the operator governing the observation error dynamics satisfies the so-called spectral mapping property.

Non-local conductance experiments using tunnel junctions can provide valuable spectroscopic information on both the transport and relaxation of quasiparticles in superconductors, as these techniques directly probe the quasiparticle charge and energy imbalance even at mK temperatures. In this work, we employ mesoscopic three terminal Cu and Al NIS devices to study non-local quasiparticle transport over length-scales on the order of the superconducting coherence length in this regime. Via a dual-bias scheme, which utilizes detector biases both above and below the superconducting gap, we are able to extract the effect of quasiparticle energy imbalance via its impact on the self consistent pair potential by symmetry considerations. We observe non-local conductance features due to pair-breaking which are anti-symmetric with respect to the polarity of the voltage bias, with a sharp onset during single electron tunneling at energies around $3Δ$. We compare these findings with quasiclassical simulations including inelastic effects to obtain estimates of the energy dependent inelastic scattering time. In addition, we demonstrate kinetic effects due to a large applied supercurrent which can also be captured in this formalism and decomposed with respect to the particle-hole symmetry and supercurrent direction, and discuss further opportunities for the advancement of this method.

We report the largest trapped-ion hardware demonstration of lattice protein-folding optimization to date, using bias-field digitized counterdiabatic quantum optimization (BF-DCQO) on a fully connected 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. Six peptide sequences with 14-16 amino-acid residues are encoded using a coarse-grained tetrahedral lattice model, yielding higher-order spin-glass Hamiltonians with long-range interactions involving up to five-body terms and mapped to 46-61 qubits. The resulting instances are demanding for near-term quantum hardware because low-energy configurations must satisfy backbone-geometry constraints while optimizing dense residue-contact interactions. BF-DCQO uses a non-variational bias-feedback mechanism, where low-energy samples from each round define longitudinal fields that guide subsequent quantum evolutions. Across the studied instances, BF-DCQO shifts raw sampled energy distributions toward lower energies than uniform random sampling, with the strongest improvements appearing in residue-contact variables. To preserve this signal, we introduce a consensus-based post-processing pipeline that combines quantum-learned contact information with feasible backbone geometries. The resulting hybrid workflow reaches the classical reference energy in multiple instances and improves over the corresponding random-seeded pipeline. These results show that BF-DCQO can generate structured samples for dense protein-folding Hamiltonians at previously unexplored trapped-ion scales.

The nanohertz gravitational waves (GW) observed by pulsar timing arrays may originate from a cosmological first-order phase transition (PT) at $\sim$ 100 MeV. Taking this possibility seriously motivates the question: why 100 MeV? We point out that a PT at exactly those scales is predicted by the generation of the baryon asymmetry from a dark asymmetry via resonant neutron-dark matter oscillations, and we prove that this PT can induce an observable GW signal compatibly with all experimental constraints. This proposal predicts dark matter self-interactions close to their observational upper limits and lowers the maximal expected mass of neutron stars. Independently of GW, this baryogenesis mechanism is tested by searches for missing-energy at the LHC and for neutron decays. We keep the model consistent with big-bang nucleosynthesis by adding heavy neutral leptons below 100 MeV, which generate neutrino masses and can induce further experimental tests.