Papers

Motivated by the work of M. L. Lapidus and M. van Frankenhuisjen on fractal explicit formulas for generalized fractal strings, we develop in this paper a distributional fractal Taylor's formula with error term and an exact distributional fractal Taylor series representation for generalized fractal strings. The explicit formulas that the aforementioned authors developed provide a way of expressing a generalized fractal string $\eta$ in terms of the underlying fractal complex dimensions, under suitable growth assumptions on its geometric zeta function, $\zeta_{\eta}$, known as the languidity assumptions. This involves a sum indexed by the complex dimensions of the generalized fractal string, summing over all residues of $\zeta_{\eta}$, multiplied by the Mellin transform of a tempered or Schwartz test function $\phi$, denoted by $\widetilde{\phi}$. Under languidity assumptions, there is an error term present. Under stronger assumptions, that is, in the case of strong languidity, no error term is present and the resulting fractal explicit formula is said to be exact. In this paper, we express the residue term in the fractional distributional explicit formulas as the fractional $(-\omega)^{\mathrm{th}}$-ordered distributional derivative of the Dirac $\delta$ distribution, denoted by $Y_{\omega}$, applied to modified test functions of the form $\phi(x) \ln^{k-1}(x)$, where $k$ runs from $1$ to the multiplicity of the pole $\omega$ of $\zeta_{\eta}$. The coefficients in this sum are written in terms of the coefficients in the principal part of the Laurent expansion at $\omega$ of the geometric zeta function $\zeta_{\eta}$, multiplied by the gamma function evaluated at $\omega$. The results obtained in this paper contribute to the broader program of characterizing fractals in terms of fractal Taylor series expansions involving their underlying fractal complex dimensions.

While the gravothermal collapse of self-interacting dark matter (SIDM) halos provides a compelling mechanism for seeding supermassive black holes (BHs), the post-collapse macroscopic co-evolution of the BH and its host halo remains largely unexplored. In this paper, we introduce a novel N-body framework to dynamically model the dark matter accretion onto the central BH. By bracketing the accretion rate with two complementary phenomenological schemes—a `multi-round core-collapse' scenario and a `continuous accretion' scenario—we establish bounds on the BH mass growth trajectory. We find that the BH mass reaches $5\%-12\%$ of the total halo mass within $\lesssim2$ Gyr post-collapse. Concurrently, this sustained mass depletion drives a `gravothermal supply chain' that forces outer dark matter inward, severely depleting the inner halo density ($\lesssim 2r_s$). This unique structural imprint qualitatively matches the recently detected anomaly in the strong lens JVAS B1938+666 (detection V), where the best-fit lens model consists of an unresolved central point mass and a shallow, uniform-surface-density extended disk, offering a distinct observational signature for SIDM-seeded BHs.

Studies of dust growth in molecular clouds often prescribe the collapse history, leaving unclear how magnetic regulation of core formation shapes dust evolution and its observable and non-ideal MHD signatures. We address this problem by performing one-zone dust evolution and ionization calculations along time-dependent density and magnetic-field histories extracted from three-dimensional non-ideal MHD simulations of core formation through filament fragmentation. A stronger initial magnetic field delays contraction and thereby gives dust grains more time to grow at a given density. In our models, this delayed contraction leads to mass-weighted mean dust sizes of $1.2\,\mu\mathrm{m}$ and $3.1\,\mu\mathrm{m}$ at $n_{\mathrm{H}}=10^6\,\mathrm{cm^{-3}}$ for $B_{\mathrm{ini}}=20$ and $50\,\mu\mathrm{G}$, respectively. The associated depletion of very small dust grains reduces the adsorption of charged particles onto dust grain surfaces and lowers the conductivity: relative to models without dust growth, the ionization fraction increases from $\sim10^{-9}$ to $\sim10^{-8}$, the ambipolar resistivity increases, and the ion–neutral drift velocity rises to several $\mathrm{m\,s^{-1}}$ in the weak-magnetic-field model and approximately $10\,\mathrm{m\,s^{-1}}$ in the strong-magnetic-field model. These drift velocities remain below the observationally suggested range of $30$–$100\,\mathrm{m\,s^{-1}}$, indicating that still stronger magnetic fields may be required. The evolved dust populations also attain single-scattering albedos of order $\omega_\lambda\sim0.8$ at $3.6$–$4.5\,\mu\mathrm{m}$, with the stronger field shifting the onset of efficient infrared scattering toward lower densities. These results demonstrate that the magnetically controlled collapse timescale, rather than density alone, links dust growth to ionization, ambipolar diffusion, and infrared scattering in prestellar cores.

On a seven-compound drug-response model, warm-start quantum approximate optimization (QAOA) on IonQ Forte-1 returned valid assignments more often than random bitstrings, but this alone did not show effective optimization. Ideal QAOA raised optimum probability above uniform feasible sampling in only four of twelve reference circuits. Hardware often fell below its own noiseless circuits, while greedy search solved all hardware models within 200 objective evaluations. Expanded simulations showed a gain over feasible sampling in 28 of 35 CAMA-1 panels and none of four 647-V panels. Annealing solved all these panels in every seed. A Grover mixer preserved feasibility and improved optimum probability over feasible sampling in all ten tested models. We analyzed 25 completed tasks containing 5,300 shots from 18 circuits and 14 instances. The encodings use 6-35 qubits and at most 4,900 feasible assignments, which we enumerated to establish exact optima. Noiseless references now cover both the original six circuits and six wider circuits. At 35 qubits, with 4,900 feasible assignments, ideal feasibility was 35.85%, compared with 7 of 200 valid hardware outputs. Its ideal optimum probability was below both sampling controls. The circuits sample assignments in a model built from measured single-agent and pairwise responses.

Structural nonlinearity enables nonlinear input–output mappings to emerge from otherwise linear wave dynamics. Repeated interactions with an input-encoded structure can enhance such mappings, but finite-depth implementations restrict the accessible functional order. Here we show that recurrent scattering in a resonant cavity provides a distinct regime for structural nonlinearity. Repeated interactions are coherently accumulated into a non-polynomial response to structural perturbations. The resulting mapping naturally takes a Kolmogorov–Arnold form: perturbation-induced resonance shifts realize the inner univariate mappings, while the resonant spectral response provides the outer mapping. We identify two complementary physical controls of representation capacity: the resonance linewidth governs the functional richness within each branch, whereas combining multiple branches expands the accessible function space. Microwave-cavity measurements validate the two-stage mapping and demonstrate a two-branch nonlinear computation through XOR classification. Our results connect recurrent resonant scattering with controllable non-polynomial computation in linear wave systems.

We study a five-dimensional realization of endothermic dark matter motivated by the recent high-recoil LUX-ZEPLIN event. A pseudo-Dirac Standard-Model singlet fermion is localized in the extra dimension and couples to a bulk $U(1)_D$ gauge field. The same localization that suppresses a distant-brane Majorana operator and generates the inelastic splitting also controls the couplings to the Kaluza–Klein (KK) dark-photon tower, producing a localization-filtered mediator propagator. We organize the phenomenology around two representative mass–splitting points: an LZ benchmark, $m_\chi=1.10~\TeV$ and $\delta=365~\keV$, and an IceCube-motivated comparison point, $m_\chi=1.08~\TeV$ and $\delta=566~\keV$. The latter is used only to compare terrestrial and solar kinematics; the published IceCube bound is Higgsino-specific and is not directly imposed on our singlet KK model. At the LZ benchmark with $R^{-1}=0.30~\GeV$ and $m_0=0.10~\GeV$, the KK tower enhances the high-recoil xenon rate by a factor of about four relative to a single dark photon at fixed microscopic coupling. The LZ point lies just below the terrestrial halo speed ceiling, whereas the $566~\keV$ comparison point is inaccessible to ordinary xenon scattering and instead lies in a kinematic regime accessible to solar capture; any neutrino constraint on the present singlet model remains dependent on its capture and annihilation dynamics. The characteristic prediction of the extra-dimensional construction is therefore a correlated interplay of localization, KK spectral distortion, and inelastic kinematics.

Recent advances in the variational quantum eigensolver (VQE) have strengthened its promise for molecular electronic-structure calculations on near-term noisy intermediate-scale quantum (NISQ) devices. However, barren plateaus (BPs) remain a major obstacle to scaling VQE, as vanishing gradients can severely obstruct optimization at large scale. While most BP studies focus on randomly initialized circuits and global gradient behavior, practical quantum chemistry VQE typically uses chemically motivated initializations and local optimization around HF- or MP2-derived states. Although chemically informed initializations are widely expected to improve VQE trainability, how they mitigate local barren plateaus remains unclear. We therefore study the occurrence of local barren plateaus in molecular UCCSD-VQE, considering both chemically motivated initialization points and iterates along the corresponding optimization trajectories. In the benchmarks considered here, chemically initialized starting points and variational trajectories show polynomial decay of local gradient variance with system size instead of the exponential BP-like decay observed for random controls, indicating that chemical initialization mitigates barren plateaus in the local optimization regions and highlights the trainability advantage of chemically motivated VQE strategies.

Residual-error preservation (REP) provides a sufficient rule for constructing concatenated composite pulses that compensate multiple systematic errors. We show that local REP is not necessary: deviations from REP can cancel across the full sequence. Using first-order error generators, we derive a necessary and sufficient condition for concatenation to retain the robustness of an outer sequence. A simple sufficient condition is that all inner pulses rescale the corresponding elementary error generators by a common real factor, not necessarily unity. We illustrate this principle using pulse-length and off-resonance errors, two systematic error models commonly considered in magnetic resonance. Short CORPSE and SCROFULOUS each compensate one error without preserving the other locally. Combining these inner pulses with suitable equal-rotation-angle outer sequences yields simultaneous first-order compensation of both errors, extending concatenated composite-pulse design beyond local REP.

Ideality factor of a diode will depend on the location of the plane of maximum recombination within the diode's depletion region. It will have a minimum of one, but can range up to infinity depending on placement of the plane. Case studies analyzed in this work demonstrate better agreement with experimental data from GaN-based p-i-n diodes.

Diffusion at interfaces governs how materials and devices form, evolve and function. It is usually measured through smooth concentration profiles and bulk transport coefficients, which average over the discrete atomic rearrangements. At nanoscale interfaces only a few atomic layers wide, however, such coarse-graining obscures the local three-dimensional (3D) atomic transport, and scalar diffusion coefficients cannot fully describe species-, layer- and facet-resolved redistribution. The essential observable is the discrete 3D redistribution of atoms themselves, beyond an averaged profile. Here we combine micro-electro-mechanical systems (MEMS) pulse-quench heating with atomic electron tomography (AET) to reconstruct five 3D atomic configurations of the same coherent Pd@Pt core-shell nanoparticle, each corresponding to a well-defined thermal state. Species-conserving one-to-one assignment links neighbouring configurations, and labelled reference simulations correct the displacement bias caused by indistinguishable same-species atoms. The corrected Pd diffusivities follow Arrhenius behaviour, giving an apparent activation energy of 1.10 eV, consistent with migration-limited vacancy-mediated transport. Atomic-layer transition statistics further show that increasing 3D mobility can coexist with declining net chemical transfer and reveal facet-dependent pathways hidden by the scalar diffusivity. Together, these measurements establish a 3D atom-by-atom framework that connects identity-corrected mobility to species-, layer- and facet-resolved transport at buried nanointerfaces.

The transport of bubbles along a curved superhydrophobic surface is not governed by buoyancy alone, but also by the interaction between the geometric confinement, the capillary and contact-line resistance, and the hydrodynamic resistance. We systematically investigated the capillary number ($Ca$) and Bond number ($Bo$) of the transported bubble, as well as the size of the rod relative to the bubble. An analytical force-balance model was developed to predict transport velocity, accounting for buoyancy, hydrodynamic drag, and capillary resistance. The transition from transport to detachment was identified. The experiments were carried out sequentially and supplemented by axisymmetric numerical simulations to investigate wake-induced interactions between bubbles. Bubble transport is strongly influenced by rod inclination and the bubble-to-rod size ratio, demonstrating that curvature-induced confinement alters the balance between driving and resistive forces. The analytical model captured the experimental trends with deviations of less than 10% in most cases. The bubble detaches from the inclined rod at a critical Bond number that depends on rod diameter, facilitating the development of a transport regime map. The study also found that the motion of successive bubbles is strongly coupled. When a following bubble enters the wake of a preceding bubble, it speeds up and attains a higher capillary number than the leading bubble. Both experiments and numerical simulations consistently reproduce this wake-mediated acceleration, which shows that bubble transport is governed by both the force balance on individual bubbles and the hydrodynamic interactions between adjacent bubbles. These findings form the basis for controlling bubble transport, detachment, and collective motion on superhydrophobic interfaces.

Classical analyses of microwave instability are built upon the longitudinal adiabatic approximation, which assumes that the bunch length remains constant around the storage ring. However, in a storage ring with small global phase slippage, the bunch length can vary around the ring and some particles can experience head-tail exchange due to the partial phase slippage and transverse-longitudinal coupling. Our theoretical study reveals that these effects can be beneficial for suppressing microwave instability. A new microwave instability threshold evaluation method has been correspondingly proposed to account for these effects. Here we present the first experimental evidence supporting our theoretical analysis. The measurements confirm that the microwave instability threshold can be increased by a factor of up to six compared to the classical prediction in our cases. Our results can also provide practical guidance for the design of extremely short bunch storage rings.

We develop a probabilistic construction of Toda field theory correlators from the Coulomb gas representation. Reinterpreting $n$-point functions of primaries as $w$-moments of random variables with respect to a Gaussian measure, we derive constraints on the Toda momenta and coupling constant. $L^2$ and $L^p$ convergence conditions for the associated random variables, triviality constraints on the correlators, and local integrability conditions for the cross-moments are derived. These constraints define an extended region of convergence for the Toda correlators and provide a systematic, probabilistic interpretation of the Seiberg bounds. We proceed to analytically continue the moment indices by employing a Mellin-Barnes representation of the random variables. The local convergence boundaries become meromorphic local integrability divisors, and, in the semiclassical $b\to0$ limit, these divisors reconstruct the Liouville charge pole lattice. For $A_n$ Toda theory, we show that natural $W_n$-closure conditions in this semiclassical limit select rank-one, Virasoro-like submodules inside the full Toda theory. On these slices, the scalar integrability conditions reduce to Liouville-like divisors and recover the corresponding Toda charge pole lattices.

We investigate the discrete-time version of the Kuramoto model with phase lag, which comprises globally-coupled phase oscillators of distributed frequencies that are evolving under a nonlinear map. In the continuum limit of an infinite number of oscillators ($N\to \infty$), we derive the exact Frobenius-Perron equation for the time evolution of the single-oscillator probability density, and study linear stability of the incoherent state. Instability signals onset of synchronization. The corresponding synchronization threshold is obtained analytically for the case of a Lorentzian distribution of the oscillator frequencies. The threshold differs from that of the continuous-time Kuramoto model, reflecting the fundamentally different stability conditions for discrete-time maps and continuous-time flows. Beyond synchronization threshold, we observe several interesting nonlinear phenomena: Unlike the classical Kuramoto model, the discrete-time version exhibits periodic and chaotic states. Numerical simulations of the finite-$N$ system confirm the analytical prediction for the synchronization threshold, while highlighting breakdown of the celebrated Ott-Antonsen ansatz invoked to conveniently study the continuous-time Kuramoto model in terms of a low-dimensional description.

Excitons in atomically thin semiconductors are almost always probed through their optical signatures, because the short lifetimes of these transient quasiparticles are generally assumed to preclude electrical detection. Here we show that photoexcited excitons in monolayer tungsten disulfide produce a large, optically tunable permittivity at gigahertz frequencies, and that the effect provides a contact-free electrical route to imaging dark excitons at the nanoscale. Using laser-illuminated microwave impedance microscopy, we find that high-purity encapsulated flakes exhibit a purely dielectric response resonant with the exciton spectrum, whereas defect-rich samples are governed by conventional photoconductivity. Spatial mapping of diffusion and sublinear power dependence identify long-lived dark excitons as the dominant contributors, and first-principles modelling of exciton polarizability reproduces the measured susceptibility. Our results establish excitons as optically tunable dielectric elements and introduce microwave microscopy as a direct electrical probe of dark-exciton transport with sub-100 nm resolution.

The axion-photon coupling, crucial for experimental axion searches and tests of the strong CP solution, receives a substantial model-independent contribution $\mathcal C_{\rm QCD}$ from QCD dynamics. Next-to-leading-order chiral perturbation theory (NLO ChPT) in different frameworks has yielded puzzling discrepancies of up to $8\%$, motivating precise first-principles calculations. We present an independent lattice QCD determination using a method complementary to the recent background-field calculation. Computing pseudoscalar-to-two-photon three-point functions and exploiting anomalous Ward identities, we separate $\mathcal C_{\rm QCD}$ into an exact anomaly contribution and a light-quark-mass-suppressed correction. The latter is computed using domain-wall fermions, whose excellent chiral symmetry strongly suppresses discretization effects. Working on two near-physical $N_f=2+1$ ensembles with continuum extrapolation, we obtain $\mathcal C_{\rm QCD}^{\rm IS}=1.619(30)$ (isospin-symmetric), $\mathcal C_{\rm QCD}^{\rm IB}=0.347(22)$ (isospin-breaking), and $\mathcal C_{\rm QCD}=1.965(35)$ in total. While direct comparisons with published NLO ChPT predictions reveal apparent tensions, we identify their sources and show that the ChPT results can be reconciled with our lattice determination. Our result provides a first-principles benchmark for the QCD contribution to the axion-photon coupling and a quantitative test of competing ChPT descriptions.

Phase matching is a fundamental problem in nonlinear optics that is normally constrained by material dispersion. The limited operation wavelengths within phase matching window limits the application, including the precise metrology using Kerr combs. Demanding applications like compact optical clock and astronomical spectroscopy requires atomic reference around 800 nm, where the natural phase matching is challenging. Here we revisit the concept of cavity phase matching (CPM), and fully reveal its advantage to engineer artificial phase matching beyond material dispersion. With the access of CPM condition in a monolithic high-Q fiber Fabry-Pérot resonator featuring a macroscopic cavity length, we achieve low noise Kerr comb generation around 800 nm, within the power budget of a single-mode laser diode. Inside a pump-integrated package of 19 cm3, low phase noise of -125 dBc/Hz at 100 kHz offset frequency is achieved for a 10.1 GHz repetition rate. Most importantly, the generated Kerr comb has been directly referenced to rubidium atomic transition for long-term stable operation. This result not only opens a new way for Kerr comb generation at arbitrary wavelengths, but also can be generalized to any other nonlinear optical frequency conversion application.

We investigate collective chirped stimulated Raman adiabatic passage (STIRAP) in a pair of identical three-level atoms using a symmetric six-state model. Numerical simulations reveal a pronounced oscillatory dependence of the population transfer to the doubly excited Rydberg state on the peak Rabi frequency, indicating dynamics beyond the conventional single-dark-state description of STIRAP. To identify the underlying mechanism, we develop a dressed-manifold description based on gauge-invariant projections onto nearly degenerate instantaneous dressed manifolds. The analysis demonstrates that the wavefunction remains predominantly confined to a two-dimensional dark manifold while becoming transiently coupled to a neighboring bright manifold during the pulse-overlap interval. We further show that in the dressed-manifold representation, the Rydberg-Rydberg interaction modifies the collective resonance structure while preserving the dark-bright manifold dynamics responsible for the oscillatory transfer; an appropriately chosen frequency chirp compensates the interaction-induced detuning and restores efficient population transfer. This dressed-manifold picture provides a consistent interpretation of oscillatory collective transfer and establishes a framework for controlling adiabatic dynamics in interacting multilevel systems by linearly chirped STIRAP, opening a route toward manifold-based control of Rydberg-mediated quantum gates, correlated-state preparation, and other coherent operations in interacting atomic systems.

We prove that the quantum code distance is NP-hard to approximate within an additive error of $c N$, for some constant $c >0$, where $N$ is the number of qubits. Our reductions are deterministic. This improves the previous square-root additive gap to $\Omega(N)$ and resolves the explicitly stated linear-gap question of Kapshikar and Kundu. Our result holds for CSS codes with identical $X$- and $Z$-check spaces, and with a constant rate and constant relative distance. For every fixed $\lambda>1$, there is a constant $c>0$ such that hardness still holds even when every nonidentity stabilizer has weight greater than $\lambda$ times the quantum distance. We also improve the hardness gap of graph state distance on $N$ vertices of Grigorescu, Jha, and Samperton from cube-root to $\Omega(N)$, resolving their explicitly stated open question. Both hardness results are asymptotically optimal since both distances are at most $N$. Our graph state distance hardness result holds for balanced bipartite graphs with a binary adjacency matrix that is its own inverse (mod 2). Our main technique for both hardness bounds above is classical: we show how to convert any code $C$ of length $m$ into a self-dual code $A(C)$ of length $N=\Theta(m)$ while exactly doubling the original coset metric. The conversion is deterministic and efficient. We call it the metric self-dual completion of $C$. It comes with a linear embedding $\tau: \mathbb F_2^m \hookrightarrow \mathbb F_2^N$. The embedding doubles all Hamming distances between vectors in $\mathbb F_2^m$ and all pairwise distances between corresponding cosets. The embedding also guarantees that all codewords of $A(C)$ of weight at most $2m$ are exactly $\tau(C)$.

Atomistic studies of grain-boundary engineering, grain-size effects and dopant enrichment require reproducible models with prescribed microstructural features. We present GRAINSMITH, an open-source Python package for generating statistically controlled polycrystalline models with selectable grain-boundary morphologies for molecular dynamics and subsequent relaxation. Within supported feature combinations, a single configuration specifies grain-size and volume distributions, crystallographic texture, boundary-area-weighted disorientation-angle distributions, phase composition and grain-boundary dopant placement. Crystal construction supports 230 crystallographic space groups. Periodic Voronoi and volume-targeted Laguerre tessellations provide planar boundaries, while distinct geometry backends generate smoothly curved and band-limited self-affine boundaries. A registry of twenty-six checks assesses applicable inputs, construction properties and outputs. Each run exports LAMMPS data and Extended XYZ files together with structural and statistical descriptors and machine-readable provenance. For a fixed software version and computational environment, the configuration and random seed determine byte-reproducible atomic configurations and scientific data across supported worker counts. By combining statistical specification, boundary-morphology control and reproducible atomistic output, GRAINSMITH supports systematic studies of microstructural effects and quantitative comparisons across generated models.

True random number generators (TRNGs) based on the dark noise of perimeter-gated single-photon avalanche diodes (pg-SPADs) naturally produce outputs that follow a tunable Bernoulli distribution. For applications requiring non-uniform random numbers, multiple such units can be coupled, or the inherent Poisson statistics of the accumulated dark events from a single pg-SPAD can be exploited. In this work, we present the principles for extending pg-SPAD-based TRNGs from the uniform to the non-uniform regime and investigate the impact of the perimeter-gate voltage on the underlying probability distributions. The proposed concepts were experimentally validated using a prototype 64 x 64 pg-SPAD chip, fabricated in a standard 0.35 $\mu$m CMOS process. Collectively, we showed that common non-uniform distributions such as Poisson, exponential, and approximated Gaussian can be achieved and tuned in real-time using pg-SPAD TRNGs.

Molecular systems have many degrees of freedom, but their metastable behavior can often be described by a few collective variables. Identifying these variables and estimating free energies along them from limited simulation data remains a challenging, important problem. Separate short trajectories may sample different metastable states without capturing transitions or establishing their relative equilibrium populations. For unbiased trajectories generated with the same Hamiltonian at a single temperature, alternate methods based on histogram reweighting cannot correct this imbalance. Here we present SPIBER, which combines the State Predictive Information Bottleneck (SPIB) with Generative Flow Networks (GFlowNets). SPIB uses deep learning to approximate slow degrees of freedom through a past-future information bottleneck, retaining information needed to predict future metastable states. We show that this compression limits conditional entropy variations in populated regions, allowing conditional mean potential energies, which are much easier to calculate, to be used to approximate free energy differences. Given sufficient local sampling to estimate these energies, they define the target distribution for GFlowNets, energy-based generative samplers that sample according to estimated thermodynamic stability rather than observed populations. For a particle in a radial double-well potential, for alanine dipeptide, and for the nine-residue peptide AIB9, SPIBER recovers free energy differences between sampled metastable states to within one thermal energy unit of reference values. The method combines collective-variable learning and free energy estimation in up to four latent dimensions, without requiring converged state populations or additional molecular dynamics simulations.

In neutrino scattering experiments, the emitted final state particles are essential for identifying interaction channels and reconstructing neutrino energies. During intranuclear propagation, neutrino-induced hadrons can interact with surrounding nucleons, altering both the number of final state particles and detectable energy depositions. As a result, neutrino experiments rely on hadron-nucleus scattering models to simulate these nuclear effects. This paper explores nucleon production predicted by hadron scattering models for common hadrons in neutrino experiments, specifically nucleons and pions. We investigate these models with simulations from the GENIE neutrino event generator, which includes implementations of Geant4 Bertini Cascade and INCL++. For popular target nuclei, we find that the number of emitted nucleons for mesonless hadron interactions can be parameterized by simple Gaussian and exponential decay functions. We present these relationships and provide reweighting tools for addressing the hadron scattering model spread in both visible energy and final state nucleon multiplicities.

Nitrogen-vacancy (NV) centers have emerged as a highly sensitive platform for spatially resolved temperature measurements. When the $\lvert0\rangle\to\lvert+1\rangle$ and $\lvert0\rangle\to\lvert-1\rangle$ transitions are nearly degenerate and the Rabi frequency is comparable to the transition splitting, the spin dynamics encountered during pulsed protocols for temperature measurement can significantly alter the intended accumulation of temperature-dependent phase. We investigate these triplet ($\lvert0\rangle$, $\lvert\pm1\rangle$) spin dynamics and their effect on pulsed thermometry protocols under these conditions. We find that the conventional thermal-echo timing produces negligible temperature-sensitive signal amplitudes at the common-mode detuning. However, we find that the nominal spin-echo timing produces resolvable oscillations at the common-mode detuning, leading to a strong temperature-sensitive carrier signal. This departure from the expected protocol behavior is qualitatively captured by an ensemble model of the triplet dynamics, which supports significant dark-state leakage as a plausible mechanism for the temperature-sensitive response. This mixing-enabled thermal echo uses a four-phase quadrature readout that resolves the signed oscillation frequency and is validated using independent sweeps of the microwave carrier frequency and fluid temperature. We further assess the ability of a four-refocusing-pulse (LDD4B) low-field dynamical-decoupling sequence to extend the NV coherence and find that while the echo retains a sensitivity to common-mode detuning, the effective phase-accumulation interval corresponds to approximately half the total evolution time. These findings could support the use of pulsed NV thermometry in biological or mobile applications where applying magnetic bias fields is impractical and microwave power may be limited.

Recent work has shown that, if a large fraction of the LIGO-Virgo-KAGRA compact binary coalescences (CBCs) occur in accretion disks around active galactic nuclei (AGNs), many such AGN-CBC systems will likely experience lensing and produce multiple gravitational-wave (GW) "images" of the CBCs that will become detectable with current or future GW detectors. However, the waveforms produced by such lensed "images" will differ from those produced by other lensing systems because the binary source is orbiting the AGN's central supermassive black hole at a close distance. Here, we show that these systems produce 2 snapshots of the same binary source from 2 different viewing angles. These differences in the effective viewing angle between the images are encoded in the GWs they emit, such that GW detectors can effectively analyse the waveforms from 2 viewpoints. Beyond such "multi-view lensing", the GW images may also differ by their Doppler shift due to the expected relativistic orbital motion of the source around the AGN, an effect which is further amplified by the proximity to the lens. If the AGN's own angular momentum can be related to the binary's orbital angular momentum, we can describe the entire AGN-CBC system using only one additional free parameter compared with a typical point-mass lens system, or with 3 additional parameters when we do not make such an assumption. In this work, we establish a framework of transformation rules that describe both the angles in the 2 points of view, and the Doppler effect that comes from the source's motion around the lens. We also provide the framework to produce consistent AGN-lensed waveforms from any currently available GW waveform. These AGN-CBC systems give 2 unique points of view on a binary merger thus opening up a new window into the merger's properties unlike any other lens system.

Dilution of precision is the standard way to describe navigation geometry and it does not apply in cislunar space: its derivation presumes a snapshot solution in which simultaneous measurements determine the state at one instant. A spacecraft tracked by inter-satellite ranging in the Earth-Moon three-body problem has no such solution: range is a function of position only, so the velocity columns of the measurement Jacobian vanish identically and the state is unobservable however many links are in view. The correct figure of merit is dynamical, because the three-body flow carries velocity information into later range measurements. We demonstrate this on four differential-corrected planar distant retrograde orbits, reporting the observability Gramian rather than a dilution of precision. Instantaneous range-only geometry has rank 2 of 4; the full state becomes observable only after a tracking arc of 2.09 h, the first sampled arc at full rank on a 0.26 h grid, and a square-root information filter recomputing the same quantity by a different route becomes well-posed at exactly that arc. Beyond it, conditioning improves monotonically with arc length, the Gramian condition number falling from 1.2e11 at 3 h to 1.4e5 at 48 h. Adding range rate lifts the instantaneous rank from 2 to 4, so a Doppler-capable link makes a snapshot solution exist where a range-only link cannot. Lifting the known-reference assumption, the joint problem of estimating a station and the satellites' states and clocks together is rank-deficient by exactly one without an external interferometric observable in all twenty realizations tested, and full rank with it; the deficiency persists only to four satellites. For the configurations studied, cislunar navigation requirements are better written as arc-length, conditioning and measurement-type budgets than as dilution-of-precision thresholds, which are undefined here.

Physics-Informed Neural Networks (PINNs) provide a mesh-free framework for solving partial differential equations but often struggle with sharp gradients and shock-dominated solutions. Extended Physics-Informed Neural Networks (XPINNs) address this challenge through domain decomposition; however, the effects of decomposition design, overlap, and local network capacity on solution accuracy remain insufficiently characterized. This work presents a systematic assessment of domain decomposition configurations for XPINNs applied to the one-dimensional viscous Burgers equation ($\nu=0.01/\pi$). We compare a standard PINN, a conventional XPINN, a shock-focused XPINN with increased network capacity in the shock-containing subdomain, and overlapping XPINNs with different overlap widths. All configurations are trained using a common protocol based on Adam, L-BFGS refinement, and ten Residual-based Adaptive Refinement (RAR) cycles. Performance is evaluated against a reference solution using global and shock-region relative $L_2$ and $L_\infty$ errors, maximum PDE residuals, and interface continuity errors. The results show that decomposition design strongly affects XPINN accuracy and shock resolution. Among the overlapping configurations, the smallest overlap provides the best accuracy, while larger overlaps degrade performance. The shock-focused XPINN achieves the lowest overall solution errors, indicating that increased local network capacity can provide greater benefit than increasing overlap alone. RAR produces the largest improvements during early refinement stages, followed by increasingly non-monotonic changes in accuracy. These findings highlight the importance of jointly considering decomposition, interface coupling, network capacity, and adaptive refinement for shock-dominated problems.

Quantum Reservoir Computing (QRC) uses fixed quantum dynamics as a high-dimensional feature map. Still, standard pipelines flatten reservoir measurements and train a linear readout, ignoring the natural tensor structure across time steps, qubits, and observables. We propose a multilinear readout for quantum reservoir computing (ML-QRC), a tensor-structured neural readout compressed through mode-wise projections. Relative to a dense hidden-width-64 neural readout, this reduces the feature-to-hidden parameter count from $64TnF$ to $d(T+n+F)+64d^3$, giving a $12.1\times$ feature-block compression at $T=50$, $n=6$, $d=8$, and $F=n+\binom{n}{2}$. Across Mackey-Glass forecasting and TFIM phase classification, ML-QRC remains statistically competitive with Ridge on Mackey-Glass and obtains the numerically highest full-data TFIM accuracy among tested methods, while using $12.0\times$ fewer parameters than the full dense MLP. Its clearest benefit is improved low-data stability relative to neural MLP readouts on Mackey-Glass; this advantage does not transfer to TFIM, where Ridge performs best at 50% data. Overall, ML-QRC is best viewed as a tensor-structured neural readout that compresses dense MLP readouts while preserving QRC tensor structure, rather than as a replacement for simple linear/Ridge readouts in the tested regime.

We propose a computationally inexpensive algorithm to determine whether an opaque spherical body eclipses a luminous one, using only classical geometrical tools. We apply this method to the Sun-Earth-Moon system and predict solar eclipses, including their type, beginning, and duration, using the three-body problem. For predictions over a one-year period, the resulting errors are in the order of minutes.

Rapid and reliable identification of pharmaceutical residues is important for safeguarding public health, ensuring food safety, and enabling practical Raman-based screening. In this study, we propose HyMLRaman, a hybrid Raman spectroscopy framework that combines deep spectral feature extraction, generative models, and classical machine-learning classifiers to identify six pharmaceutical compounds, including amoxicillin, chloramphenicol, ciprofloxacin, tetracycline, ibuprofen, and paracetamol. Raman spectra are converted into spectral images and encoded with several deep neural-network backbones, among which EfficientNet-B3 yields the most effective representation. The resulting 1536-dimensional embeddings are then used to train downstream classifiers, including SVM, KNN, logistic regression, random forest, XGBoost, and ANN, using stratified 10-fold cross-validation. The hybrid EfficientNet-B3–SVM configuration achieves the strongest baseline performance, reaching 96.31% accuracy and a macro-F1 score of 96.36%, outperforming the standalone CNN baseline. To address limited-data conditions, a generative model, a DDPM-based feature augmentation, is introduced in a PCA-reduced EfficientNet-B3 latent space. The low-data ablation results show that DDPM augmentation provides selective benefits, particularly for KNN with reduced training fractions, and that its effect remains classifier-dependent. Finally, an application-level Raman Pharmaceutical Analyzer demonstrates the feasibility of embedding the trained model into an interactive Raman analysis workflow. These results suggest that HyMLRaman provides a practical and interpretable route for rapid Raman-based pharmaceutical screening.