Papers

Matter changes the eigenvalues and mixing matrix of the neutrino propagation Hamiltonian while entering the flavor-basis Hamiltonian through a low-dimensional additive deformation. We develop a unified algebraic description of the quantities that are insensitive to this deformation. The invariant algebra is formulated as the joint kernel of commuting matter-translation derivations inside the flavor-rephasing invariant ring. For diagonal matter potentials, this gives a general decomposition into unaffected diagonal directions and an off-diagonal cycle algebra, together with an exact dimension formula for an arbitrary number of flavors and independent matter parameters. For matter spurions with common low-rank support, block-Krylov rows generate exterior-power covariants whose maximal minors are matter independent. Their mass-basis form is a Plücker expansion: rank one produces the familiar Vandermonde factorization, whereas higher rank generically produces a sum of independent Plücker terms. The standard $3+1$ system provides our principal nontrivial example. Its global off-diagonal algebra is the toric cycle ring of the complete four-vertex flavor graph, generated by edge moduli, triangle cycles, and quadrangle cycles; the commonly used eleven invariants constitute a generic local coordinate system rather than a global polynomial generating set. We further formulate independently varying matter compositions and off-diagonal nonstandard interactions as, respectively, commuting exact flows and controlled deformations of the invariant algebra. This framework separates the existence of exact invariants from the stronger and exceptional property of single-monomial spectral factorization.

This is the second of two papers discussing a new experimental signature of mixed-symmetry states (MSS) in the vibrational nuclei $^{92,94}$Zr and $^{94}$Mo based on proton and neutron transition densities. Quasiparticle-phonon model calculations for these nuclei are extensively tested by comparison to ground-state properties, energies and moments of excited states, transition probabilities between them, and the momentum transfer dependence in $(e,e^\prime)$ and $(p,p^\prime)$ reactions. The overall very good agreement permits the extraction of information on the wave functions of the MSS and their fully symmetric (FSS) counterparts. MSS can be identified by a sign change between the leading proton and neutron two-quasiparticle configurations compared to the FSS. Possible candidates for $2^+$, $3^-$, and $4^+$ MSS are identified. The modification of proton and neutron transition densities, which can be derived from a combined analysis of inelastic electron and proton scattering, by the sign change provide a new experimental signature of MSS. The collectivity of ground-state excitations of predominantly one-phonon FSS and MSS is generated to a large extent by the coupling to high-lying states forming giant resonances with the same spin and parity.

Magnetic ground states are commonly predicted using spin Hamiltonians whose interaction terms are selected a priori, potentially overlooking the microscopic interactions that govern complex magnetic order. Here, we introduce a general framework for the unbiased first-principles construction of symmetry-complete tensorial spin Hamiltonians and its automated implementation in AMATIS. The framework constructs the Hamiltonian directly from density-functional theory while rigorously enforcing quantum spin algebra and crystallographic symmetry. Applied to representative two-dimensional van der Waals magnets, the framework reproduces established magnetic interactions and uncovers hidden physics beyond conventional spin models, including chiral interactions that stabilize metastable skyrmions, higher-rank tensorial interactions that reconstruct the magnetic phase diagram and establish stabilizing competing multi-Q phases, and an emergent p-wave altermagnetic electronic structure. Our results demonstrate that unbiased tensorial Hamiltonian construction provides a predictive alternative to the conventional practice of manually selecting spin-model interactions, enabling first-principles discovery of unconventional magnetic phases.

Recent studies have shown that classical LiF simulations can reproduce low-temperature experimental spectra when performed at a simulation temperature $T^*$ higher than the physical temperature $T$. We show that the characteristic scale of this rescaling follows naturally from quantum vibrational statistics. An effective temperature $T_{\rm eff}(T)$ is obtained by matching classical and quantum harmonic energies and is evaluated using an analytic acoustic-optical model and a first-principles LiF vibrational density of states $D(\varepsilon)$. The resulting temperature reproduces the low-temperature scale of the reported spectral temperature and approaches the physical temperature in the classical regime. Our results identify zero-point motion and Planck-Bose-Einstein statistics as the origin of the reported temperature scale.

This is the first of two papers discussing a new signature of quadrupole mixed-symmetry states in the vibrational nuclei $^{92,94}$Zr and $^{94}$Mo based on proton and neutron transition densities derived from the comparison of inelastic electron and proton scattering experiments. Results of the $(e,e^\prime)$ and $(p,p^\prime)$ experiments on these nuclei as well as $(p,p^\prime)$ data for other potential cases $^{96}$Mo and $^{70}$Zn are presented. Spin and parity quantum numbers of excited states are assigned based on angular distributions from the proton scattering data in comparison to calculations employing form factors from the collective model in distorted-wave Born approximation. Possible candidates of one-phonon fully symmetric and mixed-symmetry states as well as members of two-phonon multiplets are identified.

In this paper, we investigate the cosmological dynamics of a modified gravity framework based on the function $f(T)=\beta(-T)^{1/2}+\gamma(-T)$, where $T$ denotes the torsion scalar. The matter sector is modeled using the Generalized Chaplygin Gas (GCG) with the equation of state $p=-\frac{\mathcal{A}}{\rho^{\eta}}$, allowing the model to describe the evolution from an early-time matter-like phase to a late-time accelerated universe. By deriving an analytical expression for the Hubble parameter $H(z)$, we perform parameter estimation using Bayesian statistical techniques based on the $\chi^{2}$-minimization method with the Cosmic Chronometer (CC) and joint (CC+Pantheon) observational datasets. The deceleration parameter exhibits a transition from deceleration to acceleration, while the present-day value indicates the current accelerated expansion. The model yields a present-day EoS parameter consistent with dark-energy-like behavior, while the energy conditions indicate that the NEC and DEC are satisfied and the SEC is violated at late times. The $\omega-\omega'$ plane shows a freezing quintessence behavior, approaching the $\Lambda$CDM-like point $(\omega,\omega')=(-1,0)$, while the cosmographic analysis offers additional insight into the evolution of the cosmic expansion. The estimated age of the universe is also consistent with current observational bounds. These results demonstrate that the GCG scenario within $f(T)$ teleparallel gravity provides a viable and observationally consistent framework for explaining the late-time accelerated expansion of the universe.

Real-time characterization of refractive index (RI) dispersion is pivotal for advanced optical sensing, yet conventional surface plasmon resonance (SPR) platforms are bottlenecked by the narrow bandwidth of noble metals (Au, Ag) and the mechanical instability of sequential scanning. Here, we report a novel Al-based parallel SPR platform that overcomes the bandwidth and temporal constraints of conventional noble-metal systems. Leveraging the unique low-loss broadband response of Al, enabled by the suppression of interband transitions, we engineered a system for simultaneous excitation at 450, 520, and 635 nm. By integrating spectral-angle multiplexing with RGB-channel demultiplexing on a CMOS camera, the platform achieved acquisition of dispersion profiles without mechanical motion. Validated against NaCl solutions, the system demonstrates metrological accuracy and exceptional agreement with Cauchy dispersion models. The proposed architecture eliminates temporal drift and vibration errors, establishing a new benchmark for real-time dispersion characterization. By decoupling sensing from mechanical constraints, this work pioneers a compact, robust framework for next-generation, field-deployable sensors capable of distinguishing complex analytes via their unique spectral signatures.

We consider a quantum steering scenario where Alice prepares a bipartite state, sends one subsystem to Bob through a quantum channel, and aims to convince him that their shared state is entangled. Bob, however, will never be convinced if the channel is steering-breaking, that is, if the channel destroys steerability for any input state. To verify that a channel renders a state useless for demonstrating steering, one must consider all possible measurements performed by Alice and check if the conditional states Bob receives admit a local-hidden-state (LHS) model. This is generally a hard problem since it requires considering an infinite number of measurement combinations. Here, we show that the method proposed in [Phys. Rev. Lett. 117, 190401 (2016); Phys. Rev. Lett. 117, 190402 (2016)] can be utilized to tackle this problem. Furthermore, owing to the intimate relation between steering and measurement incompatibility, our approach can faithfully certify whether a channel destroys incompatibility for any set of measurements. Finally, we propose an experimental criterion for certifying steering- and incompatibility-breaking channels, which may be of independent interest.

We develop a systematic algebraic approach, based on the Wei–Norman factorization method, to the normal ordering of exponential bosonic operators and apply it to derive analytical excitonic form factors in two-dimensional semiconducting materials. By introducing an auxiliary parameter, the normal-ordering problem is reduced to a system of ordinary differential equations determined by the commutation relations of the underlying closed Lie algebra. The approach is first illustrated for exponential operators associated with the Heisenberg–Weyl and $su(1,1)$ algebras, and is then extended to two-mode bosonic operators involving $su(2)$ and a six-generator closed algebra that contains two coupled $su(1,1)$ subalgebras. For the excitonic application, the Levi–Civita transformation maps the two-dimensional exciton problem onto an oscillator representation, providing a natural formulation in terms of bosonic creation and annihilation operators. Combined with the Laplace and Fourier representations of the Rytova–Keldysh potential, this formulation reduces the interaction matrix elements to the evaluation of exponential bosonic form factors. The isotropic problem is governed by a three-generator $su(1,1)$ algebra, whereas the anisotropic case requires the full six-generator algebra together with an additional $su(2)$ factorization. Explicit analytical expressions for both form factors, $\langle e^{-rt}\rangle$ and $\langle e^{i\mathbf q\cdot\mathbf r}\rangle$, are obtained, providing useful building blocks for matrix-element calculations in two-dimensional excitonic systems and potentially in other quantum problems involving exponential bosonic operators.

Vortex dynamics govern the dissipation and magneto-resistive properties of type-II superconductors. At large transport currents, the current-voltage ($I$-$V$) characteristics of a superconductor in the mixed state usually exhibit a nonlinear upturn followed by an abrupt jump occurring due to a flux-flow instability. However, other transition behaviors are also possible, including the formation of phase-slip lines and normal domains. Which mechanism dominates depends on the sample uniformity, its dimensions relative to the coherence length and penetration depth, and the rates of electron energy relaxation and heat removal. Here, based on the time-dependent Ginzburg-Landau equation, we present the results of numerical modeling of the $I$-$V$ curves of superconducting films with various types of disorder. For a grain-boundary defect mesh, we find multiple voltage transitions overlaid with a nonlinear upturn of the $I$-$V$ curves. For randomly arranged elongated defects, the $I$-$V$ curves exhibit voltage steps, whereas for L-shaped defects oriented perpendicular to the transport current, the $I$-$V$ curves show extended linear regimes separated by voltage transitions. We analyze the evolution of the order parameter along the $I$-$V$ curves and discuss the experimental accessibility of the revealed dynamics regimes.

The origin of the heaviest elements remains a fundamental mystery, with the "actinide-boost" (Thorium overabundance) serving as a critical diagnostic of r-process nucleosynthesis conditions. While this diversity is well documented in extremely metal-poor (EMP) stars, its frequency in the mildly metal-poor (MMP) regime ($-2.0 < $ [Fe/H] $< -0.5$) is poorly constrained due to blending issues in the commonly used 4019 angstrom line. We present a systematic abundance analysis of mildly metal-poor stars, exploiting the relatively unblended Th II 5989 angstrom line. High-dispersion spectra were obtained using the 1.5 m telescope at Gunma Astronomical Observatory with GAOES, complemented by archival data from the Subaru Telescope/HDS retrieved via SMOKA. We successfully detected Th in 32 out of 42 sample stars. Our analysis demonstrates that the 5989 angstrom line is a useful diagnostic for Th abundance measurements in cool red giants. The mean [Th/Eu] ratio remains nearly constant over the MMP metallicity range, suggesting that progressive homogenization of the interstellar medium during Galactic chemical evolution would reduce abundance variations inherited from individual r-process events, or the dominant r-process events may share similar initial Th/Eu production ratios. While the [Th/Eu] ratio is nearly constant overall in the MMP regime, its dispersion appears to increase toward the metal-rich end of this regime and reaches approximately 1 dex near solar metallicity. This behavior may reflect the combined effects of variations in the initial Th/Eu production ratios of the progenitor objects, the mixing of r-process products in the interstellar medium, and the radioactive decay of Th over stellar lifetimes.

We study intrinsic quantum uncertainty associated with a single observable from the viewpoint of skew information. By relaxing ordinary additivity while retaining the other fundamental uncertainty requirements, we introduce a class of Hiai–Petz nonadditive skew informations that contains Hansen's metric-adjusted skew informations as the boundary case $\theta=1$. Our main quantitative result is a sharp single-observable uncertainty relation for the full Hiai–Petz class. For a fixed state, the optimal coefficient depends only on its largest and smallest eigenvalues and remains sharp even after the maximal classical contribution to the variance is retained. The general theorem yields, as special cases, sharp bounds for metric-adjusted skew informations, the SLD quantum Fisher information, and the power-commutator family. We further show that $K_s(\rho,A)=\frac12\|[\rho^s,A]\|_{\mathrm{HS}}^2$, $1/2\le s<1$, is realized within the Hiai–Petz framework through Stolarsky operator means, thereby establishing its convexity for $1/2<s<1$. More generally, for each fixed operator monotone function $f$, the Hiai–Petz spectral kernel interpolates geometrically between the metric-adjusted skew information $I^f$ and the common endpoint $K_1$. The resulting family obeys an exact power-trace-weighted composition law, replacing ordinary additivity in the interior $0<\theta<1$.

Social networks shape how individuals make decisions and how opportunities are distributed. However, the mechanisms that generate these networks often reflect pre-existing inequalities, and technologies that rely on network-derived signals risk further amplifying such disparities. Algorithmic fairness research largely treats networks as a fixed background, grounding analysis almost exclusively in distributive justice and overlooking how network structures systematically bias decision-making. In this Perspective, we identify ten network effects and trace how they create structural biases in the relationship between what we intend to measure and what we observe. Using academic hiring as an example, we show that network biases are not inherently harmful or beneficial. Determining their legitimacy requires examining the entire decision-making process through the lenses of both distributive and procedural justice while engaging all affected stakeholders. We therefore call for a holistic, networked approach to fairness that moves beyond static group categories and recognizes the dynamic, relational, and structural nature of inequality.

We study the local canonical thermodynamics of the quantum Oppenheimer–Snyder (qOS) black-hole exterior previously obtained from loop quantum cosmology. The spacetime is adopted from the literature; no new black-hole solution, regular extension, or singularity-resolution mechanism is claimed here. At fixed quantum parameter $\alpha$, we rewrite the outer horizon in a dimensionless form and obtain exact expressions for the mass, Hawking temperature, entropy, and heat capacity. These expressions reproduce the logarithmic entropy term and the heat-capacity divergence reported in earlier analyses. We then place those results in an explicit, regulated canonical-ensemble framework. The off-shell canonical action has a local minimum on a near-extremal branch with positive heat capacity and a local maximum on a large-black-hole branch with negative heat capacity. The two saddles merge at $r_h/\sqrt{\alpha}=\sqrt{(4+2\sqrt{7})/3}$, where the temperature is maximal and the heat capacity diverges. Because the asymptotically flat partition function is not normalizable without boundary data, this divergence is interpreted as a Davies-type local stability transition, not by itself as a global first-order phase transition. The principal contribution of this work is therefore a transparent canonical-saddle organization of known qOS thermodynamic results, together with a precise statement of its domain and limitations.

Open quantum systems describe quantum systems that interact unavoidably with their environments. These notes introduce the physical origins of decoherence and dissipation in realistic settings, developing the theoretical framework of reduced dynamics and quantum master equations within the connection to thermodynamics in the quantum regime. Additionally, a set of relevant exercises are proposed to reinforce the acquisition of knowledge. The text equips readers with the tools to model and analyze open quantum dynamics.

How can a neural circuit rhythmically burst when none of its constituent neurons can endogenously do so? We address this question through a bottom-up reconstruction of a 4-cell neural circuit modeled after the swim central pattern generator (CPG) of the sea slug Dendronotus iris. We first map the intrinsic regimes of a swim interneuron (SiN) model neuron and show that slow mutual inhibition can generate anti-phase bursting in a half-center oscillator (HCO) assembled from tonic-spiking or quiescent cells. A slow–fast phase-space deconstruction explains this pairwise rhythm as a release mechanism. We then move on to CPG parametrization, in which cells 1 and 2 are quiescent, while cells 3 and 4 are tonic spikers but their isolated HCO can only exhibit tonic spiking or suppression. Bursting therefore does not arise at either the cellular or HCO level. It appears only after the two modules are assembled into the complete 4-cell network, where cross excitation, cross inhibition, and rectified electrical coupling act together to support a robust network rhythm-generation. Event-based symbolic encoding and GPU-parallel parameter sweeps show that this higher-order collective state occupies extended parameter domains rather than a single tuned point, and they quantify how the network interactions reshape those domains and the spike counts per burst. Symbolic sweeps identify the healthy range of activity regimes (periodic sequences) and transition boundaries; Lempel–Ziv complexity is used as a descriptor of aperiodic symbolic output rather than as proof of chaos or dynamical instability. Our results establish a hierarchy of rhythm generation—from intrinsic cell dynamics, through conditional HCO bursting, to bursting that emerges only in the fully assembled 4-cell CPG—and provide experimentally accessible predictions for perturbing its chemical and electrical couplings.

The cross sections and resonance structures of $\rm^{75}As$(n,$\gamma$)$\rm^{76}As$ reaction are critical to the neutrinoless double-$\beta$ (0$\nu\beta\beta$) decay searches of $\rm^{76}Ge$, the $s$-process nucleosynthesis of nuclear astrophysics, and Neutron Resonance Capture Analysis for determining the elemental and isotopic composition of archaeological and cultural heritage. We report a high-precision measurement of the $\rm^{75}As$ neutron capture cross sections from 1~eV to 1~MeV, performed at the Back-n facility of the China Spallation Neutron Source using the Time-of-Flight method. In the resolved resonance region, nineteen resonance structures of $\rm^{75}As$(n,$\gamma$)$\rm^{76}As$ reaction have been discovered for the first time, and inconsistencies between evaluated libraries has been resolved. Resonance parameters for the newly observed structures were extracted with the $R$-matrix code SAMMY. These findings will help refine the theoretical predictions of half-lives and decay constants for the double-$\beta$ decay searches of $\rm^{76}Ge$. Astrophysical Maxwellian-averaged cross sections were calculated based on the averaged cross sections in the unresolved resonance region. And the $\rm^{75}As$(n,$\gamma$)$\rm^{76}As$ reaction rates were derived over the astrophysically relevant temperature range in both the main and weak $s$-processes nucleosynthesis. The present reaction rates deviate significantly from the recent theoretical predictions, and the uncertainties are significantly reduced.

Quantum compilers face the test oracle problem, judged by an output-equivalence oracle: the compiled circuit must compute the same unitary as the original, modulo global phase and a qubit-layout permutation. This oracle, by construction, checks only that semantic map, not the circuit's own layout, permutation, or phase records: a defect there, or in a fixed-seed run's determinism, can pass unseen though the record is public. This empirical software engineering study of quantum transpiler correctness uses repository mining to measure how often this happens in real merged compiler fixes: a systematically identified corpus of Qiskit transpiler bug-fixes, classified by an independently dual-coded, source-validated fault-manifestation taxonomy. Nineteen of 68 fixes (28%, 95% Wilson CI 19-40%) repair faults invisible to this equivalence screen, even one augmented with compilation-validity, circuit-quality, and performance checks, and an extended 104-fix corpus over a wider window holds at the same rate with a tighter interval (29/104, 27.9%, CI 20-37%). A conservative floor remains even restricted to the one unconditionally equivalence-invisible channel (a corrupted layout or permutation record): 10 of 68 fixes (15%, CI 8-25%) beneath the 28% headline. The gap is not Qiskit-specific: it replicates in tket (7/21, 33%), with Cirq smaller but consistent. We detected no systematic differences on five inexpensive PR-level characteristics (19 vs 49, underpowered alone; the extended 29-vs-75 corpus tightens every interval toward zero). This class dominates the invisible set, concentrating at representation-boundary crossings. We release the corpus, codebook, and coding artifacts for quantum software testing research. Here we only measure it.

The deformed Noumi-Sano operator $H_{n, m}^d(x, y)$ of order $d$ is a simultaneous extension of the Macdonald operator and the Noumi-Sano operator. In this paper, we construct an integral transform associated with eigenvalue problem of $H_{n, m}^d(x, y)$. Using the integral transform, we obtain an integral representation of eigenfunctions for $H_{n, m}^d(x, y)$.

We study rare nonresonant regions in a canonical one-dimensional disordered quantum spin chain by directly implementing the iterated Schrieffer-Wolff construction underlying the recent work of De Roeck, Giacomin, Huveneers and Prosniak on subdiffusive transport. For finite systems, we compute the probability that a disorder realization remains nonresonant through successive scales of the flow, while separately monitoring operator proliferation and the spatial localization of dressed local observables. The survival probability decays at most exponentially with system size over the numerically accessible regime. Resolving this decay scale by scale yields failure rates associated with successive Schrieffer-Wolff steps. The first rate is obtained analytically in excellent agreement with numerics, while higher-scale rates decrease rapidly throughout the regime studied. These results support the summability mechanism required for exponentially rare but parametrically long nonresonant regions, which provide the insulating bottlenecks responsible for subdiffusive transport. At the smallest couplings studied, the survival probability under our conditions exceeds the rigorous lower bound by six to seven orders of magnitude, demonstrating how conservative the constants required by the proof are while confirming that its underlying physical mechanism is quantitatively visible at accessible scales. More broadly, our results show how direct numerical implementations can provide an independent and physically transparent test of technically demanding constructive proofs, a methodology that may become increasingly useful as machine-assisted proofs become more common.

We introduce a notion of viscosity solution for Hamilton–Jacobi–Bellman (HJB) equations with distributional drift, based on paracontrolled test functions and related through a Zvonkin transformation to classical viscosity theory. The equations considered are of the form \[ \left(\partial_t+\frac12\Delta+b\cdot\nabla\right)h(t,x) =-H(t,x,h(t,x),\nabla h(t,x)), \] where $b$ is singular in the sense of \cite{paradistrib} and has regularity $\mathcal C^{-\alpha}$ for $\alpha\in(1/2,2/3)$. Using doubling-of-variables arguments, we derive a priori gradient estimates that also cover Hamiltonians with slightly superquadratic growth in $\nabla h$. We also obtain probabilistic representations through singular control problems for convex $H$ and weak singular forward–backward SDEs for possibly nonconvex Hamiltonians with at most quadratic growth.

Conventional transport and optical responses, such as the Hall effect, can only distinguish material phases with substantially different symmetries. However, many quantum materials, such as candidate altermagnetic materials, host competing phases with similar structures, making it difficult to differentiate them using conventional transport or optical measurements. Here, guided by symmetry principles, we introduce a B-type quadratic planar Hall effect (B2-PHE) as a sensitive probe of magnetic structures. B2-PHE features a planar Hall current that scales quadratically with the applied magnetic field. This response originates from the interplay among external magnetic fields, intrinsic magnetic order, and quantum geometric properties of the electronic bands. We investigate B2-PHE in two altermagnetic candidates, KV2Se2O and RuO2, whose ground-state magnetic orders are under intense debate. Remarkably, B2-PHE emerges in their altermagnetic phases but is symmetry-forbidden in their antiferromagnetic (nonmagnetic) phases. We also show that B2-PHE should be detectable under a moderate magnetic field on the order of 1 Tesla. These findings establish B2-PHE as an experimentally convenient and potentially unambiguous probe of altermagnetic order, which is otherwise difficult to realize.

We study the impact of flavour-specific neutrino self-interactions on the CMB anisotropy spectrum and consistently take into account neutrino mixing. Starting from the neutrino quantum kinetic equations, we derive the neutrino Boltzmann hierarchies for the neutrino mass states. Our work shows that most scenarios of flavour-specific neutrino self-interactions are well approximated by a combined fluid approach. In practice, this implies that existing CMB bounds on the effective neutrino coupling are weakened by a factor $\sqrt{2}$ for scenarios in which only two neutrino flavours interact (irrespective of which flavours). If only one neutrino flavour interacts the bounds are weaker by a factor $\sqrt{6}$, with the only caveat that the combined fluid approach is less reliable for only $\nu_e$ interacting.

Solving inverse problems with differentiable physics simulators holds the potential to revolutionize scientific discovery and engineering design, as it enjoys both the strict physical correctness from rigorous numerical physics simulators, and the high efficiency and effectiveness from automatic differentiation and gradient-based optimization. However, currently, this paradigm faces performance issues in optimization. In this work, we target benchmarking the performance of different optimizers to solve various inverse problems. We construct 12 differentiable physics simulators spanning physics domains including discrete mechanics, continuous mechanics, atomistic simulations, rendering, and semi-empirical physics models. Based on these simulators, we design corresponding inverse problems that can be categorized into parameter identification, inverse design, and optimal control. Finally, we conduct extensive experiments to compare the performance of different optimizers, including regular first-order methods, approximate second-order methods, as well as global optimizers, on these inverse problems, and analyze the results to provide insights on how to choose and design optimizers for differentiable programming. We hope such benchmarks can inspire the development of more effective optimizers, and further promote the applications of differentiable programming in various scientific and engineering domains.

Accurate quantum number assignment for calculated molecular energy levels is a critical bottleneck in generating line broadening parameters for comprehensive line lists for radiative transfer applications. We present an automated pipeline for assigning Air Force Geophysics Laboratory (AFGL) quantum numbers to CO2 calculated rovibrational states lying below 15,000cm$^{-1}$ across all 12 stable isotopologues. A GraphSAGE graph neural network is trained transductively on empirical (MARVEL) energy levels, exploiting inter-isotopologue perturbation chains and intra-isotopologue rotational ladder edges to propagate assignment information to unlabelled calculated states. Physical uniqueness is enforced locally by a Hungarian algorithm solver operating within groups of states sharing the same polyad, rotational quantum number, and parity. A five-generation bootstrap loop iteratively promotes high-confidence predictions into the training set, expanding coverage without additional labelling effort. The pipeline assigns 224,650 previously unlabelled states over 12 isotopologues, accounting for 10.7$\%$ of all available states (including MARVEL-derived levels), with coverage now increased to 97.4$\%$ below 5000cm$^{-1}$. The pipeline includes a novel decision tree method for converting AFGL to Herzberg notation in asymmetric isotopologues, while the architecture and Hungarian uniqueness enforcement are applicable beyond CO2, any molecular system with a conserved polyad-like quantum number and a large body of unlabelled computed states is a natural target for this approach, suggesting a pathway toward automated quantum number annotation for the next generation of large-scale computed line lists.

We examine a 4-dimensional generalization of predator-prey models describing interactions among four species. We show that these systems exhibit a rich variety of asymptotic behaviors, with solutions that are either integrable, leading to non-sustainable dynamics characterized by unbounded population growth or collapse, or chaotic, where all species coexist over time. Moreover, we review the integrable cases, which are classified into two-parametric families, and examine three-parametric families that behave similarly to the known two-parametric integrable cases. We also analyze chaotic Lotka-Volterra models in terms of their Lyapunov exponents and Poincare' surfaces of section, which turn out to reveal underlying structures that are compatible with what is expected from sustainable dynamics.

We show that a class of binary optimization problems with complex non-quadratic objectives or constraints can be reformulated as multi-objective quadratic unconstrained binary optimization problems. When the objective and constraints depend on a small number of quadratic features and are monotone with respect to their preferred directions, at least one globally optimal solution lies in the Pareto set of the associated MO-QUBO. This enables the constraints to be evaluated classically on Pareto-optimal candidates rather than encoded as penalties. We demonstrate the approach for binary portfolio optimization under a Conditional Value-at-Risk constraint. Using Quantum Approximate Multi-Objective Optimization on an illustrative 100-asset instance, we approximate the mean-variance Pareto front using an IBM Quantum computer and derive mean-CVaR fronts through classical post-processing. The hardware results recover the overall structure of the classical front and yield near-optimal feasible portfolios for different risk bounds.

We investigate the thermodynamic geometry of an ideal quantum gas obeying inclusion statistics, characterized by a negative statistical parameter $g < 0$. In this framework the grand-canonical partition function admits a finite maximum fugacity, and the thermodynamic scalar curvature $R$ is strictly positive for all $g < 0$, reflecting effective attractive statistical interactions analogous to those of a bosonic system. As the fugacity approaches its maximum value, $R$ diverges, signaling a phase transition of the Bose-Einstein condensation type. A key distinction from the ordinary ideal Bose gas is that the condensation temperature is elevated relative to the bosonic case, and finite-temperature condensation occurs even in the dimensional regime $1/2 < D/\sigma \leq 1$ where standard bosons do not condense, while for $D/\sigma \leq 1/2$ the transition temperature vanishes. Three independent criteria; divergence of $R$, the maximum fugacity singularity, and the non-analytic cusp in the specific heat, coincide at the same condensation point, confirming the thermodynamic consistency of the transition.

Nuclear masses are fundamental quantities in nuclear physics, providing essential information for understanding nuclear structure, decay properties, and reaction processes. Here we develop a bidirectional recurrent neural network (Bi-RNN) that naturally incorporates sequential correlations along isotopic and isotonic chains for nuclear mass prediction. The model achieves a root-mean-square (rms) deviation of 78 keV for binding energies of 2339 nuclei with known masses, a 45% improvement over a conventional artificial neural network (ANN) with comparable parameter count. The Bi-RNN also delivers consistent accuracy across different odd-even parity groups and yields an rms of 99 keV for $Q_\beta$ values without explicit training, demonstrating that recurrent correlations encode physically relevant information beyond individual nuclear features. Extrapolation tests on 292 nuclei updated from AME2003 to AME2012 and on 109 nuclei updated from AME2012 to AME2020 reveal that the Bi-RNN maintains stable performance, substantially outperforming WS4, ANN, and earlier AME evaluations. These results demonstrate the power of recurrent architectures in capturing correlations along nuclear chains and suggest Bi-RNN as a robust tool for studying nuclear masses.

In this study, we calculate the relative frequency shift ($\Delta \nu / \nu$) caused by gravitational lensing resulting from the transverse motion of a spinning lens described by the Kerr metric \cite{Kerr:1963ud}. While the effect of transverse velocity on the frequency shift has previously been investigated using the Schwarzschild metric \cite{Rahvar_2020,10.1093/mnras/stae1938}, extending this to the Kerr metric provides a new window for measuring the transverse velocity of a lens or its spin parameter, a parameter often subject to degeneracy in gravitational microlensing observations. Recent microlensing observations have revealed black holes as viable lensing candidates \cite{2022ApJ...933...83S}. Since spinning black holes form naturally from stellar evolution, astrophysical black hole lenses are best described by the Kerr metric. Furthermore, recent observations of supermassive black holes at the centers of galaxies provide an ideal laboratory for testing the observational effects of the Kerr metric by measuring the frequency shifts of lensed sources.