Papers

This work presents a chemiluminescence tomography campaign to reconstruct time-resolved, three-dimensional reacting structures in detonation waves propagating through ethylene-based mixtures at 1 atm. Images of chemiluminescence are recorded simultaneously by five cameras through a cylindrical sapphire test section, and a custom calibration procedure is developed to account for refraction through the cylinder. The images are combined to reconstruct an effective emission source term field at megahertz rates. Reconstructions are reported for a persistent spinning detonation, a failed spinning detonation, and a case with counter-propagating transverse fronts. The reconstructed fields enable visualization of wave morphologies, determination of the axial and azimuthal wave speeds, and estimation of key geometric and kinematic parameters. These results demonstrate time-resolved chemiluminescence tomography as a non-intrusive tool for resolving volumetric detonation dynamics that are difficult to infer from point, planar, or line-of-sight diagnostics.

Quantum mechanics abandoned the classical notion of a particle trajectory, yet trajectories remain conceptually appealing for resolving foundational issues in quantum mechanics. Bohmian mechanics offers one route to associating trajectories with quantum processes, but it requires explicit non-locality to remain consistent with EPR-type experiments, placing it in tension with special relativity. We propose an alternative approach: rather than deriving trajectories from a quantum guidance equation, we search for classical trajectories whose radiated frequency spectra match those of quantum processes such as atomic transitions. Using the Liénard-Wiechert potentials, we compute the electric and magnetic fields generated by a point charge along a given trajectory, numerically solving the retarded-time and from these fields obtain the power spectrum of emitted radiation. By fitting the parameters of a chosen family of trajectories, we identify "equivalent spectrum" trajectories that reproduce a target frequency distribution, including ones of quantum mechanical origin. We discuss the implications of this method and propose future work to determine whether equivalent spectrum trajectories belong to a family governed by a differential equation, which would constitute a quantum-equivalent equation of motion.

Most of the proton mass originates not from the Higgs mechanism but from the quantum structure of the QCD vacuum. The dominant contribution arises from the gluonic trace anomaly associated with the breaking of conformal symmetry in quantum chromodynamics. We show that this anomaly contribution is experimentally accessible through scalar gravitational form factors. The key observable is the scalar gluonic trace form factor of the proton, which can be reconstructed from three measurable quantities: the quark scalar gravitational form factor accessible in deeply virtual Compton scattering, the gluon scalar gravitational form factor measurable in near-threshold heavy quarkonium production, and the nucleon sigma-term form factor. We also show that the scalar gluonic form factor extracted from the trace anomaly is quantitatively consistent with lattice QCD and the instanton liquid model over hadronic distance scales. These results provide a direct experimental path to probing the gluonic origin of visible mass.

We introduce a multimodal directed energy deposition (DED) dataset for predicting the probabilistic local geometric variation of single laser tracks produced on stainless-steel 316L substrates. The dataset supports the NSF Future Manufacturing Data Challenge and contains three complementary modalities: in-situ thermal image sequences from a Stratonics ThermaViz melt-pool sensor, scanning electron microscopy (SEM) images acquired using a Zeiss EVO MA10 system, and full-field height maps acquired using a Bruker ContourGT-K white-light 3D optical profilometer. Each experiment is a bead-on-plate scan at one of four laser powers, 200, 300, 350, and 400 W, with a fixed scan speed of 10 mm/s. The release includes a multimodal coordinate convention linking thermal, SEM, and height-map measurements over a common physical 20–100 mm window, with the raw dataset available on Zenodo and participant-facing notebooks, reusable code, and documentation available on GitHub.

Accurate photometric redshift (photo-$z$) estimation and robust uncertainty quantification are essential for the LSST to achieve its precision cosmology goals. Traditional machine learning algorithms are largely restricted to point estimates, struggling to characterize the multimodal nature of redshift PDFs and the degeneracies within the color-redshift space. To address this, we present and validate the LSTM-MDNz architecture, which integrates sequential feature extraction with flexible probability density modeling to enhance both prediction accuracy and uncertainty calibration across a broad redshift range, thereby meeting the stringent data quality requirements necessitated by next-generation cosmological analysis. The LSTM-MDNz framework treats multi-band photometry as wavelength-ordered sequences, utilizing LSTM networks to capture non-linear evolutionary correlations across the SED. A Mixture Density Network (MDN) is then employed to explicitly model posterior PDFs via Gaussian mixture models (GMMs). Performance is evaluated on the HSC GalaxiesML dataset (which serves as a small-scale proxy for next-generation surveys like LSST) and benchmarked against the BNN architecture established by Jones et al. (2024). The proposed model consistently outperforms the BNN baseline, achieving a $\sim 10\%$ improvement in point-estimation accuracy (specifically across RMSE, MAE, scatter, and $\sigma_{\text{NMAD}}$) and a $\sim 20\%$ reduction in the rates of both general and catastrophic outliers. A uniform probability integral transform (PIT) distribution confirms well-calibrated probabilistic outputs. Furthermore, the PDF-based confidence metric $z_{\text{conf}}$ enables high-purity catalog construction: excluding just approximately $4\%$ of extremely low-confidence ($z_{\text{conf}} < 0.05$) samples reduces the overall outlier rate by $\sim 48\%$.

We study a mean-field reaction network whose species are assemblies built from identical atoms by reversible coagulation and fragmentation. Each assembly is an ordered binary tree, so the number of species of a given length grows combinatorially, as the Catalan numbers. The model nonetheless admits an explicit equilibrium and tractable stochastic dynamics. A finite volume $V$ sets a crossover length $l_c \sim \ln V$ that splits the equilibrium into two sectors. Below $l_c$ each assembly occurs in many copies and the rank-frequency distribution is Zipf-like; above $l_c$ individual species are rare and fluctuation-dominated. The statistical weight of the rare sector decays slowly with volume, controlling the finite-size scaling of diversity, Shannon entropy, and other assembly-weighted observables. The equilibrium also admits a transparent grand-canonical description in terms of a bond energy and an atomic chemical potential. Together these results make the model a controlled neutral baseline against which selection and driving in richer assembly networks can be measured.

The relic abundance of thermal dark matter depends not only on its particle interactions but also on the expansion history of the early Universe. We study the freeze-out of fermionic dark matter interacting with the Standard Model through higher-dimensional electromagnetic operators in an early matter-dominated cosmology. In particular, we consider magnetic dipole, electric dipole, anapole, and charge-radius interactions, and compute the couplings required to reproduce the observed dark matter relic abundance in the presence of entropy injection from the decay of a long-lived heavy field. The resulting parameter space is compared with that obtained in the standard radiation-dominated freeze-out scenario and confront it with current constraints from direct-detection experiments and solar neutrino observations. We find that the entropy dilution associated with an early matter-dominated epoch significantly reduces the interaction strength required to obtain the observed relic abundance, thereby rendering viable regions of parameter space that are excluded in the conventional cosmological history. Our results demonstrate that the cosmological history prior to Big Bang nucleosynthesis can have an important impact on the phenomenology and experimental viability of electromagnetic multipole dark matter.

Recently it was shown that a non-local T-duality-inspired smearing of the point mass introduces a finite zero-point length, while the regularized Newtonian gravitational self-energy is promoted to an additional source for the spacetime. The result is a nonsingular black-hole geometry whose ADM mass contains a finite self-energy contribution and whose extremal Planck-scale remnant sector has been proposed as a possible dark-matter component. We study how this spacetime would affect two familiar physical signals: the ringing of a massive scalar field and the motion of particles and light near the horizon. The zero-point length smooths the central region and changes the strong-field potential outside the horizon. On the wave side, we find that making the scalar field heavier increases the oscillation frequency and makes the damping weaker, a behavior associated with long-lived ringing. On the particle side, increasing the zero-point length makes the photon orbit and the innermost stable circular orbit more compact in physical mass units. The corresponding shadow becomes smaller, the photon-ring frequency becomes larger, and the orbital binding energy increases. These results show that the same regularizing correction leaves related imprints in wave propagation, black-hole shadows and circular-orbit physics.

In this work, I analyze the zero modes of a one-loop semiclassical Yang-Mills theory in \(3+1\)d. I find that zero modes are generated by gauge redundancy of the background field. Proper gauge fixing, achieved by introducing a bosonic ghost term, together with zeta-function regularization, yields a finite one-loop effective action in closed form that reproduces the well-known one-loop Yang-Mills beta function.

Wildfire smoke events produce extreme PM$_{2.5}$ concentrations that pose severe public health risks, yet forecasting rare, hazardous-level spikes remains a fundamental challenge. Time series foundation models (TSFMs), pretrained models offering zero-shot inference and efficient adaptation, perform strongly on general benchmarks, but their behavior under extreme out-of-distribution conditions is poorly understood. We present the first systematic benchmark comparing six TSFM configurations (zero-shot TimesFM, Chronos-2, Moirai-2, and Time-MoE, plus LoRA fine-tuned Chronos-2 and Time-MoE) against fully-trained baselines (LSTM, BiLSTM, Transformer) and naive persistence on a 12-year (2013–2025) hourly PM$_{2.5}$ dataset covering 1,375 wildfire incidents across 79 California monitoring sites. A leave-one-incident-out (LOIO) protocol evaluates generalization to unseen fires, using MAE, RMSE, and exceedance F1 at EPA AQI thresholds across 6-, 12-, and 24-hour horizons. Results reveal a consistent hierarchy. The BiLSTM achieves the lowest MAE ($5.16\,\mu g/m^3$) and the highest exceedance F1 at every threshold, including the Hazardous band ($>225.5\,\mu g/m^3$), reaching 0.63 versus at most 0.54 for any foundation model. Zero-shot TSFMs improve on persistence only modestly, and zero-shot Chronos-2 exhibits severe RMSE tail instability ($23.4\,\mu g/m^3$, negative $R^2$) from sporadic large errors. LoRA fine-tuning substantially improves both adapted families and largely repairs this instability, yet no foundation model surpasses the trained recurrent baselines on any metric. These findings challenge the assumption that larger pretrained models universally dominate environmental forecasting and provide actionable deployment guidance for wildfire air quality prediction.

The free massless Majorana field in 1+1 dimensions is employed to study the Bell-CHSH inequality in Quantum Field Theory. Use of the modular wedge localization enables us to show the near saturation of the Tsirelson bound.

We study magnetic skyrmions in a two-dimensional quasicrystalline lattice using a classical Heisenberg model with Dzyaloshinskii-Moriya interactions and an external magnetic field. The competition between the skyrmion-skyrmion repulsion and an emergent quasiperiodic pinning landscape gives rise to a sequence of distinct skyrmion lattice configurations as a function of field. The resulting hierarchy of quasiperiodic pinning potentials, characterized by closely spaced quasi-degenerate minima, enables a quasi-continuous suppression of the skyrmion density as the saturation field is approached, in sharp contrast to the strongly first-order collapse of skyrmion crystals on periodic lattices. This provides a direct mechanism for controlling the topological charge and, consequently, the emergent gauge field for itinerant electrons. As a consequence, the Hall conductivity can be strongly modified with small changes in the magnetic field and driven smoothly to zero near saturation. This field-controlled tunability, rooted in the underlying multistability, identifies quasicrystalline magnets as a platform for tunable topological textures, with potential applications in magnetic memory and magnetoelectronic response.

Cryptochromes are blue-light-sensitive flavoproteins that play central roles in biological function. In European robin (Erithacus rubecula) ErCry4a proteins, optical excitation of their flavin chromophore forms a long-lived radical pair through a sequence of electron transfer steps across a tetradic chain of tryptophan residues, making them primary candidates for magnetoreception in night migratory songbirds. Recent quantum chemical calculations indicate that nonadiabatic couplings play a central role in the energy and charge transfer processes initiated by optical excitation. Here, we study these dynamics in ErCry4a using ultrafast transient absorption spectroscopy with 10-fs time resolution in the 450-nm spectral range. We uncover a rapid, sub-50 fs red shift in stimulated emission, quenched within 360 fs by electron transfer from a nearby tryptophan moiety. While high-frequency excited state vibrations are rapidly damped, coherent motion involving several low-frequency vibrations persists during both the initial energy relaxation and the subsequent electron transfer. This is evidenced by probing the coherent vibrational motion of the formed FAD$^{\bullet-}$ radical anion and is independently validated by blocking the electron transfer through site-selective tryptophan mutation. Our results only provide insight into the role of nonadiabatic couplings for the initial steps of cryptochrome photoactivation and suggest a general strategy for redox-state-specific monitoring of charge transfer dynamics by probing coherent vibrational motion.

We study tides during the inspiral of a binary neutron star system, including nonlinear hydrodynamical interactions. Using an affine approximation that treats the perturbed neutron star (NS) as an ellipsoid, we analytically derive coupling coefficients among the quadrupolar f-modes and the radial mode to the four-wave order (next-to-next-to-leading order) in the Hamiltonian, allowing for arbitrary (aligned or anti-aligned) spin of the background star. Our model reveals a series of universal relations from first-principles arguments. We show that the three-wave (next-to-leading-order) interaction coefficients in a non-spinning star are fully determined by the properties of the linear tide. They do not probe new physics of the NS. Nonetheless, three-wave nonlinear tides are significant corrections to the gravitational waveform. We support this via a hybrid approach that simultaneously captures mode resonances expected in Newtonian hydrodynamics and is consistent with relativistic calculations in the low-frequency expansion. The nonlinear tide in a single NS can cause a phase shift of around 1.8 radians accumulated up to merger compared to the linear tide model; for a binary, the phase shift is approximately doubled. In a low-frequency expansion, the nonlinear tide is degenerate with the finite-frequency correction of the linear tide, introducing systematic bias when ignored. Our calculation extends to four-wave interactions, which, for a slowly spinning neutron star, provide only small corrections. For a rapidly rotating neutron star, the nonlinear centrifugal drive of the f-mode provides a window to study the internal buoyancy that cannot be probed by the linear and three-wave f-mode tides in slowly spinning systems. The four-wave anharmonicity cannot lead to resonance locking of the f-mode.

Variational quantum algorithms depend on the geometry of their parametrised circuits: metric-aware optimisation and time evolution require the Fubini–Study metric, which has hitherto demanded costly auxiliary measurements and ill-conditioned inversions. This work introduces a hardware-efficient $n$-qubit ansatz, which parametrises states by a binary tree and whose Hilbert-space pullback metric is diagonal in closed form. Quantum natural gradient on the tree parameters, variational imaginary- and real-time evolution, and exact unitary-invariant (Haar) sampling on a symmetry sector run with no auxiliary metric circuits or matrix inversion. When the target state is supported on a subspace of $k$ computational-basis states, the redundant tree parameters carry a gauge freedom a pruning compiler converts into circuits whose two-qubit count provably grows linearly in $k$; a variant reaches near-optimal $O(nk/\log n)$ scaling with the closed-form metric intact. On electronic-structure calculations for small molecules and half-filled Hubbard quench dynamics, the method reaches reference-level accuracy with one to three orders of magnitude fewer two-qubit gates than leading alternatives. Interchangeable constructions (a Schur-transform dressing or internal reparameterisations) make the ansatz exactly spin-adapted, with fixed total spin at every parameter and no penalty terms. The bare ansatz is an exactly controllable, well-conditioned and barren-plateau-free primitive for preparing and sampling sector states: on its own, it is classically simulable in $k$ (a boundary proved for a general class of sector-sparse ansätze); composed with a classically hard dressing, it yields molecular ground states, sector-Haar benchmarking, thermal correlators, and exact effective Hamiltonians trained from energy measurements alone, with the composed circuit carrying the potential for quantum advantage.

Nanoparticle-on-mirror (NPoM) cavities enable extreme light confinement and strong light-matter interactions, but their realization with phonon-polariton materials in the mid-infrared spectral range remains largely unexplored. Here, we use nano-FTIR spectroscopy to study the near-field response of individual phononic NPoM cavities formed by gold nanoparticles on a quartz substrate supporting phonon-polaritons. By placing a metal tip on top of the NPoM and recording the tip-scattered field, we observe two reproducible cavity resonances, identified as the fundamental and a second-order antenna modes by numerical simulations. The calculations show that, in absence of the tip, the NPoM cavity exhibits ultrasmall mode volumes ($V \sim 10^3$ nm$^3$) and high quality factors ($Q \sim 100$), resulting in extraordinary field intensity enhancements ($F \sim 10^4$) and Purcell factors ($P_F \sim 10^9$). They also indicate that the nano-FTIR tip enables efficient excitation and readout of these phononic NPoM modes without perturbing them, while enhancing the intrinsic local field intensity in the NPoM gap by two orders of magnitude. Our results establish phononic NPoM cavities as a promising platform for mid-infrared nanophotonics and pave the way for ultrasensitive vibrational spectroscopy based on nano-FTIR measurements of individual cavities.

In this work, we present a \(3+1d\) scalar QED model in a constant self-dual magnetic field configuration. We provide exact closed form analytic calculations of the partition function, the \(\beta\)-function, and the propagators. To our knowledge, we present the first closed-form finite expression for the matter field propagators in a self-dual background, which is made accessible by working entirely in the Landau level basis. This theory serves as a toy model for charged particles in parallel electric and magnetic fields, with natural extensions to studies of \(3+1d\) chiral magnetic effects and pulsar physics.

Computational modeling plays a central role in advancing our understanding of electro-chemical reactions and may thus guide the rational development of sustainable energy technologies. Despite significant methodological progress, achieving predictive and quantitatively reliable simulations of electrified solid-liquid interfaces under operando conditions remains a major challenge. Recently, the European COST Action EU-CONCERT (EUropean COllaborative Network on electroCatalysis for Efficient Renewable Technologies) was launched with the aim of advancing atomistic modeling of electrochemical reactions through systematic benchmarking and cross-validation. This position paper outlines the consortium's view of the current state of the art, identifies the priority methodological challenges to be addressed, and defines the benchmark tests that are urgently needed. This paper should serve as a guide to the community and a roadmap for the EU-CONCERT COST Action.

We show the effect of gate-induced strain on the valence band of a silicon (Si) metal oxide semiconductor (MOS) confined two-dimensional hole gas (2DHG). Increasing aluminum gate thickness, and thereby the strain in the channel, results in the onset of a second subband contributing to Shubnikov-de Haas oscillations. Temperature-dependent magnetotransport measurements reveal distinct cyclotron masses of $m_c^*=(0.36\pm0.04)m_0$ and $m_c^*=(0.49\pm0.02)m_0$. The measured cyclotron masses differ from those expected for an idealized heavy-hole (HH)/light-hole (LH) picture, reflecting the combined influence of quantum confinement, strain, and HH-LH mixing on the valence band.

We generalize the analytic theory and simulation models for liquid crystal ground states on conventional cones with positive apex Gaussian curvature and study liquid crystal ground states on hyperbolic cones with a delta function of negative apex Gaussian curvature. While both the local apex curvature on a conventional cone and a hyperbolic cone lead to a fixed unquantized pseudodefect in the conformal domain and behave like conventional disclinations with opposite topological charges, there are fundamental differences in the ground states as well, which can be viewed as a violation of charge conjugation symmetry in a liquid crystal phase. To illustrate the violated charge conjugation symmetry on curved surfaces, we study two simple examples: (a) $p$-atic liquid crystals on a hyperbolic cone with free boundary conditions at the cone base. (b) $p$-atic liquid crystals on a hyperbolic cone with tangential boundary conditions at the cone base. In the simple case of $p=1$ liquid crystals (a vector order parameter field) on a hyperbolic cone with tangential boundary conditions, the positive pseudocharge caused by the apex curvature can be stably bound with a topological charge of the same sign despite their repulsive interaction, in sharp contrast to the charge conjugated situation associated with conventional cones.

We report precision measurements of the ratio of Landé $g$ factors between the $3^2D_{5/2}$ and $4^2S_{1/2}$ states of a single trapped $^{40}\text{Ca}^+$ ion. The measurements are performed in two distinct ion trap apparatus: a cryogenic surface electrode radiofrequency Paul trap and a room-temperature permanent magnet Penning trap. The Penning trap measurements rely on resonant microwave excitation of magnetic sublevels and yield a ratio of $0.599~488~813~3(2)$, which is a more than 40-fold uncertainty reduction compared to previous work. The radiofrequency trap measurements utilize optical electric quadrupole transitions and yield a concurring value of $0.599~488~813(6)$. We estimate that systematic shifts for each system are well below the respective statistical uncertainty.

A root-finding method is used to study two-body mesonic decay in the hypertriton. We validate this Newton–Raphson root-finding approach by applying it to the negative-pion decay channel ($^{3}_{\Lambda}\mathrm{H} \rightarrow {}^{3}\mathrm{He} + \pi^{-}$), for which the pion momentum and lambda binding energy were recently reported by MAMI A1 Collaboration as $p_{\pi^-} = 113.789 \pm 0.020_{\text{stat.}} \pm 0.112_{\text{syst.}} \text{ MeV}/c$ and $B_{\Lambda} = 0.523 \pm 0.013_{\text{stat.}} \pm 0.075_{\text{syst.}}$ MeV, respectively. Using their reported $\Lambda$ binding energy, the root-finding method and an exact kinematic formula both yield $p_{\pi^{-}} = 113.790$ MeV/$c$, agreeing with each other. We then apply both the Newton–Raphson method and the exact formula to the neutral-pion decay channel ($^{3}_{\Lambda}\mathrm{H} \rightarrow {}^{3}\mathrm{H} + \pi^{0}$), for which the neutral pion momentum cannot be directly measured due to difficulties in experimental setup. Both methods agree, yielding a predicted neutral-pion momentum of $p_{\pi^{0}} = 118.129$ MeV/$c$. This validates the root-finding algorithm as a robust equivalent for predicting pion momenta that may be experimentally inaccessible in some cases. Furthermore, it establishes the method as a reliable tool for extension to three-body mesonic decays, for which the pion momentum is a continuum and the exact kinematic formula can no longer be applied. In addition, the pion momentum computed allows for its 4-momentum to be completely determined, a useful input for investigating its two-photon decay ($\pi^0 \to \gamma \gamma$) in the rest frame of the hypertriton.

Machine-learning models often replace vectors by normalized directions, projectors, covariances, subspaces, ordered flags, quantum states, or density operators before any classifier is fitted. This replacement is an invariance decision: it determines which distinctions are kept and which are quotiented out. We develop a self-contained real-to-Hermitian taxonomy for auditing such representations in quantum machine learning. On the real side, we formalize Grassmann and flag projector kernels, prove positive semidefiniteness and block-gauge invariance of a weighted flag kernel, and give a same-span block-swap witness showing when whole-span Grassmann geometry must fail while ordered flags succeed. On the quantum side, we prove that a noiseless fidelity kernel is exactly the Hilbert–Schmidt inner product between the associated rank-one Hermitian projectors, and that a QVR-style return probability is exactly an overlap score between the input projector and a learned anchor operator. Rank-constrained returns correspond to complex Grassmann anchors, while mixed or multimodal class models are naturally represented by density or positive-semidefinite anchors. Controlled vector, subspace, statevector, anomaly, finite-shot, and quotient-witness experiments support the same conclusion: quantum and geometric lifts are useful when their invariances match the task, and fail correctly when discarded information is label-bearing. The paper makes no hardware-speedup or quantum-advantage claim.

Turbulence in the solar interior and atmosphere plays a crucial role in energy transport, yet modeling its subgrid-scale effects remains a major challenge. This study leverages machine learning (ML) models to predict components of the Reynolds stress tensor using high-resolution StellarBox simulations of the quiet Sun. Previously, we have compared a Multi-Layer Perceptron (MLP) and a 3D Convolutional Neural Network (CNN) against physics-based baselines to achieve a lower Mean Squared Error (MSE) and better generalization across various heights and depths in the solar atmosphere. To enhance learning, in this work, we investigate cluster-weighted training using K-Means and Hierarchical Agglomerative Clustering (HAC). By weighing the loss function based on cluster-specific prediction errors, we direct the model's attention to high-error regions. It significantly improves CNN performance, achieving 34% lower MSE and a significantly higher R2 score indicating that integrating deterministic clustering with ML is a promising technique for modeling subgrid turbulence, in particular, and regression in diverse environments, in general.

We study generalized global symmetries of the bosonic M2-brane in eleven-dimensional backgrounds with non-trivial four-form flux. Focusing on compactifications of the form $AdS_5\times S^2_{1} \times S^2_{2}\times T^2$, we show that the monopole and winding symmetry sectors of the membrane do not organize as an ordinary direct product once the Wess–Zumino coupling is included. Instead, they combine into a non-trivial 2-group global symmetry. We identify the corresponding mixed background-gauge structure and show that the quantized target space flux determines the associated Postnikov class. This provides a concrete realization of higher-group symmetry in the worldvolume theory of the M2-brane induces a flux quantization on the worldvolume and relates its global symmetry structure to the introduction of a quantized flux in M-theory.

The Minimal Supersymmetric Standard Model (MSSM) has several problems: 1. its $\mu$ term must be forbidden, then regenerated at the weak scale, 2. it allows for $R$-parity violating superpotential terms which lead to rapid proton decay, 3. it allows for dimension-5 proton decay operators. The usual imposition of $R$- or matter parity $P_M$ solves only the second of these, whereas anomaly-free discrete $\mathbb{Z}_n^R$ symmetries (consistent with grand unification) address all of them. Once the $\mu$-term is forbidden by the imposition of a discrete $\mathbb{Z}_n^R$ symmetry (which can emerge as a discrete remnant of string compactifications to 4-dimensions), the MSSM develops an accidental global $U(1)_{PQ}$ symmetry (thus providing a plausible origin for the global $U(1)_{PQ}$ needed for solving the strong CP problem). By coupling the Higgs fields to PQ-charged gauge singlet fields $X,\ Y$ (in the Kim-Nilles mechanism), and imposing SUSY breaking, one regenerates $\mu$ at the weak scale whilst breaking the discrete $\mathbb{Z}_n^R$ and the $U(1)_{PQ}$. The broken global $U(1)_{PQ}$ develops a pseudo-Goldstone boson, the DFSZ axion, thus (perhaps inadvertently) solving the strong CP problem. In this setting, SUSY develops a dark matter candidate, the SUSY DFSZ axion, and possibly, though not necessarily, a WIMP dark matter candidate as well, depending on the order of the induced $R$-parity violating operators.

We use linear programming to prove a separable version of Ky Fan's majorization relation for a sum of two operators that are each a tensor product of $n$ positive semidefinite operators. We give an example showing that such a relation does not hold in general for sums of three or more tensor products of three or more positive semidefinite operators.

The leading parity-odd mass–spin curvature invariant of the solar exterior, $P_{\odot}\equiv{}^{*}\!R\,R\simeq 288\,G^{2}M_{\odot}^{2}a_{\odot}\cos\theta/c^{4}r^{7}$, changes sign when the Earth crosses the solar equatorial plane and acts as the geometric source of the gravitational chiral anomaly. We study two minimal phenomenological responses to this structure: a long-memory reservoir $Q\propto\int(P_{\odot}-\langle P_{\odot}\rangle)\,dt$ and the local worldline derivative $D=u^{\mu}\nabla_{\mu}P_{\odot}$. Both have an annual Fourier phase fixed by ephemerides, $t^{*}=158.7$~d (June 7–8) or the opposite branch $t^{*}=341.4$~d, with a calculable secular drift of $+0.014$~d\,yr$^{-1}$ and an energy-independent geometric input phase, while predicting different semiannual fractions, $3.75\%$ and $15\%$, respectively. The response amplitudes and their microscopic origin are not predicted; the phase is. Single-amplitude fits to the digitized DAMA/LIBRA–phase2 1–3~keV residuals give $\chi^{2}/\mathrm{dof}=62.7/51$ for the reservoir and $63.6/51$ for the derivative, against $60.9/51$ for the standard-halo cosine. The most precise published phase, $t^{*}=153.5\pm3.8$~d, lies $0.3\sigma$ from the halo value and $1.4\sigma$ from the node-locked one; phase metrology at the two-day level ($\simeq3\sigma$), together with the phase-locked semiannual component, discriminates between the two clocks.

Models of eclipsing binaries require the assignment of appropriate emergent intensities to the surface elements of the binary components. For distance-dependent modelling of flux-calibrated light curves, this necessitates an approximation of the absolute normal intensities of both components of the binary, as well as how their brightness varies across the stellar disks (limb darkening). Such surface intensities are often inferred from other physical properties of the synthetic binary (effective temperature, surface gravity, etc.) through the use of model atmospheres, which in turn are generally suited to a particular range of stellar types or parameters. Here, we present the major developments included in the PHOEBE 2.5 release (publicly available from http://phoebe-project.org), which improve the fidelity of model binaries comprising hot, compact stars. These developments include the incorporation model atmospheres produced using the Tubingen Model Atmosphere Package (TMAP) and Montreal/Tremblay codes (complementing the already incorporated PHOENIX and Castelli & Kurucz models, primarily suited to main sequences stars and low-temperature giants). Similarly, PHOEBE v2.5 now allows for blending/extrapolation of model atmospheres, meaning one can continue to make use of model atmospheres in cases when a small number of surface elements have parameters outside the model atmosphere grid. As an added value product, we also present tables of limb-darkening coefficients derived from the newly incorporated model atmospheres, such that they can be used as inputs in other binary modelling codes.

The couplings of the strong to electroweak sectors of the Standard Model enable the exploration of each using our growing knowledge of the other. In this review, we will follow the sweep of history. Starting with QED as a precision theory, deep inelastic scattering served as a gateway to the strong interactions, followed by leptonic annihilation and quark-antiquark annihilation in hadron-hadron scattering. In turn, the resulting understanding of QCD helped establish the Standard Model. The same techniques form the basis for many precision electroweak measurements at high energy and searches for signs of new physics.