The sandpile automata of Bak, Tang, and Wiesenfeld (Phys. Rev. Lett., 1987) are a simple model for the diffusion of particles in space. A fundamental problem related to the complexity of the model is predicting its evolution in the parallel setting. Despite decades of effort, a classification of this problem for two-dimensional sandpile automata remains outstanding. Fungal automata were recently proposed by Goles et al. (Phys. Lett. A, 2020) as a spin-off of the model in which diffusion occurs either in horizontal $(H)$ or vertical $(V)$ directions according to a so-called update scheme. Goles et al. proved that the prediction problem for this model with the update scheme $H^4V^4$ is $\textbf{P}$-complete. This result was subsequently improved by Modanese and Worsch (Algorithmica, 2024), who showed the problem is $\textbf{P}$-complete also for the simpler updatenscheme $HV$. In this work, we fill in the gaps and prove that the prediction problem is $\textbf{P}$-complete for any update scheme that contains both $H$ and $V$ at least once.

We study Bakry-Emery curvature for fractional Laplacian generators using a Fourier representation of the carré du champ operator. For the stable generator of order gamma, the associated kernel on same-sign frequencies coincides with the covariance kernel of fractional Brownian motion with Hurst parameter equal to gamma divided by two. This observation allows the curvature inequality to be reformulated as a generalized eigenvalue problem for covariance matrices. On the one dimensional torus we analyze this matrix formulation for trigonometric polynomials. In the Cauchy case (gamma equal to one), corresponding to Brownian covariance, the eigenstructure can be computed explicitly and yields a Bakry-Emery curvature bound on the corresponding Fourier subspaces. We also study the effect of adding a confining drift to the Cauchy generator and show that the curvature spectrum undergoes a simple scalar shift. These results provide a matrix formulation of Bakry-Emery curvature for certain nonlocal operators and highlight a structural connection between fractional Laplacians and fractional Brownian covariance kernels.

We present peapods (github.com/PeaBrane/peapods), an open-source Python package for Monte Carlo simulation of Ising spin systems with arbitrary coupling constants on periodic Bravais lattices with user-specified neighbor offsets. The computational core is written in Rust and exposed to Python via PyO3, combining the ergonomic interface of Python with the performance of compiled, memory-safe code. The package implements Metropolis and Gibbs single-spin-flip algorithms, Swendsen-Wang and Wolff cluster updates, parallel tempering, and three replica cluster moves for spin glasses: the Houdayer isoenergetic cluster move, the Jorg stochastic variant, and the Chayes-Machta-Redner (CMR) blue-bond algorithm. Overlap statistics between replica pairs enable computation of the spin glass order parameter and Binder ratio. Replica-level parallelism is achieved through the Rayon work-stealing scheduler. We validate the implementation against the exact critical temperatures of the two-dimensional Ising model on the square and triangular lattices via finite-size scaling of the Binder cumulant.

We investigate qubit error bursts in 5- and 7-transmon processors of similar design, fabrication and packaging, but with different types of qubit Josephson junctions. Measurements for each are performed in two refrigerators to discern device-specific from refrigerator-dependent characteristics. The duration and rate of bursts are device specific but within the range of prior experiments and consistent with ionizing radiation. We observe two unforeseen signatures specifically in the processor with Dolan junctions. First, increasing the rate of $π$ pulsing in the detection scheme shortens the recovery time to equilibrium, which is explained by a quasiparticle pumping mechanism. The second signature is an anomalous time dependence in the burst rate: a surge happens days or weeks after cooldown, followed by a strong suppression that persists until thermal cycling.

By work of Davison and Meinhardt, the cohomological Hall algebra of a symmetric quiver with potential admits a geometrically defined filtration (the perverse filtration) whose associated graded is a supercommutative algebra. In the case of the triple quiver of a quiver with the canonical cubic potential, which corresponds to the preprojective algebra of the quiver via dimensional reduction, there is an additional filtration (the less perverse filtration), which is defined more generally for cohomological Hall algebras of suitably geometric $2$-Calabi-Yau categories in work of Davison. In this paper, we show that the degenerations of the cohomological Hall algebras of preprojective algebras and more generally $2$-Calabi-Yau categories with respect to the less perverse filtration is isomorphic to the enveloping algebra of the current Lie algebra of the BPS Lie algebra. This result applies in particular to CoHAs of local systems on Riemann surfaces and Higgs bundles on smooth projective curves. We extend this description to deformations of the cohomological Hall algebra obtained via torus actions on the arrows of the quiver and deformed canonical cubic potentials via the deformed dimensional reduction of Davison-P\u adurariu. We prove all our results at the level of sheafified CoHAs, which allows us to deduce similar statements for all versions of nilpotent CoHAs. Last, we use our results to compare the less perverse filtration on CoHAs of preprojective algebras with the order filtration on the Maulik-Okounkov Yangian, via the comparison isomorphism of Botta-Davison and Schiffmann-Vasserot.

The Sun is a promising target for dark matter (DM) searches due to its ability to accumulate DM particles via scattering and catalyze their self-annihilation. However, at low DM masses, DM particles can also "evaporate" due to subsequent collisions with the hot thermal plasma of the Sun. While several modeling studies have calculated the competitive dynamics of DM evaporation and annihilation, observational studies have typically assumed a fixed 4 GeV "evaporation limit", below which DM evaporates before it can annihilate. In this paper, we consider the competitive effects of DM evaporation and annihilation on spin-dependent DM nucleon cross-section limits, finding that Solar observations can continue to exceed terrestrial constraints by between 1-5 orders of magnitude for DM masses between 2-4 GeV, and can even provide world leading constraints below 0.2 GeV where direct detection is limited.

Purpose: This study compares two augmented reality (AR)-guided imaging workflows, one based on ultrasound shape completion and the other on cone-beam computed tomography (CBCT), for planning and executing lumbar needle interventions. The aim is to assess how imaging modality influences user performance, usability, and trust during AR-assisted spinal procedures. Methods: Both imaging systems were integrated into an AR framework, enabling in situ visualization and trajectory guidance. The ultrasound-based workflow combined AR-guided robotic scanning, probabilistic shape completion, and AR visualization. The CBCT-based workflow used AR-assisted scan volume planning, CBCT acquisition, and AR visualization. A between-subject user study was conducted and evaluated in two phases: (1) planning and image acquisition, and (2) needle insertion. Results: Planning time was significantly shorter with the CBCT-based workflow, while SUS, SEQ, and NASA-TLX were comparable between modalities. In the needle insertion phase, the CBCT-based workflow yielded marginally faster insertion times, lower placement error, and better subjective ratings with higher Trust. The ultrasound-based workflow achieved adequate accuracy for facet joint insertion, but showed larger errors for lumbar puncture, where reconstructions depended more heavily on shape completion. Conclusion: The findings indicate that both AR-guided imaging pipelines are viable for spinal intervention support. CBCT-based AR offers advantages in efficiency, precision, usability, and user confidence during insertion, whereas ultrasound-based AR provides adaptive, radiation-free imaging but is limited by shape completion in deeper spinal regions. These complementary characteristics motivate hybrid AR guidance that uses CBCT for global anatomical context and planning, augmented by ultrasound for adaptive intraoperative updates.

Molecular polaritons have drawn great interest in recent years as a possible avenue for providing optical control over chemical dynamics. A central challenge in the field is to identify physical phenomena that require a quantum rather than a classical treatment of electrodynamics. In this work, we use our recently developed mean-field quantum (mfq) and full-quantum (fq) real-time nuclear--electronic orbital (RT-NEO) time-dependent density functional theory methods to simulate polaritonic dynamics for a molecule under vibrational strong coupling when a quantized cavity mode is initialized in a Fock state rather than a coherent state. Our previous work showed that a coherent state initial condition for the cavity mode leads to polariton formation for both the mfq-RT-NEO and fq-RT-NEO methods. Herein, we show that the mfq-RT-NEO method, which does not allow light--matter entanglement, does not predict polariton formation for a Fock state initial condition. Similar to the mfq-RT-NEO method, the fq-RT-NEO method does not predict oscillations of the cavity mode coordinate and molecular dipole operator expectation values for a Fock state initial condition. However, the fq-RT-NEO method does predict oscillations of the expectation values of even powers of these operators as well as light--matter entanglement, implicating polariton formation with a Fock state initial condition. All these observations can be explained with model systems. These results suggest that using a quantized cavity mode initial condition that does not have a direct analogy to an initial condition in classical electrodynamics can lead to physical phenomena that can only be described by a quantum treatment of the cavity mode.

Effective Field Theories (EFTs) are the primary tool for interpreting precision collider data in the absence of new resonances. However, in the dimension-8 Standard Model Effective Field Theory (SMEFT), the utility of traditional algebraically minimal bases is fundamentally limited by kinematic mixing: multiple operators contribute to a single high-energy amplitude, creating degeneracies that obscure ultraviolet interpretations and complicate the application of theoretical constraints. We introduce a generative framework that resolves this by constructing operators directly from the conserved Noether currents of the Standard Model. The resulting Kinematically Diagonalized Current Basis (KDCB) ensures that each operator maps to a unique asymptotic energy scaling ($E^4$, $E^2$, $E^0$) in scattering amplitudes. This organization makes S-matrix positivity bounds manifest, enables a stable auxiliary-field formulation for Monte Carlo simulation, and provides direct diagnostics for universal versus non-universal ultraviolet completions through current decomposition. By rotating the operator space into physically interpretable sectors, the KDCB offers a transformative framework for global fits and a clear pathway from high-energy data to the structure of new physics.

We present a multi-wavelength study of nuclear outflows in the nearby dwarf Seyfert galaxy NGC~4395, which hosts an intermediate-mass black hole. Using \textit{JWST}/NIRSpec and MIRI IFU spectroscopy (1.66--28.6~$μ$m), together with ALMA and Gemini/GMOS data, we probe the ionised and molecular gas on parsec scales. The JWST nuclear spectra reveal 134 emission lines, including H\,\textsc{i}, He, numerous fine-structure lines, H$_2$ rotational/ro-vibrational transitions, and several PAH bands. Modelling of the H$_2$ rotational lines reveals three warm/hot molecular components ($T\!\approx\!580$, 1480, and 2900~K), along with a cold ($<50$~K) phase traced by ALMA CO(2--1). Outflow signatures are detected in cold and warm/hot molecular gas, in H\,\textsc{i}, and in 36 fine-structure lines spanning ionisation potentials of 7.6--300~eV. Ionised outflow velocities range from 127 to 716~km\,s$^{-1}$, with blueshifted and redshifted components consistent with a stratified biconical geometry. The cold molecular gas shows a mass outflow rate nearly 1--2 orders of magnitude larger than that of the warm/hot molecular and ionised phases. The kinetic coupling efficiency is 0.003--0.12\% for the coronal-line gas and 0.4--1.4\% for the H\,\textsc{i} outflow, indicating that only the low-ionisation gas significantly impacts the surrounding ISM. Outflow velocity and the fraction of flux in the outflowing component increase with ionisation potential, implying that the most highly ionised gas originates closest to the AGN and is most efficiently accelerated.

The Lorentz mirror model provides a clean setting to study macroscopic transport generated solely by quenched environmental randomness. We introduce a hierarchical version whose distribution of left--right crossings satisfies an exact recursion. In dimensions $d\geq 3$, we prove normal transport: the mean conductance scales as (cross-section)/(length) on all length scales. A Gaussian closure, supported by numerics, predicts that the variance-to-mean ratio of the conductance converges to the universal value $2/3$ for all $d\geq 2$ (the ``$2/3$ law''). We provide numerical evidence for the $2/3$ law in the original (non-hierarchical) Lorentz mirror model in $d=3$, and conjecture that it is a universal signature of normal transport induced by random current matching. In the marginal case $d=2$, our hierarchical recursion reproduces the known scaling of the mean conductance and its variance. A YouTube video discussing the background and the main results of the paper is available: https://youtu.be/G1nqKd6MiXo

Transition-metal nitrides in η-carbide type structures exhibit unusual bonding motifs and proximity to magnetic instabilities. Yet they remain unexplored in thin-film form due to the difficulty of stabilizing nitrogen-poor ternaries among competing phases. Here, we report the thin-film synthesis and phase-stability mapping of the η-nitride systems Fe-W-N and Fe-Mo-N. Amorphous Fe-M-N (M = W, Mo) combinatorial libraries deposited by reactive co-sputtering crystallize upon rapid thermal annealing, enabling systematic identification of synthesis windows as a function of composition and annealing temperature. Using laboratory powder X-ray diffraction and synchrotron grazing incidence wide angle X-ray scattering, we establish that Fe3Mo3N-based η-carbide phases form over a substantially broader compositional and thermal range than W-based compositions, where η structures are stabilized only when the films are Fe-rich. These trends are rationalized using mixed chemical-potential vs. composition phase diagrams that capture the narrow nitrogen chemical-potential stability of η-nitrides. Magnetic measurements reveal that ferromagnetism is induced in Fe-rich Fe3.54Mo2.46N with a small exchange-bias-like response that is absent in Fe3W3N-based compositions, highlighting the sensitivity of magnetic behavior to modest deviations from stoichiometry. This work establishes practical thin-film synthesis routes for η-nitride materials and demonstrates how composition can be tuned to access emergent magnetic phenomena in these complex nitrides.

The fractal dimension $D$ is used to map the large-scale galaxy distribution in the Universe by color types: blue, green and red. Using a $NUVrK$-complete COSMOS2020 subsample of 618,952 galaxies observed up to $z=4$, number densities were derived and plotted against two cosmological distance measures, the luminosity and comoving (galaxy area) distances, in order to estimate $D$ for each galaxy color type in two redshift intervals: $z\gtrless1$. We found a general gradient $D_{\mathrm{blue}}> D_{\mathrm{red}}>D_{\mathrm{green}}$ with $D=1.40-2.03$ for $z<1$. For $1<z\leq4$, the gradient changes to $D_{\mathrm{blue}}>D_{\mathrm{green}}>D_{\mathrm{red}}$, and the fractal dimension values are lower, $D=0.03-0.44$. These results suggest that the fractal dimension is a sensitive diagnostic for how galaxy populations trace the evolving cosmic web, and confirm the fractal dimension as a useful tool for observational mapping of large-scale structure by galaxy color.

In "Bipartite minors" [Journal of Combinatorial Theory, Series B, 2016], Chudnovsky et al. introduced the bipartite minor relation, a quasi-order on the class of bipartite graphs somewhat analogous the minor relation on general graphs and asked whether it is a well-quasi-order. We answer this question negatively by giving an infinite set of 2-connected bipartite graphs that are pairwise incomparable with respect to the bipartite minor relation. We additionally give two sets of infinitely many pairs of bipartite graphs: one set of pairs G, H such that H is a bipartite minor, but not a minor, of G, and one set of pairs G, H such that H is a minor, but not a bipartite minor, of G.

Technetium-99m ($^{99m}$Tc) is essential to more than 16 million diagnostic procedures performed annually in the United States. It is typically acquired on-site from generators containing $^{99}$Mo, in turn produced at nuclear reactor facilities. This supply chain involves multiple points of vulnerability, which can lead to shortages and delays with potentially negative patient outcomes. We report on the development of a new family of cyclotrons originally designed for the IsoDAR neutrino experiment, capable of operating at much higher current than typical cyclotrons. When operated with deuterons at 1.5 MeV/amu and an anticipated continuous beam current of 5 mA, simulations project that such a system would yield $\sim$10$^{13}$ neutrons per second using a thin beryllium target. This neutron yield is sufficient, in principle, to support $^{99}$Mo production without the use of highly enriched uranium or reliance on foreign reactors. Simulations and conceptual design studies suggest that the system's beam dynamics could make it a viable pathway toward decentralized, hospital-based isotope generation. The relatively low energy of the deuterons minimizes activation and safety concerns. This work presents the physics motivation, technical design considerations, and projected neutron yields, outlining a pathway from a neutrino-physics prototype to a biomedical isotope production platform.

The Reynolds equation is derived from the incompressible Navier Stokes equations under the lubrication assumptions of a long and thin domain geometry and a small scaled Reynolds number. The Reynolds equation is an elliptic differential equation and a dramatic simplification from the governing equations. When the fluid domain is piecewise linear, the Reynolds equation has an exact solution that we formulate by coupling the exact solutions of each piecewise component. We consider a formulation specifically for piecewise constant heights, and a more general formulation for piecewise linear heights; in both cases the linear system is inverted using the Schur complement. These methods can also be applied in the case of non-linear heights by approximating the height as piecewise constant or piecewise linear, in which case the methods achieve second order accuracy. We assess the time complexity of the two methods, and determine that the method for piecewise linear heights is linear time for the number of piecewise components. As an application of these methods, we explore the limits of validity for lubrication theory by comparing the solutions of the Reynolds and the Stokes equations for a variety of linear and non-linear textured slider geometries.

We present a microscopic theory of an atomic spin diode. Our proposed system consists of two magnetic adatoms deposited on the surface of a two-dimensional electron gas with Rashba spin-orbit coupling. A local s-d type coupling between the local spins and the spins of the electrons induces a non-local Ruderman-Kittel-Kazuya-Yoshida type interaction and a Dzyalonshinskii-Moriya interaction, in addition to dissipative interactions, between the spins. We derive the effective action for the spins using the Keldysh formalism. From the effective action, we also derive equations of motion for the spins which are shown to be of Landau-Lifshitz-Gilbert (LLG) type, and give expressions for the effective field and Gilbert damping which appear in this equation. From our microscopic theory, we find that for an in-plane magnetic field perpendicular to the vector connecting the two atoms, the magnitude of the field and the distance between the atoms can always be tuned to engender perfectly diodic coupling. Our findings may pave the way to experimental realisation of atomic spin diodes.

In this paper, we prove that biorthogonal ensembles on the real line with a specific derivative structure admit an explicit correlation kernel of double contour integral form. We will demonstrate that this expression is a valuable starting point for asymptotic analysis and that our class of biorthogonal ensembles admits a large variety of limit kernels, by proving that two new classes of limit kernels can occur. The first type is a deformation of the hard edge Bessel kernel which arises in polynomial ensembles describing the eigenvalues of the sum of two random matrices, while the second type arises for Muttalib-Borodin type deformations of polynomial ensembles.

Transcription factors (TFs) regulate gene expression by binding to specific genomic loci determined by DNA sequence. Their sequence specificity is commonly summarized by a consensus binding motif. However, eukaryotic genomes contain billions of low-affinity DNA sequences to which TFs associate with a sequence-dependent binding energy. We currently lack insight into how the genomic sequence defines this spectrum of binding energies and the resulting pattern of TF localization. Here, we set out to obtain a quantitative understanding of sequence-dependent TF binding to both motif and non-motif sequences. We achieve this by first pursuing accurate measurements of physical binding energies of the human TF Klf4 to a library of short DNA sequences in a fluorescence-anisotropy-based bulk competitive binding assay. Second, we show that the highly non-linear sequence dependence of Klf4 binding energies can be captured by combining a linear model of binding energies with an Ising model of the coupled recognition of nucleotides by a TF. We find that this statistical mechanics model parametrized by our in vitro measurements captures Klf4 binding patterns on individual long DNA molecules stretched in the optical tweezer, and is predictive for Klf4 occupancy across the entire human genome without additional fit parameters.

The results of a study of the cosmic ray composition in individual events in the energy range (2-12.5) EeV using the muon correlation method is presented. The considered sample included showers with zenith angles less than 60 degrees recorded in the period 1974-2018. The existence of four separate groups of primary particles with different origins is confirmed. The obtained results have potential importance for understanding the composition of cosmic rays in the specified primary energy range.

The dominant radiation mechanism that powers the prompt $γ$-ray emission in gamma-ray bursts (GRBs) remains poorly understood. High quality, time- and energy-resolved linear polarization measurements of prompt $γ$-ray photons can distinguish between synchrotron and inverse-Compton processes and provide crucial constraints on the outflow properties. This will be achieved by POLAR-2 that is proposed as a dedicated GRB polarimeter and successor to POLAR. The High-energy Polarimetry Detector (HPD) is one of the three instruments of POLAR-2 that features significantly improved sensitivity in the $(40-1000)$\,keV energy range and a detection area four times larger than that of POLAR. Here we demonstrate the capabilities of the HPD to constrain key physical model parameters by creating and fitting to synthetic sources using a time-resolved spectro-polarimetric theoretical model of prompt GRB emission. The time-resolved spectral and polarization fits are performed using a novel technique featuring maximum likelihood over an unbinned (in time and energy) list of detected events. The constrained model parameters directly relate to the underlying source physics that would reveal an accelerating, coasting or decelerating emission region. For a pulse fluence of $\mathcal{F}=10^{-5}\mathcal{F}_{-5}\,{\rm erg\,cm^{-2}}$ and higher we can constrain the time-integrated polarization degree to an absolute accuracy ($1\,σ$) of about $2.2\mathcal{F}_{-5}^{\,-1/2}$ per cent, as long as source photons dominate over the background. In bright GRBs, such unprecedented accuracy at these energies will allow to distinguish between different models for the prompt GRB emission mechanism and constrain the magnetic field geometry, jet angular structure and outflow composition.

We present upgraded Giant Metrewave Radio Telescope (uGMRT) observations of 0731+438, an \mbox{FR II} radio galaxy at a redshift of 2.429 with two lobes separated by 82 kpc. A blueshifted, faint and broad \mbox{H{\sc i}} 21 cm absorption line with velocity full width at half maximum (FWHM) $\sim 600\,\rm km\,s^{-1}$ is detected against the southern radio lobe that is 47 kpc from radio core, indicating a neutral hydrogen outflow associated with jet-gas interaction beyond the host galaxy. The outflow has a mass outflow rate of $\sim\,0.4T_{\rm s}Ω\rm\, M_\odot\,{\rm yr}^{-1}$, which could increase to $\sim\,4.0T_{\rm s}Ω\rm\,M_\odot\,{\rm yr}^{-1}$, corresponding to an energy outflow rate of $2.4T_{\rm s}Ω\times10^{40}$ -- $1.5T_{\rm s}Ω\times10^{41}\,\rm erg\,s^{-1}$, where $T_{\rm s}$ is the spin temperature and $Ω$ is the solid angle of the outflow. Previous optical observations identified an extended emission line region aligned with the radio axis, ionized by the central Active Galactic Nucleus (AGN). Within this region, a warm and ionized outflow with a mass outflow rate of $\sim\,50\rm\, M_\odot\,{\rm yr}^{-1}$ and an energy outflow rate of $\sim1.7\times10^{43}\,\rm erg\,s^{-1}$ was detected. We propose that both the extended emission line region and the optical outflow are results of synergistic effect between jet and AGN radiation. The AGN likely exerts negative feedback on the host galaxy, as evidenced by the gas expulsion by the jet and the high velocity dispersion of ionized gas observed optically. So far, detections of jet-driven neutral hydrogen outflows remain rare. The high redshift, large outflow radii, substantial mass outflow rate and energy outflow rate of the neutral hydrogen outflow in 0731+438 expand the known parameter space of such outflows.

The Bayesian approach provides powerful methods for variable selection. The ability to incorporate sparsity through prior beliefs and account for parameter uncertainty allows Bayesian variable selection to consistently identify which of the variables are active and exhibit strong finite-sample performance. However, Bayesian methods require the correct specification of full likelihoods for the data, and there is increasing awareness of the problems that model misspecification causes for variable selection. Current approaches to mitigate misspecification either require complex models, detracting from the interpretability of the variable selection task, or move outside rigorous Bayesian uncertainty quantification and provide no recognised method for variable selection. This paper establishes the model quasi-posterior as a principled tool for variable selection. We prove that the model quasi-posterior shares desirable properties of Bayesian variable selection without requiring full likelihood specification. Instead, the quasi-posterior combines a prior with a quasi-likelihood and requires only specification of mean and variance functions, and is therefore robust to other aspects of the data. Marginalising the quasi-likelihood is analytically possible for linear regression, and Laplace approximations are used beyond this to ensure computational tractability. Extensive simulation studies illustrate improved variable selection accuracy across diverse data-generating scenarios when compared with likelihood-based Bayesian variable selection and lasso-penalized methods. We further demonstrate practical relevance through applications to real datasets from social science and genomics.

We map out the global phase diagram of a single mobile impurity in the two-dimensional Bose-Hubbard model, spanning the bath evolution from a compressible superfluid (SF) to an incompressible Mott insulator (MI) and the full range of impurity-bath coupling. Using sign-problem-free worm-algorithm quantum Monte Carlo, we identify two distinct self-trapping mechanisms that organize the entire diagram. In the compressible SF, increasing impurity-bath coupling $|U_{\mathrm{ib}}|$ drives an interaction-driven self-trapping crossover signaled by a collapse of the \emph{impurity} winding number: a light, extended polaron evolves continuously into a heavy polaron and ultimately into a self-trapped state -- a repulsive \emph{saturated bubble} or an attractive \emph{bound cluster} -- even while the bath remains globally superfluid, demonstrating self-trapping without any bath phase transition. By contrast, when the bath is tuned across the SF-MI transition at fixed $U_{\mathrm{ib}}$, localization is compressibility controlled. The vanishing bath compressibility quenches long-wavelength density redistribution and suppresses polaronic dressing, converting the SF polaron into a weakly dressed, nearly free defect upon entering the MI when $|U_{\mathrm{ib}}| \le 8.0$. Then increasing $|U_{\mathrm{ib}}|$ triggers a distinct Mott-specific route: the impurity binds a quantized vacancy or particle excitation, manifested by discrete changes $ΔN_b=\pm1$ in the total bath occupation. Together, our results provide a unified microscopic picture of impurity self-trapping in correlated lattice bosons, governed by winding collapse in the SF and by compressibility loss and defect quantization across the SF-MI boundary.

Turning memristor arrays from efficient inference engines into systems capable of on-chip learning has proved difficult. Weight updates have a high energy cost and cause device wear, analog states drift, and backpropagation requires a backward pass with reversed signal flow. Here we experimentally demonstrate learning on standard filamentary HfOx/Ti arrays that addresses these challenges with two design choices. First, we rely on forward-only training algorithms in the Forward-Forward family that use only inference-style operations. Second, we use sub-1 V reset-only, single-pulse updates that cut energy and yield stable analog states. We train two-layer classifiers on an ImageNet-resolution four-class task using arrays up to 8,064 devices. Two forward-only variants, two-pass supervised Forward-Forward and a single-pass competitive rule, achieve test accuracies of 89.5% and 89.6%, respectively; a reference experiment using backpropagation reaches 90.0%. Across five independent runs per method, these accuracies are indistinguishable within statistical uncertainty. Trained models retain accuracy for at least one month under ambient conditions, consistent with the stability of reset-only states. Sub-1 V reset updates use 460 times less energy than conventional program-and-verify programming and require just 46% more energy than inference-only operation. Together, these results establish forward-only, sub-1 V learning on standard filamentary stacks at array scale, outlining a practical, pulse-aware route to adaptive edge intelligence.

The branching ratios of dilepton anomalous decays $η^{(\prime)}\toπ^+π^-l^+l^-$, where $l=e,μ$, are calculated in the framework of the Nambu -- Jona-Lasinio model. Particular attention is paid to studying the hadronic perturbative part of the full decay amplitudes, parameterized by two low-energy constants $δ^{(\prime)}$ and $α^{(\prime)}$. It is shown that due to the mixing of $0^{-+}$--$1^{++}$ $(J^{PC})$ states, the NJL model does not allow one to calculate the low-energy parameter $δ^{(\prime)}$, which, however, can be fixed by the experimental data on the $η^{(\prime)}\to π^+π^-γ$ decay width. We then estimate another low-energy parameter $α^{(\prime)}$. The impact of different schemes for describing $η$-$η^\prime$ mixing on the value of $δ^{(\prime)}$ and $α^{(\prime)}$ is discussed. It is shown that the model predictions are in full accordance with the available experimental data.

We present a universal concentration bound for sums of random variables under arbitrary dependence, and we prove that it is asymptotically optimal for broad families of marginals admitting a uniform integrable tail-quantile envelope. The bound follows directly from the subadditivity of expected shortfall, a property well known in the risk-measure literature. Our sharpness result relies on an explicit construction of asymptotically extremal couplings. We furthermore provide practical sufficient conditions -- based on convex transformation order comparisons with exponential and power-law envelopes -- under which the bound admits simple, explicit tail profiles.

Let $C\subset\mathbb{R}^2$ be a convex body, and for a positive integer $N$, let $\mathcal{P}$ be a configuration of $N$ points in $[0,1)^2$. The discrepancy of $\mathcal{P}$ with respect to $C$ is defined by \begin{equation*} \mathcal{D}(\mathcal{P},\, C)=\sum_{\mathbf{p}\in\mathcal{P}}\sum_{\mathbf{n}\in\mathbb{Z}^2}\mathbf{1}_C(\mathbf{p}+\mathbf{n})-N|C|, \end{equation*} and one may estimate how $\mathcal{P}$ deviates from uniformity by averaging the latter quantity over a family of sets. When considering quadratic averages over translated and dilated copies of $C$, one gets the \textit{homothetic quadratic discrepancy} \begin{equation*} \mathcal{D}_2(\mathcal{P},\, C)=\int_{0}^{1}\int_{[0,1)^2}\left|\mathcal{D}( \mathcal{P},\,\boldsymbolτ+δC)\right|^2\,{\rm d}\boldsymbolτ\,{\rm d} δ. \end{equation*} We investigate the behaviour of the optimal \textit{homothetic quadratic discrepancy}, that is \begin{equation*} \inf_{\# \mathcal{P}=N} \mathcal{D}_2(\mathcal{P},\, C)\quad\text{as}\quad N\to+\infty. \end{equation*} Beck~\cite{MR915529} and Beck and Chen~\cite{MR1489133} showed that the optimal \textit{h.q.d.} of convex polygons has an order of growth of $\log N$, and more recently, Brandolini and Travaglini~\cite{MR4358540} proved that the optimal \textit{h.q.d.} of planar convex bodies with a $\mathcal{C}^2$ boundary has an order of growth of $N^{1/2}$. We show that, in general, a single order of growth for the optimal \textit{h.q.d.} need not exist. First, by an implicit geometric construction of $C$, we obtain prescribed oscillations between $\log N$ and $N^{1/2}$. Second, by a subtler design of $\partial C$ and via Fourier-analytic methods, we obtain prescribed polynomial-order oscillations in the range $N^α$ with $α\in(2/5,1/2)$.

Spectral graph signal processing is traditionally built on self-adjoint Laplacians, where orthogonal eigenbases yield an energy-preserving Fourier transform and a variational frequency ordering via a real Dirichlet form. Directed networks break self-adjointness: the combinatorial directed Laplacian $L=D_{\mathrm{out}}-A$ is generally non-normal, so eigenvectors are non-orthogonal and classical Parseval identities and Rayleigh-quotient orderings do not apply. This paper develops a Laplacian-centric harmonic analysis for directed graphs that remains exact at the algebraic level while explicitly quantifying the geometric distortion induced by non-normality. We (i) define a Biorthogonal Graph Fourier Transform (BGFT) for $L$ using dual left/right eigenbases and show that vertex energy equals a Gram-metric quadratic form in BGFT coordinates, (ii) introduce a directed variational semi-norm $TV_{\mathcal{G}}(x)=\|Lx\|_2^2$ and prove sharp two-sided BGFT-domain bounds controlled by singular values of the eigenvector matrix, and (iii) derive sampling and reconstruction guarantees with explicit stability constants that separate sampling-set informativeness from eigenvector geometry. Finally, we provide reproducible simulations comparing a normal directed cycle to perturbed non-normal digraphs and show that filtering and reconstruction robustness track $κ(V)$ and the Henrici departure-from-normality $Δ(L)$, validating the theoretical predictions.

Polymers-macromolecular systems composed of repeating chemical units-constitute the molecular foundation of living organisms, while their synthetic counterparts drive transformative advances across medicine, consumer products, and energy technologies. While machine learning (ML) models have been trained on millions of quantum chemical atomistic simulations for materials and/or small molecular structures to enable efficient, accurate, and transferable predictions of chemical properties, polymers have largely not been included in prior datasets due to the computational expense of high quality electronic structure calculations on representative polymeric structures. Here, we address this shortcoming with the creation of the Open Polymers 2026 (OPoly26) dataset, which contains more than 6.57 million density functional theory (DFT) calculations on up to 360 atom clusters derived from polymeric systems, comprising over 1.2 billion total atoms. OPoly26 captures the chemical diversity that makes polymers intrinsically tunable and versatile materials, encompassing variations in monomer composition, degree of polymerization, chain architectures, and solvation environments. We show that augmenting ML model training with the OPoly26 dataset improves model performance for polymer prediction tasks. We also publicly release the OPoly26 dataset to help further the development of ML models for polymers, and more broadly, strive towards universal atomistic models.