Researchers increasingly use data on social and economic networks to study a range of social science questions, but releasing statistics derived from networks can raise significant privacy concerns. We show how to release network connectedness indices that quantify assortative mixing across node attributes under edge-adjacent differential privacy. Standard privacy techniques perform poorly in this setting both because connectedness indices have high global sensitivity and because a single node's attribute can potentially be an input to connectedness in thousands of cells, leading to poor composition. Our method, which is straightforward to apply, first adds noise to node attributes, then analytically debiases downstream statistics, and finally applies a second layer of noise to protect the presence or absence of individual edges. We prove consistency and asymptotic normality of our estimators for both discrete and continuous labels and show our method works well in simulations and on real networks with as few as 200 nodes collected by social scientists.

Smart active agents must allocate finite energetic resources across distinct functions, yet the underlying thermodynamic trade-offs remain poorly understood. Here, we introduce a minimal model of a self-steering particle with an internal polarity-cue sensor coupled to an external environmental field, decomposing its steady-state entropy production rate into locomotion, actuation, and sensing costs. This separation exposes an energetic bookkeeping structure underlying even the simplest form of embodied navigation. The emergence of Pareto fronts linking energetic expenditure to localisation precision and path-following performance shows that feedback-controlled active motion is constrained by quantitative thermodynamic bounds that persist across distinct task geometries.

Topological insulators host Dirac surface states (SS) protected by time-reversal symmetry. Inter-surface hybridization can gap the SS and give rise to the quantum spin Hall effect in films that are sufficiently thin compared to the SS penetration depth. However, quantifying the SS penetration depth typically requires painstaking synthesis of multiple films with varying thickness. Here we introduce a direct method to probe the SS penetration depth in bulk crystals, by studying the interplay between SS and magnetic impurities in \SVT. Using scanning tunneling microscopy and spectroscopy, we find that even sparse magnetic impurities ($\lesssim0.25\%$ vanadium) can gap the Dirac SS. However, a single V impurity induces only localized states, and does not form an impurity band, so the gapped Dirac dispersion is preserved away from the impurity. In high magnetic fields, we observe an energy shift of the $0^\text{th}$ Landau level and a suppression of quasiparticle lifetime at the Dirac point, indicating \newtext{magnetic} scattering of the SS. Crucially, by employing V impurities at different depths as precise scattering probes, we reveal the SS penetration depth on the sub-nanometer scale in a bulk crystal.

The most general Ruijsenaars-van Diejen-Takemura Hamiltonians are characterized as Heun operators defined as second order $q$-difference operators with a raising action on elementary rational functions with poles on the Askey-Wilson grid.

The scaling of turbulent premixed flames is typically described by correlations derived for unity-Lewis-number fuels. However, their validity for hydrogen (H$_{2}$) remains uncertain due to the thermodiffusive effects associated with its low Lewis number. In this study, turbulent premixed H$_{2}$ and methane (CH$_{4}$) jet flames are systematically compared over a wide range of operating conditions. Experiments were conducted for Reynolds numbers between 5000 and 60000 and effective Karlovitz numbers spanning 3-368. Flame structure and global flame geometry were characterized using spatially resolved OH$^{*}$ chemiluminescence imaging, allowing consistent comparison between the two fuels across different turbulence intensities. The results are interpreted via a unified framework that incorporates two thermodynamic- and fuel-dependent parameters: a flame speed factor, $α$, representing the enhancement of local burning rates, and a shape factor, $γ$, describing the scaling of mean flame geometry. Despite significant fuel-specific thermodiffusive effects associated with preferential diffusion and intrinsic reactivity, which lead H$_{2}$ flames to exhibit enhanced sensitivity to turbulence and more compact flame configurations, both H$_{2}$ and CH$_{4}$ flames are found to exhibit robust and consistent turbulent scaling behavior when analysed within the proposed unified framework. The resulting correlations provide a generalised description of turbulent burning velocity and flame structure, demonstrating that key turbulence-chemistry interactions can be captured within a common model across fuels with widely different Lewis numbers. Overall, the dataset spans multiple turbulence regimes and flame geometries for both fuels, providing a valuable experimental benchmark for the validation of turbulent combustion models across different regimes.

Nonequilibrium active polymers provide a minimal framework to investigate biopolymers such as DNA and chromatin under the action of molecular motors. Here we study active ring polymers with controlled topology and show that knot type qualitatively determines their nonequilibrium behaviour. We find that activity induces opposite localisation responses in different topological families: torus knots systematically delocalise and inflate, whereas twist knots tighten and remain localised. We trace this divergent behaviour to the distinct symmetry properties of their tangent fields, which control the alignment of active forces along the chain. We show that topology also governs internal and emergent dynamics. Active torus knots behave as soft chiral self-propelled particles exhibiting persistent motion with a well-defined handedness fixed by their topological chirality. In contrast, achiral knots show no net handedness. The knot thus acts as a deformable topological quasiparticle whose morphology and propulsion are selected by topology. These results suggest potential routes toward programmable soft chiral particles with controllable morphology and emergent motility modes.

Four-dimensional scanning transmission electron microscopy (4D-STEM) provides rich, atomic-scale insights into materials structures. However, extracting specific physical properties - such as polarization directions essential for understanding functional properties of ferroelectrics - remains a significant challenge. In this study, we systematically benchmark multiple machine learning models, namely ResNet, VGG, a custom convolutional neural network, and PCA-informed k-Nearest Neighbors, to automate the detection of polarization directions from 4D-STEM diffraction patterns in ferroelectric potassium sodium niobate. While models trained on synthetic data achieve high accuracy on idealized synthetic diffraction patterns of equivalent thickness, the domain gap between simulation and experiment remains a critical barrier to real-world deployment. In this context, a custom made prototype representation training regime and PCA-based methods, combined with data augmentation and filtering, can better bridge this gap. Error analysis reveals periodic missclassification patterns, indicating that not all diffraction patterns carry enough information for a successful classification. Additionally, our qualitative analysis demonstrates that irregularities in the model's prediction patterns correlate with defects in the crystal structure, suggesting that supervised models could be used for detecting structural defects. These findings guide the development of robust, transferable machine learning tools for electron microscopy analysis.

Quantum sensing of meV-scale scattering and absorption of impinging particles with electrons in solid state detectors is a challenging technological advancement with the potential to enable breakthroughs in quantum information applications and studies of fundamental physics. However, a key obstacle for current sensing schemes is the difficulty in distinguishing the signals from particles of interest and from intrinsic excitations, like phonons or magnons. Here we propose a technique to selectively detect impinging particles based not only on their imparted energy, but specifically by their dispersion relations. By harnessing interfacial orbital hybridization in van der Waals heterostructures of Dirac materials, interlayer charge transfer may be promoted only for pre-selected impinging particles of interest. Using first-principles density functional theory (DFT) calculations of heterostructures of the layered Dirac materials ZrTe5 and HfTe5, we examine the effects of strain and layer number for successfully tuning orbital hybridization in their electronic structure. We demonstrate a proof-or-principle feasibility study for using Dirac materials to construct dispersion filters to be leveraged for next-generation meV-scale quantum sensors.

Marine biogeochemical models are widely used to study nutrient dynamics, water quality, and climate-related processes in coastal and estuarine systems. However, developing models that reliably represent specific environments remains computationally demanding, which makes their application to complex systems such as river plumes and estuarine environments challenging. In addition, these models contain several parameters that must be calibrated for the region of interest, a process that is often performed empirically using limited observational data. This thesis advances the development and calibration of marine biogeochemical models in the Brazilian context through three main contributions. First, we develop a conceptual model describing nutrient-phytoplankton dynamics in the Paranagua Estuarine Complex (PEC) in southern Brazil. The model is intentionally simple and computationally inexpensive, allowing simulations to be performed on standard personal computers. Second, we propose a systematic calibration framework based on tracer datasets and derivative-free optimization techniques. Finally, we demonstrate the practical application of this approach by calibrating the PEC model using in situ observations. Results show that, despite its simplicity, the model can reproduce observed nutrient dynamics when properly calibrated. The proposed framework is general and can be extended to multi-parameter calibration, seasonal parameter variation, and the coupling of biogeochemical models with higher-fidelity hydrodynamic models.

We propose a Monte Carlo based method for simulating the open system dynamics of multiple exchange-only (EO) qubits. In the EO encoding, the total spin projection quantum number along the $z$-axis of the three constituent spins remains unchanged under exchange operations, in contrast to the open system (or multi-qubit miscalibration) setting where coherent and incoherent mixing of states with different quantum numbers occurs. In our approach, we choose to measure the total spin component along the $z$-axis of each EO qubit after every logical quantum operation, which decoheres coherent mixtures of states with different spin projection quantum numbers. Independent simulations thus give different trajectories of the system in the associated subspaces, so we refer to this method as the Subspace Monte Carlo method. With each EO qubit having a definite spin projection quantum number, the density matrix of $n$ qubits can be represented by a vector of dimension $3^{2n}$, instead of $8^{2n}$, with an additional vector of dimension $n$ to label the quantum number of each qubit. We show that this approximation of the dynamics remains faithful to the true dynamics when the simulated circuits twirl the noise, converting coherent errors to stochastic errors, which can be achieved using randomized compiling. We use this simulation approach to study how correlations in measurement outcomes of circuits with reset-if-leaked gadgets, such as a multi-round Bell state stabilization circuit that uses 6 EO qubits, are affected by the choice of CNOT implementations.

We search for 15 rare decays of $D$ mesons to hadrons accompanied by an electron-positron pair $D\to h(h^{(')})e^{+}e^{-}$, based on 20.3 fb$^{-1}$ of $e^+ e^-$ collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector at BEPCII. No significant signals are observed, and the corresponding upper limits on the branching fractions at the 90\% confidence level are determined. The sensitivities of the results are at the level of $10^{-6}$ $\sim$ $10^{-7}$. The upper limits on the branching fractions for the $D^+\to ρ^{+} e^+ e^-$, $D^+\to K^{*+} e^+ e^-$, $D^0\to K_S^0 K_S^0 e^+ e^-$, $D^0\to π^0 π^0 e^+ e^-$ and $D^0\to η^{\prime} e^+ e^-$ decay channels are measured for the first time. For the $D^0\to π^0 e^+ e^-$, $D^0\to ηe^+ e^-$, $D^0\to ωe^+ e^-$, $D^0\to K_S^0 e^+ e^-$, $D^+\to π^+ π^0 e^+ e^-$, $D^+\to K^+ π^0 e^+ e^-$, $D^+\to π^+ K_S^0 e^+ e^-$ and $D^+\to K^+ K_S^0 e^+ e^-$ decay channels, the upper limits on the branching fractions are determined, with an improvement of at least a factor of four compared to previous searches. The upper limits on the branching fractions for the $D^0\to ρ^{0} e^+ e^-$ and $D^0\to ϕe^+ e^-$ decay channels are set at $0.7 \times 10^{-6}$ and $4.6 \times 10^{-6}$, respectively.

Turbulent lean premixed hydrogen jet flames are simulated using direct numerical simulation employing detailed chemistry in both slot and round configurations at various pressures. All cases are simulated at a constant jet Reynolds number ($Re_j = 10000$) and a fixed ratio of characteristic length scales. While normalised macroscopic quantities (e.g., flame length, turbulent flame speed) appear comparable across configurations, fundamental discrepancies are observed that originate from the coupling of large- and small-scale effects. Mean local reactivity ($I_0$) decays monotonically downstream, driven by a decreasing Karlovitz number ($Ka^{*}$); however, this decay is modulated by geometry, with round jets exhibiting a faster decline due to mean negative curvature. Pressure is identified as a critical small-scale driver, fundamentally altering flame propagation by increasing the sensitivity of displacement speed to local curvature. At elevated pressures, this sensitivity induces higher flame stretch and accelerates wrinkling near the nozzle, which compounds with geometry-dependent effects, such as the slower decay of mean strain in slot configurations.

T Coronae Borealis (T CrB) is a nearby recurrent nova expected to erupt in the near future, offering a unique opportunity to study particle acceleration and high-energy emission from novae in real time. We investigate the production of gamma-rays and neutrinos following the T CrB outburst by combining three-dimensional hydrodynamical simulations with a detailed diffusive shock acceleration model. Our simulations account for the complex circumbinary medium, including the red giant wind, equatorial density enhancement, and accretion disk. We compute spatially resolved spectra of accelerated protons and electrons at the forward shock, accounting for downstream velocity gradients and variations in shock properties. Using a multi-zone approach, we synthesize hadronic gamma- ray emission from proton-proton interactions, leptonic gamma-rays from inverse-Compton scattering, and the associated neutrino emission. We present predicted gamma-ray spectra, light curves, and images from our numerical models of T CrB, and assess their detectability with current gamma-ray and neutrino observatories. We find that the early high-energy emission is dominated by the ejecta, with the accretion disk significantly boosting the gamma-ray flux and particle normalization during the first hours after the outburst. By incorporating velocity gradients in the post-shock flow, we demonstrate that maximum particle energies can reach the PeV scale in high-energy explosion scenarios. We show that while GeV gamma-rays are prominent messengers, neutrino detection is feasible primarily in models with high explosion energy and high ambient density.

Realizing error-corrected logical qubits is a central goal for the current development of digital quantum computers. Neutral atoms offer the opportunity to coherently shuttle atoms for realizing efficient quantum error correction based on long-range connectivity and parallel atom transport. Nevertheless, time overheads in shuttling atoms and complex control hardware pose challenges to scaling current architectures. Here, we introduce atom velocity as a new degree of freedom in neutral-atom architectures tailored to quantum error correction. Through controlled Doppler shifts, we demonstrate velocity-selective mid-circuit state preparation and measurement on moving atoms, leaving spectator atoms unaffected. Furthermore, we achieve on-the-fly local single-qubit rotations by mapping micron-scale atom displacements to the spatial phase of global control beams. Complementing these techniques with CZ entangling gates with a fidelity of 99.86(4)%, we experimentally implement key primitives for quantum error correction and measurement-based quantum computing. We generate an eight-qubit entangled cluster state with an average stabilizer value of 0.830(4), realize an [[4,2,2]] error-detection code with 99.0(3) % logical Bell-state fidelity, and perform stabilizer measurements using a flying ancilla. By enabling selective operations on continuously moving atoms using only global beams, this velocity-enabled architecture reduces hardware overhead while minimizing shuttling and transfer delays, opening a new pathway for fast, large-scale atom-based quantum computation.

We propose an interacting model that is exactly solvable in any spatial dimension and gives rise to a Fermi liquid (FL) featuring a pseudogapped (PG) single-particle spectral function and a vanishing quasiparticle (QP) weight at half-filling, without invoking Mott physics. The PG originates from a purely fermionic mechanism through emergent QPs arising from a correlated hopping interaction. By employing an appropriate coherent-state basis, we derive a Gaussian path-integral representation of the partition function, which enables systematic treatments of deviations from the Gaussian limit using standard many-body techniques, such as diagrammatic perturbation theory or mean-field theory. We explicitly demonstrate and discuss several properties of the exactly solvable limit on the square lattice, including the mechanism for temperature-dependent PG opening, the singular behavior of the self-energy, the violation of the Luttinger sum rule, and the role of Luttinger and Fermi surfaces. Finally, we explore quantum phase transitions between PG-FLs and Landau FLs.

In resetting dynamics, a system is repeatedly coupled to and decoupled from ancillary degrees of freedom that are reinitialized between interactions. This provides a versatile route to engineer nonequilibrium steady states and constitutes a powerful and analytically transparent framework for studying nonequilibrium dynamics in quadratic fermionic models. The baseline noninteracting resetting scheme yields an affine evolution for the subsystem single-particle density matrix (SPDM), with a clear operational interpretation: a finite environment block E mediates the interaction between the subsystem S and an ideal external thermal reservoir. In this work, we develop a controlled extension of such a framework to weakly interacting systems. We introduce a Hartree mean-field treatment of density-density interactions that preserves closure of the SPDM dynamics while producing genuinely nonlinear behavior. We further construct a completely positive (CP-safe) Gaussian Lindblad embedding that reproduces the resetting dynamics in the noninteracting limit and yields a continuous-time representation of environmental thermalization when interactions are present. Our analytical results are complemented by numerical studies of a ring segmentation geometry and a minimal two-site model, revealing interaction-enabled steady states that cannot be obtained in any purely quadratic setting. Together, these results establish a general and physically consistent route for incorporating weak interactions ino resetting-based approaches to open quantum system.

We develop a framework that enables direct and meaningful comparison of two early fault-tolerant methods for the computation of eigenenergies, namely \gls{qksd} and \gls{spe}, within which both methods use expectation values of Chebyshev polynomials of the Hamiltonian as input. For \gls{qksd} we propose methods for optimally distributing shots and ensuring sufficient non-linearity of states spanning the Krylov space. For \gls{spe} we improve rigorous error-bounds, achieving roughly a factor $2/3$ reduction of circuit depth. We provide insights into the scalability of and the practical realization of these methods by computing the maximum Chebyshev degree, linearly related to circuit depth, and the respective number of repetitions required for the simulation of molecules with active spaces up to 54 electrons in 36 orbitals by leveraging \gls{mps}/\gls{dmrg}.

In this work we investigate discrete structures in product Hilbert spaces. For monopartite systems of size $d$ one relies on the Weyl-Heisenberg group $WH(d)$, while in the case of composite Hilbert spaces we identify designs covariant with respect to the product group, $[WH(p)]^{\otimes n}$. In analogy with magic -a quantity attaining its maximum for states fiducial with respect to $WH(d)$ -we introduce a similar notion of magick, defined with respect to the product group. The maximum of this quantity over all equimodular vectors yields fiducial states that generate $d$ $\textit{a priori}$ isoentangled mutually unbiased bases (MUBs), which, when supplemented by the identity, form their complete set. Such fiducial states are explicitly constructed in all prime-power dimensions $p^n$ with $p\ge 3$. The result for $p\ge 5$ extends the construction of Klappenecker and Rötteler, whereas for $p=3$ it is mathematically distinct and is based on Galois rings. The global maximum of magick for $d=2^3$ yields fiducial states corresponding to the symmetric informationally complete (SIC) generalized measurement of Hoggar. Our approach feeds into a unifying perspective in which highly symmetric quantum designs emerge from fiducial states with extremal properties via structured group-orbit constructions.

We introduce QiboAgent, a reference implementation designed to serve as a practitioner's guideline for developing specialized coding assistants in Quantum Computing middleware. Addressing the limitations in scientific software development of general-purpose proprietary models, we explore how lightweight, open-source Large Language Models (LLMs) provided with a custom workflow architecture compare. In detail, we experiment with two complementary paradigms: a Retrieval-Augmented Generation pipeline for high-precision information retrieval, and an autonomous agentic workflow for complex software engineering tasks. We observe that this hybrid approach significantly reduces hallucination rates in code generation compared to a proprietary baseline, achieving a peak accuracy of 90.2% with relatively small open-source models of size up to 30B parameters. Furthermore, the agentic framework exhibits advanced coding capabilities, automating the resolution of maintenance issues and new features requests, or by prototyping larger-scale refactors of the codebase, such as producing a compiled Rust module with bindings of an original pure python package, Qibo in our case. The LLM workflows used for our analysis are integrated into a user interface and a Model Context Protocol server, providing an accessible tool for Qibo developers.

Pulsar wind nebulae (PWNe) are bubbles of relativistic particles, powered by the rotational energy loss of the central pulsars. The Crab Nebula, powered by the Milky Way's most energetic pulsar, was discovered by the Large High Altitude Air Shower Observatory (LHAASO) as a PeV gamma-ray emitter, thereby establishing it as an extreme particle accelerator along with multiwavelength observations. Here we report LHAASO's detection of a point-like ultrahigh-energy (UHE, photon energy $E>100\,$TeV) gamma-ray source associated with the PWN powered by PSR~J1849-0001, a pulsar of spindown power 50 times lower than the Crab pulsar. The measured gamma-ray spectrum extends to PeV energies following a power-law distribution, with the PeV luminosity a few times higher than that of the Crab Nebula. Combined X-ray observations constrain the average magnetic field within the PWN to about $3μ\,$G, and reveal an extreme particle acceleration efficiency approaching or even exceeding unity. The result challenges the particle acceleration theory in PWN and implies non-ideal magnetohydrodynamics (MHD) conditions within the accelerator, potentially involving magnetic reconnection upstream of the termination shock.

The purpose of these notes is to provide background on understanding the primal-dual algorithm of Chambolle and Pock [1] for imaging scientists. The presentation focuses on providing intuition and an algorithmic system that is amenable to pre-conditioning. The document aims to be self-contained, providing background on the essential facts of non-smooth convex analysis.[2]

Molecules containing short-lived isotopes, namely radioactive molecules, are among the most promising candidates for probing new physics beyond the Standard Model, although their production and spectroscopic measurements remain technically challenging. Here, we demonstrate an integrated methodology that combines formation of molecular ion beams in a radiofrequency quadrupole cooler-buncher with collinear laser spectroscopy. As a proof-of-principle experiment, we successfully produce molecular ions such as $\rm BaF^+$ and $\rm YbF^+$ via in-trap ion-molecule reactions and perform high-resolution laser spectroscopy of the target molecule $\rm ^{138}BaF$. Vibrational and rotational structures of $\rm ^{138}BaF$ across different electronic states are obtained using resonance-enhanced multiphoton ionization schemes, confirming the feasibility of the proposed methodology. This work establishes a practical route for future formation and spectroscopic studies of short-lived radioactive molecules, such as those containing $\rm ^{225}Ra$, at radioactive ion beam facilities.

Context. The prompt-emission time profiles of GRB 230307A and other long-duration compact object merger (COM) candidates exhibit a unique set of temporal properties, characterised by a deterministic evolution of waiting times and pulse widths. Aims. We searched the Fermi/GBM catalogue for other unidentified long COM candidates exhibiting temporal properties similar to those observed in GRB 230307A. Methods. We examined the temporal and spectral prompt-emission properties of GRBs featuring at least eight light-curve peaks. For candidates, all with unknown redshifts, that exhibited properties similar to GRB 230307A, we analysed their trajectories in the Ep,i-Eiso plane as a function of redshift. We then evaluated the joint likelihood of their compatibility with the Ep,i-Eiso relation satisfied by the bulk of long GRBs. Furthermore, we calculated their minimum variability timescales (MVTs) for comparison against known COM and collapsar populations. Results. We identified 9 COM candidates with unknown redshifts and demonstrated that there are at least two outliers of the Ep,i-Eiso relation with 3.1 sigma (Gaussian) confidence level. Furthermore, their MVTs are more consistent with those of COM than with collapsar GRBs. Conclusions. These results indicate that this specific set of temporal properties can serve as a diagnostic tool to distinguish long-duration COMs from the broader collapsar population. Furthermore, our findings suggest that the fraction of unidentified COMs among long GRBs may be larger than previously assumed.

Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat conduction to quantum mechanical systems. Despite their flexibility, PINNs offer limited insight into how their predictions deviate from the true solution, hindering trust in their prediction quality. We propose a lightweight post-hoc method that addresses this gap by producing pointwise error estimates for PINN predictions, which offer a natural form of explanation for such models, identifying not just whether a prediction is wrong, but where and by how much. For linear partial differential equations, the error between a PINN approximation and the true solution satisfies the same differential operator as the original problem, but driven by the PINN's PDE residual as its source term. We solve this error equation numerically using finite difference methods requiring no knowledge of the true solution. Evaluated on several benchmark PDEs, our method yields accurate error maps at low computational cost, enabling targeted and interpretable validation of PINNs.

Strip detectors are populating outer trackers of high-energy particle experiments. They are convenient for covering large areas of sensitive material since they use less power and have fewer readout channels compared to pixels sensors. Nevertheless, they are typically manufactured with a mask set that covers the full wafer, otherwise when using smaller reticles the strip implants have to be stitched. For this project, strip detectors were fabricated in a CMOS commercial foundry using different reticles to be stitched several times, proving the feasibility of this technology. LFoundry produced the passive CMOS strip detector with a production line of 150 nm node technology, using a 150 um thick FZ wafer. Those strip sensors have three different geometries to study different impacts of the CMOS technology. The strips have lengths of 2.1 cm and 4.1 cm, stitching 3 or 5 reticles respectively. This work shows results of 24 GeV proton irradiated passive CMOS strip detectors. The detectors were irradiated at CERN and were tested with different set-ups, not showing any effect from the strips stitching. Proving that this technology is feasible for detecting high-energy particles opens the door to future large productions of passive strip detectors and also to produce active strip sensors in commercial CMOS foundries.

Multispectral satellite imagery poses significant challenges for deep learning models due to the high dimensionality of spectral data and the presence of structured correlations across channels. Recent work in quantum machine learning suggests that unitary evolutions and Hilbert-space embeddings can introduce useful inductive biases for learning. In this work, we show that several empirical advantages often attributed to quantum feature maps can be more precisely understood as consequences of geometric structure induced by unitary group actions and the associated quotient symmetries. Motivated by this observation, we introduce a fully classical pooling mechanism that maps latent features to complex projective space via a fixed-reference unitary action. This construction effectively collapses non-identifiable degrees of freedom, leading to a reduction in the dimensionality of the learned representations. Empirical results on multispectral satellite imagery show that incorporating this quantum-inspired pooling operation into a convolutional neural network improves optimization stability, accelerates convergence, and substantially reduces variance compared to standard pooling baselines. These results clarify the role of geometric structure in quantum-inspired architectures and demonstrate that their benefits can be reproduced through principled geometric inductive biases implemented entirely within classical deep learning models.

We report the identification and proof of a universal constant, ln(3) = 1.09861, which governs the onset of bidirectional collective behavior in one-dimensional Poisson proximity networks. The constant - named the cooperative percolation constant and denoted by Lambda_c - is the unique positive solution to 2/(exp(x)-1) = 1 and equals the Shannon entropy of three equiprobable states. For agents distributed at intensity lambda and interacting within range L, bidirectional collective behavior is possible if and only if the topological density (lambda * L) >= ln(3). Below this threshold, no cooperative control policy can produce macroscopic coherence, as the proximity graph does not contain a bidirectional spanning cluster in expectation. The result is parameter-free and model-independent: the Poisson distribution is derived from memorylessness symmetry axioms, making ln(3) a fundamental consequence of spatial symmetry. The threshold is validated by two independent large-scale empirical datasets. Analysis of the Chengdu V2X OBU dataset (N = 19.7 million records) reveals a 1.60x reduction in speed variance at the predicted boundary. Furthermore, the highD German motorway dataset (N = 163,896 observations) yields a best-fit LWR exponent theta = 1.033 +/- 0.088, placing the theoretical value ln(3) within 0.75 sigma of naturalistic trajectory data (R^2 = 0.8631). The remarkable consistency across geographical and physical scales - from motorway traffic to documented thresholds in 1D biological signal transmission - suggests that ln(3) represents a fundamental topological rent for cooperative information exchange.

Van der Waals materials may be combined to form moiré patterns that are effectively crystal lattices. These systems are unique in that their in-plane unit cell sizes may be orders of magnitude larger than interlayer separations, leading to unique behaviors emerging from interlayer interactions. In this work, we investigate interlayer valley drag in lattice-matched moiré bilayers, demonstrating a remarkable enhancement due to umklapp scattering. In contrast to drag phenomena in more conventional two-dimensional systems, interlayer valley drag appears at first order in the interlayer interaction, and remains non-vanishing in the low temperature limit even at this low order in the interlayer coupling. We propose an experimental geometry, feasible with current state-of-the-art fabrication techniques, to detect and characterize this effect in moiré bilayer systems.

We study a two-dimensional, off-lattice particle model introduced to describe absorbing phase transitions in driven non-Brownian suspensions. We numerically explore the $(ϕ,ε)$ phase diagram, where $ϕ$ is the packing fraction and $ε$ controls the amplitude of particle jumps. We use a binary mixture to suppress crystallization, which allows us to disentangle the model's distinct phase transitions between amorphous states. At large $ϕ$, we find that the approach to the absorbing transition is preceded by a non-equilibrium glass transition to a non-diffusive amorphous state. This dynamic arrest makes the location of the critical absorbing transitions protocol-dependent. The $ε\to 0$ end-point of the transition line defines a jamming transition whose location is shown to vary continuously with the preparation protocol, and cannot serve as a unique definition of random close packing. Near jamming, we observe a complex landscape and marginal stability, reminiscent of Gardner phases found in thermal glasses. The critical exponents characterizing packings at the jamming transition numerically agree with alternative approaches based on energy minimization, and with analytic predictions from mean-field replica theory. We analyze hyperuniformity in fluid and glass phases, where it emerges with qualitatively distinct signatures, and show that random organization dynamics does not determine the hyperuniformity observed in jammed packings, which is found to be non-universal. Our results show that random organization models share deep physical similarities with thermal soft-particle systems undergoing glass and jamming transitions, with little impact of the non-equilibrium nature of the microscopic dynamics on emerging physical properties.

Recent advances in optical imaging and communication increasingly involve high-dimensional, partially coherent light, creating a growing need for scalable tools to measure and manipulate coherence. Here, we demonstrate the automatic separation of spatially partially coherent light into "coherence modes" -- its orthogonal and mutually incoherent components. To make this separation possible, we exploit variational processing in layered self-configuring interferometer architectures in a silicon photonic circuit. This process formally finds and measures the eigenvectors and eigenvalues of the coherency matrix, hence measuring the partially coherent state, while leaving it intact and separated after optimization. Furthermore, we show that mutually incoherent beams, if spatially orthogonal, can be automatically separated even if they are completely overlapped, hence separating unknown laser beams based only on their mutual incoherence. Our experiment finds and separates the two strongest coherence modes starting from a nine-mode sampling of the partially or fully overlapping fields from two independent lasers. The method requires a number of physical components that scales linearly with the rank $r$ of the coherency matrix and operates through a sequence of $r$ in situ gradient-based optimizations enabled by electronic drive frequency multiplexing of interferometer phase shifters. We benchmark its performance against a mixture-based tomographic method, also implemented on chip. These results establish a scalable framework for programmable coherence analysis and control in imaging, communication, and photonic information processing.