Recent advances in time-varying photonics have revealed new degrees of freedom for manipulating optical states, arising from the distinctive nature of the temporal axis: causality and open-system dynamics. A representative example is photonic time crystals (PTCs) characterized by discrete time-translational symmetry, which exhibit space-analogous yet distinct phenomena, such as momentum gaps and amplifying-decaying Floquet-mode pairs. Although PTCs enable optical-energy amplification beyond conventional gain media, their application as programmable energy-functional devices remains challenging. Here, we propose a design framework for tailoring optical energy via defective PTCs. By optimizing defect permittivity and duration using analytic gradients of time transfer matrices, we realize prescribed coherent energy amplification and suppression. We show that a single defect enables continuous energy tailoring, while revealing an intrinsic asymmetry between amplification and suppression due to the inherently amplifying nature of the momentum gap. Extending the framework to coupled defects expands the design space and markedly improves suppression, establishing temporal-defect engineering as a route to programmable coherent energy control.

Fifth-generation (5G) wireless systems are increasingly adopted in smart manufacturing to support heterogeneous industrial workloads through services such as enhanced Mobile Broadband (eMBB) and Ultra-Reliable Low-Latency Communication (URLLC). However, industrial traffic is inherently process-driven and temporally correlated. So, static or reactive schedulers in the Open Radio Access Network (O-RAN) are inadequate for such non-stationary conditions, leading to sub-optimal utilization and violation of latency-reliability guarantees. This paper proposes a temporal-aware deep reinforcement learning (DRL) xApp for proactive Physical Resource Block (PRB) allocation in O-RAN-enabled industrial networks. The proposed framework integrates a long short-term memory (LSTM) encoder within a Double Deep Q-Network (DQN) to model sequential dependencies among slice-level Key Performance Indicators (KPIs), enabling predictive and stable decision-making. A continuous-time Markov chain (CTMC) traffic model is incorporated to emulate machine concurrency and process burstiness. Experimental results show that the LSTM-Double DQN improves slice satisfaction, and buffer stability under moderate and heavy load, with the longest sequence window providing the strongest gains.

Many biophysical search processes employ searchers which enter or "immigrate" into the domain progressively over time. Existing search time estimates can become unphysical for fast immigration since they imply that searchers move at infinite speed. In this paper, we investigate search times of immigrating searchers that move at bounded speed. In the fast immigration limit, we determine the full probability distribution and all the moments of the $k$th search time in terms of the early time probability distribution of a single searcher. We apply these rigorous mathematical results to several canonical models of stochastic search. We further analyze different models of "diffusion" and use these results to investigate when and how the minutiae of searcher dynamics affect search times. We compare our theory to numerical simulations.

Oxide twistronics extends moire engineering beyond van der Waals materials, offering a promising platform for accessing emergent interfacial phenomena arising from the strong coupling of lattice, charge, and orbital degrees of freedom in complex oxides. However, deterministic fabrication of high-crystallinity oxide moire superlattices over large lateral dimensions remains challenging due to the three-dimensional bonding network of oxides. Here, we demonstrate a scalable, generalized fabrication strategy that enables the formation of high-crystallinity oxide moire superlattices with clean, chemically bonded interfaces and precisely controlled twist angles down to nominal values of 0.1 degree, achieving sub-degree twist-angle accuracy across large contiguous lateral dimensions approaching the millimeter scale. Using NaNbO3 as a model system, we show that the resulting interlayer coupling drives pronounced structural reconstruction that modifies both the phase structure and ferroelectric domain configuration. Synchrotron-based X-ray 3D reciprocal space mapping reveals the emergence of a single-phase state in twisted bilayers, in contrast to the mixed-phase structure observed in single-layer membranes prior to twist assembly. The structural signatures are further consistent with gradual lattice rotation distributed along the thickness direction that may accommodate interfacial shear strain, distinct from reconstruction observed in van der Waals moire systems, which primarily occurs through in-plane stacking rearrangement. This collective lattice response is correlated with twist-dependent nanoscale electromechanical modulations observed by piezoresponse force microscopy. These results establish a scalable materials platform for oxide twistronics and open new pathways towards integrating twist-engineered complex oxides into practical, macroscale device architectures.

We present a community-wide effort to develop a strategy and action plan to advance heliophysics and space weather modeling through open science. While open science has the potential to enhance the quality and pace of scientific discovery, its application to scientific modeling requires more careful consideration regarding open data and open software guidelines, as scientific models differ significantly from data analysis software. We gathered feedback from modeling teams worldwide through a living survey and discussion sessions at the 2024 Open Science Workshop in College Park, USA, and at the 2025 COSPAR ISWAT Working Meeting in Cape Canaveral, USA. We complement these findings with lessons learned from almost 25 years of experience at the Community Coordinated Modeling Center in enabling open use of models. We identify key roadblocks in current open science practices and guidelines and offer recommendations for future progress across four overlapping themes: open use of models and simulation results, open validation, open development, and open collaboration. An essential outcome of the discussion is the need for model developers and model users to speak with a united voice and promote the role of models in future open science efforts. We introduce a new cross-domain community initiative called the Heliophysics Open Modeling Environment (HOME), which will be integrated as an overarching activity within COSPAR ISWAT. HOME will serve as a platform for modelers and model users to work together, facilitate community modeling, improve the scientific return on modeling investment, and advance understanding, modeling, and forecasting in heliophysics and space weather.

In a first-year physics inquiry lab, pairs of students were randomly assigned to study pendulum motion using either a physical apparatus or a computer simulation. The experiment required detecting a ~1% difference in period between pendulums released at 10$^\circ$ and 20$^\circ$. This is the subtle failure of the small angle approximation and a goal that demands iteratively refined, high-precision measurements. Students using the simulation achieved significantly more reproducible timing measurements across all rounds of data collection and, by the third round, had also adopted more effective data collection strategies overall. As a result, 78% of simulation groups met the precision threshold required to identify the model failure, compared with 52% of physical apparatus groups. We attribute these outcomes primarily to a specific simulation constraint: students were required to use the simulation's built-in timer, which forced them to decouple pendulum release from the start of timing. This prevented students from pursuing a reaction-time-limited synchronization strategy that often traps users of physical apparatus in a low-precision measurement dead end. A post-lab survey further shows that students using simulations were more confident in their results than those who instead used a physical pendulum, as well as preferred greater use of simulations in future labs. These findings suggest that carefully designed simulation constraints can guide students toward productive experimental strategies while preserving their investigative autonomy.

Computational cardiovascular flow models are highly sensitive to prescribed inlet velocity profiles. While imaging-derived velocity fields provide physiologically realistic information, they can introduce increased preprocessing complexity, imaging noise, and computational burden. Simplified analytical formulations are computationally efficient but may not fully capture subject-specific flow characteristics. In this study, we present an uncertainty-aware framework that combines two-dimensional phase-contrast magnetic resonance imaging (2D PC-MRI) with mechanistic velocity-profile formulations to generate subject-specific pulmonary artery velocity representations. Imaging-derived radial velocity distributions were constructed from main pulmonary artery (MPA) PC-MRI data in canine and swine subjects using elliptical radial binning and normalization. Power-law and Womersley velocity-profile formulations were fitted within a Bayesian inference framework while accounting for uncertainty associated with imaging measurements and model representation. The two formulations were compared using regional and global weighted root mean square error (wRMSE) metrics. Both models demonstrated close agreement with the imaging-derived velocity profiles across subjects. Although the Womersley formulation provided greater flexibility near the vessel wall, it did not result in statistically significant improvements in fitting performance compared with the simpler power-law model. The proposed framework provides low-dimensional, physiologically interpretable, and uncertainty-aware velocity-profile representations that may serve as computationally efficient alternatives for subject-specific cardiovascular flow modeling.

The dayside cusp provides a direct pathway for solar wind plasma entry into the magnetosphere ionosphere system through magnetic reconnection. Using low altitude ion and electron measurements from TRACERS, together with upstream solar wind and geomagnetic conditions, we investigate the evolution of the cusp during a geomagnetic storm on 30 September 2025, spanning its rising, main, and recovery phases, and compare these with a quiet-time reference. Storm-time observations show broader and more poleward precipitation regions and enhanced electron energy flux, indicating intensified dayside coupling. To interpret these variations, we combine solar wind and IMF measurements with the maximum magnetic shear reconnection model to determine X-line locations and use a Tsyganenko field model to compute event-specific field-line transit distances between the X-line and TRACERS. The results demonstrate that cusp morphology and latitude track IMF-driven reconnection geometry, and that realistic path lengths are essential for quantitative reconnection-rate estimates, highlighting the capability of TRACERS to resolve storm-time cusp evolution. Enhanced cusp precipitation during the recovery phase is consistent with IMF conditions, indicating sustained solar wind driving rather than intrinsic storm-phase effects.

Metric temporal equilibrium logic (\MEL) extends temporal equilibrium logic (\TEL) by incorporating quantitative timing constraints, enabling the specification and analysis of deadlines and durations. \MEL\ is particularly suited for domains where time-bound properties are crucial, such as embedded systems, cyber-physical systems, and real-time software. It facilitates the precise expression of timing behaviors, such as the requirement that an event must occur within 5 milliseconds of a trigger, which often elude traditional qualitative temporal logics. In this paper, we present a Tseitin-like translation that maps any metric temporal formula into a logic programming fragment restricted to past operators. This translation provides a formal bridge to leverage existing Answer Set Programming (ASP) solvers for reasoning about metric temporal constraints. By restricting the target fragment to past operators, we enable more effective evaluation and integration with current ASP-based toolchains for multi-shot solving.

The purpose of this paper is to define normal Gaussian variables in the setting of hyperbolic probabilities, and introduce an associated Brownian motion, when both the index and the values of the process lie in the real algebra $\mathbb{H}$ of hyperbolic numbers. In Hida's white noise space, we construct two probability measures (say $P_1$ and $P_2$), and associate to them two families of $N(0,1)$ variables $(Z_n)_{n\in\mathbb N_0}$ (independent with respect to $P_1$) and $(W_n)_{n\in\mathbb N_0}$ (independent with respect to $P_2$). An important feature is that the $Z_n$ and $W_m$ need not be mutually independent either with respect to $P_1$ or $P_2$. An hyperbolic normal Gaussian variable is constructed (in non-degenerate cases) from two classical Gaussian variables and the hyperbolic Brownian motion is, in general, composed from two copies of the classical Brownian motion. Using the associated Gelfand triples we also compute the derivative of the hyperbolic Brownian motion as a stochastic distribution. The argument extends to the $\mathbb{H}$-valued fractional Brownian motion, and more generally to a wide family of $\mathbb{H}$-valued stationary-increment second order processes.

This paper develops a regression framework for the direct estimation of integrated functionals of conditional outcome distributions. The proposed method, termed rectified linear unit (ReLU) regression, projects the ReLU-transformed outcome onto covariates and admits a closed-form estimator. Its population regression function coincides with the integrated conditional distribution function of the outcome, and its convex conjugate, obtained via the Legendre-Fenchel transformation, recovers the integrated conditional quantile function. Both the regression and its conjugate require only mild distributional assumptions and accommodate non-continuous outcomes. We establish the uniform asymptotic distribution of the estimator and develop inference for the conjugate functional via the delta method for Hadamard directionally differentiable maps. Building on these results, we establish identification and inference for average quantile treatment effects over arbitrary subintervals of probability levels. This broadens the set of distributional parameters available to empirical work.

Distinguishing background heterogeneity from excess risk is a central challenge in case-control event data when both covariates and residual spatial or spatio-temporal structure matter. We develop a covariate-adjusted kernel regression framework that embeds an orthogonalized residual risk surface within a semiparametric binary model, and extend the approach from purely spatial to explicit spatio-temporal analysis. We apply the method to 959 gun violence incidents at public schools in the contiguous United States from 2000 to 2024, using incidents from the K-12 School Shooting Database linked to official school records for the corresponding year. The fitted models identify stable school-level associations, including markedly higher risk for larger schools and for middle and high schools, while also revealing substantial residual structure beyond the background distribution of schools. After adjustment for covariates, excess risk is found to remain concentrated in a persistent central-eastern corridor of the United States, with the strongest evidence appearing in recent years. More broadly, the analysis shows how residual risk surfaces can sharpen inference by separating background heterogeneity from anomalous structure in case-control event processes evolving over space and time.

In 2007, Adamczewski and Bugeaud introduced the notion of the Diophantine exponent of an infinite word as a quantitative measure of repetition, leading to new transcendence results for real numbers whose expansions in an integer base are sufficiently simple. In the present article, we introduce the refined Diophantine exponent, which detects weaker forms of repetition while preserving the full strength of the classical approach. This new exponent applies in situations where repetition is partially obscured by some form of noise. Related ideas already appear in the work of Corvaja and Zannier in 2002 and, more recently, in the works of Kebis, Luca, Ouaknine, Scoones, and Worrell. Our approach provides a unified framework that recovers and extends these results, as well as those of Adamczewski and Bugeaud. We also develop quantitative refinements of this method, leading to results about transcendence measures. The recent breakthrough of Bell, Diller, and Jonsson in the context of algebraic dynamics is partly based on a similar idea, which also served as a motivation for the present work.

We consider the substitution subshift generated by the Thue-Morse substitution $0\to01$, $1\to10$. We prove that the topological full group of the subshift contains a subgroup of intermediate growth. Namely, one group from the family known as the Grigorchuk groups embeds into this group. To obtain our main result, we prove an embedding theorem for topological full groups, and also develop a technique to prove isomorphism of groups using the Schreier graphs.

The intersection cut framework is a versatile tool for generating valid inequalities in optimization. Its main ingredients are so-called $S$-free sets: convex sets whose interiors do not intersect a given set $S$. Among these, inclusion-wise maximal $S$-free sets are particularly important, as they yield the strongest intersection cuts. In the integer programming setting, maximal lattice-free sets are well studied and admit explicit characterizations. In the quadratic optimization context, Muñoz, Paat, and Serrano (2025) characterized maximal $S$-free sets when $S$ is defined by a homogeneous quadratic inequality. In this work, we characterize maximal $S$-free sets when $S$ is defined by an inhomogeneous quadratic inequality. As in the homogeneous case, our characterization is built using non-expansive functions. Together with the results in the homogeneous case, our results complete a characterization of $every$ maximal quadratic-free set via non-expansive functions.

We present a description and analysis of a coupled pendulum experiment that has been used at the University of Auckland for many years. Although similar experiments are very common in undergraduate physics labs, both the physical system and our teaching approach are, we believe, novel. Compared to other coupled pendulum experiments, it has the advantage that the coupling can easily be varied, allowing students to observe the changing nature of the normal modes and beat frequencies. Additionally, the system displays a surprising degree of complexity, making it of interest to more advanced students in laboratory courses that are augmented with computer-based numerical modeling and algebra software.

As the largest and most recently formed stage of hierarchical structure, present-day galaxy clusters are predicted to have a broad range of late-time assembly histories. This diversity may explain much of the scatter in scaling relations and other cluster properties. Observationally, systems with more or less recent accretion should appear as unrelaxed and relaxed clusters, respectively. However, it is unclear which of the many possible structural measures best correlate with assembly history. Using the IllustrisTNG simulations, we explore the correlation between structural parameters and assembly history. To assess the effectiveness of different structural selection criteria, we define subsamples of the most and least relaxed clusters based on the values of various intrinsic, projected, and stellar structural parameters, and then compare the median assembly history of the subsamples in each case. We find that several observable quantities, including the magnitude gap between the brightest galaxies and the asymmetry of the stellar mass distribution, are very effective in selecting cluster samples with more or less recent accretion, even when applied in projection. Given the strong correlations between assembly history and present-day cluster structure, we suggest that structural classification be included explicitly in any analysis of catalogue completeness, scaling relations, or mean density profiles.

Audio bandwidth extension aims to reconstruct missing high-frequency content from bandlimited signals. This paper proposes FiPA-SR, a GAN-based perceptual architecture capable of handling different input bandwidths within a single model. Building upon the previous $\textrm{AEROMamba}_\textrm{P}$ framework, the proposed model incorporates FiLM layers to adapt the reconstruction process according to the respective bandwidth. Experiments on the MUSDB dataset show that FiPA-SR outperforms the state-of-the-art AudioSR model across 8, 20, and 32 kHz input sampling rates. Moreover, the proposed architecture uses approximately 3$\times$ less GPU memory and performs inference more than 60$\times$ faster than the diffusion-based baseline.

Luminal breast cancers represent the most prevalent molecular subtype of breast carcinoma, with Luminal A tumors generally associated with more favorable clinical outcomes than Luminal B tumors. Obesity-related inflammation and prolonged exposure to exogenous steroids have been implicated in the progression of luminal malignancies. This study evaluated 1,928 patients with Luminal A breast cancer and 1,610 patients with Luminal B breast cancer to examine associations among body mass index (BMI), age, ethnic background, menopausal status, and receptor expression, including estrogen receptor (ER), progesterone receptor (PR), and human epidermal growth factor receptor 2 (HER2). Patients with Luminal B tumors demonstrated a significantly greater mean BMI compared with those with Luminal A tumors. In addition, Luminal B tumors were more frequently observed among patients of African ancestry relative to White and Hispanic populations. Multivariable analyses revealed that elevated BMI and African ancestry were independently associated with increased odds of Luminal B carcinoma, whereas postmenopausal status was associated with lower risk. Mediation analysis further indicated that BMI partially explained the association between ancestry and Luminal B disease. These findings suggest that obesity and population-specific factors may contribute to the development of more aggressive luminal breast cancer phenotypes.

Block coherence provides a natural generalization of standard quantum coherence by treating superpositions across different subspaces as a resource. This work studies deterministic pure-state conversion under three free operations: physically block incoherent operations (PBIO), strictly block incoherent operations (SBIO), and block dephasing covariant incoherent operations (BDCO). For PBIO, we prove that, under a natural nondegeneracy condition on the active Kraus branches, any deterministic conversion from one pure state to another must be implemented by a block incoherent unitary. When the nondegeneracy requirement is removed, the condition becomes more general. It demands that the blockwise action of every active branch reproduce the target block structure with a common proportionality factor across all output blocks. For SBIO and BDCO, we show that deterministic pure-state transformation is completely characterized by the majorization relation between the input and output block probability vectors. The converse proof is constructive, yielding an explicit Kraus representation for every admissible BDCO transformation. In the rank-one limit, these conditions reduce to the known pure-state transformation criteria for physically incoherent operations (PIO), strictly incoherent operations (SIO), and dephasing covariant incoherent operations (DIO) in the standard resource theory of coherence. Using the majorization condition, a maximally block-coherent state with uniform block weights is also identified as a universal pure-state resource under BDCO and SBIO. We have also provided geometric numerical illustrations comparing the state transformation power of BDCO and DIO for a fixed input state, fixed output state and mutual convertibility scenarios.

We establish a sharp three-particle fractional Hardy inequality for the Laplacian of order $s\in(0,1)$ in dimension $d\geq 4-2s$ (Theorem 1.1), involving an explicit intrinsically three-body interaction potential $V_{s,3}$. The inequality holds with the optimal two-particle fractional Hardy constant $C_{fH}(d,s)$, which is shown to be sharp relative to the fixed potential $V_{s,3}$. This potential $V_{s,3}$ strictly dominates the standard pairwise Coulomb-type interaction and captures genuine three-body effects. As a consequence, we derive a nontrivial many-particle fractional Hardy inequality for $N\geq 3$, and, in the regime $N>d+1$, obtain an improved Coulomb-type inequality with a strictly larger constant, agreeing in spirit with the results of Hoffmann-Ostenhof et al. [M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, A. Laptev, and J. Tidblom, "Many-particle Hardy inequalities", J. Lond. Math. Soc. 77 (2008), no. 2, 99-115] and Lundholm [D. Lundholm, "Geometric extensions of many-particle Hardy inequalities", J. Phys. A: Math. Theor. 48 (2015), no. 17, 175203]. The proof relies on a fractional ground-state representation method adapted to three-particle interactions, combined with an explicit evaluation of the resulting nonlocal interaction term. This evaluation is achieved through a new singular integral identity of Selberg-type (Theorem 1.2), extending the three-fold formula of Grafakos-Morpurgo [L. Grafakos and C. Morpurgo, "A Selberg integral formula and applications", Pacific J. Math. 191 (1999), no. 1, 85-94] beyond the radial setting. This identity provides the analytic mechanism underlying the emergence of the three-body potential and may be of independent interest in harmonic analysis.

Second harmonic generation (SHG) has evolved from a probe of noncentrosymmetric crystals into a symmetry-resolved optical method for identifying order parameters in quantum and functional materials. In particular, polarization-resolved rotational anisotropy (RA) measurements of SHG can connect nonlinear susceptibility tensors to the crystallographic and magnetic point groups of the underlying materials. This capability is especially powerful when the ordered state is weak, spatially confined, multipolar, magnetic, or hidden from conventional linear probe techniques. In this review article, we provide a comprehensive overview of RA-SHG studies across a broad range of condensed matter systems. We begin with basic theoretical background for the multipole origins of SHG radiation, the construction of nonlinear susceptibility tensors, and group-theoretical framework connecting tensor components to order parameters. We then review the applications of RA-SHG to polar materials, magnetic orders, and other hidden electronic materials. Finally, we outline challenges and future research directions for using SHG to reveal, image, and control hidden, intertwined, and nonequilibrium phases in quantum and functional materials.

Measurements of tangential drifts of distant quasars and galactic nuclei on the celestial sphere provide a novel and independent method of testing cosmological hypotheses. In this work, we employ an axisymmetric Bianchi I model as a relatively simple phenomenological model that is useful for quantifying departures from the cosmological principle. Using a quality-filtered sample of 1.2 million proper motion vectors of distant quasars from Gaia Data Release 3, we perform global fits of the position drift fields with vector spherical harmonics (VSH) to second degree for five non-overlapping subsets of the sources with redshifts from 0.5 to 3, and assess the ability of the Bianchi I model to describe the signal. We theoretically demonstrate that an axisymmetric Bianchi I model produces a signal that can be described as a single quadrupole VSH term with an eigendirection which is aligned with the axis of maximum expansion anisotropy. We estimate this preferred direction from the Gaia data and the VSH fit, and perform point-estimates of the amplitude of the signal as a function of redshift. Although a significant quadrupole signal is detected in each bin, the increase of the amplitude of the signal with redshift predicted by the Bianchi I model is not confidently confirmed. The estimated value of the local expansion shear is higher than expected. Possible advances in describing the kinematic patterns of a high-redshift Universe with more complex cosmologies accommodating time-dependent anisotropy and rotation are discussed.

High-throughput sequencing technologies have enabled the collection of large-scale longitudinal -omics data, providing new opportunities for studying co-expression networks among molecular nodes such as genes and proteins. However, the high dimensionality and temporal dependence inherent in such data require specialized statistical methods. We propose a novel approach to infer dynamic co-expression networks among features over time (DCENt), where each node (feature) is modeled with a mixed-effects model, and dependencies among nodes are captured through correlated random effects. We develop two innovative penalized algorithms which harness the state of the art of threshold covariance estimators to estimate the random-effects covariance structure. Simulation studies show improved performance over existing approaches in terms of both mean square error and mean absolute error. We further apply the methods to data from the CARDIA study to investigate how the protein co-expression networks evolve over time as well as the association between protein trajectory patterns.

Photogalvanic effects arising from the quantum geometry of noncentrosymmetric materials are promising for next-generation light-harvesting devices that do not require a built-in electric field. Recent theories predict photogalvanic currents generated in magnetic systems with spin-dependent symmetry breaking as well as by bound exciton states, allowing for potential magnetic field control of the photoresponse and enhanced detection of deep sub-gap signals, respectively. We demonstrate the magnetic photogalvanic effect in a bilayer CrI3 tunnel junction with both magnetic field switching and electric field tuning of interlayer symmetry. By controlling for the polarization and energy of light illumination, we disentangle the shift and injection current contributions and find that the peak response occurs under resonant excitation of strongly bound excitons in CrI3. Our results can be captured within a many-body framework of the photogalvanic effect, while our devices function as tunable, multispectral helicity- and polarization-sensitive detectors that highlight the potential of 2D magnets for future optoelectronic applications.

Variational quantum algorithms (VQAs) offer a promising route toward simulating many-body quantum systems on noisy intermediate-scale quantum (NISQ) hardware. However, their scalability is severely limited by noise-induced barren plateaus (NIBPs), where hardware noise causes the gradients of the cost function to vanish exponentially with circuit depth, rendering optimization impossible. In this work, we demonstrate that introducing nonunitary elements into the variational ansatz can mitigate NIBPs in open-quantum systems. Using an analytically tractable infinite-range dissipative Ising model, we show that a nonunitary ansatz restores finite gradients in the presence of depolarizing noise, enabling convergence to the correct symmetry-broken steady state. We also develop a Floquet-type variational ansatz in which each layer repeats the same parameters, reducing the deep variational circuit to an effective quantum channel whose fixed points can be analyzed directly. We then extend these ideas to a realistic quantum-chemistry system by simulating electron transport through Oligophenylethynylene-sulfurmethyl (OPE-SMe) using Hamiltonians and jump operators of the model derived from first-principles polarizable QM/MM calculations. Our results show that nonunitary variational ansätze provide a scalable and physically grounded route for simulating open-system steady states on NISQ hardware, offering a pathway to overcoming one of the limitations of current quantum hardware.

Collective action often requires institutions that make cooperation individually worthwhile. We ask whether democratic allocation of public-good return can transform a repeated public good into a self-sustaining cooperative institution, and how participation costs reshape that process. A simple evolutionary model shows that voted redistribution can support a prosocial allocation order, but can also sustain an antisocial allocation order or democratic free riding, in which individuals benefit from an institution maintained by others while avoiding the cost of participation. The model predicts competing effects of voting cost. Cost can suppress use of the institution to reward low contributors under strong selection, but can also thin the active electorate and erode contributor-rewarding support. We test these predictions in a preregistered online experiment with \NIncludedGroupsVone{} five-person groups. Endogenous democratic redistribution increased contributions relative to an equal-share public-goods control, with zero-cost voting producing the strongest temporal improvement. Voting costs did not mainly turn active voters toward low-contributor-rewarding allocation. Instead, they shifted behavior toward abstention and democratic free riding, made abstention locally rewarding, and widened the gap between post-task perceptions of democratic participation and the behavioral record. Democratic allocation can therefore stabilize cooperation, but participation costs can reduce the number of people actively sustaining the institution and can make that erosion less visible to participants themselves.

Direct imaging of exoplanets requires stellar coronagraphs capable of suppressing starlight to contrast levels below $10^{-8}$. Active wavefront control with deformable mirrors (DMs) is essential to create dark holes in the image plane. However, polarization aberrations arising from beam reduction optics and the coronagraph itself produces multiple non-interfering intensity components that have correlated responses to the DM. This article introduces the concept of gratis mitigation: when a control loop minimizes one intensity component, others can be reduced concomitantly due to the correlated DM responses. Using end-to-end physical optics simulations of a Lyot coronagraph fed by a 4 m-class telescope with $f/5$ beam reduction, we demonstrate gratis mitigation and analyze its origin via a Jones matrix formalism. Gratis mitigation has significant implications for coronagraph design, calibration, and possibly wavefront control.

A classic result of Alon, Yuster, and Zwick (AYZ, Algorithmica 1997) shows that all $2k$-cycles in an $m$-edge graph can be listed in $\tilde O(m^{2-1/k}+t)$ time, where $t$ is the output size. This bound underlies the {\em submodular width} of Marx (JACM 2013) and the PANDA framework of Abo Khamis, Ngo, and Suciu (PODS 2017), which extend AYZ to arbitrary conjunctive queries with degree constraints. A central open question is whether combinatorial algorithms can beat the submodular-width barrier. Bringmann and Gorbachev (STOC 2025) gave lower-bound evidence that submodular width may be optimal for general conjunctive queries under combinatorial algorithms. The picture changes for $2k$-cycles on undirected graphs, whose queries have self-joins and symmetric EDBs: recent works improve on AYZ for even-cycle detection and listing. Pinning down the complexity of $C_{2k}$-detection and listing is thus a natural step toward overcoming the submodular-width barrier for such queries. For detection, Dahlgaard, Knudsen, and St{ö}ckel (STOC 2017) solved $C_{2k}$-detection in $\tilde O(m^{2k/(k+1)})$ time. Listing is harder. Jin and Xu (STOC 2023), and independently Abboud, Khoury, Leibowitz, and Safier (FSTTCS 2023), listed 4-cycles in $\tilde O(m^{4/3}+t)$ time; Vassilevska~Williams and Westover (ITCS 2025) listed 6-cycles in $\tilde O(m^{8/5}+t)$ time, improving the AYZ bounds of $\tilde O(m^{3/2})$ and $\tilde O(m^{5/3})$. The general case has remained open for 30 years. Building on these works, we list $2k$-cycles in $\tilde O(m^{(2k^2-k+1)/(k^2+1)}+t)$ time, improving AYZ for every $k\geq 3$. The key ingredient is an \emph{asymmetric supersaturation} result for even cycles. Our algorithms use only join and project operators over multiple tree-decomposition plans, making them naturally implementable in database systems, in contrast to prior BFS-based graph approaches.

We develop a partial integro-differential equation (PIDE) framework for option pricing under joint stochastic volatility and jump dynamics, and evaluate its empirical content using the S&P500 index option contracts across three maturities. The framework is derived from the infinitesimal generator of an affine Lévy-type process and implemented via finite-difference discretization with FFT-based treatment of the nonlocal jump operator. Calibration via GMM reveals that stochastic volatility accounts for the dominant share of pricing improvement, where relative to Black-Scholes, the Heston specification reduces implied-volatility RMSE by 39%. Jump augmentation via either Merton or CGMY specifications yields marginal improvements concentrated at short maturities and in the deep out-of-the-money region. The calibrated CGMY activity index supports a compound-Poisson structure, consistent with high-frequency evidence on S&P500 index returns.