Papers

Automatic prompt optimization (APO) uses feedback from model responses to improve prompts automatically. However, its effectiveness is usually measured through overall scores, which do not reveal which questions become correct, which previously correct answers become wrong, or whether improvements extend to unseen questions. We introduce Reflective Feedback-Driven Prompt Optimization (RFDPO), a tool that tracks recoveries (incorrect to correct), regressions (correct to incorrect), and churn (all changed outcomes). RFDPO uses this feedback to guide subsequent revisions and records prompt changes throughout optimization. We evaluate RFDPO across five benchmarks covering law, knowledge, instruction following, mathematics, and privacy, using GPT-5 as the optimizer and GPT-4o-mini and GPT-4.1 Mini as solvers. Our results show that overall accuracy can hide substantial changes: in five of nine configurations, churn was at least five times the absolute net change, and a single-item net change concealed up to 17 changed outcomes. Average validation gains were 7.9 percentage points, compared with 5.2 points on held-out tests. In a controlled ablation on LegalBench-Hearsay, item-level feedback reduced churn by 40% ($p=0.024$) while maintaining similar net gains. These findings motivate reporting recovery, regression, churn, and performance on unseen data alongside overall accuracy.

Interactions turn a gas into a fluid. We show that two-body loss can take their place. Correlated loss induces elastic scattering, as required by the optical theorem, which dominates at strong loss via the quantum Zeno effect. A nondegenerate gas with only two-body loss thus flows hydrodynamically, with viscosity and thermal conductivity close to those of the unitary Fermi gas. As loss heats the gas, both grow in time with a universal exponent 3/8. Unlike single-particle loss, two-body loss can engineer collisions, and hence transport, in quantum matter.

Robotic systems that must acquire information about a specific target often face severe occlusion from sur- rounding structures or from the target itself, such that a single camera viewpoint provides only partial information. Active perception must therefore select viewpoints that progressively reveal unobserved regions. However, conventional local next- best-view (NBV) methods typically select viewpoints according to their immediate utility, which can overlook views that provide limited information initially but enable more informative obser- vations from subsequent viewpoints. We formulated local target perception as a short-horizon sequential view-planning problem and proposed a Receding-Horizon Next-Best-View (RH-NBV) planner that evaluates candidate sequences of future viewpoints rather than isolated views. RH-NBV is evaluated on a UR5e manipulator with an eye-in-hand RGB-D camera in simulation as well as on physical robot against a gradient-based NBV planner, and random search, using a coffee mug and Stanford bunny under controlled occlusion and a tomato plant with natural self-occlusion. Under heavy occlusion, RH-NBV achieves substantially higher target information recovery, reaching 63.8% ROI coverage versus 34.2% and 85.5% occluded-surface recall versus 7.4% for the single-step NBV baselines on the most occluded mug configuration. A controlled horizon ablation shows that this improvement arises from multi-step reasoning rather than additional computation. RH-NBV provides the greatest benefit for strongly occluded targets, while myopic NBV remains competitive and substantially cheaper when visibility is less constrained.

Detecting biosignatures on Earth-like exoplanets from the Proterozoic era requires instrumentation capable of probing near-ultraviolet (NUV) spectral features, particularly ozone (\ce{O3}), which serves as an indirect proxy for molecular oxygen (\ce{O2}) when direct detection is challenging. Using a combination of photochemical-climate modeling and atmospheric retrieval simulations, we quantify fiducial instrument performance requirements for robust \ce{O3} detection and assess the risk of spectral false positives from sulfur dioxide (\ce{SO2}). Our analysis demonstrates the \ce{O3} abundances for Proterozoic Earth-like planets with \ce{O2} as low as 0.1% the present atmospheric level, can be constrained to within an order of magnitude at 1\,$\sigma$ confidence using three adjacent photometric bandpasses at a signal-to-noise ratio of 10 at 0.366\,$\upmu$m, each with a 15% width, and a short wavelength cutoff for those observations near 0.26\,$\upmu$m. The self-consistent steady state atmospheric modeling results show that \ce{SO2} buildup is difficult in a habitable environment with appreciable amounts of water vapor in its atmosphere and would require volcanic outgassing rates at least two orders of magnitude above present-day Earth to reach surface abundance levels comparable to Proterozoic Earth-like abundances of \ce{O3}. Even under these high \ce{SO2} flux scenarios, \ce{SO2} remains largely unconstrained with the recommended observational configuration, reinforcing the need for NUV coverage in coronagraphic instruments. Our findings support the inclusion of UV-optimized optics and detectors on the Habitable Worlds Observatory (HWO) to enable biosignature detection strategies sensitive to atmospheric conditions across key phases of Earth's geological history.

Reinforcement learning (RL) has substantially improved the reasoning of autoregressive and discrete-diffusion language models. Language models that generate continuous token embeddings are emerging as a strong alternative, but RL post-training for them remains understudied. We propose \method{}, a post-training framework for continuous flow language models. Such a model denoises token embeddings over multiple steps and decodes them into discrete tokens only at the last step. To obtain pathwise gradients, which backpropagate through continuous actions and have much lower variance than REINFORCE, we introduce a critic that estimates the value of intermediate token embeddings, bypassing the non-differentiable decoding step. The critic must also keep track of the value function as the policy changes; to this end, we design a critic that predicts a value from every token representation and improves policy optimization. Across four reasoning tasks, \method{} reliably improves a continuous flow language model through RL post-training and outperforms baseline methods of the same type.

The MeerKAT Observations of the Saraswati Supercluster (MOSS) is an ongoing project attempting to study the radio and optical properties of the core region of the Saraswati supercluster (z = 0.28) and will eventually entail a full survey of the entire supercluster region. Here we use radio catalogs from previous deep pilot MeerKAT L-band (1.28 GHz) observations (angular resolution of 8 arcsec) of the core region of the Saraswati supercluster. The region hosts two galaxy clusters representing distinct environments: The most massive cluster Abell 2631, and the second most massive cluster ZwCl2341, that is significantly more dynamically active. The deep radio catalogs of these clusters were combined with spectroscopic redshifts (mainly from DESI DR1 and SDSS DR16) and optical photometry catalogs of the cluster member galaxy source population. We use these redshifts together with the 1.4GHz MeerKAT flux densities to derive the dust-free star-formation rate (SFR) and evaluate various trends in the radio SFG and AGN galaxy populations. We find that the actively merging cluster ZwCL2341 has an increased star-forming galaxy population compared to A2631 with up to 4 times more star-forming galaxies. When looking at SFG-related radio processes we see s enhanced SF-related activity in ZwCL2341 with SF-related radio processes dominates entirely over AGN-related radio processes. This suggests that dynamically active environments associated with cluster assembly, such as mergers, have enhanced SF radio-activity and increased SFG (both radio and non-radio) galaxy population compared to lesser active systems.

We study coherent states of neutrinos electroweakly interacting with rotating matter. We start with the Dirac equation for a massive neutrino propagating in background matter with a coordinate dependent effective potential. Then, we consider the limit of massless particles and the specific matter velocity profile. It allows us to reduce the neutrino Hamiltonian to the harmonic oscillator form. We find the exact solutions of the Dirac equation and construct the creation and annihilation operators. Using these results, we build the generalized coherent states of neutrinos. We provide the interpretation of these coherent states in terms of the classical physics. In particular, we demonstrate that the coherent states constructed approach plane waves in the limit of slow matter rotation. We also define the effective neutrino mass owing to the interaction of a massless neutrino with rotating matter. Then, we consider a special case of the generalized coherent states which are called the neutrino coherent states. The situation of the degenerate parameters of the system is also studied. Finally, we apply our results for astrophysical neutrinos propagating in dense matter of a rapidly rotating neutron star (NS). We calculate the effective neutrino masses for different neutrino energies for realistic parameters of NS.

Quantum federated learning trains a quantum neural network (QNN) across nodes that hold quantum data, such as the states of quantum sensors. To forget data, unlearning methods for quantum models replay them, and federated unlearning from stored updates removes whole nodes only. Quantum data cannot be replayed, since a state is consumed when measured and cannot be cloned. We propose Shadow-based Data Erasure (SHADE), in which each node records a classical shadow of every training state, a few randomized single-qubit measurements taken at training time. The gradient and curvature of a QNN on a state are expectations of observables, so SHADE estimates them for the forget data from the shadows at any later parameters and removes their effect by a federated Newton correction. Only classical estimates cross the network. We prove that the shadow size needed for a target unlearning error grows exponentially in the size of the backward light cone of the measured observable and not in the number of qubits. In simulation with 50 nodes and on edge boards, SHADE matches the forget accuracy of retraining within 0.5 points, without replay and in under 0.2 s.

We investigate a discrete analogue of the Fisher information. By using a discrete Laplacian operator, we can construct a discrete analogue of the score function and hence of the information. This provides a natural framework for establishing several information-theoretic inequalities in the discrete setting.

I study randomization inference for dynamic causal effects in panels with many units and few periods when treatment is endogenous and an instrument is as good as randomly assigned only through the innovations of a first-order autoregressive assignment mechanism with unknown persistence. The persistence is a nuisance parameter in two senses: it determines which weighted average of heterogeneous causal effects the instrumented local projection estimand measures, and it governs the randomization distribution of any statistic built from the instrument. I propose tests that never estimate it. For each candidate value the innovations are recovered, rerandomized under a group that leaves their joint law invariant, and a randomization p-value is formed; the reported p-value is the supremum over candidate values or over an exact confidence set. Under a sharp null on the path of lag-specific effects the tests have level at most $\alpha$ for every persistence in finite samples, including the unit root, and the supremum is a maximum over finitely many points. Under a weak null on the heterogeneity-weighted estimand a studentized version is uniformly asymptotically valid.

Reliable uncertainty quantification remains an important challenge in AI. Hierarchical Bayesian methods provide a principled framework for this by representing unknown quantities through posterior distributions. Joint inference of neural-network parameters and prior hyperparameters is challenging for conventional Markov chain Monte Carlo (MCMC) methods due to strong dependencies. In this work, we introduce the multilevel particle marginal Metropolis-Hastings (MLPMMH) method, which combines pseudo-marginal inference for the hyperparameters with coupled sequential Monte Carlo (SMC) across hierarchy of network-width truncations for conditional parameter inference. The hierarchy is induced by a trace-class neural network (TNN) prior with width-dependent decay, motivated empirically by the compressible structure observed in trained neural-network parameters. Under standard multilevel coupling assumptions, we establish that MLPMMH achieves mean-square error (MSE) $\mathcal{O}(\varepsilon^2)$ at expected computational cost $\mathcal{O}(\varepsilon^{-2})$, and verify the predicted rate on a Bayesian regression problem. To address larger-scale applications, we further introduce S-MLPMMH, a practical approximation that replaces the exact sampling components with a PCA-based hierarchy and scalable Bayesian Monte Carlo. Experiments on MNIST demonstrate competitive predictive performance and uncertainty quantification while exploiting the parallel structure of the approximation. Software has been made publicly available at https://github.com/submission-code-anon/mlpmmh-anon.

Ultra-high-rate quantum error correction codes store many logical qubits in a single code block with few physical qubits. A fault-tolerant quantum computer, however, also requires a universal set of logical operations on individually addressable logical qubits, and the ancilla overhead of these operations may erode the advantage of the high encoding rate. Here, we propose the Cornucopia architecture, in which a universal set of logical operations is implemented at low overhead for the Cornucopia codes. In particular, we focus on the [[2844,1426,18]] Cornucopia code as an example and introduce a modular quantum computer built from such code blocks connected by bridges. Each block stores 1,426 logical qubits and serves as a universal logical processor. Exploiting the code's translation symmetry, we construct a family of reusable gadgets that individually address 1,422 logical qubits within each block. These gadgets support three universal logical instruction sets: basic, high-throughput and fixed-extractor. Excluding magic-state factories, a module with sufficient workspace to execute any instruction in the basic set requires an average of 4.1 physical qubits per logical qubit, compared with 3.0 for memory alone. The architecture thus preserves the resource advantage of ultra-high-rate quantum memory while enabling universal logical computation, providing a route towards low-overhead fault-tolerant quantum computers.

An edge server and nearby devices can train language models of different sizes together by mutual distillation. Federated unlearning (FU) and unlearning for large language models (LLMs) execute a removal request on one model. Under mutual distillation, however, the effect of the removed data has been copied into many students, and their uploads teach it back to the corrected teacher. We propose Holder-level Erasure via Replication-weighted Delta-closure (HERD), which decides which holders must be corrected. HERD records a knowledge lineage graph from the transfers that the server already performs and weights each edge by its transfer type. It computes how many times the residual at each holder will be copied and selects the cheapest set of holders whose correction bounds the cumulative residual after the request. A transfer guard and a rejoin rule cover the holders left uncorrected or offline. We prove that partial correction suffices only when the copy number of the lineage graph is below one, that averaging alone never reaches one, and that the correction set remains valid under link outages. On TOFU, HERD leaves 18% to 52% less cumulative residual than the strongest baseline at 6% to 12% of its correction cost.

Monocular 3D object detection methods increasingly rely on depth-guided transformers, but they operate entirely in the perspective image plane where spatial relationships are distorted by foreshortening. We propose MonoMIP, a dual-decoder framework that adds complementary 3D geometric reasoning through Bird's-Eye View (BEV) features constructed via Multi-Height Inverse Perspective Mapping. We perform IPM at K elevation planes spanning ground to rooftop, producing an ordered stack of height-conditioned metric BEV features that reduces above-ground misprojection and exposes depth-dependent appearance variation across planes. A BEV decoder with multi-scale deformable attention aggregates this multi-height evidence per query, while a depth-guided 3D decoder provides complementary perspective-space predictions. Without extra training data, MonoMIP attains 25.84% Moderate AP3D|R40 on KITTI val and 21.66% on the official test set for Car, outperforming recent published monocular methods on both the KITTI and Waymo benchmarks.

Forecasting optical turbulence and atmospheric parameters is crucial for science operations of present and new generation ground-based telescopes (ELT) as well as for free-space optical communication (FSOC). These forecasts are also useful to optimize the AO use, particularly in the ELT framework too. Recent research has demonstrated that the AR technique currently provides the best performances in predicting atmospheric and astroclimatic parameters on a time scale of 1 hour (e.g., RMSE 0.1" for the seeing), however deep learning offers some intriguing features that include the high adaptability, the correlation that can be found between different parameters treated simultaneously and different architectures can explore the capability for possible improvements. For this reason, it is important to investigate on the possibility to improve forecast performances beyond the score achieved by AR or simply to apply deep learning in those context in which it is not possible to apply the AR. In this contribution we investigate a set of algorithms belonging to the family of the neural networks that in principle are more suitable than the Random Forest (RF) model for this kind of application. We address specific questions related to the forecast performances in operational configurations. Besides that, we also investigate the impacts on gaps on the trained data set due to the lack of measurements of the optical turbulence during the day time. We show evidences that with measurements covering the whole 24-hours forecast performances might improve. Our test has been done on the wind speed in this contribution. This work is done in the framework of the operational forecast system for LBT (ALTA Center) and for the VLT (FATE project) that are leaded by our team.

Let M be an imaginary quadratic field and A be an abelian variety of odd dimension g defined over Q for which there is a unitary algebra embedding of M in End^0(A_M) of signature ((g+1)/2,(g-1)/2). Extending a result by Fité and Goodman, we show the existence of an elliptic curve E over Q with complex multiplication by M such that H_et^1(E_Qbar, Q_l) is a G_Q-subrepresentation of H_et^g ( A_Qbar, Q_l((g-1)/2) ). The main results of the article consist on explicit descriptions of E for A in two different families. First, when A is the Jacobian of the curve y^2 = xh(x^2), where h in Z[x] is a degree g monic separable polynomial with nonzero h(0), we show that E is given by y^2 = x^3 + h(0)x. Second, when A is the Jacobian of y^3=f(x), where h in Z[x] is a degree 4 monic separable polynomial, we show that E is given by y^2 = x^3 + 16 disc(f). This latter result builds on work by Laga and Shnidman in the bielliptic case, of which we give an alternative proof by means of a new p-adic method. As an application, we derive a practical average polynomial time algorithm to compute the Zeta functions of the reductions of a Picard curve.

Tool-augmented LLM agents discover relevant APIs from large registries before planning execution, yet finite context windows prohibit injecting all tool definitions into a single prompt. The dominant approach, which we term Retrieve-then-Plan (RtP), embeds the user query and retrieves similar tools via approximate nearest-neighbor search. We study an alternative Plan-then-Retrieve (PtR) paradigm in which the LLM first generates Abstract Tool Stubs (hypothesized function signatures describing needed capabilities) which then serve as retrieval queries against the registry. Evaluating on ToolBench (46,984 unique API endpoints, 50 categories) across single-tool (G1), intra-category multi-tool (G2), and cross-category multi-tool (G3) query subsets, we find a clear complexity-dependent crossover: RtP outperforms PtR on single-tool queries while PtR outperforms RtP on multi-tool queries. This crossover holds at every retrieval budget (k=1 to 20), is robust across registry sizes from 1k to 47k APIs, and is consistent across model families (Gemini 2.5 Flash and gpt-oss-120b). We characterize a stub-hallucination failure mode (the LLM invents plausible but non-existent API names) that acts as a double-edged sword: on simple queries PtR's stubs abstract away proper-noun signals that RtP matches directly, yet on complex queries the same mechanism decomposes multi-faceted intent into functional sub-needs. We further analyze token overhead and show that PtR's extra discovery call roughly doubles inference cost, which pays off on multi-tool queries but hurts on single-tool ones, motivating complexity-adaptive routing as a practical direction, one that can be driven by a zero-cost signal already present in the pipeline (RtP's top-1 retrieval score).

A wearable assistive robot must continuously estimate terrain, locomotion mode, gait phase, and walking speed. These quantities are commonly addressed by separate, terrain-specific models, with datasets rarely collected under a common protocol. This paper presents a visuo-inertial framework that connects these estimates through a causal pipeline using a chest-mounted camera and four lower-limb inertial measurement units (IMUs). Anticipatory Terrain Perception (ATP) classifies incoming terrain with 96.3% accuracy and anticipates terrain transitions by 1.46 s on average. Terrain-Aware Locomotion Mode Identification (TALMI) achieves 93.7% and 98.8% accuracy for its level-ground and stairs experts respectively, with mean transition latencies being below 200 ms. The relevant TALMI posterior is retained as a Probabilistic Locomotion Context (PLC) vector and provided to a shared Gait Kinematic Encoder (GKE), which supports 50-Hz bilateral gait-phase estimation and 2-Hz walking-speed estimation. Leave-one-subject-out evaluation yields gait-phase RMSEs of 1.75%, 2.97%, and 4.55% for level walking, stair ascent, and stair descent respectively while estimating speed over 3.5-5.5 km/h with a RMSE of 0.218 km/h. All inertial sensing based models use sensor-fused Euler angles as input rather than raw accelerometer and gyroscope signals, reducing dependence on sensor mounting variation.

Following the discovery of the exotic state $X(3872)$ in the charmonium spectrum, the possible existence of an analogous state, $X_b$, in the bottomonium sector has attracted considerable attention of the hadronic physics community. In this work, we lay the ground for the development of Born-Oppenheimer chiral effective field theory (BO$\chi$EFT), that allows us to include both quark and hadron degrees of freedom as well as the full complexity of the meson-exchange potential in a systematic way. For illustration, the formalism to leading order (LO) is applied to the system of $\chi_{b1}$ states and in particular the $X_b$. The two parameters that are present at this order are constrained using experimental information on the bottomonium spectrum together with lattice input on static quark-antiquark potentials, including string breaking effects. The framework identifies the observed $1^{++}$ state at 10.513 GeV with a predominantly molecular $X_b$, the bottom counterpart of the $X(3872)$, and predicts an additional predominantly compact bottomonium state at 10.544 GeV, about 60 MeV below the $B\bar{B}^*$ threshold.

Generative retrieval (GR) has emerged as a strong candidate generator for sequential recommendation as language models and semantic-item identifiers have improved. However, GR is not a uniformly stronger replacement of dense retrieval (DR) in online retail candidate generation. We examine their differences on two Amazon Toys datasets under different metrics. GR leads on best relevant item value among users both methods cover, while DR leads on exact-target recall and relevant value across the ranked list. With deep analysis, we find that popularity contributes the most to GR's measured value lead. Adding the same static item value to DR in one reranking step reverses this lead and keeps recall above GR. Finally, on an industrial-scale internal e-commerce dataset with LLM-judged relevance, we show that a 14B SID-LLM still underperforms a $47\times$ smaller dense encoder.

Training large language models (LLMs) across geographically distributed and poorly interconnected compute pools or data centers has become a topic of significant interest. This has led to increased study of local optimization methods such as DiLoco for LLMs, especially those that use local (or inner) adaptive or preconditioned optimizers, which are critical for high-performance LLM training. However, a central challenge remains: it is well known that increasing the number of model replicas (replica scaling) while fixing the total training budget leads to monotonically decreasing performance. Existing work has empirically demonstrated that the choice of inner optimizer (Muon v.s. AdamW) can significantly improve this trend, but offers only limited explanation of the performance difference. In this work, we consider a range of inner-optimizers and identify two important factors that impact replica scaling: (1) the covariance structure of the pseudo-gradients and (2) the impact of batch size on the pseudogradient's noise scale. Based on these insights, we theoretically and empirically demonstrate that whitening-based pre-conditioning is a powerful inner-optimizer desideratum. Our empirical evaluation extends the results to reveal that whitening-based inner-optimizers achieve strong replica scaling (for 8-96 replicas), with performance relative to DP improving as parameters and data are scaled.

As video models enable longer and more realistic interactive experiences, maintaining a world consistent with its history becomes essential. This requires both preserving previously observed content and ensuring coherent world evolution over time. World memory is a critical capability to evaluate alongside visual fidelity and video duration. We introduce WorldMemBench, a benchmark for systematically evaluating world memory in video world models. Across 260 test cases, it assesses static memory through the retention of human identity and appearance, object appearance and geometry, and environmental content and geometry, and dynamic memory through event progression and state persistence. Using controlled camera departures and multi-revisit trajectories, the benchmark evaluates static content against fixed initial references and dynamic events against expected state transitions. It combines appearance and geometry metrics with event-specific assessments, and reports video quality and camera-following accuracy as complementary diagnostics. Evaluation of nine representative models shows that strong static retention does not imply reliable dynamic state evolution, while repeated revisits reveal memory degradation beyond the first return. Human studies support the alignment between our automatic evaluations and human judgments. WorldMemBench provides a systematic testbed for diagnosing memory failures and guiding the development of persistent, temporally coherent video worlds.

Prompting is a widely used method for adapting general-purpose LLMs to domain-specific tasks. Effective prompts can be tedious to create manually, so prompt writing is increasingly handed to LLMs, with recent work training LLMs to write prompts for other models. These techniques either write prompts without observing how the task model behaves, blind to the failure modes the prompt should address, or must run alongside the task LLM at inference time, adding overhead to every query. Neither reflects how prompt engineering is often practiced. To close this gap, we introduce Reinforcement Learned Prompt Engineering (RLPE), which trains a model to analyze traces of a separate task model and write a prompt targeting the failures it observes. RLPE rewards the trained model strictly on prompt performance, so it learns the prompting strategies that improve the task model. The prompt is generated once and reused across the task, so inference does not require the trained model. Since RLPE needs only query access to the model it prompts, it is also compatible with closed-source models. We apply RLPE to Enigmata, BIG-Bench Extra Hard, and PlanBench. We train a 9B-parameter model that writes better prompts than state-of-the-art frontier models (gpt-5.6-sol and claude-opus-5) and prompt optimizers (GEPA and TextGrad) on 2/3 benchmarks. Although the model is never explicitly trained to iterate on prompts, this capability emerges at a level that matches or beats frontier models. The learned prompting capability also generalizes, with the trained model improving task models 6x larger than the one it trained with, including ones from entirely different model families, and matching claude-opus-5 on a fourth benchmark held out from training.

At fixed bulk criticality, every fixed nonsingular real single-end potential preserves a growing local population of real eigenvalues in an open analytic family of non-Hermitian chains. An open region of two-end real potentials removes this population. A boundary-amplitude criterion fixes the minimum number of controlled ends. The population grows as $\sqrt N$, where $N$ is chain length, although its normalized spectral weight vanishes and the local limiting bands remain unchanged. For a representative chain's four zero-detuning settings, an independent passive Hermitian double chain converts this distinction into separated resonances at one fixed local port under a common coupling scan at fixed probe carrier. Its absolute reflection contrast and stability margin both scale as $N^{-1}$, with explicit sufficient resource budgets. Boundary amplitudes thus fix a minimum control requirement that limiting bands and thermodynamic spectral density do not specify.

A long-standing open question is to characterize the classical communication cost of simulating the correlations arising from measurements on finite-dimensional quantum systems. We consider this question in the prepare-and-measure scenario. First we construct a classical simulation model involving a finite average number of bits of one-way communication that simulates exactly the correlations arising from arbitrary $d$-dimensional quantum states and arbitrary measurements. Second, we show that no classical simulation protocol involving a finite average message dimension can exist for $d\geq 4$, hence strengthening a recent result of de Gois, Santos and Vieira. Our first result relies on a more general simulation theorem which can be applied to certain continuous variable (i.e. infinite-dimensional) quantum systems, and even beyond quantum theory, e.g. to generalized probabilistic theories. In particular, we show that multimode Gaussian states of bounded average energy and general Gaussian measurements admit an exact classical simulation with a finite expected number of bits. Overall, our results show that the classical simulation cost of quantum communication is essentially as high as it could be.

This paper studies several first-order methods for low-rank matrix minimization in the Burer–Monteiro form, where the target matrix is represented as the product of a nonnegative factor matrix and its transpose. Such a factorization destroys convexity of the objective function and global Lipschitz continuity of the gradient. We prove that for a quadratic objective function that is strongly convex only on the subspace of symmetric matrices, the Burer-Monteiro factorized objective possesses generalized smoothness with a fractional exponent 2/3. For a quadratic objective, the generalized smoothness property requires positive definiteness of the operator A only on the subspace of symmetric matrices, which relaxes the assumptions of Dragomir et al. On this basis, three methods are proposed: an adaptive gradient descent method with Armijo backtracking; an unconstrained SafeAdam method combining the Adam direction with a descent-angle certificate and a fallback to the normalized gradient; and a certified projected version for the nonnegativity constraint. Global convergence and explicit convergence rates for the proposed methods have been proved. The obtained convergence rate is better than the convergence rate of ordinary unaccelerated gradient descent in the case of a sufficiently large gradient. In the small-gradient regime, the convergence guarantee is of square-root type, and the corresponding complexity scales as the inverse square of the desired accuracy. In the large-gradient regime, the convergence guarantee is of three-quarters type, and the corresponding complexity is proportional to the inverse of the accuracy raised to the power of 4/3. Experiments on SymNMF using the TDT2, Reuters and CBCL datasets, which are standard benchmarks for document and image clustering, show that the methods match or outperform Dyn-NoLips without tuning the relative-smoothness kernel parameters.

Compartment models of infectious diseases are often linear in coefficients that are physical parameters or products or ratios of them. We exploit this with closed-form least squares and equip the estimates with distribution-free uncertainty. Physics-informed regression (PIR) fits the parameters to finite-difference derivatives of the data; we introduce physics-informed weak regression (PIWR), which integrates the model in time instead, needs no derivatives of the data, estimates the initial state jointly and is high-order accurate. To quantify uncertainty we wrap both estimators in split conformal prediction, with a calibration population generated by the physics-based model itself, giving simultaneous intervals for all parameters with a finite-sample coverage guarantee. A residual-adaptive factor, computed without ground truth, scales the intervals to each data set (PIWR-RACC). On the eleven benchmark models of disease-informed neural networks (DINNs), PIWR or PIR-FD6 is one to four orders of magnitude more accurate than the reported DINN results wherever the sampling resolves the dynamics, in about a millisecond per fit instead of minutes to hours of training, and the 90% intervals achieve 87-92% coverage in all 88 settings. On the S3I3R model of the original PIR study, PIWR lowers the reported PIR errors by about three orders of magnitude. On real data from the 1978 boarding-school influenza outbreak, a variable-projection variant gives calibrated 95% intervals that overlap those of a Bayesian analysis. On a time-varying transmission benchmark, a B-spline expansion of beta(t) keeps PIR and PIWR linear; they are more accurate than physics-informed neural networks in three of four cases and comparable in the noisiest, with simultaneous bands for beta(t). The complete conformal calibration takes less than two minutes for every benchmark.

We present a mass-conservative Darcy-Brinkman-Stokes (DBS) formulation for reactive transport with cell-based surface complexation in image-based porous media, coupled to PHREEQC and implemented in GeoChemFoam, an OpenFOAM-based toolbox. Dissolved species are transported in the physical mobile-water fraction, adsorbed species are stored as conservative cell-scale surface inventories, and each reactive cell is coupled to PHREEQC. Reactive surface area is prescribed independently as a cell field, so that internal area left unresolved by segmentation of microporous phases can be represented while DBS flow and transport are retained in the resolved pore space. The implementation is verified with a test suite that isolates the coupling of transport and chemistry from the construction of reactive surface area. Aqueous and adsorbed mass balance is evaluated against a one-dimensional analytical retardation benchmark and closed-system batch calculations. The smooth-interface surface-area algorithms are tested on idealised two- and three-dimensional geometries. In a two-scale lithium micromodel, DBS reproduces fully resolved aqueous and sorbed inventories within 0.6% across Pe=0.1-10. The applications comprise Pb2+ retardation by hydrous ferric oxide coatings in a two-dimensional fracture network, competitive Mn2+/Mg2+ exchange in a three-dimensional Kelvin-cell sorbent, and Sr2+/Ca2+ exchange in Estaillades limestone. In the fracture-network and limestone cases, the formulation yields spatially resolved aqueous and adsorbed inventories even where reactive surface area is only partly resolved at the image scale. The framework therefore supports conservative surface-complexation modelling in both resolved and unresolved pore structures, with relevance to contaminant retention, selective ion capture, and radionuclide transport.

When a long liquid drop is confined in a Hele-Shaw cell, the pull of surface tension produces a rapid retraction of its tip, causing it to bulge out as it draws up the excess liquid. Using numerical simulations, we demonstrate that this retraction is self-similar at long times, with the speed of retraction slowing like $t^{-1/2}$, where $t$ is the duration of retraction. After showing how this scaling can be understood using force and mass balance, we perform an asymptotic analysis of the Hele-Shaw equations to derive both the shape of the retracting drop, as well as prefactors of the scaling laws. Excellent agreement is found between our simulations and theory, and the experimental consequences are pointed out.

Core level atomic photoionization is influenced by the molecular environment of the emitting atom. To probe this influence we used extreme ultraviolet (XUV) radiation to measure the I$\left(4d\to\varepsilon f \right)$ photoemission of four iodine substituted alkanes in the range from 60 eV to 160 eV photon energy. Using two detection angles relative to light polarization allowed us to extract and compare the asymmetry parameter of the investigated compounds. These results are in agreement with theory by Pi and Landsman (L.-W. Pi and A. Landsman, Attosecond time delay in photoionization of noble-gas and halogen atoms, Applied Sciences 8, 322 (2018)) and previous experiments by Olney et al. (T. N. Olney, G. Cooper, and C. Brion, Quantitative studies of the photoabsorption (4.5-488 ev) and photoionization (9-59.5 ev) of methyl iodide using dipole electron impact techniques, Chemical Physics 232, 211 (1998)) for iodomethane. 2-iodopropane behaves nearly identical to iodomethane, while for iodoethane and 1-iodopropane we find a distinct and consistent, energy dependant difference most prominent at around 130 eV photon energy. This further proves the influence of the chemical environment on core level photoionization. Due to the sensitivity on the exact positions of the carbon atoms and the energy dependence we hypothesise this difference is caused by intramolecular scattering of the outgoing photoelectron wave packet, causing changes in the angular distribution.