arXiv:2606.05345v1 Announce Type: new
Abstract: We unify RoPE's Fourier phase, Jordan-RoPE's finite jets, and ALiBi's affine recency into a single learnable relative-position space, and study which regions of this space are selected by different tasks. PJ-RoPE is a Fourier-Jet-Affine formulation for relative attention, with an optional Poincare-type reading as the affine completion of a homogeneous Fourier-jet positional representation. Algebraically, the same primitives form a finite constant-coefficient difference module: simple roots of the lag-shift operator give Fourier/RoPE characters, repeated nonzero roots give Jordan/Fourier jets, and the repeated unit root gives ALiBi-like affine recency.
The framework separates scalar PJ-bias kernels from exact PJ-rotary feature transforms, introduces adaptive sector diagnostics, and uses LC/rapidity coordinates to stabilize high-order jets. Controlled probes verify sector containment and selection; small language runs expose an affine/recency boundary; music-token streams provide the clearest case where LC/affine variants remain strong while carrying measurable high-order corrections; and LC diagnostics show a scale-stability gain coupled to phase-resolution loss.
Science Journals
arXiv:2503.12224v2 Announce Type: replace-cross
Abstract: Estimating the overlap between a prepared state and a target eigenstate is crucial for the efficiency of quantum phase estimation (QPE), since QPE succeeds with probability equal to this overlap. We present a systematically improvable method to compute certified upper and lower bounds on such overlaps using a finite set of Hamiltonian moments. Our approach constructs optimal polynomial upper/lower bounds on an energy-window indicator and evaluates them through linear and semidefinite programs, yielding the tightest bounds consistent with the available moment and spectral-interval information. We demonstrate the method on strongly correlated molecular Hamiltonians and study the impact of approximate moments obtained from tensor-network contractions. The resulting bounds provide a practical pre-QPE screening tool for selecting initial states and can be implemented with either classical moment computation or quantum expectation estimation.
arXiv:2606.05179v1 Announce Type: new
Abstract: Punctuation restoration improves ASR (Automatic Speech Recognition) readability. However streaming ASR requires online decisions with limited future context. In streaming ASR, the system predicts punctuation incrementally, which makes generation-based approaches prone to latency and alignment failures under boundary-wise evaluation. This paper proposes a non-autoregressive scoring method (no free-form generation) that preserves the input transcript and makes a decision at each word boundary. Our method compares punctuation insertion hypotheses against a no-insertion baseline under a bounded K-subword-token lookahead, and calibrates decisions using a weight {\alpha} and a validation-calibrated threshold {\tau} (no parameter updates during inference). On IWSLT 2017, our scoring method achieves a 4-class macro F1 of 0.893 in the no fine-tuning setting (validation-calibrated, K=2) and 0.937 after fine-tuning (K=2), outperforming the prompt-based baseline (0.566) and a fine-tuned ELECTRA baseline (0.913) under the same lookahead budget. We analyze the impact of the lookahead budget through ablation studies on K.
arXiv:2606.06167v1 Announce Type: new
Abstract: The increasing penetration of single-phase loads and distributed generation exacerbates voltage unbalance (VU) in distribution grids, raising concerns about power quality and complicating network operation. However, most market-clearing models and price-based coordination frameworks do not enforce VU limits within a three-phase AC representation, so the implications for grid-code compliance, numerical scalability, and economic signals remain unclear. This paper embeds VU in a three-phase AC optimal power flow market-clearing model and benchmarks two treatments: strict VU limit enforcement and objective function penalization. Building on these insights, an Improved Hybrid Limits (IHL) formulation is proposed that preserves compliance while using a smooth unbalance proxy in the objective to guide the optimization solver. Case studies on a European low-voltage feeder show that IHL maintains feasible operating points, yields price and curtailment signals consistent with conventional hybrid formulations, and converges substantially faster and more reliably than a penalization based on the exact unbalance metric. These results support IHL as a practical and scalable mechanism for VU mitigation in market-based operation of unbalanced distribution systems.
arXiv:2606.05987v1 Announce Type: new
Abstract: Ultrastable lasers play a key role in optical frequency metrology, setting measurement speed and ultimately impacting both stability and accuracy of optical frequency standards. Here we demonstrate laser fractional frequency instability at ${4}\times10^{-17}$ and laser frequency linewidth of $12\,$mHz full width at half maximum, employing a 68 cm long optical reference cavity operating at room temperature. To the best of our knowledge, both frequency instability and linewidth are the lowest ever reported for a room temperature system. This work highlights that state-of-the-art frequency stability and spectral purity are achievable at room temperature, making them accessible to a broader range of users.
arXiv:2606.04332v2 Announce Type: replace
Abstract: Electron spin polarization in radiative plasmas with ultrarelativistic kinetic turbulence under highly magnetized conditions is investigated using particle-in-cell simulations. We observe that a significant spin polarization can be sustained when the leptons undergo energetic photon emission accompanied by spin flips during the nonequilibrium turbulent evolution. By analyzing the time evolution of spatially dependent spin polarization, we identify an electromagnetic (EM) regime of kinetic turbulence, distinct from the well-known density-dominated regime characterized by vortex currents and magnetic islands. While in the latter regime the spin polarization exists only transiently, in the EM regime significant anisotropic net polarization emerges and persists in non-dissipative scenarios. The correlation between spin signals and turbulence features is leveraged to introduce the characteristic parameter delimiting the EM regime via the ratio of electric and magnetic energy densities and to gain insight into complex plasma turbulence. This study demonstrates the versatility of a spin-resolved study of the plasma turbulence in extreme environments, such as black holes and magnetar magnetospheres.
arXiv:2606.05187v1 Announce Type: new
Abstract: Among the many challenges hindering the responsible development and deployment of AI, arguably none has faced more intense scrutiny than bias in its various forms. This underscores the widespread concerns across AI researchers that model outputs, e.g., from generative AI, may encode structural distributional imbalances (stemming from training data or model design) that may amplify social inequality or introduce systemic distortions across application domains ranging from biodiversity to disaster mitigation. Yet, relatively little work has investigated the geographical nature of bias or developed measurable benchmarks for what it means for (generative) AI to be unbiased. In this chapter, we investigate this issue through a literature review. As foundation models are reshaping the landscape of bias research, we examine work spanning both the pre-generative AI and generative AI periods. First, we identify a range of geographic biases. These biases span from representation bias in the training data and regional disparities in the factual recall of language models to the tendency of generative AI to over-proportionally favor prototypical places (called defaults). Then, we showcase how recent studies address the latter bias by evaluating geographic diversity in the outputs of generative AI across various cognitive levels, parameter settings, and output modalities.
arXiv:2606.05620v1 Announce Type: new
Abstract: Recursion enables the generation of hierarchical linguistic structures but imposes substantial processing demands during real-time comprehension. While difficulties with complex syntax have been reported in autism spectrum disorder (ASD), the temporal dynamics of recursive processing remain poorly understood. This study used event-related potentials (ERPs) to examine how Mandarin-speaking children with ASD process two-level recursive locative constructions. Twenty-four children (12 ASD, 12 typically developing, TD) participated in a cross-modal sentence-picture matching task. Neural responses were analyzed across three processing stages associated with structural prediction (P200), semantic integration (N400), and syntactic reanalysis (P600), with mental age controlled. Results revealed a systematic divergence between groups. TD children showed clear P200 and P600 modulation in response to structural mismatch, whereas ASD children exhibited attenuated early differentiation and reduced late reanalysis effects. In contrast, ASD children showed enhanced N400 responses under mismatch conditions, indicating increased semantic integration demands. In addition, the ASD group displayed significantly greater inter-individual variability in hemispheric lateralization, although lateralization strength was not associated with receptive vocabulary performance. These findings support a cascading account in which reduced early predictive engagement in ASD leads to increased integration costs and diminished reanalysis efficiency during recursive processing. More broadly, the results highlight the importance of both temporal processing dynamics and neural variability in understanding language differences in ASD.
arXiv:2606.06232v1 Announce Type: new
Abstract: Laser plasma accelerators can deliver high-energy, quasi-monoenergetic electron beams over centimeter-scale distances. In this work, we report on the generation of narrow, quasi-monoenergetic electron bunch trains with periodic energy spacing issued from downramp injection in a laser driven wakefield accelerator. The periodicity in energy is shaped via relativistic lengthening of the wakefield during the acceleration phase, while the spatial periodicity is obtained via injection into multiple plasma periods. At the end of the accelerator, a rotation in phase-space is performed to compress each bunch in energy, producing narrow periodic spikes in the spectrum. The experimental observations are supported by particle-in-cell simulations, which reproduce the formation and evolution of the periodic bunch trains, providing an insight into the underlying plasma dynamics.
arXiv:2606.06473v1 Announce Type: new
Abstract: Large language model (LLM) agents are increasingly applied to long-horizon tasks such as scientific discovery and machine learning engineering (MLE), where sustained self-evolution becomes a key capability. However, existing MLE agents suffer from inter-branch information isolation, memoryless search, and lack of hierarchical control, which together hinder long-horizon optimization. We present MLEvolve, an LLM-based self-evolving multi-agent framework for end-to-end machine learning algorithm discovery. By extending tree search to Progressive MCGS, MLEvolve enables cross-branch information flow through graph-based reference edges and gradually shifts the search from broad exploration to focused exploitation with an entropy-inspired progressive schedule. To allow the agent to evolve with accumulated experience, we introduce Retrospective Memory, which combines a cold-start domain knowledge base with a dynamic global memory for task-specific experience retrieval and reuse. For stable long-horizon iteration, we further decouple strategic planning from code generation with adaptive coding modes. Evaluation on MLE-Bench shows that MLEvolve achieves state-of-the-art performance across multiple dimensions including average medal rate and valid submission rate under a 12-hour budget (half the standard runtime). Moreover, MLEvolve also outperforms specialized algorithm discovery methods including AlphaEvolve on mathematical algorithm optimization tasks, demonstrating strong cross-domain generalization. Our code is available at https://github.com/InternScience/MLEvolve.
arXiv:2606.05326v1 Announce Type: cross
Abstract: We study the dynamics of gradient descent in the Edge of Stability regime, where the learning rate is large enough to induce persistent oscillations in the loss and the sharpness. We propose a continuous-time effective model that tracks the evolution of the average trajectory coupled with the time-averaged covariance of its fast oscillations. Our analysis reveals that the natural quantity to monitor in such unstable regimes is an effective free energy, which combines the original risk functional with a curvature-related "entropic" term. Our model allows us to track the envelope of the oscillations even in situations where its dynamics evolve on similar timescales as the averaged weights. Otherwise stated, we can track the spikes that occur during the training of some neural network architectures. For wide two-layer neural networks optimized under stable non-vanishing oscillations, we derive a mean-field limit that results in a novel kinetic equation describing the joint distribution of weights and their fluctuations. We show that this equation can be interpreted as a Wasserstein-2 gradient flow of a macroscopic free energy. Finally, we provide numerical evidence on matrix factorization and deep learning tasks (CIFAR-10) to demonstrate the model's accuracy in capturing the envelope of the oscillations and the predictive power of the effective free energy.
arXiv:2606.05222v1 Announce Type: new
Abstract: Artificial intelligence (AI) has been applied across educational contexts to support learning. One approach to such support is "human-AI collaboration" (also termed "hybrid intelligence"), where human(s) and AI components interact to promote human learning. However, as in human-to-human computer-supported collaborative learning (CSCL), unstructured interaction does not necessarily produce an effective learning experience. This paper reports a systematic literature review of empirical studies (N=62) on human-AI collaboration and hybrid intelligence for learning support. The review characterizes collaboration processes, their structures, and contexts of application. It also extracts emerging design knowledge and research gaps. Researchers and technology designers can use these findings as a starting point for structuring more effective AI-enhanced technologies for collaboration, in educational practice and future research.
arXiv:2602.00898v2 Announce Type: replace
Abstract: We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than enforcing strict balance and separator optimality, the algorithm deliberately relaxes these design decisions to favor fast partitioning and efficient elimination-tree construction. Our method decomposes permutation into patch-level local orderings and a compact quotient-graph ordering of separators, preserving the essential structure required by sparse Cholesky factorization while avoiding its most expensive components. We integrate our algorithm into vendor-maintained sparse Cholesky solvers on both CPUs and GPUs. Across a range of graphics applications, including single factorizations and repeated factorizations, our method reduces permutation time and improves the sparse Cholesky solve performance by up to 6.27x. Our code is available at https://github.com/BehroozZare/fast-permute.
arXiv:2606.05258v1 Announce Type: cross
Abstract: Transfer learning is a natural strategy when a target population has limited data but multiple related auxiliary sources are available. A central difficulty is source heterogeneity: auxiliary sources may not be equally useful, and their usefulness may vary in a structured, cluster-like fashion. Existing transfer-learning methods often reduce source selection to a binary informative/non-informative decision, overlooking subgroups of sources with differential transferability. Motivated by a suicide-risk study using data from the Connecticut Hospital Information Management Exchange (CHIME), comprising 636,758 patients across 27 hospitals, we propose Trans-GLMC, a cluster-structured transfer-learning procedure for generalized linear models. The CHIME setting illustrates the core challenge: hospital-specific risk models are unstable because suicide attempts are rare at any single facility, whereas indiscriminate pooling across hospitals can obscure facility-level differences in patient mix and risk profiles. Trans-GLMC first constructs a coefficient-based distance among the target and candidate sources to recover latent source clusters. It then combines global fusion, within-cluster refinement, and target debiasing to produce an estimator that adapts to the detected structure. We establish a non-asymptotic error bound that improves over its unclustered counterpart whenever a meaningful target cluster exists and matches the unclustered rate up to constants otherwise. In simulations and in the CHIME study, Trans-GLMC improves facility-specific prediction, identifies interpretable communities of hospitals with mutual transferability, and recovers clinically coherent suicide-risk factors.
arXiv:2606.05219v1 Announce Type: new
Abstract: Recent analyses of multi-pathway Deep Linear Networks use Gradient Flow to predict a "winner-takes-all" specialization in which path symmetry breaks and each feature concentrates in a single pathway. In this work, we show that discrete Gradient Descent (GD) with a large step size tells a different story. We prove that single-path solutions are sharp minima, whereas distributing signals across pathways reduces sharpness by a factor that decreases with both the number of pathways and depth. Consequently, while early training reproduces the depth-driven symmetry breaking predicted by GF, oscillations at the Edge of Stability subsequently override this tendency and drive the network into a re-balancing phase, where signals redistribute across pathways. Together, these results clarify how depth shapes pathway competition and explain why large-step GD favors shared representations rather than persistent single-pathway dominance.
arXiv:2606.06240v1 Announce Type: new
Abstract: Persistent memory for an LLM agent is a write-heavy substrate: every belief update is a versioned write, and a new claim may contradict a stored one. Production systems use four resolution heuristics (last-writer-wins, evidence-weighted merge, await-confirmation, per-rule policy), yet none declares the isolation level it assumes or the write-time anomalies it admits. We show that contradiction resolution is write-time concurrency control and make the missing contract explicit. TOKI types the four heuristics as one family of bitemporal operators over a dual-row schema, each with an isolation precondition and a provenance annotation that preserves the losing fact in an audit row. Four soundness theorems close the contract across isolation, schema, and provenance, lift the guarantees to operator pipelines, and extend the fold operators to n-ary conflict sets. A tightness companion proves that, within the relational schedule model, keyed logging of the adjudicating judge is necessary for replay consistency, which every audited baseline omits. A verdict matrix over eight systems localizes the gap: every baseline that keeps a language-model judge on the write path admits at least one of three write-time anomalies (replay inconsistency, belief-drift skew, audit erasure); a content-addressed engine-layer comparator avoids them only by removing the judge, and TOKI alone excludes all three while keeping it. On its one natural-workload slice the audit-row defence moves LoCoMo by 0.86, and ablating the typed memory layer removes 0.49 accuracy on 1,444 answerable LoCoMo questions; the cross-system comparison stays underpowered and claims no superiority. The contribution is the contract: a write-time correctness specification, proved sound across isolation, schema, and provenance, pinning the guarantee every production heuristic assumes but no deployed system makes explicit.
arXiv:2606.06238v1 Announce Type: new
Abstract: We propose a statistical-field framework for text generated by large language models (LLMs), treating token embeddings as continuous spin variables on a one-dimensional chain. Defining a susceptibility from the connected two-point correlator and an order parameter from the ensemble-averaged embedding field, we vary the \texttt{softmax} temperature $T$ and observe a sharp susceptibility peak near a characteristic $T_c$ with power-law-like scaling, a concurrent rapid change in the order parameter, and a collapse onto a single semantic direction below $T_c$. The intrinsic dimension estimated by the two nearest neighbor (TwoNN) method independently corroborates these findings, reaching a minimum near $T_c$. Results are robust across model scales (Qwen3: 0.6B--32B) and prompt categories. While the phenomenology closely resembles a continuous phase transition, the non-equilibrium nature of autoregressive generation warrants further investigation. Our framework provides quantitative tools for probing the collective statistical structure of LLM outputs and suggests connections between decoding strategies and critical phenomena.
arXiv:2606.05805v1 Announce Type: new
Abstract: LLM-based guardrails typically safeguard agents by evaluating proposed actions or inputs before execution, producing safety signals such as binary allow/deny decisions, risk categories, and/or explanatory rationales about potential policy violations. However, agent risks often arise when otherwise benign tasks are contaminated by untrusted external content, unsafe instructions, or risky tool use. Existing guardrails often flag the entire task uniformly as unsafe, thereby blocking the threat but sacrificing the benign part. Moreover, existing work largely evaluates guardrails in isolation, leaving unclear whether their interventions lead to safer downstream agent behavior. To address this, we introduce TRIAD (Tripartite Response for Iterative Agent Guardrailing), a guardrail-integrated agent framework that leverages guardrail-generated verbal feedback as a guiding signal to keep the agent aligned with benign objectives at each planning step. We finetune a language model on a self-curated training dataset to output one of three decisions: proceed, refuse, or update, together with structured natural-language feedback. Rather than merely allowing or blocking execution, update guides the agent to revise its plan, avoid harmful components, and preserve the benign task where possible. TRIAD injects this feedback into the agent's context, enabling subsequent plan revision and forming a closed loop between guardrail feedback and agent planning. Extensive experiments on ASB and AgentHarm show that TRIAD reduces the average attack success rate to 10.42%, while achieving the best safety-utility trade-off among guardrail-integrated baselines. Our code is available at: https://github.com/YUHAOSUNABC/TRIAD.
arXiv:2606.05266v1 Announce Type: new
Abstract: We establish the first sharp thresholds for low-degree polynomial tests in planted-vs-planted settings, where the goal is to determine with vanishing error which of two structured planted mechanisms generated the observed data. We prove matching low-degree upper and lower bounds for counting communities in the planted submatrix and planted dense subgraph models. The resulting testing threshold coincides, down to the sharp constant, with the known low-degree recovery threshold. In contrast, the task of weak testing, where the goal is to outperform random guessing, does not have a sharp threshold but rather a smooth transition, which we identify. To prove our results, we develop a framework for planted-vs-planted testing that builds on a latent-variable expansion originating in low-degree recovery and employs new methods to identify and prune non-signal contributions.
arXiv:2606.05255v1 Announce Type: cross
Abstract: Oklab and its cylindrical representation Oklch are widely adopted in interpolation and design workflows as perceptually motivated color spaces, but their color difference prediction accuracy falls short of CIEDE2000. We propose Oklch+, a three-parameter extension of Oklab comprising a power transformation on the L-axis and a Naka-Rushton compression on the C-axis, with Euclidean distance computed in the resulting transformed Oklab coordinates. The Naka-Rushton function is bounded in [0,1], reflecting the saturating nature of chroma sensitivity at high colorimetric values. Evaluated on COMBVD -- 3,813 suprathreshold color difference pairs spanning six independent experimental datasets -- Oklch+ achieves STRESS = 29.09, closely matching CIEDE2000 (29.13; difference = 0.04), using only three parameters optimized against color difference data compared to approximately 17 for CIEDE2000. Cross-validation on a held-out BFD-P D65 subset (2,028 pairs) confirms generalization (STRESS = 26.14), with Oklch+ substantially outperforming Oklab (51.45) and achieving STRESS comparable to CIEDE2000 (24.12) on the held-out set. Improvement over Oklab (47.35) is confirmed across all six COMBVD sub-datasets. Because Oklch+ defines a coordinate system in which Euclidean distance approximates perceptual distance, linear interpolation in the transformed space offers substantially improved perceptual uniformity relative to Oklab. Current evaluation is limited to the sRGB-centered COMBVD dataset; validation in high-chroma regions with empirical observer-rated discrimination data remains future work.
arXiv:2606.05387v1 Announce Type: cross
Abstract: The encoding of classical data into quantum states constitutes the primary performance bottleneck in Quantum Machine Learning (qml) on Noisy Intermediate-Scale Quantum (nisq) devices. No existing framework jointly characterises resource cost, expressivity, and noise robustness, nor provides actionable selection guidelines for practitioners. This survey addresses that gap through a systematic review of 66 primary works (2017-2026) assembled via a PRISMA-adapted protocol across five academic databases. Four principal contributions are made. First, a three-axis cost-expressivity-robustness taxonomy classifies all major encoding families - basis, angle, dense-angle, amplitude, data re-uploading, and IQP - along independently measurable axes. Second, closed-form depth-fidelity bounds under nisq decoherence channels identify the critical gate-error rate p* ~ 10^-3 below which amplitude encoding is viable. Third, a unified treatment of Fourier expressivity, barren-plateau onset, and quantum kernel concentration as functions of the encoding circuit provides the first joint trainability analysis. Fourth, a five-regime decision framework maps (D, n, p, tau) - feature dimension, qubit budget, error rate, and task type - to a hardware-grounded encoding recommendation. The central finding is that for p >= 10^-3, shallow angle-based encodings consistently outperform amplitude encoding in practice, despite the latter's exponential qubit advantage.
arXiv:2606.03067v2 Announce Type: replace-cross
Abstract: A recurring data mining task in complex networks is to determine how individual nodes contribute to system behavior. Existing approaches rely on either static-graph centralities or control-theoretic quantities such as controllability Gramians, which assume linear, time-invariant dynamics. Estimated systems, however, are typically nonlinear and time-varying. We define "emergent contribution (EC)," a finite-horizon measure of a node's dynamical leverage: the metric-weighted energy of its impulse response accumulated along the system trajectory. Computed from the Jacobians of any differentiable model, EC is estimator-agnostic and reduces exactly to average controllability in the linear, time-invariant limit. Our contribution is a characterization of when the two measures agree and diverge. Using a controlled synthetic family with known ground-truth contribution, we construct a phase diagram spanning nonlinearity, regime structure, persistence, and perturbation amplitude. EC and average controllability agree under static or smoothly drifting dynamics and both track ground truth. Divergence emerges under persistent regime switching, is strongest under persistent sign reversal, and disappears when the sign reversal is removed. At extreme perturbation amplitudes, both measures degrade, identifying the limits of local linearization. We place five estimated real systems from several domains within this phase space. Their placement serves as a diagnostic of when EC provides information beyond static controllability and therefore justifies its additional computational cost. On one panel examined in depth, a twenty-seed retraining ensemble reveals a robust variance--leverage dissociation: nodes whose perturbations propagate widely despite low within-system variance, which is not recovered by static centralities nor variance-based summaries.
arXiv:2605.23429v3 Announce Type: replace-cross
Abstract: This study proposes a novel radar-centric signaling design and architecture for secure integrated sensing and communication (ISAC) systems. The proposed framework is designed to provide robust physical layer security for data transmission while simultaneously enhancing sensing privacy. It employs index modulation and phase coding over frequency-modulated continuous-wave radar (FMCW) chirps, where index modulation (IM) provides an outer layer of data security, and we explicitly design the phase coding (PC) to perturb the resulting signal's ambiguity function (AF) to enhance sensing privacy. This design reduces the risk of unauthorized surveillance by rendering target velocity estimation practically infeasible for unauthorized passive sensing hardware (i.e., a sensing eavesdropper, S-Eve) and significantly impairing its range estimation capabilities. Furthermore, this study also presents the transmitter and receiver architectures required for effective modulation and demodulation of the proposed ISAC signaling and for performing sensing at the legitimate sensing hardware. Simulation results show that the proposed approach achieves high data throughput while enhancing communication security and sensing privacy.
arXiv:2606.05203v1 Announce Type: new
Abstract: The interaction of charged particles with an intense laser pulse gives rise to a number of characteristic spectral features of emitted radiation, including the generation of harmonics, spectral broadening due to the phase-dependent ponderomotive red shift, and the emergence of intricate sub-harmonic structures. These effects are accumulated over the course of the interaction with the electromagnetic field and are therefore inherently nonlocal in nature. For a deeper understanding of strong-field quantum electrodynamics (SFQED) processes and their practical applications, it is desirable to employ tools that enable simultaneous analysis in the time and energy domains. In time-frequency analysis, such tools are provided by joint distributions (JDs). In this work, we demonstrate how a JD can be devised within the SFQED framework. Specifically, we focus on constructing a non-negative JD, which allows for a clear probabilistic interpretation. We study the properties of the proposed distribution and test its utility by applying it to the nonlinear Compton scattering in complex laser pulse configurations with carrier-envelope phase and variable polarization.
arXiv:2601.06655v2 Announce Type: replace
Abstract: A physics-constrained Gaussian Process regression framework is developed for predicting shocked material states and their associated uncertainties along the Hugoniot curve using data from a small number of shockwave simulations. The proposed Gaussian process is constrained by the Rankine-Hugoniot jump conditions between the various shocked material states to construct a thermodynamically consistent covariance function. This leads to the formulation of an optimization problem over a small number of interpretable hyperparameters and enables the identification of regime transitions, from a leading elastic wave to trailing plastic and phase transformation waves. Shock Hugoniots are an important measure for understanding material behavior under extreme conditions, including for the development of equations of state and determining material properties such as the Hugoniot Elastic Limit, but they are costly to generate through large-scale molecular dynamics simulations or shock experiments. Under these constraints, the proposed methodology establishes Hugoniot curves from a limited number of molecular dynamics simulations. We consider silicon carbide as a representative material and Molecular Dynamics simulations are performed using a reverse ballistic approach. The framework reproduces the Hugoniot curve with satisfactory accuracy while also quantifying the uncertainty in the predictions using the Gaussian Process posterior. These uncertain Hugoniot predictions can then be used to calibrate equation of state models, estimate material properties, or inform future experimental and/or simulation campaigns.