Papers

Generative graph models are central to understanding and simulating complex networks. However, existing approaches have complementary strengths and limitations. Mechanistic models offer interpretability but rely on instance-specific estimation methods. Deep generative models, on the other hand, offer amortized inference at the cost of interpretability and are largely limited to graph sizes seen during training. Scientific applications motivate a framework that retains the strengths of both paradigms. We bridge them by formulating both the generative model and parameter recovery in function space. A multifractal step graphon extends standard step graphons with a recursive construction that compactly parameterizes complex networks. This formulation admits a neural inverse operator to recover its parameters, enabling inference on unseen graph sizes. We evaluate our model, trained only on synthetic multifractal step graphon realizations, against both paradigms. Against a graph foundation model pretrained on empirical networks, our method achieves the best average performance on three of four metrics in a zero-shot graph-generation benchmark, indicating that the model transfers to real-world graphs. We also apply our method to single-observation networks, a regime largely inaccessible to deep models that require training corpora, where it performs comparably to an instance-specific method that optimizes on each graph. In a multi-subject EEG case study, the inferred parameters track a reversible change in brain state more sensitively than traditional network statistics. Together, these results indicate that mechanistic interpretability and amortized inference can be effectively unified in a generative graph model to enhance our understanding of complex networks.

Large language models (LLMs) have demonstrated strong performance in code generation, where success depends on both recalling relevant algorithmic knowledge and reasoning about how to apply it. However, existing LLM pipelines are opaque, with no explicit separation between these two components. We argue that for well-known algorithms whose canonical implementations are widely accessible in pretraining corpora, code generation is better measured as parametric code retrieval: reproducing a named algorithm from internalised knowledge rather than synthesizing a novel one. We introduce AlgoREval, a benchmark of 599 problems spanning classical 77 algorithms across 14 domains, 7 programming languages, and 4 graph-input representations to evaluate this capability in isolation, and assess 15 models (7B–34B parameters) in a zero-shot setting. We find substantial variation in retrieval accuracy across languages and input representations, even for widely documented algorithms and show that prompt augmentation with retrieved code snippets or structured algorithmic hints improve accuracy on complex algorithms, while SFT achieves broader language gains and GRPO achieves larger per-language gains on specific languages. Together, our results establish parametric code retrieval as a distinct, measurable capability and caution against deploying AI-generated algorithmic code without systematic validation.\footnote{Code and dataset are available at https://github.com/Nickil21/AlgoREval

Why does supervised fine-tuning (SFT) lead to more forgetting than reinforcement fine-tuning (RFT), even when all teacher demonstrations are semantically correct? We study this question on classification tasks where tokens within each semantic class express the same semantic answer in different styles. The tasks share an underlying semantic rule but differ in their prompt distributions and teachers' stylistic preferences. Using a tractable linear-softmax policy, we derive an exact decomposition of the updates into semantic and style components. We show that, at a common policy and prompt, SFT and RFT have parallel semantic updates but differ in their style dynamics. Starting from a policy with no within-class style preference, RFT with exact policy gradients preserves this symmetry, whereas SFT with a nonuniform teacher develops off-axis style drift along a nonzero task mean under population updates. We use this drift to establish a separation under explicit conditions: for population updates from a common perfectly fitted checkpoint, SFT forgetting admits a strictly positive lower bound over a finite training interval, while RFT retains zero semantic error. Simulations over task sequences support these theoretical predictions.

Fix $W\in(0,2)$ and let $\gamma\downarrow0$. We prove that a weight-$W$ quantum disk conditioned to have unit quantum area converges, in the maximum-embedded strip, to the deterministic field $\phi_W(t+i\theta)=\log(W/(4\pi))-2\log\cosh(Wt/2)$ and its constant-curvature area measure. The proof establishes a joint large-deviation principle for the radial Brownian input, the lateral Gaussian free field, and the total Gaussian multiplicative chaos mass. Diverging-order moment bounds justify both adjoining the noncontinuous area functional and retaining its unbounded positive power in the unit-area expectation. An exact radial Girsanov shift centers the candidate, and reflection together with the sharp Onofri inequality proves its unique optimality. This yields concentration without a quadratic expansion of the running maximum or an order-one partition-function asymptotic. We also identify the field rate with the renormalized Liouville action in the maximum embedding.

Stablecoins support payments, trading, collateral, and cross-chain settlement across the digital-asset ecosystem. They also concentrate value behind issuer, custody, upgrade, oracle, and bridge keys while inheriting the quantum vulnerabilities of host-chain accounts, consensus, rollups, and privacy systems. This paper presents a Systematization of Knowledge (SoK) on post-quantum stablecoins. We develop a stablecoin-specific threat model, map cryptographic dependencies to monetary control surfaces, and classify migration choices along three dimensions: who can authorize a change, where the change must occur, and whether it is hybrid, post-quantum native, or an encapsulation of a classical component. We emphasize an authority-liability gap: the party able to migrate a component is often different from the holders, exchanges, protocols, or issuers that bear the loss if it fails. We review the relevant cryptographic primitives, but distinguish general blockchain failures from their stablecoin-specific effects. We also examine recent blockchain and issuer-controlled interoperability proposals, and relate migration choices to redemption, continuity, and intervention requirements under current stablecoin regulation. Our findings identify open problems in aggregate and threshold authorization, operation-specific security levels and costs, dormant and wrapped supply, private and compliance-enabled transfers, and measurement of quantum-vulnerable stablecoin exposure.

We perform a self-consistent analysis of Doppler and photometric TESS and ground-based transit observations available for TOI-1408, known to host a system with two planets orbiting near 2:1 mean-motion commensurability and a distant companion. In general we confirm its orbital configuration derived in previous studies, however we found that the likelihood function contains multiple local maxima spread over a wider parametric domain, thus making some model uncertainties significantly larger than deemed before. In particular, the planet b radius still appears poorly constrained (from $\sim 1.2$~$R_{\rm Jup}$ to $\sim 3.5$~$R_{\rm Jup}$) because of the near-tangential transit geometry. We also show that the derived model is very prior-dependent regarding the astrophysical (spectrum-derived) constraints on the stellar mass $M_\star$ and radius $R_\star$. While such estimations may potentially contribute a significant information to the fit, their prior distribution must be accurately specified to be useful. Presently so accurate characterization (e.g. the correlation between $M_\star$ and $R_\star$) is not available in the literature.

This letter introduces an accelerated safe gradient flow (A-SGF) for strongly convex constrained optimization problems. The A-SGF filters a nominal second-order accelerated flow through a second-order control barrier function quadratic program. We establish conditions for strict feasibility and local Lipschitz continuity of the resulting vector field, prove forward invariance of a lifted safe set, and show that its unique equilibrium is the constrained minimizer. A variational Lyapunov analysis isolates the effect of the safety correction and gives explicit conditions on the barrier gains under which A-SGF retains the same convergence rate as the unconstrained Nesterov accelerated method. A nonlinear 2D example demonstrate anytime feasibility and faster convergence of the algorithm.

Large language models (LLMs) in production systems face prompt injections, trojans (backdoors), and manipulation of automatic quality metrics. This thesis develops models, methods, and algorithms for evaluating and improving LLM robustness to adversarial input sequence variations. We propose R_stab(f), a generative robustness metric based on the Jensen-Shannon divergence between per-step output distributions under small input perturbations. For localized attacks we prove V(h) <= 1 - R_class(h), where R_class(h) is the probability that a decision operator h keeps its decision under small perturbations. For non-localized attacks we propose a calibrated empirical model. For LLM-as-a-Judge systems we develop ASA, an adaptive evolutionary black-box attack that reaches an attack success rate (ASR) of up to 73.8%, with transfer between open models up to 62.6%. On Trojan Detection Challenge 2023 data (Pythia-1.4B), surrogate triggers reach REASR ~0.99 while recall of the true triggers is ~0.17 against a baseline of ~0.14. On SaTML CTF 2024 we systematize four classes of bypasses of multi-layer defenses, which reduce the ASR from 90% to 15-25%. Committees of 5-7 heterogeneous models reduce the ASR for Gemma-3-4B by 47-55 percentage points, to 19.3% with 7 models. For agentic systems based on the Model Context Protocol (MCP), we propose AttestMCP, which attests tool calls with HMAC-protected packets at under 0.1 ms per call, and the Commit Boundary isolation pattern. On the MCPBench benchmark of 847 scenarios they reduce the average ASR from 53.7% to 12.4%. The methods are implemented in the JudgeGuard and TrojanArmor software suites and the MCPSec module.

Deep neural networks achieve high accuracy through layered numerical transformations, yet their decisions remain difficult to audit because decision evidence is encoded in hidden activations rather than explicit rules. This paper introduces CRISP, a framework that reconstructs the last-layer activation vector (LLAV) of binary neural teachers as Tsetlin Machine (TM) clauses. CRISP sign-binarizes the teacher's penultimate pre-logit activations, and assigns one Individual TM (ITM) to each LLAV neuron. Each reconstructed hidden bit is represented by propositional clauses over Booleanized input features, which gives a direct symbolic trace from named input thresholds to a named teacher neuron. CRISP is evaluated on MNIST, KMNIST, FashionMNIST (FMNIST), SVHN, and CIFAR10 using a BinaryConnect convolutional neural network (BCCNN) teacher and a fully binary neural network (BNN) teacher, with an additional study on binary thresholding, thermometer encoding, and quartile binning at multiple bit depths. The results show that LLAV sign-binarization does not reduce teacher-head accuracy in the tested BNN setting, while ITM reconstruction error is the main limiting factor. Quartile one-bit Booleanization gives the strongest reconstruction fidelity on SVHN at 87.52% test fidelity and is competitive on CIFAR10, and the reconstructed LLAV preserves 78.41% teacher-head accuracy on FMNIST. Pooled clause-evidence visualizations show that the learned ITM literals concentrate on the object region in centered benchmarks. CRISP therefore provides a clause-level route for inspecting the final hidden representation of binary neural teachers.

The internal structure of hadrons is governed by nonperturbative Quantum Chromodynamics (QCD). This dissertation presents first-principles calculations of partonic observables using lattice QCD and effective field theory, with controlled systematic uncertainties, advancing from collinear structure to transverse-momentum-dependent distributions (TMDs) that encode the three-dimensional partonic structure of hadrons. Within the large momentum effective theory (LaMET) framework, this work presents state-of-the-art calculations of pion distribution amplitudes and systematic studies of nucleon parton distributions, with control of renormalization, excited-state contamination, Fourier-transform systematics, and power corrections. A Coulomb-gauge formulation of quasi-distributions simplifies ultraviolet structure by avoiding Wilson-line related linear divergences, with Gribov-copy effects found to be negligible at current statistical precision. Building on these developments, this dissertation reports lattice determinations of nucleon TMD parton distributions, the Collins-Soper kernel, the intrinsic soft function, and pion TMD observables. These results provide nonperturbative inputs for global QCD analyses and the precision hadron-structure program, including the Electron-Ion Collider. In parallel, this work explores machine-learning acceleration of lattice gauge simulations through neural field transformations embedded in Hybrid Monte Carlo. In two-dimensional U(1) tests, the method reduces autocorrelation and improves performance toward finer lattice spacing, suggesting potential applications to more efficient lattice QCD simulations.

The presence of some radio pulsars within and below the so-called “death valley” in the $P$–$\dot{P}$ diagram challenges the standard pair-cascade models based on curvature radiation (CR) and resonant inverse Compton scattering (RICS) in neutron star polar caps. We show that Cherenkov radiation from the quantum vacuum, a strong-field quantum electrodynamics (QED) phenomenon enabled by vacuum polarization, constitutes a distinct pair-creation channel within the vacuum gap model. Within this model, the acceleration length scale for Cherenkov photon emission and the subsequent photon mean free path are sufficiently short to ensure rapid conversion into $e^+e^-$ pairs. This process acts as a complementary pair-creation channel, remaining viable even in regimes where classical mechanisms become heavily suppressed. This leads to a new set of death lines in the $P$–$\dot{P}$ diagram that partially overlap with and extend beyond the CR and RICS death valleys, enlarging the viable parameter space for radio-emitting neutron stars. The result provides a physical basis for coherent radio emission from long-period neutron stars previously considered inactive, and offers a new window for testing non-linear QED with next-generation radio facilities such as the Square Kilometre Array.

Autonomous mobile robots (AMRs) increasingly perform material transport in production logistics, where their operation is governed by job generation, dispatching and robot control. We present MoRoOp, a dataset of AMR operations recorded in a laboratory kit preparation and supply scenario over nine eight-hour shifts. During each shift, an AMR executed stochastically generated kit supply, empty-box refill and charging jobs. The dataset links job specifications, the operations constituting each job, dispatch events documenting operation state transitions and outcomes, and robot-state observations comprising position, orientation, velocity, per-wheel state of charge and diagnostics. It contains 1,382 jobs, 4,815 operations, 19,352 dispatch events and 140,386 robot-state observations together with the kit specifications used during job generation. The dataset was recorded in an operating laboratory environment, and technically valid observations of delays, obstructed navigation and unsuccessful operations were retained. Both raw and cleaned robot-state tables are provided. Documented reuse directions include the evaluation of AI agents on operational decision records, disturbance detection, operation prediction, data-driven simulation and event-log analysis.

Flow-map distillation enables one- and few-step generation by learning finite-time transitions of a pretrained generative ODE. We investigate whether changing the teacher's time parameterization can make these transitions easier to learn. Motivated by the hypothesis that trajectory segments with large normal acceleration are harder to distill, we propose a geometry-aware time reparameterization that allocates more student time to these regions while preserving the teacher's geometric paths and terminal distribution. We derive a shared clock that equalizes a population normal-acceleration statistic under suitable assumptions, and construct a practical approximation from robust, regularized estimates across teacher trajectories. We incorporate this clock into Lagrangian flow-map distillation, using the transformed time coordinate to condition the student. The clock is estimated once before distillation and requires neither teacher retraining nor additional student parameters or inference-time network evaluations. Experiments on synthetic data, CIFAR-10, and CelebA-64 show improved sample quality over identity-time distillation at matched inference budgets, including improvements in one- and two-step image generation. The gains in one-step generation, where no intermediate sampling times can be adjusted, highlight the benefits of time reparameterization during distillation.

Physical aging in glasses is often described using the concept of material time, which assumes the underlying relaxation mechanism to remain the same as in equilibrium, but with a rate that changes during aging. Whether material time also captures the microscopic dynamics of metallic glasses, which differ qualitatively between the glass and the equilibrium supercooled liquid, is unclear. Using simultaneous time-resolved X-ray diffraction and X-ray photon-correlation spectroscopy, we follow the full equilibration of a metallic glass after small temperature jumps starting from equilibrium. The time evolution of the first sharp diffraction peak position exhibits the asymmetry between temperature up- and down-jumps characteristic of material-time aging and is quantitatively described by the Tool-Narayanaswamy-Moynihan model, which is based on this concept. By contrast, the microscopic density-density autocorrelation functions strongly violate material-time scaling. Compressed-exponential relaxation emerges even after temperature changes as small as 4K, irrespective of the direction of the temperature jump, and continuously evolves into a stretched-exponential relaxation shape following the equilibration of the average structure. This behavior is consistent with a transient stress-mediated contribution associated with volumetric frustration that disappears upon equilibration. Our results show that a material time can describe the evolution of average structural properties even when the corresponding microscopic dynamics do not obey material-time scaling.

Static evaluations credit a language model for naming the right move, but an agent must carry a plan through to a verified outcome while an opponent responds. We introduce XiangqiBench, an executable benchmark that measures this difference in Chinese chess: starting from 119 tactical endgames with forced mates supported by engine or checks-only search, an LLM agent must deliver checkmate against an engine defender. An interactive REPL interface separates real moves, state queries, and forward simulation, and we record 8,568 multi-turn trajectories from 12 frontier LLMs under two observation protocols. Three signals that look like competence each overstate closed-loop success. (i) The Conversion Gap: models play the stored reference first move in 26.1% of Sighted trials, yet only 13.9% of these trials end in a win. (ii) The Consistency Gap: the leading model reaches 38.7% pass@3 but only 5.9% pass^3, winning all three trials on 7 of the 46 positions it ever wins. (iii) The Simulation Gap: 32.3% of accepted simulation calls stop on an illegal move, and in 49.3% of comparable cases the real defender replies differently from the line the agent simulated; self-authored rollouts check legality but cannot anticipate the opponent. Finding the move is not winning the game: agent evaluations should score closed-loop outcomes and report reliability alongside coverage.

Since the 1980s, risk analysis for engineering systems has been defined based on a tuple of scenarios, $\mathcal{S}$, likelihoods, $L$, and consequences, $C$, where $Risk = (\mathcal{S},L,C)$. We argue that equating this triplet with risk alone is insufficient and potentially misleading. Instead, we define this tuple as a vulnerability space $\mathcal{V} = (\mathcal{S},L,C)$, which becomes risk only when one makes specific interpretations of likelihood and consequence. Here, an interpretation has mathematical meaning, and defines a map that assigns data elements about system vulnerability to a perspective. Formally, we define a vulnerability perspective as a specific choice of interpretations of likelihood and consequence data that allows vulnerability analysis measures to be defined and analyzed. We argue that risk is only one of four common perspectives on $\mathcal{V}$ and demonstrate mathematically why each perspective should remain a distinct concept. First, we show how interpretation of $C$ as a set-valued function produces reliability measures, not risk measures. Then, we show how interpretation of $L$ via possibility theory will produce adversarial and safety measures distinct from risk. This new theoretical framework clarifies the conceptual, mathematical, and practical differences between risk, reliability, adversarial, and safety perspectives—four common engineering system analyses often conflated in the literature. A consequence of our theory is that no single perspective will reveal all vulnerabilities of an engineering system, suggesting decision-making via risk analysis may incur unavoidable and underappreciated tradeoffs from other vulnerability perspectives.

We analyze two old models of black holes to see whether they realize the AdS/CFT paradigm of “multiple representations of bulk data by boundary states that differ only in the expectation value of exponentially complex operators" . We find that the explanation of the firewall paradox in these models is much simpler and corresponds to the naive way entanglement is resolved when small constituents escape from a complex chaotic quantum system. The real issue is that the quantum field theory (QFT) picture of the states near the boundary of a causal diamond is wrong. The phrase in quotes above is correct in our models because most of the states associated with any causal diamond cannot be associated with ANY states in quantum field theory.

The spatial structure of a microwave photon mode provides a degree of freedom for controlling its interaction with a localized magnetic excitation. We demonstrate site-selective magnon-photon coupling in modular arrays of discrete dielectric resonators mounted on a common microstrip line. The resonators can be added, removed, or rearranged on the same completed PCB, enabling post-fabrication geometrical reconfiguration of the collective photon modes and their nodal structure. A YIG sphere is positioned successively above individual resonators, while an in-plane magnetic field tunes its Kittel mode through the collective photon resonances. In a three-resonator array, modes with finite local microwave magnetic fields hybridize with the magnon at every measured site, whereas a mode containing a central field node exhibits no resolvable splitting when the sphere is positioned at that node. Full-wave simulations and a coupled-mode model show that the interaction is governed by the local amplitude of the collective photon mode rather than by spectral resonance alone. Extending this local-node selection rule to a five-resonator array successfully predicts the measured position-dependent coupling patterns. These results establish post-fabrication control of spatial magnon-photon hybridization and provide a route toward reconfigurable magnonic interfaces in future hybrid quantum microwave architectures.

Androgenetic alopecia (AGA) is characterized by patterned follicular miniaturization, increased single-hair follicular units, and altered hair-shaft diameter. We present an automated quantitative scalp-analysis and clinical decision-support framework combining FU localization, ordinal visible-shaft counting, calibrated shaft-width estimation, regional aggregation, and an interpretable rule layer. The clinical cohort comprised 243 patients (127 AGA, 116 non-AGA), while the computer-vision experiments used 160 expert-annotated patients, 2,400 trichoscopic images, and approximately 158,000 FU annotations. Under patientdisjoint evaluation, YOLOv8m achieved test mAP@0.5=0.920 and recall=0.860; EfficientNet-B5 with a support-map channel achieved 87.0% expert-box count accuracy (macro F1=0.85). A separate 500-image set was processed end-to-end with detector-generated boxes, yielding MAE of 6.56 for follicle detection and 16.59 for follicle classification relative to human-expert annotations. The system is intended to assist, rather than replace, dermatologist interpretation.

We investigate high energy neutrinos (HE$\nu$s) from the decay of superheavy dark matter (DM) produced during a cosmological first order phase transition. Adopting the filtered DM production mechanism, we revisit the relic abundance calculation by incorporating recent progress in determining the bubble wall velocity from hydrodynamics. We show that DM with mass $m_{\text{DM}}\simeq 4.4\times10^{8}~\text{GeV}$ can reproduce the observed relic abundance and accommodate ultra high energy neutrino events such as KM3-230213A, while the same phase transition simultaneously generates a stochastic gravitational wave (GW) background. Although the GW signal (which peaks at $10^{4}\,\text{Hz}$) is not yet observable in this example, at lower DM masses $m_{\text{DM}} \lesssim10^{6}~\text{GeV}$, the neutrino spectrum shifts into the energy range relevant for IceCube observations, while the associated GW signal moves to lower frequencies and can reach the projected sensitivities of Cosmic Explorer, BBO, and DECIGO. This gives a multimessenger connection between HE$\nu$s and GWs, with both signals connected to DM production in a first order phase transition.

The purpose of this note is to give conditional explicit formulas for the Galois action on real multiplication values of the Shintani–Faddeev modular cocycle. We assume the order 1 abelian Stark conjecture for real quadratic fields. We conclude this note by presenting our own conjecture about the Galois action. Numerical evidence for this conjecture will be provided in forthcoming work.

Modern large language models (LLMs) are trained on massive, largely unfiltered datasets, including content scraped from nearly every accessible website and user inputs. As a result, LLMs often memorize and reproduce personally sensitive information (PSI) such as birth dates, phone numbers, and home addresses. This leads to significant privacy risks, particularly for high-profile individuals such as executives, politicians, and judges. Existing mitigations largely rely on machine unlearning. However, these methods often remove more information than needed, degrade model utility and safety, and are highly vulnerable to attacks. This paper presents Whiteout, a practical tool that, upon requests by individuals, prevents LLMs from regurgitating their genuine PSIs, by overwriting them using precise and carefully designed obfuscation samples. We evaluate Whiteout on modern LLMs of varying sizes and makers, including a widely-used OpenAI model. Results show that Whiteout effectively prevents disclosure of the targeted PSIs, has negligible impact on model utility and safety, and outperforms existing alternatives. We also test Whiteout against a wide range of countermeasures, from black-box attacks like jailbreaking to white-box adaptive attacks like relearning and quantization. Finally, we conclude with a discussion on the security and ethical implications of Whiteout.

Advances in experimental instrumentation and automation generate increasingly rich datasets, but turning experimental observations into microscopic understanding remains a bottleneck in scientific discovery. To accelerate this process, we introduce AI Theorist, a system of artificial intelligence (AI) agents for autonomous discovery of physical models through hypothesis generation, first-principles calculations and evidence-driven refinement. We apply the framework to $\alpha$-RuCl$_3$, a leading candidate material for realizing a Kitaev quantum spin liquid, to investigate its electronic structure through optical spectra. AI Theorist develops a new interpretation of the optical and photocurrent observations, identifying distinct excitonic states with contrasting optical selection rules and real-space distributions. To our knowledge, this is the first demonstration of an AI system autonomously developing a physical model to explain previously unpublished experimental observations in a quantum material, utilizing first-principles electronic-structure and many-body calculations. Our results establish a route to autonomous theoretical discovery in materials science, in which AI agents use first-principles calculations to turn experimental observations into physical models and testable predictions.

The convergence of hydrodynamics is commonly investigated by Taylor-expanding the gapless dispersion relations $\omega(k)$ around $k=0$. We show that this diagnostic can fail arbitrarily close to the hydrodynamic limit: sound modes can collide at arbitrarily small wave number, rendering $\omega(k)$ nonanalytic, while the relationship between densities and fluxes remains analytic there. We instead formulate the gradient expansion off-shell (i.e. in the presence of external forces), directly at the level of the constitutive relations. For causal theories with relaxational spectra, we establish convergence for $|i\omega|+w|ik|<1/\tau_g$, where $w$ is the maximal information speed and $1/\tau_g$ the nonhydrodynamic gap. On the naturally Lorentzian $\{i\omega,ik\}$ plane, this region is a causal diamond, whose boundary marks the first possible encounter with nonhydrodynamic modes. Beyond it, analytic continuation reveals the nonhydrodynamic spectrum through singularities of the resummed constitutive relations. Thus, hydrodynamics is aware of the degrees of freedom beyond hydrodynamics, but this information becomes fully accessible only off-shell.

The effective action at one-loop for the quantum electrodynamics (QED) in the presence of background vectors and tensors that break the Lorentz symmetry is calculated in this work. We highlight that just the Lorentz symmetry violation through the Dirac matrices in the fermionic sector is considered since investigations in others sectors of the extended QED has been explored in recent papers. Using the proper time method, we show that some background vectors and tensors do not contribute to the effective action at one-loop and in the linear approximation. Thereby, only two background tensors contribute to the effective action at one-loop for small components of these tensors, and that a new combination of cubic and quartic non-linear electrodynamics emerge in the weak field regime.

Differential privacy (DP) admits several notions, but the choice among them may affect both privacy analysis and utility. In this paper, we consider four mainstream curve-based privacy notions within a unified information-theoretic framework. For a fixed ordered pair of output distributions, we establish information equivalence among the two directional privacy profiles of $(\varepsilon,\delta)$-DP, the pair of hypothesis-testing trade-off functions, and the extended privacy-loss distribution. The exact Rényi differential privacy (RDP) curve joins this equivalence class whenever it is finite at some order greater than one. Under this mild condition, choosing among these notions changes only their semantic interpretation and computational requirements. In contrast, taking the maximum of the directional privacy profiles or compressing the RDP curve into a single zero-concentrated differential privacy (zCDP) parameter can lose information. We quantify the information loss between the exact RDP curve and its zCDP bound for standard noise mechanisms. This gap is zero for Gaussian noise but generally positive for Gaussian-mixture, Laplace, discrete Gaussian, and Poisson-subsampled Gaussian mechanisms. Moreover, this gap grows linearly with the number of independently composed mechanisms. Our information-theoretic perspective has practical consequences. At the same certified privacy level, retaining the full RDP curve rather than using zCDP reduces the required noise variance by up to $45\%$ for Gaussian-mixture noise in workloads comparable in size to the American Community Survey. For DP-SGD on Fashion-MNIST under Poisson subsampling, an RDP-based privacy accountant improves test accuracy by up to $8.73$ percentage points compared to a zCDP-based accountant when both are calibrated to the same $(\varepsilon,\delta)$ guarantee.

LLM agents increasingly rely on activation probes as runtime monitors for prompt injection, jailbreaks, and unsafe requests, reading the model's own hidden state to catch a harmful input before the agent acts on it. A cheap, increasingly common move, borrowed from LLM-as-judge prompting, is to append a short classification instruction after the user's turn and read the probe at that point, to sharpen it: the instruction asks the model to represent the incoming request as a class, concentrating the signal the probe must separate, at negligible serving cost. But does the wording of that suffix matter, and does its benefit hold in the wild, on attack types the probe never saw in training, the regime a deployed monitor faces? We test this with a controlled ladder of post-user suffixes under strict leave-one-dataset-out (LODO) evaluation across 13 safety benchmarks (jailbreak, injection, and benign chat) and three open-weight model families (Llama-3.1-8B, Qwen3.5-9B, Gemma-4-12B). On a single-position probe, a classification suffix consistently improves out-of-distribution detection over no suffix (up to ~4 AUC points); yet which suffix matters: prompting the model to classify the input, even into content-free labels, reliably wins; an off-topic or merely-attentive suffix helps little. The gain comes from the classification format, not the named criterion: a content-free suffix matches the real malicious/benign one, with the criterion adding precision only at strict thresholds. This is not an artifact of the single-position read: the benefit carries to the multi-position pooling probes used in production (attention, multi-max, MLP), though the best-performing suffix there is readout-dependent. Served through a KV-cache fork, it is a cheap drop-in for any activation-probe monitor, though not an automatic win: which suffix helps, and by how much, depends on the model and the readout.

Fractional Brownian motion provides a useful framework for modeling random phenomena with anti-persistent temporal correlations that arise in applications such as anomalous diffusion, hydrology, finance, and geophysical processes. In this paper, we study a class of semilinear stochastic partial differential equations driven by additive fractional Brownian motion with Hurst parameter $H\in(0,\frac12)$. We establish the well-posedness and space-time regularity of the mild solution and investigate the strong convergence of a stochastic exponential integrator for the temporal discretization. The analysis allows the linear operator to be non-self-adjoint and combines analytic semigroup estimates with the canonical Hilbert-space structure associated with fractional Brownian motion and Malliavin calculus to handle the low temporal regularity of the noise. We derive an $H$-dependent strong temporal convergence rate, which reaches $H+\frac12$ under maximal spatial regularity. Numerical experiments for a stochastic advection–diffusion–reaction problem with heterogeneous Darcy flow confirm the theoretical temporal convergence rates. We also estimate the mean of the solution with different Hurst parameters $H\in(0,\frac12)$ using the Monte Carlo method.

Hard carbons are promising anodes for sodium-ion energy storage, yet the relationship between their heterogeneous microstructure and sodium transport remains poorly understood. Here, we combine machine-learning-generated hard-carbon structures with molecular dynamics simulations of explicit 1 M NaPF6 in ethylene carbonate/dimethyl carbonate electrolyte to investigate sodium storage and transport across carbon structures with densities from 0.5 to 2.0 g cm-3. Increasing carbon density produces less accessible pore networks and greater graphitic local ordering, allowing the influence of microstructure on electrochemical response and Na+ transport to be examined systematically. Sodium uptake increases with applied potential but decreases strongly with carbon density, while electrode charging persists even in the densest structure, where Na+ uptake remains very small. Coordination analysis shows increasing interaction with the carbon framework under applied potential, while Na+ retains a partially solvated environment. Three-dimensional trajectory analysis reveals heterogeneous, predominantly tortuous transport pathways, with the more open HC-C1 structure supporting broader penetration and greater sustained displacement. Maximum penetration depth and retained displacement are not equivalent: ions can transiently reach deep regions of denser carbon structures before returning towards the electrolyte interface. Potential-of-mean-force analysis further shows that deep penetration occurs across a range of projected free-energy changes and cannot be described by a single energetic criterion. These results show that Na+ storage and transport are governed by the interplay between electrostatic driving force, electrolyte solvation, pore accessibility and confinement, highlighting carbon microstructure as a key determinant of sustained ionic penetration.

Implicit neural representations (INRs) provide a flexible framework for modeling high-dimensional continuous fields, but their training is often inefficient due to uniform subsampling that ignores spatial heterogeneity. Existing adaptive sampling methods partially address this issue by prioritizing high-error samples, but typically operate at the point level, often leading to redundant sampling in localized regions and insufficient coverage of the domain. We propose ACES (Adaptive Coverage-aware Efficient Sampling), a structured sampling framework that improves training efficiency by decoupling coverage and importance. ACES constructs adaptive spatial partitions to ensure domain coverage and reduce redundancy, and applies region-level importance weighting to prioritize informative regions during training. We provide a theoretical analysis showing that adaptive partitioning reduces gradient variance by increasing within-region homogeneity, and that controlled bias in region-level weighting may improve optimization efficiency relative to standard unbiased estimators. Experiments on scientific field learning tasks demonstrate that ACES achieves faster convergence and lower error than uniform and pointwise adaptive sampling baselines, with the largest gains in fields with highly localized complexity.