Papers

In this paper, we propose the Dissipative Lagrangian Neural Network (dLNN), a continuous-time system identification technique that separately learns the conservative and dissipative dynamics of a mechanical system directly from data. A key contribution is a novel parametrisation of dissipative forces that (i) is structurally constrained to be dissipative, enforcing passivity of the learned model, (ii) cannot absorb conservative mechanics, and (iii) retains sufficient expressivity to represent a broad family of state-dependent damping and regularised friction forces. The model is validated on prediction tasks on two real-world mechanical systems: trajectory prediction of a chaotic double pendulum and inverse-dynamics modelling of a six-degree-of-freedom industrial robot. Across these tasks, the dLNN demonstrates improved predictive performance over existing Lagrangian architectures while remaining competitive with a black-box neural model. The imposed physical structure also improves generalisation to unseen states, with the benefits becoming particularly pronounced when training data is limited. Finally, we introduce a symbolic distillation procedure that extracts closed-form expressions from the learned physical components. Applied to the industrial robot, this produces interpretable symbolic models that retain high predictive accuracy while reducing the computational overhead associated with evaluating neural Lagrangian models.

This paper presents AutoSec-RAN, a specification-grounded large language model (LLM) framework for automated security triage of Open Radio Access Network (O-RAN) testing. Unlike approaches relying on static rule sets or privileged access to raw packet captures, AutoSec-RAN fine-tunes Mistral-7B-Instruct through two Low-Rank Adaptation (LoRA) stages over a curated corpus of 69 O-RAN, 3GPP, and adjacent standards documents, then selectively augments inference with retrieval-augmented generation (RAG) over the same specification index. At inference, the model receives only an investigator-style question and a scenario metadata block, simulating an automated analyst operating without raw packet evidence. AutoSec-RAN is validated on a purpose-built 5G/O-RAN testbed across labeled fronthaul distributed denial of service replay scenarios. A Gemma-4-31B judge LLM scores each candidate's answer on faithfulness, correctness, and actionability relative to a reference authored from full packet capture and log evidence. AutoSec-RAN achieves a mean judge overall score of 0.713 across all 313 evaluation items (0.755 restricted to the five supervised taxonomy classes), clearing the 0.70 reporting threshold, and a blended score of 0.778 (0.808 supervised-only) when cosine similarity over Beijing Academy of Artificial Intelligence (BAAI) General Embedding (BGE) is incorporated as a secondary semantic signal. The framework performs strongest on mitigation and threat-model reasoning (with a mean overall of 0.849 and 0.848, respectively) and identifies a measurable gap on the held-out attack-direction class (0.515), a controlled result that exposes a specific training data requirement. These results establish specification-grounded LoRA fine-tuning combined with RAG retrieval as a viable foundation for automated security validation of AI-native O-RAN.

Representing individual-level behavioral heterogeneity is challenging in epidemiological modeling, particularly when empirical behavioral data are sparse. We assess the potential of large language model (LLM)-generated behavioral outputs in addressing this challenge, using hepatitis C virus-related behaviors among people who inject drugs as a case study. Correspondence with epidemiological patterns was evaluated using external benchmarks: literature-informed association directions, correlations from an agent-based model (ABM), and survey associations. Across three LLMs, unconditional directional recovery across 28 retained literature-informed associations was 46-68%, compared with 82-93% agreement when LLMs were directly asked to classify the same associations. Mean absolute differences from ABM and survey correlation patterns were 0.11-0.13 and 0.15-0.18, respectively. Together, these findings show partial alignment between LLM-generated behavioral relationships and epidemiological evidence, despite higher knowledge-probe agreement. More systematic evaluation is needed before incorporating LLM-generated behavioral outputs into epidemiological models that simulate transmission dynamics.

We study how initial model selection, later handoff, and training targets affect success and cost in LLM tasks that span multiple turns. We compare several router architectures using handoff curves, which record task success and cost as the handoff step changes. Our dataset contains 34,204 complete executions of three Qwen models across BFCL, MultiWOZ, and $\tau$-retail, providing offline supervision for routing decisions. In our primary comparison, with Qwen3.5 35B-A3B as the starting model, allowing a later handoff does not establish an improvement in utility over initial selection on BFCL or MultiWOZ, and increases cost on BFCL across a range of cost weights. Changing the supervision targets improves router performance on both our dataset and TwinRouterBench. On our dataset, replacing noisy training success curves with monotone fits raises success by 0.2 to 4.1 percentage points at the same cost across the reported operating points. On TwinRouterBench, we construct targets that describe the model capability needed for the remaining work and difficult steps ahead. Compared with training on the benchmark's per-step labels, these targets raise trajectory pass scores by 7.8 percentage points and cost savings by 6.3 percentage points on the full static bank. A live deployment of the router trained with these targets resolves 79 of 100 instances at a router cost of 0.59 US dollars per instance.

Let $1<s\le2$ and let $H_{s}[0,1]$ consist of the real-valued continuous functions on $[0,1]$ whose graphs have Hausdorff dimension $s$. We prove that every finite-dimensional subspace $E\subset C[0,1]$ with $E\setminus\{0\}\subset H_{s}[0,1]$ is contained in a closed complemented subspace isomorphic to $c_0$, all of whose nonzero elements still belong to $H_{s}[0,1]$. This settles a question of Liu, Shi and Zhang. We also obtain the exact criterion: $H_{s}[0,1]$ is $(\alpha,\mathfrak{c})$-spaceable precisely when $\alpha$ is finite. We also show that every admissible finite-dimensional subspace is contained in a dense subspace of Hamel dimension $\mathfrak{c}$ whose nonzero elements have the same prescribed graph dimension. This also recovers maximal pointwise dense-lineability of $H_{s}[0,1]$.

Distributed agent workflows cache delegated authority at tool gateways. Revocation may be reported at issuer commit, transport acknowledgment, or receiver persistence, although none of these observations establishes that all gateways enforced the change or that guarded effects stopped. We define C0-C5, a bounded outcome contract spanning issuer commit through effect prevention, and implement it as a persistent monitor over a frozen gateway set, call set, and observation window. A 14-case fault matrix checks conservative classification, sticky violations, restart persistence, and evidence immutability. In a derived audit of its eight semantic cases, treating C3 or C4 as completion produces seven or five false positives, respectively; the bounded C0-C5 verdict produces none. Descriptive scaling covers 1,024 gateways and 10,000 effect vectors. The primary experiment uses the maintained Keycloak 26.7 identity server and measures the contract across two durable receivers, eight physical agent-tool gateways, Filesystem and PostgreSQL effects, and 16 AWS hosts in three availability zones. Normal delivery and recovery commit no effects. Under receiver-selective non-delivery, transport acknowledgment and receiver persistence still succeed, but 112 of 225 calls (49.78%) are admitted, and all 112 effects commit in every treatment block. A separately provisioned execution repeats the result. OPA/Toxiproxy and a live three-role LLM workflow with networked MCP tools reproduce the persisted-but-not-enforced boundary on narrower surfaces. Finally, an unmodified external MCPMark agent executes 60 closed-loop task arms. Normal C4 denies all 31 exposed post-barrier calls and commits no effect; selective C3 allows 344 calls and commits 145 effects across Filesystem and PostgreSQL. Transport success is therefore evidence of progress, not a revocation-completion verdict.

Spontaneous symmetry breaking (SSB) is conventionally understood through static vacuum selection in low-energy approximations. However, the nonperturbative dynamical pathways connecting symmetric configurations to asymmetric states remain an open question. In this paper, we propose an operator-theoretic framework that characterizes $Z_{2}$ symmetry breaking in scalar field theory through spectral branching. Specifically, we identify an effective invariant manifold of the nonlinear Klein-Gordon equation termed the "symmetric dual breather mode," whose phase-space geometry is traced using a $t$-dependent finite-dimensional representation. Our analysis demonstrates that static SSB represents merely a small-amplitude limit ($A \ll \phi_{v1}$). As the amplitude increases into the heteroclinic regime ($A > \phi_{v1}$), the field dynamically overflows the central barrier, yielding a vanishing time-averaged order parameter ($\langle \phi \rangle = 0$) and driving a geometric curvature cancellation ($\langle V''(\phi) \rangle_{t} \to 0$). Governed by a universal scaling function $\mathfrak{F}(y)$, the logarithmic period divergence near the heteroclinic boundary naturally generates sub-eV effective mass scales without fine-tuning bare parameters. Furthermore, this dynamic barrier overflow naturally favors Majorana-like self-conjugate states over Dirac-type states. Additionally, nonlinear phase interference along the heteroclinic channel induces asymmetric phase-space contraction, decoupling the right-handed mode and dynamically giving rise to the left-handed Weyl equation. These results bridge nonperturbative wave dynamics, topological mass suppression, chiral selection, and the dynamic origin of active neutrino masses.

We deduce zero-density estimates in short vertical strips from short-interval moments of globally tempered automorphic $L$-functions, by adapting the large-value estimate of Guth and Maynard and the Type II zero argument of Maynard and Pratt to the framework of Ye and Zhang. For the Riemann zeta function, we obtain $N_\zeta(\sigma;T,T+T^a)\ll T^{15a(1-\sigma)/(3+5\sigma)+\varepsilon}$ for $2/3\le a\le1$ and $7/10\le\sigma\le4/5$, improving Ye–Zhang's exponent in the interior of this range. Combining the localized density bound with the recent quasi-Riemann theorems, we estimate smoothed prime-power sums with phase $\exp(2\pi i\alpha n^\beta)$ on intervals of length $K^\delta$. For $0<\beta<13/20$, we obtain a power saving whenever $\max\{17/30,1-\beta\}<\delta<1$; in particular the square-root phase admits every $\delta>17/30$. A revised transform estimate retains both the stationary spread and the Fourier width $K/L$. For example, the bound at $\beta=1/2$, $\delta=3/5$ is $K^{15/26+\varepsilon}$, uniformly for frequencies $m\alpha$ with $1\le m\le K^{1/10}$. We also retain power savings for certain self-dual $GL(2)$ twists and self-dual $GL(3)$ cusp forms, without assuming Ramanujan. All three applications have explicit frequency dependence.

Authorization checks at individual tool calls do not reveal how long earlier authority remains usable. We study this lifecycle failure as privilege creep: a capability stays reachable after its last justified workflow step. We present CreepScope, a trace-oriented evaluation protocol that samples reachable authority at every step and separates no-remaining-use exposure into stale-after-use and never-required components; Capability-Step Exposure (CSE) counts total stepwise overexposure and Residual Privilege Debt (RPD) the terminal residue, while stale-after-use exposure is the direct privilege-creep measure. A 96-cell deterministic replay over 12 controlled storage, communication, and cloud-operation workflows validates these semantics: Static Task Scope and Monotonic On-Demand retain mean CSEs of 26 and 13, whereas an oracle-controlled Step Lease has zero CSE and zero residual debt by construction. All three persistent regimes share the same stale-after-use exposure of 13, so their CSE differences come from scope and grant timing rather than post-use retention; Full Access alone adds 91.33 never-required capability-steps. A separate 24-episode local case then lets Qwen2 7B choose tools in one simulated mail workflow: the injected stale send executes in all nine persistent-policy episodes and in none of the three Step-Lease episodes, while all 24 required action sequences complete. These results establish a reproducible containment case, not cross-workflow or cross-model effectiveness. Core metrics are reconstructed from raw events, and exact gates reject incomplete or duplicated evaluation grids.

Muscle fatigue limits the effectiveness of functional electrical stimulation (FES), yet fatigue monitoring during active stimulation remains challenging because electromyography (EMG) is severely contaminated by stimulation artifacts. To address this issue, this study proposes an integrated mechanomyography-based sensing framework (MMG-FES) for artifact-resistant fatigue monitoring during stimulation. Fatigue states were first characterized during voluntary movement using established EMG spectral indicators, including median frequency (MF) and mean power frequency (MPF), and then linked to MMG-derived features, including high-frequency energy ratio (HFER) and spectral bandwidth (BW), for fatigue recognition under stimulation conditions. Experimental results showed consistent fatigue-related trends, with EMG spectral features decreasing and MMG features exhibiting coordinated spectral redistribution across repeated contractions. Using these features, the proposed framework achieved fatigue-state recognition accuracies of 0.93 and 0.96 with logistic regression and random forest, respectively. These findings support MMG as a physiologically meaningful and stimulation-compatible modality for fatigue-aware closed-loop neuromuscular stimulation.

Superionic conductors are promising electrolyte candidates for all-solid-state batteries, thanks to their liquid-like ionic mobility. In the prototypical lithium-ion oxide superionic conductor with antifluorite structure, the high-temperature transition to the fast-ion regime has long been attributed to volume-driven harmonic phonon softening. However, this quasi-harmonic picture neglects the strong lattice anharmonicity inherent to the fast-ion regime, leaving the microscopic origin of the transition unresolved. Here, we apply non-perturbative lattice dynamics combined with a first-principles-accurate machine-learning interatomic potential to study the phase transition in Li$_2$O. We demonstrate that anharmonicity, rather than volume expansion alone as commonly assumed, plays the decisive role in determining the transition temperature and the underlying mechanism. Finally, we analyze the spectral properties using the time-dependent self-consistent harmonic approximation, revealing the breakdown of the quasi-particle picture in this material. The spectral function and the infrared response provide signtures of the phase transition that can be investigated experimentally using inelastic neutron or X-ray scattering and infrared spectroscopy. All these results establish the extreme anharmonicity of Li$_2$O near the superionic regime and provide a lattice-dynamic framework for understanding and engineering the fast-ion transition in this type of materials.

The accurate estimation of the ionic activity coefficients is paramount for the characterization of the electrochemical reactions driving energy storage processes as well as the biological mechanisms involving ATP hydrolysis. The numerical evaluation of the ionic activity coefficients by computational methods is rendered difficult by the infinite dilution limit involved in the integral identity between the Helmholtz free energy and the equation of state of the electrolyte. By combining a recently introduced self-consistent Debye-Huckel formalism and its analytically tractable low density limit, we develop a computationally efficient approach enabling the accurate calculation of the free energy and the related thermodynamic functions of aqueous electrolytes over a broad range of ionic concentration and electrostatic coupling strength. Via comparison with numerical simulations and experimental data, it is shown that our approach can predict the salt dependence of the Helmholtz free energy, the entropy, and the ionic activity coefficients from the electrostatically driven submolar ion concentrations to the hard-core dominated molar density regime.

We generalize Moser's stability theorem for minimal hypersurface foliations to arbitrary codimension. Let $\mathbb{T}^N=\mathbb{R}^N/\mathbb{Z}^N$ be the standard torus, and let $P\subset\mathbb{R}^N$ be an $m$-plane satisfying a Diophantine condition relative to $\mathbb{Z}^N$. We prove that, under every sufficiently small smooth $\mathbb{Z}^N$-periodic perturbation of the Euclidean metric, the affine foliation of $\mathbb{T}^N$ induced by $P$ persists as a smoothly conjugate foliation by minimal $m$-dimensional submanifolds. The normalized conjugating displacement depends smoothly and tamely on the metric and is locally unique. The proof uses Hamilton's formulation of the Nash-Moser implicit function theorem.

In this work we present a probabilistic model for predicting the temporal evolution of wildfire size using conditional generative algorithms, namely flow matching. Rather than predicting spatially resolved fire progression, the proposed model forecasts a time series of fire acreage, substantially reducing computational cost and enabling efficient integration with downstream applications such as early warning systems and risk assessment tools. Given estimates of the fire size at the current and previous forecasting steps, alongside spatially averaged weather conditions, terrain characteristics, and fuel composition, the model predicts the change in fire area over a 3-hour interval. Training data are drawn from 140 coupled atmosphere-wildfire simulations generated using WRF-SFIRE, paired with weather data from the North American Mesoscale (NAM) model. Sensitivity analysis demonstrates that the model captures physically-consistent responses to variations in wind speed, temperature, and relative humidity. Model performance is evaluated against reference solutions from WRF-SFIRE. For single-step predictions, the model achieves a symmetric mean absolute percentage error (sMAPE) of 0.39 relative to the reference WRF-SFIRE solutions. Recursive multi-step predictions over 24 hours are performed for 12 held-out test cases, where the flow matching model achieves a final fire area sMAPE of 0.39 while further providing meaningful quantification of forecast uncertainty.

In nonparametric density estimation without privacy constraints, it is known that a confidence set whose coverage holds uniformly over a `rough' class of regularity $r\geq0$ can simultaneously attain, in $L^2$-diameter, the minimax rate over a smaller, smoother class of regularity $s>r$ if and only if $s \le 2r$. We study such adaptive honest confidence sets under non-interactive $\alpha$-local differential privacy (LDP) constraints. Our main result is that, for bounded $\alpha$, such `smooth-rate adaptation' is now possible if and only if $s \le 4r/3$. In this smaller range we construct an honest private confidence set whose diameter is of the private minimax order on each of the two classes. As in the non-private case, the threshold arises because an honest set cannot, at a smooth density, be narrower than the separation rate arising in a related testing problem. Under LDP we prove that this private testing rate is of order $(n\alpha^2)^{-2r/(4r+3)}$, which is at most the private estimation rate $(n\alpha^2)^{-s/(2s+2)}$ over the smooth class exactly when $s \le 4r/3$. For $s > 4r/3$, however, we show that smooth-rate adaptation becomes possible once one discards from the rough class the densities that lie outside the smooth class but within an $L^2$-radius of the order of the private testing rate.

We prove that round circles $C_L$ are the unique minimisers of integral Menger curvature among embedded closed $C^1$ curves $\gamma$ of prescribed length $L$ for every $p\geq 2$, i.e. $M_p(C_L) \leq M_p(\gamma)$, with equality if and only if $\gamma$ parametrises a round circle. The proof combines a three-point symmetrisation, an analysis of diagonal truncations, and the periodic Wirtinger inequality. For $p>3$, known self-avoidance and regularity results extend the minimisation result to closed rectifiable curves without assuming embeddedness or smoothness, provided the length of the curve image equals $L$. In particular, $M_p$ detects the unknot and is basic for $p>3$, thereby answering a question posed repeatedly in the literature.

Radio map estimation (RME), also known as spectrum cartography, aims to recover radio signal strength across multiple domains (e.g., spatial and spectral domains) from sparse measurements, naturally leading to a tensor completion problem. Recent advances show that deep learning-based generative models can provide data-driven structural constraints for RME, yielding substantial performance improvements over traditional model-based approaches. Diffusion models (DMs) represent the current state of the art in generative modeling and hold strong promise for advancing RME. However, existing diffusion-based RME methods often require extensive training data, necessitate retraining when scenarios or measurement formats change, and lack recoverability guarantees. This paper proposes a latent factor diffusion framework for spatio-spectral radio map tensor completion. By training two independent DMs on single-emitter's spatial loss field and spectral signature and embedding them into the factors of the radio map tensor, the proposed approach enables diffusion posterior sampling-based recovery with reduced training complexity as well as enhanced measurement format/sensing pattern flexibility. Recoverability and sample complexity guarantees under the proposed approach are also established. Numerical experiments validate the effectiveness of the proposed method, showing strong generalization across city environments unseen in training data.

Let $g$ be a fixed primitive Hecke–Maass cusp form, and let $f$ vary with spectral parameter $k_f=K$, at a fixed level and with trivial nebentypus. We study smooth sums of $\lambda_f(n)\lambda_g(n)e(\alpha n^\beta)$ for fixed real $\alpha\ne0$. The crucial input is the smooth spectral second moment of Lau, Liu, and Ye, for which the window length can be taken to be $L=K^{1/3+a}$ for arbitrarily small fixed $a>0$. We show that, for every $\kappa>0$, there is $\beta_0>0$ such that the sum is $O(K^{2/3+\kappa}X^{1/2})$ for $1\le X\le K^2$ and $0<\beta\le\beta_0$. We give a detailed Baire category argument which makes the dependence on the smooth weight uniform through one finite derivative norm. A second argument keeps the phase explicit, applies Voronoi summation and shifted convolution estimates, and gives the numerical bound $O(K^{423/224+(5/7)\beta+\varepsilon})$ at $X=K^2$ for $0<\beta<5/32$.

Linking speakers across independently recorded rooms is difficult because microphone, room, and codec mismatch distort speaker embeddings. We study visitor linking without visitor enrollment or identity labels in simulated outpatient workflows. The proposed method combines per-device embedding centering, concurrency constraints, room-type-specific visit constraints, and a clustering threshold calibrated from concurrent visitors and identified staff voices. On simulated days built from VOiCES recordings, with companions, return visits, walk-ins, silent visits, and acoustic leakage, it improves B$^3$-F1 over the best label-free baseline for all 11 extractors, by 5.3-14.6 points (all 95% intervals exclude zero). ECAPA-TDNN reaches 86.6, compared with 76.4 for the best label-free baseline and 87.7 for the best oracle-informed baseline. Gains persist across the reported workflow perturbations, but depend on removing duplicated cross-room speech: without this step, the method wins for only 2 of 11 extractors. Single-visit patients also remain vulnerable to false merges. These results support structure-aware linking while identifying preprocessing and identity-safety limitations that must be addressed before clinical deployment.

Emotion datasets are routinely mapped onto positive and negative valence, by assigning each emotion category one polarity. We test where this works and where it fails, using SemEval-2018 Affect in Tweets (English, Arabic, Spanish), Affective Text aligned with EmoBank, raw GoEmotions annotations, naturalistic hashtag corpora, and a controlled annotation study. Fixed projection works well when a text carries labels of one valence. It fails on a subset identifiable from the labels alone: tweets whose emotion labels point in opposite directions. These are 9.0% of polar SemEval test tweets but cause 54.8% of the polarity errors of a learned projection, are more than twice as likely to receive a neutral-or-mixed gold label, and are not rescued by modeling the full label set. Annotators produce such configurations routinely: 16.3% of multilabel GoEmotions judgments combine emotions from the dataset's own positive and negative parents. In a controlled study holding word and reader constant, context changes the coarse valence judgment in 56.8% of cases, against 19.9% for controls. We recommend projecting label configurations rather than labels, abstaining or keeping a mixed class where labels conflict, and reporting coverage alongside accuracy.

This paper investigates a new role of randomness in stochastic policies–as a medium for embedding and communicating information. Specifically, we consider an agent interacting with an environment according to a prescribed stochastic policy. By carefully modulating the random action realizations of the policy, information can be embedded into the agent's behavior without altering the prescribed action distribution. We cast this problem as a channel coding problem, in which the controlled system implicitly serves as a communication channel. We then propose a coding scheme, termed posterior-matching randomness modulation (PRAM), that selects actions according to the message to be transmitted. With the aid of common randomness independent of the control system, PRAM preserves the prescribed action distribution for every state and every message. We further prove that PRAM is asymptotically reliable: the message can be decoded with arbitrarily small error probability as the observed state trajectory becomes sufficiently long. Experiments demonstrate the effectiveness of the proposed framework in applications including multi-bit policy watermarking and trajectory provenance.

Fault-tolerant quantum design relies on simulating noisy quantum error correction (QEC) circuits with hundreds to thousands of physical qubits and large circuit depths. High-throughput stabilizer simulators, such as Stim, are the de facto tools for this regime. However, these simulators typically support only Clifford gates and stochastic Pauli noise. As a result, more realistic device noise models-such as coherent control errors and thermal relaxation-are often approximated using Pauli Twirling. This replacement offers speed but can introduce inaccuracies. To address this, we propose QuasiStim for scalable exact QEC simulation of realistic noise, with QuasiFold as a compiler frontend and DeltaFrame as a sampling backend. QuasiFold lowers sampling overhead by merging equivalent non-Pauli sites in the quantum circuit. DeltaFrame samples the resulting stabilizer trajectories by reusing precomputed predicted references instead of resimulating the full tableau for each shot. QuasiFold can reduce the number of shots by over $100\times$ on bivariate-bicycle (BB) codes. Compared to a per-shot tableau simulator, DeltaFrame is $166\times$–$1331\times$ faster on rotated surface-code memory under coherent $R_Z$ noise as $d$ grows from 5 to 35. QuasiStim also makes the PTA bias measurable: the gap is non-negligible and varies with noise strength, decoder, and circuit schedule. QuasiStim will be open-sourced upon publication at https://github.com/isaachyw/QuasiStim

The median-of-means (MoM) estimator is a robust alternative to the sample mean for heavy-tailed or contaminated data. While its non-asymptotic properties are well understood for i.i.d.\ samples, much less is known for dependent sequences. We establish non-asymptotic deviation bounds for the MoM estimator computed from consecutive blocks of an identically distributed $\alpha$-mixing sequence, both for a single mean and uniformly over a class of functions (the median-of-means process). All bounds remain valid, with explicitly adjusted constants, when a sufficiently small fraction of the blocks is adversarially corrupted. As applications, we obtain deviation bounds for a median-of-means Nadaraya–Watson regression estimator, for the MoM kernel density estimator, and for empirical and Bahadur-type estimators of Value-at-Risk and Conditional Value-at-Risk. Finally, we show that the sampling of bulk materials, where the measurements form a spatially dependent random field, reduces to the one-dimensional setting if the samples are taken in well-separated groups.

We test whether shared action ordering changes executed credit in a simulated collateralized lending market. Three small open-weight language models face a borrowing cap that values collateral at the pool price; only two of the three model families traded. A validation campaign, hash-locked locally before its first model call, pairs 12 common-order markets with 12 balanced-order markets under a revised interface. An exact randomization test rejects the sharp null that common-market net debt is invariant to complete-order assignment (two-sided p = 2/8,100). The pre-specified estimate of the lever-up-first versus delever-first common-market contrast is 1.12 units of initial unused reference borrowing capacity, combining a 0.828 gap between the two groups of common markets with a 0.293 balanced-baseline component. All 24 markets increased debt. An exploratory accounting split shows that lever-up-first common markets borrowed more and repaid less. With requests held fixed, reference-priced collateral narrows the observed common-market order gap from 0.828 to 0.688 capacity units. No market experienced liquidation or realized bad debt. Under the pre-specified fixed-price 30 percent shock benchmark, individual high-LTV loans generate scenario write-offs even though aggregate LTVs remain below the write-off threshold. Most benchmark write-off arises from collateral consumed by the liquidation bonus. The experiment establishes an effect of action order on executed credit; accounting identities and deterministic counterfactuals explain how collateral constraints and borrower-level debt allocation shape conditional creditor recovery.

Full-support local randomizers can incur unnecessary reporting distortion on ordered alphabets. We study randomized response whose output is restricted to a radius-$t$ neighborhood of the private input. Input-dependent supports create privacy leakage at their boundaries, so ordinary likelihood-ratio calibration is no longer sufficient. Under approximate local privacy restricted to input pairs at distance at most $H$, we derive the exact hockey-stick defect of the mechanism. We then solve the joint design of the truthful probability, off-truth probability, and support radius. The fixed-radius optimum is available in closed form, while the global optimum requires only a one-dimensional integer search. We characterize both the privacy floor and its inverse, namely the smallest defect attainable under a reporting-distortion budget. We further prove that stringent approximate privacy forces the support size to scale as $\Omega(H/\delta)$. Deterministic evaluations illustrate the resulting tradeoff.

It is shown that certain finite partially ordered sets arising from unit interval determinantal facet ideals satisfy the $\lambda$-chain condition. In addition, their applications to commutative algebra are briefly discussed.

Due to the importance of studying quantum-gravity-induced corrections to Einstein's theory of gravity, it is of interest to consider non-extensive entropies whose potential applications include identifying such corrections. In this Letter, we investigate possible corrections to a universal relation associated with the extremality bound of the mass of a black hole by employing entropies defined as functions of the Bekenstein-Hawking entropy.

In multi-agent reinforcement learning, exposing a cooperator to partners with diverse strategies during training is key to better collaboration at test time. However, existing methods typically rely on trajectory-level proxies to measure diversity, which may label two distinct trajectories of the same strategy as diverse. Instead, our key insight is to leverage LLMs' ability to describe behaviorally distinct agents in environments, similar to how humans can recognize high-level strategies. To this end, we introduce PopGen, a framework that synthesizes semantically diverse agents from scratch using LLMs. PopGen first generates a diverse set of textual descriptions of agent behaviors, then translates each behavior into a code policy that can be executed within the environment. We show that cooperators trained against PopGen populations achieve robust zero-shot cooperation with unseen partners, outperforming population-play baselines across four collaborative environments. We further show that semantic diversity scales with PopGen population size, improving the cooperator's worst-case performance, and we identify design choices that preserve population quality while maximizing diversity. Our code is available at https://github.com/labicon/PopGen.

Spiking Transformers achieve energy efficiency by discarding softmax normalization in favor of thresholded, binary attention. However, this removal breaks the thermodynamic framework used to analyze attention networks, as the normalized measure and partition function cease to exist. We restore this theoretical foundation by proving that softmax-free spiking attention operates exactly as the zero-temperature limit of a product of independent two-level systems. This correspondence places spiking attention strictly in the frozen ordered phase of the thermodynamic phase diagram for all inputs. Consequently, the entropic cost of organizing attention collapses, replaced by a Landauer-type physical floor governed by action-potential generation. Furthermore, this ordered-phase pinning mathematically explains the optimization difficulty caused by vanishing surrogate gradients. We validate this theory with forward-relaxation experiments, placing both standard and neuromorphic attention mechanisms on a unified thermodynamic axis.

We consider the problem of mono-to-stereo audio upmixing: generating a high-fidelity two-channel stereo signal from a single-channel recording. The task is fundamentally ill-posed i.e., many stereo signals are consistent with a given mono recording. An effective upmixer must therefore generate a realistic, musically coherent stereo image while preserving the underlying audio content. Previous approaches have relied on signal-processing driven decorrelation, ambience extraction and supervised learning, offering limited spatial control or requiring task-specific training. In response, we propose Aura (Audio Upmixing using Reward-tilted Flows), which reformulates upmixing as a generative inverse problem using a pretrained flow prior. To enable controllable spatial imaging, we design a reward-tilted posterior sampler whose reward penalizes divergences between generated and target distributions of inter-channel cues. Composing forward operators further enables joint restoration and upmixing without retraining or fine-tuning. Objective and subjective evaluations on real-world music recordings from MUSDB18-HQ demonstrate our method's effectiveness relative to several baselines.